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The paper makes no sense at all as long as the concept of "measurement" is not precisely dynamically defined within quantum theory
So let's assume the wave function is real. does that mean that qm needs no further interpretations? (consciousness, many worlds, etc)
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.
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 ?
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.
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 ?
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
Why do complex numbers accurately model real experimental results?
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?
I think there is nothing problematic with giving the wave function the status of reality.
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.
Are there any lectures or books you can suggest that explain C*-algebras for QM to non-mathematicians?
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
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.
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.
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.
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.
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.
...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.
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.
Apparently, if we say that reality is objectively defined, we can ask whether or not quantum states are objectively defined as well.
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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.
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.
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.
.. It just happened that we have 2 measured/observed realities
So, this leaves me with the question... Is the information content of the quantum state what is objectively "real". Is it, in fact, all that is "real"?
In the double slit experiment, the detector collapse the wave function in Copenhagen. If it doesn't collapse, then it automatically forms Many Worlds?
Whoa, finally an explanation that I can understand.
Microworld is very different in approaches from the macroworld. Quantum nonlocality disappears as things get bigger. My monitor doesn't appear to be in places at the same time or jittery. It looks different to me?2 measured/observed realities? I have zero I idea where you are getting stuff like that from, or even what it means, but in physics, and science in general, we try to be concise and not obscure.
Thanks
Bill