Can Quantum Computers Validate the Many-Worlds Interpretation?

[ThomasT]

If you don't believe in other branches you need to provide (and prove) some branch-cutting mechanism, like wavefunction collapse in CI. Or particles in BM which go into some waves, leaving other waves empty (as I understand it).

Only if I assume that these other branches actually exist, or are describing reality -- which I don't.

A realistic description is going to require a somewhat different and more detailed approach than this virtual branching stuff, imo.

 

[Dmitry67]

Other branches exist for the very same reason. Because they are not different from the branch we observe.

Tell me, when is more logical:
1. To expect that space exists beyond what we call our cosmological Horizon (say, 100Billions ly away) because we don't expect that far from us there is something fundamentally different;
2. To claim that the existence of the space beyond our Hubble volume can not be proved, hence, it is logical to assume that there is nothing there.

 

[ThomasT]

Other branches exist for the very same reason. Because they are not different from the branch we observe.

Tell me, when is more logical:
1. To expect that space exists beyond what we call our cosmological Horizon (say, 100Billions ly away) because we don't expect that far from us there is something fundamentally different;
2. To claim that the existence of the space beyond our Hubble volume can not be proved, hence, it is logical to assume that there is nothing there.

We believe that our universe extends beyond the cosmo horizon because our ability to see farther and farther, ie. see more and different stuff, has increased.

In constrast, we have zero ability to see the parallel worlds of MWI. They exist as a fantasy interpretation of standard QM. This branching or splitting into parallel worlds is an unsatisfactory explanation (actually it's no explanation at all) for how the recorded instrumental results are generated vis an underlying reality (ie., vis a realistic description).

The MWI approach to a realistic theory is doomed because it's born out of (pun intended) a mostly non-realistic, statistical theory.

 

[Count Iblis]

Actually, it is precisely the unitary time evolution that restricts the way information can flow. Theories that postulate non-unitary time evolution are potentially vulnerable to making strange predictions like being able to observe what happens in another parallel world.

You cannot rule out that if CI turns out to be correct you could build a quantum computer and then control the non-unitary effects such that the thought experiment in my OP could be modified such that the observer now can have knowledge of what the spin was in the two branches.

 

[Dmitry67]

We believe that our universe extends beyond the cosmo horizon because our ability to see farther and farther, ie. see more and different stuff, has increased.

So, how much did it increase during our lives? :)
No, no, comsologists do not need to wait billion years to be sure how universe looks like in other Hubble spaces. So what you are saying is right, but please admit, it plays NO role.

 

[Fredrik]

If you don't believe in other branches you need to provide (and prove) some branch-cutting mechanism, like wavefunction collapse in CI. Or particles in BM which go into some waves, leaving other waves empty (as I understand it).

Other branches exist for the very same reason. Because they are not different from the branch we observe.

As I pointed out in #30, there are two possible intepretations of a density matrix. (Either it represents an ensemble, or it represents a single system in a specific but unknown state). If your claim is that the fact that "system+environment" is in a mixed state after a measurement implies the existence of other worlds (because there's no difference between the terms that represent reality and the other terms), then you're making a non sequiteur. There's no valid reason to assume that the mixed state can only be interpreted as an ensemble. It can also be interpreted as a specific but unknown state of a single system.

Another possibility is that Hilbert spaces don't actually describe reality, and are nothing more than convenient mathematical tools used in calculations of probabilities of possible results of experiments.

What you said about what's outside of the visible region of the universe is very different, because the theories we have actually predict unambiguously that there is something out there, so if there's nothing there, it would invalidate the theory. (We would never find out, but that's another matter). QM doesn't predict the existence of many worlds, at least not unambiguously, since there are at least two other possibilities.

 

[Hurkyl]

But we only see one instrumental possibility per trial actualized

MWI agrees that we only see one "instrumental possibility per trial actualized".

which of course leads to the only logical conclusion that the other possible results must have happened in other universes.

MWI says, given that we saw result X, that result Y didn't happen.


The point you're missing is that you keep trying to turn these conditional statements into absolute ones. It is physically impossible (for internal observers) to differentiate between a universe of definite outcomes and a universe of indefinite outcomes.

If we've seen result X, it is impossible to empirically test whether or not result Y happened -- the only thing we can now test is whether or not Y happened given that we've already seen result X.

Sure, we can always change "reference frames"^* to switch our physical description of the system from one where the result is indeterminate to one where the result is determinate if we so desire -- but that's a very different thing than insisting there's some physical mechanism that forces the universe to be in that particular reference frame.

*: I am not sure if this is actually a feature of MWI. But it is definitely a philosophical position I support.

I believe that QM (along with other things) gives us good reasons to assume that Nature is fundamentally waves in a hierarchy of media. But I'm pretty sure that this 'picture' doesn't necessarily lead to an infinitude of virtual universes or virtual worlds in our universe.

"Many worlds" is what Schrödinger's equation says happens... Heck, even classical waves have superpositions and what-not.

There are reasons to believe that other universes are possible, even highly probable. But, these are cosmological, and of course highly speculative anyway. I don't think that MWI provides the reason for, or any indication of, their existence.

MWI has absolutely nothing to do with "cosmological universes". (Or, at least what I understand that term to mean)

Since the results of the individual trials are random, it seems that the description of the system vis evolution in unitary space is somewhat at odds (pun intended - really ) with reality.

Don't forget that probabilities naturally deal with indefinite outcomes. It takes a lot of jumping through hoops to reconsile probability theory with having definite outcomes.

We can all agree that there's something moving from emitter to detector, and that it has wavelike characteristics. Then again, it also has particlelike characteristics.

It has wave-function like characteristics, always. Some situations approximate classical waves. Some situations approximate classical particles. But only approximately.

Decoherence doesn't solve the problem. So I don't understand why you think it affirms the 'reality' of quantum wavefunctions.

What relative states solved is how quantum wavefunctions evolving unitarily could be physically indistinguish from a collapsed state. What decoherence proved that wavefunctions (rapidly) tend to such situations.

Thus, quantum states evolving unitarily is known to yield (approximately) classical behavior as an emergent property. The only remaining question is whether or not it yields the right (approximately) classical behavior.

It says what can be said from the experimental evidence

There is no experimental evidence of definite outcomes. There cannot be. Yet, CI insists upon it.

 

[sokrates]

MWI agrees

MWI has absolutely nothing to do with "cosmological universes". (Or, at least what I understand that term to mean)

There is a somewhat vague connection proposed by Tegmark.

http://space.mit.edu/home/tegmark/multiverse.pdf"

If you are interested...

 

[ThomasT]

MWI says, given that we saw result X, that result Y didn't happen.

MWI is no different, in this respect, than the standard way of looking at it.

The point you're missing is that you keep trying to turn these conditional statements into absolute ones. It is physically impossible (for internal observers) to differentiate between a universe of
definite outcomes and a universe of indefinite outcomes.

The universe of our perception, the universe of experiments and statistics, is the universe of definite outcomes. From the organization of the universe as it
reveals itself to us vis physical science we can infer some things about the underlying reality.

If we've seen result X, it is impossible to empirically test whether or not result Y happened ...

If X and Y are mutually exclusive results of the same experimental trial, then yes.

... the only thing we can now test is whether or not Y happened given that we've already seen result X.

No, not if X and Y are mutually exclusive results of the same trial.

It seems like you're thinking of probability distributions as descriptions of reality.

Sure, we can always change "reference frames"^* to switch our physical description of the system from one where the result is indeterminate to one where the result is determinate if we so desire -- but that's a very different thing than insisting there's some physical mechanism that forces the universe to be in that particular reference frame.

I'm not sure what you mean by switching reference
frames.

Are you talking about the underlying physical mechanisms as one frame of reference and the definite outcomes of our experience as another?

Afaik, the assumption is that there are underlying dynamics determining the definite outcomes of our experience. Exactly what those dynamics are is still an open question. They're somewhat different for different experimental preparations.

"Many worlds" is what Schrödinger's equation says happens ...

There's no physical basis for that 'interpretation'. The 'many worlds' are just the mutually exclusive, possible instrumental configurations at the end of each trial. So, the 'many worlds' terminology is somewhat misleading regarding what's known, and what should be inferred about the underlying reality from that.

... Heck, even classical waves have superpositions and what-not.

Of course, we can actually see wave superpositions in various media. And, afaik, and along with you I think,
there's no obvious reason to assume that waves in the reality underlying our perception, in media that we can't see, are governed by essentially different mechanics than waves in media that we can see. But the 'superpositions' of instrumental level configurations vis QM probability distributions aren't themselves descriptions of underlying wave interactions. Part of the confusion is due to the close relationship between probability theory and the mechanics of physical waves. The unitarity of the wave
equation is due to the requirements of probability, isn't it?

Don't forget that probabilities naturally deal with indefinite outcomes. It takes a lot of jumping through hoops to reconsile probability theory with having definite outcomes.

No it doesn't. Just roll some dice.

It has wave-function like characteristics, always. Some situations approximate classical waves. Some situations approximate classical particles. But only approximately.

Both
particles and waves exist. Assuming that waves are fundamental, then the measurement problem is how do particulate structures and media arise in a universe that is fundamentally waves. That is, how do persistent, bound structures, or quantum protectorates, or higher organizing principles which seem to be independent of a fundamental wave dynamic, or basketballs, or toasters, or individual data bits emerge? The Schrodinger equation isn't the solution to this problem.

There are lots of hints from everyday experience about how this happens. Remember those videos on YouTube? Suppose you put some sand on a drum head and set the drum to vibrating at some frequency. The sand assumes specific configurations depending on the vibrational frequencies. We can't see it but we know that there's wave interactions, superpositions happening in the drum head, the drum, and the air in the drum media that produce those static and persistent configurations in the sand medium.

Of course, reality is quite a bit more complex, and the various media aren't just interfacing with each other, they're interspersed.

What relative states solved is how quantum wavefunctions evolving unitarily could be physically indistinguish from a collapsed state. What decoherence proved that wavefunctions (rapidly)
tend to such situations.

Thus, quantum states evolving unitarily is known to yield (approximately) classical behavior as an emergent property. The only remaining question is whether or not it yields the right (approximately) classical
behavior.

The unitarity has to do with the probabilities. The probabilities have to do with the behavior of instruments, ie., an accounting of definite results amenable to our senses without an associated description of the underlying dynamics, and the hardware technology, precise enough to produce anything but random results for individual trials. The question(s) is(are) much deeper than that. And the answers to those questions, the solution to the real measurement problem will have to do with developing a more realistic fundamental conceptual approach. As a famous physicist (Robert Laughlin I think) once said, "Seeing is the beginning of understanding."

There is no experimental evidence of definite outcomes. There cannot be. Yet, CI insists upon it.

Actually, conventional usage insists on it vis the definition of 'definite outcomes' in statistics.

 

[Dmitry67]

There's no physical basis for that 'interpretation'. The 'many worlds' are just the mutually exclusive, possible instrumental configurations at the end of each trial.

1. What is a trial, in terms of QM? What configuration/interaction of particles is called a trial?
2. They are not absolutely mutually exclusive. Quantum decoherence is a gradual process, so you can actually study how 'other branch' is starting to go away... like when you driving on a highway and hit a fork, you see cars taking other root dissapearing from your sight... not immediately...

 

[mn4j]

I think this thread is more appropriate for my reply:

In MWI there are no particles, just waves.
So there is absolutely no surprise that there is an interference pattern
The the wave hits the detector and it after a decoherence with it you see a tiy spot. Multiple branches are created in the Universe, in each universe spot is in a different place.

Your answer is not at all clear to me:

1) There are as many sources as there are worlds?
2) There are as many slit setups as there are worlds?
3) There are as many waves as there are worlds?
4) There are as many interference patterns as there are worlds?
5) At what point does the branching occur and what is the nature of this branching you talk about?
6) How does a spot originate from a wave?
7) How is probability defined in MWI?

 

[Dmitry67]

1,2 yes, there are even branches where Earth does not exist or is ruled by the dinasaurs.
But if we chose the subbranch with the same setup and particular time whe a photon is emitted, (* in fact, you cn be sure in it until it is absorbed/decoherenced, but I don't want to overcomplicate things now). Below by the 'worlds' I mean only the branches of the original branch.
3 There is only one wave which is going thru 2 slits.
4 No, there is only one because there is one wave
5 at first, the words 'branch' and 'split' are bad like a 'big bang'. 'Branching' is not instantaneous and is not universe-wide. So when wave hits the wall, it is decoherenced with it, but if YOU are sitting on the Moon you are NOT decoherenced with it at least you absord at least few photons from the radio transmission, or any other photons which carry information about it. I am not talking about usefulinformation, but rather about the QM information (which is not even destroyed in the black hole). If you are in the same room and not looking at the wall you'll be decoherenced because there are many infrared photons flying in different directions.
6. The systems state becomes diagonal. If a wall is a photomatrix with 1000000 pixels, then there are 1000000 'branches', in each you observer different cells hit.
7. This is still a point of controversy, there are some clais that Born rule ca be derived. If not, it sould be included as an axiom.

Here is a draft. Every question, if replied in details is huge, so let me know what you are interested in.

 

[mn4j]

1,2 yes, there are even branches where Earth does not exist or is ruled by the dinosaurs.

So then in MWI circles, the following makes perfect sense?:
- The probability that the Earth does not exist is greater than zero
- The probability that the Earth is ruled by dinosaurs is greater than zero
Note that what you said is equivalent the above two statements. If you disagree please explain why they are not equivalent.

But if we chose the subbranch with the same setup and particular time whe a photon is emitted, (* in fact, you cn be sure in it until it is absorbed/decoherenced, but I don't want to overcomplicate things now). Below by the 'worlds' I mean only the branches of the original branch.

Since apparently every "world" is branching at some point, the number of worlds is exponentially increasing over time. Or is there a mechanism by which some "world"s cease existing?

3 There is only one wave which is going thru 2 slits.
4 No, there is only one [pattern] because there is one wave

What about the slits in the other "worlds", is there no wave going through them. Or does the slit then exist only in one world?

5 at first, the words 'branch' and 'split' are bad like a 'big bang'. 'Branching' is not instantaneous and is not universe-wide. So when wave hits the wall, it is decoherenced with it, but if YOU are sitting on the Moon you are NOT decoherenced with it

What then is branching if it isn't the world that is branching? What are the characteristics of branching? Give me an example of a "world" before and after branching so I may better understand what you mean. Also I would appreciate if you could clarify "what" initiates a branching. Is it spontaneous? HOW does branching occur? I really want to understand the ontology of branching because I still don't see how replacing wave function collapse with reality explosion solves the measurement problem, when the real question of how it happens remains unanswered.

6. The systems state becomes diagonal. If a wall is a photomatrix with 1000000 pixels, then there are 1000000 'branches', in each you observer different cells hit.

So if one of those pixels was bad, there is going to be one less world? What if instead of a photomatrix we had a photographic film plus a scanner to digitize the signal. Will you then have as many worlds as are excitable molecules in the film? Or will you have only as many worlds as the resolution of the scanner used to digitize the image. And if the branching is occurring when the wave hits the screen then contrary to your previous claim, there must be multiple patterns, one in each branch!

7. This is still a point of controversy, there are some clais that Born rule ca be derived. If not, it sould be included as an axiom.

I was asking about the meaning of probability, not whether Born rule can be derived or not. Put another way, if I say the probability of the cat being dead is 0.149325, what does that mean in MWI.

 

[Dmitry67]

1
So then in MWI circles, the following makes perfect sense?:
- The probability that the Earth does not exist is greater than zero
- The probability that the Earth is ruled by dinosaurs is greater than zero
Note that what you said is equivalent the above two statements. If you disagree please explain why they are not equivalent.

2
Since apparently every "world" is branching at some point, the number of worlds is exponentially increasing over time. Or is there a mechanism by which some "world"s cease existing?

3
What about the slits in the other "worlds", is there no wave going through them. Or does the slit then exist only in one world?

4
What then is branching if it isn't the world that is branching? What are the characteristics of branching? Give me an example of a "world" before and after branching so I may better understand what you mean. Also I would appreciate if you could clarify "what" initiates a branching. Is it spontaneous? HOW does branching occur? I really want to understand the ontology of branching because I still don't see how replacing wave function collapse with reality explosion solves the measurement problem, when the real question of how it happens remains unanswered.

5
So if one of those pixels was bad, there is going to be one less world? What if instead of a photomatrix we had a photographic film plus a scanner to digitize the signal. Will you then have as many worlds as are excitable molecules in the film? Or will you have only as many worlds as the resolution of the scanner used to digitize the image. And if the branching is occurring when the wave hits the screen then contrary to your previous claim, there must be multiple patterns, one in each branch!

6
I was asking about the meaning of probability, not whether Born rule can be derived or not. Put another way, if I say the probability of the cat being dead is 0.149325, what does that mean in MWI.

1 Probability relative to WHAT BRANCH? In our branch it is zero, as Earth exists and there are no dinasaurs.

2 Of course worlds do not cease to exist, and the number of worlds increase and it is huge.

3 I don't understand the question. Roll a dice and if you see 1,2,3 make an experiment, if 4,5,6 then don't do it.Then in some worlds you will make a 2 slit experiment, in other you will not.

4 Could you take the Wiki quantum decoherence article (it is quite long so I don't want to repeat it) and tell what parts are not clear or not convincing?

5 No, even a pixel was bad it heated a little bit after absorbing a photon, so theoretically you could detect it. And yes, there are more branches then pixels because photon can be absorbed by a different parts of the pixel, and theoretically you can detect what parts. The number of branches is, however, less, then the number of molecules because you can't even theoretically have that precision. The number of branches is equivalent to the number of different macroscopically distinguishable states a film can form after hitting a single photon in all possible ways.

6 In MWI the definition of the probability is frequentist in the birds view and bayesian in the frog's view. This is very beautiful and unique, this is the only theory which can make them equivalent in some sense.

 

[mn4j]

1 Probability relative to WHAT BRANCH? In our branch it is zero, as Earth exists and there are no dinasaurs.

2 Of course worlds do not cease to exist, and the number of worlds increase and it is huge.

3 I don't understand the question. Roll a dice and if you see 1,2,3 make an experiment, if 4,5,6 then don't do it.Then in some worlds you will make a 2 slit experiment, in other you will not.

4 Could you take the Wiki quantum decoherence article (it is quite long so I don't want to repeat it) and tell what parts are not clear or not convincing?

5 No, even a pixel was bad it heated a little bit after absorbing a photon, so theoretically you could detect it. And yes, there are more branches then pixels because photon can be absorbed by a different parts of the pixel, and theoretically you can detect what parts. The number of branches is, however, less, then the number of molecules because you can't even theoretically have that precision. The number of branches is equivalent to the number of different macroscopically distinguishable states a film can form after hitting a single photon in all possible ways.

6 In MWI the definition of the probability is frequentist in the birds view and bayesian in the frog's view. This is very beautiful and unique, this is the only theory which can make them equivalent in some sense.

Your bird's view and frog's view answer is too generic to be useful. What is confusing is that sometimes you use probability as though it involved taking multiple worlds into account (3) and other times you restrict it to a single world (1). What rules determine when to switch between both?

Could you maybe clarify by answering the last question specifically? Here it is again for your convenience:
if I say the probability of the cat being dead is 0.149325, what does this mean in MWI?
(Please while you answer be specific about identities, when you say YOU or "I", clarify if you are restricting the "YOU" to a single branch or not)

... A probability is a theoretical construct on the epistemological level, which we assign in order to represent a state of knowledge, or that we calculate from other probabilities according to the rules of probability theory. A frequency is a property of the real world, on the ontological level, that we measure or estimate. So for us, probability theory is not an Oracle telling how the world must be; it is a mathematical tool for organizing, and ensuring the consistency of our own reasoning. But it is from organized reasoning that we learn whether our state of knowledge is adequate to describe the real world.

Jaynes, E. T., 1989, "Clearing up Mysteries - The Original Goal" in Maximum-Entropy and Bayesian Methods, J. Skilling (ed.), Kluwer, Dordrecht, p. 1

The above is a standard bayesian view of the meaning of probability. Please explain how this applies to what you call MWI bird's.

 

[Dmitry67]

I had almost typed my answer, but then I started to think more and more about it and I had lost the clear vision I had before :)

I have to take a timeout - I need to rethink a lot. I agree that the question is very important.

Obviously, no matter how small the probability is of a branch we don't feel less 'real' in that branch. For example, if we generate 100 random digits from 0 to 9 and read this random number, we chose one of 10^100 branches, and we are on a branch with a probability of 10^-100 in comparison with what we had before. Still, we don't feel ourselves less 'real'

But still the probability plays a very important role in the Universe.

I have to say I am very optimistic - it is not a 'bad' problem (a problem which requires adding more and more epicycles, or adding more and more adhoc tricks to fit the observations, like our BM proponents like to do :) ) - it is a 'good' problem, I have a feeling that nature is trying to tell us something important here.

(Please while you answer be specific about identities, when you say YOU or "I", clarify if you are restricting the "YOU" to a single branch or not)

As a side note, I agree, it is important I believe to define some kind of a formalism. Most of the sentences does not make any sense until you specify the Interpretation, then Frog or birds view, and in MWI specific branch or all branches.

 

[Fra]

I can't resist adding a comment to this independent on MWI.

But still the probability plays a very important role in the Universe.

MWI or not, I agree that the meaning of "probability" - not in pure mathematics - but in the context of reality and physics is a key.

IMO a lot of confusion arises because of the mistake to not analyse the physical basis of probability.

Alot of my somewhat "solipsist" personal views, are partly a result from reflecting upon the meaning of probability, probability spaces, transition probablities. In particular when you acknowledge that usually the meaning of an observer assigning a subjective probability to possible futures IS reflected in this observers ACTIONS. Thus, the probability or the observers "belief" is evolving, because there is always a backreaction to the actions, this backreaction favours actions that are somewhat constructive and consistent with the environment, so that the backreaction is non-destructive.

So self-desctructive actions, self-destruct their own backbone(observer-hardware) so to speak.

In this sense, probability P(x|O) is not a matter of objectively beeing right or wrong, it's more as I see it at least, about how the conditional observer O, acts. If you then think of the probability SPACE, or the microSTRUCTURE, whos state (distribution or microSTATE) encodes information, then the microSTRUCTURE or probability SPACE playes the role of memory HARDWARE.

And either you add this hardware as a ad hoc baggage, or you try to explain how this hardware is emergent, in this recursive process itself. And I've come to not find another resolution but to identifty this "flow" with the flow of time. And dependence on the observer, of how this flow, could correspond to the observer dependence of time as well.

This background indepdendence measn that the dice is deforming after each throw, and in a way that is indeterministic in advanced. The dice can even shrink or grow.

So I think the problem at hand is, how can be imagine howto construct a dice, starting from NO dice? Could a random fluctuation be taken as an initial dice, and then be made to grow? And would this game produce a random distribution of dies in nature, or would only certain families of dices come out of this mad game alive?

/Fredrik

 

[ThomasT]

1. What is a trial, in terms of QM? What configuration/interaction of particles is called a trial?
2. They are not absolutely mutually exclusive. Quantum decoherence is a gradual process, so you can actually study how 'other branch' is starting to go away... like when you driving on a highway and hit a fork, you see cars taking other root dissapearing from your sight... not immediately...

1. It would depend on the setup. For the purpose of this discussion we can refer to a filter/ PMT setup where photon detections are being sequentially registered, and define a single trial as a single photon detection.

2. A detection is either registered or it isn't. Those are the possible outcomes -- and they're absolutely mutually exclusive wrt the real world.

Wrt your highway analogy, of course the detection process isn't instantaneous. We don't need MWI/decoherence to tell us that, do we?
The picture of a fork in the road with one possible outcome taking one fork and the other possible outcome taking the other fork isn't a realistic one.

Is MWI/decoherence contributing in any way to a realistic picture of what's happening at the quantum level?

 

[t_siva03]

A lot of replies have invoked Occam's razor, and MWI being a simpler theory because of the lack of requirement of wave function, but I ask:

What is simpler? A wave function collapsing, or an entire universe being duplicated because measurement of one quantum particle has been made? What is the mechanism of such a duplication? I mean we are talking about duplicating an entire universe instantly! A universe which will exist forever and continue to multiply. And all of this just to avoid collapse of a single wave function?

hmmm...what would Occam think?

 

[Fredrik]

A lot of replies have invoked Occam's razor, and MWI being a simpler theory because of the lack of requirement of wave function

The claim was that the MWI is simpler because the collapse axiom can be derived from the other axioms. As far as I can tell this claim is false. The MWI proponents aren't just removing the axiom that says that a measurement of observable B on a system in state |u> gives us the result b and leaves the system in state |b> with probability |<b|u>|². They're replacing it with another axiom which is essentially equivalent to the one they dropped. (See #27 in this thread).

What is simpler? A wave function collapsing, or an entire universe being duplicated because measurement of one quantum particle has been made? What is the mechanism of such a duplication? I mean we are talking about duplicating an entire universe instantly!

Actually we're not. The the time evolution of the state of the universe is a curve in a Hilbert space. (The curve defined by the Schrödinger equation and an initial condition). A measurement is just an interaction, and the only thing that happens to the wavefunction of the universe during that interaction is that it moves forward along the curve. So it's clear that no information is duplicated anywhere.

In order to get something that can be interpreted as worlds, we must decompose the Hilbert space of the universe into a tensor product of Hilbert spaces representing subsystems. When we describe the state of the universe in terms of the states of its subsystems, we use a mathematical expression (a density matrix), which can be interpreted as representing many worlds.

 

[t_siva03]

Hi Fredrik,

Thank you for your explanation. Please help me to understand better, as my background is in the biomedical sciences, and I have little physics/mathematics training.

Aside from the mathematical explanation of moving along the curve in Hilbert space during decoherence, does there currently, in actuality, exist a universe in which dinosaurs are roaming the world, and others in which hostile aliens have conquered our world in Dewitt's description of MWI. If so, then doesn't this require the existence of all of the information within each of those separate universes? How is it then that information does not multiply with each decoherence?

Or am I not understanding something fundamental about how hilbert spaces work?

 

[Fredrik]

Aside from the mathematical explanation of moving along the curve in Hilbert space during decoherence, does there currently, in actuality, exist a universe in which dinosaurs are roaming the world, and others in which hostile aliens have conquered our world in Dewitt's description of MWI.

Unfortunately science doesn't answer questions like that. The situation right now is that we have a single mathematical expression that can can be interpreted as representing either an ensemble of systems in different states (i.e. many worlds), or a single system in an unknown state. Experiments can't distinguish between those two options, because they both exist within a single theory. I mean, they are both possible interpretations of the same axioms, and experiments can't tell us anything more than how accurate the predictions derived from those axioms are.

I myself prefer a third option. Quantum mechanics is an algorithm that tells us how to calculate probabilities of the possible results of future experiments given the results of past experiments. It does that without actually describing what the world is like.

If so, then doesn't this require the existence of all of the information within each of those separate universes? How is it then that information does not multiply with each decoherence?

If I specify that the state of the universe is represented by a point f in the Hilbert space of the universe, I haven't given you any more or any less information than if I had instead specified that the state of the universe is represented by the point g. To specify a single point in this Hilbert space is to specify the state of all the worlds, or equivalently to specify the possible states that the world can be in and the corresponding probabilities.

To specify a point in a Hilbert space is equivalent to specifiying its projection on each basis vector, and this Hilbert space is infinite-dimensional, so there's an infinite number of them. So we don't have to worry about a single point not containing enough information.

 

[atyy]

I myself prefer a third option. Quantum mechanics is an algorithm that tells us how to calculate probabilities of the possible results of future experiments given the results of past experiments. It does that without actually describing what the world is like.

In your view, would it be ok to say this is true of all science, not just quantum mechanics?

 

[vanesch]

I once wrote a small paper on this thing, you can find it on the arxiv in ph-quant under the number 0505059. I have to warn that I didn't get it published, so this is, according to the PF rules, not a viable reference. However, the comments were more of the kind of "well-known" or "not of interest to our readership", but never about any specific problem with the content.

I just tried to play "Gauss" in the paper, by seeing whether or not the projection postulate is somehow derivable from "unitary quantum theory", and tried to apply the same reasoning as Gauss (and others) did when examining Euclid's fifth postulate by constructing non-Euclidean geometry, by seeing whether it is possible to construct another theory which is consistent (though of course not experimentally correct) in which the projection postulate is different. The consistency of such a theory would then prove the independence of this postulate from the others. The details are written down in that paper. As I said, it is not an accepted peer-reviewed paper, so take it for what it is.

 

[Fredrik]

(Continuing what I started in #82...)

I'm not sure that answers your question though. "How is it then that information does not multiply with each decoherence?" My point is that you'd have to specify two points in the Hilbert space of the universe to double the information, and there is never any need to.

Also, the decomposition of the universe into subsystems seems to be arbitrary. We can choose to decompose it into "Felix the cat" and "everything else" during an interaction that starts with the cat being alive and ends with the cat either being alive or dead. This particular decomposition makes it look like we started with something relatively uncomplicated, and ended up with something more complicated, but this seems to be an artifact of the decomposition that we chose to make. If we had chosen another way to decompose the universe into subsystems, maybe all of the subsystems would been just as complicated at the start of the interaction as at the end.

Actually, I think that if we choose that particular decomposition, we are already "cheating" a bit. The degrees of freedom (the basis vectors) of the Hilbert space that we think of as representing a cat that's alive, should be a representation of a lot more. In many-worlds terminology, there's already a very large (infinite?) number of worlds, and those degrees of freedom only represent a cat that's alive in some small fraction of them. What we're doing when we describe the cat as being alive at the start of the experiment, is to only consider that small fraction of worlds where the relevant degrees of freedom represent a live cat, and not e.g. a collection of gas in space. So the apparent simplicity of the state of the subsystem at the beginning of the measurement is very artificial. It's an artifact of the choice to decompose the universe into those particular subsystems, and the choice to only consider the worlds that are relevant to us.

 

[Fredrik]

In your view, would it be ok to say this is true of all science, not just quantum mechanics?

I would say that all we can know about a theory (I define that concept as "a set of statements that tell us the probabilities of the possible results of experiments") is how accurate its predictions are. (Note the distinction between this and ending the sentence with e.g. "...if its predictions are accurate"). We can't ever know if the theory really describes the relevant aspects of the universe. However, I still think that all the classical theories are descriptions of the relevant aspects of the universe. To be more precise, they can be thought of either as approximate descriptions of our universe, or as exact descriptions of fictional universes that resemble our own. The mathematical concepts defined by the theories correspond to things in the real world.

I think that quantum mechanics is the first example we have found of a theory that isn't like that. It's just an algorithm, and not a description. It can be interpreted as a description of a fictional universe (which is what the MWI is about), but that universe doesn't really resemble our own. It's just a tool we can use to predict probabilities of possibilities. There's nothing in the real world that corresponds to a state vector. QM is also the first example of a theory that predicts non-trivial probabilities, i.e. probabilities that aren't 0 or 1.

I once wrote a small paper on this thing, you can find it on the arxiv in ph-quant under the number 0505059.

Thanks for the reference. I'll check it out later. Right now I have to do something else.

 

[Fra]

A question for the user=Fredrik:

There's nothing in the real world that corresponds to a state vector.

Then you seem to not think of the context of your "algorithm"(QM) as part of the real world?

Are not human scientists, and their stuff part of the real world and nature?

Do you adhere to the camp that thinks the observer in QM can only make sense if it's a human scientist?

I think that even though, the theories currently under corroboration, does not correspond to the reality out there in the realist sense (here I agree fully), the IMAGE or even ILLUSION itself, must have a physical basis in an observer. IE. no observer - no illusion. (To have a microstate, you need a microstructure)

I'm curious if user=Fredrik hols a shut up an calculate view, and considers the algorithm satisfactory described by say "Poppian evolution", by "human/scientist" level corroboration and falsification?

/Fredrik
(user=Fra)

 

[atyy]

I think that quantum mechanics is the first example we have found of a theory that isn't like that. It's just an algorithm, and not a description. It can be interpreted as a description of a fictional universe (which is what the MWI is about), but that universe doesn't really resemble our own. It's just a tool we can use to predict probabilities of possibilities. There's nothing in the real world that corresponds to a state vector. QM is also the first example of a theory that predicts non-trivial probabilities, i.e. probabilities that aren't 0 or 1.

Hmm, what about statistical mechanics? Do you think its ensembles could qualify as a fictional universe?

 

[Hurkyl]

The mathematical concepts defined by the theories correspond to things in the real world.

I think that quantum mechanics is the first example we have found of a theory that isn't like that.

What is this other theory that tells us about "things in the real world", and why should it overrule what quantum mechanics has to say?

 

[Fredrik]

Then you seem to not think of the context of your "algorithm"(QM) as part of the real world?

Not sure if I understand the question. We can obviously use the algorithm to calculate probabilities of possible results of experiments.

Are not human scientists, and their stuff part of the real world and nature?

They are.

Do you adhere to the camp that thinks the observer in QM can only make sense if it's a human scientist?

Not at all. In fact, I consider that camp to be a bunch of crackpots.

I think that even though, the theories currently under corroboration, does not correspond to the reality out there in the realist sense (here I agree fully), the IMAGE or even ILLUSION itself, must have a physical basis in an observer. IE. no observer - no illusion. (To have a microstate, you need a microstructure)

If you mean that what we perceive must be the result of physical interactions, then I agree. If you meant something very different, you may have to explain.

I'm curious if user=Fredrik hols a shut up an calculate view,

I don't. "Shut up and calculate" is a suggestion that it doesn't matter which of the interpretations of QM describes what "really happens" during a measurement, and that it's not important to understand the theory. I would never suggest either of those things.

What I'm saying is that there's no reason to believe that any of the interpretations of QM describes what really happens, and that it takes a fairly deep understanding of the concepts "theory" and "science" just to understand that QM doesn't need an interpretation.

and considers the algorithm satisfactory described by say "Poppian evolution", by "human/scientist" level corroboration and falsification?

I don't understand this question, maybe because I don't know what "Poppian evolution" is.

Hmm, what about statistical mechanics? Do you think its ensembles could qualify as a fictional universe?

I haven't really thought about it, but I don't see why not. I'm more concerned by questions like "Is space really curved?" (recently discussed in another thread). It seems that the standard formulation of GR, and the alternative (in which spacetime is flat, and measuring devices are "rubbery") are exact descriptions of two different fictional universes. If one of them is an approximate description of our universe, the other one isnt. That's actually a pretty good argument to think of classical theories as exact descriptions of fictional universes, rather than as approximate descriptions of our own.

What is this other theory that tells us about "things in the real world", and why should it overrule what quantum mechanics has to say?

I don't understand your question, but there's no theory that overrules what QM has to say.