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In particular, if the state of all information in reality pertaining to a quantum system is given by some set of variables [itex]\lambda[/itex], we can ask whether the quantum state [itex]|\psi\rangle[/itex] is uniquely defined by [itex]\lambda[/itex].

It's a bit tricky, but what they try to show is that different states [itex]|\psi\rangle[/itex] correspond to different (disjoint) sets of [itex]\lambda[/itex].

Since they appear to affirm this experimentally (within certain tolerances), it would mean that if one wants to consider the information encoding reality as objective, then one must also consider the quantum state of a system as objectively determined, and not something particular to the observer's state of knowledge.

Pretty awesome work, I must say!

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bhobba

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It is precisely defined - see for example section 2.5 of the following:The paper makes no sense at all as long as the concept of "measurement" is not precisely dynamically defined within quantum theory

https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20&tag=pfamazon01-20

Decoherence is a dynamic process.

Thanks

Bill

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bhobba

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http://arxiv.org/pdf/1412.6213v2.pdf

Note what it says:

'Assuming that some underlying reality exists, our results strengthen the view that the entire wavefunction should be real'

Its the same thing as the PBR theorem - its simply that if you assume some kind of reality in the first place, even in a weak sort of way, the wave function is in a stronger sense real. Interesting and likely quite important, but that assumption of reality, even in a weak sense, is precisely what many interpretations reject.

For example it doesn't apply to the ignorance ensemble interpretation - and quite a few others.

Thanks

Bill

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bhobba

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No.

It changes none of the various interpretations where the wavefunction is real eg BM, MW, nelson stochastics, primary state diffusion etc.

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Bill

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What is confusing (to me) is that the authors appear to argue that this assumption of preparation independence used by the PBR theorem is analogous to Bell's local causality. They write:Crucially, our theoretical derivation and conclusions do not require any assumptions beyond the ontological models framework, such as preparation independence, symmetry or continuity...

I still don't understand this. I didn't think that preparation independence and local causality are analogous? Regardless, the fact that one can narrow down the available "realistic" interpretations that are still viable is still progress.For example, Pusey et al. assume that independently-prepared systems have independent physical states. This requirement has been challenged as being analogous to Bell's local causality, which is already ruled out by Bell's theorem.

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Hello,

What is the meaning to be "ontologically real" in the framework of the physics ?

Patrick

What is the meaning to be "ontologically real" in the framework of the physics ?

Patrick

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That the wave function is a mathematical entity/map that represents/refers to something that actually exists in the world, independently of any observer or agent.What is the meaning to be "ontologically real" in the framework of the physics ?

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bhobba

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The wavefunction is simply the representation of the state in the position basis. The state is the key thing.That the wave function is a mathematical entity/map that represents/refers to something that actually exists in the world, independently of any observer or agent.

To understand the issue see post 137 of the following:

https://www.physicsforums.com/threads/the-born-rule-in-many-worlds.763139/page-7

The state and its physical interpretation by the Born rule is in fact derivable from the operator formalism of QM - that's the import of Gleason's theorem the modern version of which the above link proved. This raises the question of is it real or simply something required by the math. Gleason's theorem suggests it's simply a mathematical requirement - but opinions vary.

Thanks

Bill

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Complex numbers are like a two part epoxy, having A and B components

Would the reality of the blobular blobulous wave function imply, that at some nano scoptic fempto scopic Planckoscoptic scale, that there actually is some two-component field, of which particles are storm like disturbances, which whirlwinds obey the SWE ?

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bhobba

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Sorry - but that's utter gibberish.Would the reality of the blobular blobulous wave function imply, that at some nano scoptic fempto scopic Planckoscoptic scale, that there actually is some two-component field, of which particles are storm like disturbances, which whirlwinds obey the SWE ?

The reason we have complex numbers is the need for continuous transformations between pure states:

http://arxiv.org/pdf/quant-ph/0101012.pdf

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Bill

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Why do complex numbers accurately model real experimental results?Sorry - but that's utter gibberish.

The reason we have complex numbers is the need for continuous transformations between pure states:

http://arxiv.org/pdf/quant-ph/0101012.pdf

Thanks

Bill

If the wave function is real, and if a wave function is a complex valued field, then something corresponding to complex numbers would be real too, yes?

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bhobba

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Why not? Exactly what limits the mathematical objects that can be used in physical models?Why do complex numbers accurately model real experimental results?

Here is the reason they are required in QM.

Suppose we have a system in 2 states represented by the vectors [0,1] and [1,0]. These states are called pure. These can be randomly presented for observation and you get the vector [p1, p2] where p1 and p2 give the probabilities of observing the pure state. Such states are called mixed. Probability theory is basically the theory of such mixed states. Now consider the matrix A that say after 1 second transforms one pure state to another with rows [0, 1] and [1, 0]. But what happens when A is applied for half a second. Well that would be a matrix U^2 = A. You can work this out and low and behold U is complex. Apply it to a pure state and you get a complex vector. This is something new. Its not a mixed state - but you are forced to it if you want continuous transformations between pure states.

QM is basically the theory that makes sense of such weird complex pure states (which are required to have continuous transformations between pure states) - it does so by means of the so called Born rule.

You do realise that complex numbers are specified by two real numbers? If the wave-function is real then its specified by two real numbers. But that view isn't required to understand what's going on. QM is a mathematical model - any mathematical entity can appear in such models - complex numbers, Grassmann numbers, tensors - the list is endless.If the wave function is real, and if a wave function is a complex valued field, then something corresponding to complex numbers would be real too, yes?

The mathematical objects of a model aren't real - the reality lies in the correspondence rules of the model. For example show me a negative number of apples - but if you have borrowed some apples from a friend and need to return them that would be a reasonable model.

Thanks

Bill

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The wave function is always the result of a preparation procedure. And a preparation procedure is a measurement. We measure something, so the measurement result exists. Really, without any doubt really. And this measurement result, together with the history of the experiment itself, which has also happened really, is what defines the wave function.

In de Broglie-Bohm theory, this dependence is explicit. We have a wave function of the whole preparation procedure, [itex]\psi(q_{system},q_{device},t)[/itex], and to obtain the effective wave function of the system, we need the trajetory of the measurement device: [itex]\psi(q_{system},t) = \psi(q_{system},q_{device}(t),t)[/itex].

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bhobba

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Of course not.I think there is nothing problematic with giving the wave function the status of reality.

There are many interpretations where its real.

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Bill

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Whoa, finally an explanation that I can understand. I kept reading this thing in the usually linked arxiv articles and not getting it. Are there any lectures or books you can suggest that explain C*-algebras for QM to non-mathematicians? I mean physicists trained in a standard way, no math gibberish (or yes, but explained from scratch).Suppose we have a system in 2 states represented by the vectors [0,1] and [1,0]. These states are called pure. These can be randomly presented for observation and you get the vector [p1, p2] where p1 and p2 give the probabilities of observing the pure state. Such states are called mixed. Probability theory is basically the theory of such mixed states. Now consider the matrix A that say after 1 second transforms one pure state to another with rows [0, 1] and [1, 0]. But what happens when A is applied for half a second. Well that would be a matrix U^2 = A. You can work this out and low and behold U is complex. Apply it to a pure state and you get a complex vector. This is something new. Its not a mixed state - but you are forced to it if you want continuous transformations between pure states.

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bhobba

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No - its very hard even for trained mathematicians. Its an extremely mathematically advanced formulation of QM.Are there any lectures or books you can suggest that explain C*-algebras for QM to non-mathematicians?

Thanks

Bill

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But in Bohm, given the ontological nature of the WF it's hard to see how you avoid infinite Many Worlds with 1 special particle world.I think there is nothing problematic with giving the wave function the status of reality. Because there exists, anyway, some real values which correspond to it.

[....]

In de Broglie-Bohm theory, this dependence is explicit

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Sorry, but for me it is extremely difficult to see how one can obtain infinite many worlds out of a function defined on imaginable worlds.But in Bohm, given the ontological nature of the WF it's hard to see how you avoid infinite Many Worlds with 1 special particle world.

Say, a function on all imaginable worlds can easily exist in my mind - as a collection about ideas about all such worlds. My mind really exists. Thus, the ideas about all these worlds also exists. But all these other worlds do not exist. Even if this example may be slightly artificial, but the conceptual problem that a function on some space of objects can easily exist without the objects

Ok, let's make the statement a little bit more nontrivial: It is not even a problem for an epistemic interpretation. Because one has to distinguish the epistemic interpretation of the wave function of the universe from the interpretation of the wave function of the particular subsystem.Of course not.

There are many interpretations where its real.

The wave function of the whole system, which prepares the particular system, is in itself not prepared - this would give an infinite regress. Thus, what we know about it? Nothing. And it is this nothingness which suggests that this unprepared wave function is epistemic. But, when, we compute the effective wave function of the subsystem, by using some element of reality - the trajectory of the measurement device. Thus, the effective wave function of the subsystem depends on elements of reality. Thus, it is not purely epistemic, but at least partially ontic.

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http://physics.stackexchange.com/questions/154431/are-wave-functions-real-physical-objects

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zonde

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But there are conjugate variables. Remember EPR paradox?I think there is nothing problematic with giving the wave function the status of reality.

There are only probabilities. Probabilities are not real.Because there exists, anyway, some real values which correspond to it.

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Maybe in a classical continuous view but we don't have or can't proved that.. In general QM sense. The x always goes to infinite, states of which each is independent to one another -- individual states.There are only probabilities. Probabilities are not real.

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