Can Quantum Computers Validate the Many-Worlds Interpretation?

[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.

 

[Fra]

Perhaps I misunderstood your postion, here are some additional questions. I do not argue in favour of MWI of any other big camp, I am just curious about your position.
(My own view doesn't quite fit into any of the big camps)

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.

The problem I have in mind here is the ontological status of probability, and thus implicitly the algorithm from which it (in standard QM) follows deterministically.

If we are talking about some kind of standard frequentist interprettion, then the question of wether a calculated probabiliy, is "correct" can only be determined for past predictions, given that the time history is retained intact, which I think is not generally the case. Also even if the history IS retained perfectly, we can not affect the recorded time history by noting that our probability estimate was right or wrong. I argue that in this sense, at the point where the correctness of the prediction can be established, the question of wether the guess was right or wrong, has lost it's significance, because whatever actions that was based on the flawed conception is history.

So assuming the question is more clear - do you, or do you not agree that the most sensible meaning of probability is simly operational in the sense that the probability determines the actions of the one having calculated the probability (the observer that is)?

So what I sugges is that, states and processes are mutually confirming. They confirm each other. It makes no sense to talk about a statevector, unless the context in where it is confirmed is attached. What I picutre here is that probability and state vectors, can be understood in terms of the actions implied.

Assuming you agree? then I found it puzzling that you say there is no correspondence to the state vector. As I see it, the correspondence of the state vector is the observers expectation of the future, given a finite memory record of the past. Howto describe this mathematically is still an open question, but IMHO it involves an evolving view of law, where the observers encodes physical law, and the objectivity we see, is manifested in the population of physical observers (not humans). It's from an inside point of view IMO not simply a matter of choosing a basis, it's worse, it's a matter of choosing the (hilbert) space. Given a "choice", all expectations relate to that, and determines the actions. But the space can deform.

I think the view to picture the state space of the universe in a realist sense is nonsense. Such notions has no place in my view.

So maybe you meant to say that there is no OBJECTIVE/observer independent correspondence to the state vector in the sense of old style realism? If so, I agree. But if you think that it is only a mathematical abstraction that does not in any way have anything todo with reality then I disagree.

About your other comments, they are mostly in line with what I think. I might have misinterpreted you about "objective" vs "subjective" correspondence.

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

I don't think it's a standard terminology, but what I mean is if you think that: Poppers view of the scientific method is satisfactory, and what's beyond that is also the beyond the point of this discussion?

Have a nice Valborg and try to stay ontop of things ;-)

/Fredrik
(user=Fra)

 

[Dmitry67]

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.

Thank you, it was interesting, especially the 'strangeness of AQT'
P.S. Still thinking about 'what does probability mean in MWI'

 

[ueit]

So assuming the question is more clear - do you, or do you not agree that the most sensible meaning of probability is simply operational in the sense that the probability determines the actions of the one having calculated the probability (the observer that is)?

I see some problems with this view:

1. A clear definition of "observer" is missing.
2. The observer itself is a complex system that follows the same laws like the "observed" system. I see no reason to build a theory that explains the behavior of a simple entity (like a molecule for example) in terms of its influence upon an enormously complex system like a brain (or something else that is capable of calculating probabilities).

 

[t_siva03]

(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.

Thank you for your extensive explanation.

If we consider representing the universe by using hilbert spaces, then you would not have to ever use two points. But you would have to use additional dimensions in Hilbert space to represent that information using a single point, right? Doesn't this use of additional dimensions represent the gain of information? (I.e. can we not say that a point in two dimensional hilbert space represents less information than a point in 10 dimensional hilbert space?)

 

[ueit]

If we consider representing the universe by using hilbert spaces, then you would not have to ever use two points. But you would have to use additional dimensions in Hilbert space to represent that information using a single point, right? Doesn't this use of additional dimensions represent the gain of information? (I.e. can we not say that a point in two dimensional hilbert space represents less information than a point in 10 dimensional hilbert space?)

I don't think we can speak of any actual increase in information in a theory that is deterministic. In principle, all "branches" can be calculated from the initial wavefunction. No new information added.

 

[Fra]

This gets slippery and I suppose takes us into possible ideas of beyond the standard model. Maybe the thread should be moved? Anyway I go ahead and respond brielf.

So assuming the question is more clear - do you, or do you not agree that the most sensible meaning of probability is simply operational in the sense that the probability determines the actions of the one having calculated the probability (the observer that is)?

I see some problems with this view:

1. A clear definition of "observer" is missing.

Yes. There IS no clear (certain, definite and observer independent) physical definition. There are no static stable observers. This is a basic trait if this view, this is why the observer does not have a static definition independent of it's context.

But the fact that it's uncertain, doesn't mean it's arbitrary - it's still constrained.

Most other approaches fail even worse. The often try to think of the observer as a classical limit, which clearly can't cover all scenarios OR define the observer relative to a completely unphysical an unaccessible (from a scientific poitn of ivew) birds view.

I try to attack the problem right at face, but witout denying the importance of htte observer. And the evolving picture is my suggestion.

2. The observer itself is a complex system that follows the same laws like the "observed" system.

1. I probably agree in the way you mean about treating the observer on the same basis as other things. But the possible difference lies in what you mean by law. I do not have any realist illusions of law. In addition there is in the very nature of observation and science ALWAYS an observer.

2. Not all observers are complex. In my view, what old school QM calls classical observers are indeed complex, VERY complex. But I see no reason why the observer couldn't be an atom, or even sub-planck observers, whatever that is. So in my view, an observer can have ANY complexity from zero to infinity. And the interesting this is how _observed_ and inferred law, as seen from this inside observer, scales with it's complexity.

This has nothing at all to do with the biology of the brain, other than the obvious fact that it takes a human brain to type in the char sequences on this forum. But that's my language.

There is predictive power to gain, if we can exploit the analogy of the intelligence of a massive complex observer, and the physical action of a low complexity observer. I'm convinced there is an analogy.

I see no reason to build a theory that explains the behavior of a simple entity (like a molecule for example) in terms of its influence upon an enormously complex system like a brain (or something else that is capable of calculating probabilities).

In the extended abstraction, "calculating probability" is only a metaphor. Litteralty speaking it's obviosu that only humans with the right edyyucation actually calculate probabiilities. But from that there are downwards various levels of indirect "risk assessments", that's used in their life.

Humans have been aware of risks before probability theory was formalized.

But at physical microphysics level, the state of a system reflects it's "expectations" in the sense that internal re-equilibration is chosing to optimize the presumed preservation of the system itself. Environmental disturbance will ensure this, because non-constructive systems will destabilize.

So microstructures "compute probabilities" by evolving a system of internal microstructure that corresponds to the mathematical computation of expectation from input. Ie. given an observation, the collapse of your previous "opinion", is the re-assessment of the expected future.

I think the state of an observer _IS_ a manifestation of it's expectation of the future, GIVEN itself (which is a evolved memory record). In turn this expectations, constrains strongly the observers actions.

There is no way to separate the observer, from it's behaviour, no more than it makes sense to picture a squirrell during the first 3 minuters of the universe. The squirrel is total baloney unless it's context is specificed. The same with and observer - IMHO that is. This is my highly personal but considered opinion.

The poitn of all this, is that IMO it has the potential to solve a lot of problems.
Also if every subsystem of the universe evolve as per this "logic", then the states of all parts will predict it's interaction.

/Fredrik

 

[Fredrik]

Fra, I'm sorrry, but I understood almost nothing of what you were trying to say or ask before the text I'm quoting below.

I found it puzzling that you say there is no correspondence to the state vector. As I see it, the correspondence of the state vector is the observers expectation of the future, given a finite memory record of the past.

OK, I see your point here. The vector that represents the state of a quantum system is represented in the real world by the observer's expectation, which is a property of a physical system (the observer). So yes, in this case, there is something in the real world that corresponds to the state vector of a quantum system. But what about the state vector of some arbitrary speck of dust in intergalactic space? There's no observer who can have any expectations about it.

So maybe you meant to say that there is no OBJECTIVE/observer independent correspondence to the state vector in the sense of old style realism? If so, I agree. But if you think that it is only a mathematical abstraction that does not in any way have anything todo with reality then I disagree.

It obviously has something to do with reality, since we can use it to calculate probabilities.

I don't think it's a standard terminology, but what I mean is if you think that: Poppers view of the scientific method is satisfactory, and what's beyond that is also the beyond the point of this discussion?

I'm not really familiar with what his contributions to the scientific method were, but I don't think I would have any objections. I would however state the definition of a theory more clearly, and emphasize that a theory doesn't have to be an "explanation" or a "description". It just has to make predictions about the probabilities of possible results of experiments, because that's all it needs to do to be falsifiable.

 

[Fra]

Can anyone give a clear definition of a squirrel?

Squirrels has evolved, and is evolving. The difficulty of definition doesn't stop us from having a FAPP type of definition.

The importance is to understand how things evolve, not to try to find timless definitions.

/Fredrik

 

[ueit]

Yes. There IS no clear (certain, definite and observer independent) physical definition. There are no static stable observers. This is a basic trait if this view, this is why the observer does not have a static definition independent of it's context.

I didn't ask for a definition of the observer that is "static", "stable", "independent of it's context". As the "observer" seems to be some sort of primitive in your theory there should be some definition of it, don't you think? I mean, what is your theory about?

But the fact that it's uncertain, doesn't mean it's arbitrary - it's still constrained.

I do not understand the meaning of this. For now, I don't know what an observer means in your theory, much less what an uncertain/ constrained observer refers to.

Most other approaches fail even worse. The often try to think of the observer as a classical limit, which clearly can't cover all scenarios OR define the observer relative to a completely unphysical an unaccessible (from a scientific poitn of ivew) birds view.

May be, but at least the observer is defined somehow.

1. I probably agree in the way you mean about treating the observer on the same basis as other things. But the possible difference lies in what you mean by law. I do not have any realist illusions of law. In addition there is in the very nature of observation and science ALWAYS an observer.

I don't think it is possible to build a theory without laws because you cannot calculate/predict anything.

2. Not all observers are complex. In my view, what old school QM calls classical observers are indeed complex, VERY complex. But I see no reason why the observer couldn't be an atom, or even sub-planck observers, whatever that is. So in my view, an observer can have ANY complexity from zero to infinity. And the interesting this is how _observed_ and inferred law, as seen from this inside observer, scales with it's complexity.

So, do you just redefine the term "quantum system" as "observer"? Are there systems that are not observers?

There is predictive power to gain, if we can exploit the analogy of the intelligence of a massive complex observer, and the physical action of a low complexity observer. I'm convinced there is an analogy.

There should be a analogy because "a massive complex observer" can be reduced in principle to a large group of interacting particles and those particles are identical with the particles of the observed system.

In the extended abstraction, "calculating probability" is only a metaphor. Litteralty speaking it's obviosu that only humans with the right edyyucation actually calculate probabiilities. But from that there are downwards various levels of indirect "risk assessments", that's used in their life.

Humans have been aware of risks before probability theory was formalized.

But at physical microphysics level, the state of a system reflects it's "expectations" in the sense that internal re-equilibration is chosing to optimize the presumed preservation of the system itself. Environmental disturbance will ensure this, because non-constructive systems will destabilize.

So microstructures "compute probabilities" by evolving a system of internal microstructure that corresponds to the mathematical computation of expectation from input. Ie. given an observation, the collapse of your previous "opinion", is the re-assessment of the expected future.

I think the state of an observer _IS_ a manifestation of it's expectation of the future, GIVEN itself (which is a evolved memory record). In turn this expectations, constrains strongly the observers actions.

How can a observer compute probabilities if there are no objective physical laws?

There is no way to separate the observer, from it's behaviour, no more than it makes sense to picture a squirrell during the first 3 minuters of the universe. The squirrel is total baloney unless it's context is specificed. The same with and observer - IMHO that is. This is my highly personal but considered opinion.

QM is a contextual theory, indeed.

The poitn of all this, is that IMO it has the potential to solve a lot of problems.
Also if every subsystem of the universe evolve as per this "logic", then the states of all parts will predict it's interaction.

Again, I am not sure how one can predict anything in the absence of a law.

 

[Hurkyl]

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

Then upon what grounds can you claim that what QM has to say does not actually correspond to things in the real world?

 

[Fredrik]

Then upon what grounds can you claim that what QM has to say does not actually correspond to things in the real world?

I'm not claiming that as a fact. I was just stating an opinion. I thought that was clear. My point is that all the older theories had a more or less obvious correspondence between things in the model and things in the real world, and quantum mechanics does not. Also, a theory doesn't have to be a description of the real world to be both "a good theory" and falsifiable. It just has to make predictions about probabilities of possible results of experiments. That means that it doesn't make sense to assume that if we find a good theory, it must be a description of the real world, and yet, that seems to be what most people are doing with QM.

Yes, I believe that QM isn't a description of the real world, and I can't prove that I'm right. In fact, I don't even have any strong arguments for it. The reason I still feel the need to mention it is that the people who believe that QM is a description of the real world don't seem to understand that it doesn't have to be. The fact that it can predict probabilities very accurately doesn't imply that it is.

 

[Fra]

Thanks for your responses Fredrik.

Fra, I'm sorrry, but I understood almost nothing of what you were trying to say or ask before the text I'm quoting below.

Ok, sorry. My objection has a philosophical inclination, perhaps that is what makes it unclear.

So yes, in this case, there is something in the real world that corresponds to the state vector of a quantum system. But what about the state vector of some arbitrary speck of dust in intergalactic space? There's no observer who can have any expectations about it.

In my view - a speck of dust in intergalactic space can for sure in principle quality as an observer. The microstructure of the dust, and the inter-particle forces can hold end encode information. The state vector of it's environment, relative to itself, is manifest by the collective microstructure of the cloud, including the internal structure of the dust particles.

However, such an observer would have a low degree of coherence and probably not maintain it's integrity very long. It's possible a very volatile observer - just like the squirrel during big bang. The fitness of an observer is related to the environment. But it could well be relatively speaking that in some environments, such in space, clouds of dusts is the most evolve observers around.

Then you may think that it's ambigous to define the cloud, why not individual dust particles beeing observers? But that's no contradiction. In as much as my entire human body is an observer, the single cells in my body are also individual observers interacting with their environments and other cells. There is no problem with that different decompositions is possible. Because from the external view, this is not important.

An observer has one decomposition, the self, and it's environment.

In my view observer are evolving, and only the observers that maintain their integrity and have a strong degree of coherence over time would be have a clear identity. But I see a transition all the way from unidentifiable observers, to very identifiable objective observers that correspond to classial ones.

I'm not really familiar with what his contributions to the scientific method were, but I don't think I would have any objections. I would however state the definition of a theory more clearly, and emphasize that a theory doesn't have to be an "explanation" or a "description". It just has to make predictions about the probabilities of possible results of experiments, because that's all it needs to do to be falsifiable.

The reason why I asked is because it seems to me that often peoples view of the scientific method correlate with their preference for physical theories.

About predictions, I agree with you. But in that view, there is an important think that Popper doesn treat very well. It's the description of how new hypothesis are constructed. Once you have a theory on the table for testing, that's ethier corroborated or falsified, it's easy. That is the SIMPLE part. The hard part is, what happens when the theory is shot down, and it has to generate a new hypotheis. Clearly this procedure would not work well unless there is a development also of an algorithm for hypotheis generations.

I think this is closely related to physical interactions and physical law.

As we know in biology, the fitness of spieces is not always a simple function of it's instant properties. Since they are constantly challanged by a dynamical environment their ability to adapt promtly and correctly is of high survival value.

In short, the important trait is not only to be able to tell when you are wrong, but to know what do to when your world view collapses. It's easy to know what to do when you keep beeing right - then you don't change anyway, and just keep following the "geodesic" in your "hypothesis space".

/Fredrik

 

[atyy]

Then upon what grounds can you claim that what QM has to say does not actually correspond to things in the real world?

On the basis that in corresponds to things in the real many worlds?

 

[Hurkyl]

That means that it doesn't make sense to assume that if we find a good theory, it must be a description of the real world, and yet,

Of course. But the point is that QM is the least incorrect description of the real world.

On the basis that in corresponds to things in the real many worlds?

This doesn't make any sense.

 

[atyy]

This doesn't make any sense.

Ah well, not too good a stupid joke then.