Can Quantum Computers Validate the Many-Worlds Interpretation?

[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.

 

[Fra]

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?
...
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.
...
May be, but at least the observer is defined somehow.
...
So, do you just redefine the term "quantum system" as "observer"? Are there systems that are not observers?

Ok, now I see what you mean. I thought the basic meaning of observer was clear but may not. I'm sorry.

I'll note that I don't yet have a complete theory, I am working and looking for a reconstruction of current models. But some starting points and design principles are in place.

Roughly my view is like this.

About observers, to avoid confusion I'll note that there are two views of that.

* The inside view

- is the view of the universe an inside observer has.
This VIEW defines the observer.

analogies:

1. It's like the distinction between the self, and non-self. But this is difficult because since the observer is not static, this boundary is fuzzy and evolving.

2. Another interesting analogy is like the distinction between what you know FOR SURE and what you are only guessing. I'm sure you would agree that there is a fuzzy boundary here, in particular where you are "almost sure" but not quite. Or you can argue that you are never sure and it's all about various degrees of certainty - this view matches in my view as well.

Since I'm picturing a reconstruction I avoid using too much standard QM terminology since people would tend to think I in an unreserved way refers to existing concetps.

But loosely speaking, I think the hilbert space is part of the observers identity. And I am not talking about the hilbert space of the environment in a decomposition H_univers = H_observer x H_remainder, I'm suggesting that math makes no sense because it mixes inside view and birds views in an IMHO conceptually illegal way.

So the hilbert space of the universe, as seen from the inside observer, is CONSTRAINED by the complexity of the observer. A simple observer can not relate to the full complexity of it's environment.

So from the inside view, I call the home of the information and state vectors as a system of microstructures. And this can not be questioned objectively by the inside observer. It just is. However, as to the question how it became to me, then there is an evolutionary picture in which this microstructure evolves and can gain complexity (which I associate also to mass in some form)

The "problem" for the inside view, is to survive the challange of the environment. In this picture, what was usually called an inconsistency between views, is here instead just exactly what causes the evolution (both time an large perspective)

* external view

This is the view, where ONE observer ponders that parts of this own environment can be thought of as separate observers that are mutually interacting. IE. One observer observes other observers.

In this view, the notion of observer is farily unclear. But my point is that this is not a big problem. It is only a problem for those who can't let go of some realist ideals.

I don't think it is possible to build a theory without laws because you cannot calculate/predict anything.
...
How can a observer compute probabilities if there are no objective physical laws?
...
Again, I am not sure how one can predict anything in the absence of a law.

This is an example of a very general an repeating problem. It also comes in other disguises.

It's the origin problem.

I didn't say I think there is no law, whatn I mean is that IN GENERAL there is no objective law which we can be sure all observers agree upon.

Instead, I am suggesting that objective LAW is emergent.

There are predictions, but they only live in an evolving context, so even faulty prediction has a place. The observer which embodies consistently flawed predictions, will have his microstructure destroyed and deformed by environmental feedback.

So in an near equilibrium scenario, there are fapp type of objective laws, and we recover pretty much the standard physics, but what I am suggesting is a possible way to in a deeper way understand why the laws of physics are like they are, and wether they are better seen as evolving or fixed.

I'm suggesting that you can LEARN and improve, without having fixed rules for learning, because whole point is that you do not only learn as per fixed rules, you even learn the learning rules. The context is evolution.

The evolutionary context is IMO the best way to see law. Wether these observed laws are the same as some "real laws" is something to which nature is indifferent.

Not sure if that made sense...

/Fredrik

 

[Fra]

More: Thus do I think that the "measurement" operators are evolving together with the hilbert space (this is what I mean by evolving observer). The hilbert space as SUCH also contains information, that is usually not accounted for. I think this is constrained by the mass or complexity of the observer. Thus the complexity of an observer, and it's history, does actually contrains what possible interactions it can participate it. This is the idea on howto eventually make predictions.

The fact that ALL observers participate in gravity and has inertia, gets a natural explanation here since the inertial mass is the "complexity count" of the system of microstructures (which includes the _inside observed_ hilbert space).

The information theoretic primordal of inertia is an evidence count. It's the resistance against perturbation. All structurs have this, including what is currently thought of as abstract things, such as hilbert spaces. HIlber space relates to the state vector as the memory state to the memory hardware. The memory hardware itself, contains information too. This is not acknowledge in current formalism. I think we can do better.

/Fredrik

 

[Dmitry67]

Regarding the subject.

I have a raw idea, may be it is incorrect, but anyway.

After the decoherence the off-diagonal elements quickly approach 0, so only diagoal elements are left. But let's chose the diagonal element with a very low probability - almost impossible event.

If the probability is very low, then value in that diagonal cell can be in the same range as the neighbour off-diagonal elements. Hence, if you are on a very unprobable branch then there might be an interaction with the 'other branches' or more precisely, with the 'bath' of the yet non-decoherenced states.

Oversimplifying, MWI predicts that if you roll the dice 1000000 times and always get 6, then look around, very probable there are other weird things happening around, like you can see 2 semi-transparent images of both cats.

 

[Count Iblis]

More likely, you'll hear the 7 am alarm go off.

 

[atyy]

More likely, you'll hear the 7 am alarm go off.

I would like to be in that world! Wait - "I" already am?

 

[Fredrik]

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

I'm not convinced that even that view can be justified. The axioms of QM are supposed to be these:

i) all isolated systems evolve in time according to the Schrödinger equation
ii) [the probability rule -- you know the details already]

The weird thing is that ii describes the time evolution of the system and the measuring device during a measurement, but i is supposed to describe the time evolution. We clearly don't want two time evolution axioms, since we might end up with a contradiction.

So how do we avoid contradictions? I'm glad you asked. I only see two possibilities:

1. The time evolution in ii is only a special case of the time evolution in i.
2. You are only allowed to use the time evolution axiom on systems that you are not a part of.

If 1 is correct, it must be possible to prove it. But attempts to do so have failed. The successful attempts to derive the probability rule all used another axiom, which is essentially equivalent to ii).

If 1 is incorrect, then we are left with 2, and in that case I really don't see how to justify the view that QM is a description of the universe (Edit: I don't see how we can even think of it as a description of a fictional universe). 2 is however completely consistent with the view that QM is just an algorithm that tells us how to calculate probabilities of possible results of future experiments, given the results of past experiments.

 

[mn4j]

Regarding the subject.
After the decoherence the off-diagonal elements quickly approach 0, so only diagoal elements are left. But let's chose the diagonal element (1) with a very low probability - almost impossible event.

If the probability is very low, then value in that diagonal cell can be in the same range as the neighbour off-diagonal elements. Hence, if you are on (2) a very unprobable branch then there might be an interaction with the 'other branches' or more precisely, with the 'bath' of the yet non-decoherenced states.

Oversimplifying, MWI predicts that (3) if you roll the dice 1000000 times and always get 6, then look around, very probable there are other weird things happening around, like you can see 2 semi-transparent images of both cats.

(1) seems to imply that you define probability as "degree of plausibility" so that an event assigned a high probability has a high likelihood of occurring and vice versa.

(2) seems to imply that probabilities can be assigned or calculated for branches. In MWI a branch either exists or does not exist. If you are certain that those branches exist, then their degree of plausibility should be 1. So how can a branch have a low degree of plausibility. This is the part where it is not clear what the probability of a branch is supposed to mean. Do you mean, the ratio of the number of identical branches to the total number of branches? That is a frequency not a probability.

(3) If you roll a die 1000000 times and always get a 6, there is no need to suspect weirdness (unless of course you have a penchant for mysticism). Rather it tells you that the probability of the next roll giving a 6 is almost 1.0. Note that this probability has changed from 1/6 at the first throw to almost 1. Even though the die is the same and nothing else has changed ontologically. That is why the only consistent application of probability is as an epistemological representation of degree of plausibility.

If you recognize that frequency is ontological then you will interpret an observed frequency only as telling you that the die is really biased. But if you mix frequency and probability, you may suspect that since the world does not obey what is in your mind (1/6), then something weird is going on. Rather, what is happening is that, prior to the experiment you formed an opinion (probability 1/6) about how the die might behave based on limited information about the specific die. Then as the experiment proceeded, you learned more information about the die, and updated your opinion accordingly (probability ~1). Mean while all along, the die has not changed. No worlds have branched. The only thing that has happened is that your state of knowledge about the die has improved.

If I say the probability of a cat being dead is 0.129245, I am simply saying, based on the information at my disposal, the cat is less likely to be dead than alive and on a scale from 0 to 1, where 0 means certainly not, and 1 means certainly, the degree of plausibility can be assiged to 0.129245. It does not mean I have to measure a large number of cats to be able to count the frequency and then divide the number of dead cats over the total to get 0.129245. Some experiments can only ever be performed once. Still we can assign a probability to them.

 

[Fra]

Just for fun, here are my reflections on parts of the discussion coloured by my personal view.

We clearly don't want two time evolution axioms, since we might end up with a contradiction.

How about if instead, what you think of as a contradiction (=a problem), is nothing but a physical interaction between physical views? Becase after all, it seems a lot of people on here keep mixing different views, bird views and frogs views and IMHO some of the "logical contradictions" are not valid because they mix different context.

An alternative interpretation is that we are in fact facing contradictory views, which results not in a "logical contradiction" but in a "physical interaction".

In a certain sense, the wave function collapse is the RESULT of a kind of contradiction. The conflict between prior opinion and new evidence. The wave function collapse is in my view the physical realisation of negotiation.

2 is however completely consistent with the view that QM is just an algorithm that tells us how to calculate probabilities of possible results of future experiments, given the results of past experiments.

This is a rephrasing of what I tried to say before but where the vision didn't get through:

I argue that the utility of this probability, is not to in historical-retrospect conclude wether our expectations were right, rather the probability expression our opinon of the future, determines our actions Now. Thus the context of probability need not be as historial frequencies, instead its something more involve that has to do with actions.

In this picture, two views(two physical observers) having different expectations of the future, and computing different probabilities, are not a logical contradiction. Instead my conclusion is that the implications is a physical interaction.

/Fredrik

 

[Fredrik]

How about if instead, what you think of as a contradiction (=a problem), is nothing but a physical interaction between physical views? Becase after all, it seems a lot of people on here keep mixing different views, bird views and frogs views and IMHO some of the "logical contradictions" are not valid because they mix different context.

The time parameter is supposed to be the same in both views, and it's clear that there are some statements that we could make about time evolution in the frog's view that would contradict the statement about time evolution in the bird's view. We can't just state an axiom about time evolution in the frog's view and expect it to not contradict the statement we have already made about time evolution in the bird's view. If the frog's view axiom doesn't contradict the bird's view axiom, then it must be possible to use the latter to prove that the former holds. But it doesn't seem to be possible.

An alternative interpretation is that we are in fact facing contradictory views, which results not in a "logical contradiction" but in a "physical interaction".

If it's just an interaction, then I wouldn't call it a contradiction. The contradictions I talked about above are actual contradictions, which would make the theory invalid. You should use another word for what you're talking about, e.g. "complementary". If the second kind of time evolution is a special case of the first, then we have two complementary views. I don't have a problem with that, except for the fact that the second kind of time evolution doesn't seem to be a special case of the first.

 

[Fra]

I'm just throwing in my views to fuel the fire. I'm well aware that I probably have a different view on this, and they we may not reach an agreement.

The time parameter is supposed to be the same in both views, and it's clear that there are some statements that we could make about time evolution in the frog's view that would contradict the statement about time evolution in the bird's view.

As a note first, I do not believe in some strict axiomatic approach to solve open problems.
Axiomatisations are useful when a theory is maturing and as a way to clean it up. But I don't think the creative process are usefully abstracted in terms of axiomatisation.

What I mean is that - in the general case - the time evolution does not necessarily describe what WILL happen, not even statistically. It describes which evolution the observer expects tp to happen, and it's actions are then consistent with expectations, not consistent with the yet unknown future.

If two observers, have different expectations on the future, clearly a conflict appears. And since I see law and symmetry as evolving, the objective law or transformation symmetry simply can't be established from the inside view, to correct for this conflict in advance. The only way is to play your cards to the best of your information, and face the consequences.

In the normal/custom view of law and symmetry in physics the transformation laws that generates all frogs, does in deed recover a bird view consistency. I am suggesting that's a special, idealised case. In general, the symmetry that recovers the different views are subject to the same measurement process.

In human science this "measurement process" is the scientific development itself, years and years to modelling, experimenting etc. Has produced a set of symmetry transformations and abstractions. I am suggesting that in the next awareness and revolution of physics, this process must itself be seen as part of PHYSICS. I think in particular the problem of quantum gravity suggests this.

So the birds view or gods view that a lot of people have, are IMHO invalid as a physical view. It's an imagined (we can all imagine mathematically such view) view that really never is realized in nature.

If it's just an interaction, then I wouldn't call it a contradiction. The contradictions I talked about above are actual contradictions, which would make the theory invalid.

Hmmm maybe I misunderstood again. I'm not sure to what extent I disagree with your personal view, I just throwed in this reflection.

From my view I'd say the inconsistency appears because there are invalid uses of different physical views. Just because one from the armchair position can consider a "birds view", doesn't mean it has any place in the real world.

I'm not saying it can't have a place, it sure can. I'm just saying it isn't sure, and my personal view is that such a view is an illusion that is misleading.

So in this case I agree that if you keep insisting on the bird views like is often done, that makes no sense.

You should use another word for what you're talking about, e.g. "complementary". If the second kind of time evolution is a special case of the first, then we have two complementary views. I don't have a problem with that, except for the fact that the second kind of time evolution doesn't seem to be a special case of the first.

> i) all isolated systems evolve in time according to the Schrödinger equation

The property of a system to be isolated is a hypotetical constraint IMO. It make sense in same cases, not in general.

In a realistic scenario I think the inference of this closedness must be described.

Somehow the closedness, is defined relative to a fictive birds view. A real inside observer,
can only have indications of that it's closed, and act as if it was. Wether contradicting evidence for this will appear the future he don't know. But neither does that matter.

I think the whole notion of closed systems is one of my objections to the standard formalism. It's perfectly fine as a FAPP constraint in particle physics. But that's because the scale between the observer, human scientists and subatomic systems is so large that the idealisation is perfectly valid.

But what about on the cosmological scales, or other extreme scenarios involving black holes, then I think the abstraction falls flat.

> ii) [the probability rule -- you know the details already]

I'm sorry if I missed something, but are you talking about borns rule or something else?
If it's borns rule, how do you mean that is a time evolution? I think I missed some part of your previous reasoning sorry. I didn't follow the details of all the past discussions inthis long thread.

/Fredrik

 

[Dmitry67]

(1) seems to imply that you define probability as "degree of plausibility" so that an event assigned a high probability has a high likelihood of occurring and vice versa.

(3) If you roll a die 1000000 times and always get a 6, there is no need to suspect weirdness (unless of course you have a penchant for mysticism). Rather it tells you that the probability of the next roll giving a 6 is almost 1.0. Note that this probability has changed from 1/6 at the first throw to almost 1. Even though the die is the same and nothing else has changed ontologically. That is why the only consistent application of probability is as an epistemological representation of degree of plausibility.

1 No, I still owe you an answer to you question: what is a probability in MWI. In my previous post I've just ignored that subject, thinking about the proof. I have to admit I need more time.

3 Yes, you can suspect that dice is not fair, but you can repeat the same xperiment with elementary particles, which are well known to be identical. This is what guys on colliders do - thay repeat the same experiment billions of times, and few times they get what they want. So they are waiting for quite unprobable events.

 

[Fredrik]

> ii) [the probability rule -- you know the details already]

I'm sorry if I missed something, but are you talking about borns rule or something else?
If it's borns rule, how do you mean that is a time evolution?

Yes, the Born rule, with the associated "collapse". It describes a time evolution because it doesn't just say that a measurement of B on a system in state |u> will give us the result b with probability |<b|u>|². It also says that if we got the result b, the system is now in state |b>, at least to a very good approximation. I called this a "Copenhagenish" formulation of QM rather than "the Copenhagen formulation" because I didn't assume that the "collapse" to state |b> is exact.

 

[Fra]

Yes, the Born rule, with the associated "collapse". It describes a time evolution because it doesn't just say that a measurement of B on a system in state |u> will give us the result b with probability |<b|u>|². It also says that if we got the result b, the system is now in state |b>, at least to a very good approximation. I called this a "Copenhagenish" formulation of QM rather than "the Copenhagen formulation" because I didn't assume that the "collapse" to state |b> is exact.

Ok, but I'm still not sure where you see the contradiction. Are you thinking that because in one view there is a collapse, and in another view there is no collapse this is inconsistent?

To me the collapse is simply an information update. But I agree that there are details around this that is ignored in standard QM. But to me that's not an interpretational issue, it's a suggestion that QM as it stands, is not quite satifsfactory. QM pretendes to be a measurement theory, but it ignores how the data is stored, and in particular how MUCH data that CAN be stored. Here I think the internal structure of the oberver needs to be taken into account.

In this sense I can agree with you. The "classical observer" concept is simplification.

If we instead ponder the structure of the prior information of the observer, and that this has a certain inertia, then the measurement must be rate as well, and then it could be the information update actually isn't instantaneous due to the inertia. The collapse somehow assumes that the new data is so convincing that it totally crushes the prior state. This isn't realistic in the general case. If this is what you refer to I agree.

But to cure this, I think reinterpretations won't help. We need to reformulate QM, in a way that the current formalism becomes a limiting case only. I think this can be done.

But even so, I think the collpase will not go away completelt. This is why I didn't see hte above objection as cleanly related to the collapse issue.

In principle the collapse is simply an information update, and the unitary evolution is simply our expected change of our environment, to guides us in between information updates.

This I see as no contradiction? And this will I think stay. What will change however, is probably the logic of hte information update. The simple projection concept coming from the hilbert space abstraction is only a simple model, that ignorees the internal structure of the observer.

It tries to be a theory of communication, but only having communication channels, not seeing that you can not choose the channels indepdent of the nodes. the nodes can be saturated.

You see it as an algorithm, and I can make sense of that too. If I were to take your view, I would like to go more extreme (away from human meant algorithms) and idenfity the observer with the algorithm, and thus suggest a picture where the algorithm is evolving. This picture constrains your algorithm.

How about if the physical observer is the physical manifestation and encodign of your algorithm? The physical observers acts and behaves in accordance to your algorithm, which defines his actions as a function of this state of info about his environment? That's quite close to by view. What's missing in QM, is to describe this evolution of algorithms, which would extend the formalism and make the rigid state spaces mroe dynamical too.

/Fredrik

 

[Fredrik]

Ok, but I'm still not sure where you see the contradiction. Are you thinking that because in one view there is a collapse, and in another view there is no collapse this is inconsistent?

No, that's not it. Even if the "collapse" in the frog's view is only approximate, we still have two rules describing a time evolution. Think of rule 1 as describing the time evolution of every part of your body, and and rule 2 as describing the time evolution of your feet when your feet interacts with the other parts of your body. If it's not possible to derive rule 2 from rule 1, then rule 2 contradicts rule 1. For example, your entire body including your feet goes to France. A logical consequence of that is that your feet are in France. If rule 2 says your feet are in Finland, we have a contradiction.

By the way, if you'd like to see a very different argument that arrives at the same conclusion (that it doesn't make sense to think of a wavefunction as describing the system), expressed in a way that sounds very different, check out sections 9.2-9.3 in Ballentine. I just got my copy yesterday, so I hadn't read those sections when this discussion started.

 

[Fra]

No, that's not it. Even if the "collapse" in the frog's view is only approximate, we still have two rules describing a time evolution. Think of rule 1 as describing the time evolution of every part of your body, and and rule 2 as describing the time evolution of your feet when your feet interacts with the other parts of your body.

Ok, now I see your point.

1. The time evolution in ii is only a special case of the time evolution in i.
2. You are only allowed to use the time evolution axiom on systems that you are not a part of.
...
If 1 is correct, it must be possible to prove it. But attempts to do so have failed. The successful attempts to derive the probability rule all used another axiom, which is essentially equivalent to ii).

First, I personally don't think the schrödinger equation is fundamental. In the reconstruction I picture, the expected time evolution of the state vector should follow from a new understanding of the least action principe, which I think of as a form om minimum speculation, or minimum information divergence picture. From this I think the born rule should follow as well. The basic idea is to not take the hilbert state space as axiomatic starting points. Instead the hilbert space, and the evolution of states within it, should be emergent from a more fundamental abstraction.

Now that hasn't happened yet, and maybe it will fail, but if it works, your points will be adressed.

In that sense, it's close to whay hurky said that QM beeing the least wrong description. As it would describe not what WILL happen (becase this is never known) it describes, in a principle of minimum speculation, what is expected to happen, given the current state and statespace structures.

I've decomposed my vision of this reconstruction in steps named metaphorically, two are

1. The logic of guessing
2. The logic of correction

It also aims to contains a reconstruction of probability theory itself, from an hypotetical inside view. The probability spaces are constrained by the complexity in the image. This implies goodbye to the continuum as fundamental.

It also suggests that the born rule, and the feymann action (transition probability) are united. Because in a model of evolving law, states and laws are treated on somewhat similar footing, the only difference is their inertia. Law doesn't change because it's encoded with larger inertia.

This is what I mean with my "ineterpretation" doesn't adhere to the big camps, and it demands a reformulation of QM. I don't see how plain re-interpretations is going to make any difference.

/Fredrik