Quantum state: Reality or mere probability?

Demystifier

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There is an old controversy in quantum mechanics, with arguments on the borderline between science and philosophy, on the question whether the quantum state describes an objective reality associated with a single system, or mere probability describing properties of a large ensemble of equally prepared systems. The recent PBR theorem* provides the strongest argument so far that the quantum state is real, which elevates the controversy to a higher scientific level.

Here I attach the presentation of a recently presented talk, in which these things are explained at a level suitable for a general physicist audience.

*M.F. Pusey, J. Barrett, T. Rudolph, Nature Phys. 8, 476 (2012); arXiv:1111.3328 (v3)
 

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atyy

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Can it be said that the Bohmian answer to this question is reality and mere probability?
 

DrChinese

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Demystifier:

On page 18, I see that the 4 outcomes 00, 0+, +0, and ++ should be consistent with any initial preparation of 0/+ for the 2 similar systems. The choice of how to measure these 2 should not rule those out.

I see that the 4 phi options consistent with QM's predictions rule each rule out 1 of those outcomes. All 4 are rules out by an phi option.

What I don't understand is how the 4 phi options are constructed in some kind of setup. The first and forth, phi 1 and 4, looks like a traditional entangled state description.

What do the other 2 map to? Can you enlighten me in any way? And it seems as it the 2 systems are prepared in a known state that they couldn't be entangled. If they are separate, they seem classical. Help! :smile:
 
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The recent PBR theorem* provides the strongest argument so far that the quantum state is real, which elevates the controversy to a higher scientific level.
What definition of "real" are we using here? In any case, I don't see why any equation that describes something probabilistically would necessarily imply the thing it describes is not precisely defined both spatially and temporally. We can describe rain probabilistically, but that doesn't mean every drop of water doesn't actually have a unique position and standard properties at every point in time, until it hits the ground.
 
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What definition of "real" are we using here?
Good point.

To fully understand the theorem and its implications you need to go back to the original paper:
http://arxiv.org/pdf/1111.3328v2.pdf

'Here we present a no-go theorem: if the quantum state merely represents information about the real physical state of a system, then experimental predictions are obtained which contradict those of quantum theory. The argument depends on few assumptions. One is that a system has a 'real physical state' not necessarily completely described by quantum theory, but objective and independent of the observer. This assumption only needs to hold for systems that are isolated, and not entangled with other systems. Nonetheless, this assumption, or some part of it, would be denied by instrumentalist approaches to quantum theory, wherein the quantum state is merely a calculational tool for making predictions concerning macroscopic measurement outcomes. The other main assumption is that systems that are prepared independently have independent physical states.'

Also we have a very beautiful theorem, called Gleason's Theorem, that shows the state is really a requirement of what observations in QM are - see post 137:
https://www.physicsforums.com/showthread.php?t=763139&page=8

The foundational principle is:
An observation/measurement with possible outcomes i = 1, 2, 3 ..... is described by a POVM Ei such that the probability of outcome i is determined by Ei, and only by Ei, in particular it does not depend on what POVM it is part of.

That completely bypasses the real physical state assumption of the theorem. The state is simply a mathematical device that helps us calculate those probabilities.

Its the view of the Copenhagen-information interpretation mentioned in Dymystifyers paper - although my view is not Copenhagen which associates a state with subjective knowledge - I associate it with an ensemble view as in the ensemble interpretation. It not a biggie though IMHO - its basically the same as frequentest and Bayesian type interpretations of Kolmogorov's probability axioms.

That said, its still a very important theorem worthy of the praise it received.

And guys like Schlosshauer have extended it in an interesting way elucidating the kind of interpretations that it applies to and those that evade it:
http://arxiv.org/pdf/1306.5805v3.pdf

Thanks
Bill
 
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Can it be said that the Bohmian answer to this question is reality and mere probability?
I would say BM is real, and completely deterministic. Probabilities simply result from lack of knowledge of initial conditions.

Thanks
Bill
 
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'Here we present a no-go theorem: if the quantum state merely represents information about the real physical state of a system, then experimental predictions are obtained which contradict those of quantum theory. The argument depends on few assumptions. One is that a system has a 'real physical state' not necessarily completely described by quantum theory, but objective and independent of the observer. This assumption only needs to hold for systems that are isolated, and not entangled with other systems. Nonetheless, this assumption, or some part of it, would be denied by instrumentalist approaches to quantum theory, wherein the quantum state is merely a calculational tool for making predictions concerning macroscopic measurement outcomes. The other main assumption is that systems that are prepared independently have independent physical states.'
If "non-locality" is the same thing as "action at distance", then everything can still be uniquely defined at every point in time.

If we can measure something at any moment we wish, and we always obtain the same result, why would we think those properties do not actually exist until we intrude with our measuring apparatus? It's like saying there are no rain drops in the rain until they hit the ground.
 
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If "non-locality" is the same thing as "action at distance", then everything can still be uniquely defined at every point in time.
Non locality in QM is much more subtle than that. Its exact expression is the so called cluster decomposition property:
https://www.physicsforums.com/showthread.php?t=547574

Classically though you are correct, as for example the early pages of Landau's beautiful book - Mechanics - explains - instantaneous action at a distance is encoded into the foundations of classical mechanics.

You really need to go to relativity for it to be an issue - and when you do that - that's when you come face to face with the Cluster Decomposition Property. BUT that only applies to uncorrelated systems. And correlation in QM is much more subtle than classically - as shown by Bells Theorem.

If we can measure something at any moment we wish, and we always obtain the same result
But QM says you don't always obtain the same result except in very simple situations eg in EPR type situations where if you measure it's spin as up for example and conduct the same measurement again it will always be spin up. Most of the time however the state changes eg for a free particle if you measure its position exactly, the wave-function spreads so you cant say anything about its later position.

Thanks
Bill
 
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Non locality in QM is much more subtle than that.
Isn't Bohmian mechanics direct contradiction to that? And if Bohmian mechanics is possible answer, then classical QM can't really exclude the possibility things do actually exist even if no one is looking.


But QM says you don't always obtain the same result except in very simple situations eg in EPR type situations where if you measure it's spin as up for example and conduct the same measurement again it will always be spin up. Most of the time however the state changes eg for a free particle if you measure its position exactly, the wave-function spreads so you cant say anything about its later position.
Yeah, but if photons are supposed to always move at c, that means their path from point of interaction to another point of interaction must always be a precisely defined straight line, the shortest distance or geodesic. I don't see how we can define our unit of distance with the speed of light and then say photons really travel over many possible paths, at once, or something among those lines.
 

atyy

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If we can measure something at any moment we wish, and we always obtain the same result, why would we think those properties do not actually exist until we intrude with our measuring apparatus? It's like saying there are no rain drops in the rain until they hit the ground.
In quantum mechanics, we can measure position and momentum, but we can also show that position and momentum are not uniquely defined at all times. For this reason, position and momentum are not "real" until they are measured.

However, this does not mean that the system is not fully and uniquely defined by "true properties" that exist at all times. It's just that those true properties are not position and momentum. Let X represent the true properties of the system, and let ψ represent the wave function.

In the definition of reality used in this paper, ψ is real if knowing X uniquely specifies ψ. On the other hand, ψ is at least partly a matter of belief if knowing X does not uniquely specify ψ.
 
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In quantum mechanics, we can measure position and momentum, but we can also show that position and momentum are not uniquely defined at all times. For this reason, position and momentum are not "real" until they are measured.
That would be good enough reason, but how can we show position and momentum are not uniquely defined at all times?
 

atyy

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That would be good enough reason, but how can we show position and momentum are not uniquely defined at all times?
If we have a state and we measure position x we get some distribution F(x). If we have the same state and we measure momentum p we get another distribution G(p). If the particles in the state have simultaneous position and momentum, then we should be able to write a joint distribution W(x,p), such that F(x) = ∫W(x,p)dp and G(p) = ∫W(x,p)dx. But we cannot. We can find a W(x,p), but we find that W is not always positive, and so cannot be a probability density. This W is called the Wigner function.
http://en.wikipedia.org/wiki/Wigner_quasiprobability_distribution
http://dspace.mit.edu/bitstream/handle/1721.1/49800/50586846.pdf [Broken]
 
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If we have a state and we measure position x we get some distribution F(x). If we have the same state and we measure momentum p we get another distribution G(p). If the particles in the state have simultaneous position and momentum, then we should be able to write a joint distribution W(x,p), such that F(x) = ∫W(x,p)dp and G(p) = ∫W(x,p)dx. But we cannot.
If we catch an electron or photon with a sensor, don't we measure both their position and momentum, and isn't it their momentum always equally proportional to electron speed and photon wavelength?
 
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Yeah, but if photons are supposed to always move at c, that means their path from point of interaction to another point of interaction must always be a precisely defined straight line, the shortest distance or geodesic. I don't see how we can define our unit of distance with the speed of light and then say photons really travel over many possible paths, at once, or something among those lines.
Photons are problematical in basic QM because there is no frame where they are at rest.

We define our unit of distance via classical EM without QM issues.

Thanks
Bill
 

Demystifier

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What I don't understand is how the 4 phi options are constructed in some kind of setup. The first and forth, phi 1 and 4, looks like a traditional entangled state description.

What do the other 2 map to? Can you enlighten me in any way?
If you ask me how to do it in the laboratory, then I don't know. Perhaps the PBR guys who invented this thought experiment know better. At the botton of page 4 you will also see a reference to an experimental realization of this.

And it seems as it the 2 systems are prepared in a known state that they couldn't be entangled. If they are separate, they seem classical. Help! :smile:
The two systems are initially prepared in a classical non-entangled state, but the meassurement is performed in a non-classical entangled basis. In other words, the measurement makes them entangled. This should not be surprising, because measurement in a specific basis can often be viewed as a preparation.
 
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That would be good enough reason, but how can we show position and momentum are not uniquely defined at all times?
We cant show a negative like that.

All we know is no one has ever been able to figure out how measure the position of a photon.

Intuitively such would seem rather difficult for a particle that always, regardless of frame, travels at c. But you are most welcome to give it a try. The bugbear is while photons can be made to interact at a point, it is always destroyed by such, so you cant say it had such and such position.

Thanks
Bill
 
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Why would you think that?

Thanks
Bill
Because of deterministic causality and continuous trajectories, which I think imply whatever it is moving along those paths is defined and existing. The guiding wave thing looks more like "hidden variable" type of thing, something unknown rather than non-local.
 
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Because of deterministic causality and continuous trajectories, which I think imply whatever it is moving along those paths is defined and existing.
Again I can't follow your concern.

I said that non locality is subtle in QM.

BM has this inherently unobservable pilot wave that's non local - sounds rather subtle to me.

But - yes BM and the cluster decomposition property requires a bit of analysis - I am not an expert on that - best to ask Dymystifyer about it.

Thanks
Bill
 
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Because of deterministic causality and continuous trajectories, which I think imply whatever it is moving along those paths is defined and existing. The guiding wave thing looks more like "hidden variable" type of thing, something unknown rather than non-local.
This was brought up previously in Demystefier's blog, but are bohmian trajectories any more "hidden" than the wave function?

Bohmian trajectories are no longer "hidden variables"
https://www.physicsforums.com/blog.php?b=3622&goto=prev [Broken]

Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer
http://materias.df.uba.ar/labo5Aa2012c2/files/2012/10/Weak-measurement.pdf [Broken]
 
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atyy

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If we catch an electron or photon with a sensor, don't we measure both their position and momentum, and isn't it their momentum always equally proportional to electron speed and photon wavelength?
Let's stick with electrons here, because talking about photon position is tricky. If you wish to think of an electron as a wave, and momentum as proportional to wavelength, then one way to see it is that a wave with a well defined wavelength cannot be precisely localized in space. The position-momentum uncertainty principle in quantum mechanics is mathematically exactly the same as time-frequency uncertainty in classical signal processing.
 

DrChinese

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Because of deterministic causality and continuous trajectories, which I think imply whatever it is moving along those paths is defined and existing.
If you assume deterministic causality, continuous trajectories make sense. If you assume continuous trajectories, then determinism is your likely conclusion. Circular reasoning, although a common viewpoint.

However, a lot of analyses question both of these assumptions/conclusions. The most obvious thing about determinism is that every quantum outcome appears completely random (and has no known cause). So the data is against you. If you could demonstrate a violation of the HUP, you might have something. Barring that, it is just your faith and nothing else.
 

naima

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Several authors like Fuchs say that "there is no quantum states" only probabilities.
They argue that (according to Gleason Bush) a state is only a set of probabilities.

I read in scientific american (Fuchs june 2013): Quantum states are only tools used to calculate our personal confidence in outputs
The problem is that in interferometry, you cannot get probabilities without adding those quantum states.
I never found someone hereagreeing with Fuch's opinion. Could anyone be the devil's advocate?
 

atyy

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Several authors like Fuchs say that "there is no quantum states" only probabilities.
They argue that (according to Gleason Bush) a state is only a set of probabilities.

I read in scientific american (Fuchs june 2013): Quantum states are only tools used to calculate our personal confidence in outputs
The problem is that in interferometry, you cannot get probabilities without adding those quantum states.
I never found someone hereagreeing with Fuch's opinion. Could anyone be the devil's advocate?
As a Bohmian, I agree fully with Fuchs! If degrees of freedom can be emergent, then so can ontology:)

Maybe a more serious question to which I don't know the answer - can we take the Bohmian quantum equilibrium distribution in the sense of subjective probability, say de Finetti? If so, then can we make Bohmian mechanics subjective too?

Actually, Wiseman had some comments on subjective probability in Bohmian mechanics, but I think along somehwat different lines: http://arxiv.org/abs/0706.2522.
 
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