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

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

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

Now, let $T_{n, p, \epsilon}$ 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 $(p -\epsilon, p+\epsilon)$
• 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 $v_1$ gives A with probability p" is the claim that

$$\lim_{n \to \infty} P\left( T_{n, p, \epsilon} v_n \right)$$
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?

 

[Hurkyl]

Many world supporters.. so what do you think is the most promising approach to solve the "Measure" problem in Many Worlds

Note that a "solution" for MWI is a solution for pretty much any interpretation. (Since MWI is a theory of wavefunctions undergoing unitary evolution, a feature that appears in most interpretations of quantum mechanics)

IMO a large portion of the problem is just psychological -- that people have trouble accepting a solution that is observationally indistinguishable from definite outcomes without actually having definite outcomes.

We don't have to dive into quantum mechanics to wrap our heads around the idea of indefinite outcomes -- the idea already exists in terms of a statistical ensemble. An observer "inside" the ensemble cannot infer any information about the ensemble, including whether or not it's a trivial ensemble with just one component. So all that's left, psychologically, is to wrap your head around the idea of an ensemble really being the state of reality, rather than being a collection of (possibly hypothetical) subsystems of reality.


Once you can accept indefinite outcomes, the potential solution space to the measurement problem becomes much larger -- e.g. subsystems in mixed states become a good substitute for the notion of a physical collapse. Now, the question becomes:

1. Does unitary evolution cause subsystems to transition into mixed states compatible with the observation of apparent collapse?
2. Can we effectively study mixtures? (e.g. by decomposing into individual components and studying those, or maybe thermodynamically)

Aside: classically, it is justifiable to reject this line of thought due to Occam's razor, because the components perfectly fail to interact. But when applied in QM, the razor only really implies the need for a theory of quantum thermodynamics.

 

[Fyzix]

Hurkyl: no it's not psychological at all.
It may be for some layman down the street, but not for scientists and philosophers.

If you partake in this discussion you will see the born/probability problems.
Not to mention in the bare theory of MWI you don't get determinate outcomes at all...

You can't count branches in it, because there is no determinate way to say "here starts world X".

From your naive optimism that MWI has no problems, I guess you are a MWI proponent?

 

[Hurkyl]

Hurkyl: no it's not psychological at all.
It may be for some layman down the street, but not for scientists and philosophers.

Education does not free one from biased viewpoints. There's even a famous quote:

Science progresses one death at a time​

Not to mention in the bare theory of MWI you don't get determinate outcomes at all...

This fact is central to my point -- I think you've severely misunderstood what I was saying.

 

[Fyzix]

no, from what I've seen you are advocating for MWI / born rule.
yesterday you claimed that my example of why branch counting doesn't work was the same as playing lotto and thinking it was 50-50 if you win or not.
If I'm mistaken, please elaborate.

 

[Demystifier]

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?

Yes.

 

[Fyzix]

Demystifier: You said something about MWI not being able to explain consciousness?
What did you mean?

 

[Demystifier]

Demystifier: You said something about MWI not being able to explain consciousness?
What did you mean?

I mean that no current theory in physics can explain consciousness.

 

[Fyzix]

Ok, but let's assume consciousness isn't any mysterious at all.
Functionalism, that's it. A system that is aware, nothing more, nothingless.

Do you then see how it is incoherent to say there are 2 outcomes, a observer in both, but one is higher probability?

 

[Hurkyl]

no, from what I've seen you are advocating for MWI / born rule.
yesterday you claimed that my example of why branch counting doesn't work was the same as playing lotto and thinking it was 50-50 if you win or not.
If I'm mistaken, please elaborate.

In a statistical mixture, the different components don't have to be equally weighted. This is true even in classical statistical mechanics -- a probability distribution on configuration space doesn't have to be uniform, or even resemble uniformity.

The new wrinkles that relative states add that I can think of off the top of my head are:
Wrinkle 1:
The decomposition into a statistical mixture of states is not unique -- e.g. the following three qubit states are identical:

• 50% weight on |X+> and 50% weight on |X->
• 50% weight on |Y+> and 50% weight on |Y->
• 50% weight on |Z+> and 50% weight on |Z->

and there are other more esoteric ways to achieve the decomposition.

(note: the qubit state $(1/\sqrt{2}) |X+\rangle + (1/\sqrt{2}) |X-\rangle$ is very very different from the state mentioned above)
Wrinkle 2:
A decomposition of the state of a subsystem into a statistical mixture is not eternal -- the different components can be a coherent superposition in the entire state, and thus interfere and what-not.

 

[Hurkyl]

For fun, here's a more complicated decomposition.

Let V be the vector (0, 3/5, 4/5), and W be the vector (0, -3/5, 4/5)

Then, the following states are identical:

• 50% weight on |V+> and 50% weight on |W+>
• 90% weight on |Z+> and 10% weight on |Z->
• 80% weight on |Z+> and 50% weight on |X+> and 50% weight on |X->
• 25% weight on |W+> and 15% weight on |Y+> and 60% weight on |Z+>

This particular post has nothing to do with MWI -- that each of these statistical mixtures describe the same quantum state of a qubit is pure "shut up and calculate" quantum mechanics.

 

[Fyzix]

I must admit I understood nothing of what you just said :P
I'm sure someone else will and comment on it tho
But could you explain it a little less technical?

 

[Hurkyl]

I must admit I understood nothing of what you just said :P
I'm sure someone else will and comment on it tho
But could you explain it a little less technical?

A Pointa
The non-technical short version is "MWI studies wavefunctions evolving unitarily". Everything MWI studies is already there in "shut up and calculate" quantum mechanics. Among all approaches to quantum mechanics, MWI is the most interested in fully understanding the wavefunction.

An Exercise
Try to imagine classical statistical mechanics, but rather than thinking of a probability distribution as referring to a collection of separate experiments, think of the probability distribution as being what is actually real. e.g. after one trial of your red-blue experiment, 10% of reality is "there was one red outcome" and 90% of reality is "there was one blue outcome". Just one reality, but that reality is a distribution among many real configurations.

This is a purely classical thought exercise -- no quantum involved.

 

[Fyzix]

Yes I'm aware that everything in MWI is already present in shut up and calculate, but this rings true for every interpretation.

I don't see how your thought exercise shows Putnam's argument wrong.
If you are going to insist on 2 REAL outcomes, you instantly have 50/50.
if there is only 2 observers and 2 outcomes after and both stem from the same "Original", there is simply NO other way to get around this argument.

 

[Hurkyl]

Yes I'm aware that everything in MWI is already present in shut up and calculate, but this rings true for every interpretation.

Not really. The various Copenhagen variants assume that a collapse occurs, with probabilities computed via shut-up and calculate. Bohmian mechanics adds a collection of bohmian particles to the state of the system.

I don't see how your thought exercise shows Putnam's argument wrong.

Putnam's argument is wrong because of the lottery thing. The "number of worlds" -- if that phrase even makes sense -- has absolutely no reason to coincide with any probability that is supposed to have bearing on reality.

My thought exercise has nothing to do with whether or not Putnam's argument is wrong. It's to give you a better chance of really understanding the idea of indefinite outcomes. It's very easy for people suppress all critical thought towards an argument against something they dislike (in this case, your dislike of MWI). It's also very easy to obfuscate the issue if you are trying to learn two or three new things at once, rather than just one thing at once. (I'm assuming classical mechanics is not a "new thing" to you)

 

[Fyzix]

First: this had nothing to do with me disliking MWI, I dislike MWI for technical reasons, not some aesthetical reason.
Stop assuming so much, it's so typical of MWI'ers to assume I guess...
I'm detecting a trend.

I guess I'll just take Putnam's argument and my own logic over your twisted logic.
You have demonstrated twice that you don't understand the argument by stating "it's the same as believing lotto is 50/50".

Well yea, if the lottery only has 2 balls and you get one, I get one, but I have 90% chance of getting the ball, but you only got 10% of getting the ball, yet both of us have a 100% chance of getting the ball.
Are you starting to see the error of your thinking?

 

[Hurkyl]

Well yea, if the lottery only has 2 balls and you get one, I get one, but I have 90% chance of getting the ball, but you only got 10% of getting the ball, yet both of us have a 100% chance of getting the ball.
Are you starting to see the error of your thinking?

Now imagine one person getting a ball, but what color it is is given by a probability distribution, rather than a definite outcome.

 

[Varon]

Let's try this clear statement by Barrett:

"In order to capture the usual predictions of quantum mechanics, one would like to say that the probability that I would end up in the world described by the first term is 1/4 and the probability that I will end up in the world described by the second term is 3/4. If one could say this, then one would have an explanation for the fact that I get results that tend to be close to the usual statistical predictions of quantum mechanics. But, as Albert and Loewer point out, on the splitting-words theory, as it stands, one cannot say say. Rather, the splitting-worlds theory tells me that both worlds are equally real and that there will be a fully real copy of me in each world, so presumably neither has a better claim than the other to being the one that I end up experiencing."

[...]

"DeWitt seems to have noticed that the splitting-worlds theory alone did not explain why one should expect the usual quantum statistics. After presenting his interpretation of probability, he confessed that

The alert reader may not object that the above argument in circular, that in order to derive the physical probability interpretation of quantum mechanics, based on sequences of observations, we have introduced a nonphysical probability concept, namely that of the measure of a subspace in Hilbert Space. (DeWitt and Graham 1973: 163)

And he continued:

It should be stressed that no element of the superposition is, in the end, excluded. All the worlds are there, even those in which everything goes wrong and all the statistical laws break down. (186; see also 163)."

~~~~~~~~~~~~~~~~~~~~~~~~~

Now Hurkyl, JesseM, Dmittry and other Many worlders. How do you make the splitting worlds exhibit the correct quantum statistics? In the above example. If there is probability of the outcomes being 1/4 and 3/4. But the world splitting is equal. How do you make it match the quantum statistics. You can't say the world is real in one 1/4 of the time and the real 3/4 of the time. All worlds or branches are real the same time.

This question bugs me for weeks. So what's the solution?

 

[Hurkyl]

How do you make the splitting worlds exhibit the correct quantum statistics?
...
This question bugs me for weeks. So what's the solution?

Nobody knows. It would be really neat if you could arrange for them to be equal or simply related, but there is no prior reason why they should have anything to do with each other.

 

[Varon]

Nobody knows. It would be really neat if you could arrange for them to be equal or simply related, but there is no prior reason why they should have anything to do with each other.

Then why entertain Many Worlds. Maybe because we hope ways could be made someday to make the splitting worlds match the quantum statistics?

Or if you are saying they don't necessarily have to match. Then Many worlds doesn't match the predictions of standard QM or Copenhagen. Then we may as well just stick to Copenhagen and accept the ad hocness of Collapse as part of the world.

 

[Hurkyl]

Then why entertain Many Worlds.

Because MWI is the interpretation that asserts "reality is described by quantum states that undergo unitary evolution". (full stop)

TBH, the only good^* reasons I know not to entertain MWI is pessimism that quantum mechanics won't extend beyond microscopic scales, and an old no-go theorem that unitary evolution cannot turn a pure state into a mixed state has been rendered irrelevant by relative states and especially by decoherence.

*: meaning not based on availability of learning materials or based on misconceptions of the interpretation (or on faulty logic) or things like these

 

[Varon]

Because MWI is the interpretation that asserts "reality is described by quantum states that undergo unitary evolution". (full stop)

TBH, the only good^* reasons I know not to entertain MWI is pessimism that quantum mechanics won't extend beyond microscopic scales, and an old no-go theorem that unitary evolution cannot turn a pure state into a mixed state has been rendered inapplicable relative states and especially by decoherence.

*: meaning not based on availability of learning materials or based on misconceptions of the interpretation (or on faulty logic) or things like these

In both MWI and Copenhagen. What constitutes a measurement is a mystery. So you are kinda saying that if we can solve one of them.. we can apply it to the other in full force?.

 

[Demystifier]

Ok, but let's assume consciousness isn't any mysterious at all.
Functionalism, that's it. A system that is aware, nothing more, nothingless.

Do you then see how it is incoherent to say there are 2 outcomes, a observer in both, but one is higher probability?

Well, if one accepts functionalism (which I don't, but it doesn't matter here), and if one assumes that there is nothing else in the world but a wave function, and if no other assumptions are taken, THEN it is hard to see how probability could by anything else but 50:50. Yet, even though it is hard to see it, I have no idea how to formalize this argument. If you do, then you have a NEW argument against MWI possibly stronger than any other existing one, in which case you should publish it. But if it merely "seems obvious" to you (as it seems to me) without being able to formalize it, then, unfortunately, it is not good enough.

 

[Dmitry67]

I must admit I understood nothing of what you just said :P
I'm sure someone else will and comment on it tho
But could you explain it a little less technical?

Then how could you deny the commonly accepted (check wiki) point of view that Decoherence DOES explain the appearance of collapse?

Anyway, looks like you had stopped denying that but you're are attacking MWI on purely Born rule, is that correct?

 

[Dmitry67]

As we are discussing MWI here, does anyone see additional beauty of MWI because it explains Bell/EPR in a locally realistic (*) way?

(*) I know that not all definitions of 'realism' classify MWI as 'realistic', but in some wider sense it is definitely realistic.

 

[Fyzix]

Then how could you deny the commonly accepted (check wiki) point of view that Decoherence DOES explain the appearance of collapse?

Anyway, looks like you had stopped denying that but you're are attacking MWI on purely Born rule, is that correct?

I don't see how decoherence not being sufficient to explain determinate outcomes had anything to do with his statement ?

No, my position on that is still the same.
I've given you tons of information as to why it doesn't work, citing a lot of physicists and philosophers, yet you don't see the point they are getting across, so I stopped trying:P

By the way, whether MWI is truly local or not is still far from decided.

Ruth E Kastner made a paper refuting Deutsch's work on this: http://arxiv.org/ftp/arxiv/papers/1011/1011.3078.pdf