I have read that the Pilot Wave Theory is nonlocal and can therefore be excluded.
Why is the PW Theory nonlocal?
Isn't QM also nonlocal, as we can see it from entanglement?
I already googled the second question, here they said: non-locality and entanglement are often treated to be the same. But this is wrong. My question here is, why is it not the same?
Consider an entangled system of two photons moving away from each other in the Schrödinger picture, e.g., given by the wavefunction: $$ \Psi(t,x) = \psi_1(t,x) + |\psi_2(t,x). $$ The photons have the same source, so at $t=0$ they are located at the same point. However, at large $t$ they will be far apart from each other and $\Psi(t,x)$ will be a highly non-local object (a single object that exists in two places at the same time). In this sense, the Schrödinger picture of QM works with non-local objects.
In the Heisenberg picture, on the other hand, you would work only with
$$ \Psi(0,x) = \psi_1(0,x) + |\psi_2(0,x). $$
The state here is local because the entangled photons are both located at the source (say at $x=0$) at $t=0$.
The time-dependence is now in the observables $O(t,x)$, which are also local quantities (or at least can be defined as such). So we avoid it here to work with non-local objects. The Heisenberg picture only works with local objects!
To say that QM is local, we have to define what is physical and what is not. In the Copenhagen interpretation, the wave-function is not seen as physical, or as Wikipedia states it:
Generally, Copenhagen-type interpretations deny that the wave function provides a directly apprehensible image of an ordinary material body or a discernible component of some such or anything more than a theoretical concept.
Therefore, it allows us to discard the non-local wave-function in the Schrödinger picture as non-physical and be satisfied with the local Heisenberg picture.
Pilot wave QM and Copenhagen QM are equivalent in that they produce the same predictions and thus cannot be distinguished by measurements.
The most important difference of PWT is that the wave-function is seen as physical. To say it with WP:
According to pilot wave theory, the point particle and the matter wave are both real and distinct physical entities (unlike standard quantum mechanics, where particles and waves are considered to be the same entities, connected by wave–particle duality). The pilot wave guides the motion of the point particles as described by the guidance equation.
So the only reason to discard PWT for its non-locality is due to its claim that "(entangled) wave-functions are physical objects". But it just works with a non-local wave-function, just as the Schrödinger picture of Copenhagen QM does.
Whether that sounds convincing to you or makes you want to discard the Copenhagen interpretation, too, because it doesn't tell you what a wave-function is... Well, that's up to you.
Let me blunder in where angels fear to tread:
What is a locus, hence locality. In my definition a locus is an (x,y,z) point in space at a time t, which theoretically has infinite precision and experimentally has a measurement error.
Quantum mechanical solutions of the wave equation together with the postulates of quantum mechanics calculate with precision the probability that a measurement will give the locus of a particle at (x,y,z) at time t.
That is, in my opinion, the locality of the solutions=the-wavefunctions of quantum mechanical equations.
What is entanglement? The wavefunction is dependent on space time and energy-momentum variables and on the group structures of the solutions for the specific QM model, i.e.the quantum numbers. As long as the wavefunction is undisturbed, i.e. there is no interaction, all the variables and the conservation etc rules of the quantum numbers are interleaved with the particular solution. When an interaction happens conservation laws allow non local knowledge using partial measurements: The pi0 decays into two gamma, if the spin direction of one of the gammas is measured automatically from angular momentum conservation the spin direction of the other is known, no matter how far it has gone.
So locality and entanglement are two different concepts, imo, and should not be confused.
