Quantum myth 4: The only reality is the measured reality

[reilly]

Then please stop posting. If you prefer not to talk about MWI, but instead about cartoony sci-fi bastardizations of it, then do so elsewhere.


Please remind me how that went. I seem to recall you spent most of your effort recounting fanciful "everything you can imagine is true" science fiction fantasies and marveling over thermodynamics. You briefly asked about dynamics (which is precisely the familiar unitary evolution of quantum mechanics) so if that is the content of your accusation of lack of rigour, then it is rather disingenious to post as if it is MWI you are criticizing, which instead you are criticizing quantum mechanics as a whole.

As for Hans, all he seems to be doing is demonstrating a lack of knowledge of the dynamics of mixed states.

MWI is concerned only with the analysis of the unitary evolution of quantum states -- so that means if you really and truly have a criticism of 'lack of rigor' that is applicable only to MWI (and assuming you aren't making a strawman argument), then that means your criticisms specifically regard the analytical methods. However, all of your fanciful imaginings describe incredulity as to the dynamics -- which means you either have deep misgivings about quantum mechanics as a whole, or you simply don't know what you're talking about.

hurkyl

With all due respect, your characterization of my two recent posts is misleading -- count the words dealing with "imagination and science fiction" -- they are less than 10%. You have not dealt with any of my or Han's questions, but rather have just accused us of not getting it.

What is it that we do not know?

I talked about the problematic role of Poisson processes in the MWI approach -- Poisson chains seem dangerously close to generating a non-separable Hilbert space. What's your understanding of this issue?

My concern, re rigor is, for example: in what space does this unitary evolution take place? Can you demonstrate that MWI works with a separable Hilbert space?

Let's suppose that I wish to do an electron scattering experiment.During the time in which the experiment is conducted, many universes will be created, as, for example, all of our perceptions involve some random elements -- which our perceptual systems average out. How do we know what universe to use when doing the analysis of the scattering data? How much history do we need to consider?
Regards,
Reilly

 

[Hurkyl]

What is it that we do not know?

That the state space analyzed by MWI is exactly the one ordinarily used in QM. That the relative state of a subsystem would be mixed or that mixed states do not interact under unitary evolution.

The brief history as I know it (and hopefully reasonably accurate) is that MWI started with the relative state interpretation: if you have a state for the entire system, you could restrict it to a particular subsystem (e.g. via partial trace). In this way, it was seen to be possible that subsystems could be in a mixed state, even if the entire state was pure. Then MWI got a huge boost from the discovery of decoherence, which indicated that the coupling of the subsystem with the environment naturally caused subsystem states to tend to statistical mixtures of a particular basis. Everything else in MWI has been efforts to analyze the behavior of these things.

I talked about the problematic role of Poisson processes in the MWI approach -- Poisson chains seem dangerously close to generating a non-separable Hilbert space. What's your understanding of this issue?

I can't see how. What state space you would ordinarily use to quantum mechanically study a mole of silver atoms? MWI would assign that very same state space to that system. Are you suggesting quantum mechanics is incapable of describing such systems with a separable Hilbert space?

My concern, re rigor is, for example: in what space does this unitary evolution take place? Can you demonstrate that MWI works with a separable Hilbert space?

MWI works in a separable Hilbert space if and only if that is what you would ordinarily use in quantum mechanics.

 

[Phrak]

Hurkyl- thanks for the clarification regarding toy observes. It goes a long way in clearing things up.

Other than coming to terms with the googleplex of unmeasurable "parallel" universes, there are a couple of things one would want out of a decent interpretation.

In the Copenhagen non-interpretation interpretation the energy-momentum that curves spacetime has no position until it is measured. But it's difficult to see if MWI disambiguates this problem. If one were in possession of the state of the universe, evolved from the beginning, that would be fine, perhaps. But supposedly, we still have a predictively correct accounting using general relativity, even when we don't have the entire description of state, but begin instead with some sort of subspace slice through Hilbert space. I'm wondering if this could be seen as some sort of gauge invariance, but that's as far as I get.

Sencondly, I've heard objections made (Wheeler, and others) that MWI, in the original form by Hughes Everett, fails to correctly predict probobility densities, or some such, without an additional postulate that adds a correction factor.

Thanks for any sort of clarification on these.

 

[Hurkyl]

In the Copenhagen non-interpretation interpretation the energy-momentum that curves spacetime has no position until it is measured.

Details of approaches to quantum gravity are well beyond my current understanding.

Sencondly, I've heard objections made (Wheeler, and others) that MWI, in the original form by Hughes Everett, fails to correctly predict probobility densities, or some such, without an additional postulate that adds a correction factor.

I know I have seen people suggest that the probability of an outcome should be proportional to the number of worlds containing that outcome (and I think this is what you're referring to). I don't know if this was ever a part of any form of MWI.

I know I have managed to derive the Born rule in a simple toy case, with a mild continuity assumption. I have since read that it has been proven (but I don't know the precise statement, nor the proof method) that the Born rule is the only possible statistical rule that can be observed in a 'world'.


A sketch of my derivation is as follows:
1. Suppose you have N identical, independent qubits, each in the state \alpha |0\rangle + \beta |1\rangle
2. Choose a positive number \varepsilon.
3. Construct an observable X_{N,\beta,\epsilon} representing the following experiment:

Measure each of the qubits.
If the proportion of |1\rangle's is within \epsilon of |\beta|^2, output '1'
Otherwise, output '0'​

4. Compute \lim_{N \rightarrow +\infty} E(X_{N, \beta, \epsilon}) = 1

I interpret this final result as telling me that as we repeat the (independent) experiment of observing qubits in the state \alpha | 0 \rangle + \beta 1 \rangle, the proportion of |1\rangle's converges to |\beta|^2 with probability 1 -- therefore, the Born rule satisfies the frequentist interpretation of probabilities.


In my opinion, the key conceptual point is 'internalization' -- the observation of frequencies was made into an experiment modeled by the formalism of QM.

 

[Hans de Vries]

As for Hans, all he seems to be doing is demonstrating a lack of knowledge of the dynamics of mixed states.

Hurkyl,

Nobody will find an answer to the questions, and the worries, we have about MWI by
just studying Decoherence theory.

Why we don't feel the gravitation of a star we are moving through in a parallel universe
is not explained by looking at manipulations with the non relativistic Schroedinger theory.
The same is true for many other interactions.

Of course you are not expected to provide the answers either. Nobody can.



Regards, Hans

 

[Phrak]

Details of approaches to quantum gravity are well beyond my current understanding.

All I know of quantum gravity are the two words stuck together (i.e.: nothing). But my point was that any interpetation that admits no objective realism, of one sort or another, to the wave equation is incompatible with the differentiable manifold of general relativity. This would apply equally well to a theory of quantum gravity that doesn't replace the differentiable manifold with something else.

If I understand you correctly, MWI does attach physical significance to the wave equation, so it has at least half a chance of being compatible with general relativity.

The hard part, is as Hans noted, describing how a mass in one decoherence has no effect in another decoherence where the mass is located elsewhere; one would want to account for how the shape of spacetime seamlessly transitions from one decoherence to another.

I know I have seen people suggest that the probability of an outcome should be proportional to the number of worlds containing that outcome (and I think this is what you're referring to). I don't know if this was ever a part of any form of MWI.

After a little internet searching, I see that Everett's 1957 MW interpetation has been understood in several different ways by various people, giving rise to at least 3 distinct interpretations; MWI being one of them.

This is what I was referring to, concerning total probability outcomes:

http://plato.stanford.edu/entries/qm-everett/"

Another problem with a splitting-worlds theory concerns the statistical predictions of the theory. The standard collapse theory predicts that J will get the result "spin up" with probability a-squared and "spin down" with probability b-squared in the above experiment. Insofar as there will be two copies of J in the future, J is guaranteed to get each of the two possible measurement results; so, in this sense, the probability of J getting the result "spin up", say, is one. But that is the wrong answer. A principle of indifference might lead one to assign probability ½ to each of the two possible measurement outcomes. But such a principle would be difficult to justify, and probability ½ is the wrong answer anyway. The moral is that it is impossible to get the right answer for probabilities without adding something to the theory.

In hindsight, I don't see that it matters that the total probability outcome should be greater than one, only that the experimenter should, in the least, subjectively deduce that the total probability outcome, as indicated from his results, imply that it is unity.

I know I have managed to derive the Born rule in a simple toy case, with a mild continuity assumption. I have since read that it has been proven (but I don't know the precise statement, nor the proof method) that the Born rule is the only possible statistical rule that can be observed in a 'world'.


A sketch of my derivation is as follows:
1. Suppose you have N identical, independent qubits, each in the state \alpha |0\rangle + \beta |1\rangle
2. Choose a positive number \varepsilon.
3. Construct an observable X_{N,\beta,\epsilon} representing the following experiment:

Measure each of the qubits.
If the proportion of |1\rangle's is within \epsilon of |\beta|^2, output '1'
Otherwise, output '0'​

4. Compute \lim_{N \rightarrow +\infty} E(X_{N, \beta, \epsilon}) = 1

I interpret this final result as telling me that as we repeat the (independent) experiment of observing qubits in the state \alpha | 0 \rangle + \beta 1 \rangle, the proportion of |1\rangle's converges to |\beta|^2 with probability 1 -- therefore, the Born rule satisfies the frequentist interpretation of probabilities.

In my opinion, the key conceptual point is 'internalization' -- the observation of frequencies was made into an experiment modeled by the formalism of QM.

Forgive me, but your posts have become a bit difficult to follow. Do you think your toy case addresses the objection concerning total probability in a manner favorably to MWI?

Edit: Rather than referring to "splitting", and "many worlds" or "parallel universe", that are conceptually misleading, I think the term "decoherence group", or simply a "decoherence" (used as a noun), should replace "parallel universe".

 

[Hurkyl]

All I know of quantum gravity are the two words stuck together (i.e.: nothing). But my point was that any interpetation that admits no objective realism, of one sort or another, to the wave equation is incompatible with the differentiable manifold of general relativity. This would apply equally well to a theory of quantum gravity that doesn't replace the differentiable manifold with something else.

If I understand you correctly, MWI does attach physical significance to the wave equation, so it has at least half a chance of being compatible with general relativity.

I should point out that some flavors of Copenhagen view quantum states as being objectively real -- they just undergo collapses now and then. I am under the (vague) impression that Bohmian mechanics also takes something functionally equivalent to the wavefunction as being objectively real. And then there are flavors of (what I understand as) the relational interpretation, in which it views quantum states as directly corresponding to something real -- it's just that many different quantum states can correspond to the same physical 'state'.

So MWI doesn't have a monopoly on treating quantum states as being real.

In hindsight, I don't see that it matters that the total probability outcome should be greater than one,

I'm sorry, I missed where that came from.

Edit: Rather than referring to "splitting", and "many worlds" or "parallel universe", that are conceptually misleading, I think the term "decoherence group", or simply a "decoherence" (used as a noun), should replace "parallel universe".

That might be reasonable; alas, history often saddles us with unfortunate terms (e.g. we're still saddled with 'imaginary numbers', despite Gauss's best efforts). I confess I generally prefer to think of the quantum state 'abstractly' -- so while I can see why some people like such terminology and others don't, I really don't have an informed opinion.

 

[Phycho]

Hurkyl, I'd just like to point out Bohm is 100% realistic objective interpretation.
It's nickname are "The realist interpretation".

I've never heard of any CInterpretation that treats reality as objective.

 

[Phrak]

Thanks for all that, Hyrkl. I've found a website on qbits, gates, computing and algorithms. I'll be studying the first half of it. It seems to be the way to go, to evaluate MWI, if not other interpretations.

It looks be well done, if not a bit verbose: http://beige.ucs.indiana.edu/M743-talk-2/node2.html"

 

[Count Iblis]

Hurkyl's proof amounts to replacing the Born rule by a weaker rule that says that if a system is in an eigenstate of an observable, then a measurement will yield that eigenstate with 100% probability.