Quantum state


by shounakbhatta
Tags: quantum, state
Maui
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#19
Jan28-13, 03:38 PM
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Quote Quote by f95toli View Post
But all of these experiments can be interpreted within the framework of orthodox QM, or any interpretation you like.

And macroscopic quantum effects have also been around for ages (part of my PhD was on macroscopic quantum tunnelling in superconducting systems), so this again is nothing new.


In historical plan the main motivation for postulating that the wavefunction isn't real has been the logical contradiction of having mutually exclusive properties at the same time. We are now seeing that that logical contradiction is actually part of how nature works at the bottom and every similar experiment in the last couple of years confirms it time after time. I'd say that the claim of the author of the standard interpretaion(and which is largely accepted as true) that there is no quantum world is, to put it mildly, weird given what is known today.
bhobba
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Jan28-13, 08:00 PM
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One of the fundamental axioms of quantum mechanics is that given any observable R, while we cannot predict what the outcome of a measurement will be we can determine its average or expectation value E(R). It is E(R) = Tr(PR) where P is a positive definite operator of unit trace. This P, by definition, is called the state of the system and given the state and an observable we can always determine the expected value of measurements using that observable.

States of the form |u><u| are called pure while the rest are called mixed. It can be shown that any mixed state is the sum of pure states - but not necessarily uniquely.

Another thing that can be shown is from the assumption the state of a system changes only infinitesimally in an infinitesimal amount of time after an observation (this is called the continuity assumption) the system, after the observation, will be in a pure state |u><u| where |u> is the eigenvector of the observable R associated with the actual outcome. Because of this in many texts, especially at the introductory level, they basically associate states with elements of a vector space. Strictly speaking it isn't - its a an operator but we all have to start somewhere.

If you want the correct detail see Ballentines excellent book - Quantum Mechanics - A Modern Development:
http://www.amazon.com/Quantum-Mechan.../dp/9810241054

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Bill
bohm2
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Jan29-13, 08:48 AM
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That is really at the heart of the interpretational debate. If you favour a Copenhagen or informational interpretation then quantum states are just calculational tools used by physicists to predict correlations among their perceptions. Realists, however, are not satisfied with this view. They would probably like to go further by asking: "perceptions about what" or "knowledge about what"? Realists will argue something along the lines suggested by Tim Maudlin:
Quantum states (wave functions) are not merely reflections of someone’s information or knowledge of a system. As David Mermin once remarked, one can’t explain the interference effects visible in a two-slit experiment by holding that our knowledge of the position of the particle went through both slits. Nor does it make sense to regard Schrodinger’s equation as a claim about epistemology, that is, about how our knowledge of a particle evolves in time. The interference effects show that something physical is sensitive to the fact that both slits are open, so the “spread” of the wave function is something more objective than our mere lack of knowledge concerning the location of the particle. But what kind of thing is the quantum state? The temptation is to try to assimilate it to something we are already familiar with in classical physics: a field, perhaps, or a law. There is no good reason, however, to expect classical physics or common sense to provide us with any good analogues. Better to try to characterize the features the quantum state must have to do the physical work we require of it. The quantum state appears to be something intrinsically holistic. The state ascribed to a pair of particles, for example, contains more physical information than the states ascribed to the particles individually (i.e., the reduced states).
I guess I'm probably in the minority in favouring the latter interpretation/approach.
f95toli
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Jan29-13, 03:07 PM
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Quote Quote by Maui View Post
In historical plan the main motivation for postulating that the wavefunction isn't real has been the logical contradiction of having mutually exclusive properties at the same time. We are now seeing that that logical contradiction is actually part of how nature works at the bottom and every similar experiment in the last couple of years confirms it time after time. I'd say that the claim of the author of the standard interpretaion(and which is largely accepted as true) that there is no quantum world is, to put it mildly, weird given what is known today.
But the "standard intepretation" is now what you seem to think. That there is such as thing as superposition of states has been known for a very long time, not just the past couple of years. Rabi did his work some 80 year ago (1936?) and all you are doing in a qubit experiment is to apply his technique to a single particle instead of an ensemble, the physics is the same.
Moreover there are a LOT of experiments and techniques that are fundamentaly "quantum mechanical" in this way, including for example MRI (used at all major hospitals).

My point is that all of this is already known and has been known for a very long time, and it STILL does not "solve" anything when it comes to interpretations because all of the main ones predict exactly the same outcome of experiments.

The only class of experiments that I can think of that have any relevance would be test of Bell-like inequalities. However, the fact that QM passed this "test" with flying colours (killing off local realist theories in the process) has ALSO been known for quite some time time (>20 years); experiments that attempt to solve various loopholes are still being done and are interesting from a technical point of view, but no one seriously belive that they are going to teach us anything fundamentally new about nature.
bhobba
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Jan29-13, 04:06 PM
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Quote Quote by f95toli View Post
My point is that all of this is already known and has been known for a very long time, and it STILL does not "solve" anything when it comes to interpretations because all of the main ones predict exactly the same outcome of experiments.
That is true. However progress has been made, and continues to be made, on exactly what is going on eg it is now known for every interpretation where the state is real there is one where it simply represents knowledge and conversely:
http://arxiv.org/abs/1203.4779

Really that's all that can be asked.

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Simon Bridge
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Jan29-13, 09:47 PM
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... I thought the question was about what a quantum state was - and it seems to me that we already know what we mean by "state" in general: a quantum state is, therefore,
that concept applied to quantum physics. There are lots of states and some have more direct physical interpretation than others.

The original question also includes a context - due to the mention of "wave-function". Shouldn't a useful answer try to stick to that model and let OP learn the rest as it comes?

Isn't the question answered?

Probably past time to hear from OP.
Maui
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Jan30-13, 04:44 PM
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Quote Quote by f95toli View Post
Moreover there are a LOT of experiments and techniques that are fundamentaly "quantum mechanical" in this way, including for example MRI (used at all major hospitals).


That's quite true, however my impression is(it's become a conviction) that this 'quantum mechanical' behavior has never been interpreted the way these latest experiments require. They were mostly interpreted as only that which is observed is real, that which happens between measurements is well characterized by the formalism and altogether everything is well defined and understood.

However, never to this day have people seen or been exposed to mostly mathematical entities like electrons and protons manifesting as having mutually exclusive and at the same time measurably real properties. To me this is the most mind-boggling discovery post Bell/Aspect. This is right at the border between mathematics and physical reality and has very real bearing to understanding matter and personal experience. I am giving it as much significance as Bell/Aspect.



My point is that all of this is already known and has been known for a very long time, and it STILL does not "solve" anything when it comes to interpretations because all of the main ones predict exactly the same outcome of experiments.

It's still profoundly weird but we have more details about 'particles' or whatever you want to call them. More details on their behavior means less confusion. At this point it's not obvious to me that labelling quantum states either real or non-real captures the essense seen in these experiments.


The only class of experiments that I can think of that have any relevance would be test of Bell-like inequalities. However, the fact that QM passed this "test" with flying colours (killing off local realist theories in the process) has ALSO been known for quite some time time (>20 years); experiments that attempt to solve various loopholes are still being done and are interesting from a technical point of view, but no one seriously belive that they are going to teach us anything fundamentally new about nature.


I agree it may be relevant, but even physicists themselves don't believe what the violation of Bell's inequalities implies, so change won't happen fast, if it happens at all. It's a no-go theorem by itself, as it leads nowhere.


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