Many Worlds Interpretation and act of measuring

[julcab12]

I have zero idea what you mean by a real-multi space operator.

Thanks
Bill

Consider a general real-space operator

. When this operator acts on a general wavefunction

the result is usually a wavefunction with a completely different shape. However, there are certain special wavefunctions which are such that when

acts on them the result is just a multiple of the original wavefunction. These special wavefunctions are called eigenstates, and the multiples are called eigenvalues...

 

[bhobba]

Can you provide me a link to elaborate this claim. Thanks!

Its very basic. The textbook that explains with just a first course in QM (which usually doesn't cover it) it is the following:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

The following also covers it, but not in the same depth:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

Thanks
Bill

 

[bhobba]

Consider a general real-space operator

. When this operator acts on a general wavefunction

the result is usually a wavefunction with a completely different shape. However, there are certain special wavefunctions which are such that when

acts on them the result is just a multiple of the original wavefunction. These special wavefunctions are called eigenstates, and the multiples are called eigenvalues...

Yes - your point being?

Here is even more detail on exactly what's going on (see post 137):
https://www.physicsforums.com/threads/the-born-rule-in-many-worlds.763139/page-7

It is a foundational axiom of QM, in fact the foundational axiom because Born's Rule can be derived from it, that the outcomes of observations can be mapped to a POVM which leads to what you said above, as the above link explains.

In MW what happens is you have a mixed state ∑pi |bi><bi| after decoherence. The interpretation is each |bi><bi| is a separate world. MW also has a decision theory argument that shows the pi is the probability of experiencing the world with |bi><bi|. Note - despite what Gragi says that probability has nothing to do if an observer is actually in the world or not any more than if you have a machine that throws a dice the probability changes depending on if someone observes it or not.

Thanks
Bill

 

[stevendaryl]

That is incorrect. Its got nothing to do with an observer but for some reason you keep harping on it.

I'm sure that what I'm about to say is exactly on-topic, but to me, observers are relevant in MWI in the following sense:

• MWI is a completely deterministic theory.
• Yet, from the subjective view of an observer, the universe seems non-deterministic.

So observers come into play simply because of the need to explain why things appear the way they do. Without observers, there is no reason to introduce probability into the theory at all.

It's not that observers necessarily involve any different physics than any other system, it's just that they are the systems that have a point of view that needs explaining.

 

[stevendaryl]

Not quite - it refers to a superposition being converted to a mixed state - but to understand it you need to know what those terms mean.

At this point, I'm not sure what objections are legitimate, and what objections are quibbling. But in MWI, there is never a conversion to a mixed state. Instead, the wave function is FAPP (for all practical purposes) in a mixed state if it is impossible to observe interference between the different elements of the superposition. Mathematically, this means something like: the density matrix becomes that of a mixed state after "environmental degrees of freedom" are traced out.

 

[bhobba]

So observers come into play simply because of the need to explain why things appear the way they do.

I can't follow that at all.

Probabilities enter due to a decision theory rational agent argument - this is a Bayesian view - namely what would a rational agent assign the probability to be where its a subjective thing. Its got nothing to do if observers are in the world or not.

Thanks
Bill

 

[stevendaryl]

I can't follow that at all.

Probabilities enter due to a decision theory rational agent argument

And some people use the word "observer" instead of "decision theory rational agent". The notion of a "decision theory rational agent" is a way to formalize those aspects of an "observer" that are relevant to reasoning about probability.

 

[bhobba]

And some people use the word "observer" instead of "decision theory rational agent". The notion of a "decision theory rational agent" is a way to formalize those aspects of an "observer" that are relevant to reasoning about probability.

If that's what they mean then they should state it. However its obvious that is not affected by if there are actual observers in the world or not. In particular the following is false - 'An exception occurs when a singnificant fraction of possible outcomes do not contain the observer.' That a rational agent decides on a particular probability has nothing to do if there are observers in the world or not, or even if the rational agent is in the world or not. Its simply what the rational agent would conclude if they were experiencing it. Whether they actually do is obviously irrelevant any more than it would be relevant if a machine flipped a coin and a rational agent decided it had a 50-50 chance of being heads or tales.

Thanks
Bill

 

[julcab12]

The interpretation is each |bi><bi| is a separate world

Of course. You can create a model dependent on that axiom simple because it is essential within the demand of the framework. But it can be utterly indistinguishable whether each individual system is in an eigenstate of some multiple hilbert spaces , or each individual system is in a superposition state with huge constraint like MWI. I'm not saying i ignore the superposition. Almost everything I've read about QM invovles a crude formalism of separation and interpretation -- "That is how the system literally looks like. It appears multiple, let's assign each multiple state to be real create worlds pragmatic to ours. Let's make it independent to any specific interpretation and built something within that framework -- It works!". Ok here's an image of 4 supernovas in single frame must be 4 distinct supernovas. Actually we can create a model within that premise and can still work..Well, Lensing will tell you it's not the case anyways..

 

[stevendaryl]

If that's what they mean then they should state it. However its obvious that is not affected by if there are actual observers in the world or not.

By "actual observers" do you mean human beings (or intelligent aliens, or whatever)? I certainly agree with that; you can substitute a mechanical device for a human, and get the same "appearance" of probability. Or do you mean that the decision-theoretic notion of probability doesn't require any rational agents to exist, only that IF they existed, THEN they would do ... (whatever).

In particular the following is false - 'An exception occurs when a singnificant fraction of possible outcomes do not contain the observer.' That a rational agent decides on a particular probability has nothing to do if there are observers in the world or not, or even if the rational agent is in the world or not. Its simply what the rational agent would conclude if they were experiencing it. Whether they actually do is obviously irrelevant any more than it would be relevant if a machine flipped a coin and a rational agent decided it had a 50-50 chance of being heads or tales.

Okay, so you do mean the counterfactual: if such agent did exist, then it would behave in such and such a way.

 

[jimmylegss]

If MW is purely deterministic, what determines what will happen in which universe? So If something can go left or right, what will determine which thing will happen to the universe that I am in now?

The whole MW thing seems to me they put another layer in between that mechanism, to kind of put a distance between us and that whole pure randomness thing?

For example it might still be completely random what will happen in which universe? Unless you can observe this mechanism, it does not really do anything about the whole pure randomness problem at all. You just moved it around a bit.

 

[bhobba]

By "actual observers" do you mean human beings (or intelligent aliens, or whatever)?

Well here is where we run into semantic difficulties with QM and that this observer business was even introduced in the first place. Cragi wasn't forthcoming in detailing exactly what he means but by observer I assume he means rational observer. Its utterly obvious if a rational observer is there or not the probability of an outcome does not change. In fact the decision theoretical argument used contains nothing of that nature.

Thanks
Bill

 

[stevendaryl]

If MW is purely deterministic, what determines what will happen in which universe? So If something can go left or right, what will determine which thing will happen to the universe that I am in now?

Nothing determines it.Initially, you have one universe. Then after a random event, the universe splits into two universes, one in which the something went left, and another in which the something went right.

Of course, the language of "splitting" is not completely accurate.

 

[bhobba]

ISo If something can go left or right, what will determine which thing will happen to the universe that I am in now?

One world will be left, the other right. The issue is which will a rational agent, if they were there, experience. All you can do is give a probability. It may seem the rational choice is 50-50. But if you analyse it carefully it turns out to have problems - the detail can be found on page 149 of Wallaces reference. In fact the only one that works properly is one that is basis independent so Gleason applies and you get the Born rule. However for the detail you need to consult the reference.

Thanks
Bill

 

[craigi]

Yes you do. I can recall nothing you have posted doing that.

Wallace is an acknowledged expert on the interpretation and his text a definitive reference. If he doesn't include it the VERY strong odds are its a crock. But it goes beyond that. I spent quite a bit of time studying it to understand the interpretation and can say it has nothing to do with observers - nothing.

The issue isn't if the world contains observers - of course if they do they will be split and copied with each observation just like everything is - that's utterly obvious - the issue is if it in anyway affects the interpretation. It doesn't - and obviously so.

However, if, as required by forum rules, you have a peer reviewed physics paper (not a philosophy one) that shows otherwise post it. Also rather than me going through the paper you should be able to present a précis of the argument.

Thanks
Bill

I don't have a copy of Wallace's book at hand, but I suggest that you read again his final chapter entitled, "A Cornucpia of Everettian Consqeuences", particularly, "10.2 Exotic Consqeuences of Quantum Probability", "10.2.1. Cosmoloigical Probabilities and Anthropic Reasoning" and "10.2.2. Quantum Russian Roulette". I have no doubt that it will make my comments crystal clear to you.

Tegmark, another highly respected MWI expert, discusses a significant difference for an observer, under the MWI compared to other interpretations, in this paper:
The Interpretation of Quantum Mechanics: Many Worlds or Many Words?
http://arxiv.org/abs/quant-ph/9709032

It's a short paper and not very technical. I won't summarise it, because I'd like you to read it all, since you obviously have an interest in the MWI and it also addresses your "too weird" objection in direct terms, amongst other things that you really should read.

I trust that this now clears this all up, but if you do still have questions, when you have read the final chapter of Wallace's book and the paper by Tegmark, then please get back to me.

BTW we are discussing MW not astronomy or cosmology.

Don't be fooled by incorrect comments that the multiverse of the many worlds interpretation is the same as the multiverse in cosmology (eg eternal inflation) - it isn't.

Although there has been speculation linking the two:
http://arxiv.org/abs/1105.3796

Thanks
Bill

Tegmark also offers an interpretation of QM which makes Everetts worlds real beyond our cosmological horizon, linking different types of multiverse:
Born in an Infinite Universe: a Cosmological Interpretation of Quantum Mechanics
http://arxiv.org/abs/1008.1066

By "actual observers" do you mean human beings (or intelligent aliens, or whatever)? I certainly agree with that; you can substitute a mechanical device for a human, and get the same "appearance" of probability. Or do you mean that the decision-theoretic notion of probability doesn't require any rational agents to exist, only that IF they existed, THEN they would do ... (whatever).

It really doesn't matter what form the observer or observation device takes, since if in a significant proportion of the worlds, it doesn't exist then no such observation can be made. The observer cannot find itself in those worlds. The probability of an observer making an observation, where the observer does not exist is zero. This is distinctly different from other interpretations.

To me, this seems like obvious stuff and I'm suprised that there's so much debate about it. It's most notable by the fact that Everett believed that the interpretation rendered him immortal.

 

[bhobba]

Added Later:

Since this concerns Quatum Suicide I thought I would do a preamble about it to lay the background.

Here is the description of it with the relevant bit posted:
http://rationalwiki.org/wiki/Quantum_suicide
What makes this interesting, is that if the many-worlds interpretation of quantum mechanics is true, then at the point at which a decay might happen, the universe splits in two — into one universe in which it decays and I die, and another in which it does not decay and I live. Assuming there is no afterlife, I will cease to exist in one universe but not in another. So, the argument goes, although there will be others who will exist in the universes in which I die, I will only ever exist in the universes in which I survive, so I will only ever observe the universes in which I survive. From my perspective, I will never die, I will always be saved from death by quantum indeterminancy.

One point to note that reduces it to absurdity is its symmetrical - you can just as well argue you never live. But it is irrelevant. Each observation causes the world to split and each subworld evolves on its own with no effect on the others.

A cleaner version would be if the appartus like a spin detector destroyes itself when it detects up and you supply it with a stream of particles to measure. There will always be a world where its destroyed, and a world where its not. But since they can never communicate - its makes zero difference.

Wallace knows, and details, the trick involved here in his book. It relies on a certain feeling we have about death that makes it philosophically complicated and the idea is to entangle those complications with this interpretation (see page 371). The key point however, again from the same page, and this time I quote 'I should stress though, the question, however interesting, does not bear on the epistemic status of the Everett interpretation'

Of course being a philosophy type that enjoys such questions he examines it a bit more and looks at those that disagree with his (and my) position. You can read it if that sort of thing interests.

The bottom line is it proves diddley squat, and to be blunt, is simply what I call philosophical waffle.

Anyway that's just a preamble to set the stage so to speak

I don't have a copy of Wallace's book at hand, but I suggest that you read again his final chapter entitled, "A Cornucpia of Everettian Consqeuences", particularly, "10.2 Exotic Consqeuences of Quantum Probability", "10.2.1. Cosmoloigical Probabilities and Anthropic Reasoning" and "10.2.2. Quantum Russian Roulette". I have no doubt that it will make my comments crystal clear to you.

I reacquainted myself with them last night.

They do not do what you suggest. For example, like me he gives the suicide argument short thrift (not as short as I do - he is slightly kinder) challenging it, correctly IMHO, as sensationalist and being of little consequence. The argument is symmetrical - you can equally have the experience of being dead. He is a bit kinder than me, conceding the experience of being dead is not that well defined - me I say you experience nothing.

Anyway none of this affects the MW interpretation which in no way depends on if rational observers are present or not.

Tegmark, another highly respected MWI expert, discusses a significant difference for an observer, under the MWI compared to other interpretations, in this paper:
The Interpretation of Quantum Mechanics: Many Worlds or Many Words?
http://arxiv.org/abs/quant-ph/9709032

I read it. A waste of time.

What it does is exactly what it says:
Common objections to the MWI are discussed. It is argued that when environment-induced decoherence is taken into account, the experimental predictions of the MWI are identical to those of the Copenhagen interpretation except for an experiment involving a Byzantine form of “quantum suicide”. This makes the choice between them purely a matter of taste, roughly equivalent to whether one believes mathematical language or human language to be more fundamental.

It does not prove what you said: 'An exception occurs when a singnificant fraction of possible outcomes do not contain the observer.'

The quantum suicide argument I already have dealt with - but even aside from that it is irrelevant to your point. But for completeness will go through it in detail. The paper says 'This time the shut-up-and-calculate recipe is inapplicable, since probabilities have no meaning for an observer in the dead state, and the contenders will differ in their predictions.' That is incorrect. It makes no difference if the observer is alive or dead to the predictions of the theory. Sure the assistant will not hear anything if they are dead - but QM doesn't concern itself with that - it only predicts the probabilities of quantum observations. The observation occurs at the apparatus that measures the spin - that is where decoherence occurs and the world spits - everything is classical from that point. Its exactly the same trap people fall into when discussing Schroedinger's Cat. The observation there occurs at the particle detector - the world is classical from that point on - the cat is never in a strange alive and dead superposition. Yes there will always be a world where the assistant is alive and hears the click - but so? It is utterly irrelevant to anything. And, this is the symmetry bit, there will also be a world where the assistant is dead and feels nothing. Again so? We have differing worlds where differing things happen. Big deal.

Now please, this time can you give a link to a paper that proves your claim, and give a summary of the argument, because I won't waste my time again.

Thanks
Bill

 

[bhobba]

It really doesn't matter what form the observer or observation device takes, since if in a significant proportion of the worlds, it doesn't exist then no such observation can be made.

Please describe to me a world where an observational device doesn't exist? An observation can occur, when for example, a few stray photons from the CBMR decoheres a dust particle and gives it a definite position. In fact observations are occurring around us all the time and that is how the classical world we experience comes about. The answer to Einstein's question is the moon not there when nobody looks is its being looked at all the time by the environment.

Or are you talking about the same observational device? In the quantum suicide the assistant is an observational device - not the one doing the quantum observing - that is at whatever is measuring the spin - but an observational device nonetheless. Its obvious whether or not things in the world are destroyed or not by the observation is of no relevance.

One can of course remove that constraint and have the observational device destroy itself if it detects something. Again all it means is in another world it can't make that observation. Big deal.

Thanks
Bill

 

[craigi]

Bill,

You now have it from me, Tegmark and you have it from Wallace, your chosen authority on the subject, in the very book that you read and insisted that he made no reference to it.

[mentor's note - edited a bit to keep it on topic]

 

[bhobba]

You now have it from me, Tegmark and you have it from Wallace, your chosen authority on the subject, in the very book that you read and insisted that he made no reference to it..

He specifically disagreed that quantum suicide is of any relevance. I explained exactly why its of no relevance.

[mentor's note - edited a bit to keep it on topic]

 

[carllooper]

If MW is purely deterministic, what determines what will happen in which universe? So If something can go left or right, what will determine which thing will happen to the universe that I am in now?

The whole MW thing seems to me they put another layer in between that mechanism, to kind of put a distance between us and that whole pure randomness thing?

For example it might still be completely random what will happen in which universe? Unless you can observe this mechanism, it does not really do anything about the whole pure randomness problem at all. You just moved it around a bit.

As I understand it each possible world (in a probability model) is an actual world in the many worlds model. All possible worlds exist. An infinity of such. The concept of splitting is somewhat awkward, for what would make a world split? If a world is deterministic then it has no way of splitting into two or more different worlds. However a slightly different take can resolve this apparent problem. We can pose a multiplicity of worlds that are partly the same and partly different in an infinity of varying ways. That which is the same in each world (the cat is alive in both worlds) is that aspect of each world which is not in fact two worlds (or sub-worlds) but one sub-world (A1 = A2 = A). Deutsch suggests such a definition of identity - that given a number of identical things we're really talking about just one thing - if indeed we do mean "they" are identical.

So we can propose (or select), for example, two worlds (out of an infinity of all possible worlds) where there is an overlap between these two worlds - where a part of each is identical, and everywhere else not so. Following Deutsch we can say the identical parts are one world (or sub-world) - and the non-identical parts belong to two worlds. Set theory can provide us with the requisite concepts for describing such a situation.

Within one of these worlds we have a situation where the non-intersecting part of such is completely free to interact, in a classical way, with the intersecting part, but in each world the outcome is different, due to what differed between each world.

So, for example, as I await the results of a lottery I entered, there is an infinite number of worlds in which I am awaiting the results of a lottery (so each of which contain the same sub-world) but in each world, outside the sub-world which is identical (or 'shared'), there is the sub-world which differs (some of which the lottery goes in my favour, some which don't). This unshared sub-world will eventually infect the shared sub-world (in which I'm awaiting the result of a lottery) and 'split' the otherwise shared sub-world. That part of a world in which I'm awaiting the lottery results (in an identical fashion), becomes no longer identical.

In one world I win the lottery and in another I don't, before which it was just one of me awaiting the results of the lottery (according to our definition of identity).

C

 

[mfb]

for what would make a world split?

Decoherence.

If a world is deterministic then it has no way of splitting into two or more different worlds.

The contrary, it is impossible to have unitary evolution of quantum mechanics without something that can be called "splitting". This is exactly the deterministic evolution, in contrast to nondeterministic ones like collapses where you just get one world.

 

[carllooper]

Decoherence.
The contrary, it is impossible to have unitary evolution of quantum mechanics without something that can be called "splitting". This is exactly the deterministic evolution, in contrast to nondeterministic ones like collapses where you just get one world.

The question was rhetorical rather then requiring an answer, and I answer it according to a version of the many worlds model. An alternative answer is decoherence but that doesn't address the question on how a many worlds model might otherwise resolve the same question. We need to distinguish between the "universe" and a "world". The universe is the set of all worlds. A world is one of such worlds. The evolution of the wave function is in terms of the universe, and in terms of such is deterministic. In the Many Worlds model we're talking about each world, on it's own being deterministic and classically so: ie. where the same conditions must give the same results. However the take I pursue is in relation to those worlds where the same conditions are not world wide nor entirely absent, but where each of the considered worlds are deterministic (in a classical way) yet provide a solution to how the "same" world can split. The answer being that the considered worlds are not entirely the same world - only in part - be it a very large part or a very small part.

We can propose an infinity of worlds that are entirely identical but following a Deutschean definition of identity we must drop the concept of there being many such worlds: if they really are identical they are really the same world: ie. just one world. (A1=A2=A3 ... = A). For every one of these singular worlds there will be an infinitely more worlds that are entirely different. But more interesting are not these entirely different worlds but those that are partly identical (and of course partly different). The identical parts become singular (following Deutchean identity) and the different parts become plural. This provides for a concept of deterministic splitting and no need to introduce randomness as a mechanism.

C

 

[RUTA]

Here are a couple papers that are interesting http://philsci-archive.pitt.edu/9542/1/Decoherence_Archive.pdf and http://arxiv.org/abs/1504.01063

 

[rootone]

Here are a couple papers that are interesting http://philsci-archive.pitt.edu/9542/1/Decoherence_Archive.pdf and http://arxiv.org/abs/1504.01063

Skimmed it, an interesting read, not math heavy, will go back to it I hope, marked it anyway.
"subjective uncertainty", hmm

Thanks.

 

[RUTA]

My understanding of these papers, correct me if I'm wrong, is that they are a response to a response. That is, Adrian Kent (and others) pointed out that splitting worlds in accord with the Born rule would leave most branches producing (empirically) the wrong probabilities. For example, if the correct probability is 50-50 for a given experiment, there would be many branches that would not see 50-50 outcomes. How would we know for sure that the probability we measure is the "right" one? The response to that was "subjective uncertainty" and these two papers are a response to that.

 

[stevendaryl]

My understanding of these papers, correct me if I'm wrong, is that they are a response to a response. That is, Adrian Kent (and others) pointed out that splitting worlds in accord with the Born rule would leave most branches producing (empirically) the wrong probabilities. For example, if the correct probability is 50-50 for a given experiment, there would be many branches that would not see 50-50 outcomes. How would we know for sure that the probability we measure is the "right" one? The response to that was "subjective uncertainty" and these two papers are a response to that.

But the objection applies equally to any probabilistic theory. If you a flip a coin some number of times, it's possible to get arbitrarily long sequences of heads-up. Strictly speaking, no finite amount of information can confirm or refute a probabilistic theory. That's true whether or not we consider many-worlds. In practice, we use a cut-off and declare that a probabilistic theory has been refuted if the chance that it is correct is below the cut off. But this leaves a possibility that we come to the wrong conclusion--accept a false theory, or reject a true theory--just because we by chance had an "atypical" run.

When we consider many-worlds, there will obviously be some worlds where the results of experiments will differ significantly from the predictions of QM, and in those worlds, the researchers will come to the wrong conclusion that QM is mistaken.

 

[stevendaryl]

But the objection applies equally to any probabilistic theory. If you a flip a coin some number of times, it's possible to get arbitrarily long sequences of heads-up. Strictly speaking, no finite amount of information can confirm or refute a probabilistic theory. That's true whether or not we consider many-worlds. In practice, we use a cut-off and declare that a probabilistic theory has been refuted if the chance that it is correct, given the experimental data^* is below the cut off. But this leaves a possibility that we come to the wrong conclusion--accept a false theory, or reject a true theory--just because we by chance had an "atypical" run.

When we consider many-worlds, there will obviously be some worlds where the results of experiments will differ significantly from the predictions of QM, and in those worlds, the researchers will come to the wrong conclusion that QM is mistaken.

^*Speaking like a Bayesian, that is. We can switch that around, and talk about the probability of getting those experimental results, under the assumption that the theory is true.

 

[Rajkovic]

Seriously, this idea of many universes, universe splitting in two, is far beyond the fantasy, more like fairy tale walt disney. lol.
You know how MWI should be called?
FOI = 'failure of interpretation'

That's the price of trying to understand the quantum world. I don't even know why you discuss it.

 

[RUTA]

You're right, we do talk as if there is a "weird" place in the universe where someone is always seeing heads when they flip a coin. Likewise, if all possibilities are realized with equal weight and the universe is infinite, then there are many places that don't agree with the 50-50 outcome of flipping a coin. And, we can't say by virtue of our experience, that indeed the probability is 50-50 just because that's what we observe. Yet, we're talking as if our 50-50 observation represents the "real" probability and those other "anomalous" regions are occurring according to our probability. It's exactly Kent's complaint with MWI, which is a legitimate complaint, so what we must *really* believe, despite claims otherwise, is that *every* region in the universe finds empirically the 50-50 outcome -- there are no "anomalous" regions. Otherwise, we can't do empirical probabilistic science.

 

[Rajkovic]

You're right, we do talk as if there is a "weird" place in the universe where someone is always seeing heads when they flip a coin

hahaha, where are this "weird place" ?
and from what I've read on many forums and wikipedia, the theory says that there are many Universes, and all other possibilities happen in OTHER universes, not in our universe.

"MWI's main conclusion is that the universe (or multiverse in this context) is composed of a quantum superposition of very many, possibly even non-denumerably infinitely[2] many, increasingly divergent, non-communicating parallel universes or quantum worlds."
Many-worlds interpretation - Wikipedia, the free encyclopedia