The size of the universe

[Jason Resch]

I recently wrote an article on the size of the universe and the scope of reality:

https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are largely inspired by some of the conversations I've enjoyed here. It covers many topics including the historic discoveries, the big bang, inflation, string theory, and mathematical realism.

Jason

[Brent Meeker]

Friedmann discovered the expanding universe solution to Einstein's equations in 1922, well before Lamaitre.  And Friedmann met with Einstein and proposed the expanding universe cosmology to him.  Sadly he died in 1925.  Lamaitre independently discovered some of the same solutions in 1927.  When he showed them to Einstein, Einstein showed him Friedmann's papers.  Lamaitre did invent the term "cosmic atom" and he connected the solutions to Hubble's measurements.

Brent

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[Jason Resch]

Hi Brent,

I appreciate your comment. I've updated the article to reflect your suggestion and credit Friedmann.

Jason

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[Bruno Marchal]

It has not been proved that the decimal expansion of PI contains all (finite codes of all) sequences.

It is easy to fiw, as you can take the number of Champernow, which trivially  contain all sequences:

C = 0,12345678910111213141516….

OK?

Now, this is different from the universal dovetailing, which *executes* (semantically) all computations, and makes unavoidable that to solve the mind body problem, we have to extract the believes in bodies from the statistics on the first person continuation determined by all computations. It is here that it is crucial to distinguish between a computation (a notion involving counterfactuals) and a description of a computation, which does not.

With Mechanism, physics is reduced to number psychology or theology, and theology is reduced to arithmetic (through the Gödel-Löb-Solovay theorems).

Bruno

[Bruno Marchal]

Hi Jason,

When you say that Reality is infinite, are you alluding to the (phenomenological) physical reality? Or the absolute reality?

With mechanism, it is very plausible that the physical reality is infinite, as it is a sort of broder of the universal mind (the mind of the “virgin” universal machine).

But even with an infinite physical reality, it is unclear if we are alone or not, in the physical reality. We are numerous in the arithmetical reality (which can be taken as the absolute one, modulo a change of universal machinery). But to have alien fellows in the physical reality, you need some homogeneity in that reality, which is not obvious at first sight.

In fact, I get the impression that we might be rare, if not alone. The probability for life might be as close to zero as von Neumann thought, but even the possibility of its evolution requires many conditions, so many that we might be alone in the cosmos (not in the multiverse, as there we have even doppelangers).

I have no certainty, and this needs to progress in the universal machine canonical physics.

Bruno

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[Jason Resch]

On Wed, May 20, 2020 at 7:05 AM Bruno Marchal <mar...@ulb.ac.be> wrote:

On 19 May 2020, at 05:20, Jason Resch <jason...@gmail.com> wrote:

I recently wrote an article on the size of the universe and the scope of reality:

https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are largely inspired by some of the conversations I've enjoyed here. It covers many topics including the historic discoveries, the big bang, inflation, string theory, and mathematical realism.

It has not been proved that the decimal expansion of PI contains all (finite codes of all) sequences.

I understand that Pi is proven to be normal, but is it true for the irrational numbers (Pi, e, sqrt(2), etc.) that probabilistically the chance of not finding a given finite sequence of digits goes to zero? Is it correct to say that almost surely any sequence can be found?

If it does not hold for Pi, are there other numbers that would be better examples for the type of analogy I am making? I want to show why statistically an infinite space leads to near certainty of repetitions of material arrangements assuming some kind of infinite uniformity, just like the infinity of random-looking digits of an irrational number leads to infinite repetitions among any finite sequence.

 

It is easy to fiw, as you can take the number of Champernow, which trivially  contain all sequences:

C = 0,12345678910111213141516….

OK?

Now, this is different from the universal dovetailing, which *executes* (semantically) all computations, and makes unavoidable that to solve the mind body problem, we have to extract the believes in bodies from the statistics on the first person continuation determined by all computations. It is here that it is crucial to distinguish between a computation (a notion involving counterfactuals) and a description of a computation, which does not.

Indeed. To be clear I am not making the case here that our universe is contained within Pi, only showing that infinity leads to repeats so long as the description is finite, be it a volume of matter and energy, or a finite length of decimal digits.

 

With Mechanism, physics is reduced to number psychology or theology, and theology is reduced to arithmetic (through the Gödel-Löb-Solovay theorems).

I am working on a post now which will get more into this, about why there is something rather than nothing. How to bootstrap reality and universes from arithmetical truth will be part of that. :-)

I appreciate your comments. Thank you.

Jason

 

[Jason Resch]

On Wed, May 20, 2020 at 8:39 AM Bruno Marchal <mar...@ulb.ac.be> wrote:

Hi Jason,

When you say that Reality is infinite, are you alluding to the (phenomenological) physical reality? Or the absolute reality?

Hi Bruno. I describe several different cases of an infinite universe, roughly:

1. A spatially infinite universe, implied by a flat geometry of spacetime and GR
2. An eternally, exponentially growing vacuum populated by infinite big bangs (which manifest over infinite time)
3. Infinite and diverse or comprehensive realities (the infinite landscape of universes described by string theory, or the infinite structures inherent to mathematical realism).

 

With mechanism, it is very plausible that the physical reality is infinite, as it is a sort of broder of the universal mind (the mind of the “virgin” universal machine).

But even with an infinite physical reality, it is unclear if we are alone or not, in the physical reality. We are numerous in the arithmetical reality (which can be taken as the absolute one, modulo a change of universal machinery). But to have alien fellows in the physical reality, you need some homogeneity in that reality, which is not obvious at first sight.

I make no claims as to how close they aliens be, though I suppose if the nearest alien life is beyond the horizon then we are for all intents and purposes still alone.

Homogeneity and infinite space are conclusions from standard cosmological assumptions and models: the big bang, inflation, flat space. Would these not imply the existence of alien life directly (moreover, the existence of other earths and other copies of ourselves should you look far enough)?

 

In fact, I get the impression that we might be rare, if not alone. The probability for life might be as close to zero as von Neumann thought, but even the possibility of its evolution requires many conditions, so many that we might be alone in the cosmos (not in the multiverse, as there we have even doppelangers).

Good point. I am still reading: https://www.amazon.com/Universe-Teeming-Aliens-WHERE-EVERYBODY/dp/0387955011 I think the author leans towards the "rare earth" conclusion. I am somewhat partial to the trancension hypothesis, but that might be due to my hopeful nature.

Jason

 

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[Brent Meeker]

On 5/20/2020 6:39 AM, Bruno Marchal wrote:
> Hi Jason,
>
> When you say that Reality is infinite, are you alluding to the
> (phenomenological) physical reality? Or the absolute reality?
>
> With mechanism, it is very plausible that the physical reality is
> infinite, as it is a sort of broder of the universal mind (the mind of
> the “virgin” universal machine).
>
> But even with an infinite physical reality, it is unclear if we are
> alone or not, in the physical reality. We are numerous in the
> arithmetical reality (which can be taken as the absolute one, modulo a
> change of universal machinery). But to have alien fellows in the
> physical reality, you need some homogeneity in that reality, which is
> not obvious at first sight.
>
> In fact, I get the impression that we might be rare, if not alone. The
> probability for life might be as close to zero as von Neumann thought,
> but even the possibility of its evolution requires many conditions, so
> many that we might be alone in the cosmos (not in the multiverse, as
> there we have even doppelangers).

I think the evidence suggests that there is a lot of life in the visible
universe and even a lot of technological civilizations...but they are so
sparse that we are effectively alone.

Brent

[Brent Meeker]

On 5/20/2020 9:45 AM, Jason Resch wrote:
> I understand that Pi is proven to be normal, but is it true for the
> irrational numbers (Pi, e, sqrt(2), etc.) that probabilistically the
> chance of not finding a given finite sequence of digits goes to zero?

In a normal number, every sequence of n digits has density base^-n.   I
don't think it has been proven that pi is normal, but it's been proven
that the measure of non-normal numbers is zero.

Brent

[Brent Meeker]

Given the human curiosity about life on different planets combined with the impossibility of traveling to them, or even getting data from probes within a human lifetime, I expect that (assuming we can survive another century or so) we will engage in virtual exploration, i.e. we will develop physically accurate simulations, like the Star Trek holodeck, and explore all possible worlds...and our world in alternate histories.

Brent

[Lawrence Crowell]

I think we might be able to send photon driven sail craft to stars within 20 light years or so.  The Starshot initiative envisions spacecraft with v = .2c, or γ ≈ 1.02. I think that with large solar collimating Fresnel lenses we could get to v = .5c or γ ≈ 1.15. An interesting star such as Tau Ceti at 12 light years away it would take over 24 years to get there. The upper limit where redshifting of your photon beam becomes a significant loss is v = .87C or γ ≈ 2. Breaking can be arranged with plasma breaking with the stellar wind. Then signals would take 12 years to get here. It could then take 40 years to get data. However, the Voyager spacecrafts are still giving data and they have been at it for over 40 years. 

We of course might find a planet with signatures of biology. If we are doubly fortunate one might be close enough to send a probe to. If we could get a probe to a nearby bioactive planet, which could still be in this solar system, that would be tremendous. 

I doubt humans will even actually travel to another star. The logistical scale of things is truly enormous. Even firmer I think the limitation of light speed will never be overcome. This means the often-used ideas of warp drives and the rest will not happen. There is the Alcubierre warp drive, but this requires energy conditions that are not physical. Even now interplanetary travel is a difficult prospect.

Contact with another IGUS or ETI is I think unlikely. Of course, the effort should continue, but it may well support the hypothesis that intelligent life is exceedingly rare. The discovery of a planet with signatures of biology would be a huge find and double so if such a planet were close enough to send a probe to. I suspect though we may never get any ET to phone here.

If we end up at some point simulating life elsewhere that would be sort of a digital version of what people complain about with string theory and the rest. It might still be worthwhile in some ways, but it could be disconnected from empirical data, This is particularly the case if we never find any evidence of a bioactive planet.

LC

[Bruno Marchal]

On 20 May 2020, at 18:45, Jason Resch <jason...@gmail.com> wrote:

On Wed, May 20, 2020 at 7:05 AM Bruno Marchal <mar...@ulb.ac.be> wrote:

On 19 May 2020, at 05:20, Jason Resch <jason...@gmail.com> wrote:

I recently wrote an article on the size of the universe and the scope of reality:

https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are largely inspired by some of the conversations I've enjoyed here. It covers many topics including the historic discoveries, the big bang, inflation, string theory, and mathematical realism.

It has not been proved that the decimal expansion of PI contains all (finite codes of all) sequences.

I understand that Pi is proven to be normal,

But that is not the case. Pi win all experimental test, but the normality of basically all irrational numbers are open problems. It is generally conjectured that they are all normal.

For the Champernow number, the normality is easy to prove, but it has been build that way.

but is it true for the irrational numbers (Pi, e, sqrt(2), etc.) that probabilistically the chance of not finding a given finite sequence of digits goes to zero?

Most would bet that this is indeed the case, but that is unsolved today.

Is it correct to say that almost surely any sequence can be found?

Hmm… “almost” has already a technical meaning in computer science. It means for all but a finite number exceptions. It  existential dual is “there is infinitely many …”.

Then, I don’t want to look like pick nicking, but “almost” and “sure” seems a bit antinomic. 

Some intuition of infinite decimal series, and of irrational numbers (which have no infinite repetition, etc.) gives a feeling that it would be quite astonishing that it is not the case, even for sqrt(2), and we can say that this has been experimentally verified, but mathematicians ask for proof, and some ask for an elementary proof (not involving second order arithmetic or analysis).

If it does not hold for Pi, are there other numbers that would be better examples for the type of analogy I am making?

The Champernowne Number

https://mathworld.wolfram.com/ChampernowneConstant.html

I want to show why statistically an infinite space leads to near certainty of repetitions of material arrangements assuming some kind of infinite uniformity, just like the infinity of random-looking digits of an irrational number leads to infinite repetitions among any finite sequence.

You get this with Champernowne number. It is normal, despite extraordinarily compressible.  It is about equal to 0.123.., but all kids can easily write the decimals without ending!  It is obviously normal, as it goes through all the numbers, and thus all the sequences. 

It has not be confused with a universal dovetailing which is a computation which happens to execute all computations, which are peculiar number relations.

The problem is that each of us (us, the universal number) are implemented in many computations, and indeed, below our substitution level, we get infinitely many computations). Physics, conceptually, becomes a statistical measure on uncertainty on which are our most probable computations, as “seen from inside”. Here the mathematical logicians have a tool which lacks to the physicalists, which is “transparent” mathematical theory of self-reference, indeed, they get both the machines’ own theory (G) and the true theory (G*), and the difference (G* minus G) which is so important to get the difference between the quanta and the qualia. 

 

It is easy to fiw, as you can take the number of Champernow, which trivially  contain all sequences:

C = 0,12345678910111213141516….

OK?

Now, this is different from the universal dovetailing, which *executes* (semantically) all computations, and makes unavoidable that to solve the mind body problem, we have to extract the believes in bodies from the statistics on the first person continuation determined by all computations. It is here that it is crucial to distinguish between a computation (a notion involving counterfactuals) and a description of a computation, which does not.

Indeed. To be clear I am not making the case here that our universe is contained within Pi, only showing that infinity leads to repeats so long as the description is finite, be it a volume of matter and energy, or a finite length of decimal digits.

As long as you don’t assume simultaneously Mechanism and some “physical universe” (making it or its elements primitive), there is no (logical) problem.

With mechanism, the laws of physics emerges from the statistics on the dreams/computations of the natural number.

The “god” of the universal Löbian machine, G*, provides the truth, the believable, the knowable, the observable, and the one which feels. And this, modulo Mechanism at the metalevel, assuming only two equations, like Kxy = x, and Sxyz = xz(yz). 

 

With Mechanism, physics is reduced to number psychology or theology, and theology is reduced to arithmetic (through the Gödel-Löb-Solovay theorems).

I am working on a post now which will get more into this, about why there is something rather than nothing. How to bootstrap reality and universes from arithmetical truth will be part of that. :-)

I appreciate your comments. Thank you.

The discovery of the universal machine, and especially the Löbian one, is an event more important than the Big Bang. Of course, that discovery is made an infinite number of times in very elementary arithmetic.

The Lôbian machines are the universal machines which knows (even in a rather weak sense) that they are universal, and they know the complicated consequences that happens, especially if they want to remain universal …They oscillate easily between freedom and security in a not entirely vain attempt to fill the gap between G* and G and their necessary intensional variants.

With universality, you get free will, but you need löbianity, to get responsibility. All universal machine, like RA, with enough induction axioms, like PA, is Löbian.

Their weakness? They are credulous, and hallucinate easily, like seeing far away galaxies, sun, moon, and Higgs bosons…, but eventually they can explain the why and the how of all sharable aspect of their experiences, and detect possible oracles, who knows.

The G*/G gap is really the difference between Computer Science (where there is no hallucinations) and Computer’s Computer Science, which can contains many hallucination, like notions of some absolute harwdare. 

With Mechanism, the laws of physics does not depend on the universal machinery chosen for the ontology. The choice of a universal machinery, is equivalent with the choice of a base for the recursive enumeration of all partial computable functions.

Thanks to QM, Nature fits well with the most startling aspect of mechanism (or self-multiplication at the basic level).

The theology of machine will not replace physics, on the contrary, it predicts that larger and larger part of mathematics will be “known”  “experimentally” (betting).

Concerning our local cosmos, I am fascinated by the black holes, but very ignorant, I see it implies multiverses of different kinds, super-imposed to the Everett-Omen-Griffith entangled consistent histories. With Mechanism, it is an open problem to just define a notion of a singular physical universe, without mentioning the complex “intermediate histories” between Earth and Heaven …

Did you know that contrary to some myth (that I were “almost sure”  about), even quarks can maintain the social distancing, if you provide enough energy! That is what happen in the gluon-quark plasma!  I guess that is very hot.

Bruno

Jason

 

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[Bruno Marchal]

You might be right. I thought along those lines, but since I understood the role of Jupiter, and the rarity of system with Jupiter-like planet, I mean, the number of condition for life to appear, and to evolve, has grown in my head, and yes, if other civilisation exists they can be very sparse, in the galaxies filaments…

In arithmetic, we met recurrently with all possible creatures (except one) in all consistent universes/histories, which might not be that much reassuring...

Bruno


>
> Brent

>
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[Jason Resch]

You might be right. My next post is actually on this very topic: The Drake Equation, SETI, Extremophiles, and the various proposed solutions to The Fermi Paradox.

Jason

[Jason Resch]

This was Q's prediction in the final episode of Next Generation: https://www.youtube.com/watch?v=YvDWtCM_ch8   Also described by John M. Smart as the transcension hypothesis: https://www.sciencedirect.com/science/article/abs/pii/S0094576511003304

A Jupiter brain could simulate the entire evolutionary history of a planet in minutes or hours, compared to the many thousands years it would take to travel there, or the slow drip of information that would come in from looking at far off planets, even using planet-sized telescopes.

Jason

[Jason Resch]

On Thu, May 21, 2020 at 1:33 PM Bruno Marchal <mar...@ulb.ac.be> wrote:

On 20 May 2020, at 18:45, Jason Resch <jason...@gmail.com> wrote:

On Wed, May 20, 2020 at 7:05 AM Bruno Marchal <mar...@ulb.ac.be> wrote:

On 19 May 2020, at 05:20, Jason Resch <jason...@gmail.com> wrote:

I recently wrote an article on the size of the universe and the scope of reality:

https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are largely inspired by some of the conversations I've enjoyed here. It covers many topics including the historic discoveries, the big bang, inflation, string theory, and mathematical realism.

It has not been proved that the decimal expansion of PI contains all (finite codes of all) sequences.

I understand that Pi is proven to be normal,

(Oops I meant to say "Pi is not proven to be normal" somehow I deleted the not while refactoring the sentence)

 

But that is not the case. Pi win all experimental test, but the normality of basically all irrational numbers are open problems. It is generally conjectured that they are all normal.

For the Champernow number, the normality is easy to prove, but it has been build that way.

but is it true for the irrational numbers (Pi, e, sqrt(2), etc.) that probabilistically the chance of not finding a given finite sequence of digits goes to zero?

Most would bet that this is indeed the case, but that is unsolved today.

Is it correct to say that almost surely any sequence can be found?

Hmm… “almost” has already a technical meaning in computer science. It means for all but a finite number exceptions. It  existential dual is “there is infinitely many …”.

Then, I don’t want to look like pick nicking, but “almost” and “sure” seems a bit antinomic. 

Some intuition of infinite decimal series, and of irrational numbers (which have no infinite repetition, etc.) gives a feeling that it would be quite astonishing that it is not the case, even for sqrt(2), and we can say that this has been experimentally verified, but mathematicians ask for proof, and some ask for an elementary proof (not involving second order arithmetic or analysis).

If it does not hold for Pi, are there other numbers that would be better examples for the type of analogy I am making?

The Champernowne Number

https://mathworld.wolfram.com/ChampernowneConstant.html

I want to show why statistically an infinite space leads to near certainty of repetitions of material arrangements assuming some kind of infinite uniformity, just like the infinity of random-looking digits of an irrational number leads to infinite repetitions among any finite sequence.

You get this with Champernowne number. It is normal, despite extraordinarily compressible.  It is about equal to 0.123.., but all kids can easily write the decimals without ending!  It is obviously normal, as it goes through all the numbers, and thus all the sequences. 

But the universe appears more random than something so well structured like the Champernowne constant. What about Chaitin's Omega? Hasn't Chaitin proved a certain randomness for that digits of that constant?

 

It has not be confused with a universal dovetailing which is a computation which happens to execute all computations, which are peculiar number relations.

The problem is that each of us (us, the universal number) are implemented in many computations, and indeed, below our substitution level, we get infinitely many computations). Physics, conceptually, becomes a statistical measure on uncertainty on which are our most probable computations, as “seen from inside”. Here the mathematical logicians have a tool which lacks to the physicalists, which is “transparent” mathematical theory of self-reference, indeed, they get both the machines’ own theory (G) and the true theory (G*), and the difference (G* minus G) which is so important to get the difference between the quanta and the qualia. 

 

It is easy to fiw, as you can take the number of Champernow, which trivially  contain all sequences:

C = 0,12345678910111213141516….

OK?

Now, this is different from the universal dovetailing, which *executes* (semantically) all computations, and makes unavoidable that to solve the mind body problem, we have to extract the believes in bodies from the statistics on the first person continuation determined by all computations. It is here that it is crucial to distinguish between a computation (a notion involving counterfactuals) and a description of a computation, which does not.

Indeed. To be clear I am not making the case here that our universe is contained within Pi, only showing that infinity leads to repeats so long as the description is finite, be it a volume of matter and energy, or a finite length of decimal digits.

As long as you don’t assume simultaneously Mechanism and some “physical universe” (making it or its elements primitive), there is no (logical) problem.

With mechanism, the laws of physics emerges from the statistics on the dreams/computations of the natural number.

The “god” of the universal Löbian machine, G*, provides the truth, the believable, the knowable, the observable, and the one which feels. And this, modulo Mechanism at the metalevel, assuming only two equations, like Kxy = x, and Sxyz = xz(yz). 

 

With Mechanism, physics is reduced to number psychology or theology, and theology is reduced to arithmetic (through the Gödel-Löb-Solovay theorems).

I am working on a post now which will get more into this, about why there is something rather than nothing. How to bootstrap reality and universes from arithmetical truth will be part of that. :-)

I appreciate your comments. Thank you.

The discovery of the universal machine, and especially the Löbian one, is an event more important than the Big Bang. Of course, that discovery is made an infinite number of times in very elementary arithmetic.

The Lôbian machines are the universal machines which knows (even in a rather weak sense) that they are universal, and they know the complicated consequences that happens, especially if they want to remain universal …They oscillate easily between freedom and security in a not entirely vain attempt to fill the gap between G* and G and their necessary intensional variants.

With universality, you get free will, but you need löbianity, to get responsibility. All universal machine, like RA, with enough induction axioms, like PA, is Löbian.

Their weakness? They are credulous, and hallucinate easily, like seeing far away galaxies, sun, moon, and Higgs bosons…, but eventually they can explain the why and the how of all sharable aspect of their experiences, and detect possible oracles, who knows.

The G*/G gap is really the difference between Computer Science (where there is no hallucinations) and Computer’s Computer Science, which can contains many hallucination, like notions of some absolute harwdare. 

With Mechanism, the laws of physics does not depend on the universal machinery chosen for the ontology. The choice of a universal machinery, is equivalent with the choice of a base for the recursive enumeration of all partial computable functions.

Thanks to QM, Nature fits well with the most startling aspect of mechanism (or self-multiplication at the basic level).

The theology of machine will not replace physics, on the contrary, it predicts that larger and larger part of mathematics will be “known”  “experimentally” (betting).

Concerning our local cosmos, I am fascinated by the black holes, but very ignorant, I see it implies multiverses of different kinds, super-imposed to the Everett-Omen-Griffith entangled consistent histories. With Mechanism, it is an open problem to just define a notion of a singular physical universe, without mentioning the complex “intermediate histories” between Earth and Heaven …

I read this lately, and found it very interesting:

https://cse.buffalo.edu/~rapaport/111F04/lloyd-ng-sciam-04.pdf

Among some of the most interesting conclusions: quantum mechanics/Planck's constant imposes an upper bound on the speed of computation, general relativity/Newton's constant imposes an upper bound on the density of computation. There are various intermediate possibilities of parallel vs. sequential computing, but the maximum sequential information processing speed is reached only for black holes. There the number of bits that can be processed per step is given by Bekenstein's bound, and the "clock cycle" is the amount of time it takes light to cross the diameter of the black hole.

Another fascinating consequence: given that the matter-energy density of the universe as a whole is right at the cusp of gravitational collapse, the total mass of the observable universe is exactly equal to the density of a black hole of the same volume of the observable universe. The estimated number of bits within the universe is also exactly equal to the total number of bit operations that have occurred in the universe since the big bang. In other words: for every one of the 10^120 bits in the universe, each has been processed (flipped) exactly once (on average) in the time since the big bang.

There are incredible relations between fundamental physics and computation which amaze me.

 

Did you know that contrary to some myth (that I were “almost sure”  about), even quarks can maintain the social distancing, if you provide enough energy! That is what happen in the gluon-quark plasma!  I guess that is very hot.

I read recently that it's estimated 90% of our mass comes from the relativistic speed of quarks and other particles inside the nucleus.  If you could somehow still that motion, we'd weigh only a few pounds. Something to ponder next time we step on a scale. :-)

Jason

 

Bruno

Jason

 

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[Bruno Marchal]

On 21 May 2020, at 21:43, Jason Resch <jason...@gmail.com> wrote:

On Thu, May 21, 2020 at 1:33 PM Bruno Marchal <mar...@ulb.ac.be> wrote:

On 20 May 2020, at 18:45, Jason Resch <jason...@gmail.com> wrote:

On Wed, May 20, 2020 at 7:05 AM Bruno Marchal <mar...@ulb.ac.be> wrote:

On 19 May 2020, at 05:20, Jason Resch <jason...@gmail.com> wrote:

I recently wrote an article on the size of the universe and the scope of reality:

https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are largely inspired by some of the conversations I've enjoyed here. It covers many topics including the historic discoveries, the big bang, inflation, string theory, and mathematical realism.

It has not been proved that the decimal expansion of PI contains all (finite codes of all) sequences.

I understand that Pi is proven to be normal,

(Oops I meant to say "Pi is not proven to be normal" somehow I deleted the not while refactoring the sentence)

OK. 

 

But that is not the case. Pi win all experimental test, but the normality of basically all irrational numbers are open problems. It is generally conjectured that they are all normal.

For the Champernow number, the normality is easy to prove, but it has been build that way.

but is it true for the irrational numbers (Pi, e, sqrt(2), etc.) that probabilistically the chance of not finding a given finite sequence of digits goes to zero?

Most would bet that this is indeed the case, but that is unsolved today.

Is it correct to say that almost surely any sequence can be found?

Hmm… “almost” has already a technical meaning in computer science. It means for all but a finite number exceptions. It  existential dual is “there is infinitely many …”.

Then, I don’t want to look like pick nicking, but “almost” and “sure” seems a bit antinomic. 

Some intuition of infinite decimal series, and of irrational numbers (which have no infinite repetition, etc.) gives a feeling that it would be quite astonishing that it is not the case, even for sqrt(2), and we can say that this has been experimentally verified, but mathematicians ask for proof, and some ask for an elementary proof (not involving second order arithmetic or analysis).

If it does not hold for Pi, are there other numbers that would be better examples for the type of analogy I am making?

The Champernowne Number

https://mathworld.wolfram.com/ChampernowneConstant.html

I want to show why statistically an infinite space leads to near certainty of repetitions of material arrangements assuming some kind of infinite uniformity, just like the infinity of random-looking digits of an irrational number leads to infinite repetitions among any finite sequence.

You get this with Champernowne number. It is normal, despite extraordinarily compressible.  It is about equal to 0.123.., but all kids can easily write the decimals without ending!  It is obviously normal, as it goes through all the numbers, and thus all the sequences. 

But the universe appears more random than something so well structured like the Champernowne constant.

I doubt this. Most subsequence of the Champernowne number are completely random, and *very* long. Only the tiny initial segment does not look random, when you know the algorithm to generate it. It can be proved that most natural number have incompressible sequences. The number of compressed algorithm grows much less that the numbers of number (for each finite length). 

What about Chaitin's Omega? Hasn't Chaitin proved a certain randomness for that digits of that constant?

Up to see constant related to the universal machine used to make that number precise, it can be shown that indeed, that number (Omega) is random and incompressible. But all the finite subsequences of Omega appears in the Champernowne number, and only for that last one have we a proof of normality. Omega is so compressed that it has no useful pattern in it. 

Much more interesting is the Post number, which is 0,0001101111010101001… with 1 (res 0) at the nth place if phi_n converges (or not), where phi_i is an enumeration of the programs without arguments.

Post number is compressible (indeed Chaitin’s Omega is Post number when maximally compressed: both gives the halting oracle). But post number illustrates the needed redundancy that we need to get the pattern from which the physical laws can evolve. It is an “interesting” number (in the sense of Bennett).

 

It has not be confused with a universal dovetailing which is a computation which happens to execute all computations, which are peculiar number relations.

The problem is that each of us (us, the universal number) are implemented in many computations, and indeed, below our substitution level, we get infinitely many computations). Physics, conceptually, becomes a statistical measure on uncertainty on which are our most probable computations, as “seen from inside”. Here the mathematical logicians have a tool which lacks to the physicalists, which is “transparent” mathematical theory of self-reference, indeed, they get both the machines’ own theory (G) and the true theory (G*), and the difference (G* minus G) which is so important to get the difference between the quanta and the qualia. 

 

It is easy to fiw, as you can take the number of Champernow, which trivially  contain all sequences:

C = 0,12345678910111213141516….

OK?

Now, this is different from the universal dovetailing, which *executes* (semantically) all computations, and makes unavoidable that to solve the mind body problem, we have to extract the believes in bodies from the statistics on the first person continuation determined by all computations. It is here that it is crucial to distinguish between a computation (a notion involving counterfactuals) and a description of a computation, which does not.

Indeed. To be clear I am not making the case here that our universe is contained within Pi, only showing that infinity leads to repeats so long as the description is finite, be it a volume of matter and energy, or a finite length of decimal digits.

As long as you don’t assume simultaneously Mechanism and some “physical universe” (making it or its elements primitive), there is no (logical) problem.

With mechanism, the laws of physics emerges from the statistics on the dreams/computations of the natural number.

The “god” of the universal Löbian machine, G*, provides the truth, the believable, the knowable, the observable, and the one which feels. And this, modulo Mechanism at the metalevel, assuming only two equations, like Kxy = x, and Sxyz = xz(yz). 

 

With Mechanism, physics is reduced to number psychology or theology, and theology is reduced to arithmetic (through the Gödel-Löb-Solovay theorems).

I am working on a post now which will get more into this, about why there is something rather than nothing. How to bootstrap reality and universes from arithmetical truth will be part of that. :-)

I appreciate your comments. Thank you.

The discovery of the universal machine, and especially the Löbian one, is an event more important than the Big Bang. Of course, that discovery is made an infinite number of times in very elementary arithmetic.

The Lôbian machines are the universal machines which knows (even in a rather weak sense) that they are universal, and they know the complicated consequences that happens, especially if they want to remain universal …They oscillate easily between freedom and security in a not entirely vain attempt to fill the gap between G* and G and their necessary intensional variants.

With universality, you get free will, but you need löbianity, to get responsibility. All universal machine, like RA, with enough induction axioms, like PA, is Löbian.

Their weakness? They are credulous, and hallucinate easily, like seeing far away galaxies, sun, moon, and Higgs bosons…, but eventually they can explain the why and the how of all sharable aspect of their experiences, and detect possible oracles, who knows.

The G*/G gap is really the difference between Computer Science (where there is no hallucinations) and Computer’s Computer Science, which can contains many hallucination, like notions of some absolute harwdare. 

With Mechanism, the laws of physics does not depend on the universal machinery chosen for the ontology. The choice of a universal machinery, is equivalent with the choice of a base for the recursive enumeration of all partial computable functions.

Thanks to QM, Nature fits well with the most startling aspect of mechanism (or self-multiplication at the basic level).

The theology of machine will not replace physics, on the contrary, it predicts that larger and larger part of mathematics will be “known”  “experimentally” (betting).

Concerning our local cosmos, I am fascinated by the black holes, but very ignorant, I see it implies multiverses of different kinds, super-imposed to the Everett-Omen-Griffith entangled consistent histories. With Mechanism, it is an open problem to just define a notion of a singular physical universe, without mentioning the complex “intermediate histories” between Earth and Heaven …

I read this lately, and found it very interesting:

https://cse.buffalo.edu/~rapaport/111F04/lloyd-ng-sciam-04.pdf

Black hole are very interesting, including for the role they give to quantum information. But, from a quick look at the paper this is till “digital physicalism”, and it refutes itself. Indeed, it entails computationalism, but computationalism entails that the physical universe is not simulable exactly by a computer. Mechanism (aka computationalism) entails that even to simulate a nanometer^3 of vacuum, you need to run instantaneously the entire universal dovetailing, and compute the probabilities from there, which is not possible. As far as the paper is physically sound, if Mechanism ic correct, it can only be an approximation. It is interesting for physics, but does not address the fundamental question, like where there is a an appearance of a physical universe, and where does all appearances come from.

Among some of the most interesting conclusions: quantum mechanics/Planck's constant imposes an upper bound on the speed of computation, general relativity/Newton's constant imposes an upper bound on the density of computation. There are various intermediate possibilities of parallel vs. sequential computing, but the maximum sequential information processing speed is reached only for black holes. There the number of bits that can be processed per step is given by Bekenstein's bound, and the "clock cycle" is the amount of time it takes light to cross the diameter of the black hole.

Another fascinating consequence: given that the matter-energy density of the universe as a whole is right at the cusp of gravitational collapse, the total mass of the observable universe is exactly equal to the density of a black hole of the same volume of the observable universe. The estimated number of bits within the universe is also exactly equal to the total number of bit operations that have occurred in the universe since the big bang. In other words: for every one of the 10^120 bits in the universe, each has been processed (flipped) exactly once (on average) in the time since the big bang.

That looks interesting, but if this is not derivable from Kxy = x + Sxyz = xz(yz), it will have to eve abandoned.

There are incredible relations between fundamental physics and computation which amaze me.

Honestly, how could that been amazing? If we assume mechanism in cognitive science, the physical universe is entirely explainable in term of a statistics on *all* computations.

In mathematics, “all computation” is the only place where “all” is well defined, thanks to the “miracle” of the Church-Turing thesis. 

Have you understand that all computations are run in arithmetic? Here “in arithmetic” can be replaced by “in all models of arithmetic” or “in the standard model of arithmetic” or “provable in RA”, or provable in all combinatory algebra, etc. 

We don’t need to postulate a physical universe, nor even induction axioms, to explain where the quantum computations come from, and why we tend to trust the induction axioms.

But in theology (aka philosophy of mind, metaphysics) the situation is worst than that/ We just cannot postulate a physical universe, if we want it to be related to any conscious first person experience by machines.

 

Did you know that contrary to some myth (that I were “almost sure”  about), even quarks can maintain the social distancing, if you provide enough energy! That is what happen in the gluon-quark plasma!  I guess that is very hot.

I read recently that it's estimated 90% of our mass comes from the relativistic speed of quarks and other particles inside the nucleus.

Interesting.

  If you could somehow still that motion, we'd weigh only a few pounds. Something to ponder next time we step on a scale. :-)

Is there some mass which is not kinetic energy in disguise? 

If yes, I will have to revise my understanding of the Higgs-Englert-Brout boson ...

Bruno

Jason

 

Bruno

Jason

 

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[Jason Resch]

I think like Pi, reality itself could be generated by a short compressible algorithm (like the UD).

But also like Pi, if you find yourself at some arbitrary offset, it looks like it is irreducibly random (like the quantum fluctuations that appear in the distribution of galaxies and CMB of our universe).

Perhaps there is some law where when you combine a deterministic process with infinite steps, the result is random. I have some familiarity with the design of secure random number generates computers use to generate encryption keys and other values that are necessary for security. All are based on the process of taking a very large number (so large it can't be guessed) then combining it with a deterministic, but difficult-to-reverse (one-way) function.

The simplest example I cold easily describe is the one built into Java called SHA1PRNG. It starts with a random number (a seed value) that is on the order of 256 bits. Then to generate a sequence of random looking bits, it puts this random number through a one-way hash function (called SHA1). The output of this function only produces 160 random bits. If more are needed the random seed value is incremented by 1, and the process is repeated. What seems random is just counting and mixing up the result. Only it is counting from a starting position so large it could only be guessed with negligible probability.

The hallmark of a secure random number generator, as opposed to an unsecure one, is if it takes exponential time (in relation to the number of bits in the seed value) to guess the next bit output by the generator with greater than 0.5 probability, given all the bits output by the random number generator so far.

If I recall correctly the main focus of the paper is less about the nature of reality (upon which it might speculate) and more about what are the physical limits of computation in the universe.

 

Indeed, it entails computationalism, but computationalism entails that the physical universe is not simulable exactly by a computer. Mechanism (aka computationalism) entails that even to simulate a nanometer^3 of vacuum, you need to run instantaneously the entire universal dovetailing, and compute the probabilities from there, which is not possible. As far as the paper is physically sound, if Mechanism ic correct, it can only be an approximation. It is interesting for physics, but does not address the fundamental question, like where there is a an appearance of a physical universe, and where does all appearances come from.

Among some of the most interesting conclusions: quantum mechanics/Planck's constant imposes an upper bound on the speed of computation, general relativity/Newton's constant imposes an upper bound on the density of computation. There are various intermediate possibilities of parallel vs. sequential computing, but the maximum sequential information processing speed is reached only for black holes. There the number of bits that can be processed per step is given by Bekenstein's bound, and the "clock cycle" is the amount of time it takes light to cross the diameter of the black hole.

Another fascinating consequence: given that the matter-energy density of the universe as a whole is right at the cusp of gravitational collapse, the total mass of the observable universe is exactly equal to the density of a black hole of the same volume of the observable universe. The estimated number of bits within the universe is also exactly equal to the total number of bit operations that have occurred in the universe since the big bang. In other words: for every one of the 10^120 bits in the universe, each has been processed (flipped) exactly once (on average) in the time since the big bang.

That looks interesting, but if this is not derivable from Kxy = x + Sxyz = xz(yz), it will have to eve abandoned.

Perhaps there is something about black holes and the physical limits of computation there that could more easily be derived from  Kxy = x + Sxyz = xz(yz). If so, it could lend additional support.

 

There are incredible relations between fundamental physics and computation which amaze me.

Honestly, how could that been amazing? If we assume mechanism in cognitive science, the physical universe is entirely explainable in term of a statistics on *all* computations.

I don't know, there is something elegent about how deep the connection is. Planck's constant directly determines maximum speed of computation per unit of mass-energy in the universe. Mass times Volume directly tell us maximum number of bits that can be stored. Speed of light and G tell us the maximum speed of a serial computation. The volume of the universe and Bekenstein bound tell us the number of bits that are stored in the universe, and that each bit has flipped an average of exactly once in the 13.8 billion years since the BB.

It is more amazing perhaps starting from the view that the universe is not derived from the machine self-reflection (where most people start). Then these connections seem very mysterious.

 

In mathematics, “all computation” is the only place where “all” is well defined, thanks to the “miracle” of the Church-Turing thesis. 

Have you understand that all computations are run in arithmetic? Here “in arithmetic” can be replaced by “in all models of arithmetic” or “in the standard model of arithmetic” or “provable in RA”, or provable in all combinatory algebra, etc. 

I subscribe to this idea. I think it's the best hope at revolutionizing theoretical physics, which seems preoccupied on the problem of how to make everything predictable in finite time (i.e. string theory). Does COMP have anything to say about whether such efforts can succeed? Should we expect there to be ways to chase out the infinities? Are they in effect, is the string theory community chasing for the equivalent of a classical algorithm for predicting the behavior of a quantum computer?

 

We don’t need to postulate a physical universe, nor even induction axioms, to explain where the quantum computations come from, and why we tend to trust the induction axioms.

But in theology (aka philosophy of mind, metaphysics) the situation is worst than that/ We just cannot postulate a physical universe, if we want it to be related to any conscious first person experience by machines.

 

Did you know that contrary to some myth (that I were “almost sure”  about), even quarks can maintain the social distancing, if you provide enough energy! That is what happen in the gluon-quark plasma!  I guess that is very hot.

I read recently that it's estimated 90% of our mass comes from the relativistic speed of quarks and other particles inside the nucleus.

Interesting.

  If you could somehow still that motion, we'd weigh only a few pounds. Something to ponder next time we step on a scale. :-)

Is there some mass which is not kinetic energy in disguise? 

I suspect that too. That all apparent mass is just confined energy moving at C. Have you seen how mass appears in a "light box" https://www.youtube.com/watch?v=gSKzgpt4HBU ?

Jason

 

If yes, I will have to revise my understanding of the Higgs-Englert-Brout boson ...

Bruno

Jason

 

Bruno

Jason

 

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[Bruno Marchal]

Neither the mathematical reality, nor the physical reality can be generated by an algorithm. The physical reality emerges from all algorithm. Keep in mind that if you are cut and paste in two places at very different “moments of time” (like with delay of a billions years for one of the reconstitution), that delays is not first person knowable. So the number of steps is not relevant for a computational state to exist. What is relevant is the relative measure on the continuations, but we have to take them all into account, and that is not a recursive set, making the physical reality NOT Turing emulable. This means also that only the UD can bring it (or anything Turing equivalent at some level of description, like the collection of true sigma_1 sentences in arithmetic).

If the physical reality was generated by a program, that would entail Mechanism, but Mechanism entails that the physical appearances cannot be Turing emulable, so the thesis that the physical universe if brought by a programs, or by a proper subset of programs is self-defeating. 

But also like Pi, if you find yourself at some arbitrary offset, it looks like it is irreducibly random (like the quantum fluctuations that appear in the distribution of galaxies and CMB of our universe).

Perhaps there is some law where when you combine a deterministic process with infinite steps, the result is random.

Deterministic self-duplication, or the multiple preparation of identical state, by programs run in arithmetic, does that, but only from the first person point of view. Now, long complex program can certainly imitate some pseudo-random sequences.

I have some familiarity with the design of secure random number generates computers use to generate encryption keys and other values that are necessary for security. All are based on the process of taking a very large number (so large it can't be guessed) then combining it with a deterministic, but difficult-to-reverse (one-way) function.

OK.

The simplest example I cold easily describe is the one built into Java called SHA1PRNG. It starts with a random number (a seed value) that is on the order of 256 bits. Then to generate a sequence of random looking bits, it puts this random number through a one-way hash function (called SHA1). The output of this function only produces 160 random bits. If more are needed the random seed value is incremented by 1, and the process is repeated. What seems random is just counting and mixing up the result. Only it is counting from a starting position so large it could only be guessed with negligible probability.

The hallmark of a secure random number generator, as opposed to an unsecure one, is if it takes exponential time (in relation to the number of bits in the seed value) to guess the next bit output by the generator with greater than 0.5 probability, given all the bits output by the random number generator so far.

 

<snip>

The G*/G gap is really the difference between Computer Science (where there is no hallucinations) and Computer’s Computer Science, which can contains many hallucination, like notions of some absolute harwdare. 

With Mechanism, the laws of physics does not depend on the universal machinery chosen for the ontology. The choice of a universal machinery, is equivalent with the choice of a base for the recursive enumeration of all partial computable functions.

Thanks to QM, Nature fits well with the most startling aspect of mechanism (or self-multiplication at the basic level).

The theology of machine will not replace physics, on the contrary, it predicts that larger and larger part of mathematics will be “known”  “experimentally” (betting).

Concerning our local cosmos, I am fascinated by the black holes, but very ignorant, I see it implies multiverses of different kinds, super-imposed to the Everett-Omen-Griffith entangled consistent histories. With Mechanism, it is an open problem to just define a notion of a singular physical universe, without mentioning the complex “intermediate histories” between Earth and Heaven …

I read this lately, and found it very interesting:

https://cse.buffalo.edu/~rapaport/111F04/lloyd-ng-sciam-04.pdf

Black hole are very interesting, including for the role they give to quantum information. But, from a quick look at the paper this is till “digital physicalism”, and it refutes itself.

If I recall correctly the main focus of the paper is less about the nature of reality (upon which it might speculate) and more about what are the physical limits of computation in the universe.

That’s the problem. It seems to take the notion of “universe” for granted. But as you say, it does not really address the fundamental question, although it might look that way.

I have few doubt that black hole have a lot to say about physical information and physical computers. But to understand why things like black hole and computer exists, with mechanism, we have to derive them from arithmetic or combinators, or any non physical computer.

 

Indeed, it entails computationalism, but computationalism entails that the physical universe is not simulable exactly by a computer. Mechanism (aka computationalism) entails that even to simulate a nanometer^3 of vacuum, you need to run instantaneously the entire universal dovetailing, and compute the probabilities from there, which is not possible. As far as the paper is physically sound, if Mechanism ic correct, it can only be an approximation. It is interesting for physics, but does not address the fundamental question, like where there is a an appearance of a physical universe, and where does all appearances come from.

Among some of the most interesting conclusions: quantum mechanics/Planck's constant imposes an upper bound on the speed of computation, general relativity/Newton's constant imposes an upper bound on the density of computation. There are various intermediate possibilities of parallel vs. sequential computing, but the maximum sequential information processing speed is reached only for black holes. There the number of bits that can be processed per step is given by Bekenstein's bound, and the "clock cycle" is the amount of time it takes light to cross the diameter of the black hole.

Another fascinating consequence: given that the matter-energy density of the universe as a whole is right at the cusp of gravitational collapse, the total mass of the observable universe is exactly equal to the density of a black hole of the same volume of the observable universe. The estimated number of bits within the universe is also exactly equal to the total number of bit operations that have occurred in the universe since the big bang. In other words: for every one of the 10^120 bits in the universe, each has been processed (flipped) exactly once (on average) in the time since the big bang.

That looks interesting, but if this is not derivable from Kxy = x + Sxyz = xz(yz), it will have to eve abandoned.

Perhaps there is something about black holes and the physical limits of computation there that could more easily be derived from  Kxy = x + Sxyz = xz(yz). If so, it could lend additional support.

I am not sure it could be done “easily”, but it has to be done that way if we want to keep intact the difference between quanta and qualia, between first person experience and the first person plural one, etc. If we get different sort of black hole, or no black hole at all, we would got evidences to doubt Mechanism.

 

There are incredible relations between fundamental physics and computation which amaze me.

Honestly, how could that been amazing? If we assume mechanism in cognitive science, the physical universe is entirely explainable in term of a statistics on *all* computations.

I don't know, there is something elegent about how deep the connection is. Planck's constant directly determines maximum speed of computation per unit of mass-energy in the universe. Mass times Volume directly tell us maximum number of bits that can be stored.

Except that for black hole it seems the information is on the surface of the volume (strangely enough).

Speed of light and G tell us the maximum speed of a serial computation. The volume of the universe and Bekenstein bound tell us the number of bits that are stored in the universe, and that each bit has flipped an average of exactly once in the 13.8 billion years since the BB.

I am not sure I can make sense of this, but it is very plausibly only due to my incompetence. 

It is more amazing perhaps starting from the view that the universe is not derived from the machine self-reflection (where most people start). Then these connections seem very mysterious.

 

In mathematics, “all computation” is the only place where “all” is well defined, thanks to the “miracle” of the Church-Turing thesis. 

Have you understand that all computations are run in arithmetic? Here “in arithmetic” can be replaced by “in all models of arithmetic” or “in the standard model of arithmetic” or “provable in RA”, or provable in all combinatory algebra, etc. 

I subscribe to this idea.

Well, those are theorem provable in very weak theories. It is more a question of grasping the proof than subscribing to a philosophical idea. That arithmetic executes all programs is a theorem similar to Euclid’s theorem that there is no biggest prima numbers. It is more a fact, than an idea which could be debated. I insist on this as I realise this is less known by the general scientists than 20 years ago. We knew this implicitly since Gödel 1931, and explicitly since Church, Turing and Kleene 1936.

I think it's the best hope at revolutionizing theoretical physics, which seems preoccupied on the problem of how to make everything predictable in finite time (i.e. string theory). Does COMP have anything to say about whether such efforts can succeed? Should we expect there to be ways to chase out the infinities? Are they in effect, is the string theory community chasing for the equivalent of a classical algorithm for predicting the behavior of a quantum computer?

With COMP (aka digital mechanism), the laws of physics her to be explained from the laws of computations and numbers, which are not based on any physical concept.

To study the physical reality, we must do physics. Using comp is just the only way to address the relation between first person plural physical prediction, and the first person confirmation. The goal is to understand why there is something instead of nothing, and this in a way which does not eliminate consciousness and persons, like materialism is enforced to do. To sump up the reason in a "physicalist terms”, no laws of physics can predict any first person confirmation without integrating on all “Boltzmann Brain” which are all executed in arithmetic. The physical reality is a sum on all dreams/consistent-histories/computations-seen-from-inside.

The goal is not find new physics, although that might happens some day, but to solve the mind-body problem, and this without eliminating mind, which eventually forces us to eliminate matter from the ontology.

 

We don’t need to postulate a physical universe, nor even induction axioms, to explain where the quantum computations come from, and why we tend to trust the induction axioms.

But in theology (aka philosophy of mind, metaphysics) the situation is worst than that/ We just cannot postulate a physical universe, if we want it to be related to any conscious first person experience by machines.

 

Did you know that contrary to some myth (that I were “almost sure”  about), even quarks can maintain the social distancing, if you provide enough energy! That is what happen in the gluon-quark plasma!  I guess that is very hot.

I read recently that it's estimated 90% of our mass comes from the relativistic speed of quarks and other particles inside the nucleus.

Interesting.

  If you could somehow still that motion, we'd weigh only a few pounds. Something to ponder next time we step on a scale. :-)

Is there some mass which is not kinetic energy in disguise? 

I suspect that too. That all apparent mass is just confined energy moving at C. Have you seen how mass appears in a "light box" https://www.youtube.com/watch?v=gSKzgpt4HBU ?

Very good video indeed, but it will take a lot of work to get this from mechanism. Energy remains pretty mysterious. It has to be related with fundamental symmetries, and why the physical laws are (or should be) time symmetrical. There is no Kestrel (Kxy = x) nor Starling (Sxyz = xz(yz)) in the physical universe . K eliminates information/energy, and S duplicates it, which is eventually impossible physical events. Th reason might be related to the necessity of group theory in physics. The measure one might necessitate some Lie group role in the picture. Why SU(1) or SO(3)? It is here that I suspect the number 24 to play a key role, for gravitation. The progress here will still comes from physics for a very long time I’am afraid. Or worst: from Number theory, which might might again demotivate people for theology (if 1500 years of lie was not enough!).

Recently, I have come up with some possible reason why the physical should appear three dimensional, and this could be related to some relations between prime number and knots. This again suppose the existence of braids in the theory Z1* and X1*, which unfortunately remains based on intractable conjectures. This could give some reason why we have no qualia corresponding to 4 dimensional geometry. That is a big mystery. I use it often to explain qualia. We do have qualia for 0, 1, 2, 3 dimensions, and not for those > 3, which is a bit mysterious. Can we program a machine to have 4D qualia? I thought so but now I got the shadow of a reason to doubt this, and this would explain the 3D appearances in the available physical reality for numbers…

Bruno

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CA%2BBCJUjNes2EY7%2BVfwxJbpK6CxS8Hb3cD%3Dr%2B_xhtaF5kxehc9A%40mail.gmail.com.

[Brent Meeker]

On 5/23/2020 4:42 AM, Bruno Marchal wrote:
>
> Well, those are theorem provable in very weak theories. It is more a
> question of grasping the proof than subscribing to a philosophical
> idea. That arithmetic executes all programs is a theorem similar to
> Euclid’s theorem that there is no biggest prima numbers. It is more a
> fact, than an idea which could be debated. I insist on this as I
> realise this is less known by the general scientists than 20 years
> ago. We knew this implicitly since Gödel 1931, and explicitly since
> Church, Turing and Kleene 1936.

Recently you have said that your theory is consistent with finitism,
even ultrafinitism.  But the idea that arithemtic exectues all programs
certainly requires infinities.

Brent

[Russell Standish]

On Thu, May 21, 2020 at 08:33:03PM +0200, Bruno Marchal wrote:
>
> Is it correct to say that almost surely any sequence can be found?
>
>
> Hmm… “almost” has already a technical meaning in computer science. It means for
> all but a finite number exceptions. It existential dual is “there is
> infinitely many …”.
>
> Then, I don’t want to look like pick nicking, but “almost” and “sure” seems a
> bit antinomic.

Not to pick nits, but it actually means the exceptions are of measure
zero. There may well still be an infinite number of them. After all,
the set of rational numbers (which is infinite) is of measure zero.


--

----------------------------------------------------------------------------
Dr Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders hpc...@hpcoders.com.au
http://www.hpcoders.com.au
----------------------------------------------------------------------------

[Russell Standish]

Only potential infinities, not actual infinities. For the UD (a finite
object) to execute any given program, one only needs to wait a finite
amount of time.

However, I would think that ultrafinitism would change COMP's
predictions, and in a sense be incompatibe with it. Some programs will
not exist, because one would need to wait too long for them to be
executed by the UD. In fact, the choice of reference universal machine
would be significant in ultrafinitism, IIUC.

[Bruce Kellett]

On Sun, May 24, 2020 at 9:37 AM Russell Standish <li...@hpcoders.com.au> wrote:

On Sat, May 23, 2020 at 12:05:08PM -0700, 'Brent Meeker' via Everything List wrote:
>
>
> On 5/23/2020 4:42 AM, Bruno Marchal wrote:
> >
> > Well, those are theorem provable in very weak theories. It is more a
> > question of grasping the proof than subscribing to a philosophical idea.
> > That arithmetic executes all programs is a theorem similar to Euclid’s
> > theorem that there is no biggest prima numbers. It is more a fact, than
> > an idea which could be debated. I insist on this as I realise this is
> > less known by the general scientists than 20 years ago. We knew this
> > implicitly since Gödel 1931, and explicitly since Church, Turing and
> > Kleene 1936.
>
> Recently you have said that your theory is consistent with finitism, even
> ultrafinitism.  But the idea that arithemtic exectues all programs certainly
> requires infinities.

Only potential infinities, not actual infinities. For the UD (a finite
object) to execute any given program, one only needs to wait a finite
amount of time.

I thought the UD executing in arithmetic was timeless: so all the infinity of possible programs have already been executed before you even start thinking about it. So computationalism has actual infinities built in.

Bruce

[Philip Thrift]

On Saturday, May 23, 2020 at 6:37:20 PM UTC-5, Russell Standish wrote:

 I would think that ultrafinitism would change COMP's
predictions, and in a sense be incompatibe with it. Some programs will
not exist, because one would need to wait too long for them to be
executed by the UD. In fact, the choice of reference universal machine
would be significant in ultrafinitism, IIUC.

Here I think Max Tegmark's claim is totally right:

There is nothing in physics (2020) or any empirical observations that requires anything beyond a finite "machine" model.

Max Tegmark, in an instance of not being "Mad".

@philipthrift

[Lawrence Crowell]

On Saturday, May 23, 2020 at 6:48:06 PM UTC-5, Bruce wrote:

On Sun, May 24, 2020 at 9:37 AM Russell Standish <li...@hpcoders.com.au> wrote:

On Sat, May 23, 2020 at 12:05:08PM -0700, 'Brent Meeker' via Everything List wrote:
>
>
> On 5/23/2020 4:42 AM, Bruno Marchal wrote:
> >
> > Well, those are theorem provable in very weak theories. It is more a
> > question of grasping the proof than subscribing to a philosophical idea.
> > That arithmetic executes all programs is a theorem similar to Euclid’s
> > theorem that there is no biggest prima numbers. It is more a fact, than
> > an idea which could be debated. I insist on this as I realise this is
> > less known by the general scientists than 20 years ago. We knew this
> > implicitly since Gödel 1931, and explicitly since Church, Turing and
> > Kleene 1936.
>
> Recently you have said that your theory is consistent with finitism, even
> ultrafinitism.  But the idea that arithemtic exectues all programs certainly
> requires infinities.

Only potential infinities, not actual infinities. For the UD (a finite
object) to execute any given program, one only needs to wait a finite
amount of time.

I thought the UD executing in arithmetic was timeless: so all the infinity of possible programs have already been executed before you even start thinking about it. So computationalism has actual infinities built in.

Bruce

This depends on what one considers as the domain of computation, whether that is some global content or what is accessible to a local observer. In the first case it is infinite, at least countably infinite. In the latter case it is unbounded above, but finite and given by the finite area of an event horizon or boundary of space on a holographic screen. Both constructions have some relevancy, for in the infinite case we can imagine well enough there is some Cantor diagonalization of quantum states, qubits or information the define a horizon or limit. This would then enforce the locality of any possible observer as bounded by a computational or epistemological horizon. So the two perspective may have a sort of dualism.

LC

[Bruno Marchal]

On 23 May 2020, at 21:05, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 5/23/2020 4:42 AM, Bruno Marchal wrote:

Well, those are theorem provable in very weak theories. It is more a question of grasping the proof than subscribing to a philosophical idea. That arithmetic executes all programs is a theorem similar to Euclid’s theorem that there is no biggest prima numbers. It is more a fact, than an idea which could be debated. I insist on this as I realise this is less known by the general scientists than 20 years ago. We knew this implicitly since Gödel 1931, and explicitly since Church, Turing and Kleene 1936.

Recently you have said that your theory is consistent with finitism,

It has always been a finitism. Judson Webb wrote a book explaining exactly this. 

even ultrafinitism. 

Yes. This I have realised more recently. But that was obvious, given that we assume RA for the ontology, and it has no axiom of infinity, nor the induction axioms. So it is consistent with the idea of a biggest natural numbers.

Of course, to prove this to be consistent, you need the notion of model. But “in real life” we can never prove that we are consistent. 

We need to separate the assumptions from the meta level goal like showing that the assumptions make sense.

That is the BABA of mathematical logic, but I have realised few people understand this, and confuse easy theories and the meta theories? Of course, Gödel did confuse the two for proving incompleteness, but that confusion is only partial, and done with all the needed precautions.

But the idea that arithemtic exectues all programs certainly requires infinities.

At the meta level, yes. But with mechanism, the “meta-level” is brought by the observer, whose existence is guarantied by the ground level (or ontology).

The axioms of RA are just CL +

1) 0 ≠ s(x)

2) x ≠ y -> s(x) ≠ s(y)

3) x ≠ 0 -> Ey(x = s(y)) 

4) x+0 = x

5) x+s(y) = s(x+y)

6) x*0=0

7) x*s(y)=(x*y)+x

There is no axiom of infinity, nor induction axioms. All ultrafinitst people accept them, and you can add the axiom

8) Ex(Ay(x bigger-or-equal y)

without being led to a contradiction.

1)-7) is the mathematical ontology. Of course, to prove this to be Turing universal, you will need at least the induction axiom. But RA is Turing universal even if you don’t prove it …

Note that RA can prove the existence of machine believing in RA + induction, or in ZFC, even of ZFC + large cardinal axiom, etc. 

We must not confuse what RA can prove, and what the creature (whose existence can be proved by RA) can prove. RA can simulate ZF, does not make it possible toi identify RA and ZF, like the fact that I can imitate Einstein’s brain does not make me equivalent with Einstein. On the contrary, if I emulate Einstein’s brain, the best I can get is a conversation with Einstein. That does not entail that I will agree with him, or understand what he says.

Bruno

Brent

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[Bruno Marchal]

> On 24 May 2020, at 01:02, Russell Standish <li...@hpcoders.com.au> wrote:
>
> On Thu, May 21, 2020 at 08:33:03PM +0200, Bruno Marchal wrote:
>>
>> Is it correct to say that almost surely any sequence can be found?
>>
>>
>> Hmm… “almost” has already a technical meaning in computer science. It means for
>> all but a finite number exceptions. It existential dual is “there is
>> infinitely many …”.
>>
>> Then, I don’t want to look like pick nicking, but “almost” and “sure” seems a
>> bit antinomic.
>
> Not to pick nits, but it actually means the exceptions are of measure
> zero. There may well still be an infinite number of them. After all,
> the set of rational numbers (which is infinite) is of measure zero.

Fair enough.
Like I said, “almost” in theoretical computer science means "all but a finite number of exceptions”.

Take an infinite row of dominoes. Then make the first one falling. We will have that all dominoes will fall, but at any time, almost all of them still stand up!

It might make sense to say, for “almost" in the non countable domain, all except a countable number of exceptions. It really depends on the applications in mind. With the notion of measure in mind, your remark makes sense.



Bruno

>
>
> --
>
> ----------------------------------------------------------------------------
> Dr Russell Standish Phone 0425 253119 (mobile)
> Principal, High Performance Coders hpc...@hpcoders.com.au
> http://www.hpcoders.com.au
> ----------------------------------------------------------------------------
>

> --
> You received this message because you are subscribed to the Google Groups "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com.

> To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/20200523230215.GB27696%40zen.

[Bruno Marchal]

> On 24 May 2020, at 01:37, Russell Standish <li...@hpcoders.com.au> wrote:
>
> On Sat, May 23, 2020 at 12:05:08PM -0700, 'Brent Meeker' via Everything List wrote:
>>
>>
>> On 5/23/2020 4:42 AM, Bruno Marchal wrote:
>>>
>>> Well, those are theorem provable in very weak theories. It is more a
>>> question of grasping the proof than subscribing to a philosophical idea.
>>> That arithmetic executes all programs is a theorem similar to Euclid’s
>>> theorem that there is no biggest prima numbers. It is more a fact, than
>>> an idea which could be debated. I insist on this as I realise this is
>>> less known by the general scientists than 20 years ago. We knew this
>>> implicitly since Gödel 1931, and explicitly since Church, Turing and
>>> Kleene 1936.
>>
>> Recently you have said that your theory is consistent with finitism, even
>> ultrafinitism. But the idea that arithemtic exectues all programs certainly
>> requires infinities.
>
> Only potential infinities, not actual infinities. For the UD (a finite
> object) to execute any given program, one only needs to wait a finite
> amount of time.
>
> However, I would think that ultrafinitism would change COMP's
> predictions, and in a sense be incompatibe with it. Some programs will
> not exist, because one would need to wait too long

“Too long” is still finite.

The biggest natural number is of course “infinite”, but the ultrafinitist cannot know that.

That is why a “real ultrafinitiste” will never say that he is ultrafinitist. He has no means to explains why ultra-finitism means. Only a finitists can prove that ultra-finitsime is consistent (indeed PA can prove that RA is consistent).

> for them to be
> executed by the UD. In fact, the choice of reference universal machine
> would be significant in ultrafinitism, IIUC.

Why? As long as the theory is Turing complete, all programs are run (in all interpretation of the theory), including all finite segment of the executions of all non terminating programs, and this with the usual redundancy.

Bruno

>
>
> --
>
> ----------------------------------------------------------------------------
> Dr Russell Standish Phone 0425 253119 (mobile)
> Principal, High Performance Coders hpc...@hpcoders.com.au
> http://www.hpcoders.com.au
> ----------------------------------------------------------------------------
>

> --
> You received this message because you are subscribed to the Google Groups "Everything List" group.
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[Philip Thrift]

On Sunday, May 24, 2020 at 5:59:42 AM UTC-5, Bruno Marchal wrote:

On 23 May 2020, at 21:05, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

Recently you have said that your theory is consistent with finitism,

It has always been a finitism. Judson Webb wrote a book explaining exactly this. 

Worth checking out:

http://www.bu.edu/philo/profile/judson-c-webb/ :

Mechanism, Mentalism, and Metamathematics: An Essay on Finitism (by Judson Webb, Reidel 1980), a full length study of the bearing of incompleteness and undecidability theorems of Gödel and Church on the Turing thesis and artificial intelligence, as well as on Hilbert’s Program.

sample @

https://play.google.com/store/books/details/J_Webb_Mechanism_Mentalism_and_Metamathematics?id=eWl-BgAAQBAJ

@philipthrift 

[Bruno Marchal]

On 24 May 2020, at 01:47, Bruce Kellett <bhkel...@gmail.com> wrote:

On Sun, May 24, 2020 at 9:37 AM Russell Standish <li...@hpcoders.com.au> wrote:

On Sat, May 23, 2020 at 12:05:08PM -0700, 'Brent Meeker' via Everything List wrote:
>
>
> On 5/23/2020 4:42 AM, Bruno Marchal wrote:
> >
> > Well, those are theorem provable in very weak theories. It is more a
> > question of grasping the proof than subscribing to a philosophical idea.
> > That arithmetic executes all programs is a theorem similar to Euclid’s
> > theorem that there is no biggest prima numbers. It is more a fact, than
> > an idea which could be debated. I insist on this as I realise this is
> > less known by the general scientists than 20 years ago. We knew this
> > implicitly since Gödel 1931, and explicitly since Church, Turing and
> > Kleene 1936.
>
> Recently you have said that your theory is consistent with finitism, even
> ultrafinitism.  But the idea that arithemtic exectues all programs certainly
> requires infinities.

Only potential infinities, not actual infinities. For the UD (a finite
object) to execute any given program, one only needs to wait a finite
amount of time.

I thought the UD executing in arithmetic was timeless:

OK.

so all the infinity of possible programs have already been executed before you even start thinking about it.

OK. 

So computationalism has actual infinities built in.

Not really. But you need certainly MUCH MORE than RA, like PA. But PA is still finitiste (but not ultrafinitist).

Computationalism, like physicalism, like mathematical logic, assumes as much math than we need. We know that for the phenomenology of numbers, there is no bound possible on the number and power of axioms needed. 

I “interview” PA  and ZFC in RA, to get the laws of physics. Interviewing RA gives only the universal dovetlaing, which is not Löbian.

So we agree, computationalism allows (and necessitates) an ultrafinitist ontology (or an ultraginit presentation of that ontology), but is not itself ultrafinitist. It needs at least one potential infinite, but the measure existence might need large cardinals in set theory, which is part of the phenomenology (quite beyond the ontology).

With mechanism, we have a Skolem situation, with a small structure seen from outside (like a countable model of RA or PA), which, seen from inside is beyond all big transfinite set conceivable.

It is counter-intuitive, but it is not so much different than imagining that a brain (finite small object) can coneviedd far away galaxies, and infinite possible universes.

Bruno

Bruce

However, I would think that ultrafinitism would change COMP's
predictions, and in a sense be incompatibe with it. Some programs will
not exist, because one would need to wait too long for them to be
executed by the UD. In fact, the choice of reference universal machine
would be significant in ultrafinitism, IIUC.

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[Bruno Marchal]

This has been proven indeed. With mechanism, that is already entailed by the dream argument. 

Bruno

Max Tegmark, in an instance of not being "Mad".

@philipthrift

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[Brent Meeker]

On 5/24/2020 3:30 AM, Lawrence Crowell wrote:

On Saturday, May 23, 2020 at 6:48:06 PM UTC-5, Bruce wrote:

On Sun, May 24, 2020 at 9:37 AM Russell Standish <li...@hpcoders.com.au> wrote:

On Sat, May 23, 2020 at 12:05:08PM -0700, 'Brent Meeker' via Everything List wrote:
>
>
> On 5/23/2020 4:42 AM, Bruno Marchal wrote:
> >
> > Well, those are theorem provable in very weak theories. It is more a
> > question of grasping the proof than subscribing to a philosophical idea.
> > That arithmetic executes all programs is a theorem similar to Euclid’s
> > theorem that there is no biggest prima numbers. It is more a fact, than
> > an idea which could be debated. I insist on this as I realise this is
> > less known by the general scientists than 20 years ago. We knew this
> > implicitly since Gödel 1931, and explicitly since Church, Turing and
> > Kleene 1936.
>
> Recently you have said that your theory is consistent with finitism, even
> ultrafinitism.  But the idea that arithemtic exectues all programs certainly
> requires infinities.

Only potential infinities, not actual infinities. For the UD (a finite
object) to execute any given program, one only needs to wait a finite
amount of time.

I thought the UD executing in arithmetic was timeless: so all the infinity of possible programs have already been executed before you even start thinking about it. So computationalism has actual infinities built in.

Bruce

This depends on what one considers as the domain of computation, whether that is some global content or what is accessible to a local observer. In the first case it is infinite, at least countably infinite. In the latter case it is unbounded above, but finite and given by the finite area of an event horizon or boundary of space on a holographic screen. Both constructions have some relevancy, for in the infinite case we can imagine well enough there is some Cantor diagonalization of quantum states, qubits or information the define a horizon or limit. This would then enforce the locality of any possible observer as bounded by a computational or epistemological horizon. So the two perspective may have a sort of dualism.

That's still thinking of them being physically implemented.  Bruno's UD is simply a mathematical construct and hence exists Platonically indpendent of spacetime.

Brent

[Jason Resch]

Hi Brent,

As promised I've just finished writing about the existence of life and intelligent life in the universe. I'd appreciate your thoughts.

Though life could be very rare I describe another possibility, which is that it miniaturizes and becomes so unlike and alient to the biological life we're familiar with and looking for that we don't notice it.

https://alwaysasking.com/are-we-alone/

Jason

[Brent Meeker]

But we do know that even the most microscopic "life", even viruses grow and reproduce using the same mechanism at the molecular level as we do: DNA, RNA, mRNA, proteins, ATP=>ADp,...  That's really the basis for thinking that all life on Earth had a single origin.  Even archea and bacteria use the same metabolic pathways.

https://alwaysasking.com/are-we-alone/

Not just matter, energy, and time.  Life needs an entropy gradient.  Your whole section on "Energy" reads as though energy is consumed.  But energy is conserved.  It is low entropy (mostly of sunlight) that is "consumed" by turning it into higher entropy infrared radiation.  The best theories of the origin of life postulate alkaline vents as the locus (which are not so hot as hydrothermal vents).  Have you read Nick Lane's "The Vital Question"?

I think you make a mistake in jumping right into "what life needs".  You should first define what you mean by life.  Life as we know it: carbon, hydrogen based?  Anything that reproduces.  Anything that metabolizes?...what?

It took a billion to two billion years for eukaryotes to evolve...not multicellular life.  Multicellular life only arose 0.6 billion ya.

Tardigrades are not going to survive on the Moon...that's fantasy.  They don't eat rocks. Surface temperature on the Moon near the equator varies from -183 degC to +106degC.  And there's no protection from occassional cosmic ray showers.  Tardigrades might survive hours or weeks, but they are not going to survive as a species on the Moon.

The Drake equation rewritten in terms of "detectable" civilizations is wrong because it only considers sending out signals.  To be detectable there has to be a receiver in the forward light cone.  Assuming technologically advanced civilizations last 500yrs that means two of them have to be withing detection range during that 500yr band.  I'm not sure what the detection range is within a noisy galaxy but I think it's less than 100lyr.  One problem is that as communication becomes more technologically advance it becomes less distinguishable from noise.

 "the Arecibo Telescope on the receiving end could pick up the signal from a distance of tens of thousand of light years–on the other side of the galaxy."
The other side of the galaxy is a hundred thousand light years away.

"The vast distances implied by being the only intelligence in the observable universe would, for all practical purposes, mean we are alone, even if infinite other intelligences exist across our infinite universe."
I think this is the important take-home point.  And it doesn't have much to do with the observable universe and how many planets may have life.  Even the closest stars are already too far away for us to not be alone.  We might conceivably send a probe to alpha centauri.  We might talk to a technological civilization 50 light years away...but that would be about the limit, 100year send/reply cycle.

No doubt intelligence is evolutionarily useful...but human level intelligence, speech, mathematics, technology?  It's not so clear.  In fact it may be the kiss of death.  You used 500yr as the life time of a technological civilization...do you think we'll make another 400yrs?

I think you miss one possibility at the other extreme.  Maybe there are aliens that are so big we don't notice them.  There was a scifi story, I believe by the Strugatsky brothers, in which aliens visit Earth but they are vaporous thin structures of gases and stand many kilometers tall.  They are almost completely transparent so they are not even noticed at first.  And they never give any sign of noticing us despite attempts to get their attention.  Eventually they just leave as mysteriously as they came.

Brent

Jason

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[Jason Resch]

I agree life will likely start in more or less recognizable ways, but I believe that after a few thousand or million years of being a technological civilization, it will reach stages that are unrecognizable to us. They will most likely be non-biological, and non-corporeal, living in virtual realities. Computers are substrate independent and can take many different forms. Moreover they can be arbitrarily efficient so long as they are logically reversible. There need not be any significant heat signature.

 

https://alwaysasking.com/are-we-alone/

Not just matter, energy, and time.  Life needs an entropy gradient.  Your whole section on "Energy" reads as though energy is consumed.  But energy is conserved. 

Good point. I meant energy in the colloquial sense (energy available for useful work). Is there a another word I could use for this concept that isn't as technical/scary sounding as entropy gradient?

 

It is low entropy (mostly of sunlight) that is "consumed" by turning it into higher entropy infrared radiation.  The best theories of the origin of life postulate alkaline vents as the locus (which are not so hot as hydrothermal vents).  Have you read Nick Lane's "The Vital Question"?

I haven't. Thanks for the suggestions, I will have to read more about alkaline vents.

 

I think you make a mistake in jumping right into "what life needs".  You should first define what you mean by life.  Life as we know it: carbon, hydrogen based?  Anything that reproduces.  Anything that metabolizes?...what?

You're right, that is an oversight. I will add a definition. Something like: self-maintaining processes that convey information across generations.

 

It took a billion to two billion years for eukaryotes to evolve...not multicellular life.  Multicellular life only arose 0.6 billion ya.

Thank you, I will correct this.

 

Tardigrades are not going to survive on the Moon...that's fantasy.  They don't eat rocks. Surface temperature on the Moon near the equator varies from -183 degC to +106degC.  And there's no protection from occassional cosmic ray showers.  Tardigrades might survive hours or weeks, but they are not going to survive as a species on the Moon.

The Tardigrades were in their tun state where they wrap up their genes to protect them from radiation and reduce their metabolism by orders of magnitude. I agree they would not thrive and reproduce on the moon, but they may exist for perhaps a year (maybe longer?), at least if some landed in an indentation in the soil where they were shielded from direct sunlight) and remain revivable. Some recovered tardigrades in the antarctic were revived after 30 years. I don't know the lower temperatures on the moon would extend or shorten that time frame.

 

The Drake equation rewritten in terms of "detectable" civilizations is wrong because it only considers sending out signals.  To be detectable there has to be a receiver in the forward light cone.  Assuming technologically advanced civilizations last 500yrs that means two of them have to be withing detection range during that 500yr band.  I'm not sure what the detection range is within a noisy galaxy but I think it's less than 100lyr.  One problem is that as communication becomes more technologically advance it becomes less distinguishable from noise.

That's true bout going silent with new technologies, and I mention that. I would say that the Drake Equation is in terms of "detectable in principle" rather than "detectable in practice". Detecting unaimed broadcasts from across the galaxy might require planet-sized detection dishes. But regardless of whether or not two-way communication is possible, the equation is based on a constant star creation rate. Assuming that constant rate applies, then even if civilizations appear, broadcast for 500 years, then wipe themselves out, the total number of presently detectable (in principle) civilizations should be approximated by the equation. 

 

 "the Arecibo Telescope on the receiving end could pick up the signal from a distance of tens of thousand of light years–on the other side of the galaxy."
The other side of the galaxy is a hundred thousand light years away.

But we're about midway to the center. Even if they were as far apart as possible, the farthest they could be from us and still be in the galaxy is 70K ly. Perhaps I should say across, rather than on the other side to be more clear.

 

"The vast distances implied by being the only intelligence in the observable universe would, for all practical purposes, mean we are alone, even if infinite other intelligences exist across our infinite universe."
I think this is the important take-home point.  And it doesn't have much to do with the observable universe and how many planets may have life.  Even the closest stars are already too far away for us to not be alone.  We might conceivably send a probe to alpha centauri.  We might talk to a technological civilization 50 light years away...but that would be about the limit, 100year send/reply cycle.

For our present state of technology, and biology, where we live as bags of meat with 100-year lifespans, those distances are inaccessible. But for a civilization that uploads their minds into starchip-like computer chips, effectively copying their entire civilization and storing them on each von Neumann probes as it replicates and spreads, they could build a civilization that spans the galaxy, and is present in every solar system (assuming they had the will to).

 

No doubt intelligence is evolutionarily useful...but human level intelligence, speech, mathematics, technology?  It's not so clear.  In fact it may be the kiss of death.  You used 500yr as the life time of a technological civilization...do you think we'll make another 400yrs?

I think if we can survive the next century, we can last another million years. But I hold that optimism only because I see super-intelligence arising in that time, which could intervene to relieve us from making suicidal missteps.

 

I think you miss one possibility at the other extreme.  Maybe there are aliens that are so big we don't notice them.  There was a scifi story, I believe by the Strugatsky brothers, in which aliens visit Earth but they are vaporous thin structures of gases and stand many kilometers tall.  They are almost completely transparent so they are not even noticed at first.  And they never give any sign of noticing us despite attempts to get their attention.  Eventually they just leave as mysteriously as they came.

That sounds like a great story. I'll see if I can find it. Is it Roadside Picnic? ( https://en.wikipedia.org/wiki/Roadside_Picnic ) It reminds me a bit of this episode: https://www.youtube.com/watch?v=3oO3tUVLpIM

Jason

 

[Bruno Marchal]

On 24 May 2020, at 13:33, Philip Thrift <cloud...@gmail.com> wrote:

On Sunday, May 24, 2020 at 5:59:42 AM UTC-5, Bruno Marchal wrote:

On 23 May 2020, at 21:05, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

Recently you have said that your theory is consistent with finitism,

It has always been a finitism. Judson Webb wrote a book explaining exactly this. 

Worth checking out:

http://www.bu.edu/philo/profile/judson-c-webb/ :

Mechanism, Mentalism, and Metamathematics: An Essay on Finitism (by Judson Webb, Reidel 1980), a full length study of the bearing of incompleteness and undecidability theorems of Gödel and Church on the Turing thesis and artificial intelligence, as well as on Hilbert’s Program.

It is the best introduction to my work, especially to the mathematical part, with perhaps the book edited by Hoftstadter and Dennett “Mind’s I” for some training in the relevant thought experiments to make the link with the Mechanist philosophy of mind.. 

Judson Webb shows that incompleteness acts as a sort of guardian angel of the Church thesis, by showing that without Gödel’s incompleteness, the Church-Turing thesis (usually called “Church’s thesis, and it is due to Kleene) would be wrong. That is why I called G* the guardian angel of the machine, sometimes ago on this forum.

Kleene himself wrote an excellent paper on this, praising the book of Webb: “Reflections on Church’s Thesis”, Notre Dame Journal of Formal Logic, Vol 28, N° 4, 1987.

Bruno

sample @

https://play.google.com/store/books/details/J_Webb_Mechanism_Mentalism_and_Metamathematics?id=eWl-BgAAQBAJ

@philipthrift 

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[Brent Meeker]

That's why I said you needed to say what your definition of "life" was at the beginning.  Computers can't be logically reversible and still act within the universe...so most people would say that can't be life.  I'm not sure a computer can even have thoughts if exists only in a reversible superposition of states.

 

https://alwaysasking.com/are-we-alone/

Not just matter, energy, and time.  Life needs an entropy gradient.  Your whole section on "Energy" reads as though energy is consumed.  But energy is conserved. 

Good point. I meant energy in the colloquial sense (energy available for useful work). Is there a another word I could use for this concept that isn't as technical/scary sounding as entropy gradient?

 

It is low entropy (mostly of sunlight) that is "consumed" by turning it into higher entropy infrared radiation.  The best theories of the origin of life postulate alkaline vents as the locus (which are not so hot as hydrothermal vents).  Have you read Nick Lane's "The Vital Question"?

I haven't. Thanks for the suggestions, I will have to read more about alkaline vents.

 

I think you make a mistake in jumping right into "what life needs".  You should first define what you mean by life.  Life as we know it: carbon, hydrogen based?  Anything that reproduces.  Anything that metabolizes?...what?

You're right, that is an oversight. I will add a definition. Something like: self-maintaining processes that convey information across generations.

 

It took a billion to two billion years for eukaryotes to evolve...not multicellular life.  Multicellular life only arose 0.6 billion ya.

Thank you, I will correct this.

 

Tardigrades are not going to survive on the Moon...that's fantasy.  They don't eat rocks. Surface temperature on the Moon near the equator varies from -183 degC to +106degC.  And there's no protection from occassional cosmic ray showers.  Tardigrades might survive hours or weeks, but they are not going to survive as a species on the Moon.

The Tardigrades were in their tun state where they wrap up their genes to protect them from radiation and reduce their metabolism by orders of magnitude. I agree they would not thrive and reproduce on the moon, but they may exist for perhaps a year (maybe longer?), at least if some landed in an indentation in the soil where they were shielded from direct sunlight) and remain revivable. Some recovered tardigrades in the antarctic were revived after 30 years. I don't know the lower temperatures on the moon would extend or shorten that time frame.

 

The Drake equation rewritten in terms of "detectable" civilizations is wrong because it only considers sending out signals.  To be detectable there has to be a receiver in the forward light cone.  Assuming technologically advanced civilizations last 500yrs that means two of them have to be withing detection range during that 500yr band.  I'm not sure what the detection range is within a noisy galaxy but I think it's less than 100lyr.  One problem is that as communication becomes more technologically advance it becomes less distinguishable from noise.

That's true bout going silent with new technologies, and I mention that. I would say that the Drake Equation is in terms of "detectable in principle" rather than "detectable in practice". Detecting unaimed broadcasts from across the galaxy might require planet-sized detection dishes. But regardless of whether or not two-way communication is possible, the equation is based on a constant star creation rate. Assuming that constant rate applies, then even if civilizations appear, broadcast for 500 years, then wipe themselves out, the total number of presently detectable (in principle) civilizations should be approximated by the equation.

That's very well if you're just aiming to convince people that there are a lot of civilizations out there in spacetime.  But it's useless in answering Fermi's question.  The answer to that question depends on us being a civilization capable of hearing another one as well as there being another one near enough in space and time.

 

 "the Arecibo Telescope on the receiving end could pick up the signal from a distance of tens of thousand of light years–on the other side of the galaxy."
The other side of the galaxy is a hundred thousand light years away.

But we're about midway to the center. Even if they were as far apart as possible, the farthest they could be from us and still be in the galaxy is 70K ly. Perhaps I should say across, rather than on the other side to be more clear.

 

"The vast distances implied by being the only intelligence in the observable universe would, for all practical purposes, mean we are alone, even if infinite other intelligences exist across our infinite universe."
I think this is the important take-home point.  And it doesn't have much to do with the observable universe and how many planets may have life.  Even the closest stars are already too far away for us to not be alone.  We might conceivably send a probe to alpha centauri.  We might talk to a technological civilization 50 light years away...but that would be about the limit, 100year send/reply cycle.

For our present state of technology, and biology, where we live as bags of meat with 100-year lifespans, those distances are inaccessible. But for a civilization that uploads their minds into starchip-like computer chips, effectively copying their entire civilization and storing them on each von Neumann probes as it replicates and spreads, they could build a civilization that spans the galaxy, and is present in every solar system (assuming they had the will to).

 

No doubt intelligence is evolutionarily useful...but human level intelligence, speech, mathematics, technology?  It's not so clear.  In fact it may be the kiss of death.  You used 500yr as the life time of a technological civilization...do you think we'll make another 400yrs?

I think if we can survive the next century, we can last another million years. But I hold that optimism only because I see super-intelligence arising in that time, which could intervene to relieve us from making suicidal missteps.

More to the point, it will replace us completely.  But then who knows what values will motivate it?  It may just sit and live in Platonia.

 

I think you miss one possibility at the other extreme.  Maybe there are aliens that are so big we don't notice them.  There was a scifi story, I believe by the Strugatsky brothers, in which aliens visit Earth but they are vaporous thin structures of gases and stand many kilometers tall.  They are almost completely transparent so they are not even noticed at first.  And they never give any sign of noticing us despite attempts to get their attention.  Eventually they just leave as mysteriously as they came.

That sounds like a great story. I'll see if I can find it. Is it Roadside Picnic? ( https://en.wikipedia.org/wiki/Roadside_Picnic ) It reminds me a bit of this episode: https://www.youtube.com/watch?v=3oO3tUVLpIM

No.  I think it was well before "Roadside Picnic" and it was short story...only a few pages as I recall.  But Stanislaw Lem has also written a couple of stories about the radical impossibility of communicating with aliens, simply because they are so alien.

Brent

[Lawrence Crowell]

There is a tendency in science fiction to see alien life as similar to Earth life. Intelligent life is again similar to us. The problem is that alien life may be profoundly different on just a molecular level. On Earth there are three major branches of multicellular life, animals, plants and fungi, with slime molds a minor branch. If there is complex life on some other planet chances are good it will have few resemblances to any of these. There might be photosynthetic life forms, but even here on Earth there are bacteria with photo active pigments that are orange or violet. So, the planet might not have a green color, but orange or violet. There might be life forms that have motor abilities, but this might be very different from actin-myosin process in muscles. There might be processing networks, but most likely they would not be what we call brains.

The diversity of possible forms is enormous. There might be some life form that has the ability to manipulate matter and energy, or what we might call technology. If they develop the ability to transmit signals by electromagnetic fields then in some ways it is a fair conjecture that they process information according to mathematical rules. Physics is physics, no matter what, or maybe we might ask who, the ET life form happens to be. However, the difference in processing such ET life forms have might map this into something similar to what an encryption code does. In other words, they might be doing and thinking, if thinking is even the right term, the same as we do, but it is expressed in ways that are almost undecipherable.

It is also possible there are self-organizing systems that are entirely different from what we call biology. These might exist on planets or they might exist elsewhere, whether in vacuum or on something such as a white dwarf star.

LC

[Russell Standish]

On Sun, May 24, 2020 at 01:21:38PM +0200, Bruno Marchal wrote:
>
> > On 24 May 2020, at 01:37, Russell Standish <li...@hpcoders.com.au> wrote:
> >
> > However, I would think that ultrafinitism would change COMP's
> > predictions, and in a sense be incompatibe with it. Some programs will
> > not exist, because one would need to wait too long
>
> “Too long” is still finite.
>
> The biggest natural number is of course “infinite”, but the ultrafinitist cannot know that.
>
> That is why a “real ultrafinitiste” will never say that he is ultrafinitist. He has no means to explains why ultra-finitism means. Only a finitists can prove that ultra-finitsime is consistent (indeed PA can prove that RA is consistent).
>
>
>
> > for them to be
> > executed by the UD. In fact, the choice of reference universal machine
> > would be significant in ultrafinitism, IIUC.
>
> Why? As long as the theory is Turing complete, all programs are run (in all interpretation of the theory), including all finite segment of the executions of all non terminating programs, and this with the usual redundancy.
>

For an ultrafinitist, there is a biggest number (perhaps unknowable),
and consequently computer programs that don't get run (because they
take more steps than that biggest number.

The CT thesis is strictly false in such a case, but could possibly
apply in an approximate sense.

> Bruno
>
>
>
> >
> >
> > --
> >
> > ----------------------------------------------------------------------------
> > Dr Russell Standish Phone 0425 253119 (mobile)
> > Principal, High Performance Coders hpc...@hpcoders.com.au
> > http://www.hpcoders.com.au
> > ----------------------------------------------------------------------------
> >
> > --
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[Bruno Marchal]

> On 31 May 2020, at 09:50, Russell Standish <li...@hpcoders.com.au> wrote:
>
> On Sun, May 24, 2020 at 01:21:38PM +0200, Bruno Marchal wrote:
>>
>>> On 24 May 2020, at 01:37, Russell Standish <li...@hpcoders.com.au> wrote:
>>>
>>> However, I would think that ultrafinitism would change COMP's
>>> predictions, and in a sense be incompatibe with it. Some programs will
>>> not exist, because one would need to wait too long
>>
>> “Too long” is still finite.
>>
>> The biggest natural number is of course “infinite”, but the ultrafinitist cannot know that.
>>
>> That is why a “real ultrafinitiste” will never say that he is ultrafinitist. He has no means to explains why ultra-finitism means. Only a finitists can prove that ultra-finitsime is consistent (indeed PA can prove that RA is consistent).
>>
>>
>>
>>> for them to be
>>> executed by the UD. In fact, the choice of reference universal machine
>>> would be significant in ultrafinitism, IIUC.
>>
>> Why? As long as the theory is Turing complete, all programs are run (in all interpretation of the theory), including all finite segment of the executions of all non terminating programs, and this with the usual redundancy.
>>
>
> For an ultrafinitist, there is a biggest number (perhaps unknowable),
> and consequently computer programs that don't get run (because they
> take more steps than that biggest number.

The biggest number is a non-standard number, meaning that a genuine ultra-finest machine will be, in the eye of a non ultra-finitist, be a “non standard machine”, making a non-standard computations (quite out of the one defined by CT)

>
> The CT thesis is strictly false in such a case,

Indeed.

> but could possibly
> apply in an approximate sense.

That remains to be made more precise, but will require non finitism, … It is the general problem of the ultrafinitist, which is that they cannot define “ultrafinitist”. An ultrafinitst cannot say “I am an ultrafinitist” !

Bruno

>
>
>> Bruno
>>
>>
>>
>>>
>>>
>>> --
>>>
>>> ----------------------------------------------------------------------------
>>> Dr Russell Standish Phone 0425 253119 (mobile)
>>> Principal, High Performance Coders hpc...@hpcoders.com.au
>>> http://www.hpcoders.com.au
>>> ----------------------------------------------------------------------------
>>>
>>> --
>>> You received this message because you are subscribed to the Google Groups "Everything List" group.
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>>
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>
> --
>
> ----------------------------------------------------------------------------
> Dr Russell Standish Phone 0425 253119 (mobile)
> Principal, High Performance Coders hpc...@hpcoders.com.au
> http://www.hpcoders.com.au
> ----------------------------------------------------------------------------
>
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[Alan Grayson]

On Monday, May 18, 2020 at 9:20:36 PM UTC-6, Jason wrote:

I recently wrote an article on the size of the universe and the scope of reality:

https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are largely inspired by some of the conversations I've enjoyed here. It covers many topics including the historic discoveries, the big bang, inflation, string theory, and mathematical realism.

Jason

I see you agree with the MUH that there are infinite, identical repeats of any universe. I tend to think the opposite is true; namely, that in an infinite universe, there are no identical repeats; that is, every universe is unique. I've seen that the theory of infinite repeats is often "repeated", but where is the proof? AG 

[Alan Grayson]

On Monday, May 18, 2020 at 9:20:36 PM UTC-6, Jason wrote:

I recently wrote an article on the size of the universe and the scope of reality:

https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are largely inspired by some of the conversations I've enjoyed here. It covers many topics including the historic discoveries, the big bang, inflation, string theory, and mathematical realism.

Jason

You claim, 

"Every very finite sequence recurs an infinite number of times precisely because Pi goes on forever." Can you prove it? AG

"Similarly, should space go on forever then every possible finite arrangement of matter occurs in an infinite number of locations." Even in a finite universe, assuming space is infinitely divisible, this is false IMO. For example, if we live in a finite 4 dimensional hypersphere with only one particle, it can be placed in infinitely different locations and no repeats is plausible.  AG

[Alan Grayson]

On Monday, June 1, 2020 at 7:31:14 AM UTC-6, Alan Grayson wrote:

On Monday, May 18, 2020 at 9:20:36 PM UTC-6, Jason wrote:

I recently wrote an article on the size of the universe and the scope of reality:

https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are largely inspired by some of the conversations I've enjoyed here. It covers many topics including the historic discoveries, the big bang, inflation, string theory, and mathematical realism.

Jason

You claim, 

"Every very finite sequence recurs an infinite number of times precisely because Pi goes on forever." Can you prove it? AG

What you claim above is probably true, but doesn't apply to a universe where space is infinitely divisible since there exists an uncountable set of possible material configerations, as my example below demonstrates. AG

[Jason Resch]

Speaking of large but finite numbers, I think sometimes we forget just how big some finite numbers can be:

This article really stretched my brain/hurt my head: https://waitbutwhy.com/2014/11/1000000-grahams-number.html Numbers can be so big they become scary.

Jason

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[Jason Resch]

On Mon, Jun 1, 2020 at 6:26 AM Alan Grayson <agrays...@gmail.com> wrote:

On Monday, May 18, 2020 at 9:20:36 PM UTC-6, Jason wrote:

I recently wrote an article on the size of the universe and the scope of reality:

https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are largely inspired by some of the conversations I've enjoyed here. It covers many topics including the historic discoveries, the big bang, inflation, string theory, and mathematical realism.

Jason

I see you agree with the MUH that there are infinite, identical repeats of any universe.

To be clear, the MUH is separate theory from the idea of a spatially infinite universe (which is just the standard cosmological model that working cosmologists assume today, that the universe is infinite, homogeneous, and seeded by random quantum fluctuations occurring at all scales during the expansion of the universe).

 

I tend to think the opposite is true; namely, that in an infinite universe, there are no identical repeats; that is, every universe is unique. I've seen that the theory of infinite repeats is often "repeated", but where is the proof? AG 

The idea is not that the universe itself repeats, only that any finite volume in that space repeats. This can be proved from the pigeon hole principle (which can prove that there is at least one repeat). The proof is as follows.

Let's consider a volume of the mass and size of the Earth. That is a sphere with a radius of 6,371 km and a mass of 5.8 × 10^24 kg. According to Jacob Bekenstein's bound, the total number of distinct quantum states possible is given by: 2.57 * 10^43 bits per (kg * meter).

For Earth that works out to: 2.57 × 10^43 bits/(kg * meter) * 5.8 × 10^24 kg * 6,371,000 meters = 9.49 × 10^74 bits.

Given that many bits, it means there are 2 to the power of (9.49 × 10^74), let's say 2^(10^75), possible configurations for an Earth-sized object of similar mass and volume.  It's a large, but finite number. Let's call this number N = 2^(10^75).

If the universe is infinite, and contains infinite numbers of planets, then there is a finite number of possibilities equal to N. Let's assume the first N such planets are all unique and different from each other. The problem occurs once you get that (N+1)th planet. It can't be unique from all the other N planets which came before it, since there are only N possibilities. Therefore it has to be identical to one of the other N planets.

It's like sequences of flipping coins. There are only 16 possible results (in terms of heads/tails) from flipping 4 coins. Once you are on your 17th set of flipping the coins, you are  guaranteed to have a repeated sequence that is identical to one of the 16 other times you flipped 4 coins.

Jason

[Jason Resch]

You are right, if there are continuous variables of unlimited precision then repeats are infinitely unlikely.

Where this assumption appears to break down, however, is that quantum mechanics implies an upper bound on the number of distinguishable (in principle) states for a given quantity of mass/energy distributed across a given volume of space. So while you could suppose that two similar-seeming regions are in fact in different states, there would be no test you could perform to distinguish between the two. (Given the quantum bounds on information storage).

Jason

[Alan Grayson]

The spectrum for an unbound particle, such as a free electron, is continuous (not discrete). Thus, if the background space is finite OR infinite in extent, there will be no repeats of such a universe since the initial position of any particle, is uncountable.  Although it might not be possible to distinguish two distinct initial states by measurement, I don't see how their existence can be denied. AG 

[Jason Resch]

Let's say time and space are continuous. Now lets design a stop watch that works as follows:

1. Start button: shoots a photon with a wavelength of 300 nanometers down the length of a ruler.

2. Stop button: raises the ruler so that the photon hits it at a certain point that we can measure.

Question: Even if space and time are continuous can this stop watch provide measurements of continuous/unlimited precision?

Answer: Due to the uncertainty principle, the location the photon cannot be determined to a location finer than the photon's wavelength. Accordingly, even if space/time are continuous, such a stop watch has a discrete time-resolution of (300 nanometers / speed of light ) ~= 10^-15 seconds. So for all practical purposes, there's no difference between this stop-watch 1.000000000000000000001 and 1.000000000000000000002 seconds after pressing "Start". Given this, can we be so sure that reality is continuous?

David Deutsch has speculated that the appearance of a continuum may be an artifact of living within an infinite ensemble of independently discrete realities. As we see a continuous variable evolve to reach some final state, it may be an increasing fraction of realities evolving to reach that state (with each one discretely changing). This would explain why a photon might seem to have an arbitrary polarization, or an electron some arbitrary fraction of spin, but when measured it only have one of two possible values.

In summary, I agree with you that a continuous reality rules out exact duplicates. But I would add that quantum mechanics says two regions of space can be so similar to each other that no one, and no experiment, even in theory, could tell the difference between them.

Jason

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[Bruce Kellett]

On Tue, Jun 2, 2020 at 5:39 AM Jason Resch <jason...@gmail.com> wrote:

On Mon, Jun 1, 2020 at 6:26 AM Alan Grayson <agrays...@gmail.com> wrote:

On Monday, May 18, 2020 at 9:20:36 PM UTC-6, Jason wrote:

I recently wrote an article on the size of the universe and the scope of reality:

https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are largely inspired by some of the conversations I've enjoyed here. It covers many topics including the historic discoveries, the big bang, inflation, string theory, and mathematical realism.

Jason

I see you agree with the MUH that there are infinite, identical repeats of any universe.

To be clear, the MUH is separate theory from the idea of a spatially infinite universe (which is just the standard cosmological model that working cosmologists assume today, that the universe is infinite, homogeneous, and seeded by random quantum fluctuations occurring at all scales during the expansion of the universe).

Define what you mean by "quantum fluctuations". There are no such things in standard quantum mechanics.

 

 

I tend to think the opposite is true; namely, that in an infinite universe, there are no identical repeats; that is, every universe is unique. I've seen that the theory of infinite repeats is often "repeated", but where is the proof? AG 

The idea is not that the universe itself repeats, only that any finite volume in that space repeats. This can be proved from the pigeon hole principle (which can prove that there is at least one repeat). The proof is as follows.

Let's consider a volume of the mass and size of the Earth. That is a sphere with a radius of 6,371 km and a mass of 5.8 × 10^24 kg. According to Jacob Bekenstein's bound, the total number of distinct quantum states possible is given by: 2.57 * 10^43 bits per (kg * meter).

For Earth that works out to: 2.57 × 10^43 bits/(kg * meter) * 5.8 × 10^24 kg * 6,371,000 meters = 9.49 × 10^74 bits.

Given that many bits, it means there are 2 to the power of (9.49 × 10^74), let's say 2^(10^75), possible configurations for an Earth-sized object of similar mass and volume.  It's a large, but finite number. Let's call this number N = 2^(10^75).

If the universe is infinite, and contains infinite numbers of planets, then there is a finite number of possibilities equal to N. Let's assume the first N such planets are all unique and different from each other. The problem occurs once you get that (N+1)th planet. It can't be unique from all the other N planets which came before it, since there are only N possibilities. Therefore it has to be identical to one of the other N planets.

That does not preclude the possibility of infinite repeats of just one of the states -- all others being unique. To have repeats of every possible state requires very strong homogeneity assumptions; assumptions that cannot ever be justified.

Bruce

[Jason Resch]

On Monday, June 1, 2020, Bruce Kellett <bhkel...@gmail.com> wrote:

On Tue, Jun 2, 2020 at 5:39 AM Jason Resch <jason...@gmail.com> wrote:

On Mon, Jun 1, 2020 at 6:26 AM Alan Grayson <agrays...@gmail.com> wrote:

On Monday, May 18, 2020 at 9:20:36 PM UTC-6, Jason wrote:

I recently wrote an article on the size of the universe and the scope of reality:

https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are largely inspired by some of the conversations I've enjoyed here. It covers many topics including the historic discoveries, the big bang, inflation, string theory, and mathematical realism.

Jason

I see you agree with the MUH that there are infinite, identical repeats of any universe.

To be clear, the MUH is separate theory from the idea of a spatially infinite universe (which is just the standard cosmological model that working cosmologists assume today, that the universe is infinite, homogeneous, and seeded by random quantum fluctuations occurring at all scales during the expansion of the universe).

Define what you mean by "quantum fluctuations". There are no such things in standard quantum mechanics.

Variations in the decay of the inflaton field that seeded the variations in density that led to stars and galaxies, and confirmed by observations by COBE and Planck.

 

 

 

I tend to think the opposite is true; namely, that in an infinite universe, there are no identical repeats; that is, every universe is unique. I've seen that the theory of infinite repeats is often "repeated", but where is the proof? AG 

The idea is not that the universe itself repeats, only that any finite volume in that space repeats. This can be proved from the pigeon hole principle (which can prove that there is at least one repeat). The proof is as follows.

Let's consider a volume of the mass and size of the Earth. That is a sphere with a radius of 6,371 km and a mass of 5.8 × 10^24 kg. According to Jacob Bekenstein's bound, the total number of distinct quantum states possible is given by: 2.57 * 10^43 bits per (kg * meter).

For Earth that works out to: 2.57 × 10^43 bits/(kg * meter) * 5.8 × 10^24 kg * 6,371,000 meters = 9.49 × 10^74 bits.

Given that many bits, it means there are 2 to the power of (9.49 × 10^74), let's say 2^(10^75), possible configurations for an Earth-sized object of similar mass and volume.  It's a large, but finite number. Let's call this number N = 2^(10^75).

If the universe is infinite, and contains infinite numbers of planets, then there is a finite number of possibilities equal to N. Let's assume the first N such planets are all unique and different from each other. The problem occurs once you get that (N+1)th planet. It can't be unique from all the other N planets which came before it, since there are only N possibilities. Therefore it has to be identical to one of the other N planets.

That does not preclude the possibility of infinite repeats of just one of the states -- all others being unique. To have repeats of every possible state requires very strong homogeneity assumptions; assumptions that cannot ever be justified.

True, but I think you would need to add additional (far stronger) assumptions to explain why something could happen exactly once but never again throughout infinite space and those assumptions run counter to standard cosmological ones.

Jason

[Alan Grayson]

On Monday, June 1, 2020 at 3:58:01 PM UTC-6, Jason wrote:

Let's say time and space are continuous. Now lets design a stop watch that works as follows:

1. Start button: shoots a photon with a wavelength of 300 nanometers down the length of a ruler.

2. Stop button: raises the ruler so that the photon hits it at a certain point that we can measure.

Question: Even if space and time are continuous can this stop watch provide measurements of continuous/unlimited precision?

Answer: Due to the uncertainty principle, the location the photon cannot be determined to a location finer than the photon's wavelength. Accordingly, even if space/time are continuous, such a stop watch has a discrete time-resolution of (300 nanometers / speed of light ) ~= 10^-15 seconds. So for all practical purposes, there's no difference between this stop-watch 1.000000000000000000001 and 1.000000000000000000002 seconds after pressing "Start". Given this, can we be so sure that reality is continuous?

David Deutsch has speculated that the appearance of a continuum may be an artifact of living within an infinite ensemble of independently discrete realities. As we see a continuous variable evolve to reach some final state, it may be an increasing fraction of realities evolving to reach that state (with each one discretely changing). This would explain why a photon might seem to have an arbitrary polarization, or an electron some arbitrary fraction of spin, but when measured it only have one of two possible values.

In summary, I agree with you that a continuous reality rules out exact duplicates. But I would add that quantum mechanics says two regions of space can be so similar to each other that no one, and no experiment, even in theory, could tell the difference between them.

Jason

I don't see what measurements of similarity has to do with this issue. Fact is that if space is continuous, there cannot be any exact repetitions. And not only is position continuous, but so are other variables, which makes the case of uniqueness even stronger. And it doesn't matter whether the universe is finite or infinite in spatial extent. So from my perspective, every universe is unique (provided continuity of spatial extent exists). AG 

On Mon, Jun 1, 2020 at 4:24 PM Alan Grayson <agrays...@gmail.com> wrote:

On Monday, June 1, 2020 at 1:43:09 PM UTC-6, Jason wrote:

On Mon, Jun 1, 2020 at 8:31 AM Alan Grayson <agrays...@gmail.com> wrote:

On Monday, May 18, 2020 at 9:20:36 PM UTC-6, Jason wrote:

I recently wrote an article on the size of the universe and the scope of reality:

https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are largely inspired by some of the conversations I've enjoyed here. It covers many topics including the historic discoveries, the big bang, inflation, string theory, and mathematical realism.

Jason

You claim, 

"Every very finite sequence recurs an infinite number of times precisely because Pi goes on forever." Can you prove it? AG

"Similarly, should space go on forever then every possible finite arrangement of matter occurs in an infinite number of locations." Even in a finite universe, assuming space is infinitely divisible, this is false IMO. For example, if we live in a finite 4 dimensional hypersphere with only one particle, it can be placed in infinitely different locations and no repeats is plausible.  AG

You are right, if there are continuous variables of unlimited precision then repeats are infinitely unlikely.

Where this assumption appears to break down, however, is that quantum mechanics implies an upper bound on the number of distinguishable (in principle) states for a given quantity of mass/energy distributed across a given volume of space. So while you could suppose that two similar-seeming regions are in fact in different states, there would be no test you could perform to distinguish between the two. (Given the quantum bounds on information storage).

Jason

The spectrum for an unbound particle, such as a free electron, is continuous (not discrete). Thus, if the background space is finite OR infinite in extent, there will be no repeats of such a universe since the initial position of any particle, is uncountable.  Although it might not be possible to distinguish two distinct initial states by measurement, I don't see how their existence can be denied. AG 

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[Bruce Kellett]

On Tue, Jun 2, 2020 at 9:59 AM Jason Resch <jason...@gmail.com> wrote:

On Monday, June 1, 2020, Bruce Kellett <bhkel...@gmail.com> wrote:

On Tue, Jun 2, 2020 at 5:39 AM Jason Resch <jason...@gmail.com> wrote:

On Mon, Jun 1, 2020 at 6:26 AM Alan Grayson <agrays...@gmail.com> wrote:

On Monday, May 18, 2020 at 9:20:36 PM UTC-6, Jason wrote:

I recently wrote an article on the size of the universe and the scope of reality:

https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are largely inspired by some of the conversations I've enjoyed here. It covers many topics including the historic discoveries, the big bang, inflation, string theory, and mathematical realism.

Jason

I see you agree with the MUH that there are infinite, identical repeats of any universe.

To be clear, the MUH is separate theory from the idea of a spatially infinite universe (which is just the standard cosmological model that working cosmologists assume today, that the universe is infinite, homogeneous, and seeded by random quantum fluctuations occurring at all scales during the expansion of the universe).

Define what you mean by "quantum fluctuations". There are no such things in standard quantum mechanics.

Variations in the decay of the inflaton field that seeded the variations in density that led to stars and galaxies, and confirmed by observations by COBE and Planck.

That is not how inflation models work.

 

I tend to think the opposite is true; namely, that in an infinite universe, there are no identical repeats; that is, every universe is unique. I've seen that the theory of infinite repeats is often "repeated", but where is the proof? AG 

The idea is not that the universe itself repeats, only that any finite volume in that space repeats. This can be proved from the pigeon hole principle (which can prove that there is at least one repeat). The proof is as follows.

Let's consider a volume of the mass and size of the Earth. That is a sphere with a radius of 6,371 km and a mass of 5.8 × 10^24 kg. According to Jacob Bekenstein's bound, the total number of distinct quantum states possible is given by: 2.57 * 10^43 bits per (kg * meter).

For Earth that works out to: 2.57 × 10^43 bits/(kg * meter) * 5.8 × 10^24 kg * 6,371,000 meters = 9.49 × 10^74 bits.

Given that many bits, it means there are 2 to the power of (9.49 × 10^74), let's say 2^(10^75), possible configurations for an Earth-sized object of similar mass and volume.  It's a large, but finite number. Let's call this number N = 2^(10^75).

If the universe is infinite, and contains infinite numbers of planets, then there is a finite number of possibilities equal to N. Let's assume the first N such planets are all unique and different from each other. The problem occurs once you get that (N+1)th planet. It can't be unique from all the other N planets which came before it, since there are only N possibilities. Therefore it has to be identical to one of the other N planets.

That does not preclude the possibility of infinite repeats of just one of the states -- all others being unique. To have repeats of every possible state requires very strong homogeneity assumptions; assumptions that cannot ever be justified.

True, but I think you would need to add additional (far stronger) assumptions to explain why something could happen exactly once but never again throughout infinite space and those assumptions run counter to standard cosmological ones.

The standard assumption of homogeneity, etc, made in cosmological models are made for convenience only -- there is no theoretical or practical basis for those assumptions rather than any other assumptions. We can have initial conditions of zero measure, after all.

Bruce

[Bruno Marchal]

On 1 Jun 2020, at 13:26, Alan Grayson <agrays...@gmail.com> wrote:

On Monday, May 18, 2020 at 9:20:36 PM UTC-6, Jason wrote:

I recently wrote an article on the size of the universe and the scope of reality:

https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are largely inspired by some of the conversations I've enjoyed here. It covers many topics including the historic discoveries, the big bang, inflation, string theory, and mathematical realism.

Jason

I see you agree with the MUH that there are infinite, identical repeats of any universe.

With mechanism “universe” does not make sense, but there is an infinity of emulations of each computations (in very elementary arithmetic, i.e. PA without induction axioms).

Strictly speaking, the digital mechanist theory leads to 0 universes, but many histoires/ computations.

I tend to think the opposite is true; namely, that in an infinite universe, there are no identical repeats; that is, every universe is unique. I've seen that the theory of infinite repeats is often "repeated", but where is the proof? AG 

The many computations in RA is provable in PA, ZF, etc.

Bruno

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[Bruno Marchal]

On 1 Jun 2020, at 15:55, Alan Grayson <agrays...@gmail.com> wrote:

On Monday, June 1, 2020 at 7:31:14 AM UTC-6, Alan Grayson wrote:

On Monday, May 18, 2020 at 9:20:36 PM UTC-6, Jason wrote:

I recently wrote an article on the size of the universe and the scope of reality:

https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are largely inspired by some of the conversations I've enjoyed here. It covers many topics including the historic discoveries, the big bang, inflation, string theory, and mathematical realism.

Jason

You claim, 

"Every very finite sequence recurs an infinite number of times precisely because Pi goes on forever." Can you prove it? AG

I asked Jason, why use PI? It has not been proved fro Pi, but it has been proved for some other constructive real numbers.

Bruno

What you claim above is probably true, but doesn't apply to a universe where space is infinitely divisible since there exists an uncountable set of possible material configerations, as my example below demonstrates. AG

"Similarly, should space go on forever then every possible finite arrangement of matter occurs in an infinite number of locations." Even in a finite universe, assuming space is infinitely divisible, this is false IMO. For example, if we live in a finite 4 dimensional hypersphere with only one particle, it can be placed in infinitely different locations and no repeats is plausible.  AG

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[Bruno Marchal]

On 1 Jun 2020, at 19:31, Jason Resch <jason...@gmail.com> wrote:

Speaking of large but finite numbers, I think sometimes we forget just how big some finite numbers can be:

This article really stretched my brain/hurt my head: https://waitbutwhy.com/2014/11/1000000-grahams-number.html Numbers can be so big they become scary.

And I have explained how such graham numbers are infinitesimal, compared to what logicians can do. I did this to illustrate the transendental power of diagonalsiation, on this list, some years ago. I did this to better explain why Gödel is right to call the CT thesis a “miracle”. It makes “all computations” an explanatively close theory/realm, even close for the most transcendental mathematical operation (diagonalisation). It tools a long time for me to believe in CT, but I knew since long that if CT is true, physics cannot be the fundamental science, and has to be reduced to arithmetic, or to any universal machinery.

Arithmetic seen from inside is inconceivably bigger than the physical observable universe, in fact it is bigger than the set-theoretical universe … yes, it can be scary …

Bruno 

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[Bruno Marchal]

With mechanism, the computations simulating our entire cluster of galaxies, at the QED and QCD level (probably lower than our substitution level) occurs (in the sigma_1 arithmetical reality, or in the universal dovetailing) in infinitely many occurrences.

Indeed the only reason white rabbit disappear is that the normal histories have a measure one, in the (mechanist) theory. In nature, that remains to be verify again and again …

Bruno 

Jason

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[Bruno Marchal]

On 2 Jun 2020, at 03:07, Alan Grayson <agrays...@gmail.com> wrote:

On Monday, June 1, 2020 at 3:58:01 PM UTC-6, Jason wrote:

Let's say time and space are continuous. Now lets design a stop watch that works as follows:

1. Start button: shoots a photon with a wavelength of 300 nanometers down the length of a ruler.

2. Stop button: raises the ruler so that the photon hits it at a certain point that we can measure.

Question: Even if space and time are continuous can this stop watch provide measurements of continuous/unlimited precision?

Answer: Due to the uncertainty principle, the location the photon cannot be determined to a location finer than the photon's wavelength. Accordingly, even if space/time are continuous, such a stop watch has a discrete time-resolution of (300 nanometers / speed of light ) ~= 10^-15 seconds. So for all practical purposes, there's no difference between this stop-watch 1.000000000000000000001 and 1.000000000000000000002 seconds after pressing "Start". Given this, can we be so sure that reality is continuous?

David Deutsch has speculated that the appearance of a continuum may be an artifact of living within an infinite ensemble of independently discrete realities. As we see a continuous variable evolve to reach some final state, it may be an increasing fraction of realities evolving to reach that state (with each one discretely changing). This would explain why a photon might seem to have an arbitrary polarization, or an electron some arbitrary fraction of spin, but when measured it only have one of two possible values.

In summary, I agree with you that a continuous reality rules out exact duplicates. But I would add that quantum mechanics says two regions of space can be so similar to each other that no one, and no experiment, even in theory, could tell the difference between them.

Jason

I don't see what measurements of similarity has to do with this issue. Fact is that if space is continuous,

That is not a fact. The fact is that we don’t know, neither with Mechanism, nor with physics which has not yet successfully explain how to marry the quantum and GR.

With mechanism, the continuum comes from the necessary random oracle of the first person posts of view.

there cannot be any exact repetitions. And not only is position continuous, but so are other variables, which makes the case of uniqueness even stronger. And it doesn't matter whether the universe is finite or infinite in spatial extent. So from my perspective, every universe is unique (provided continuity of spatial extent exists). AG 

Better to not assume a universe, or a god, as those things are what we need to explain.

Bruno

On Mon, Jun 1, 2020 at 4:24 PM Alan Grayson <agrays...@gmail.com> wrote:

On Monday, June 1, 2020 at 1:43:09 PM UTC-6, Jason wrote:

On Mon, Jun 1, 2020 at 8:31 AM Alan Grayson <agrays...@gmail.com> wrote:

On Monday, May 18, 2020 at 9:20:36 PM UTC-6, Jason wrote:

I recently wrote an article on the size of the universe and the scope of reality:

https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are largely inspired by some of the conversations I've enjoyed here. It covers many topics including the historic discoveries, the big bang, inflation, string theory, and mathematical realism.

Jason

You claim, 

"Every very finite sequence recurs an infinite number of times precisely because Pi goes on forever." Can you prove it? AG

"Similarly, should space go on forever then every possible finite arrangement of matter occurs in an infinite number of locations." Even in a finite universe, assuming space is infinitely divisible, this is false IMO. For example, if we live in a finite 4 dimensional hypersphere with only one particle, it can be placed in infinitely different locations and no repeats is plausible.  AG

You are right, if there are continuous variables of unlimited precision then repeats are infinitely unlikely.

Where this assumption appears to break down, however, is that quantum mechanics implies an upper bound on the number of distinguishable (in principle) states for a given quantity of mass/energy distributed across a given volume of space. So while you could suppose that two similar-seeming regions are in fact in different states, there would be no test you could perform to distinguish between the two. (Given the quantum bounds on information storage).

Jason

The spectrum for an unbound particle, such as a free electron, is continuous (not discrete). Thus, if the background space is finite OR infinite in extent, there will be no repeats of such a universe since the initial position of any particle, is uncountable.  Although it might not be possible to distinguish two distinct initial states by measurement, I don't see how their existence can be denied. AG 

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[Alan Grayson]

On Tuesday, June 2, 2020 at 4:33:39 AM UTC-6, Bruno Marchal wrote:

On 2 Jun 2020, at 03:07, Alan Grayson <agrays...@gmail.com> wrote:

On Monday, June 1, 2020 at 3:58:01 PM UTC-6, Jason wrote:

Let's say time and space are continuous. Now lets design a stop watch that works as follows:

1. Start button: shoots a photon with a wavelength of 300 nanometers down the length of a ruler.

2. Stop button: raises the ruler so that the photon hits it at a certain point that we can measure.

Question: Even if space and time are continuous can this stop watch provide measurements of continuous/unlimited precision?

Answer: Due to the uncertainty principle, the location the photon cannot be determined to a location finer than the photon's wavelength. Accordingly, even if space/time are continuous, such a stop watch has a discrete time-resolution of (300 nanometers / speed of light ) ~= 10^-15 seconds. So for all practical purposes, there's no difference between this stop-watch 1.000000000000000000001 and 1.000000000000000000002 seconds after pressing "Start". Given this, can we be so sure that reality is continuous?

David Deutsch has speculated that the appearance of a continuum may be an artifact of living within an infinite ensemble of independently discrete realities. As we see a continuous variable evolve to reach some final state, it may be an increasing fraction of realities evolving to reach that state (with each one discretely changing). This would explain why a photon might seem to have an arbitrary polarization, or an electron some arbitrary fraction of spin, but when measured it only have one of two possible values.

In summary, I agree with you that a continuous reality rules out exact duplicates. But I would add that quantum mechanics says two regions of space can be so similar to each other that no one, and no experiment, even in theory, could tell the difference between them.

Jason

I don't see what measurements of similarity has to do with this issue. Fact is that if space is continuous,

That is not a fact.

The fact is you can't read plain English. Do you know what "if" means? AG

 

The fact is that we don’t know,

Another fact is that our best measurements are consistent with continuity. LC has posted about this. AG

 

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[Jason Resch]

On Mon, Jun 1, 2020 at 8:51 PM Bruce Kellett <bhkel...@gmail.com> wrote:

On Tue, Jun 2, 2020 at 9:59 AM Jason Resch <jason...@gmail.com> wrote:

On Monday, June 1, 2020, Bruce Kellett <bhkel...@gmail.com> wrote:

On Tue, Jun 2, 2020 at 5:39 AM Jason Resch <jason...@gmail.com> wrote:

On Mon, Jun 1, 2020 at 6:26 AM Alan Grayson <agrays...@gmail.com> wrote:

On Monday, May 18, 2020 at 9:20:36 PM UTC-6, Jason wrote:

I recently wrote an article on the size of the universe and the scope of reality:

https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are largely inspired by some of the conversations I've enjoyed here. It covers many topics including the historic discoveries, the big bang, inflation, string theory, and mathematical realism.

Jason

I see you agree with the MUH that there are infinite, identical repeats of any universe.

To be clear, the MUH is separate theory from the idea of a spatially infinite universe (which is just the standard cosmological model that working cosmologists assume today, that the universe is infinite, homogeneous, and seeded by random quantum fluctuations occurring at all scales during the expansion of the universe).

Define what you mean by "quantum fluctuations". There are no such things in standard quantum mechanics.

Variations in the decay of the inflaton field that seeded the variations in density that led to stars and galaxies, and confirmed by observations by COBE and Planck.

That is not how inflation models work.

Are you sure about that? If so could you explain the error in this or in my understanding of it: https://www.youtube.com/watch?v=chsLw2siRW0&t=6m43s

Jason

 

[Bruno Marchal]

On 2 Jun 2020, at 14:05, Alan Grayson <agrays...@gmail.com> wrote:

On Tuesday, June 2, 2020 at 4:33:39 AM UTC-6, Bruno Marchal wrote:

On 2 Jun 2020, at 03:07, Alan Grayson <agrays...@gmail.com> wrote:

On Monday, June 1, 2020 at 3:58:01 PM UTC-6, Jason wrote:

Let's say time and space are continuous. Now lets design a stop watch that works as follows:

1. Start button: shoots a photon with a wavelength of 300 nanometers down the length of a ruler.

2. Stop button: raises the ruler so that the photon hits it at a certain point that we can measure.

Question: Even if space and time are continuous can this stop watch provide measurements of continuous/unlimited precision?

Answer: Due to the uncertainty principle, the location the photon cannot be determined to a location finer than the photon's wavelength. Accordingly, even if space/time are continuous, such a stop watch has a discrete time-resolution of (300 nanometers / speed of light ) ~= 10^-15 seconds. So for all practical purposes, there's no difference between this stop-watch 1.000000000000000000001 and 1.000000000000000000002 seconds after pressing "Start". Given this, can we be so sure that reality is continuous?

David Deutsch has speculated that the appearance of a continuum may be an artifact of living within an infinite ensemble of independently discrete realities. As we see a continuous variable evolve to reach some final state, it may be an increasing fraction of realities evolving to reach that state (with each one discretely changing). This would explain why a photon might seem to have an arbitrary polarization, or an electron some arbitrary fraction of spin, but when measured it only have one of two possible values.

In summary, I agree with you that a continuous reality rules out exact duplicates. But I would add that quantum mechanics says two regions of space can be so similar to each other that no one, and no experiment, even in theory, could tell the difference between them.

Jason

I don't see what measurements of similarity has to do with this issue. Fact is that if space is continuous,

That is not a fact.

The fact is you can't read plain English. Do you know what "if" means? AG

 

The fact is that we don’t know,

Another fact is that our best measurements are consistent with continuity. LC has posted about this. AG

You don’t quote enough. My statements were not on the “if”, but what followed. As I have explained many time, Mechanism enforced the presence of continuity in physics, and even of some non computable feature of the physical reality (and indeed that is why digital physicalism is self-defeating: it is always wrong, with or without mechanism (an hypothesis in the cognitive science, not in physics).

Bruno 

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[Bruce Kellett]

You video gives an oversimplified comic-book version of inflation. If you want to understand inflation, you have to go to a professional, expert review, such as Bassett, Tsujikawa, and Wands, Rev. Mod. Phys. 78:537-589 (2006). (Also in arXiv:0507632). You will see from this that density perturbations are just Guassian random fields, put in by hand, with parameters adjusted to fit the data. There are no intrinsic "quantum fluctuations".

Bruce

[Jason Resch]

According to the theory what is the source of this gaussian randomnesses? What makes a field random if not quantum mechanics?

Jason

Bruce

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[smitra]

There obviously do exist quantum fluctuations. A down to Earth example
is Johnson noise. Connect a sensitive voltmeter to a resistor and you'll
detect fluctuations in the voltage. The average voltage is zero, but
there are fluctuations due to thermal motion of the electrons. If you
cool down the resistor these fluctuations will become smaller, but even
at absolute zero there will still be fluctuations in the voltage. These
fluctuations at zero temperature are what we call "quantum fluctuations"
in physics. Now I remember an old discussion with Bruce on this list
about this, and insisted that what I called quantum fluctuations are
actually "thermal fluctuations at 0 K". But at 0 K the system is in the
ground state, so it doesn't matter what you name you give to the
fluctuations, these are purely quantum mechanical in nature, they don't
arise from an initial randomness in the initial state.

Saibal

[Bruce Kellett]

On Sat, Jun 6, 2020 at 3:11 AM smitra <smi...@zonnet.nl> wrote:

There obviously do exist quantum fluctuations. A down to Earth example
is Johnson noise. Connect a sensitive voltmeter to a resistor and you'll
detect fluctuations in the voltage. The average voltage is zero, but
there are fluctuations due to thermal motion of the electrons. If you
cool down the resistor these fluctuations will become smaller, but even
at absolute zero there will still be fluctuations in the voltage.

Can you point to experimental evidence of this? As far as I know, absolute zero temperature is intrinsically unattainable.

These fluctuations at zero temperature are what we call "quantum fluctuations"
in physics.

 

I think you are confusing the zero point energy of quantum fields with "quantum fluctuations". The zero point energy, whatever it might be, does not "fluctuate". "Fluctuate means change with time, and the zero point energy is just a value, and it does not change with time -- it does not "fluctuate".

Bruce

[Bruce Kellett]

On Sat, Jun 6, 2020 at 2:08 AM Jason Resch <jason...@gmail.com> wrote:

On Fri, Jun 5, 2020, 5:55 AM Bruce Kellett <bhkel...@gmail.com> wrote:

You video gives an oversimplified comic-book version of inflation. If you want to understand inflation, you have to go to a professional, expert review, such as Bassett, Tsujikawa, and Wands, Rev. Mod. Phys. 78:537-589 (2006). (Also in arXiv:0507632). You will see from this that density perturbations are just Guassian random fields, put in by hand, with parameters adjusted to fit the data. There are no intrinsic "quantum fluctuations".

According to the theory what is the source of this gaussian randomnesses? What makes a field random if not quantum mechanics?

There is no theory behind this -- the gaussian "fluctuations" are just put in by hand. There is the unspoken implication that the origin of these fluctuations is quantum, but there is no theory for this, and, as has been pointed out, there are no such things as "quantum fluctuations" in this sense. Tim Maudlin has commented on this in Sabine Hossenfelder's blog:

https://www.blogger.com/comment.g?blogID=22973357&postID=264282891971221826

Bruce

[Alan Grayson]

On Friday, June 5, 2020 at 5:07:58 PM UTC-6, Bruce wrote:

On Sat, Jun 6, 2020 at 3:11 AM smitra <smi...@zonnet.nl> wrote:

There obviously do exist quantum fluctuations. A down to Earth example
is Johnson noise. Connect a sensitive voltmeter to a resistor and you'll
detect fluctuations in the voltage. The average voltage is zero, but
there are fluctuations due to thermal motion of the electrons. If you
cool down the resistor these fluctuations will become smaller, but even
at absolute zero there will still be fluctuations in the voltage.

Can you point to experimental evidence of this? As far as I know, absolute zero temperature is intrinsically unattainable.

These fluctuations at zero temperature are what we call "quantum fluctuations"
in physics.

 

I think you are confusing the zero point energy of quantum fields with "quantum fluctuations". The zero point energy, whatever it might be, does not "fluctuate". "Fluctuate means change with time, and the zero point energy is just a value, and it does not change with time -- it does not "fluctuate".

Another point worth mentioning is that when a quantum system is measured, we get some specific eigenvalue. And if THAT system is measured again, the measured value remains the same. No fluctuation. (I forget exactly why that's the case.). But if we measure a different system represented by the same wave function, the measured value changes. So the message is, again, that no single system fluctuates. AG 

[Alan Grayson]

On Friday, June 5, 2020 at 7:31:56 PM UTC-6, Alan Grayson wrote:

On Friday, June 5, 2020 at 5:07:58 PM UTC-6, Bruce wrote:

On Sat, Jun 6, 2020 at 3:11 AM smitra <smi...@zonnet.nl> wrote:

There obviously do exist quantum fluctuations. A down to Earth example
is Johnson noise. Connect a sensitive voltmeter to a resistor and you'll
detect fluctuations in the voltage. The average voltage is zero, but
there are fluctuations due to thermal motion of the electrons. If you
cool down the resistor these fluctuations will become smaller, but even
at absolute zero there will still be fluctuations in the voltage.

Can you point to experimental evidence of this? As far as I know, absolute zero temperature is intrinsically unattainable.

These fluctuations at zero temperature are what we call "quantum fluctuations"
in physics.

 

I think you are confusing the zero point energy of quantum fields with "quantum fluctuations". The zero point energy, whatever it might be, does not "fluctuate". "Fluctuate means change with time, and the zero point energy is just a value, and it does not change with time -- it does not "fluctuate".

Another point worth mentioning is that when a quantum system is measured, we get some specific eigenvalue. And if THAT system is measured again, the measured value remains the same. No fluctuation. (I forget exactly why that's the case.). But if we measure a different system represented by the same wave function, the measured value changes. So the message is, again, that no single system fluctuates. AG 

Oh, now I recall.  After the measurement, the system's state is the eigenfunction of the eigenvalue measured. Previously, it was in a superposition of states. So when we measure that specific system again, the probability of measuring the same eigenvalue is unity. AG 

[Bruno Marchal]

Eventually, they do arise from the fact that no universal machine can know in which history she belongs, and that even the physical void is a phenomenological product of infinitely many computations. Actually, when we assume Mechanism.

Bruno

>
> Saibal

>
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[smitra]

On 06-06-2020 01:07, Bruce Kellett wrote:
> On Sat, Jun 6, 2020 at 3:11 AM smitra <smi...@zonnet.nl> wrote:
>
>> There obviously do exist quantum fluctuations. A down to Earth
>> example
>> is Johnson noise. Connect a sensitive voltmeter to a resistor and
>> you'll
>> detect fluctuations in the voltage. The average voltage is zero, but
>>
>> there are fluctuations due to thermal motion of the electrons. If
>> you
>> cool down the resistor these fluctuations will become smaller, but
>> even
>> at absolute zero there will still be fluctuations in the voltage.
>
> Can you point to experimental evidence of this? As far as I know,
> absolute zero temperature is intrinsically unattainable.
>

There exists a vast literature on detectors that operate in the regime
where most of the noise is due to quantum effects rather than thermal
effects.

>> These fluctuations at zero temperature are what we call "quantum
>> fluctuations"
>> in physics.
>
> I think you are confusing the zero point energy of quantum fields with
> "quantum fluctuations". The zero point energy, whatever it might be,
> does not "fluctuate". "Fluctuate means change with time, and the zero
> point energy is just a value, and it does not change with time -- it
> does not "fluctuate".

The ground state energy does not fluctuate, but other observables such
as the field strengths obviously do in the sense of having a variance.
The energy is quadratic in the field and this has nonzero expectation
value, while the expectation value of the field will usually be zero.
So, one can say that the zero point energy represents the quantum
fluctuations of the field, because it is the variance of the field.
While one can argue about the word "fluctuation" used here, what matters
is that the field strength will take on random values when measured in
the ground state. It is this phenomena what Jason referred to. In the
scientific papers on inflation they may go about computing the effects
of the fluctuations in a semi-classical way by putting in the
fluctuations by hand in classical equations of motion, but there is a
solid theoretical basis for such an approach.

Saibal

[smitra]

It seems plausible to me that one should be able to derive quantum
mechanics from such ideas involving some form of a mathematical
multiverse. The multiverse aspect of the MWI is likely correct but it's
problematic when considering the detailed physics. It's similar to how
Einstein got the idea that gravity must be linked to curved space-time
long before he had discovered the precise mathematical formulation of
general relativity. Had he or someone else stuck to just vague ideas
then critics would have thrashed the whole idea of curved space-time,
and they would worked with retarded gravitational
potentials analogous to those used in electromagnetism.

Michio Kaku has said that if Einstein had not developed general
relativity that physicists would have used such a wrong relativistic
formalism to describe gravity, general relativity would not have been
developed before the 1970s.

Saibal

[Brent Meeker]

Except that Hilbert was only weeks behind Einstein in developing GR. 
Supposedly he had gotten sidetracked by trying to include EM in a
unified theory as Kaluza and Klein did later.

Brent

[Bruce Kellett]

On Sat, Jun 6, 2020 at 11:54 PM smitra <smi...@zonnet.nl> wrote:

On 06-06-2020 01:07, Bruce Kellett wrote:
> On Sat, Jun 6, 2020 at 3:11 AM smitra <smi...@zonnet.nl> wrote:

>> These fluctuations at zero temperature are what we call "quantum
>> fluctuations"
>> in physics.
>
> I think you are confusing the zero point energy of quantum fields with
> "quantum fluctuations". The zero point energy, whatever it might be,
> does not "fluctuate". "Fluctuate means change with time, and the zero
> point energy is just a value, and it does not change with time -- it
> does not "fluctuate".

The ground state energy does not fluctuate, but other observables such
as the field strengths obviously do in the sense of having a variance.
The energy is quadratic in the field and this has nonzero expectation
value, while the expectation value of the field will usually be zero.
So, one can say that the zero point energy represents the quantum
fluctuations of the field, because it is the variance of the field. 
While one can argue about the word "fluctuation" used here, what matters
is that the field strength will take on random values when measured in
the ground state.

OK, so nothing actually "fluctuates": it is just that measurement gives random values. That is what the standard deviation or variance is actually about -- the statistical scatter over repeated measurements of similar systems.

I think a lot of confusion arises from statements such as this in Wikipedia: "quantum systems constantly fluctuate in their lowest energy state as described by the Heisenberg uncertainty principle." (Wiki article on zero point energy.) This is false, because the HUP again refers to results from repeated measurements, not intrinsic variation in the state.

Applying the idea of quantum fluctuations to the inflaton field is a mistake, since inflation is based on a classical field. And you do not quantize a classical field by adding "quantum fluctuations". Jason was claiming that quantum fluctuations in the energy of the inflaton field caused variation in the time of exit from inflation, and this led to the density perturbations. Such a model is incorrect. To get density variations, you have to have variations in energy density. And these cannot be "quantum fluctuations", because energy is conserved in all quantum interactions -- given a state of a particular energy, that energy does not fluctuate. Variation between different measurements can arise only if the original state is a superposition of components of different basic energy, and that state is then repeatedly measured. That does not happen in inflation.

 

It is this phenomena what Jason referred to. In the
scientific papers on inflation they may go about computing the effects
of the fluctuations in a semi-classical way by putting in the
fluctuations by hand in classical equations of motion, but there is a
solid theoretical basis for such an approach.

No, there is not. It is entirely ad hoc. The problem stems from the fact that the scalar inflaton field has the dimensions of energy, so, because energy is strictly conserved, the field value cannot fluctuate.

Bruce

[Jason Resch]

On Saturday, June 6, 2020, Bruce Kellett <bhkel...@gmail.com> wrote:

On Sat, Jun 6, 2020 at 11:54 PM smitra <smi...@zonnet.nl> wrote:

On 06-06-2020 01:07, Bruce Kellett wrote:
> On Sat, Jun 6, 2020 at 3:11 AM smitra <smi...@zonnet.nl> wrote:

>> These fluctuations at zero temperature are what we call "quantum
>> fluctuations"
>> in physics.
>
> I think you are confusing the zero point energy of quantum fields with
> "quantum fluctuations". The zero point energy, whatever it might be,
> does not "fluctuate". "Fluctuate means change with time, and the zero
> point energy is just a value, and it does not change with time -- it
> does not "fluctuate".

The ground state energy does not fluctuate, but other observables such
as the field strengths obviously do in the sense of having a variance.
The energy is quadratic in the field and this has nonzero expectation
value, while the expectation value of the field will usually be zero.
So, one can say that the zero point energy represents the quantum
fluctuations of the field, because it is the variance of the field. 
While one can argue about the word "fluctuation" used here, what matters
is that the field strength will take on random values when measured in
the ground state.

OK, so nothing actually "fluctuates": it is just that measurement gives random values. That is what the standard deviation or variance is actually about -- the statistical scatter over repeated measurements of similar systems.

I think a lot of confusion arises from statements such as this in Wikipedia: "quantum systems constantly fluctuate in their lowest energy state as described by the Heisenberg uncertainty principle." (Wiki article on zero point energy.) This is false, because the HUP again refers to results from repeated measurements, not intrinsic variation in the state.

Applying the idea of quantum fluctuations to the inflaton field is a mistake, since inflation is based on a classical field. And you do not quantize a classical field by adding "quantum fluctuations". Jason was claiming that quantum fluctuations in the energy of the inflaton field caused variation in the time of exit from inflation, and this led to the density perturbations. Such a model is incorrect. To get density variations, you have to have variations in energy density. And these cannot be "quantum fluctuations", because energy is conserved in all quantum interactions -- given a state of a particular energy, that energy does not fluctuate. Variation between different measurements can arise only if the original state is a superposition of components of different basic energy, and that state is then repeatedly measured. That does not happen in inflation.

When you look up at the sky you are indirectly performing a measurement of the inflaton field's energy in different parts of the early universe.

Jason

 

 

It is this phenomena what Jason referred to. In the
scientific papers on inflation they may go about computing the effects
of the fluctuations in a semi-classical way by putting in the
fluctuations by hand in classical equations of motion, but there is a
solid theoretical basis for such an approach.

No, there is not. It is entirely ad hoc. The problem stems from the fact that the scalar inflaton field has the dimensions of energy, so, because energy is strictly conserved, the field value cannot fluctuate.

Bruce

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[Bruce Kellett]

That is the mythology that remains to be explained. Energy conservation forbids fluctuations in the energy density of the inflaton field.

Bruce

[Jason Resch]

Uncertainty implies you can't know the energy density exactly, does it not? Accordingly, wouldn't measurements of it at different places and times yield differing results?

Jason

[Bruce Kellett]

Not really. If you mean the HUP, then it doesn't imply this at all. If you mean merely that we are ignorant about the energy density at different places, then maybe. But you then have to explain these energy differences. The problem is that the inflation models tend to have a classical inflaton field, and that is not a superposition of anything.

Accordingly, wouldn't measurements of it at different places and times yield differing results?

The only way for this to happen in QM is if the initial state is a superposition of different energy states. You then have the problem of explaining exactly what you mean by a measurement of these states in this context. If you read the paper I referenced, you see that at the end of inflation, the temperature everywhere was exactly zero, so there are no thermal fluctuations. Any variations in the energy density over the universe must, therefore, have been frozen in during the inflation period. Reheating after the end of inflation is a whole other problem.

Bruce

[Bruno Marchal]

The theorem in metaphysics is that if Digital Mechanism is true, the “multiverse” ontology is limited to elementary arithmetic, which execute all computations (as we know since the 1930s). Church’s thesis makes this notion of “whole” quite solid, and formalism independent.

But it is more a multi-dream or multi-histories (a machine first person plural construct) than a multi-world, or multi-universe (which is rarely well defined). Yet, the physical phenomenology might have a distinctive look of quantum multiverse, but there too, the universes are only apparent, and do not belong to the ontology. (Like God and the Noùs in Plotinus).

> The multiverse aspect of the MWI is likely correct but it's problematic when considering the detailed physics.

I am not sure which problems you allude too. It is very complex, but if Mechanism is true, it is the only way to get both the quanta right, and the qualia right.

> It's similar to how Einstein got the idea that gravity must be linked to curved space-time long before he had discovered the precise mathematical formulation of general relativity. Had he or someone else stuck to just vague ideas
> then critics would have thrashed the whole idea of curved space-time, and they would worked with retarded gravitational
> potentials analogous to those used in electromagnetism.
>
> Michio Kaku has said that if Einstein had not developed general relativity that physicists would have used such a wrong relativistic formalism to describe gravity, general relativity would not have been developed before the 1970s.

The difference is that with mechanism, we have just no choice: physics is reduce to machine theology, and so we can derive as much of physics as possible, and always test it by comparing with nature.

Once we understand that all computations are executed in virtue of the elementary natural numbers relations, it is the believer in an ontological physical reality which needs to provide evidences. Up to now, there are none.
Digital Mechanism makes the antic dream argument into a theorem of elementary arithmetic (RA + induction).

IF GR is correct, and If Einstein has not developed it, someone else would have. IF GR belongs to physics (and not to geography), all universal machine get it, soon or later.

Bruno



>
> Saibal
>
> --
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[smitra]

> [1]." (Wiki article on zero point energy.) This is false, because the

> HUP again refers to results from repeated measurements, not intrinsic
> variation in the state.
>

Yes, I agree with this.

> Applying the idea of quantum fluctuations to the inflaton field is a
> mistake, since inflation is based on a classical field. And you do not
> quantize a classical field by adding "quantum fluctuations".

It's an approximate way to do computations that can be justified
rigorously, see e.g. these lecture notes:

https://www.nikhef.nl/~mpostma/inflation.pdf

section 3 on page 15 and further.

Jason was
> claiming that quantum fluctuations in the energy of the inflaton field
> caused variation in the time of exit from inflation, and this led to
> the density perturbations. Such a model is incorrect. To get density
> variations, you have to have variations in energy density. And these
> cannot be "quantum fluctuations", because energy is conserved in all
> quantum interactions -- given a state of a particular energy, that
> energy does not fluctuate.

There are fluctuations in the local energy density, and there is also
nontrivial correlation between the local energy density at two different
points. But I was wrong about the average of the filed vanishing. While
that's generally true, i case of the inflaton, a local fluctuation in
the field average is going to be stretched out so much that the entire
region inside the horizon gets a nonzero value for the field.

> Variation between different measurements
> can arise only if the original state is a superposition of components
> of different basic energy, and that state is then repeatedly measured.
> That does not happen in inflation.
>
>> It is this phenomena what Jason referred to. In the
>> scientific papers on inflation they may go about computing the
>> effects
>> of the fluctuations in a semi-classical way by putting in the
>> fluctuations by hand in classical equations of motion, but there is
>> a
>> solid theoretical basis for such an approach.
>
> No, there is not. It is entirely ad hoc. The problem stems from the
> fact that the scalar inflaton field has the dimensions of energy, so,
> because energy is strictly conserved, the field value cannot
> fluctuate.
>

It's not ad hoc, it's all explained here:

https://www.nikhef.nl/~mpostma/inflation.pdf

Saibal

[Bruce Kellett]

On Mon, Jun 8, 2020 at 7:09 PM smitra <smi...@zonnet.nl> wrote:

On 07-06-2020 01:16, Bruce Kellett wrote:

> Applying the idea of quantum fluctuations to the inflaton field is a
> mistake, since inflation is based on a classical field. And you do not
> quantize a classical field by adding "quantum fluctuations".

It's an approximate way to do computations that can be justified
rigorously, see e.g. these lecture notes:

https://www.nikhef.nl/~mpostma/inflation.pdf

section 3 on page 15 and further.

If that is your idea of a rigorous justification.............my mind boggles.

It seems to rely on the old failed heuristic of "vacuum fluctuations" as particle-antiparicle pairs: "The quantum vacuum is never empty, particle and anti-particle pairs constantly pop out of the vacuum and annihilate again. During inflation, due to the enormous expansion, the particle and antiparticle are ripped apart, and they may get separated by a distance larger than the causal horizon H−1, and cannot find each other again to annihilate. They remain as perturbations on the background."

This is nonsense, since there are no such particle-antiprticle pairs continuously formed in the vacuum state -- the vacuum does not fluctuate.

 

>> It is this phenomena what Jason referred to. In the
>> scientific papers on inflation they may go about computing the
>> effects
>> of the fluctuations in a semi-classical way by putting in the
>> fluctuations by hand in classical equations of motion, but there is
>> a solid theoretical basis for such an approach.
>
> No, there is not. It is entirely ad hoc. The problem stems from the
> fact that the scalar inflaton field has the dimensions of energy, so,
> because energy is strictly conserved, the field value cannot
> fluctuate.
>

It's not ad hoc, it's all explained here:

https://www.nikhef.nl/~mpostma/inflation.pdf

That article is a reasonably comprehensive account of the standard notions of inflation -- but it still relies on failed heuristics and ad hoc notions. Nothing rigourous here.

Closed virtual particle loops in the vacuum are a well-known phenomenon in perturbation approaches to QFT, but because of energy conservation, these loops are strictly of zero energy-momentum. Since they are not coupled to anything, so they do not affect any measurable physics. At most they add an overall undetectable phase to the wave function.

Bruce

[smitra]

You are confusing the nontechnical introduction for the rigorous content
that comes later.

>
>>>> It is this phenomena what Jason referred to. In the
>>>> scientific papers on inflation they may go about computing the
>>>> effects
>>>> of the fluctuations in a semi-classical way by putting in the
>>>> fluctuations by hand in classical equations of motion, but there
>> is
>>>> a solid theoretical basis for such an approach.
>>>
>>> No, there is not. It is entirely ad hoc. The problem stems from
>> the
>>> fact that the scalar inflaton field has the dimensions of energy,
>> so,
>>> because energy is strictly conserved, the field value cannot
>>> fluctuate.
>>>
>>
>> It's not ad hoc, it's all explained here:
>>
>> https://www.nikhef.nl/~mpostma/inflation.pdf
>
> That article is a reasonably comprehensive account of the standard
> notions of inflation -- but it still relies on failed heuristics and
> ad hoc notions. Nothing rigourous here.
>
> Closed virtual particle loops in the vacuum are a well-known
> phenomenon in perturbation approaches to QFT, but because of energy
> conservation, these loops are strictly of zero energy-momentum. Since
> they are not coupled to anything, so they do not affect any measurable
> physics. At most they add an overall undetectable phase to the wave
> function.
>

They do proceed in a heuristic way, but this is not unjustified. Your
arguments against it based on energy conservation are not valid. And if
it were as simple as that then no one in that field who are all big
experts in QFT would write articles saying that quantum fluctuations are
a source of the density fluctuations. The energy density of a field does
have a variance just like the field strength itself has, and this then
does couple to gravity.

Saibal

[Bruce Kellett]

Where later? The only justification offered for the addition of a random "fluctuation" field to the classical background inflaton field is the hand-waving heuristics of the introduction. Sure, he is reasonably rigorous in his quantization of this added "fluctuation" field, but that does not justify it in the first place.

>>>> It is this phenomena what Jason referred to. In the
>>>> scientific papers on inflation they may go about computing the
>>>> effects
>>>> of the fluctuations in a semi-classical way by putting in the
>>>> fluctuations by hand in classical equations of motion, but there
>>>> is a solid theoretical basis for such an approach.
>>>
>>> No, there is not. It is entirely ad hoc. The problem stems from
>>> the fact that the scalar inflaton field has the dimensions of energy,
>>> so, because energy is strictly conserved, the field value cannot
>>> fluctuate.
>>>
>>
>> It's not ad hoc, it's all explained here:
>>
>> https://www.nikhef.nl/~mpostma/inflation.pdf
>
> That article is a reasonably comprehensive account of the standard
> notions of inflation -- but it still relies on failed heuristics and
> ad hoc notions. Nothing rigourous here.
>
> Closed virtual particle loops in the vacuum are a well-known
> phenomenon in perturbation approaches to QFT, but because of energy
> conservation, these loops are strictly of zero energy-momentum. Since
> they are not coupled to anything, so they do not affect any measurable
> physics. At most they add an overall undetectable phase to the wave
> function.
>

They do proceed in a heuristic way, but this is not unjustified. Your
arguments against it based on energy conservation are not valid.

Oh! Where do my arguments based on energy conservation fail?

And if
it were as simple as that then no one in that field who are all big
experts in QFT would write articles saying that quantum fluctuations are
a source of the density fluctuations.

That is just an argument from authority -- which justifies nothing. After all, there was a time when all the authorities thought that the stars were attached to a crystalline "celestial sphere", and that the earth was the centre of the universe (and flat!).

The energy density of a field does
have a variance just like the field strength itself has, and this then
does couple to gravity.

In quantum mechanics, all that can have variances are superpositions of eigenstates. Conservation laws forbid variations of energy (or other conserved quantities) in eigenstates. The vacuum is, by definition, an energy eigenstate (the lowest possible energy state), so its energy cannot fluctuate, and does not have a variance. Similarly for a simple harmonic oscillator, and the SHO is a model for the modes (energy eigenstates) that make up a general quantum field.

The vacuum energy from zero point energies of quantum fields does not couple to gravity -- that is the 120 orders of magnitude mistake about the origin of the cosmological constant. The non-connected vacuum loops of perturbation theory are all of strictly zero energy, and they do not cou[ple to gravity. If they did, they would no longer be non-connected, and would merely form standard radiative corrections to propagators or vertex functions. 

Bruce

[smitra]

It is mentioned that the field can be treated in a classical way with
refs to the literature. You then only need a quantum description for the
fluctuations, so the classical field is treated as effective background
field.

Your arguments fail because you are considering the total energy of the
entire universe. If you consider the energy of a field in a box and
impose boundaryy conditions then you have closed system and you can
consider the system to be in an eigenstate of the Hamiltonian where the
total energy and the square of the energy are well defined and the
expectation value of the latter is then equal to the square of the
former, so no fluctuations.

But the problem at hand is to consider the local energy density at some
position. This is not conserved!

>
>> And if
>> it were as simple as that then no one in that field who are all big
>> experts in QFT would write articles saying that quantum fluctuations
>> are
>> a source of the density fluctuations.
>
> That is just an argument from authority -- which justifies nothing.
> After all, there was a time when all the authorities thought that the
> stars were attached to a crystalline "celestial sphere", and that the
> earth was the centre of the universe (and flat!).

What I'm saying is not that we just need to blindly trust the experts,
but rather that it's not plausible that with their level of expertise
they could have overlooked a counterargument based on elementary quantum
mechanics.

>
>> The energy density of a field does
>> have a variance just like the field strength itself has, and this
>> then
>> does couple to gravity.
>
> In quantum mechanics, all that can have variances are superpositions
> of eigenstates. Conservation laws forbid variations of energy (or
> other conserved quantities) in eigenstates. The vacuum is, by
> definition, an energy eigenstate (the lowest possible energy state),
> so its energy cannot fluctuate, and does not have a variance.
> Similarly for a simple harmonic oscillator, and the SHO is a model for
> the modes (energy eigenstates) that make up a general quantum field.
>
> The vacuum energy from zero point energies of quantum fields does not
> couple to gravity -- that is the 120 orders of magnitude mistake about
> the origin of the cosmological constant. The non-connected vacuum
> loops of perturbation theory are all of strictly zero energy, and they

> do not couple to gravity. If they did, they would no longer be

> non-connected, and would merely form standard radiative corrections to
> propagators or vertex functions.
>

You only have decoupled SHO in momentum space, assuming that there are
no couplings to other fields or a phi^4 self-interaction. In real space
the SHO are coupled via the 1/2 (nabla psi)^2 term. So, the local energy
in a small volume is not contained in a set of SHO that are decoupled
from the other oscillators. The coupling is trivial in the sense that
one can decouple the oscillators by performing a Fourier-transform, but
you are then working with linear combinations of the SHO in real space.

The simplest analogue is to consider a system of two SHOs:

H = 1/(2 m) (p1^2 + p2^2) + m/2 omega^2 (x1^2 + x2^2) + g (x1-x2)^2

If g = 0 then we have two independent oscillators with angular frequency
omega. But g is not zero, this is analogous to the squared gradient term
in field theory. Just like in that case the coupling can be eliminated
by a transformation. You then get two independent oscillators, but they
are now not localized in the old coordinates. You need to consider the
energy of not the new oscillators, but the energy contained in each of
the original oscillator:

H1 = p1^2/(2m) + (m/2 omega^2 +g)x1^2 -g x1 x2

H2 = p2^2/(2m) + (m/2 omega^2 +g)x2^2 -g x1 x2


The expectation value of these energies do fluctuate.

Saibal

[Bruce Kellett]

On Wed, Jun 10, 2020 at 11:48 PM smitra <smi...@zonnet.nl> wrote:

On 09-06-2020 01:32, Bruce Kellett wrote:
> On Mon, Jun 8, 2020 at 10:33 PM smitra <smi...@zonnet.nl> wrote:
>>
>> You are confusing the nontechnical introduction for the rigorous
>> content that comes later.
>
> Where later? The only justification offered for the addition of a
> random "fluctuation" field to the classical background inflaton field
> is the hand-waving heuristics of the introduction. Sure, he is
> reasonably rigorous in his quantization of this added "fluctuation"
> field, but that does not justify it in the first place.

It is mentioned that the field can be treated in a classical way with
refs to the literature. You then only need a quantum description for the
fluctuations, so the classical field is treated as effective background
field.

I am aware of this. This was, in fact, the problem that I pointed to. This addition of "fluctuations", even if they are quantized rigorously, is still unjustified and ad hoc.

>>
>> They do proceed in a heuristic way, but this is not unjustified.
>> Your arguments against it based on energy conservation are not valid.
>
> Oh! Where do my arguments based on energy conservation fail?

Your arguments fail because you are considering the total energy of the
entire universe. If you consider the energy of a field in a box and
impose boundaryy conditions then you have closed system and you can
consider the system to be in an eigenstate of the Hamiltonian where the
total energy and the square of the energy are well defined and the
expectation value of the latter is then equal to the square of the
former, so no fluctuations.

But the problem at hand is to consider the local energy density at some
position. This is not conserved!

Energy and momentum are conserved locally, even in GR where global energy conservation fails in a non-static universe.

 

>> And if
>> it were as simple as that then no one in that field who are all big
>> experts in QFT would write articles saying that quantum fluctuations
>> are a source of the density fluctuations.
>
> That is just an argument from authority -- which justifies nothing.
> After all, there was a time when all the authorities thought that the
> stars were attached to a crystalline "celestial sphere", and that the
> earth was the centre of the universe (and flat!).

What I'm saying is not that we just need to blindly trust the experts,
but rather that it's not plausible that with their level of expertise
they could have overlooked a counterargument based on elementary quantum
mechanics.

What we need is a coherent argument. As pointed out, experts are frequently wrong, and science is not decided by consensus.

>> The energy density of a field does
>> have a variance just like the field strength itself has, and this
>> then does couple to gravity.
>
> In quantum mechanics, all that can have variances are superpositions
> of eigenstates. Conservation laws forbid variations of energy (or
> other conserved quantities) in eigenstates. The vacuum is, by
> definition, an energy eigenstate (the lowest possible energy state),
> so its energy cannot fluctuate, and does not have a variance.
> Similarly for a simple harmonic oscillator, and the SHO is a model for
> the modes (energy eigenstates) that make up a general quantum field.
>
> The vacuum energy from zero point energies of quantum fields does not
> couple to gravity -- that is the 120 orders of magnitude mistake about
> the origin of the cosmological constant. The non-connected vacuum
> loops of perturbation theory are all of strictly zero energy, and they
> do not couple to gravity. If they did, they would no longer be
> non-connected, and would merely form standard radiative corrections to
> propagators or vertex functions.
>

You only have decoupled SHO in momentum space, assuming that there are
no couplings to other fields or a phi^4 self-interaction.

Do you not know what 'decoupled' means? It means that although fields may self-interact (through phi^4 terms, for instance), and may interact with the other fields in the theory, there are no external legs, or couplings to external systems. Such decoupled closed loops in QFT do not contribute to the physics, and they are strictly of zero energy.

In real space
the SHO are coupled via the 1/2 (nabla psi)^2 term.

I think that in inflation theory, gradient terms in the fields are generally neglected as irrelevant compared to the time variation. Besides, such non-local effects are irrelevant for local energy conservation.

So, the local energy
in a small volume is not contained in a set of SHO that are decoupled
from the other oscillators. The coupling is trivial in the sense that
one can decouple the oscillators by performing a Fourier-transform, but
you are then working with linear combinations of the SHO in real space.

Maybe that is what I mean when I say that only in superpositions of energy eigenstates can you have fluctuations, or a variance of the expectation value over repeated measurements.

The simplest analogue is to consider a system of two SHOs:

H = 1/(2 m) (p1^2 + p2^2) + m/2 omega^2 (x1^2 + x2^2) + g (x1-x2)^2

If g = 0 then we have two independent oscillators with angular frequency
omega. But g is not zero, this is analogous to the squared gradient term
in field theory.

If you couple the oscillators, they are not independent. Duh!

Just like in that case the coupling can be eliminated
by a transformation. You then get two independent oscillators, but they
are now not localized in the old coordinates. You need to consider the
energy of not the new oscillators, but the energy contained in each of
the original oscillator:

H1 = p1^2/(2m) + (m/2 omega^2 +g)x1^2 -g x1 x2

H2 = p2^2/(2m) + (m/2 omega^2 +g)x2^2 -g x1 x2


The expectation value of these energies do fluctuate.

You can introduce coupled harmonic oscillators, but that is not how you form a quantized field theory. Such fluctuations arise from non-local couplings -- they are not fluctuations of the original quantum field. Energy-momentum is locally conserved, even in GR and an expanding universe.

Bruce

[smitra]

Not in the sense you are suggesting. Energy and momentum are constant in
a closed volume and one can then write down the conservation law in a
local form. But this so-called "local conservation of energy and
momentum" does not mean that it's conserved in the sense of having a
constant value everywhere.

>
>>>> And if
>>>> it were as simple as that then no one in that field who are all
>> big
>>>> experts in QFT would write articles saying that quantum
>> fluctuations
>>>> are a source of the density fluctuations.
>>>
>>> That is just an argument from authority -- which justifies
>> nothing.
>>> After all, there was a time when all the authorities thought that
>> the
>>> stars were attached to a crystalline "celestial sphere", and that
>> the
>>> earth was the centre of the universe (and flat!).
>>
>> What I'm saying is not that we just need to blindly trust the
>> experts,
>> but rather that it's not plausible that with their level of
>> expertise
>> they could have overlooked a counterargument based on elementary
>> quantum
>> mechanics.
>
> What we need is a coherent argument. As pointed out, experts are
> frequently wrong, and science is not decided by consensus.

That doesn't mean that it's plausible that they are could be wrong about
a the very elementary issues you are raising here.

The Casimir effect, the effective negative pressure of the vacuum is
another way to see that your arguments based on local energy
conservation are wrong. Vacuum fluctuations in the local energy density
do exist and they have measurable effects.

Saibal

[Bruce Kellett]

On Fri, Jun 12, 2020 at 1:53 AM smitra <smi...@zonnet.nl> wrote:

On 11-06-2020 02:01, Bruce Kellett wrote:

> Energy and momentum are conserved locally, even in GR where global
> energy conservation fails in a non-static universe.

Not in the sense you are suggesting. Energy and momentum are constant in
a closed volume and one can then write down the conservation law in a
local form. But this so-called "local conservation of energy and
momentum" does not mean that it's conserved in the sense of having a
constant value everywhere.

Bullshit. Energy-momentum conservation comes from translational invariance of the Lagrangian in space and time. Local conservation is ensured in GR by the vanishing of the covariant derivative of the Stress-Energy tensor. Local in this sense means on the scale of the galaxy or more. In the absence of a time-like Killing vector in an expanding universe, this conservation breaks down on larger scales, such as the scale of the Hubble expansion.

If you have a theory that violates local energy-momentum conservation in the above sense, then your theory is wrong. Local conservation does not mean that energy necessarily has the same constant value everywhere.

.........

>> The expectation value of these energies do fluctuate.
>
> You can introduce coupled harmonic oscillators, but that is not how
> you form a quantized field theory. Such fluctuations arise from
> non-local couplings -- they are not fluctuations of the original
> quantum field. Energy-momentum is locally conserved, even in GR and an
> expanding universe.
>

The Casimir effect, the effective negative pressure of the vacuum is
another way to see that your arguments based on local energy
conservation are wrong. Vacuum fluctuations in the local energy density
do exist and they have measurable effects.

I wondered when this would come up. It is always the last resort of those who contend that vacuum fluctuations in local energy densities are real. I remember reading a comprehensive review of the Casimir effect in a scholarly article in Rev. Mod. Phys. a few years ago. Unfortunately, I did not keep a reference, and I have been unable to find this paper again. But I do remember the main points of the analysis: They discuss the Mickey-Mouse Comic-Book explanation of the Casimir effect in terms of supposed vacuum fluctuations, but they dismiss this approach as insufficiently general. They give a detailed account of the Casimir effect in terms of generalized van der Waals forces. The reason for preferring this explanation (over vacuum fluctuations, sidestepping the question of whether these fluctuations exist or not)  is that the van der Waals explanation extends seamlessly to the Casimir effect between irregular surfaces -- indeed, to the attractive force between a point and a plane surface -- where the fluctuation model is silent.

Bruce

[Alan Grayson]

On Thursday, June 11, 2020 at 7:31:18 PM UTC-6, Bruce wrote:

On Fri, Jun 12, 2020 at 1:53 AM smitra <smi...@zonnet.nl> wrote:

On 11-06-2020 02:01, Bruce Kellett wrote:

> Energy and momentum are conserved locally, even in GR where global
> energy conservation fails in a non-static universe.

Not in the sense you are suggesting. Energy and momentum are constant in
a closed volume and one can then write down the conservation law in a
local form. But this so-called "local conservation of energy and
momentum" does not mean that it's conserved in the sense of having a
constant value everywhere.

Bullshit. Energy-momentum conservation comes from translational invariance of the Lagrangian in space and time. Local conservation is ensured in GR by the vanishing of the covariant derivative of the Stress-Energy tensor. Local in this sense means on the scale of the galaxy or more. In the absence of a time-like Killing vector in an expanding universe, this conservation breaks down on larger scales, such as the scale of the Hubble expansion.

If you have a theory that violates local energy-momentum conservation in the above sense, then your theory is wrong. Local conservation does not mean that energy necessarily has the same constant value everywhere.

.........

>> The expectation value of these energies do fluctuate.
>
> You can introduce coupled harmonic oscillators, but that is not how
> you form a quantized field theory. Such fluctuations arise from
> non-local couplings -- they are not fluctuations of the original
> quantum field. Energy-momentum is locally conserved, even in GR and an
> expanding universe.
>

The Casimir effect, the effective negative pressure of the vacuum is
another way to see that your arguments based on local energy
conservation are wrong. Vacuum fluctuations in the local energy density
do exist and they have measurable effects.

I wondered when this would come up. It is always the last resort of those who contend that vacuum fluctuations in local energy densities are real. I remember reading a comprehensive review of the Casimir effect in a scholarly article in Rev. Mod. Phys. a few years ago. Unfortunately, I did not keep a reference, and I have been unable to find this paper again.

If it's in this scholarly journal, I would think it's accessible and could put the Casimir explanation where it belongs; in the trash heap of history. AG

[Alan Grayson]

Alternatively, you might approach this issue by discussing the alleged violation of energy conservation by showing the interpretive flaw in the time-energy form of the UP. Recently, I posed this issue to Brent, several times; precisely, what this means since time isn't a quantum operator. What does the "variance of time" mean in this context? But I never received a reply, from anyone. AG 

[Brent Meeker]

On 6/11/2020 8:34 PM, Alan Grayson wrote:

Alternatively, you might approach this issue by discussing the alleged violation of energy conservation by showing the interpretive flaw in the time-energy form of the UP. Recently, I posed this issue to Brent, several times; precisely, what this means since time isn't a quantum operator. What does the "variance of time" mean in this context? But I never received a reply, from anyone. AG 

I thought I did reply to this by pointing to Asher Peres book "Quantum Theory, Concepts and Methods".  It's available free online

https://www.academia.edu/35687651/Peres_-_Quantum_Theory_Concepts_and_Methods.pdf

and has a good chapter discussing the problem of time.  The time-energy UP applies to energy and time as measured by a physical clock, not by "t" in the equation.

Brent

[smitra]

On 12-06-2020 03:31, Bruce Kellett wrote:
> On Fri, Jun 12, 2020 at 1:53 AM smitra <smi...@zonnet.nl> wrote:
>
>> On 11-06-2020 02:01, Bruce Kellett wrote:
>>
>>> Energy and momentum are conserved locally, even in GR where global
>>> energy conservation fails in a non-static universe.
>>
>> Not in the sense you are suggesting. Energy and momentum are
>> constant in
>> a closed volume and one can then write down the conservation law in
>> a
>> local form. But this so-called "local conservation of energy and
>> momentum" does not mean that it's conserved in the sense of having a
>>
>> constant value everywhere.
>
> Bullshit. Energy-momentum conservation comes from translational
> invariance of the Lagrangian in space and time. Local conservation is
> ensured in GR by the vanishing of the covariant derivative of the
> Stress-Energy tensor. Local in this sense means on the scale of the
> galaxy or more. In the absence of a time-like Killing vector in an
> expanding universe, this conservation breaks down on larger scales,
> such as the scale of the Hubble expansion.
>
> If you have a theory that violates local energy-momentum conservation
> in the above sense, then your theory is wrong. Local conservation does
> not mean that energy necessarily has the same constant value
> everywhere.
>

Indeed, it doesn't have the same value everywhere. And that makes the
original point you were arguing wrong.

The mere fact that the Casimir force exists proves you wrong. It doesn't
matter that the naive method to compute this doesn't always work.

Saibal

[Bruce Kellett]

Get a grip, Saibal. Are you really claiming that local energy-momentum conservation is false?

About the Casimir effect, in the absence of the paper I mentioned, I refer you to the Wikipedia article:

     https://en.wikipedia.org/wiki/Casimir_effect

where you will find:

Alternatively, a 2005 paper by Robert Jaffe of MIT states that "Casimir effects can be formulated and Casimir forces can be computed without reference to zero-point energies. They are relativistic, quantum forces between charges and currents. The Casimir force (per unit area) between parallel plates vanishes as alpha, the fine structure constant, goes to zero, and the standard result, which appears to be independent of alpha, corresponds to the alpha approaching infinity limit," and that "The Casimir force is simply the (relativistic, retarded) van der Waals force between the metal plates."^[17] Casimir and Polder's original paper used this method to derive the Casimir-Polder force. In 1978, Schwinger, DeRadd, and Milton published a similar derivation for the Casimir Effect between two parallel plates.^[18] In fact, the description in terms of van der Waals forces is the only correct description from the fundamental microscopic perspective,^[19][20] while other descriptions of Casimir force are merely effective macroscopic descriptions.

The Wiki article states that, although the vacuum polarization explanation is conceptually simpler, and widely quoted, the Casimir effect really has nothing to do with vacuum polarization (or energy non-conservation -- whatever that might mean).

Bruce

[Alan Grayson]

Actually, I've downloaded it in the past, and will check out your reference. However, off the top of my head, I don't see the distinction between a physical clock and the "t" in the equation. AG  

[smitra]

I never said that it it false. My point is that your arguments are
totally flawed. You stated that a free field theory is analogous to a
set of independent harmonic oscillators in real space, which is nonsense
as they are coupled via the (nabla phi)^2 term, it's only in k-space
that you have independent oscillators. Then you argued that it's really
the time derivative square term that's the most important in case of
inflation, but that's only because of the rapid expansion of the
universe causing the field to become homogeneous and gain an nonzero
expectation value over regions larger than the horizon, which the allows
one to treat the filed as musical and the fluctuations in there using
QFT. But you then pretend that all the scientists in that field are
wrong for treating the field classical and only treating the
fluctuations quantum mechanically, which is in principle if the proper
conditions are met, a rigorous approximation method.

>
> About the Casimir effect, in the absence of the paper I mentioned, I
> refer you to the Wikipedia article:
>
> https://en.wikipedia.org/wiki/Casimir_effect
>
> where you will find:

> Alternatively, a 2005 paper by Robert Jaffe [1] of MIT states that

> "Casimir effects can be formulated and Casimir forces can be computed
> without reference to zero-point energies. They are relativistic,
> quantum forces between charges and currents. The Casimir force (per
> unit area) between parallel plates vanishes as alpha, the fine
> structure constant, goes to zero, and the standard result, which
> appears to be independent of alpha, corresponds to the alpha
> approaching infinity limit," and that "The Casimir force is simply the

> (relativistic, retarded [2]) van der Waals force between the metal
> plates."[17] [3] Casimir and Polder's original paper used this method

> to derive the Casimir-Polder force. In 1978, Schwinger, DeRadd, and
> Milton published a similar derivation for the Casimir Effect between

> two parallel plates.[18] [4] In fact, the description in terms of van

> der Waals forces is the only correct description from the fundamental

> microscopic perspective,[19] [5][20] [6] while other descriptions of

> Casimir force are merely effective macroscopic descriptions.
>
> The Wiki article states that, although the vacuum polarization
> explanation is conceptually simpler, and widely quoted, the Casimir
> effect really has nothing to do with vacuum polarization (or energy
> non-conservation -- whatever that might mean).
>
> Bruce

This doesn't matter and note that the dependence on alpha of which you
only find the alpha to infinity limit is also clear if you do the
derivation by summing the vacuum energies as pointed out in Itzickson &
Zuber, it's just that it's easy to not see this in the formal treatment.
The boundary conditions imposed on the field requires this as they point
out.

Now, the Casimir effect, whether or not you consider it as van der
Waals force or something else, makes it clear that the total energy
content inside an isolated box made of conducting plates in which we put
a conducting plane, depends on way the plate partitions the volume of
the box. This follows from the fat that the total energy inside the box
is conserved and that there exists a Casimir force between conducting
plates. How you do the calculations, whether or not you attribute the
force to a van der Waals force etc. doesn't matter here.

The Casimir force in the plate is then different from that of two
infinite plates, but there will in general be some Casimir force. Moving
the plate all the way until it merges with a boundary plate the box is
made out of will thus change the total energy contained in the box. So,
the initial state where the vacuum energy is forced to be localized in
either one part of the volume or the other part has a different energy
content compared to the situation without this restriction. This proves
wring your assertion that you can just consider a free field theory in a
box as a collection of independent SHO in real space. The gradient term
does matter.

Saibal





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> [7].
>
>
> Links:
> ------
> [1] https://en.wikipedia.org/wiki/Robert_Jaffe
> [2] https://en.wikipedia.org/wiki/Retarded_potential
> [3] https://en.wikipedia.org/wiki/Casimir_effect#cite_note-17
> [4] https://en.wikipedia.org/wiki/Casimir_effect#cite_note-18
> [5] https://en.wikipedia.org/wiki/Casimir_effect#cite_note-19
> [6] https://en.wikipedia.org/wiki/Casimir_effect#cite_note-20
> [7]
> https://groups.google.com/d/msgid/everything-list/CAFxXSLTTenx4Ehi39vJR9rD%2B1b3Z8ypNVnnqriZLLk-pEnwcFw%40mail.gmail.com?utm_medium=email&utm_source=footer

[Bruce Kellett]

On Sat, Jun 13, 2020 at 2:05 AM smitra <smi...@zonnet.nl> wrote:

On 12-06-2020 06:33, Bruce Kellett wrote:
> On Fri, Jun 12, 2020 at 2:08 PM smitra <smi...@zonnet.nl> wrote:
>>
>> Indeed, it doesn't have the same value everywhere. And that makes
>> the original point you were arguing wrong.

No, all I was arguing twas that the time value at any point does not change arbitrarily -- it does not fluctuate. There is no requirement for the value to be the same at every point. But that does not violate energy conservation -- it just started out that way.

>> The mere fact that the Casimir force exists proves you wrong. It
>> doesn't
>> matter that the naive method to compute this doesn't always work.
>
> Get a grip, Saibal. Are you really claiming that local energy-momentum
> conservation is false?

I never said that it it false.

You implied that energy was not conserved when you related density fluctuations in the inflaton field to quantum fluctuations. Fluctuations are variations with time. Spatial variation is distinct.

My point is that your arguments are
totally flawed. You stated that a free field theory is analogous to a
set of independent harmonic oscillators in real space, which is nonsense
as they are coupled via the (nabla phi)^2 term, it's only in k-space
that you have independent oscillators.

Momentum space and position space are related by a Fourier transform. Are you claiming that a Fourier transform violates the conservation laws?

QFT is strictly local. Micro-causality, implemented by the fact that field commutators vanish for space-like separations, enforces locality. So quantum fluctuations cannot cause spatial variations in the field.

Then you argued that it's really
the time derivative square term that's the most important in case of
inflation, but that's only because of the rapid expansion of the
universe causing the field to become homogeneous and gain an nonzero
expectation value over regions larger than the horizon, which the allows
one to treat the filed as musical and the fluctuations in there using
QFT. But you then pretend that all the scientists in that field are
wrong for treating the field classical and only treating the
fluctuations quantum mechanically, which is in principle if the proper
conditions are met, a rigorous approximation method.

There is no need to misrepresent what I have said. I have no problem with treating the background as a classical field, and quantizing only the variations from uniformity. That works, and is not a conceptual problem. The issue has always been the justification for the gaussian random field superposed on the classical background in terms of quantum fluctuations. Variations from a uniform density everywhere require different changes in energy at different locations. Quantum effects cannot do this, because quantum effects cannot change the energy anywhere -- energy and momentum are locally and strictly conserved in QFT. The random gaussian variations in energy density must be part of the boundary conditions -- they do not have a quantum origin.

Now, the Casimir effect,  whether or not you consider it as van der
Waals force or something else, makes it clear that the total energy
content inside an isolated box made of conducting plates in which we put
a conducting plane, depends on way the plate partitions the volume of
the box. This follows from the fat that the total energy inside the box
is conserved and that there exists a Casimir force between conducting
plates. How you do the calculations, whether or not you attribute the
force to a van der Waals force etc. doesn't matter here.

The Casimir force in the plate is then different from that of two
infinite plates, but there will in general be some Casimir force. Moving
the plate all the way until it merges with a boundary plate the box is
made out of will thus change the total energy contained in the box.

So what? If you move the plate against the Casimir force you must do work on the plate. This naturally changes the energy -- the box is not a closed system in that case.

Bruce

[Alan Grayson]

I think you're avoiding an important issue here; namely, it's claimed that the time-energy form of the UP implies energy fluctuations (and temporary violations of energy conservation) at a particular region of space, and we know the UP is implied by the principles of  QM. What is the flaw in this argument? TIA, AG

[Bruce Kellett]

On Sat, Jun 13, 2020 at 11:50 AM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, June 12, 2020 at 6:57:29 PM UTC-6, Bruce wrote:

There is no need to misrepresent what I have said. I have no problem with treating the background as a classical field, and quantizing only the variations from uniformity. That works, and is not a conceptual problem. The issue has always been the justification for the gaussian random field superposed on the classical background in terms of quantum fluctuations. Variations from a uniform density everywhere require different changes in energy at different locations. Quantum effects cannot do this, because quantum effects cannot change the energy anywhere -- energy and momentum are locally and strictly conserved in QFT. The random gaussian variations in energy density must be part of the boundary conditions -- they do not have a quantum origin.

I think you're avoiding an important issue here; namely, it's claimed that the time-energy form of the UP implies energy fluctuations (and temporary violations of energy conservation) at a particular region of space, and we know the UP is implied by the principles of  QM. What is the flaw in this argument? TIA, AG

That is another old hoary misconception. The time-energy form of the HUP is an inequality, and it can set a lower limit on something -- never an upper limit. So if you borrow an energy of delta-E, it must be repayed in a time GREATER THAN hbar/delta-t, not LESS THAN this time. If it were the case that energy could be 'borrowed' in this way, then energy could never be conserved.

Bruce

[Alan Grayson]

So why not conclude that energy is never conserved!? My problem with this form of the UP is that I have no idea what the variance of time means in this context. Brent claims it has something to do with using physical clocks, according to Peres. But I am skeptical of this explanation. AG 

[Bruce Kellett]

On Sat, Jun 13, 2020 at 12:14 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, June 12, 2020 at 8:08:28 PM UTC-6, Bruce wrote:

On Sat, Jun 13, 2020 at 11:50 AM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, June 12, 2020 at 6:57:29 PM UTC-6, Bruce wrote:

There is no need to misrepresent what I have said. I have no problem with treating the background as a classical field, and quantizing only the variations from uniformity. That works, and is not a conceptual problem. The issue has always been the justification for the gaussian random field superposed on the classical background in terms of quantum fluctuations. Variations from a uniform density everywhere require different changes in energy at different locations. Quantum effects cannot do this, because quantum effects cannot change the energy anywhere -- energy and momentum are locally and strictly conserved in QFT. The random gaussian variations in energy density must be part of the boundary conditions -- they do not have a quantum origin.

I think you're avoiding an important issue here; namely, it's claimed that the time-energy form of the UP implies energy fluctuations (and temporary violations of energy conservation) at a particular region of space, and we know the UP is implied by the principles of  QM. What is the flaw in this argument? TIA, AG

That is another old hoary misconception. The time-energy form of the HUP is an inequality, and it can set a lower limit on something -- never an upper limit. So if you borrow an energy of delta-E, it must be repayed in a time GREATER THAN hbar/delta-t, not LESS THAN this time. If it were the case that energy could be 'borrowed' in this way, then energy could never be conserved.

Bruce

So why not conclude that energy is never conserved!?

Because the HUP does not say this!

My problem with this form of the UP is that I have no idea what the variance of time means in this context.

The usual explanation is that delta-t in this context is the time taken to do the energy measurement -- the longer the time taken, the more accurate the measurement can be.

Bruce

[Alan Grayson]

On Friday, June 12, 2020 at 8:18:41 PM UTC-6, Bruce wrote:

On Sat, Jun 13, 2020 at 12:14 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, June 12, 2020 at 8:08:28 PM UTC-6, Bruce wrote:

On Sat, Jun 13, 2020 at 11:50 AM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, June 12, 2020 at 6:57:29 PM UTC-6, Bruce wrote:

There is no need to misrepresent what I have said. I have no problem with treating the background as a classical field, and quantizing only the variations from uniformity. That works, and is not a conceptual problem. The issue has always been the justification for the gaussian random field superposed on the classical background in terms of quantum fluctuations. Variations from a uniform density everywhere require different changes in energy at different locations. Quantum effects cannot do this, because quantum effects cannot change the energy anywhere -- energy and momentum are locally and strictly conserved in QFT. The random gaussian variations in energy density must be part of the boundary conditions -- they do not have a quantum origin.

I think you're avoiding an important issue here; namely, it's claimed that the time-energy form of the UP implies energy fluctuations (and temporary violations of energy conservation) at a particular region of space, and we know the UP is implied by the principles of  QM. What is the flaw in this argument? TIA, AG

That is another old hoary misconception. The time-energy form of the HUP is an inequality, and it can set a lower limit on something -- never an upper limit. So if you borrow an energy of delta-E, it must be repayed in a time GREATER THAN hbar/delta-t, not LESS THAN this time. If it were the case that energy could be 'borrowed' in this way, then energy could never be conserved.

Bruce

So why not conclude that energy is never conserved!?

Because the HUP does not say this!

It does seem to say this; borrow some energy and pay it back any time later one wants. AG

 

My problem with this form of the UP is that I have no idea what the variance of time means in this context.

The usual explanation is that delta-t in this context is the time taken to do the energy measurement -- the longer the time taken, the more accurate the measurement can be.

Why would the energy measurement be more accurate if one takes more time to measure it? AG 

[Brent Meeker]

On 6/12/2020 6:50 PM, Alan Grayson wrote:

I think you're avoiding an important issue here; namely, it's claimed that the time-energy form of the UP implies energy fluctuations (and temporary violations of energy conservation) at a particular region of space, and we know the UP is implied by the principles of  QM. What is the flaw in this argument? TIA, AG

No.  The UP is about ideal measurement (preparation) results.

Brent

[Brent Meeker]

You mean delta-t > hbar/delta-E.

Brent

not LESS THAN this time. If it were the case that energy could be 'borrowed' in this way, then energy could never be conserved.

Bruce

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