A Boolean logic is an event algebra that follows from a sample space of elementary event propositions. If you construct a Boolean logic around a sample space appropriate for the ##S_x## measurement you made, you cannot include propositions like ##S_z = \uparrow##, as you cannot construct a...
I don't think it was a simplified version of this. But let my try to address possible ambiguities.
If we have a Hilbert space of the X apparatus ##\mathcal{H}_X##, Y apparatus ##\mathcal{H}_Y##, the microscopic system ##\mathcal{H}_s##, and a coin ##\mathcal{H}_c##, and if we model the...
If the selection of a subexperiment can be modelled by some appropriate variable like the outcomes of a coin flip that perfectly correlates with the subexperiment, there would be a common sample space, yes. E.g. The outcomes (heads, A),(heads,B),(tails,C),(tails,D).
If you can carry out the...
In classical physics, different samples spaces can be related to one another by coarsening or refining, and there is a single sample space that is a common refinement of all others. In quantum physics, there isn't a common refinement.
Is the protean nature of ensembles in QM a weakness in the minimalist ensemble interpretation?
My understanding so far: The theory of a given system is the double ##(H,\rho)##, the dynamics and the preparation. I.e. All physical content is contained in these terms. The triple...
Bohmian Mechanics is the main subject of the book. The quotes are from chapter 11.5: "A Universal Bohmian Theory". Specifically, the wavefunction is described as nomological in response to the objection that the wavefunction in BM doesn't experience any back-action from the existing configuration.
Hmm, I'm not sure that's necessarily the case. BM can frame the wavefunction as nomological rather than ontological. I.e. Instead of being a thing that exists, it is a representation of the behaviour of things that exist.
From "Quantum Physics Without Quantum Philosophy" by Goldstein et al
"It...
Sorry, I forgot to respond to this even though I said I would.
I got some interesting (and hopefully correct) results. For simplicity, I'll represent Wigner's friend, his device, and his lab all with ##F##, and Wigner's own lab including himself with ##W##. I'll also ignore the coin toss (which...
Ok so it sounds like it ultimately boils down to a matter of interpretation regarding the nature of collapse. Anyway:
The histories formalism iiuc would imply direct analogue between the FR experiment and the WF experiment. In the WF experiment we have an isolated system that evolves into...
Hmm, I guess the issue is Wigner predicts his measurement outcome with certainty, which would not be the case if he used a collapsed state or a mixture. Richard Healey argues that Wigner can use the pure state for setting credence about his own measurement, and a mixed state to set credence...
Sorry, by macroscopic subspaces I mean the very large subspaces associated with pointer properties. But this just raises a similar question about pointer properties. Both Wigner and his friends use different pointer properties, each suitable for their own measurement purposes.
Wigner's friend...
Interesting. In the conventional WF thought experiment, it's usually supposed that Wigner is able to model his friend's lab with unitary evolution, right up to the point of measurement. If he should not do that, can he still know beforehand, with certainty, the result of his measurement outcome...
To expand a bit on my last messages, and to lay out my understanding of events: Let's say Wigner prepares eveything in the state ##\rho = [\psi_0,D_\mathrm{ready},F_\mathrm{ready},L_\mathrm{ready}]\otimes\frac{1}{2}([\mathrm{heads}]+[\mathrm{tails}])## (Where I have included an additional...
Actually my previous answer might be completely wrong and your intuition correct. If Wigner's friend wants to compute a prediction that Wigner definitely records ##1##, he needs a record of his entire lab including himself, which should be incompatible with his record of his own measurement. I...
One problem might be that Wigner talking to his friend, while simultaneously being aware of his measurement result, would constitute a record of both measurements, which CH would forbid. It's likely that Wigner's friend would be rearranged in a very fatal way.
Going to do a few quick...
Hmm, In the CH formalism, the friend should be free to employ whichever boolean event algebra/framework is fit for purpose, without having to commit to one as correct. This might be a departure from conventional QM where a measurement context selects the right framework.
I think it is, insofar as not everyone in the foundations community would be cool with using a multiplicity of sample spaces to make "realistic" claims. I.e. It's the case that there is a probabilistic sample space such that ##P(A) = 1##, and another sample space such that ##P(B) = 1##, but no...
It should be ok for Wigner's friend to use one context to reason that Wigner's measurement will yield ##1##, and another context to reason that his next measurement will yield (say) ##S_z = \uparrow##. Both of these properties have a subspace associated with them. I think he only runs into...
Ah ok. Would you also need to include ##|0,-\rangle## and ##|1,-\rangle## for completeness? ([edit]-actually nvm that's not the problem, I have to think about it). I just used ##|+\rangle## and ##|-\rangle## which might not have been kosher. And yeah they're super weird to work with. A lot of...
Yeah this is what some consistent historians call a "measurement scenario", whereby the property/event that is measured correlates with the event that does the measuring, such that (as you mentioned) ##P(\left[ 0\right] \mid \left[W_{0}\right] ) = P(\left[ 1\right] \mid\left[W_{1}\right] ) = 1##...
The stuff you can construct with CH can be pretty out there for sure.
One question: Typically a family of histories is a projective decomposition of the identity, such that the probabilities of the histories sum to one. For the families above, I compute a probability of 0.25 for each history...
That's definitely the case on a practical level, though I think the formalism is robust enough to handle them. E.g. If we have a Wigner's friend scenario characterised by an initial state ##|\Psi\rangle = |\psi\rangle_p|\Omega\rangle_F|\Omega\rangle_W## that evolves unitarily into a final state...
This basis is often an energy eigenbasis, which is why quantum chemists are interested in the von Neumann entropy as the Shannon entropy of the natural orbitals/modes of the system (It's a step in various investigations about the relationship between independent fermion entropy and wavefunction...
Since the diagonals of rho and the eigenvalues of rho are the same when rho is expressed in its eigenbasis, and this eigenbasis corresponds to a measurement for which knowledge of possible outcomes is maximal, could we interpret von Neumann entropy in terms of the measurement for which knowledge...
The interference pattern does not return if the detecting barrier is removed. But we can filter out a subset of photons that will exhibit interference terms.
Let ##|A\rangle## and ##|B\rangle## be the respective states of a photon travelling through slit ##A## and ##B##. If the photons are...
I don't see how this is different from our previous talk about the detector in the miniverse. My understanding so far:
We both agree that a fully quantum theory of the miniverse will consist of an appropriate density operator and dynamics. I say this theory lets us run a simulation that returns...
Well, so far we have only considered a detector, which obviously does not use quantum mechanics to understand its surroundings. But if the miniverse is suitably prepared, quantum mechanics will permit a description of it in terms of possible planetary formations and emergences of biological...
We have a miniverse that contains a detector and an observable X. If the detector measures X to some suitable standard, this implies that, if we decompose the identity operator into possible detector properties and values of X, there will be some suitably high correlation between possible...
A chosen decomposition is just an expression of the properties/events we want to make predictions about. We always need some procedure to connect the content of a theory to predicted consequences.
If a decomposition was instead used as a physical explanation for why events happen, i.e. if a...