But before you had said,
An ensemble of proton beams (prepared moving blops consisting of many protons) is not an ensemble of protons. Protons are never seen in the LHC experiments, prepared are the blops
and measured are the traces of the collision products. In the spirit of the quote by...
Nature ensures in perfect correlation experiments with entangled photon pairs (the ''certain experiments'') that whenever Alice measures $Ak$ to get ##a_k## then Bob measures $Bk$ and also gets ##a_k##, while for Bob it seems that his results are random. In spite of (and consistent with) the...
But the argument (2) given there is for an idealized model case, where (in the interaction picture), the interaction has no off-diagonal terms in the selected basis. This seems appropriate only if the selected basis is invariant under the dynamics of the system alone (before the interaction...
Are the three derivations mathematically equivalent?
I looked at https://arxiv.org/pdf/1811.11643.pdf =
since you are its author:
This is not strictly on topic here but how do you reduce to position the color of an object (surely a perceptible) sitting at the macroscopic position x? It is...
Situations like these are precisely what induced Heisenberg 1927 to talk about state reduction (aka reduction of the state vector, aka collapse). That you don"t like the commonly used words for it doesn't mean that you don't make use of the same concept.
I had done so in an earlier post to the same topic:
It is a meaningful play with words. It means that something happens at a distance - namely that nature cooperates globally at long distance to ensure that the perfect nonclassical correlations predicted by quantum mechanics in certain...
In this case you need to rearrange the 4 entries of the matrix into a vector of length 4 in a way conforming to the content, usually rowwise or columnwise.
If only one photon is around at the time of measurement, there can be only one detection event.
(But you seem to be discussing here the case of an entangled pair of photons, an idler photon and a signal photon. For this, there are two possible detection events.)
No. One can detect a given...
The simplest way to look at the tensor product of two Hilbert spaces of n-dimensional vectors representing two systems 1 and 2 is as a space of ##n\times n## matrices. n=2 for two spins. The general pure state is such a matrix ##\psi##, and the inner product is...
BM has additional variables that makes the position basis preferred, and if one only looks at probabilities for position alone, these integrate to 1. In contrast to standard quantum mechanics, these are the only probabilities that matter in BM.
Indeed, BM has no probabilities for spin or...
Nevertheless, the only correct B-level answer to the original question
is no.
The experimental evidence is overwhelming that a photon passing undetected a slit always results in zero or one screen point, never more. A zero count is due to detector inefficiencies.
On the other hand, if the...
Suppose a beam is split into a superposition of two beams. At positions where the two beams are very far apart, a beam dump collapse is obtained if one destroys one of the resulting beams (by position measurements there) and makes measurements on the other one. This is a bilocal activity created...
Only in finite-dimensional Hilbert spaces. There kets may be viewed as column vectors (matrices with one column) = vectors of ##C^N##, bras as row vectors (matrices with one row) = covectors = linear forms, and the inner product is just the matrix product of these.
But in order that the...
The preparation of many independent systems may define an ensemble in the quantum case, but
then it is not consistent with what you describe here:
But a Stern-Gerlach experiment does not constitute a measurement: it is a unitary operation.
Thus in such an experiment you are not sorting...
Taking the exponential of a distribution is ill-defined and needs a regularization to give it a meaning. The result is a state not described by the original Fock basis.
That was indeed the context in which ftr posted his original query (if you follow the links in post #1 a few steps backward).
But I don't really have a concern, I can live easily with the way science is done in our culture.
The same. But your definition conflicts with your earlier usage of the word subensemble, which makes no sense with this meaning. Hence I wondered what you mean.
Or does your notion of ensemble have some sort of temporal permanence so that it remains the same when you change its momentum through...
Nothing is wrong per se. But there is the blemish that you create your example in a way that presupposes Born's rule.
The Gaussian used in the introductory lab to analyze a sample of measurement results has little to do with the Gaussian used to model a POVM. For in the POVM, all positions...
Yes. tradition in the form of Lehrmeinung has a lot of authority.
In the case of Copenhagen even though there always have been prominent opposing authorities, such as Einstein and Schrödinger.
I know that you call it that. But I still do not know what properties of a physical setup makes it qualify as an ensemble in your sense. You are using the term without explaining what it should mean.
I provided a detailed example for momentum measurement in the POVM thread.