From: *Bruno Marchal* <marc...@ulb.ac.be <mailto:marc...@ulb.ac.be>>
On 15 Aug 2018, at 13:33, Bruce Kellett <bhkell...@optusnet.com.au
<mailto:bhkell...@optusnet.com.au>> wrote:
Do you really no know how to pick out a typical component from an
ensemble?
I cannot when the elements cannot be distinguished.
The fact that they cannot be distinguished is what makes picking a
typical element so easy, and so useful.
Alice cannot do that, but each Bob and Alice picks their counterparts
by doing their measurements, but that take some times.
That is not what I was talking about.
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!
No problem with this, but Alice can choose to measure that spin in any
direction.
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
<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.)
I do not see any problem between what I said and that wiki pages,
which is rather neutral on the interpretations. They do not provide
the “many-worlds” view on this, and some links there suggests they use
the Copenhagen formulation.
This is not a matter of many-worlds vs Copenhagen.
You seem to reintroduce implicitly some collapse in the picture.
Why do you think that picking a typical branch in a superposition
involves some collapse? That is daft.
That’s my feeling, as this is not clear. When measuring a spin: there
are two possible values *for all possible direction of the spin*.
No, there are only two possible values for the direction in which the
measurement is made. There are no "possible directions of the spin"
prior to the measurement. You are reverting to a hidden variable account
again. These "possible directions of the spin" would be hidden variables
in any mathematical account of such a theory, and we eschew hidden
variables.
That makes infinitely many worlds. Same for an electronic orbital.
There are as many world that the possible position of the electron in
the orbitals.
You are using a very strange notion of a "world". As I have frequently
explained, a 'world' arises only when decoherence has caused the
elements of a superposition to become effectively orthogonal -- disjoint
FAPP. And FAPP is sufficient because worlds are defined for practical
purposes. This does not happen in either the singlet case, or the case
of electron orbitals. So if there is no infinity of worlds in either
case: there is not an infinite number of copies of Alice measuring the
singlet state.
Are you OK with this? I try to figure out what is your interpretation
of the SWE.
No, I am not OK with your notion of a 'world'. It makes no sense, and it
serves no purpose to confuse this peculiar notion with the well-defined
notion of disjoint components of the wave function.
Bruce
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