Probability in Everettian QM

[Brent Meeker]

An interesting discussion of Everettian QM in two parts.  The first part

https://www.youtube.com/watch?v=FyvgBe9VV70

is just David Albert and Sean Carroll.  It's quite reminiscent of JKC and Bruno, using the same thought experiments (but more civil).

Brent

[Bruce Kellett]

I experienced growing deja vu throughout Albert's talk! (I saw the interview with Carroll in Sean's 'Mindscape' series some time ago. Albert has had time to think through the problems of self-locating uncertainty in a lot more detail since then.) It seems to me that I have made essentially the same points many times, and at length, on this list: without much success in convincing anyone. It is clear from the concluding discussion that Sean Carroll was not convinced either; but then, he has not really come to terms with the problems raised by self-locating uncertainties.

Bruce

[John Clark]

I don't understand Albert's position or the distinction he is trying to make. He says that If the world is deterministic and given his knowledge of the macro state of the world right now he thinks there is a 75% chance the Yankees will win the World Series this year. If things are deterministic then the Yankees will either win or they will not, but for practical reasons he knows he has limited knowledge of the micro state of the world so he can't be certain (or at least he shouldn't be) thus he needs to devise a number between zero and one to express his degree of confidence that his prediction express is a fundamental truth.  As time goes on as he gains more knowledge he will need to change the value of that number, and if he is a professional gambler and makes many bets of that nature and if he updates that number according to the rules laid out by Thomas Bayes then he will maximize his profits over the long term. So if you say there is a 75% chance the Yankees will win it tells me nothing objectively true about the Yankees it just tells me something about your state of mind. 

Hugh Everett would say pretty much the same thing because he also believes we live in a deterministic world. Originally he may have only a vague idea of which branch of the multiverse is being observed and so he thinks there's a 50% chance, but as time goes on and he gains more information he still can't narrow it down to one particular branch but there are a great many branches that he can rule out and so by using the exact same Bayesian statistical rules that Albert used he now says the Yankees have a 75% chance of winning the World Series this year. But again If the world is deterministic then that number says nothing intrinsically true about the Yankees, it just says something about the state of mind of the speaker who made the utterance.

John K Clark

[Philip Thrift]

This sort of way of approaching physics is no different really from theological debates about some esoteric Christian doctrine.

The last of Carroll's The Biggest Ideas in the Universe series is actually interesting at the end:

    https://www.youtube.com/watch?v=ZqphkIO7yt4

He has nowhere to go asn has no idea what to do.

@philipthrift

[Brent Meeker]

Albert makes an interesting argument against Everettian QM, i.e. that repeated experiments will not produce statistics that converge to the Born rule, i.e. there will necessarily (not just probabilistically) be experimenters in worlds supporting every possible probability value. 

Brent

--
You received this message because you are subscribed to the Google Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/052f01fa-5d3e-4dfe-ac27-50c83668b0c0n%40googlegroups.com.

[Quentin Anciaux]

Hi,

as there will be persons in self duplicate experiment who'll see WWW...WW.

But most should converge on 50%.

Quentin

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/5F513A7D.3080106%40verizon.net.

[John Clark]

On Thu, Sep 3, 2020 at 2:48 PM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

 

> repeated experiments will not produce statistics that converge to the Born rule, i.e. there will necessarily (not just probabilistically) be experimenters in worlds supporting every possible probability value. 

Not if the same experimenter also existed on a very large number of those possible worlds, and I would maintain that 2 Everettian worlds that were identical except that a grain of sand was moved one inch to the left on one planet in orbit around one star in the Andromeda galaxy could be said in any meaningful way to have two different experimenters on the planet earth performing the experiment. Red is not a noun it is an adjective describing a noun, describing something that reflects red light, and John K Clark is not a noun either, it is describing something that behaves in a johnkclarkian way. There are lots of Everettian worlds that contain something that behaves in a johnkclarkian way and those who follow the Born Rule and follow bayesian statistics will make better predictions than those that don't.

John K Clark

[Brent Meeker]

Yes, it was very much like the long argument we had about branching weights and the Born rule, 5/17 and 5/18/2020.  The crux of the problem seemed to be how Everett's deterministic theory related to probabilities...whether they could be inferred from Everett or Born had to be added.  I think we concluded largely in agreement, as below:

Brent

================================================================================

On 5/18/2020 4:28 PM, Bruce Kellett wrote:

On Mon, May 18, 2020 at 10:57 PM Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Monday, May 18, 2020 at 12:12:28 AM UTC-5, Brent wrote:

On 5/17/2020 6:20 PM, Lawrence Crowell wrote:

On Sunday, May 17, 2020 at 1:57:19 AM UTC-5, Bruce wrote:

On Sat, May 16, 2020 at 11:04 PM Lawrence Crowell <goldenfield...@gmail.com> wrote:

There is nothing wrong formally with what you argue. I would though say this is not entirely the Born rule. The Born rule connects eigenvalues with the probabilities of a wave function. For quantum state amplitudes a_i in a superposition ψ = sum_ia_iφ_i with φ*_jφ_i = δ_{ij} the spectrum of an observable O obeys

⟨O⟩ = sum_iO_ip_i = sum_iO_i a*_ia_i.

Your argument has a tight fit with this for O_i = ρ_{ii}.

The difficulty in part stems from the fact we keep using standard ideas of probability to understand quantum physics, which is more fundamentally about amplitudes which give probabilities, but are not probabilities. Your argument is very frequentist.

I can see why you might think this, but it is actually not the case. My main point is to reject subjectivist notions of probability:  probabilities in QM are clearly objective -- there is an objective decay rate (or half-life) for any radioactive nucleus; there is a clearly objective probability for that spin to be measured up rather than down in a Stern-Gerlach magnet; and so on.

Objective probabilities are frequentism.

No necessarily.  Objective probabilities may be based on symmetries and the principle of insufficient reason.  I agree with Bruce; just because you measure a probability with frequency, that doesn't imply it must be based on frequentism.

That is not what I meant. Bruce does sound as if he is appealing to an objective basis for probability based on the frequency of occurrences of events. I am not arguing this isy wrong, but rather that this is an interpretation of probability. 

I am sorry if I have given the impression that I thought that objective probabilities were possible only with frequentism. I thought I had made it clear that frequentism fails as a basis for the meaning of probability. There are many places where this is argued, and the consensus is that long-run relative frequencies cannot be used as a  definition of probability.

I was appealing to the propensity interpretation, which says that probabilities are intrinsic properties of some things.; such as decay rates; i.e., that probability is an intrinsic property of radio-active nuclei. But I agree with Brent, probabilities can be taken to be anything that satisfies the basic axioms of probability theory -- such as non-negative, normalisable, and additive. So subjective degrees of belief can form the basis for probabilities, as can certain symmetry properties, relative frequencies, and so on.

The point is that while these things can be understood as probabilities in ordinary usage, they don't actually define what probability is. One can use frequency counts to estimate many of these probabilities, and one can use Bayes's theorem to update estimates of probability based on new evidence. But Bayes's theorem is merely an updating method -- it is not a definition of probability. People who consider themselves to be Bayesians usually have a basically subjective idea about probability, considering it essentially quantifies personal degrees of belief. But that understanding is not inherent in Bayes' theorem itself.

As Brent says, these different approaches to probability have their uses in everyday life, but most of them are not suitable for fundamental physics. I consider objective probabilities based on intrinsic properties, or propensities, to be essential for a proper understanding of radio-active decay, and the probability of getting spin-up on a spin measurement, and so on. These things are properties of the way the world is, not matters of personal belief, or nothing more than relative frequencies. Probabilities may well be built into the fabric of the quantum wave-function via the amplitudes, but the probabilistic interpretation of these amplitudes has to be imposed via the Born rule:  Just as with any mathematical theory -- one needs correspondence rules to say how the mathematical elements relate to physical observables. From that point of view, attempts to derive the Born rule from within the theory are doomed to failure -- contrary to the many-worlders' dream, the theory does not contain its own interpretation.

But even if you're right (and I think you are) does that affect the MWI.  In an Everett+Born theory there will still be other worlds and the interpretation will still avoid the question, "When and where is a measurement?"...answer "Whenever decoherence has made one state orthogonal to all other states."   Of course we could then as the question, "When and where has the wave function collapsed?" and give the same answer.  Which would be CI+Zurek.

Brent

[Brent Meeker]

On 9/3/2020 7:17 AM, John Clark wrote:

I don't understand Albert's position or the distinction he is trying to make. He says that If the world is deterministic and given his knowledge of the macro state of the world right now he thinks there is a 75% chance the Yankees will win the World Series this year. If things are deterministic then the Yankees will either win or they will not, but for practical reasons he knows he has limited knowledge of the micro state of the world so he can't be certain (or at least he shouldn't be) thus he needs to devise a number between zero and one to express his degree of confidence that his prediction express is a fundamental truth.  As time goes on as he gains more knowledge he will need to change the value of that number, and if he is a professional gambler and makes many bets of that nature and if he updates that number according to the rules laid out by Thomas Bayes then he will maximize his profits over the long term. So if you say there is a 75% chance the Yankees will win it tells me nothing objectively true about the Yankees it just tells me something about your state of mind. 

Hugh Everett would say pretty much the same thing because he also believes we live in a deterministic world. Originally he may have only a vague idea of which branch of the multiverse is being observed and so he thinks there's a 50% chance, but as time goes on and he gains more information he still can't narrow it down to one particular branch but there are a great many branches that he can rule out and so by using the exact same Bayesian statistical rules that Albert used he now says the Yankees have a 75% chance of winning the World Series this year. But again If the world is deterministic then that number says nothing intrinsically true about the Yankees, it just says something about the state of mind of the speaker who made the utterance.

I think the Everttenian view is that it is intrinsically true that there is deterministically a world branch (or set of branches) in which the Yankees win and a world branch (or set of branches) in which deterministically they lose and our probability of being in the former is 0.75.

Brent

[Brent Meeker]

Sure.  But Albert's argument is that in a single, probabilistic world that implements Born's rule, the number of scientist who find something contrary to Born's rule goes to zero as the number of repetitions increases.  But in the multiverse there are always contrary worlds and, while their fraction decreases, their number increases with repetitions.

Brent

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAMW2kAqpMSBV%2BcS2Z%3D9Gb6iCi3SDUphc9M%2B7xtww736119z1HA%40mail.gmail.com.

[Bruce Kellett]

On Fri, Sep 4, 2020 at 8:01 AM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

Sure.  But Albert's argument is that in a single, probabilistic world that implements Born's rule, the number of scientist who find something contrary to Born's rule goes to zero as the number of repetitions increases.  But in the multiverse there are always contrary worlds and, while their fraction decreases, their number increases with repetitions.

That is really the essential difference between Everettian notions of probability and standard probabilistic theory/practice. In the Everettian repeated experiment case, disconfirming cases occur with probability one, so it is strictly incoherent to claim (as Everettians, such as Sean Carroll, do) that these "monster" results can be ignored because they have low probability. The only thing that that can mean is that you are justified in ignoring them because they have low frequency: but that is a different definition of probability -- a frequentist notion that all reject. At best, what they might mean is that if you take all outcomes as equally likely, then the probability that you will get a low frequency outcome by chance in a random selection from the uniform distribution over all possibilities, is low. But that introduces yet another source of probability. It might be what is necessarily entailed in a definition of probability in terms of self-locating uncertainty, but it still involves one in the absurdity of claiming that things that necessarily happen have low probability. We cannot consistently claim in one breath that the probability is one, and in another breath, that  probability is "low".

Bruce

[Bruce Kellett]

On Fri, Sep 4, 2020 at 12:18 AM John Clark <johnk...@gmail.com> wrote:

I don't understand Albert's position or the distinction he is trying to make. He says that If the world is deterministic and given his knowledge of the macro state of the world right now he thinks there is a 75% chance the Yankees will win the World Series this year. If things are deterministic then the Yankees will either win or they will not,

It has nothing to do with whether the world is deterministic or not: all that is involved is that there is some objective chance of this particular result, whether we know that chance or not. I.e., the chance that the Yankees will win is independent of what we happen to think about it.

Bruce

[Quentin Anciaux]

Le ven. 4 sept. 2020 à 00:01, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> a écrit :

Sure.  But Albert's argument is that in a single, probabilistic world that implements Born's rule, the number of scientist who find something contrary to Born's rule goes to zero as the number of repetitions increases.  But in the multiverse there are always contrary worlds and, while their fraction decreases, their number increases with repetitions.

That's an interpretation... because I think there is no increasing or decreasing of numbers of worlds.... there are an infinity of them always, similar / identical "world" differentiate but there is no increase or decrease, there is no meaningfull way of "counting"... The frequency is all there is.

Quentin

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/5F5167A5.3090502%40verizon.net.

--

All those moments will be lost in time, like tears in rain. (Roy Batty/Rutger Hauer)

[Bruce Kellett]

On Fri, Sep 4, 2020 at 4:40 PM Quentin Anciaux <allc...@gmail.com> wrote:

Le ven. 4 sept. 2020 à 00:01, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> a écrit :

Sure.  But Albert's argument is that in a single, probabilistic world that implements Born's rule, the number of scientist who find something contrary to Born's rule goes to zero as the number of repetitions increases.  But in the multiverse there are always contrary worlds and, while their fraction decreases, their number increases with repetitions.

That's an interpretation... because I think there is no increasing or decreasing of numbers of worlds.... there are an infinity of them always, similar / identical "world" differentiate but there is no increase or decrease, there is no meaningfull way of "counting"... The frequency is all there is.

That does not detract from the fact that in Everett, the low probability worlds always occur with probability one. In other words, the theory is intrinsically self-contradictory -- incoherent.

Bruce

[Lawrence Crowell]

I am not so sure this is self-contradictory, but rather that with the renormalization of probability in each branched world there is a sort of catastrophe where for some oscillating probability amplitude there is one point where P = 0 or P = 1 and the branching has a discontinuity. Hence there is this interesting nonlocal property where an eigenbranch can occur continuously along the time parametrization or evolution of a wave function, but this is not continuous.  For extremely high frequency quantum states this has a sort of quantum Zeno phenomenology to it. At these break-points there is only one possible outcome and for a set of events corresponding to these there is no consistent Bayesian interpretation of them. In that sense there is something funny going on.

LC

[Bruce Kellett]

You do talk a lot of nonsense, don't you, Lawrence.

Bruce

[smitra]

Even if the MWI is false and the wavefunction collapses to produce only
one of the possible outcomes with a probability given by the Born rule,
you'll still get all possibilities realized in a generic infinite
universe, whether it's spatially infinite or a universe that exists for
an infinite long time.

The only way to find out what exists beyond the realm we've explored s
to do experiments. No philosophical reasoning about the interpretation
of probabilities can ever settle whether or not the universe is so large
or will exists for such a long time that another copy of me exists.
That's why these discussions are not so useful as an argument of whether
the MWI is correct or not.

Saibal

On 04-09-2020 00:01, 'Brent Meeker' via Everything List wrote:
> Sure. But Albert's argument is that in a single, probabilistic world
> that implements Born's rule, the number of scientist who find
> something contrary to Born's rule goes to zero as the number of
> repetitions increases. But in the multiverse there are always
> contrary worlds and, while their fraction decreases, their number
> increases with repetitions.
>
> Brent
>
> On 9/3/2020 12:02 PM, Quentin Anciaux wrote:
>
>> Hi,
>> as there will be persons in self duplicate experiment who'll see

>> WWW...WW [1].

>> [2].

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

> https://groups.google.com/d/msgid/everything-list/5F513A7D.3080106%40verizon.net
> [3].

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

> https://groups.google.com/d/msgid/everything-list/CAMW2kAqpMSBV%2BcS2Z%3D9Gb6iCi3SDUphc9M%2B7xtww736119z1HA%40mail.gmail.com
> [4].

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

> https://groups.google.com/d/msgid/everything-list/5F5167A5.3090502%40verizon.net
> [5].
>
>
> Links:
> ------
> [1] http://WWW...WW
> [2]
> https://groups.google.com/d/msgid/everything-list/052f01fa-5d3e-4dfe-ac27-50c83668b0c0n%40googlegroups.com
> [3]
> https://groups.google.com/d/msgid/everything-list/5F513A7D.3080106%40verizon.net?utm_medium=email&amp;utm_source=footer
> [4]
> https://groups.google.com/d/msgid/everything-list/CAMW2kAqpMSBV%2BcS2Z%3D9Gb6iCi3SDUphc9M%2B7xtww736119z1HA%40mail.gmail.com?utm_medium=email&amp;utm_source=footer
> [5]
> https://groups.google.com/d/msgid/everything-list/5F5167A5.3090502%40verizon.net?utm_medium=email&utm_source=footer

[Bruce Kellett]

On Fri, Sep 4, 2020 at 9:32 PM smitra <smi...@zonnet.nl> wrote:

Even if the MWI is false and the wavefunction collapses to produce only
one of the possible outcomes with a probability given by the Born rule,
you'll still get all possibilities realized in a generic infinite
universe, whether it's spatially infinite or a universe that exists for
an infinite long time.

The only way to find out what exists beyond the realm we've explored s
to do experiments. No philosophical reasoning about the interpretation
of probabilities can ever settle whether or not the universe is so large
or will exists for such a long time that another copy of me exists.
That's why these discussions are not so useful as an argument of whether
the MWI is correct or not.

I think something along those lines was Sean Carroll's answer to the points David Albert raised. Unfortunately, it doesn't wash!

Applying the Born rule to the repeated measurement scenario tells you that the probability of the extreme branches is low; whereas, the idea that all possible outcomes occur on every trial trivially implies that the probability of the extreme cases is exactly one. The contradiction couldn't be more stark, and waffling about infinite universes isn't going to change that -- the theory gives two, mutually contradictory, results.

Bruce

[John Clark]

On Thu, Sep 3, 2020 at 7:59 PM Bruce Kellett <bhkel...@gmail.com> wrote:

> It has nothing to do with whether the world is deterministic or not: all that is involved is that there is some objective chance of this particular result

If things are deterministic then there's no such thing as objective chance, and probability would just be a measure of our degree of ignorance of hidden causes.

>  the chance that the Yankees will win is independent of what we happen to think about it.

If Everett is right then there's a 100% chance the Yankees will win and a 100% chance the Yankees will lose because neither eventuality violates the laws of physics.

John K Clark

[John Clark]

On Fri, Sep 4, 2020 at 2:54 AM Bruce Kellett <bhkel...@gmail.com> wrote:

> in Everett, the low probability worlds always occur with probability one. 

I don't know what you mean by "low probability world", as Quentin says you can't count Everettian worlds, it would be like counting the number of points on a line. Each Everettian world has an amplitude, which is a Complex Number not a Rational Number or even a Real number like a probability, associated with it. The square of the absolute value of that Complex Number can give you the probability that you are in that world, and Gleason's theorem proved that is the only way Schrodinger's Wave Equation can produce a probability without self contradictions.

There are worlds where the scientific method would fail, for example there is a world where you flip a fair coin 1000 times and get heads each time, in such a world you would incorrectly conclude that the coin was not fair, but the square of the absolute value of the amplitude of such a world would be very small. So You're probably in a world where the scientific method works very well.

> always occur with probability one. 

Probability is the wrong word to use in this case, a Everettian world either doesn't violate the laws of physics and thus exists or it does so it doesn't. However probability can be a useful concept in trying to figure out which world you're in. 

John K Clark

[John Clark]

On Fri, Sep 4, 2020 at 7:43 AM Bruce Kellett <bhkel...@gmail.com> wrote:

> Applying the Born rule to the repeated measurement scenario tells you that the probability of the extreme branches is low; whereas, the idea that all possible outcomes occur on every trial trivially implies that the probability of the extreme cases is exactly one. The contradiction couldn't be more stark,

If it does it violate the laws of physics then the probability of an Everettian world existing is always exactly one, which means that probability is not a useful concept when discussing the existence or nonexistence of such a world, although probability can be useful for other things, like self localization.

John K Clark

[Brent Meeker]

If there are an infinite number then frequency is ill defined and you have to introduce some measure...which is essentially the same as just postulating a probability.  This is something like Carroll's solution which is to give "weights" to branches.

Brent

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAMW2kAowopoA-FLEfBZo6WFty4L%2BGKUhSsQGKTJ%2B8OjVyUZKrw%40mail.gmail.com.

[Brent Meeker]

But the probability of observing extreme cases isn't 1 for a given observer.

Brent

[John Clark]

On Fri, Sep 4, 2020 at 2:03 PM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

> If there are an infinite number then frequency is ill defined

That is incorrect. There are an infinity Ii of prime numbers but the Prime Number Theorem allows you to determine the likely frequency of primes less than any given number.

Prime number calculator

And besides, Everettian worlds don't have real number probabilities, they have complex number amplitudes, eo get a probability you need to take the square of the Absolute Value of the amplitude. 

John K Clark

[Bruce Kellett]

And the probability isn't 1/2^N for a given observer either. The observer observes what he observes. Probability is relevant for predictions, not post hoc observations.

We are talking about the predictions of the theory, not the experiences of individual observers. I think Sean tried this evasive tactic as well, and Albert rightly pointed out that that just makes everything idexical, and ultimately makes science impossible.

And it is not just the extreme branches that have low probability. Given the repeated measurement scenario we have been talking about, there are N repetitions of the experiment, giving 2^N distinct binary sequences of results. Applying the Born rule to each possible sequence shows that it has probability 1/2^N. But if every result obtains on every trial, the probability of each sequence is exactly one. In other words, Everett is incompatible with the Born rule. You can abandon the Born rule if you like, or abandon the Everettian idea of every outcome occurring on every trial, but you can't have both.

The twisting and turning we are seeing by participants on this list is not going to alter this basic observation.

Bruce

[Lawrence Crowell]

What is nonsense? All I am saying is when the probability for an amplitude is 0 or 1 there is no branching. So in general a quantum amplitude has a discrete set of branching evolutes separated by no branching points. What is wrong?

LC

[Bruce Kellett]

Your comments are not relevant to the discussion, which was about probability in a branching scenario. If you predict that a certain branch will certainly exist, then you are assigning a probability equal to one to the possibility of this branch. The trouble is that the Born rule assigns a probability of 1/2^N to the same branch. Hence the contradiction.

If your theory gives two ways to predict the probability of a particular outcome, and these two calculations give different results, then your theory is inconsistent.

Bruce

[Lawrence Crowell]

Then as I said, these cases are not as amenable to Bayesian statistics. Suppose I make a measurement of a quantum wave as it oscillates and time this the amplitude of interest is zero each time. I then have 000 ... 0 as a string. What is the meaning of a probability for this string?

LC 

[Bruce Kellett]

/*sarcasm mode on*/    Is that all?    /*sarcasm mode off*/

Suppose I make a measurement of a quantum wave as it oscillates and time this the amplitude of interest is zero each time. I then have 000 ... 0 as a string. What is the meaning of a probability for this string?

That is not the case under consideration. You are raising irrelevancies in order to avoid the elephant in the room.

Bruce

[Brent Meeker]

That's because the natural measure on the integers is implicitly assumed.  But if you simply have an infinite set of world's, some of them |up> and some of them |down> , there's no natural measure.

Brent

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv36NhY6TFTZbE3n5oXWWVZeoyUAVEhP8Qk7ujvohjOLYg%40mail.gmail.com.

[Brent Meeker]

On 9/4/2020 4:00 PM, Bruce Kellett wrote:

On Sat, Sep 5, 2020 at 5:37 AM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/4/2020 4:43 AM, Bruce Kellett wrote:

On Fri, Sep 4, 2020 at 9:32 PM smitra <smi...@zonnet.nl> wrote:

Even if the MWI is false and the wavefunction collapses to produce only
one of the possible outcomes with a probability given by the Born rule,
you'll still get all possibilities realized in a generic infinite
universe, whether it's spatially infinite or a universe that exists for
an infinite long time.

The only way to find out what exists beyond the realm we've explored s
to do experiments. No philosophical reasoning about the interpretation
of probabilities can ever settle whether or not the universe is so large
or will exists for such a long time that another copy of me exists.
That's why these discussions are not so useful as an argument of whether
the MWI is correct or not.

I think something along those lines was Sean Carroll's answer to the points David Albert raised. Unfortunately, it doesn't wash!

Applying the Born rule to the repeated measurement scenario tells you that the probability of the extreme branches is low; whereas, the idea that all possible outcomes occur on every trial trivially implies that the probability of the extreme cases is exactly one. The contradiction couldn't be more stark, and waffling about infinite universes isn't going to change that -- the theory gives two, mutually contradictory, results.

But the probability of observing extreme cases isn't 1 for a given observer.

And the probability isn't 1/2^N for a given observer either. The observer observes what he observes. Probability is relevant for predictions, not post hoc observations.

We are talking about the predictions of the theory, not the experiences of individual observers. I think Sean tried this evasive tactic as well, and Albert rightly pointed out that that just makes everything idexical, and ultimately makes science impossible.

And it is not just the extreme branches that have low probability. Given the repeated measurement scenario we have been talking about, there are N repetitions of the experiment, giving 2^N distinct binary sequences of results. Applying the Born rule to each possible sequence shows that it has probability 1/2^N.

But the theory isn't about the probability of a specific sequence, it's about the probability of |up> vs |down> in the sequence without regard for order.  So there will, if the theory is correct, be many more sequences with a frequency of |up> near some theoretically computed proportion |a|^2 than sequences not near this proportion. 

Brent

But if every result obtains on every trial, the probability of each sequence is exactly one. In other words, Everett is incompatible with the  qBorn rule. You can abandon the Born rule if you like, or abandon the Everettian idea of every outcome occurring on every trial, but you can't have both.

The twisting and turning we are seeing by participants on this list is not going to alter this basic observation.

Bruce

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQ4r6SmArnJMrO_-JGgeRCOmeX%3DCDUq4RkWg4_X5sCzSw%40mail.gmail.com.

[Bruce Kellett]

On Sat, Sep 5, 2020 at 11:29 AM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/4/2020 4:00 PM, Bruce Kellett wrote:

On Sat, Sep 5, 2020 at 5:37 AM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/4/2020 4:43 AM, Bruce Kellett wrote:

On Fri, Sep 4, 2020 at 9:32 PM smitra <smi...@zonnet.nl> wrote:

Even if the MWI is false and the wavefunction collapses to produce only
one of the possible outcomes with a probability given by the Born rule,
you'll still get all possibilities realized in a generic infinite
universe, whether it's spatially infinite or a universe that exists for
an infinite long time.

The only way to find out what exists beyond the realm we've explored s
to do experiments. No philosophical reasoning about the interpretation
of probabilities can ever settle whether or not the universe is so large
or will exists for such a long time that another copy of me exists.
That's why these discussions are not so useful as an argument of whether
the MWI is correct or not.

I think something along those lines was Sean Carroll's answer to the points David Albert raised. Unfortunately, it doesn't wash!

Applying the Born rule to the repeated measurement scenario tells you that the probability of the extreme branches is low; whereas, the idea that all possible outcomes occur on every trial trivially implies that the probability of the extreme cases is exactly one. The contradiction couldn't be more stark, and waffling about infinite universes isn't going to change that -- the theory gives two, mutually contradictory, results.

But the probability of observing extreme cases isn't 1 for a given observer.

And the probability isn't 1/2^N for a given observer either. The observer observes what he observes. Probability is relevant for predictions, not post hoc observations.

We are talking about the predictions of the theory, not the experiences of individual observers. I think Sean tried this evasive tactic as well, and Albert rightly pointed out that that just makes everything idexical, and ultimately makes science impossible.

And it is not just the extreme branches that have low probability. Given the repeated measurement scenario we have been talking about, there are N repetitions of the experiment, giving 2^N distinct binary sequences of results. Applying the Born rule to each possible sequence shows that it has probability 1/2^N.

But the theory isn't about the probability of a specific sequence, it's about the probability of |up> vs |down> in the sequence without regard for order.  So there will, if the theory is correct, be many more sequences with a frequency of |up> near some theoretically computed proportion |a|^2 than sequences not near this proportion. 

The theory is about the probabilitiies of observations. The observation in question here is a sequence of |up> / |down> results, given that the probability for each individual outcome is 0.5. If the theory cannot give a probability for the sequence, then multiply the probabilities for each particular result in your sequence of measurements. The number of sequences with particular proportions of up or down results is irrelevant for this calculation.

Again, you are just attempting to divert attention from the obvious result that the Born rule calculation gives a different probability than expected when every outcome occurs for each measurement. In the Everett case, every possible sequence necessarily occurs. This does not happen in the genuine stochastic case, where only one (random) sequence is produced.

Bruce

Brent

But if every result obtains on every trial, the probability of each sequence is exactly one. In other words, Everett is incompatible with the Born rule. You can abandon the Born rule if you like, or abandon the Everettian idea of every outcome occurring on every trial, but you can't have both.

[Brent Meeker]

It can. But QM only predicts the p=0.5.  To have a prediction for a specific sequence HHTTHHHTTHTHTH... you need extra assumptions about indenpendence.  And given those assumptions your theory will be contradicted with near certainty.  Which is why I say the test of QM is whether p=0.5 is consistent with the observed sequence in the sense of predicting the relative frequency of H and T, not in the sense of predicting HHTTHHHTTHTHTH...

then multiply the probabilities for each particular result in your sequence of measurements. The number of sequences with particular proportions of up or down results is irrelevant for this calculation.

Again, you are just attempting to divert attention from the obvious result that the Born rule calculation gives a different probability than expected when every outcome occurs for each measurement. In the Everett case, every possible sequence necessarily occurs. This does not happen in the genuine stochastic case, where only one (random) sequence is produced.

In the Everett theory a measurement of spin up for a particle prepared in spin x results in two outcomes...only one is observed. If that is enough to dismiss Everett then all the this discussion of probability and the Born rule is irrelevant.

Brent

Bruce

Brent

But if every result obtains on every trial, the probability of each sequence is exactly one. In other words, Everett is incompatible with the Born rule. You can abandon the Born rule if you like, or abandon the Everettian idea of every outcome occurring on every trial, but you can't have both.

The twisting and turning we are seeing by participants on this list is not going to alter this basic observation.

Bruce

--

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLRo26Q6booHiKNZr5yUPfJZeVQVjdvFpnPG6bvV2S-xQA%40mail.gmail.com.

[Bruce Kellett]

On Sat, Sep 5, 2020 at 2:42 PM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/4/2020 7:02 PM, Bruce Kellett wrote:

On Sat, Sep 5, 2020 at 11:29 AM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

But the theory isn't about the probability of a specific sequence, it's about the probability of |up> vs |down> in the sequence without regard for order.  So there will, if the theory is correct, be many more sequences with a frequency of |up> near some theoretically computed proportion |a|^2 than sequences not near this proportion. 

The theory is about the probabilitiies of observations. The observation in question here is a sequence of |up> / |down> results, given that the probability for each individual outcome is 0.5. If the theory cannot give a probability for the sequence,

It can. But QM only predicts the p=0.5.  To have a prediction for a specific sequence HHTTHHHTTHTHTH... you need extra assumptions about indenpendence.

Sure. And independence of the sequential observations is clearly implied by the set up.

And given those assumptions your theory will be contradicted with near certainty.

Why?

Which is why I say the test of QM is whether p=0.5 is consistent with the observed sequence in the sense of predicting the relative frequency of H and T, not in the sense of predicting HHTTHHHTTHTHTH...

I am not attempting to predict a particular sequence. All that I have said is that the probability of any such sequence in N independent trials is 1/2^N. And that is simple probability theory, which cannot be denied.

then multiply the probabilities for each particular result in your sequence of measurements. The number of sequences with particular proportions of up or down results is irrelevant for this calculation.

Again, you are just attempting to divert attention from the obvious result that the Born rule calculation gives a different probability than expected when every outcome occurs for each measurement. In the Everett case, every possible sequence necessarily occurs. This does not happen in the genuine stochastic case, where only one (random) sequence is produced.

In the Everett theory a measurement of spin up for a particle prepared in spin x results in two outcomes...only one is observed. If that is enough to dismiss Everett then all the this discussion of probability and the Born rule is irrelevant.

I have no idea what you are talking about! Nothing like that was ever suggested. Everett predicts that in such a measurement, both outcomes obtain -- in separate branches. But the probability of this is one. Repeat N times. N time one is still just one. There is nothing more to it than that. I think you are being desperate in your attempts to play 'advocatus diaboli'. The point is that the Born rule is inconsistent with Everett.

Bruce

[Brent Meeker]

On 9/4/2020 10:18 PM, Bruce Kellett wrote:

On Sat, Sep 5, 2020 at 2:42 PM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/4/2020 7:02 PM, Bruce Kellett wrote:

On Sat, Sep 5, 2020 at 11:29 AM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

But the theory isn't about the probability of a specific sequence, it's about the probability of |up> vs |down> in the sequence without regard for order.  So there will, if the theory is correct, be many more sequences with a frequency of |up> near some theoretically computed proportion |a|^2 than sequences not near this proportion. 

The theory is about the probabilitiies of observations. The observation in question here is a sequence of |up> / |down> results, given that the probability for each individual outcome is 0.5. If the theory cannot give a probability for the sequence,

It can. But QM only predicts the p=0.5.  To have a prediction for a specific sequence HHTTHHHTTHTHTH... you need extra assumptions about indenpendence.

Sure. And independence of the sequential observations is clearly implied by the set up.

And given those assumptions your theory will be contradicted with near certainty.

Why?

The probability of getting any given entry in the sequence is 1/2, so the probability of getting the whole sequence right is 1/2^N .

Which is why I say the test of QM is whether p=0.5 is consistent with the observed sequence in the sense of predicting the relative frequency of H and T, not in the sense of predicting HHTTHHHTTHTHTH...

I am not attempting to predict a particular sequence.

That's what you seemed to reply when I said QM was only predicting the relative frequency of H within the sequence.  If you now agree with that, then you will also agree that there will many sequences with a relative frequency of 0.5 for H and given any epsilon the fraction of such sequences repetitions with 0.5-epsilon<frequency(H)<0.5+epsilon goes 1 as N->oo.  Which is what we mean by confirming the QM prediction of 0.5.

All that I have said is that the probability of any such sequence in N independent trials is 1/2^N. And that is simple probability theory, which cannot be denied.

then multiply the probabilities for each particular result in your sequence of measurements. The number of sequences with particular proportions of up or down results is irrelevant for this calculation.

Again, you are just attempting to divert attention from the obvious result that the Born rule calculation gives a different probability than expected when every outcome occurs for each measurement. In the Everett case, every possible sequence necessarily occurs. This does not happen in the genuine stochastic case, where only one (random) sequence is produced.

In the Everett theory a measurement of spin up for a particle prepared in spin x results in two outcomes...only one is observed. If that is enough to dismiss Everett then all the this discussion of probability and the Born rule is irrelevant.

I have no idea what you are talking about! Nothing like that was ever suggested. Everett predicts that in such a measurement, both outcomes obtain -- in separate branches.

As I understand your argument you're saying Everett is falsified because, no matter what N is, it predicts a branch HHHHHHHHHH...H which...What?  Is wrong?  Doesn't occur?  Is inconsistent with the Born rule (it isn't)? Is not observed?

If you just say it predicts something which is not observed; then my point is that it always predicts outcomes that are not observed unless P=1.

Brent

But the probability of this is one. Repeat N times. N time one is still just one. There is nothing more to it than that. I think you are being desperate in your attempts to play 'advocatus diaboli'. The point is that the Born rule is inconsistent with Everett.

Bruce

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLRcLwLQa2SLzViEqkZX6nU1%3Dp6SXUd7WA0nuzaiyOw0yg%40mail.gmail.com.

[Bruce Kellett]

On Sat, Sep 5, 2020 at 3:52 PM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/4/2020 10:18 PM, Bruce Kellett wrote:

On Sat, Sep 5, 2020 at 2:42 PM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/4/2020 7:02 PM, Bruce Kellett wrote:

On Sat, Sep 5, 2020 at 11:29 AM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

But the theory isn't about the probability of a specific sequence, it's about the probability of |up> vs |down> in the sequence without regard for order.  So there will, if the theory is correct, be many more sequences with a frequency of |up> near some theoretically computed proportion |a|^2 than sequences not near this proportion. 

The theory is about the probabilitiies of observations. The observation in question here is a sequence of |up> / |down> results, given that the probability for each individual outcome is 0.5. If the theory cannot give a probability for the sequence,

It can. But QM only predicts the p=0.5.  To have a prediction for a specific sequence HHTTHHHTTHTHTH... you need extra assumptions about indenpendence.

Sure. And independence of the sequential observations is clearly implied by the set up.

And given those assumptions your theory will be contradicted with near certainty.

Why?

The probability of getting any given entry in the sequence is 1/2, so the probability of getting the whole sequence right is 1/2^N .

I thought I had said that quite clearly. And that that is true for any one of the possible 2^N different sequences.

Which is why I say the test of QM is whether p=0.5 is consistent with the observed sequence in the sense of predicting the relative frequency of H and T, not in the sense of predicting HHTTHHHTTHTHTH...

I am not attempting to predict a particular sequence.

That's what you seemed to reply when I said QM was only predicting the relative frequency of H within the sequence.  If you now agree with that, then you will also agree that there will many sequences with a relative frequency of 0.5 for H and given any epsilon the fraction of such sequences repetitions with 0.5-epsilon<frequency(H)<0.5+epsilon goes 1 as N->oo.  Which is what we mean by confirming the QM prediction of 0.5.

You are off on the wrong track. I am not disagreeing with this. It is just that this is not what I am talking about. In the single world, stochastic case, it is, as Albert said, true that as N goes to infinity, all sequences converge in probability to the relative frequency of 0.5. But that is not my point.

 

All that I have said is that the probability of any such sequence in N independent trials is 1/2^N. And that is simple probability theory, which cannot be denied.

Which is what you have said above, and I agree.

then multiply the probabilities for each particular result in your sequence of measurements. The number of sequences with particular proportions of up or down results is irrelevant for this calculation.

Again, you are just attempting to divert attention from the obvious result that the Born rule calculation gives a different probability than expected when every outcome occurs for each measurement. In the Everett case, every possible sequence necessarily occurs. This does not happen in the genuine stochastic case, where only one (random) sequence is produced.

In the Everett theory a measurement of spin up for a particle prepared in spin x results in two outcomes...only one is observed. If that is enough to dismiss Everett then all the this discussion of probability and the Born rule is irrelevant.

I have no idea what you are talking about! Nothing like that was ever suggested. Everett predicts that in such a measurement, both outcomes obtain -- in separate branches.

As I understand your argument you're saying Everett is falsified because, no matter what N is, it predicts a branch HHHHHHHHHH...H which...What?  Is wrong?  Doesn't occur?  Is inconsistent with the Born rule (it isn't)? Is not observed?

No, listen carefully. Everett predicts that such a sequence will certainly occur for any N. In other words, the probability of the occurrence of such a sequence is one. Whereas the Born rule, as we both now seem to agree, predicts that the probability for the occurrence of such a sequence is 1/2^N. It is the fact that Everett and the Born rule predict different probabilities for the same sequence that is the point --  not that either predicts the impossibility of such a sequence. It is the predicted probabilities that differ, not the sequences.

And if you have a theory that predicts two different values for some result, then your theory is inconsistent. Everett and the Born rule are inconsistent because they predict different probabilities for this sequence of N |up>s in N trials  (or any other particular sequence, for that matter. Even though that latter point seems to have confused you!)

 

If you just say it predicts something which is not observed; then my point is that it always predicts outcomes that are not observed unless P=1.

Whether the sequence is observed or not was never the point.  Although, in Everett, there is always one observer of the sequence of all |up>s. This may occur with the Born rule, but not inevitably. The probabilities differ, which was the actual point.

Brent

But the probability of this is one. Repeat N times. N time one is still just one.

I did not say that very well. I mean one multiplied by itself N times, or 1^N = 1.

[Bruno Marchal]

On 3 Sep 2020, at 16:17, John Clark <johnk...@gmail.com> wrote:

I don't understand Albert's position or the distinction he is trying to make. He says that If the world is deterministic and given his knowledge of the macro state of the world right now he thinks there is a 75% chance the Yankees will win the World Series this year. If things are deterministic then the Yankees will either win or they will not, but for practical reasons he knows he has limited knowledge of the micro state of the world so he can't be certain (or at least he shouldn't be) thus he needs to devise a number between zero and one to express his degree of confidence that his prediction express is a fundamental truth.  As time goes on as he gains more knowledge he will need to change the value of that number, and if he is a professional gambler and makes many bets of that nature and if he updates that number according to the rules laid out by Thomas Bayes then he will maximize his profits over the long term. So if you say there is a 75% chance the Yankees will win it tells me nothing objectively true about the Yankees it just tells me something about your state of mind. 

Hugh Everett would say pretty much the same thing because he also believes we live in a deterministic world. Originally he may have only a vague idea of which branch of the multiverse is being observed and so he thinks there's a 50% chance, but as time goes on and he gains more information he still can't narrow it down to one particular branch but there are a great many branches that he can rule out and so by using the exact same Bayesian statistical rules that Albert used he now says the Yankees have a 75% chance of winning the World Series this year. But again If the world is deterministic then that number says nothing intrinsically true about the Yankees, it just says something about the state of mind of the speaker who made the utterance.

The analogy does not work, in Everett, like in the WM-self-duplication, we are in different histories at the same time, as long as we cannot distinguish them. If two identical brain/computer are run in two different rooms, there is an objective probability on the possible subjective future self-locating outcome. Here the 3p determinism ensures the 1p-indeterminism. It is not a bayesian type of uncertainty (and Everett is confusing when he called it “subjective probabilities” where he meant more something like “objective first-person indeterminacy”.  Mechanism + 3p determinism entails 1p indeterminism.

(I have not yet look at the video, but I can guess the content from the posts).

Bruno

John K Clark

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv1s-Z51XEyExV4x8KctRsBxhWfK6Sa_8Ls6EAsSMpLNTQ%40mail.gmail.com.

[smitra]

Reading also the other replies in this thread, it seems to me that you
are actually disagreeing with the MWI on the issue of how this
interpretation should work. But then you have a different version of the
MWI that you can then falsify. In the MWI one ends up copies of an
observer who observer the different possible outcomes, but with the
density given by the Born rule, such that in a classical ensemble with
those densities you also would have those same Born rule probabilities.

Saibal

[Bruno Marchal]

On 4 Sep 2020, at 00:55, Bruce Kellett <bhkel...@gmail.com> wrote:

On Fri, Sep 4, 2020 at 8:01 AM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

Sure.  But Albert's argument is that in a single, probabilistic world that implements Born's rule, the number of scientist who find something contrary to Born's rule goes to zero as the number of repetitions increases.  But in the multiverse there are always contrary worlds and, while their fraction decreases, their number increases with repetitions.

That is really the essential difference between Everettian notions of probability and standard probabilistic theory/practice. In the Everettian repeated experiment case, disconfirming cases occur with probability one, so it is strictly incoherent to claim (as Everettians, such as Sean Carroll, do) that these "monster" results can be ignored because they have low probability. The only thing that that can mean is that you are justified in ignoring them because they have low frequency: but that is a different definition of probability -- a frequentist notion that all reject.

I know more people rejecting the Bayesian definition than the frequentist one. Graham (and Preskill, Selesnick, …) make the frequency approach making sense by defining (in the limit of course) a frequency operator, and associating an observable to it. This makes sense with mechanism, where the probabilities are defined on some limit on the number of step of the universal dovetailer, due to the fact that this number of the UD steps is not available to the first person pov.

At best, what they might mean is that if you take all outcomes as equally likely, then the probability that you will get a low frequency outcome by chance in a random selection from the uniform distribution over all possibilities, is low. But that introduces yet another source of probability. It might be what is necessarily entailed in a definition of probability in terms of self-locating uncertainty, but it still involves one in the absurdity of claiming that things that necessarily happen have low probability. We cannot consistently claim in one breath that the probability is one, and in another breath, that  probability is "low”.

But there are no reason to have a relative probability one. It is one only "after the facts”, with classical with self-duplication, and quantum Mechanically with Born rules, which are unique by Gleason theorem.

Descrpitive set theory justifies the existence of a measure of probability for the first person views, and its uniqueness is justified by the completeness theorem of Solovay (plausibly), so, as long as this is not experimentally refuted, or as long as someone find a discrepancy between what mechanism predicts and the facts, Mechanism remains the simplest explanation for quanta and qualia.

The problem of Sean Carroll is that he seems not aware of the very strong constraints put on self-referential correctness, and which get a mathematical definition when the digital Mechanist hypothesis (or some weakening of it) is in play.

Bruno

Bruce

Brent

On 9/3/2020 12:02 PM, Quentin Anciaux wrote:

Hi,

as there will be persons in self duplicate experiment who'll see WWW...WW.

But most should converge on 50%.

Quentin

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQukPmz5mM2FMRXgbsfvD1pFYJsXCbstej0NZi7yC5QzQ%40mail.gmail.com.

[Bruno Marchal]

On 4 Sep 2020, at 08:54, Bruce Kellett <bhkel...@gmail.com> wrote:

On Fri, Sep 4, 2020 at 4:40 PM Quentin Anciaux <allc...@gmail.com> wrote:

Le ven. 4 sept. 2020 à 00:01, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> a écrit :

Sure.  But Albert's argument is that in a single, probabilistic world that implements Born's rule, the number of scientist who find something contrary to Born's rule goes to zero as the number of repetitions increases.  But in the multiverse there are always contrary worlds and, while their fraction decreases, their number increases with repetitions.

That's an interpretation... because I think there is no increasing or decreasing of numbers of worlds.... there are an infinity of them always, similar / identical "world" differentiate but there is no increase or decrease, there is no meaningfull way of "counting"... The frequency is all there is.

That does not detract from the fact that in Everett, the low probability worlds always occur with probability one.

After the facts. That is true for any probability theory.

In other words, the theory is intrinsically self-contradictory -- incoherent.

Only by confusing []p and ([]p & p), or a third person description and a first person prescription. It is actually an error equivalent to Penrose error when arguing that Gödel’s incompleteness refute Mechanism. Penrose compare his knowledge ([]p & p) with the machine’s believability ([]p). But the machine refute this by showing that this distinction is unavoidable from its personal point of view. 

The incoherence comes only from the physicalist identity thesis between mind and brain, which makes no sense once we postulate digital mechanism.

Bruno

Bruce

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLRtrQw8kc_grKMxRYLpwC-fJuX07sAfpWOMGYYtEVZp%3Dw%40mail.gmail.com.

[Bruno Marchal]

> On 4 Sep 2020, at 13:32, smitra <smi...@zonnet.nl> wrote:
>
> Even if the MWI is false and the wavefunction collapses to produce only one of the possible outcomes with a probability given by the Born rule, you'll still get all possibilities realized in a generic infinite universe, whether it's spatially infinite or a universe that exists for an infinite long time.
>
> The only way to find out what exists beyond the realm we've explored s to do experiments. No philosophical reasoning about the interpretation of probabilities can ever settle whether or not the universe is so large or will exists for such a long time that another copy of me exists. That's why these discussions are not so useful as an argument of whether the MWI is correct or not.

But we need some philosophical assumption about what is the “universe”. If we bet on mechanism, we have to bet on elementary arithmetic, but then we get the theorem that there is an infinity of computations going through our states, and that physics must be recovered through a measure on the relative computational histories. And this works, without eliminating the qualia (consciousness), which is not the case in physicist metaphysics.

The burden of the proof is in the hand of the materialist (believer in ontological physical universe), and we already know that he has to abandon “indexical digital Mechanism”.

Bruno

> To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/99d4da60baa28cf13d4597a8ea82edb9%40zonnet.nl.

[Bruno Marchal]

On 4 Sep 2020, at 13:43, Bruce Kellett <bhkel...@gmail.com> wrote:

On Fri, Sep 4, 2020 at 9:32 PM smitra <smi...@zonnet.nl> wrote:

Even if the MWI is false and the wavefunction collapses to produce only
one of the possible outcomes with a probability given by the Born rule,
you'll still get all possibilities realized in a generic infinite
universe, whether it's spatially infinite or a universe that exists for
an infinite long time.

The only way to find out what exists beyond the realm we've explored s
to do experiments. No philosophical reasoning about the interpretation
of probabilities can ever settle whether or not the universe is so large
or will exists for such a long time that another copy of me exists.
That's why these discussions are not so useful as an argument of whether
the MWI is correct or not.

I think something along those lines was Sean Carroll's answer to the points David Albert raised. Unfortunately, it doesn't wash!

Applying the Born rule to the repeated measurement scenario tells you that the probability of the extreme branches is low; whereas, the idea that all possible outcomes occur on every trial trivially implies that the probability of the extreme cases is exactly one.

Not true for the relative probability, as the average witnesses (of the most numerous histories) knows.

The contradiction couldn't be more stark, and waffling about infinite universes isn't going to change that -- the theory gives two, mutually contradictory, results.

There is no contradiction if you add the words “relative” and “first person” to “probability” in this case.

Bruno

Bruce

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLRE7C3xLzGjgDm3Ceyy%3DXH18vhy2KiJ48g2r6%3D6Kgnutg%40mail.gmail.com.

[Bruno Marchal]

On 4 Sep 2020, at 14:24, John Clark <johnk...@gmail.com> wrote:

On Thu, Sep 3, 2020 at 7:59 PM Bruce Kellett <bhkel...@gmail.com> wrote:

> It has nothing to do with whether the world is deterministic or not: all that is involved is that there is some objective chance of this particular result

If things are deterministic then there's no such thing as objective chance, and probability would just be a measure of our degree of ignorance of hidden causes.

What would be an hidden cause in the case of the self-duplication? 

>  the chance that the Yankees will win is independent of what we happen to think about it.

If Everett is right then there's a 100% chance the Yankees will win and a 100% chance the Yankees will lose because neither eventuality violates the laws of physics.

You cannot have a 100% probability for A, and for B, when A and B are incompatible events (like "feeling to be in W", and “feeling to be in M”, or like “seeing the spin up” and seeing the spin down.

There is no problem once we distinguish the 3P and 1P notions, which is also the base of the understanding of the mind-body problem.

Bruno

John K Clark

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv2ETLL%2Bu1GShLpzyEvdxWe8A2ZBN0xYEBfc1id7mNQm%2Bw%40mail.gmail.com.

[Bruno Marchal]

Nice! You make my point. I hope you can keep this about self-localisation in the classical mechanist self-multiplication. The situation are isomorphic, and entanglement becomes partial collective self-multiplication. The math justifies that this gives a quantum logic and quantum probability calculus. Some work remains to be done so that we can apply Gleason theorem in the phenomenological reality of he machine multiplied by at least aleph_zero in the arithmetical reality.

Bruno

John K Clark

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv0jbCU4D4oF62_khK60cowJT4%2BGg6cA3gqedWpdHkgRzw%40mail.gmail.com.

[Bruno Marchal]

On 5 Sep 2020, at 01:00, Bruce Kellett <bhkel...@gmail.com> wrote:

On Sat, Sep 5, 2020 at 5:37 AM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/4/2020 4:43 AM, Bruce Kellett wrote:

On Fri, Sep 4, 2020 at 9:32 PM smitra <smi...@zonnet.nl> wrote:

Even if the MWI is false and the wavefunction collapses to produce only
one of the possible outcomes with a probability given by the Born rule,
you'll still get all possibilities realized in a generic infinite
universe, whether it's spatially infinite or a universe that exists for
an infinite long time.

The only way to find out what exists beyond the realm we've explored s
to do experiments. No philosophical reasoning about the interpretation
of probabilities can ever settle whether or not the universe is so large
or will exists for such a long time that another copy of me exists.
That's why these discussions are not so useful as an argument of whether
the MWI is correct or not.

I think something along those lines was Sean Carroll's answer to the points David Albert raised. Unfortunately, it doesn't wash!

Applying the Born rule to the repeated measurement scenario tells you that the probability of the extreme branches is low; whereas, the idea that all possible outcomes occur on every trial trivially implies that the probability of the extreme cases is exactly one. The contradiction couldn't be more stark, and waffling about infinite universes isn't going to change that -- the theory gives two, mutually contradictory, results.

But the probability of observing extreme cases isn't 1 for a given observer.

And the probability isn't 1/2^N for a given observer either. The observer observes what he observes. Probability is relevant for predictions, not post hoc observations.

Exactly.

We are talking about the predictions of the theory, not the experiences of individual observers.

We are talking about the prediction of the theory, about the experiences of individual observers.

I think Sean tried this evasive tactic as well, and Albert rightly pointed out that that just makes everything idexical,

He is right on this.

and ultimately makes science impossible.

On the contrary, it reduces everything to the theory of machine indexical self-reference. Sean is not aware of the  mathematical theory of self-reference (G and G*).

And it is not just the extreme branches that have low probability. Given the repeated measurement scenario we have been talking about, there are N repetitions of the experiment, giving 2^N distinct binary sequences of results. Applying the Born rule to each possible sequence shows that it has probability 1/2^N. But if every result obtains on every trial, the probability of each sequence is exactly one.

But as you said yourself just above: probability is relevant for predictions, not post hoc observations.

In other words, Everett is incompatible with the Born rule. You can abandon the Born rule if you like, or abandon the Everettian idea of every outcome occurring on every trial, but you can't have both.

You can derive both from arithmetic, once you distinguish the first and third person notions.

The twisting and turning we are seeing by participants on this list is not going to alter this basic observation.

The universal Turing machine knows that this twisting is just a consequence of its inability to know that []p and ([]p & p) have to put different logics on the believable and the knowable, the observable, etc.

Bruno

Bruce

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQ4r6SmArnJMrO_-JGgeRCOmeX%3DCDUq4RkWg4_X5sCzSw%40mail.gmail.com.

[Bruno Marchal]

The probability is one for the existence of the branch does not entail that I will see, or feel to be in, that branch. This is again a case of obliterating  the 1P / 3P distinction.

The trouble is that the Born rule assigns a probability of 1/2^N to the same branch. Hence the contradiction.

The Born rule assign 1/2^N before the experience, and 1 after (and 0 for all other branches). But with Everett, that does not make the other branches getting non existence, just non accessibility.

If your theory gives two ways to predict the probability of a particular outcome, and these two calculations give different results, then your theory is inconsistent.

It is the 1p-3p confusion which leads to an inconsistency.

Bruno

Bruce

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLRK4_v75h7bnbqdfHLpyjBRsxvdQ7TFN6GBAwRbWXw8rg%40mail.gmail.com.

[Bruno Marchal]

In the eye of God, not in the eye of the individual making the experience. He cannot get both 00010... and 10100…

You talk like if in the WM-dup experience, you can bet on both W and M, which is a case of not remembering that the question is about what we will feel, not about in which branch some other people can find us. You can find me in both W and M, but from what I feel, in any branch, I feel to be only in that branch. 

Bruno

This does not happen in the genuine stochastic case, where only one (random) sequence is produced.

Bruce

Brent

But if every result obtains on every trial, the probability of each sequence is exactly one. In other words, Everett is incompatible with the Born rule. You can abandon the Born rule if you like, or abandon the Everettian idea of every outcome occurring on every trial, but you can't have both.

The twisting and turning we are seeing by participants on this list is not going to alter this basic observation.

Bruce

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLRo26Q6booHiKNZr5yUPfJZeVQVjdvFpnPG6bvV2S-xQA%40mail.gmail.com.

[Bruno Marchal]

On 5 Sep 2020, at 08:27, Bruce Kellett <bhkel...@gmail.com> wrote:

On Sat, Sep 5, 2020 at 3:52 PM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/4/2020 10:18 PM, Bruce Kellett wrote:

On Sat, Sep 5, 2020 at 2:42 PM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/4/2020 7:02 PM, Bruce Kellett wrote:

On Sat, Sep 5, 2020 at 11:29 AM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

But the theory isn't about the probability of a specific sequence, it's about the probability of |up> vs |down> in the sequence without regard for order.  So there will, if the theory is correct, be many more sequences with a frequency of |up> near some theoretically computed proportion |a|^2 than sequences not near this proportion. 

The theory is about the probabilitiies of observations. The observation in question here is a sequence of |up> / |down> results, given that the probability for each individual outcome is 0.5. If the theory cannot give a probability for the sequence,

It can. But QM only predicts the p=0.5.  To have a prediction for a specific sequence HHTTHHHTTHTHTH... you need extra assumptions about indenpendence.

Sure. And independence of the sequential observations is clearly implied by the set up.

And given those assumptions your theory will be contradicted with near certainty.

Why?

The probability of getting any given entry in the sequence is 1/2, so the probability of getting the whole sequence right is 1/2^N .

I thought I had said that quite clearly. And that that is true for any one of the possible 2^N different sequences.

Which is why I say the test of QM is whether p=0.5 is consistent with the observed sequence in the sense of predicting the relative frequency of H and T, not in the sense of predicting HHTTHHHTTHTHTH...

I am not attempting to predict a particular sequence.

That's what you seemed to reply when I said QM was only predicting the relative frequency of H within the sequence.  If you now agree with that, then you will also agree that there will many sequences with a relative frequency of 0.5 for H and given any epsilon the fraction of such sequences repetitions with 0.5-epsilon<frequency(H)<0.5+epsilon goes 1 as N->oo.  Which is what we mean by confirming the QM prediction of 0.5.

You are off on the wrong track. I am not disagreeing with this. It is just that this is not what I am talking about. In the single world, stochastic case, it is, as Albert said, true that as N goes to infinity, all sequences converge in probability to the relative frequency of 0.5. But that is not my point.

So add “relative” in all situation, as we are always concerned with relative probability, and personal outcomes.

 

All that I have said is that the probability of any such sequence in N independent trials is 1/2^N. And that is simple probability theory, which cannot be denied.

Which is what you have said above, and I agree.

then multiply the probabilities for each particular result in your sequence of measurements. The number of sequences with particular proportions of up or down results is irrelevant for this calculation.

Again, you are just attempting to divert attention from the obvious result that the Born rule calculation gives a different probability than expected when every outcome occurs for each measurement. In the Everett case, every possible sequence necessarily occurs. This does not happen in the genuine stochastic case, where only one (random) sequence is produced.

In the Everett theory a measurement of spin up for a particle prepared in spin x results in two outcomes...only one is observed. If that is enough to dismiss Everett then all the this discussion of probability and the Born rule is irrelevant.

I have no idea what you are talking about! Nothing like that was ever suggested. Everett predicts that in such a measurement, both outcomes obtain -- in separate branches.

As I understand your argument you're saying Everett is falsified because, no matter what N is, it predicts a branch HHHHHHHHHH...H which...What?  Is wrong?  Doesn't occur?  Is inconsistent with the Born rule (it isn't)? Is not observed?

No, listen carefully. Everett predicts that such a sequence will certainly occur for any N. In other words, the probability of the occurrence of such a sequence is one.

But the question is not on the probability of that occurence, but on the relative probability that I will find myself in this or that sequence. 

Whereas the Born rule, as we both now seem to agree, predicts that the probability for the occurrence of such a sequence is 1/2^N.

No, in your sense, the probability of the occurrence of that sequence is 1, but the Born rule, or Mechanism, measure the chance that I will live it, or not live it, from y personal pov. 

It is the fact that Everett and the Born rule predict different probabilities for the same sequence

You are confusing the probability one for the existence of all sequence, which is one in the universal wave, and the relative probability implied by this for the observers first person (plural by linearity of superposition, or by sharing the teleportation box) pov. Mathematically that is the confusion between []p (3p) and ([]p & p) (1p).

that is the point --  not that either predicts the impossibility of such a sequence. It is the predicted probabilities that differ, not the sequences.

And if you have a theory that predicts two different values for some result, then your theory is inconsistent.

It is the confusion between body and mind, or more abstractly 3p and 1p which makes you into deriving a contradiction.

Everett and the Born rule are inconsistent because they predict different probabilities for this sequence of N |up>s in N trials  (or any other particular sequence, for that matter. Even though that latter point seems to have confused you!)

 

If you just say it predicts something which is not observed; then my point is that it always predicts outcomes that are not observed unless P=1.

Whether the sequence is observed or not was never the point. 

It has always been the point. The probabilities are about (personal) results of observation (like when we look at a needle).

Although, in Everett, there is always one observer of the sequence of all |up>s. This may occur with the Born rule, but not inevitably. The probabilities differ, which was the actual point.

The relative probability differ, and that is what has to be taken when we talk about a measurement or an observation. All branches occurs, but I can only feel to be in one branch (modulo non distinguishability of course).

Bruno

Brent

But the probability of this is one. Repeat N times. N time one is still just one.

I did not say that very well. I mean one multiplied by itself N times, or 1^N = 1.

There is nothing more to it than that. I think you are being desperate in your attempts to play 'advocatus diaboli'. The point is that the Born rule is inconsistent with Everett.

Bruce

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLRErSGWg9pM08ph5ahTg%3Du9HYXu9WMKo4zHDtzvwm0W9A%40mail.gmail.com.

[John Clark]

On Sat, Sep 5, 2020 at 5:28 AM Bruno Marchal <mar...@ulb.ac.be> wrote:

> Hugh Everett would say pretty much the same thing because he also believes we live in a deterministic world. Originally he may have only a vague idea of which branch of the multiverse is being observed and so he thinks there's a 50% chance, but as time goes on and he gains more information he still can't narrow it down to one particular branch but there are a great many branches that he can rule out and so by using the exact same Bayesian statistical rules that Albert used he now says the Yankees have a 75% chance of winning the World Series this year. But again If the world is deterministic then that number says nothing intrinsically true about the Yankees, it just says something about the state of mind of the speaker who made the utterance.

> The analogy does not work, in Everett, like in the WM-self-duplication, we are in different histories at the same time, as long as we cannot distinguish them.

If the multiple copies of John K Clark in different worlds can not distinguish the tiny historical differences between those worlds then it would be meaningless to insist that they are different people. If later one of them notices something about his environment that the other does not then they would no longer be identical and then and only then would it make sense to say there are two different   John K Clark's.

> If two identical brain/computer are run in two different rooms,

If the two rooms are different and the brain/computer has sense organs then the brain/computer will detect those differences and so the brain/computers will no longer be identical.

> there is an objective probability on the possible subjective future self-locating outcome.

I don't know what the hell to make of a "objective probability of a possible subjectivity". And if things are deterministic, as they are in Everett's Multiverse, then nothing is objectively probabilistic, thus probability must just be a measure of an observer's ignorance. What else could it be?
 

> Here the 3p [...]

 Bruno, can you write a post about anything without getting into Peepee?

John K Clark

[John Clark]

On Sat, Sep 5, 2020 at 6:05 AM Bruno Marchal <mar...@ulb.ac.be> wrote:

>> If things are deterministic then there's no such thing as objective chance, and probability would just be a measure of our degree of ignorance of hidden causes.

> What would be an hidden cause in the case of the self-duplication? 

 

I don't know because I don't know what self-duplication effect you want a causal explanation for.

>> If Everett is right then there's a 100% chance the Yankees will win and a 100% chance the Yankees will lose because neither eventuality violates the laws of physics.

> You cannot have a 100% probability for A, and for B, when A and B are incompatible events

Sure you can. If Everett Is right then there's a 100% chance that John K Clark saw the Yankees win and there's a 100% chance that John K Clark saw the Yankees lose, and there is a 0% chance that John K Clark found a valid logical mathematical proof that 2+2 = 5. If everything has a probability of either zero or 100% then probability is obviously of little use when discussing the entire multiverse, although it can be quite useful in individual branches of it. As I've said over and over again, Everettian worlds don't have positive Real Number probabilities associated with them, they have Complex Number amplitudes.

> like "feeling to be in W", and “feeling to be in M”, or like “seeing the spin up” and seeing the spin down.

If Everett is right then "John K Clark" can see both, but "I" can not.

 

> we distinguish the 3P and 1P [...]

Peepee, it's always Peepee!

John K Clark

[Philip Thrift]

If Everett is right then "John K Clark" can see both, but "I" can not.

John K Clark

This is how physics has become worse than flat-earth theory.

@philipthrift

 

[Brent Meeker]

But you are not using Everett's theory.  You're strawmanning Evertt.  You're saying that since Everett says some sequence occurs he is predicting it with probability 1.  But that's only predicting that it occurs in evolution of the wave function.  It's not a prediction of the QM probability that is being tested.  And it's not following thru on Everett's interpretation that connects the theory to observation.  It's imposing your idea of how it connects to observation; essentially cutting off Everett's interpretation part way thru.

Everett's theory is deterministic so it's not relevant to criticize it for "predicting probability 1" when it predicts all the results.  I agree with you that you can't get a probability out of a deterministic theory unless you put in some additional postulate...like ignorance or coarse graining...and that's exactly what Everttian's do.  They say that the branches are an ensemble and you have some probability of being the observer in one of the ensemble...an ignorance based probability measured by either branch counting or weighting of branches.  I think this is a kind of cheat, since it is not simply a consequence of Schroedinger's equation.  On the other hand, Gleason's theorem is a consequence.  So once you cheat enough to introduce the probability concept, getting to Born's rule is just a matter of making up a story you like.

So my view is that once you've developed decoherence theory and you've shown that the reduced density matrix is diagonalized, you might as well then bite-the-bullet and postulate that the theory is probabilistic.  Then the math (Gleason's theorem) forces the interpretation that those diagonals are the probabilities of results.  Then "everything happens" is just a story attempting to back-fill a picture of how you got there based on ignorance (self-locating uncertainty).  There are some people who can't abide probabilistic theories and will invent fantastic worlds in order to have a deterministic ensemble which then must be reduced by ignorance to agree with observation.  They then feel they've made great progress because they think their theory is deterministic.

Brent

 

If you just say it predicts something which is not observed; then my point is that it always predicts outcomes that are not observed unless P=1.

Whether the sequence is observed or not was never the point.  Although, in Everett, there is always one observer of the sequence of all |up>s. This may occur with the Born rule, but not inevitably. The probabilities differ, which was the actual point.

Brent

But the probability of this is one. Repeat N times. N time one is still just one.

I did not say that very well. I mean one multiplied by itself N times, or 1^N = 1.

There is nothing more to it than that. I think you are being desperate in your attempts to play 'advocatus diaboli'. The point is that the Born rule is inconsistent with Everett.

Bruce

--

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLRErSGWg9pM08ph5ahTg%3Du9HYXu9WMKo4zHDtzvwm0W9A%40mail.gmail.com.

[Brent Meeker]

On 9/5/2020 2:28 AM, Bruno Marchal wrote:

On 3 Sep 2020, at 16:17, John Clark <johnk...@gmail.com> wrote:

I don't understand Albert's position or the distinction he is trying to make. He says that If the world is deterministic and given his knowledge of the macro state of the world right now he thinks there is a 75% chance the Yankees will win the World Series this year. If things are deterministic then the Yankees will either win or they will not, but for practical reasons he knows he has limited knowledge of the micro state of the world so he can't be certain (or at least he shouldn't be) thus he needs to devise a number between zero and one to express his degree of confidence that his prediction express is a fundamental truth.  As time goes on as he gains more knowledge he will need to change the value of that number, and if he is a professional gambler and makes many bets of that nature and if he updates that number according to the rules laid out by Thomas Bayes then he will maximize his profits over the long term. So if you say there is a 75% chance the Yankees will win it tells me nothing objectively true about the Yankees it just tells me something about your state of mind. 

Hugh Everett would say pretty much the same thing because he also believes we live in a deterministic world. Originally he may have only a vague idea of which branch of the multiverse is being observed and so he thinks there's a 50% chance, but as time goes on and he gains more information he still can't narrow it down to one particular branch but there are a great many branches that he can rule out and so by using the exact same Bayesian statistical rules that Albert used he now says the Yankees have a 75% chance of winning the World Series this year. But again If the world is deterministic then that number says nothing intrinsically true about the Yankees, it just says something about the state of mind of the speaker who made the utterance.

The analogy does not work, in Everett, like in the WM-self-duplication, we are in different histories at the same time, as long as we cannot distinguish them. If two identical brain/computer are run in two different rooms, there is an objective probability on the possible subjective future self-locating outcome.

Is there?  Can it be p=0.5000001 and q=0.4999999 ?  I think you are helping yourself to probabilities by implicitly assuming a measure.

Brent

Here the 3p determinism ensures the 1p-indeterminism. It is not a bayesian type of uncertainty (and Everett is confusing when he called it “subjective probabilities” where he meant more something like “objective first-person indeterminacy”.  Mechanism + 3p determinism entails 1p indeterminism.

(I have not yet look at the video, but I can guess the content from the posts).

Bruno

John K Clark

--
You received this message because you are subscribed to the Google Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv1s-Z51XEyExV4x8KctRsBxhWfK6Sa_8Ls6EAsSMpLNTQ%40mail.gmail.com.

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/46D82175-D55C-4F74-AC9A-5AEDD7FF4E6F%40ulb.ac.be.

[Brent Meeker]

On 9/5/2020 2:46 AM, Bruno Marchal wrote:

On 4 Sep 2020, at 00:55, Bruce Kellett <bhkel...@gmail.com> wrote:

On Fri, Sep 4, 2020 at 8:01 AM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

Sure.  But Albert's argument is that in a single, probabilistic world that implements Born's rule, the number of scientist who find something contrary to Born's rule goes to zero as the number of repetitions increases.  But in the multiverse there are always contrary worlds and, while their fraction decreases, their number increases with repetitions.

That is really the essential difference between Everettian notions of probability and standard probabilistic theory/practice. In the Everettian repeated experiment case, disconfirming cases occur with probability one, so it is strictly incoherent to claim (as Everettians, such as Sean Carroll, do) that these "monster" results can be ignored because they have low probability. The only thing that that can mean is that you are justified in ignoring them because they have low frequency: but that is a different definition of probability -- a frequentist notion that all reject.

I know more people rejecting the Bayesian definition than the frequentist one. Graham (and Preskill, Selesnick, …) make the frequency approach making sense by defining (in the limit of course) a frequency operator, and associating an observable to it. This makes sense with mechanism, where the probabilities are defined on some limit on the number of step of the universal dovetailer, due to the fact that this number of the UD steps is not available to the first person pov.

It's a confusion to talk about "the Bayesian defintion" vs "the frequentist definition".  Anything satisfying Kologorov's axioms is a probability measure.  It's a concept, like energy or wealth, that is useful because it applies to different things and you can transform among them.  You can make a calculation based on symmetry (e.g. P(die->::) = 1/6) and then test it using frequency and then apply it using decision theory.

Brent

At best, what they might mean is that if you take all outcomes as equally likely, then the probability that you will get a low frequency outcome by chance in a random selection from the uniform distribution over all possibilities, is low. But that introduces yet another source of probability. It might be what is necessarily entailed in a definition of probability in terms of self-locating uncertainty, but it still involves one in the absurdity of claiming that things that necessarily happen have low probability. We cannot consistently claim in one breath that the probability is one, and in another breath, that  probability is "low”.

But there are no reason to have a relative probability one. It is one only "after the facts”, with classical with self-duplication, and quantum Mechanically with Born rules, which are unique by Gleason theorem.

Descrpitive set theory justifies the existence of a measure of probability for the first person views, and its uniqueness is justified by the completeness theorem of Solovay (plausibly), so, as long as this is not experimentally refuted, or as long as someone find a discrepancy between what mechanism predicts and the facts, Mechanism remains the simplest explanation for quanta and qualia.

The problem of Sean Carroll is that he seems not aware of the very strong constraints put on self-referential correctness, and which get a mathematical definition when the digital Mechanist hypothesis (or some weakening of it) is in play.

Bruno

Bruce

Brent

On 9/3/2020 12:02 PM, Quentin Anciaux wrote:

Hi,

as there will be persons in self duplicate experiment who'll see WWW...WW.

But most should converge on 50%.

Quentin

--
You received this message because you are subscribed to the Google Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQukPmz5mM2FMRXgbsfvD1pFYJsXCbstej0NZi7yC5QzQ%40mail.gmail.com.

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CD20DF4C-958A-4252-86F8-F1AE65B43EA6%40ulb.ac.be.

[John Clark]

How so?

 John K Clark

[Brent Meeker]

On 9/5/2020 3:05 AM, Bruno Marchal wrote:

On 4 Sep 2020, at 14:24, John Clark <johnk...@gmail.com> wrote:

On Thu, Sep 3, 2020 at 7:59 PM Bruce Kellett <bhkel...@gmail.com> wrote:

> It has nothing to do with whether the world is deterministic or not: all that is involved is that there is some objective chance of this particular result

If things are deterministic then there's no such thing as objective chance, and probability would just be a measure of our degree of ignorance of hidden causes.

What would be an hidden cause in the case of the self-duplication?

Whatever resolves the "self-locating uncertainty".  It seems to me this concept is sneaking ignorance based probability in to avoid the deterministic contradiction that I see both Moscow and Washtington.

Brent

>  the chance that the Yankees will win is independent of what we happen to think about it.

If Everett is right then there's a 100% chance the Yankees will win and a 100% chance the Yankees will lose because neither eventuality violates the laws of physics.

You cannot have a 100% probability for A, and for B, when A and B are incompatible events (like "feeling to be in W", and “feeling to be in M”, or like “seeing the spin up” and seeing the spin down.

There is no problem once we distinguish the 3P and 1P notions, which is also the base of the understanding of the mind-body problem.

Bruno

John K Clark

--
You received this message because you are subscribed to the Google Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv2ETLL%2Bu1GShLpzyEvdxWe8A2ZBN0xYEBfc1id7mNQm%2Bw%40mail.gmail.com.

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/DC154255-0CE4-4FC0-BC6F-2A3D2AF8D5EF%40ulb.ac.be.

[Tomas Pales]

On Friday, September 4, 2020 at 8:03:55 PM UTC+2 Brent wrote:

If there are an infinite number then frequency is ill defined and you have to introduce some measure...which is essentially the same as just postulating a probability.  This is something like Carroll's solution which is to give "weights" to branches.

Don't we need to postulate a measure to calculate the (frequentist) probabilities of classical coin toss outcomes too? I mean, if we assume an unlimited (infinite) repetition of a fair coin toss then the probabilities of heads and tails are no longer 0.5 but become undefined despite the fact that the coin is fair (so its properties don't favor either side). Similar problem like calculating the proportion of even integers out of all integers - the proportion is not defined without choice of a particular measure. So it seems that we can't avoid using a particular probability measure also in classical physics.

The probabilities in QM are obviously defined, as expressed by the Born rule or the Gleason theorem. Which means (if I understand correctly) that if MWI is right then the number of branches arising at a decoherence event is either finite, or it is infinite but the structure of our quantum multiverse also has a particular measure that is expressed by Born and Gleason or by Carroll's weights of branches. The reason why our quantum multiverse has this particular measure may be that we happen to live in such a multiverse and other multiverses may have other measures.

[Tomas Pales]

On Saturday, September 5, 2020 at 8:11:57 PM UTC+2 Brent wrote:

There are some people who can't abide probabilistic theories and will invent fantastic worlds in order to have a deterministic ensemble which then must be reduced by ignorance to agree with observation.  They then feel they've made great progress because they think their theory is deterministic.

They are trying to give an answer why a particular possible outcome is observed while others just give a shrug.

[Brent Meeker]

If the other universe has the physics of quantum mechanics then the only consistent way of assigning probabilities to observation is Born's rule.  That's what Gleason proved.

Brent

[Tomas Pales]

Ok, that reduces options for other multiverses.

[Bruce Kellett]

On Sun, Sep 6, 2020 at 4:11 AM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/4/2020 11:27 PM, Bruce Kellett wrote:

No, listen carefully. Everett predicts that such a sequence will certainly occur for any N. In other words, the probability of the occurrence of such a sequence is one. Whereas the Born rule, as we both now seem to agree, predicts that the probability for the occurrence of such a sequence is 1/2^N. It is the fact that Everett and the Born rule predict different probabilities for the same sequence that is the point --  not that either predicts the impossibility of such a sequence. It is the predicted probabilities that differ, not the sequences.

And if you have a theory that predicts two different values for some result, then your theory is inconsistent. Everett and the Born rule are inconsistent because they predict different probabilities for this sequence of N |up>s in N trials  (or any other particular sequence, for that matter. Even though that latter point seems to have confused you!)

But you are not using Everett's theory.  You're strawmanning Evertt.

It is ultimately a waste of time to argue over exactly what Everett (or any other figure in the history of physics) actually said or thought. That can be the realm of historians of science, but it is not really relevant for the working physicist. What the working physicist is (or should be) concerned with, is the basic ideas; regardless of how the historical figure might have worked with them.

So you can think that I am strawmanning Everett -- I actually disagree, but I don't really care. The important point that I am taking from Everett is that the Schrodinger equation is the whole of quantum physics (Carroll's idea). If the wave function of the SE does not collapse (and there is no collapse in the Schrodinger equation), then every possible component of any superposition certainly exists, and continues to exist. This means that when you consider the superposition relevant to a measurement interaction, all possible outcomes of the measurement exist (in separate branches of the universal wave function).

 

You're saying that since Everett says some sequence occurs he is predicting it with probability 1.  But that's only predicting that it occurs in evolution of the wave function.

 

Sure. I think that is what I just said -- the branch corresponding to any possible outcome exists in the universal wave function. And, ipso facto, by linearity, there is an observer on that branch who sees that outcome.

It's not a prediction of the QM probability that is being tested.  And it's not following thru on Everett's interpretation that connects the theory to observation.  It's imposing your idea of how it connects to observation; essentially cutting off Everett's interpretation part way thru.

I disagree. The existence of observers who see sequences of results far from the relative frequencies predicted by the Born rule is an unambiguous consequence of Everett's approach -- nothing is being cut off, or left out.

Everett's theory is deterministic so it's not relevant to criticize it for "predicting probability 1" when it predicts all the results.

I am not criticizing it for "predicting probability one" -- I see that as a necessary consequence of the theory, since it certainly predicts that every outcome obtains on some branch. I am criticizing the theory for also claiming that the Born rule probabilities obtain. The Born rule predicts low probability for certain sequences, whereas Everett predicts that such sequences necessarily occur. In other words, the charge is one of inconsistency -- I am not objecting to the fact that the theory postulates that all outcomes occur in every interaction. I doubt that that is true, but that is Everett's theory, not mine.

 

I agree with you that you can't get a probability out of a deterministic theory unless you put in some additional postulate...like ignorance or coarse graining...and that's exactly what Everttian's do.  They say that the branches are an ensemble and you have some probability of being the observer in one of the ensemble...an ignorance based probability measured by either branch counting or weighting of branches.

Self-locating uncertainty is not resolved by either branch counting or by weighting branches. You, yourself, have pointed to the fact that in the 2^N binary sequences in the repeated two-outcome experiment peak around the centre, corresponding to p = 0.5. If you implement self-locating uncertainty in the abstract as the operation of taking a random history from this set (assuming sampling from a uniform distribution over the set), then you are more likely to end up in a history towards the peak of the distribution rather than in a history far out in one of the tails. If this is what one means by self-locating uncertainty, then this has nothing to do with either branch counting, or with differential weighting of branches. As an interesting aside, it is relatively easy to see that there is no way in this picture for the self-locating uncertainty to favour any probability other that p = 0.5 -- the set of possible histories is independent of the branch amplitudes (weights) so there is no way the Born rule can get any purchase, and branch weights are strictly irrelevant.

In other words, for the interpretation to get off the ground at all, one has to deviate considerably from the "purity of the Schrodinger equation". Increasing the number of branches on any interaction according to the desired Born weights simply contradicts the Schrodinger equation, and adding ad hoc weights according to the Born rule and treating these as probabilities also throws the basic assumption that every possible outcome occurs on every interaction under the bus. (In practice, Everettians simply ignore this fact, and treat the Born weights as the full story. It is not surprising that one has to do this, because there is essentially no other way to avoid the glaring inconsistency at the heart of the theory.) It is a bit rich, therefore, for you to criticize me for "departing from the original spirit of Everett."

I think this is a kind of cheat, since it is not simply a consequence of Schroedinger's equation.  On the other hand, Gleason's theorem is a consequence.  So once you cheat enough to introduce the probability concept, getting to Born's rule is just a matter of making up a story you like.

Exactly. It depends on how much you are prepared to fool yourself into thinking that the MWI makes sense.

So my view is that once you've developed decoherence theory and you've shown that the reduced density matrix is diagonalized, you might as well then bite-the-bullet and postulate that the theory is probabilistic.  Then the math (Gleason's theorem) forces the interpretation that those diagonals are the probabilities of results.  Then "everything happens" is just a story attempting to back-fill a picture of how you got there based on ignorance (self-locating uncertainty).  There are some people who can't abide probabilistic theories and will invent fantastic worlds in order to have a deterministic ensemble which then must be reduced by ignorance to agree with observation.  They then feel they've made great progress because they think their theory is deterministic.

So why do you defend Carroll and Everett? Even self-locating uncertainty is an essentially probabilistic idea.

Bruce

[Brent Meeker]

I don't defend them.  I criticize your argument against them because I think it is unconvincing for the reasons I have given; essentially because you cut off the MWI interpretation before the step in which it extracts probabilistic statements by using self-locating uncertainty in the ensemble of worlds.

Brent

[Bruce Kellett]

I think that the only way this comment makes sense is if the number of worlds multiplies in proportion to the Born probabilities on each interaction. That is an even bigger departure from Everett than anything you might have accused me of doing.

Let us revisit this problem using David Albert's example of Captain Kirk's transporter malfunction, so that when Kirk is beamed down to the surface of a planet, two "Kirks" arrive, one dressed in blue and the other in green. (One could make the same argument in terms of Bruno's WM duplication experiment.)

If, after transportation, the Kirks re-ascend to the Enterprise and each copy again transports down: being duplicated in the same way. After N iterations, there are 2^N Kirks on the surface of the planet. If each carries a notebook in which he has recorded the sequence of colours of his outfits, all possible binary sequences of B and G will be recorded in some book or the other. A simple application of the binomial distribution shows that the notebook records peak around sequences showing approximately equal numbers of blue and green outfits. This is experimental verification of the probability of p(blue) = 0.5 = p(green).

Now let us try to vary the probabilities, say to p(blue) = 0.9 and p(green) = 0.1. How do we do this?

OK, we transport Kirk and, with probability p = 0.9, we colour one of the uniforms blue. The other must, therefore, be coloured green. But then we simply have two Kirks on the surface of the planet, one in a blue uniform and one in a green uniform -- exactly as we had before. It is easy to see that, no matter how we imagine that we have changed the relative probabilities of uniform colours, we must always end up with just one blue uniform and one green uniform. Our attempt to change the probabilities has failed.

There is a way out, however. If, instead of simply duplicating the Kirks on transportation, the transporter manufactures 10 copies on the surface of the planet. Then we can suppose that 9 of these have blue uniforms, and the remaining Kirk is dressed in green. Iterating this procedure, we end up with 10^N Kirks on the surface of the planet, the vast majority of whom are dressed in blue. We have, thereby, changed the probability of a blue uniform for Kirk to 0.9 -- in the majority of cases.

The trouble with this is that such a scenario cannot be reproduced with the Schrodinger equation. If the universal wave function is represented by a vector in Hilbert space, for a two-outcome experiment the Hilbert space is two-dimensional, and we cannot fit 10 independent basis vectors into such a two-dimensional space. So the multiple branches for each outcome solution is not available in quantum mechanics. We might be able to dream up a theory in which this multiplication of branches would work, but that is not Everett, and it is not quantum mechanics as we know it. (Carroll and Zurek attempt to get around this by expanding the dimensionality of the operative Hilbert space by "borrowing" degrees of freedom from environmental decoherence. I doubt that this is actually convincing, or even possible. Whatever, it is a hopelessly ad hoc violation of the underlying dynamics.)

I can, therefore, see no way in which the Born rule can be made compatible with strictly deterministic Everettian Schrodinger evolution.

Note that (pace Bruno) this conclusion does not depend on any 1p/3p confusion. It depends only on the details of the assumed dynamics.

Bruce

[Brent Meeker]

On 9/5/2020 6:07 PM, Bruce Kellett wrote:

On Sun, Sep 6, 2020 at 10:25 AM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/5/2020 4:59 PM, Bruce Kellett wrote:

So why do you defend Carroll and Everett? Even self-locating uncertainty is an essentially probabilistic idea.

I don't defend them.  I criticize your argument against them because I think it is unconvincing for the reasons I have given; essentially because you cut off the MWI interpretation before the step in which it extracts probabilistic statements by using self-locating uncertainty in the ensemble of worlds.

I think that the only way this comment makes sense is if the number of worlds multiplies in proportion to the Born probabilities on each interaction.

Or if you postulate some kind of weighting as Carroll does.

That is an even bigger departure from Everett than anything you might have accused me of doing.

I didn't mean Everett himself.  He didn't even propose multiple worlds; he talked about the relative state of the observer (meaning relative to the observed value).  I was saying you were not attacking the argument actually put forward by Everttians, i.e. MWI advocates.

Let us revisit this problem using David Albert's example of Captain Kirk's transporter malfunction, so that when Kirk is beamed down to the surface of a planet, two "Kirks" arrive, one dressed in blue and the other in green. (One could make the same argument in terms of Bruno's WM duplication experiment.)

If, after transportation, the Kirks re-ascend to the Enterprise and each copy again transports down: being duplicated in the same way. After N iterations, there are 2^N Kirks on the surface of the planet. If each carries a notebook in which he has recorded the sequence of colours of his outfits, all possible binary sequences of B and G will be recorded in some book or the other. A simple application of the binomial distribution shows that the notebook records peak around sequences showing approximately equal numbers of blue and green outfits. This is experimental verification of the probability of p(blue) = 0.5 = p(green).

Now let us try to vary the probabilities, say to p(blue) = 0.9 and p(green) = 0.1. How do we do this?

OK, we transport Kirk and, with probability p = 0.9, we colour one of the uniforms blue. The other must, therefore, be coloured green. But then we simply have two Kirks on the surface of the planet, one in a blue uniform and one in a green uniform -- exactly as we had before. It is easy to see that, no matter how we imagine that we have changed the relative probabilities of uniform colours, we must always end up with just one blue uniform and one green uniform. Our attempt to change the probabilities has failed.

There is a way out, however. If, instead of simply duplicating the Kirks on transportation, the transporter manufactures 10 copies on the surface of the planet. Then we can suppose that 9 of these have blue uniforms, and the remaining Kirk is dressed in green. Iterating this procedure, we end up with 10^N Kirks on the surface of the planet, the vast majority of whom are dressed in blue. We have, thereby, changed the probability of a blue uniform for Kirk to 0.9 -- in the majority of cases.

The trouble with this is that such a scenario cannot be reproduced with the Schrodinger equation.

I agree.  That's why MWI advocates must resort to "weights", which are just amplitudes.  Or add some structure like an infinite or very large ensemble of already existing worlds that just get distinguished by results.

Brent

If the universal wave function is represented by a vector in Hilbert space, for a two-outcome experiment the Hilbert space is two-dimensional, and we cannot fit 10 independent basis vectors into such a two-dimensional space. So the multiple branches for each outcome solution is not available in quantum mechanics. We might be able to dream up a theory in which this multiplication of branches would work, but that is not Everett, and it is not quantum mechanics as we know it. (Carroll and Zurek attempt to get around this by expanding the dimensionality of the operative Hilbert space by "borrowing" degrees of freedom from environmental decoherence. I doubt that this is actually convincing, or even possible. Whatever, it is a hopelessly ad hoc violation of the underlying dynamics.)

I can, therefore, see no way in which the Born rule can be made compatible with strictly deterministic Everettian Schrodinger evolution.

Note that (pace Bruno) this conclusion does not depend on any 1p/3p confusion. It depends only on the details of the assumed dynamics.

Bruce

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQZbZpG755LrRTV52OyOEO-rEDX9-izt%3DDY3N8saHyThQ%40mail.gmail.com.

[Bruce Kellett]

On Sun, Sep 6, 2020 at 3:37 PM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/5/2020 6:07 PM, Bruce Kellett wrote:

On Sun, Sep 6, 2020 at 10:25 AM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/5/2020 4:59 PM, Bruce Kellett wrote:

So why do you defend Carroll and Everett? Even self-locating uncertainty is an essentially probabilistic idea.

I don't defend them.  I criticize your argument against them because I think it is unconvincing for the reasons I have given; essentially because you cut off the MWI interpretation before the step in which it extracts probabilistic statements by using self-locating uncertainty in the ensemble of worlds.

I think that the only way this comment makes sense is if the number of worlds multiplies in proportion to the Born probabilities on each interaction.

Or if you postulate some kind of weighting as Carroll does.

That is an even bigger departure from Everett than anything you might have accused me of doing.

I didn't mean Everett himself.  He didn't even propose multiple worlds; he talked about the relative state of the observer (meaning relative to the observed value).  I was saying you were not attacking the argument actually put forward by Everttians, i.e. MWI advocates.

Let us revisit this problem using David Albert's example of Captain Kirk's transporter malfunction, so that when Kirk is beamed down to the surface of a planet, two "Kirks" arrive, one dressed in blue and the other in green. (One could make the same argument in terms of Bruno's WM duplication experiment.)

If, after transportation, the Kirks re-ascend to the Enterprise and each copy again transports down: being duplicated in the same way. After N iterations, there are 2^N Kirks on the surface of the planet. If each carries a notebook in which he has recorded the sequence of colours of his outfits, all possible binary sequences of B and G will be recorded in some book or the other. A simple application of the binomial distribution shows that the notebook records peak around sequences showing approximately equal numbers of blue and green outfits. This is experimental verification of the probability of p(blue) = 0.5 = p(green).

Now let us try to vary the probabilities, say to p(blue) = 0.9 and p(green) = 0.1. How do we do this?

OK, we transport Kirk and, with probability p = 0.9, we colour one of the uniforms blue. The other must, therefore, be coloured green. But then we simply have two Kirks on the surface of the planet, one in a blue uniform and one in a green uniform -- exactly as we had before. It is easy to see that, no matter how we imagine that we have changed the relative probabilities of uniform colours, we must always end up with just one blue uniform and one green uniform. Our attempt to change the probabilities has failed.

There is a way out, however. If, instead of simply duplicating the Kirks on transportation, the transporter manufactures 10 copies on the surface of the planet. Then we can suppose that 9 of these have blue uniforms, and the remaining Kirk is dressed in green. Iterating this procedure, we end up with 10^N Kirks on the surface of the planet, the vast majority of whom are dressed in blue. We have, thereby, changed the probability of a blue uniform for Kirk to 0.9 -- in the majority of cases.

The trouble with this is that such a scenario cannot be reproduced with the Schrodinger equation.

I agree.  That's why MWI advocates must resort to "weights", which are just amplitudes.  Or add some structure like an infinite or very large ensemble of already existing worlds that just get distinguished by results.

Don't you see that the argument I have made above shows that the idea of adding 'weights' to the branches does not work?: you cannot consistently graft the Born rule on to a model in which every possible outcome occurs on every trial. The set of 2^N possible branches resulting from N repetitions of the binary measurement is independent of the original amplitudes or weights. I think I made that point months ago -- it was, in effect, my starting point. The idea of a large ensemble of pre-existing worlds that just get distinguished by results has never been taken seriously by anyone outside of this list. It has never been worked through in detail, and it is doubtful if it even makes sense. It certainly has nothing to do with the Schrodinger equation.

I suppose you can explore such ideas if you wish, but my purpose was more limited -- I merely wished to show that MWI as advocated by the likes of Carroll, Zurek, and Wallace, is incoherent. Since I have shown that adding weights, or multiplying branches, is inconsistent with the Born rule and/or the Schrodinger equation, I have made my point. All else is idle chatter.

Bruce

[Philip Thrift]

In one case (MWI): The consciousness you have now splits - again and again and again - and there are many, many "you-#x" consciousnesses an hour from  now that are "you" right now. 

In the other case (FET): All the so-called measurements that people say the earth is not flat are an illusion, like a hologram.

MWI, FET: Equally fantastic.

@philipthrift

[scerir]

Bruce: "The idea of a large ensemble of pre-existing worlds that just get distinguished by results has never been taken seriously by anyone outside of this list. It has never been worked through in detail, and it is doubtful if it even makes sense. It certainly has nothing to do with the Schrodinger equation."

Vaidman, speaking of quantum teleportation, https://en.wikipedia.org/wiki/Quantum_teleportation , pointed out that when Bob receives the message from Alice, he will know which of the four states his particle is in, and using this information he performs a unitary operation on his particle to transform it to the desired state. But (as Vaidman pointed out) before Bob receives the message from Alice there are four pre-existing equiprobable states, one of them (Bob doesn't know which one) is already the right one.  α | 0 ⟩ B + β | 1 ⟩ B {\displaystyle \alpha |0\rangle _{B}+\beta |1\rangle _{B}}

[Bruce Kellett]

On Sun, Sep 6, 2020 at 6:55 PM 'scerir' via Everything List <everyth...@googlegroups.com> wrote:

Bruce: "The idea of a large ensemble of pre-existing worlds that just get distinguished by results has never been taken seriously by anyone outside of this list. It has never been worked through in detail, and it is doubtful if it even makes sense. It certainly has nothing to do with the Schrodinger equation."

Vaidman, speaking of quantum teleportation, https://en.wikipedia.org/wiki/Quantum_teleportation , pointed out that when Bob receives the message from Alice, he will know which of the four states his particle is in, and using this information he performs a unitary operation on his particle to transform it to the desired state. But (as Vaidman pointed out) before Bob receives the message from Alice there are four pre-existing equiprobable states, one of them (Bob doesn't know which one) is already the right one. 

Serafino,

 I am sorry to have to say this, but Lev Vaidman is something of an idiot about these things. Don't take anything he says seriously, even though he has been around for many years. This quote is irrelevant to my point. MWI is incompatible with the Born rule. The Born rule makes sense only in single world settings.

Bruce

[John Clark]

On Sat, Sep 5, 2020 at 7:59 PM Bruce Kellett <bhkel...@gmail.com> wrote:

> The important point that I am taking from Everett is that the Schrodinger equation is the whole of quantum physics (Carroll's idea). If the wave function of the SE does not collapse (and there is no collapse in the Schrodinger equation), then every possible component of any superposition certainly exists, and continues to exist. 

Yes, many worlds is bare-bones Quantum Mechanics, it contains everything that's needed and nothing more. The only reason people add additional mathematical gunk is they personally dislike all those worlds for one reason or another and want to get rid of them. I think Schrodinger's Equation is hard enough to solve as it is and needlessly making it even more complicated is not progress.

> You're saying that since Everett says some sequence occurs he is predicting it with probability 1.

Everett Is saying a world exists where 30 seconds from now all the air molecules in the room you're in right now gather in one small corner due to random motion and you suffocate. But all Everettian worlds are not equal, they have different Complex Number amplitudes. The square of the absolute value of the amplitude of such a world would be the probability of you being in such a world and experiencing suffocation, and that positive real number although greater than zero would be extremely small. And I do mean extremely!

> it is relatively easy to see that there is no way in this picture for the self-locating uncertainty to favour any probability other that p = 0.5

That is just flat out untrue. If you want to know the probability that you will be in a universe (there will be many not just one) in which you observe the electron go left rather than right you need to take the square of the absolute value of the amplitude of that electron and, depending on the specific circumstances of how the experiment is set up, that might or might not be 0.5. It can't be emphasized too much that Everettian worlds don't have positive real number probabilities associated with them, they have complex number amplitudes.

 

> The existence of observers who see sequences of results far from the relative frequencies predicted by the Born rule is an unambiguous consequence of Everett's approach

Yes, Everett says there will be observers who see all sorts of bazaar astronomically unlikely events, but the square of the absolute value of the amplitude of such worlds is extremely small, so the probability you will observe such a world is also extremely small.

  > The Born rule predicts low probability for certain sequences, 

Yes.

> Everett predicts that such sequences necessarily occur. 

Yes.

 > the charge is one of inconsistency

Yes that is the charge. No I don't see any inconsistency. 

John K Clark

[Bruno Marchal]

On 5 Sep 2020, at 14:26, John Clark <johnk...@gmail.com> wrote:

On Sat, Sep 5, 2020 at 5:28 AM Bruno Marchal <mar...@ulb.ac.be> wrote:

> Hugh Everett would say pretty much the same thing because he also believes we live in a deterministic world. Originally he may have only a vague idea of which branch of the multiverse is being observed and so he thinks there's a 50% chance, but as time goes on and he gains more information he still can't narrow it down to one particular branch but there are a great many branches that he can rule out and so by using the exact same Bayesian statistical rules that Albert used he now says the Yankees have a 75% chance of winning the World Series this year. But again If the world is deterministic then that number says nothing intrinsically true about the Yankees, it just says something about the state of mind of the speaker who made the utterance.

> The analogy does not work, in Everett, like in the WM-self-duplication, we are in different histories at the same time, as long as we cannot distinguish them.

If the multiple copies of John K Clark in different worlds can not distinguish the tiny historical differences between those worlds then it would be meaningless to insist that they are different people. If later one of them notices something about his environment that the other does not then they would no longer be identical and then and only then would it make sense to say there are two different   John K Clark’s.

OK

> If two identical brain/computer are run in two different rooms,

If the two rooms are different and the brain/computer has sense organs then the brain/computer will detect those differences and so the brain/computers will no longer be identical.

OK

> there is an objective probability on the possible subjective future self-locating outcome.

I don't know what the hell to make of a "objective probability of a possible subjectivity”.

I give you an example. A person is multiplied by 100 and put in 100 different, but identical from inside rooms. Just the number of the room differs, like in some hostel. You seem to agree that, as long as they stay in the room, there is only one person. But the copies are asked to open the room, and the person was asked, before the experience what is the probability that when going out of the room, its number is prime.

I use the usual first person non transitive identity notion, where the identity if preserve in experience without amnesia.

So the HM and HW person are both the H-person, despite the HM and HW person have become different.

(H, M, and W refers to Helsinki, Moscow, and Washington in the Helsinki——> {Washington, Moscow} self-duplication experience.

And if things are deterministic, as they are in Everett's Multiverse, then nothing is objectively probabilistic, thus probability must just be a measure of an observer's ignorance. What else could it be?

The objective ignorance of a subject about which branch of the universal wave he belongs, in Everett.

Or the objective ignorance of all universal Turing machines about which computations emulate them in arithmetic.

 

> Here the 3p [...]

 Bruno, can you write a post about anything without getting into Peepee?

The 3p/1p distinction need it to get the theory of both quanta and qualia, and to understand why they are different, and how they are related.

It is also imposed by incompleteness once you define the first person by the definition of Theatetus (the true justified-opinion) using Gödel’s beweisbar predicate for true opinion. That works well, quantum and intutionistoc logic appears where predicted, and verified by the actual observation until now.

With Mechanism, the burden of the proof is given to the believer in some irreducible physical universe. He has to explain what it is, and how it select the computation in arithmetic (or to abandon the digital mechanist hypothesis in the cognitive science).

Bruno

John K Clark

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv0rJmt6COWMN1giSGdjQuVmjLGHCbn6O%3Dq2fY%2BtjdGsJw%40mail.gmail.com.

[Bruno Marchal]

Right. It is more a consequence of the theory of mind used in the definition of what is an observer (a machine with memory). 

Everett used “naive mechanism”, which works very well in this setting, but eventually, a definition of machine requires the Church-Turing-Post-Kleene thesis, and then the wave itself has to be retrieved from all computations.

Mechanism provides a testable explanation for the appearance of the physical laws. It extends Darwin in a many histories interpretation of arithmetic on which all sound universal (oracular) machine converges. 

That explains quanta and qualia from elementary arithmetic (or any universal machinery phi_i).

We can’t do better. Elementary arithmetic + induction can already prove that elementary arithmetic is not obtainable by simpler notions (up to Turing-equivalence).

On the other hand, Gleason's theorem is a consequence.  So once you cheat enough to introduce the probability concept,

It is not cheating. It is the acknowledgement of the universal machine that she does not know which computations support them. 

getting to Born's rule is just a matter of making up a story you like.

?

The corresponding theorem of Gleason is still lacking for arithmetic, but the fact that the universal machine get the quantum logic where needed illustrates that the "Gleason theorem" of Gleason will be plausibly directly applicable. 

So my view is that once you've developed decoherence theory and you've shown that the reduced density matrix is diagonalized, you might as well then bite-the-bullet and postulate that the theory is probabilistic.  Then the math (Gleason's theorem) forces the interpretation that those diagonals are the probabilities of results.  Then "everything happens" is just a story attempting to back-fill a picture of how you got there based on ignorance (self-locating uncertainty). 

OK

There are some people who can't abide probabilistic theories and will invent fantastic worlds in order to have a deterministic ensemble which then must be reduced by ignorance to agree with observation.  They then feel they've made great progress because they think their theory is deterministic.

It is ontological attachment. It is the same error than saying that “God made it” is an explanation, instead of a problem to solve.

Bruno

Brent

 

If you just say it predicts something which is not observed; then my point is that it always predicts outcomes that are not observed unless P=1.

Whether the sequence is observed or not was never the point.  Although, in Everett, there is always one observer of the sequence of all |up>s. This may occur with the Born rule, but not inevitably. The probabilities differ, which was the actual point.

Brent

But the probability of this is one. Repeat N times. N time one is still just one.

I did not say that very well. I mean one multiplied by itself N times, or 1^N = 1.

There is nothing more to it than that. I think you are being desperate in your attempts to play 'advocatus diaboli'. The point is that the Born rule is inconsistent with Everett.

Bruce

--
You received this message because you are subscribed to the Google Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLRErSGWg9pM08ph5ahTg%3Du9HYXu9WMKo4zHDtzvwm0W9A%40mail.gmail.com.

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/5F53D4E6.8010702%40verizon.net.

[Bruno Marchal]

On 5 Sep 2020, at 21:08, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/5/2020 2:28 AM, Bruno Marchal wrote:

On 3 Sep 2020, at 16:17, John Clark <johnk...@gmail.com> wrote:

I don't understand Albert's position or the distinction he is trying to make. He says that If the world is deterministic and given his knowledge of the macro state of the world right now he thinks there is a 75% chance the Yankees will win the World Series this year. If things are deterministic then the Yankees will either win or they will not, but for practical reasons he knows he has limited knowledge of the micro state of the world so he can't be certain (or at least he shouldn't be) thus he needs to devise a number between zero and one to express his degree of confidence that his prediction express is a fundamental truth.  As time goes on as he gains more knowledge he will need to change the value of that number, and if he is a professional gambler and makes many bets of that nature and if he updates that number according to the rules laid out by Thomas Bayes then he will maximize his profits over the long term. So if you say there is a 75% chance the Yankees will win it tells me nothing objectively true about the Yankees it just tells me something about your state of mind. 

Hugh Everett would say pretty much the same thing because he also believes we live in a deterministic world. Originally he may have only a vague idea of which branch of the multiverse is being observed and so he thinks there's a 50% chance, but as time goes on and he gains more information he still can't narrow it down to one particular branch but there are a great many branches that he can rule out and so by using the exact same Bayesian statistical rules that Albert used he now says the Yankees have a 75% chance of winning the World Series this year. But again If the world is deterministic then that number says nothing intrinsically true about the Yankees, it just says something about the state of mind of the speaker who made the utterance.

The analogy does not work, in Everett, like in the WM-self-duplication, we are in different histories at the same time, as long as we cannot distinguish them. If two identical brain/computer are run in two different rooms, there is an objective probability on the possible subjective future self-locating outcome.

Is there?  Can it be p=0.5000001 and q=0.4999999 ? 

Assuming a perfect protocol, it is 1/2. 

I think you are helping yourself to probabilities by implicitly assuming a measure.

It is not obvious, but there is a measure for the first person views, plural ([]p & <>t) and singular ([]p & p, []p & <>t & p).

I have realised more or less recently that the measure is inherited from a measure on the sigma_1 set + arbitrary oracles, that is the union of all sigma_1(a) for a being a real (or complex number). This requires a bit of Descriptive Set theory. 

So, there is a measure, even a Lebesgue Measure. There is an integral, normally Feynman’s one, if both Mechanism, and Quantum Mechanics are correct.

It took me some time to admit that the invariance of the first person for the Universal-Dovetailer-steps “delays” enforces the presence of all oracular computations. It is a continuum, with a complicated structure determined by the modes of self-reference (which are 8, although there are more like 4 + 4 * infinity).

Bruno

Brent

Here the 3p determinism ensures the 1p-indeterminism. It is not a bayesian type of uncertainty (and Everett is confusing when he called it “subjective probabilities” where he meant more something like “objective first-person indeterminacy”.  Mechanism + 3p determinism entails 1p indeterminism.

(I have not yet look at the video, but I can guess the content from the posts).

Bruno

John K Clark

--
You received this message because you are subscribed to the Google Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv1s-Z51XEyExV4x8KctRsBxhWfK6Sa_8Ls6EAsSMpLNTQ%40mail.gmail.com.

--
You received this message because you are subscribed to the Google Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/46D82175-D55C-4F74-AC9A-5AEDD7FF4E6F%40ulb.ac.be.

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/5F53E223.4030109%40verizon.net.

[Bruno Marchal]

On 5 Sep 2020, at 21:16, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/5/2020 2:46 AM, Bruno Marchal wrote:

On 4 Sep 2020, at 00:55, Bruce Kellett <bhkel...@gmail.com> wrote:

On Fri, Sep 4, 2020 at 8:01 AM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

Sure.  But Albert's argument is that in a single, probabilistic world that implements Born's rule, the number of scientist who find something contrary to Born's rule goes to zero as the number of repetitions increases.  But in the multiverse there are always contrary worlds and, while their fraction decreases, their number increases with repetitions.

That is really the essential difference between Everettian notions of probability and standard probabilistic theory/practice. In the Everettian repeated experiment case, disconfirming cases occur with probability one, so it is strictly incoherent to claim (as Everettians, such as Sean Carroll, do) that these "monster" results can be ignored because they have low probability. The only thing that that can mean is that you are justified in ignoring them because they have low frequency: but that is a different definition of probability -- a frequentist notion that all reject.

I know more people rejecting the Bayesian definition than the frequentist one. Graham (and Preskill, Selesnick, …) make the frequency approach making sense by defining (in the limit of course) a frequency operator, and associating an observable to it. This makes sense with mechanism, where the probabilities are defined on some limit on the number of step of the universal dovetailer, due to the fact that this number of the UD steps is not available to the first person pov.

It's a confusion to talk about "the Bayesian defintion" vs "the frequentist definition”. 

OK. I should have said the Dutch book definition. It uses Bayes theorem to provide a definition of probability. That probability obey Kolmogorov axioms, but the reverse is not necessarily the case. I am not sure. The distinction if more conceptual than technical perhaps.

Anything satisfying Kologorov's axioms is a probability measure.  It's a concept, like energy or wealth, that is useful because it applies to different things and you can transform among them.  You can make a calculation based on symmetry (e.g. P(die->::) = 1/6) and then test it using frequency and then apply it using decision theory.

OK

Bruno

Brent

At best, what they might mean is that if you take all outcomes as equally likely, then the probability that you will get a low frequency outcome by chance in a random selection from the uniform distribution over all possibilities, is low. But that introduces yet another source of probability. It might be what is necessarily entailed in a definition of probability in terms of self-locating uncertainty, but it still involves one in the absurdity of claiming that things that necessarily happen have low probability. We cannot consistently claim in one breath that the probability is one, and in another breath, that  probability is "low”.

But there are no reason to have a relative probability one. It is one only "after the facts”, with classical with self-duplication, and quantum Mechanically with Born rules, which are unique by Gleason theorem.

Descrpitive set theory justifies the existence of a measure of probability for the first person views, and its uniqueness is justified by the completeness theorem of Solovay (plausibly), so, as long as this is not experimentally refuted, or as long as someone find a discrepancy between what mechanism predicts and the facts, Mechanism remains the simplest explanation for quanta and qualia.

The problem of Sean Carroll is that he seems not aware of the very strong constraints put on self-referential correctness, and which get a mathematical definition when the digital Mechanist hypothesis (or some weakening of it) is in play.

Bruno

Bruce

Brent

On 9/3/2020 12:02 PM, Quentin Anciaux wrote:

Hi,

as there will be persons in self duplicate experiment who'll see WWW...WW.

But most should converge on 50%.

Quentin

--
You received this message because you are subscribed to the Google Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQukPmz5mM2FMRXgbsfvD1pFYJsXCbstej0NZi7yC5QzQ%40mail.gmail.com.

--
You received this message because you are subscribed to the Google Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CD20DF4C-958A-4252-86F8-F1AE65B43EA6%40ulb.ac.be.

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/5F53E415.9040002%40verizon.net.

[Bruno Marchal]

On 5 Sep 2020, at 21:21, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/5/2020 3:05 AM, Bruno Marchal wrote:

On 4 Sep 2020, at 14:24, John Clark <johnk...@gmail.com> wrote:

On Thu, Sep 3, 2020 at 7:59 PM Bruce Kellett <bhkel...@gmail.com> wrote:

> It has nothing to do with whether the world is deterministic or not: all that is involved is that there is some objective chance of this particular result

If things are deterministic then there's no such thing as objective chance, and probability would just be a measure of our degree of ignorance of hidden causes.

What would be an hidden cause in the case of the self-duplication?

Whatever resolves the "self-locating uncertainty".  It seems to me this concept is sneaking ignorance based probability in to avoid the deterministic contradiction that I see both Moscow and Washtington.

But Mechanism explains why the contradiction does not occur. It explains why the W-machine feel to be in W and not in Moscow, and vice versa. It explains also why the prediction in the dairy “I will see both Moscow and Washington, but feel to be seeing only one of them” is verified by both copies, so that it leads to some probability calculus.

Bruno

Brent

>  the chance that the Yankees will win is independent of what we happen to think about it.

If Everett is right then there's a 100% chance the Yankees will win and a 100% chance the Yankees will lose because neither eventuality violates the laws of physics.

You cannot have a 100% probability for A, and for B, when A and B are incompatible events (like "feeling to be in W", and “feeling to be in M”, or like “seeing the spin up” and seeing the spin down.

There is no problem once we distinguish the 3P and 1P notions, which is also the base of the understanding of the mind-body problem.

Bruno

John K Clark

--
You received this message because you are subscribed to the Google Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv2ETLL%2Bu1GShLpzyEvdxWe8A2ZBN0xYEBfc1id7mNQm%2Bw%40mail.gmail.com.

--
You received this message because you are subscribed to the Google Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/DC154255-0CE4-4FC0-BC6F-2A3D2AF8D5EF%40ulb.ac.be.

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/5F53E532.5070701%40verizon.net.

[Bruno Marchal]

On 6 Sep 2020, at 01:59, Bruce Kellett <bhkel...@gmail.com> wrote:

So why do you defend Carroll and Everett? Even self-locating uncertainty is an essentially probabilistic idea.

Glad to hear that :)

Bruno

[Bruno Marchal]

On 6 Sep 2020, at 08:15, Bruce Kellett <bhkel...@gmail.com> wrote:

On Sun, Sep 6, 2020 at 3:37 PM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/5/2020 6:07 PM, Bruce Kellett wrote:

On Sun, Sep 6, 2020 at 10:25 AM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 9/5/2020 4:59 PM, Bruce Kellett wrote:

So why do you defend Carroll and Everett? Even self-locating uncertainty is an essentially probabilistic idea.

I don't defend them.  I criticize your argument against them because I think it is unconvincing for the reasons I have given; essentially because you cut off the MWI interpretation before the step in which it extracts probabilistic statements by using self-locating uncertainty in the ensemble of worlds.

I think that the only way this comment makes sense is if the number of worlds multiplies in proportion to the Born probabilities on each interaction.

Or if you postulate some kind of weighting as Carroll does.

That is an even bigger departure from Everett than anything you might have accused me of doing.

I didn't mean Everett himself.  He didn't even propose multiple worlds; he talked about the relative state of the observer (meaning relative to the observed value). 

According to some biographer, Everett did mentioned the “many-worlds” in the title of his first paper, but was asked by the publisher to use something less shocking, and that is why he used the notion of relative state.

I was a bit disappointed by this, as “relative state” is more general a priori, and help to avoid taking the “world” notion to much seriously or ontologically. 

I was saying you were not attacking the argument actually put forward by Everttians, i.e. MWI advocates.

Let us revisit this problem using David Albert's example of Captain Kirk's transporter malfunction, so that when Kirk is beamed down to the surface of a planet, two "Kirks" arrive, one dressed in blue and the other in green. (One could make the same argument in terms of Bruno's WM duplication experiment.)

If, after transportation, the Kirks re-ascend to the Enterprise and each copy again transports down: being duplicated in the same way. After N iterations, there are 2^N Kirks on the surface of the planet. If each carries a notebook in which he has recorded the sequence of colours of his outfits, all possible binary sequences of B and G will be recorded in some book or the other. A simple application of the binomial distribution shows that the notebook records peak around sequences showing approximately equal numbers of blue and green outfits. This is experimental verification of the probability of p(blue) = 0.5 = p(green).

Now let us try to vary the probabilities, say to p(blue) = 0.9 and p(green) = 0.1. How do we do this?

OK, we transport Kirk and, with probability p = 0.9, we colour one of the uniforms blue. The other must, therefore, be coloured green. But then we simply have two Kirks on the surface of the planet, one in a blue uniform and one in a green uniform -- exactly as we had before. It is easy to see that, no matter how we imagine that we have changed the relative probabilities of uniform colours, we must always end up with just one blue uniform and one green uniform. Our attempt to change the probabilities has failed.

There is a way out, however. If, instead of simply duplicating the Kirks on transportation, the transporter manufactures 10 copies on the surface of the planet. Then we can suppose that 9 of these have blue uniforms, and the remaining Kirk is dressed in green. Iterating this procedure, we end up with 10^N Kirks on the surface of the planet, the vast majority of whom are dressed in blue. We have, thereby, changed the probability of a blue uniform for Kirk to 0.9 -- in the majority of cases.

The trouble with this is that such a scenario cannot be reproduced with the Schrodinger equation.

I agree.  That's why MWI advocates must resort to "weights", which are just amplitudes.  Or add some structure like an infinite or very large ensemble of already existing worlds that just get distinguished by results.

Don't you see that the argument I have made above shows that the idea of adding 'weights' to the branches does not work?: you cannot consistently graft the Born rule on to a model in which every possible outcome occurs on every trial. The set of 2^N possible branches resulting from N repetitions of the binary measurement is independent of the original amplitudes or weights.

If you define the frequency operator, like in Preskill’s course, or Selesnick book, or Graham in the DeWitt-Graham selected papers, there is arguably some explanation of why we have to weight the relatives states, or the Griffith-Omnes consistent and relative histories.

I think I made that point months ago -- it was, in effect, my starting point. The idea of a large ensemble of pre-existing worlds that just get distinguished by results has never been taken seriously by anyone outside of this list.

Nor in this list, I think. Except by you, perhaps. 

It has never been worked through in detail, and it is doubtful if it even makes sense. It certainly has nothing to do with the Schrodinger equation.

It has to do with the superposition principle. 

I suppose you can explore such ideas if you wish, but my purpose was more limited -- I merely wished to show that MWI as advocated by the likes of Carroll, Zurek, and Wallace, is incoherent. Since I have shown that adding weights, or multiplying branches, is inconsistent with the Born rule and/or the Schrodinger equation, I have made my point. All else is idle chatter.

I think that your argument only shows that a naive conception of “world” should be abandoned. That happens already when we assume only mechanism in the cognitive science, due to the mathematical fact that all universal machine state is accessed in infinitely many computations (in arithmetic).

Bruno

Bruce

If the universal wave function is represented by a vector in Hilbert space, for a two-outcome experiment the Hilbert space is two-dimensional, and we cannot fit 10 independent basis vectors into such a two-dimensional space. So the multiple branches for each outcome solution is not available in quantum mechanics. We might be able to dream up a theory in which this multiplication of branches would work, but that is not Everett, and it is not quantum mechanics as we know it. (Carroll and Zurek attempt to get around this by expanding the dimensionality of the operative Hilbert space by "borrowing" degrees of freedom from environmental decoherence. I doubt that this is actually convincing, or even possible. Whatever, it is a hopelessly ad hoc violation of the underlying dynamics.)

I can, therefore, see no way in which the Born rule can be made compatible with strictly deterministic Everettian Schrodinger evolution.

Note that (pace Bruno) this conclusion does not depend on any 1p/3p confusion. It depends only on the details of the assumed dynamics.

Bruce

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLTUxo8Jduo7fHeuAPpdNpbJ_b8SUoJhnAJOyanqQzomwA%40mail.gmail.com.

[Lawrence Crowell]

A part of what I was trying to point out earlier is that where MWI has some issues with the definition of probability and then by corollary issues with the Born rules is a tiny measure over possible sets of outcomes. I am not a primary exponent of MWI, just as I don't uphold any interpretation of QM, but I fail to see the fatal inconsistency that Bruce sees. There are issues with all interpretations, usually in the form of various addition assumptions required. The most notorious for the need of auxiliary assumptions if Bohm's QM. MWi requires we abandon strings of outcomes that are outliers in Bayesian statistics, such as a long sequence of the same outcomes. This was the point of my discussing the infinitesimal time intervals in a quantum oscillation when a probability is 0 or 1. However, these are measure ε and contribute little. Unless there is some singular point associated with these this should not be that fatal a problem. 

LC

[scerir]

BTW I've found that quote by Vaidman.

'In the framework of the MWI, the teleportation procedure does not move the quantum state: the state was, in some sense, in the remote location from the beginning. The correlated pair, which is the necessary item for teleportation, incorporates all possible quantum states of the remote particle, and, in particular, the state which has to be teleported. The local measurement of the teleportation procedure splits the world in such a manner that in each of the worlds the state of the remote particle differs form the state by some known transformation. The number of such worlds is relatively small. This explains why the information which has to be transmitted for teleportation of a quantum state—the information which world we need to split into, i.e., what transformation has to be applied—is much smaller than the information which is needed for the creation of such a state. For example, for the case of a spin-1/2 particle there are only 4 different worlds, so in order to teleport the state we have to transmit just 2 bits.' – Lev Vaidman in https://arxiv.org/abs/quant-ph/9810089

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLTkPzTANfkGUhF1YZ74oRktqeyTwLX8dC8ktnOqPeYoqA%40mail.gmail.com.

[Brent Meeker]

It's because Bruce takes the Born probability as the probability that some sequence exists (i.e. 1) instead of the probability it is the observed sequence, ( |a|^2 ).

Brent

[Brent Meeker]

Do you have a paper explaining this?

Brent

[Lawrence Crowell]

This is a reasonable account of teleporation.

LC

[John Clark]

On Sun, Sep 6, 2020 at 9:34 AM Bruno Marchal <mar...@ulb.ac.be> wrote:

>> I don't know what the hell to make of a "objective probability of a possible subjectivity”.

> I give you an example. A person is multiplied by 100 and put in 100 different, but identical from inside rooms. Just the number of the room differs, like in some hostel. You seem to agree that, as long as they stay in the room, there is only one person. But the copies are asked to open the room, and the person was asked, before the experience what is the probability that when going out of the room, its number is prime.

In that thought experiment there is no objective probability because John Clark is always in a prime numbered room or John Clark is not. So there is only subjective probability. There is a 100% chance John Clark will walk out, look at the number on the door and see a prime number, and a 100% chance he will not see a prime number. And the question "What is the probability I will see a prime number?" has no answer because in this hypothetical the personal pronoun "I" is ambiguous. 

However if you were to ask one of the individual John Clarks in one of those rooms AFTER the duplication "What is the probability you will see a prime number on the door when you walk out?" then that would be a legitimate unambiguous question, and the answer would be 25% because there are 25 prime numbers less than 100. But that probability would just be a subjective probability because he is either in a prime numbered room or he is not, So that probability figure must just be a measure of that John Clark's ignorance.

John K Clark

[Bruce Kellett]

On Mon, Sep 7, 2020 at 3:34 AM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

It's because Bruce takes the Born probability as the probability that some sequence exists (i.e. 1) instead of the probability it is the observed sequence, ( |a|^2 ).

That is the source of the disagreement. There are two possible questions: 1) In the N repeats of the binary outcome experiment, what is the probability that the sequence containing all ones will occur?; and 2) what is the probability in this scenario that I will experience the sequence of all ones?

If we are using the theory to calculate probabilities, the first question is the relevant one, and the theory gives two different answers , so the theory is inconsistent. If our concern is only about ourselves, and not about what the theory says, then the second question is the appropriate one. Then there is no inconsistency, because we know that we will only see one sequence -- which one we do see can only be determined post hoc, and that is not a probabilistic matter. The 1p/3p confusion here is all yours, not mine. What gives you the right to maintain that the Born rule is only about what you will experience? And not about objective probabilities?

Bruce

[Stathis Papaioannou]

An observer knows (under MWI) with certainty that some version of him will see a particular outcome, but he wants to know what the probability is that he will see that outcome. If you think that this is not a legitimate interest then it is more a psychological issue than a scientific one.

--

Stathis Papaioannou

--

Stathis Papaioannou

[John Clark]

On Sun, Sep 6, 2020 at 6:50 PM Bruce Kellett <bhkel...@gmail.com> wrote:

>> Bruce takes the Born probability as the probability that some sequence exists (i.e. 1) instead of the probability it is the observed sequence, ( |a|^2 ).

> That is the source of the disagreement. There are two possible questions: 1) In the N repeats of the binary outcome experiment, what is the probability that the sequence containing all ones will occur?

If all possible outcomes of N coin flips exist, as in the case in the set up to your question, then obviously the probability that one of those coin flips is all ones is 100%. It's the same answer as the answer to the question "If X exists then what is the probability that X exists?".

> and 2) what is the probability in this scenario that I will experience the sequence of all ones?

And that question has the same answer as "How long is a piece of string?".  It takes more than just the ASCII symbol "?" to make a question.

 John K Clark

 

[Bruno Marchal]

On 6 Sep 2020, at 19:53, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

Do you have a paper explaining this?

No. It is a recent finding. But it is almost trivial, the difficulties are in the "descriptive set theory". I have thought wrongly that allowing the full measure on the sigma_1(a) would make it trivial, but I was wrong. My intuition was based on the fact that the determinacy axioms is incompatible with the axioms of choice, but that is mitigated by the consistency of the axiom of choice and a restricted form of determinacy, called “projective determinacy” in set theory. It happens that mechanism seems to require only that restricted form of “determinacy”.

My paper:

Marchal B. The Universal Numbers. From Biology to Physics, Progress in Biophysics and Molecular Biology, 2015, Vol. 119, Issue 3, 368-381.

Get close to those issues, but to explain descriptive set theory require some amount of both topology and mathematical logic.

Bruno

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/5F5521FF.5080005%40verizon.net.

[Bruno Marchal]

On 6 Sep 2020, at 19:58, Lawrence Crowell <goldenfield...@gmail.com> wrote:

This is a reasonable account of teleporation.

I agree too, … except for minor technical details (already discussed with Bruce, and I guess Bruce will not be convinced by Vaidman, nor by my slight corrections, which is mainly that a quantum state always refer to infinity of worlds/histories/relative-states).

Bruno

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/0695c3ce-8d0b-48e5-b1a2-483a987cd64fn%40googlegroups.com.

[Bruno Marchal]

On 6 Sep 2020, at 20:40, John Clark <johnk...@gmail.com> wrote:

On Sun, Sep 6, 2020 at 9:34 AM Bruno Marchal <mar...@ulb.ac.be> wrote:

>> I don't know what the hell to make of a "objective probability of a possible subjectivity”.

> I give you an example. A person is multiplied by 100 and put in 100 different, but identical from inside rooms. Just the number of the room differs, like in some hostel. You seem to agree that, as long as they stay in the room, there is only one person. But the copies are asked to open the room, and the person was asked, before the experience what is the probability that when going out of the room, its number is prime.

In that thought experiment there is no objective probability because John Clark is always in a prime numbered room or John Clark is not. So there is only subjective probability. There is a 100% chance John Clark will walk out, look at the number on the door and see a prime number, and a 100% chance he will not see a prime number.

You make the same error than Bruce (curiously enough). Because all the alternative are realised, you take as 1 the probability that you feel them. But if we do the experience, those who see that the number is prime, or that it is not prime, can understand that the prediction asked, (which is a prediction on possible subjective experiences, and not on body localisation) cannot be 100% for prime. Indeed the John Clark of room 1, 4, 6, 8, 9, … admits that their prediction (on their subjective experiences) are wrong, and that is what makes those probabilities on subjective experiences objective. That are personally refutable, and unless you negate the conscious experience, they make sense.

And the question "What is the probability I will see a prime number?" has no answer because in this hypothetical the personal pronoun "I" is ambiguous. 

It is not ambiguous, or it is ambiguous in Everett too. The point is that it is the same “ambiguity”, i.e. indeterminacy of personal outcomes.

However if you were to ask one of the individual John Clarks in one of those rooms AFTER the duplication "What is the probability you will see a prime number on the door when you walk out?" then that would be a legitimate unambiguous question, and the answer would be 25% because there are 25 prime numbers less than 100.

In this case, there were no explicit duplication, as in the start they are all identical brain in the rooms, and you have agree that there is only one, non ambiguous person/consciousness.

Let me ask you this: do you agree that if I can predict with certainty that I will be indeterminate about what I will see after opening the door of the reconstitution box, then, I am unambiguously already indeterminate on that outcome? If yes, you can no mire say that there is a unique person, when two brains run identically. If not, you get the point.

But that probability would just be a subjective probability because he is either in a prime numbered room or he is not, So that probability figure must just be a measure of that John Clark's ignorance.

Which is the same as the one before the multiplication, as we have accepted that all copies are continuation of the candidate (we use the non transitive notion of personal identity on which we have always agreed on).

In your sense of “subjective probability” here, Mechanism makes all probability subjective, even the frequentist notion, despite it is also an observable (after Graham-Hartle-Omnes-Griffith type of treatment).  I have no problem with that. By objective, we can mean here 3p, or 1p-plural. That does not change the probability calculus.

Bruno

John K Clark

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv374jtaN-qwF4t6sw1PcN-1DtZpVRK%3DGNP%2BeCLSF-iknw%40mail.gmail.com.

[Bruno Marchal]

On 7 Sep 2020, at 00:49, Bruce Kellett <bhkel...@gmail.com> wrote:

On Mon, Sep 7, 2020 at 3:34 AM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

It's because Bruce takes the Born probability as the probability that some sequence exists (i.e. 1) instead of the probability it is the observed sequence, ( |a|^2 ).

That is the source of the disagreement. There are two possible questions: 1) In the N repeats of the binary outcome experiment, what is the probability that the sequence containing all ones will occur?; and 2) what is the probability in this scenario that I will experience the sequence of all ones?

If we are using the theory to calculate probabilities, the first question is the relevant one,

?

and the theory gives two different answers , so the theory is inconsistent.

No, the theory is inconsistent here, only if you negate the distinction between 3p and 1p. 

If our concern is only about ourselves, and not about what the theory says, then the second question is the appropriate one. Then there is no inconsistency, because we know that we will only see one sequence —

Good!

which one we do see can only be determined post hoc, and that is not a probabilistic matter. The 1p/3p confusion here is all yours, not mine. What gives you the right to maintain that the Born rule is only about what you will experience? And not about objective probabilities?

Define “objective probabilities”. It is clearly in a stronger sense than the one I have given and used  in this thread, and I am not sure what you are talking about. I am not sure your “objective probability” makes sense. I would say that the Boin rules, and their constant verification, is what makes those probabilities objective, because, like with Mechanism, no machine can know which fine-grained histories she is living, among an infinity (realised in arithmetic, notably).

Bruno

Bruce

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLRjVMNg8oNs3uTgNb4MyQPr9QCTXTG6jGZwowmc%3D47soA%40mail.gmail.com.

[Bruno Marchal]

On 7 Sep 2020, at 13:06, John Clark <johnk...@gmail.com> wrote:

On Sun, Sep 6, 2020 at 6:50 PM Bruce Kellett <bhkel...@gmail.com> wrote:

>> Bruce takes the Born probability as the probability that some sequence exists (i.e. 1) instead of the probability it is the observed sequence, ( |a|^2 ).

> That is the source of the disagreement. There are two possible questions: 1) In the N repeats of the binary outcome experiment, what is the probability that the sequence containing all ones will occur?

If all possible outcomes of N coin flips exist, as in the case in the set up to your question, then obviously the probability that one of those coin flips is all ones is 100%. It's the same answer as the answer to the question "If X exists then what is the probability that X exists?”.

Except that when you look at the outcome, you are yourself multiplied, and so, in the 3p description, you experience all sequences. Yet, you will never experience all sequences, but only one of them, from your personal subjective pov, so, once you understand that the question is about those pov, the objective probability, on the subjective experience, is logically unavoidable.

> and 2) what is the probability in this scenario that I will experience the sequence of all ones?

And that question has the same answer as "How long is a piece of string?".  It takes more than just the ASCII symbol "?" to make a question.

Only because you mix the 1p description (about which we are asking), and the 3p global description, in which indeed there is no probabilities at all.

Bruno

 John K Clark

 

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

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv0aGQqyYknHW6vP%2B8g8q5bL8kL_K%2B2qyf0EUSGqCs%2BEoQ%40mail.gmail.com.

[John Clark]

On Mon, Sep 7, 2020 at 9:29 AM Bruno Marchal <mar...@ulb.ac.be> wrote:

>> In that thought experiment there is no objective probability because John Clark is always in a prime numbered room or John Clark is not. So there is only subjective probability. There is a 100% chance John Clark will walk out, look at the number on the door and see a prime number, and a 100% chance he will not see a prime number.

> You make the same error than Bruce (curiously enough). Because all the alternative are realised, you take as 1 the probability that you feel them.

And you make the exact same error over and over and over and over again!  If I made a mistake in the above it certainly wasn't that one because I said absolutely nothing about what Mr.You would or would not do or say or think, and could not even if I wanted to because due to the circumstances of the thought experiment the personal pronoun "you" has no referent, so any "question" using that word has no answer because it is not a question, it's just some words and a question mark.

>> However if you were to ask one of the individual John Clarks in one of those rooms AFTER the duplication "What is the probability you will see a prime number on the door when you walk out?" then that would be a legitimate unambiguous question, and the answer would be 25% because there are 25 prime numbers less than 100.

> In this case, there were no explicit duplication,

Exactly, and therefore the personal pronoun "you" would not be ambiguous.so a question that started as "what would you" would not automatically be an ambiguous question.

> Let me ask you this: do you agree that if I can predict with certainty that I will be [...]

I don't need to read another word. No I do not agree, and I don't disagree either because gibberish is not the sort of thing one can agree or disagree with, it's just gibberish. 

John K Clark

[Stathis Papaioannou]

The probability of interest is that one particular John Clark will see a prime number, not that some John Clark will see a prime number. A gambler who buys a lottery ticket is interested in the probability that one particular gambler will buy the winning ticket, not the probability that some gambler will buy the winning ticket, which he knows is 1 if all the tickets are sold.

 

[Bruce Kellett]

On Tue, Sep 8, 2020 at 8:49 AM Stathis Papaioannou <stat...@gmail.com> wrote:

On Mon, 7 Sep 2020 at 04:41, John Clark <johnk...@gmail.com> wrote:

On Sun, Sep 6, 2020 at 9:34 AM Bruno Marchal <mar...@ulb.ac.be> wrote:

>> I don't know what the hell to make of a "objective probability of a possible subjectivity”.

> I give you an example. A person is multiplied by 100 and put in 100 different, but identical from inside rooms. Just the number of the room differs, like in some hostel. You seem to agree that, as long as they stay in the room, there is only one person. But the copies are asked to open the room, and the person was asked, before the experience what is the probability that when going out of the room, its number is prime.

In that thought experiment there is no objective probability because John Clark is always in a prime numbered room or John Clark is not. So there is only subjective probability. There is a 100% chance John Clark will walk out, look at the number on the door and see a prime number, and a 100% chance he will not see a prime number. And the question "What is the probability I will see a prime number?" has no answer because in this hypothetical the personal pronoun "I" is ambiguous. 

However if you were to ask one of the individual John Clarks in one of those rooms AFTER the duplication "What is the probability you will see a prime number on the door when you walk out?" then that would be a legitimate unambiguous question, and the answer would be 25% because there are 25 prime numbers less than 100. But that probability would just be a subjective probability because he is either in a prime numbered room or he is not, So that probability figure must just be a measure of that John Clark's ignorance.

The probability of interest is that one particular John Clark will see a prime number,

How do you avoid the clear dualist implications of this? What is it that singles out the particular John Clark in whom you are interested?

Bruce

[Stathis Papaioannou]

On Tue, 8 Sep 2020 at 09:06, Bruce Kellett <bhkel...@gmail.com> wrote:

On Tue, Sep 8, 2020 at 8:49 AM Stathis Papaioannou <stat...@gmail.com> wrote:

On Mon, 7 Sep 2020 at 04:41, John Clark <johnk...@gmail.com> wrote:

On Sun, Sep 6, 2020 at 9:34 AM Bruno Marchal <mar...@ulb.ac.be> wrote:

>> I don't know what the hell to make of a "objective probability of a possible subjectivity”.

> I give you an example. A person is multiplied by 100 and put in 100 different, but identical from inside rooms. Just the number of the room differs, like in some hostel. You seem to agree that, as long as they stay in the room, there is only one person. But the copies are asked to open the room, and the person was asked, before the experience what is the probability that when going out of the room, its number is prime.

In that thought experiment there is no objective probability because John Clark is always in a prime numbered room or John Clark is not. So there is only subjective probability. There is a 100% chance John Clark will walk out, look at the number on the door and see a prime number, and a 100% chance he will not see a prime number. And the question "What is the probability I will see a prime number?" has no answer because in this hypothetical the personal pronoun "I" is ambiguous. 

However if you were to ask one of the individual John Clarks in one of those rooms AFTER the duplication "What is the probability you will see a prime number on the door when you walk out?" then that would be a legitimate unambiguous question, and the answer would be 25% because there are 25 prime numbers less than 100. But that probability would just be a subjective probability because he is either in a prime numbered room or he is not, So that probability figure must just be a measure of that John Clark's ignorance.

The probability of interest is that one particular John Clark will see a prime number,

How do you avoid the clear dualist implications of this? What is it that singles out the particular John Clark in whom you are interested?

Nothing singles him out, one is picked at random out of the 100, and the question is asked, what is the probability that this particular one will see a prime number? This is a different question to what is the probability that some John Clark will see a prime number. You are saying that the first question is - what? - boring, invalid, incomprehensible?

--

Stathis Papaioannou

[Bruce Kellett]

The question of dualism arises more acutely from the 1p perspective: "if I am duplicated in the 100 rooms, what is the probability that I will see a prime number?" Take a random selection from the 100: will that one be me? If, for any possible selection, the answer is "yes, that will be me" (all the copies are "me"), then the probability that "I" will see a prime is one, since 25 of the "mes" will see primes. If only one selection will give me, then you have dualism, and a 25% chance that I will see a prime. In your account above, the selection is equivalent to just asking "if I select a room at random, what is the probability that the door will have a prime number?" The fact that there is a copy of JC in the room becomes irrelevant to the probability, which is simply determined by the ratio of the number of primes to the number of doors.

Bruce

[Stathis Papaioannou]

Dualism is the idea that there is a spirit separate from the body. If I am duplicated, there will be many versions of me. If I ask, “am I a version that sees a prime number?” that does not entail that I am a spirit separate from the body. If I ask “what is the probability that after duplication I will be a version that sees a prime number?” that also does not entail that I am a spirit separate from the body. As you say, the fact that there is a person who identifies as being me in the room does not make any difference to the calculation, and that is the probability I am interested in. I may be interested in this number, for example, if I am going to bet on whether I will see a prime number after duplication. If I have the opportunity to bet $20 for a $100 reward if I see a prime number I will accept the bet, whereas if I have to bet $30 for a $100 reward I will not.

--

Stathis Papaioannou

[John Clark]

On Mon, Sep 7, 2020 at 6:49 PM Stathis Papaioannou <stat...@gmail.com> wrote:

> The probability of interest is that one particular John Clark will see a prime number, not that some John Clark will see a prime number. A gambler who buys a lottery ticket is interested in the probability that one particular gambler will buy the winning ticket, not the probability that some gambler will buy the winning ticket

 

BEFORE the duplication "one particular John Clark" and "some John Clark" are exactly the same person, that is Bruno's Mr.You, that is the person Bruno makes his bet with. Thus AFTER the duplication the identity of Mr.You becomes completely ambiguous, there is now no way to tell who he made the bet with, or how to determine the outcome and figure out who won and who lost. And that's why Bruno loves personal pronouns so much and refuses to stop using them, they can be used to sweep logical contradictions and absurdities under the rug, and that can be very useful if the towering logical edifice of your theory is built on a foundation of sand. The only way Bruno can stop using personal pronouns is by means of Bruno's patented peepee terminology and start talking about THE First Person Perspective, when of course after the duplication there is no such thing as THE First Person Perspective, there is only A First Person Perspective.

> Nothing singles him out, one is picked at random out of the 100,

But this entire thought experiment Is about what "you" can predict BEFORE the duplication, Back then nobody can single anybody out because there is only one John Clark. And this thought experiment is about what "you" can expect to see, so the gambler must be Mr.You, so the gambler is also duplicated 100 times. 

> and the question is asked, what is the probability that this particular one will see a prime number? 

I can predict today with 100% certainty that tomorrow AFTER the duplication when the John Clark in room #11 walks out turns around and looks at the number on his door he will see a prime number, but that is a very VERY long way from the original ambiguous question that was asked BEFORE the duplication, namely "AFTER the duplication what is the probability "you" will see a prime number?".  And that has no answer because it is not a question, it's gibberish.

 John K Clark

[Stathis Papaioannou]

I think what you and Bruce Kellett are perhaps objecting to is the dualist idea that there is a unique John Clark soul, with the question of probability with duplicates implicitly asking which one of the duplicates this soul will fly into. We know that souls are delusional, and this applies to a single world situation also. If you survive the night, it means that an entity identifying as John Clark wakes up in your bed tomorrow morning, not that your soul has persisted in the one body. If there are 100 John Clarks tomorrow then John Clark has survived, because all it takes is one, and there is a 25/100 probability that a randomly chosen John Clark will see a prime number. This is the non-delusional interpretation of the question “what is the probability that you will see a prime number?”. The “you” cannot refer to a magical soul, because such a thing never existed in the first place.

[Bruce Kellett]

I am certainly objecting to the perceived dualist assumption in your response to the question (asked before duplication): "What is the probability that you will see a prime number on your door when you wake tomorrow?". As JC points out, by tomorrow there will be 100 individuals in the frame. Who is the "You" to whom you posed the question yesterday? If the question in that form has an answer, then you must assume that just one of the 100 individuals next morning has inherited the soul of JC, and is the person to whom you originally referred. By subtly changing the question so that you refer only to asking the question of some random individual the next morning, you avoid this dualist implication by essentially saying that the initial "You" referred to, is the random individual you selected in the morning. If the two questions are to be related at all, then you must make the dualist assumption.

I agree with you that such dualist assumptions are unacceptable, so I conclude that your initial question has no answer. When you ask JC on the night before duplication: "What is the probability that you will see a prime number in the morning?" that question has no answer, because there is no unique referent of "You" tomorrow morning after duplication.

Bruce

[Stathis Papaioannou]

I have given you the non-dualist interpretation of the question: "what is the probability that you will see a prime number tomorrow" is "what is the probability that a randomly chosen John Clark will see a prime number". Perhaps some people assume that a magical soul will fly into one, and only one, of the John Clarks, but they are wrong, just as they are wrong about a magical soul persisting in a single John Clark waking up in his bed normally, ensuring that it is him and not someone who merely believes he is him.

--

Stathis Papaioannou