kith:
Well, then we agree, because that's exactly what I'm trying to say. Without intermediate collapse, it is impossible to compute such joint and conditional probabilities and hence QM without collapse doesn't work. With collapse, you can compute the joint probability also in this setting...
Well, but I don't see how that helps. What if Wigner's friend already forgot the result of the ##t_1## measurement at ##t=t_2##? Introducing Wigner's friend is just another way of evading my constraint that the intermediate measurement result at ##t_1## shouldn't be recorded in an auxiliary...
Or let me formulate the question in an equivalent way: Let's say we already have the complicated wave function of the full system after all the measurements and after only unitary time evolution: ##\psi(\mathbf{X},t_2)##. How do I extract the information ##P(y(t_1) \in A_1 \wedge y(t_2) \in...
Hmm, I don't see what you gain by making the example more complicated. Of course I was lazy and modeled the device by only one variable, but how does including additional variables fix the problem? At ##t=t_1##, the state will be a superposition of the many possible measurement results and we...
Well, I didn't want to discuss this issue initially in the first place ;-) I was just forced to, because Elias1960 claimed that standard QM can be done without collapse, attempting to circumvent my question regarding the consistency of BM.I don't agree that wave function collapse is in...
Well, but this part of the discussion is neither about MWI nor BM. It's about the question whether intermediate collapse is necessary in standard QM. My argument is that it is required, because otherwise, standard QM has no way to calculate the joint probability that I asked for.
Can you...
Well, let me make it very precise:
I have a Hamiltonian ##H=\frac{p^2}{2}## and an initial state ##\psi_0(x)=\frac{1}{2\pi}e^{-\frac{x^2}{2}}##. What is the probability to find the particle in the set ##A_1 = [2,3]## at ##t_1 = 1## and in the set ##A_2 = [0,1]## at ##t_2 = 2##?
In standard QM...
I didn't defame you at any point. This is simply what I understood from your post and I still don't see the difference.
Anyway, the challenge still stands: Compute ##P(x(t_1) \in A_1 \wedge x(t_2) \in A_2)## without intermediate collapse. You haven't done this so far. You have computed a...
Well, the textbook by Ballentine may be an exception, but I think it is universally agreed that this part of the book is flawed.
I don't assume a specific version of collapse. I'm just asking: How do you calculate ##P(x(t_1) \in A_1 \wedge x(t_2) \in A_2)## in standard QM without inserting...
Here's another question for you: If you think one can do QM without intermediate collapse, then how do you calculate probabilities such as ##P(\mathbf{X}(t_1) \in A_1 \wedge \mathbf{X}(t_2) \in A_2)##? In orthodox QM, you would just calculate ##\int...
Alright, then thanks for the discussion, I think it enhanced my understanding of BM quite a bit. Initially I thought that BM is really an exact interpretation of QM and gives the exact same results and I was just missing some basic argument. Now that I understand the difference, I think one...
Demystifier:
"I argue in the paper that they do not exist"
Well, but I don't see any quantitative argument in the paper. You make a lot of approximations and you don't quantify how good these approximations are. You would have to work in an actual model to calculate such deviations. Only then...
How could such predictions be misguided? Either BM and QM can be shown to be equivalent. This seems not to be the case. Or we need to understand their difference quantitatively, in order to test which of them is correct. Without quantitative computations, BM can't be said to be compatible with...
"I agree, but the claim is that this difference cannot be measured in practice."
Well that's the problem I'm having. The BM community seems to shy away from making predictions with their theory. I'm trying to understand the (in)equivalence by looking at some actual calculations, but I'm just...
Well, in order for the different predictions to be measured in practice, one would need an actual prediction of BM in the frist place. However, I don't think any experimentally relevant prediction of BM has ever been computed at all. There is only the claim that BM will make the same predictions...