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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: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.
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).
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).
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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: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?
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--
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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: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 NumberI 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.
--BrunoJason--
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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: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 NumberI 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:
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. :-)
JasonBrunoJason--
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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 ...BrunoJasonBrunoJason--
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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.
<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:
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.
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 ?
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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 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.
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
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,
even ultrafinitism.
But the idea that arithemtic exectues all programs certainly requires infinities.
Brent
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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.
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:
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.
BruceHowever, 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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Max Tegmark, in an instance of not being "Mad".@philipthrift
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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.
Jason
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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.
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: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.
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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
I recently wrote an article on the size of the universe and the scope of reality:
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 recently wrote an article on the size of the universe and the scope of reality: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
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: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.JasonYou claim,"Every very finite sequence recurs an infinite number of times precisely because Pi goes on forever." Can you prove it? AG
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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: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.JasonI 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
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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: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.JasonI 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? AGThe 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.
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: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.JasonI 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? AGThe 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.
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
On Mon, Jun 1, 2020 at 4:24 PM Alan Grayson <agrays...@gmail.com> wrote:
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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: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.JasonYou 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. AGYou 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).JasonThe 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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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: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.JasonI 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? AGThe 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.
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: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.JasonI 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
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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: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.JasonYou 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"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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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.
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Jason
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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.JasonI 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: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.JasonYou 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. AGYou 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).JasonThe 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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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.JasonI 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,
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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: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.JasonI 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.
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.JasonI 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? AGThe 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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Bruce
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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.
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?
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".
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
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.
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.
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
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Accordingly, wouldn't measurements of it at different places and times yield differing results?
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.
>> 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
>>>> 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.
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.
>>
>> 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!
>> 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.
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.
>> 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.
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.
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
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.
>> 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.
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.
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.
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
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, AGThat 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.BruceSo 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.
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, AGThat 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.BruceSo 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.
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
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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