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Quantum state 
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#19
Jan2813, 03:38 PM

P: 724

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. 


#20
Jan2813, 08:00 PM

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PF Gold
P: 2,442

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/QuantumMechan.../dp/9810241054 Thanks Bill 


#21
Jan2913, 08:48 AM

PF Gold
P: 674

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:



#22
Jan2913, 03:07 PM

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PF Gold
P: 2,241

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 Belllike 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. 


#23
Jan2913, 04:06 PM

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PF Gold
P: 2,442

http://arxiv.org/abs/1203.4779 Really that's all that can be asked. Thanks Bill 


#24
Jan2913, 09:47 PM

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P: 12,359

... 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 "wavefunction". 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. 


#25
Jan3013, 04:44 PM

P: 724

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 mindboggling 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. 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 nonreal captures the essense seen in these experiments. 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 nogo theorem by itself, as it leads nowhere. 


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