From: *Bruno Marchal* <marc...@ulb.ac.be <mailto:marc...@ulb.ac.be>>
On 15 Aug 2018, at 01:48, Bruce Kellett <bhkell...@optusnet.com.au
<mailto:bhkell...@optusnet.com.au>> wrote:
From: *Bruno Marchal* <marc...@ulb.ac.be <mailto:marc...@ulb.ac.be>>
On 14 Aug 2018, at 04:30, Bruce Kellett <bhkell...@optusnet.com.au
<mailto:bhkell...@optusnet.com.au>> wrote:
If they are space separated, I am not sure I can make sense of
being in the same branch.
You appear to be referring to the presence of quantum fluctuations
continually splitting the classical Alice and Bob into multiple
copies -- the point that Jason has made.
That points is correct, but I was alluding to the infinity of Bob
and Alice couples associated with the singlet state. That is needed
to tackle the case where Alice and Bob makes non orthogonal
measurements.
I was trying to make sense of the suggestion of many Alices and Bobs
before any measurement. That can easily be implemented by havingÂ
Alice select her measurement angle according to the time of some
radioactive decay. Since an infinity of decay times is possible, we
get a superposition of an infinite number of copies of Alice.
OK. But we have this in our context too.
But this makes not difference to the basic argument -- one just picks
out a typical Alice.
How?
Do you really no know how to pick out a typical component from an ensemble?
You are wrong when you claim that an infinity of couples are required
to make sense of measurements made at arbitrary angles.
Why?
Because that is not how angular momentum operators in quantum mechanics
work.
The singlet state is rotationally symmetric,
That’s why.
That's why what?
and can be expressed in any base. But this does not mean that there
actually exists a copy of the observer for each of the potential
bases. That idea makes no sense at all; it is not part of quantum
mechanics in any possible formulation.
?
That would contradict the complementary principle. A well localised
particle is a particle having almost all possible momenta in many
different histories.
For fuck's sake, Bruno. Do you understand nothing of elementary quantum
mechanics? The angular momentum operators do not commute, sure, so that
if one has a precise measurement in one direction, one has no knowledge
of the projection in an orthogonal direction. But the possible values of
any such operator on the spin-1/2 state are +1 or -1 (in units of
hbar/2). So there is no infinity as there is in the case of the
complementarity of position and momentum operators!
Besides, it is possible to have exact values for both the total angular
momentum operator (L^2) and any particular component, say L_z if we are
measuring in that direction, and that is all we require here. See the
Wikipedia article:
https://en.wikipedia.org/wiki/Angular_momentum_operator#Uncertainty_principle
The singlet state does not single out one base, despite the
notation. It describes an infinite of Alice and Bob right at the start.
Sure, the singlet state does not single out one base. But that does
not mean that it describes an infinity of observers. Just because you
can measure at any angle does not mean that there is actually an
infinity of observers making all those possible measurements. That
notion is just crazy.
?
It is just what the wave described literally.
No, it is not. Look up some reference on the application of the
uncertainty principle to angular momentum operators. (Such as the
Wikipedia article above.)
Bruce
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