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
No.So lets 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.
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.
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 ?
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:
Why not? Exactly what limits the mathematical objects that can be used in physical models?Why do complex numbers accurately model real experimental results?
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?
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.
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
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.