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> 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.
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: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.
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.
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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.
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,
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.
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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.
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.
> 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
> the chance that the Yankees will win is independent of what we happen to think about it.
> in Everett, the low probability worlds always occur with probability one.
> always occur with probability one.
> 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,
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> If there are an infinite number then frequency is ill defined
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?
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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 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
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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 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.
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.
The twisting and turning we are seeing by participants on this list is not going to alter this basic observation.
Bruce
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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.
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.
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
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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.
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.
John K Clark
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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.
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
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
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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.
In other words, the theory is intrinsically self-contradictory -- incoherent.
Bruce
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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.
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
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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 resultIf 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
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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.
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
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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.
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This does not happen in the genuine stochastic case, where only one (random) sequence is produced.BruceBrent
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
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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.
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.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
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> 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 [...]
>> 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?
>> 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.
> we distinguish the 3P and 1P [...]
If Everett is right then "John K Clark" can see both, but "I" can not.
John K Clark
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
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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
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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%.
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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
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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.
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.
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.
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.
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.
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
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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.
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.
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.
> 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.
> You're saying that since Everett says some sequence occurs he is predicting it with probability 1.
> 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 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
> The Born rule predicts low probability for certain sequences,
> Everett predicts that such sequences necessarily occur.
> the charge is one of inconsistency
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.
> 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
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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
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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
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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 ?
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
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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”.
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%.
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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.
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
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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.
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).
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
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
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BTW I've found that quote by Vaidman.
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>> 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.
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 ).
>> 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?
On 6 Sep 2020, at 19:53, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:Do you have a paper explaining this?
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On 6 Sep 2020, at 19:58, Lawrence Crowell <goldenfield...@gmail.com> wrote:This is a reasonable account of teleporation.
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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.
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.
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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.
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
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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?”.
> 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
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>> 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.
>> 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,
> Let me ask you this: do you agree that if I can predict with certainty that I will be [...]
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,
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?
> 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
> 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?