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entropy1

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Is it imparative that the "worlds" given by MWI all ontologically exist?

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- #1

entropy1

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Is it imparative that the "worlds" given by MWI all ontologically exist?

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Yes and yes.Is MWI equivalent to a superposition of possible Collapse-worlds? That is, is it equal to a superposition of the possible scenario's given by Collapse Interpretation?

No.Is it imparative that the "worlds" given by MWI all ontologically exist?

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Is it imparative that the "worlds" given by MWI all ontologically exist?

Do you mean according to the MWI? According to the MWI, yes, they all exist, because they're all part of the wave function, and the wave function exists.

If you mean, does the MWI have to be true, no, it doesn't.

- #4

DarMM

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In simple situations currently modeled yes. Though in general it's not exactly certain what constitutes a "world" and there is a possibility that observers in the same world could disagree on the "world" of distant objects.Is MWI equivalent to a superposition of possible Collapse-worlds? That is, is it equal to a superposition of the possible scenario's given by Collapse Interpretation?

I know Renato Renner's group in Zurich is currently investigating violations of the Born rule in MWI and these kind of inter-agent consistency issues.

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When taken to the extreme, all of the worlds cancel out except one which is the one we experience. This would be an attempt to reconcile the MWI with the fact that we only experience one world.

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I read somewhere

Please give a specific reference. We can't discuss vague statements about what an unknown source said.

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- #8

DarMM

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If it helps, I think you might be talking about Feynman's sum over paths where all the paths cancel except one (our classical) one. Plenty of pop science books explain each path as another world and use this to explain our classical looking world.

It's not very accurate to the physics itself, but I think that might be your source.

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Any time you find yourself saying "I read somewhere", you should stop posting and go find where, and if you can't, don't post. Again, we can't discuss vague descriptions of something said by an unknown source.

- #10

entropy1

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- #11

DarMM

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Because if you model a measurement with quantum mechanics, including the main macroscopic features of the experimental device itself in your model and you ignore the environment (environment here can be either the actual external environment, e.g. the air, or the atomic structure of the device itself) you get one term for each combination of "state of the quantum system and state of the device"

For example if you are measuring a particle that is in a superposition of spin up and spin down you get a superposition of "particle is spin up and device reads up" and "particle is spin down and device reads down". That's what quantum mechanics naturally gives.

Now in reality you only see one of these alternatives, so you have to use a "collapse" rule to get rid of the other.

Many Worlds doesn't need to because it simply says both alternatives occur, hence it doesn't need collapse as it isn't pruning away one of the options.

- #12

A. Neumaier

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ButMany Worlds doesn't need to because it simply says both alternatives occur

- #13

DarMM

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Even beyond this there is no non-circular reason for why each alternative is seen with the frequencies we observe, hence it cannot be said to be an interpretation of any of the formalisms of Quantum Mechanics (QM has three formalisms, no collapse, objective collapse and subjective collapse which give different predictions in certain obscure scenarios such as the Frauchiger Renner experiment. MWI cannot yet be said to be a functioning no collapse interpretation)Butit does not explain whyeach observer sees only one alternative, and why different observers usually agree on the alternative seen.

In addition one will often see the claim that MWI is local, but this is still an open issue.

- #14

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Even beyond this there is no non-circular reason for why each alternative is seen with the frequencies we observe, hence it cannot be said to be an interpretation of any of the formalisms of Quantum Mechanics (QM has three formalisms, no collapse, objective collapse and subjective collapse which give different predictions in certain obscure scenarios such as the Frauchiger Renner experiment. MWI cannot yet be said to be a functioning no collapse interpretation)

In addition one will often see the claim that MWI is local, but this is still an open issue.

It's true that it's difficult to understand probabilities in MWI, but I sort of feel like that's because there is no really good way to understand probabilities, when you get right down to it.

Let me sketch a "many-worlds" version of classical probabilities.

Suppose that we have a world that is deterministic except for one little aspect: There is a special coin such that flipping it produces heads/tails with equal probability, and there's no way, even in principle, to predict which.

Now, as far as anybody is concerned, the coin flip is completely nondeterministic. But secretly, this world is not real, but is a simulation in a gigantic computer. Every time in the simulation when someone (one of the simulated beings) flips the coin, the computer halts the simulation, makes a duplicate of the state, and then continues simulating both branches, giving one branch the result "heads" and the other branch the result "tails". As time goes on, there are more and more simulated universes, with different histories of coin flips.

Now for any simulated being living in one of the simulations, the coin seems perfectly random, with equal chance of heads and tails. But the operation of the master computer is deterministic. So determinism in an ensemble is perfectly compatible with nondeterminism in each element of the ensemble.

But what about probability? As the number of flips gets larger and larger, the number of simulations in which half the coin flips turned up "heads" gets much larger than the number of simulations in which there is a large imbalance of "heads" and "tails". So we can sort of understand the probabilistic statement "the coin has 50/50 chance of landing heads or tails" in terms of "typical" and "atypical" branches. The overwhelming majority of simulations will have 50/50 results, so we can call those "typical" worlds. In the typical worlds, the relative frequency of heads approaches 1/2.

However, this is really unsatisfying, for the following reason: What if, instead of creating two copies every time a coin is flipped, the computer creates 3 copies, and allows two copies that are given result "heads" and 1 copy that is given the result "tails"? Now, the "typical" branch has 2/3 heads, rather than 1/2. So with this variation, the coin does not have 50/50 odds, but 33/67 odds. That makes sense, except for the fact that in each world, the simulated people empirically determine the odds of heads and tails by just flipping many times and counting. Obviously, the counting process is not affected by the existence of more alternate worlds. What's changed by the addition of alternate worlds is not the experience of anyone in any of the worlds, but simply the definition of which worlds are considered "typical".

I claim that there is no completely satisfying way to give meaning to the claim "the coin has 50/50 chance of being heads". You want it to be the case that probabilities correspond to relative frequencies, but that will only be true in some possible worlds, and not others. You can make it true by definition by calling the worlds where it is false "atypical", and restricting your probabilistic claims to the typical worlds. But that makes it all pretty tautological.

It seems to me that there is no good explanation for probability in a many-worlds setting, and furthermore, you can't empirically distinguish between such a many-worlds setting and a single-world with nondeterminism (as far as you're concerned, there is no difference, as long as there is no interaction between possible worlds---you can just define your world to be the "real" one, and consider the others just hypotheticals).

- #15

bhobba

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It's the assertion all there is, is a universal wave-function. There are a few variations from that point on - some are like you suggest, others are more subtle. Best you study an actual paper on it:

https://arxiv.org/ftp/arxiv/papers/1801/1801.08587.pdf

And listen to Gell-Mann:

Thanks

Bill

- #16

bhobba

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It seems to me that there is no good explanation for probability in a many-worlds setting, and furthermore, you can't empirically distinguish between such a many-worlds setting and a single-world with nondeterminism (as far as you're concerned, there is no difference, as long as there is no interaction between possible worlds---you can just define your world to be the "real" one, and consider the others just hypotheticals).

You and many others - its one of it disputed features as the paper I posted above explains:

'Finally, a still disputed claim of Everett’s and DeWitt’s was that the probabilistic predictions of standard quantum theory arose naturally from the formalism with no necessity of postulating a statistical interpretation (i.e., the Born rule).'

That's one reason I say its a bit subtle - there are points of disagreement about it.

Thanks

Bill

- #17

bhobba

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Butit does not explain whyeach observer sees only one alternative, and why different observers usually agree on the alternative seen.

Yes there are a number of hidden assumptions in the theory. I think some like Wallace believe that one is solved - but it has been thrashed out a number of times on this forum - no need to go over it again.

Personally I am with Gell-Mann who thinks decoherent histories is just MW without the many worlds and doesn't really understand why some want to invoke the actual existence of many worlds. That's his view - I can say mine - but it is just a view and will only lead to stuff that has been discussed a number of times before.

Thanks

Bill

- #18

DarMM

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The typical resolution is simply to say one should prove that the typical worlds have Born frequencies, which becomes a deterministic statement in Many Worlds as the whole ensemble is real.

However there is no non-circular proof of this either.

I should say recent work has shown that in Many Worlds there isn't a countable number of worlds, but a world volume. So then you are hoping to show that the volume of worlds that experience an outcome is given by the worlds' amplitude squared. It's been shown that the square of the amplitude is the only volume preserving way of subdividing world volumes.

In addition, one should look to more recent work, like the Pusey-Leifer theorem concerning operational time symmetry, which show Many Worlds would have to be fine tuned to avoid disagreeing with QM.

- #19

A. Neumaier

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You may like Bertrand Russell's The metaphysician's nightmare.Every time in the simulation when someone (one of the simulated beings) flips the coin, the computer halts the simulation, makes a duplicate of the state, and then continues simulating both branches, giving one branch the result "heads" and the other branch the result "tails".

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Butit does not explain whyeach observer sees only one alternative, and why different observers usually agree on the alternative seen.

It's not clear to me that there is anything to explain here. You have to ask what it would mean to see more than one alternative.

Suppose you decide, in the case of Schrodinger's cat, that you will write down on a piece of paper, either the word "Dead", "Alive" or "Both", depending on what kind of cat you see (both meaning a superposition of dead and alive). Then if the cat is dead, you'll definitely write "Dead". If the cat is alive, you'll definitely write "Alive". But given those two facts, what you do in the case of a half-dead/half-alive cat is determined: You will be put into a superposition of writing "Dead" and writing "Alive". To write "Both" would violate the linearity of quantum mechanics.

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Personally I am with Gell-Mann who thinks decoherent histories is just MW without the many worlds and doesn't really understand why some want to invoke the actual existence of many worlds.

Here's what I don't understand about decoherent histories. Given an initial state ##|\psi\rangle##, a hamiltonian ##H##, a sequence of times ##t_1, t_2, ...## and a sequence of projection operators ##\Pi_1, \Pi_2, ...##, then the Born rule can give a probability associated with the history:

The proposition corresponding to ##\Pi_1## is true at time ##t_1## and the proposition corresponding to ##\Pi_2## is true at time ##t_2##, etc.

To me, this is double-many worlds. For every sequence of ##N## propositions, you have ##2^N## possible sequences of yes/no answers. So have a different world for each choice of a sequence of questions, and for each possible sequence of answers.

Now, you can pare down the many worlds to just one world evolving nondeterministically by fixing the sequence of questions and allowing the history to grow nondeterministically according to the Born Rule. However, is the sequence of questions an additional structure? Who determines the sequence of questions (projection operators)?

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A. Neumaier

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and to write either Dead or Alive, too.You will be put into a superposition of writing "Dead" and writing "Alive". To write "Both" would violate the linearity of quantum mechanics.

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- #23

bhobba

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Who determines the sequence of questions (projection operators)?

Well in decoherent histories QM is considered the stochastic theory of all history's. It just like anything a theorist can define.

My issue with it is it seems to be skirting a number of key issues such as exactly what is an observation and trying to define your way out of trouble. It may work - but seems somewhat artificial - still its not a completed program yet - some key theorems are missing.

Thanks

Bill

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Well in decoherent histories QM is considered the stochastic theory of all history's. It just like anything a theorist can define.

But to turn it into a stochastic theory, you have to specify the projection operator used. How does that get determined?

- #25

bhobba

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But to turn it into a stochastic theory, you have to specify the projection operator used. How does that get determined?

A projection operator is an operator such that P^2 = P. A sequence of such operators is called a history. Its well defined. Its supposedly the stochastic theory of all such sequences. Obviously some will have zero or so close to zero probability so as to be of no value. There is a general theorem built from the Born Rule that gives that probability.

Added Later

Some histories are not stable and it seems decoherence places certain conditions on what histories actually can occur and those that cant. Its been a while since I went deep into it but managed to find the following theses on it:

http://www.cs.ox.ac.uk/people/bob.coecke/Roman.pdf

Thanks

Bill

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