Is MWI Self-Contradictory and Does Time Travel Need a New Approach?

[Fyzix]

I create this thread to discuss the different objections to MWI.
Hopefully creating some interresting debate.

First I'd like to start with the Born Rule.

What are the views of proponents and opponents of MWI on this?

 

[A. Neumaier]

I create this thread to discuss the different objections to MWI.

My objections are formulated in the entries '' Circularity in Everett's measurement theory'' and ''On the Many-Worlds-Interpretation'' in Chapter A4 of my theoretical physics FAQ at http://arnold-neumaier.at/physfaq/physics-faq.html#everett

Hopefully creating some interresting debate.

First I'd like to start with the Born Rule.

What are the views of proponents and opponents of MWI on this?

You should first provide yourself the information you know rather than ask others to do all the work for you.

 

[Demystifier]

We already had a thread with a similar subject
https://www.physicsforums.com/showthread.php?t=364063
where I already said what I think about it.

 

[Fyzix]

How exactly does your argument differ from the following:

Instead of Schroedinger's Cat, we have Hilary Putnam's Light Bulps.

1 RED and 1 BLUE

10% chance of the red being turned on, 90% chance of the blue on being turned on.
After performing this a hundred times, we get 90 blue ones and 10 red ones, if not QM would have been falsified.

So how does this relate to MWI?
Well in MWI the worlds "split" at each possible outcome, so essentially this becomes a 50-50% probability.
After conducting this experiment which can only have 2 outcomes at a time, we should expect in MWI to have 50 red and 50 blueones.

Now this is the gist of the basic argument against MWI that most physicists and philosophers hold, but from what I gather you hold a slightly different position, yet I can't seem to quite figure out exactly what this is?

 

[Hurkyl]

Well in MWI the worlds "split" at each possible outcome, so essentially this becomes a 50-50% probability.
...
Now this is the gist of the basic argument against MWI that most physicists and philosophers hold,

This is a ridiculously bad argument. It's usually told in joke form, e.g. some form of:

There are two possible outcomes of playing the lottery: either you win, or you won't. Therefore you have a 50% of winning if you play!​

 

[Fyzix]

No...

This is the ridiculous reality demonstrating the falsehood of MWI.

If there will always be 2 outcomes of a certain experiment, ONLY 2 different outcomes.
What happens after conducting the experiment once?

1 blue 1 red

twice?
another 1 blue 1 red world

It's just MWI taken seriously.

It's weird you decide to comment on a thread regarding MWI if you are not aware of the number one argument against it.

 

[Demystifier]

Two points:

1. I partially agree with Hurkyl: if there are only two possible outcomes, it does not necessarily mean that each of them is equally probable.

2. Yet, the example of Hurkyl is not completely fair, because "to loose in lottery" actually corresponds to many possible different outcomes.

MWI people are, of course, aware of both points above (as is Hurkyl, I'm convinced). Essentially, they try to argue that larger |psi|^2 somehow corresponds to a larger number of different possible outcomes - and hence to a larger probability. But they cannot find a convincing argument for that without taking some additional assumptions. This is not necessarily wrong, but additional assumptions make the whole MWI idea less attractive. Not necessarily because these assumptions by themselves are not attractive (it is a matter of taste), but because MWI usually proclaims the smallest number of assumptions as its main virtue with respect to other interpretations. The smallest number of assumptions is indeed a virtue, but with the smallest number of assumptions the Born rule cannot be explained. To explain it one necessarily must introduce additional ones, but then MWI is no longer better than other interpretations, as long as quality of an interpretation is measured by the inverse number of assumptions.

 

[Demystifier]

If there will always be 2 outcomes of a certain experiment, ONLY 2 different outcomes.
What happens after conducting the experiment once?

1 blue 1 red

Oh, now I see where the mistake in your reasoning is. If there are two different outcomes, what happens after conducting the experiment once? Your answer is wrong, and the correct answer is

1 blue OR 1 red

In other words, only one of the outcomes will appear (according to MWI) to one experimentalist, not both of them. In your argument you count the frequencies in the whole multiworld, but it is not what the Born rule is supposed to describe. To count what the Born rule is really supposed to describe (successfully or not), you should count frequencies appearing to one experimentalist only.

 

[Fyzix]

Nono, ofcourse I don't think the experimentalist will see both.

he splits just like whole world including the experiment.
However,

Pre-experiment you got:

1 Experimenter
A experiment with 2 possible outcomes

After the experiment

You got 2 experimenters each observing one of the 2 outcomes.
They repeat the experiment and this occurs again.

However unless MWI ASSUMES that there is something very special about consciousness that makes the universe somehow put the observers in the universe which would then correspond to the correct probability, they will see 50/50.

It's that simple.

Just draw it on a piece of paper and you will understand exactly what I mean (this thought experiment is Putnam's not mine originally).

 

[Fyzix]

Also, I'm well aware of the fact that Deutsch and Wallace thinks this can be solved by desicion-theoretic approach.

However most disagree strongly with this and there are tons of litterature explaining just why this fails (Adrian Kent, Peter Lewis, Hemmo Meir, Jacques Mallah, David Albert etc. etc. etc.).

However Demystifier, what exactly are the simplest way to show why MWI fails with born rule in your opinion? As I don't really see the difference.

 

[Dmitry67]

"why this fails" is based on faulty assumptions - we had discussed it many times :)

 

[Fyzix]

"why this fails" is based on faulty assumptions - we had discussed it many times :)

I was under the impression that you too realized this problem?
Otherwise, why don't you just fully adopt the Deustch-Wallace approach instead of some mystic consciousness approach?

If by "faulty assumptions" you mean, that there is actually 2 worlds with 2 outcomes after the experiment, then sure.

 

[Dmitry67]

My quote was about other critics you will probably use later (about "splitting the worlds" etc)

I admit that there is a problem with the Born rule. To begin with, I don't know how to even formulate Born rule is the MWI framework. This is why I tend to believe that this is an illusion (like a very special moment 'NOW', which is also not explained by physics). But of course it is not an explanation, rather than a "stub" for a future one.

 

[Fyzix]

My quote was about other critics you will probably use later (about "splitting the worlds" etc)

I admit that there is a problem with the Born rule. To begin with, I don't know how to even formulate Born rule is the MWI framework. This is why I tend to believe that this is an illusion (like a very special moment 'NOW', which is also not explained by physics). But of course it is not an explanation, rather than a "stub" for a future one.

Aha, so have you read and understood Deutsch/Wallace's approach through?

I think it's a bit unfair that you are saying that these arguments we have discussed in PM's are based on false assumptions.

I will have to ask the authors for permission for citing any of them public.
However quite a few "pro-Everettian"s actually feel the exact same way, that you need to add something to the "bare idea" to get a coherent hypothesis.

 

[Dmitry67]

It would be very nice to have quotes. Also, I suggest clearly stating what are we discussing: Born rule or something else - otherwise it could be a mess.

Regarding the Born rule - can anyone formulate Born rule in the MWI framework? Before solving a problem, sometimes it is useful to read the description of the problem.

 

[Demystifier]

However Demystifier, what exactly are the simplest way to show why MWI fails with born rule in your opinion?

I have already answered it several times.

As I don't really see the difference.

The difference is that you think that MWI contradicts Born rule, while I only think that MWI cannot explain the Born rule. Do you see a difference now?

 

[Demystifier]

However unless MWI ASSUMES that there is something very special about consciousness that makes the universe somehow put the observers in the universe which would then correspond to the correct probability, they will see 50/50.

It's that simple.

It may be simple to you, but to me (and not only to me) your argument is totally vague.

Just draw it on a piece of paper and you will understand exactly what I mean (this thought experiment is Putnam's not mine originally).

Again, you should give the source, so that we can judge by ourselves whether the Putnam's argument is really identical to yours. (I would bet it isn't.)

 

[Fyzix]

I have already answered it several times.


The difference is that you think that MWI contradicts Born rule, while I only think that MWI cannot explain the Born rule. Do you see a difference now?

Not really, could you make another simple example?

 

[Fyzix]

It may be simple to you, but to me (and not only to me) your argument is totally vague.


Again, you should give the source, so that we can judge by ourselves whether the Putnam's argument is really identical to yours. (I would bet it isn't.)

Unfortunately the paper isn't free online.
He just gave me the example a long time ago...

Most other physicists I've talked to agree though, that this shows what MWI's main problem is.

Let me ask you this: do you buy the desicion-theoertic approach?
If that's the case, I understand better why you don't accept this argument.

 

[Demystifier]

Not really, could you make another simple example?

Sure.

The assumption that there is life outside the planet Earth cannot explain why humans have 2 legs. Yet, that assumption does not contradict the fact that humans have 2 legs.

 

[Demystifier]

Let me ask you this: do you buy the desicion-theoertic approach?

Yes and no. I accept that from the assumptions taken in this approach the Born rule can be derived. Yet, I do not accept the assumptions themselves.

More precisely, I do not accept one of these assumptions, not because I can prove that this assumption is wrong, but because this assumption is too artificial and taken ONLY for the purpose of getting the Born rule. This is nicely explained in
http://xxx.lanl.gov/abs/0808.2415

 

[Fyzix]

Sure.

The assumption that there is life outside the planet Earth cannot explain why humans have 2 legs. Yet, that assumption does not contradict the fact that humans have 2 legs.

I'm not really sure how this relates to probability ?!
Maybe I'm missing something obvious in your anology.

 

[Demystifier]

I'm not really sure how this relates to probability ?!

It doesn't. It relates to the difference between "contradicts" and "cannot explain".

 

[Fyzix]

So your main born rule argument is that MWI can't explain where it came from?

However you disagree with the majority that says MWI has evn deeper problems in regards to Born Rule?

 

[Demystifier]

So your main born rule argument is that MWI can't explain where it came from?

However you disagree with the majority that says MWI has evn deeper problems in regards to Born Rule?

Yes.

 

[Fyzix]

How exactly does Bohm explain where it came from though?

 

[Demystifier]

I'm not really sure how this relates to probability ?!

Here is a more useful analogy:

Assume that we have 2 tunnels (a red tunnel and a blue tunnel), and that some sort of consciousness is present in both of them. Assume that we know almost nothing about the nature of that consciousness. (Are there additional beings in tunnels which are conscious about tunels? Or are tunnels themselves self-conscious? We simply don't know.) All we know is that each consciousness is conscious about one tunnel only.

Now we ask the following question: What is the probability that a consciousness is in the red tunnel?

If Fyzix were right, then the answer would be unique: the probability is 50%. This, indeed, is not a stupid answer at all. It is the most reasonable guess. Yet, it's not the only possibility. In particular, as we know almost nothing about the nature of consciousness, various possibilities are conceivable. For example, maybe the red tunnel contains a larger number of conscious beings, so it is more likely that a randomly chosen consciousness is from the red tunnel. Or maybe ... well, use your imagination. The point is that, from the assumptions given, we cannot exclude a possibility that the probability of the red tunnel is different from 50%.

 

[Demystifier]

How exactly does Bohm explain where it came from though?

It explains it dynamically. It starts from an arbitrary probability distribution of particle positions at initial time and explores its evolution. It turns out that, in most cases, after some time the distribution reaches an equilibrium distribution which turns out to be equal to the Born-rule one. Moreover, ones the system reaches the equilibrium, it stays there forever. More generally, ones the system reaches a close-to-equilibrium distribution, it stays close to that most of the time.

 

[Fyzix]

Here is a more useful analogy:

Assume that we have 2 tunnels (a red tunnel and a blue tunnel), and that some sort of consciousness is present in both of them. Assume that we know almost nothing about the nature of that consciousness. (Are there additional beings in tunnels which are conscious about tunels? Or are tunnels themselves self-conscious? We simply don't know.) All we know is that each consciousness is conscious about one tunnel only.

Now we ask the following question: What is the probability that a consciousness is in the red tunnel?

If Fyzix were right, then the answer would be unique: the probability is 50%. This, indeed, is not a stupid answer at all. It is the most reasonable guess. Yet, it's not the only possibility. In particular, as we know almost nothing about the nature of consciousness, various possibilities are conceivable. For example, maybe the red tunnel contains a larger number of conscious beings, so it is more likely that a randomly chosen consciousness is from the red tunnel. Or maybe ... well, use your imagination. The point is that, from the assumptions given, we cannot exclude a possibility that the probability of the red tunnel is different from 50%.

Well, then we are over in a different realm I think.
It seems you are suggesting that if the probability is way higher in the red tunnel versus the blue one, there may be more observers there.
This would suggset that the world does not branch into 2 worlds, but way more for the red one than the blue one at each initial experiment.
This is a completely new assumption and is very hard to back up.
How are you to say "this is enough to make 1 world, this isn't enough, this is enough to make 50,7 worlds" etc. what the **** is a .7 world? A half alive world?

I don't think this is what they have in mind with the desicion-theoretic approach at all..

 

[Fyzix]

It explains it dynamically. It starts from an arbitrary probability distribution of particle positions at initial time and explores its evolution. It turns out that, in most cases, after some time the distribution reaches an equilibrium distribution which turns out to be equal to the Born-rule one. Moreover, ones the system reaches the equilibrium, it stays there forever. More generally, ones the system reaches a close-to-equilibrium distribution, it stays close to that most of the time.

Ah, thanks.
However why can't MWI ever reach this equilibrium?

 

[Demystifier]

This would suggset that the world does not branch into 2 worlds ...

No, this would only suggest that consciousness is not described by MWI.

I don't think this is what they have in mind with the desicion-theoretic approach at all..

You are right. But both approaches (my example with consciousness and the decision-theoretic approach) have something in common: Both have SOME additional assumptions (not spelled out in the minimal set of axioms common to all variants of MWI). That's why I say that MWI could be right (or wrong), but it can't be complete.

 

[Demystifier]

Ah, thanks.
However why can't MWI ever reach this equilibrium?

Because it does not have the particles the distribution of which could have this (or any other) distribution. Of course, you can add particles to MWI as an additional axiom (as I repeated a million times, any variant of MWI needs some additional axioms/assumptions) and then explain the Born rule easily, but once you do that you cease to be an orthodox MWI believer and become a member of an unorthodox MWI church, the members of which like to call themselves Bohmians.

 

[A. Neumaier]

It explains it dynamically. It starts from an arbitrary probability distribution of particle positions at initial time and explores its evolution. It turns out that, in most cases,

... only in most cases of the few thousand simulations done so far, for extremely simple (but not too simple) systems. As we had seen in another discussion

If the Boltzmann's H-therorem were any evidence for the universe being in global equilibrium then we would observe this global equilibrium - which means we wouldn't exist, contradiction.

Thus the Boltzmann's H-therorem is no evidence at all evidence for reaching global equilibrium, and because you agreed to the first part of my statement, you have also no evidence for that the state of the universe reached quantum equilibrium in BM.

there is not the slightest trace of a proof that it does so in most cases realized in Nature.

after some time the distribution reaches an equilibrium distribution which turns out to be equal to the Born-rule one.

 

[Hurkyl]

Regarding the Born rule - can anyone formulate Born rule in the MWI framework? Before solving a problem, sometimes it is useful to read the description of the problem.

The literal statement is sort of a trivial one; the Born rule as it relates to propensity is already built-in to the linear algebra used by quantum mechanics. e.g. in the relationship between density matrices and kets, or in the partial trace.

The more interesting question is can we connect to other interesting things. Here's one possible way to cast probabilities as being frequentist probabilities in a decoherence-based interpretation.

e.g. let [itex]v_1[/itex] be a pure quantum state of a qubit. As usual in QM, we use [itex]v_2 = v_1 \otimes v_1[/itex] to describe a system that contains two independent copies of [itex]v_1[/itex], and so forth -- [itex]v_n = v_{n-1} \otimes v_1[/itex] is a state that describes n independent copies of a qubit in state [itex]v_1[/itex].

Let S be an observable on a qubit with basis vectors A and B.

Now, let [itex]T_{n, p, \epsilon}[/itex] be the operator that acts on n-qubit states with eigenvalues 0 and 1, whose action on basis states (relative to S) is multiplication by:

• 1, if the proportion of A's in the basis state is in the interval [itex](p -\epsilon, p+\epsilon)[/itex]
• 0 otherwise

(So T represents an experiment to detect if the proportion of n trials is near p)

With this, there is a projection P (a partial trace) from n-qubit states to (possibly impure) 1-qubit states that discards everything except the one bit of information related to T.

One can now state the frequentist probability as saying the claim "a measurement of [itex]v_1[/itex] gives A with probability p" is the claim that

[tex]\lim_{n \to \infty} P\left( T_{n, p, \epsilon} v_n \right)[/tex]
converges to the eigenstate |1>.

(For simplicity in the above, I've written states as kets when possible -- but I'm not really working in the Hilbert space of kets)​

 

[Fyzix]

No, this would only suggest that consciousness is not described by MWI.

Only?
So you are saying that this only suggests that you have to make the additional assumption that consciousness is infact not part of the wavefunction?
I would say this is worse than copenhagen!

You are right. But both approaches (my example with consciousness and the decision-theoretic approach) have something in common: Both have SOME additional assumptions (not spelled out in the minimal set of axioms common to all variants of MWI). That's why I say that MWI could be right (or wrong), but it can't be complete.

When you say "it can be right or wrong, but it can't be complete", what exactly do you mean?
I understand that you regard Bohm as a "MWI"-ish interpretation, so I gues this is what you mean by "could be right", but that the bare theory can't be right?