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From: ramsay@unixg.ubc.ca (Keith Ramsay)
Newsgroups: sci.physics
Subject: Re: Photon pair Mach-Zehnder Interferometer IV
Date: 20 Nov 1992 04:46:51 GMT
Organization: University of British Columbia, Vancouver, B.C., Canada
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Sarfatti discusses a "Mach-Zehnder Interferometer":
|* Note that phi is definite. There is no reason to assume that phi is
|random as Ramsay requires.

I do not so "require" for *all* experiments. I only require that if
there are phase differences, that they be taken accurately into
account.

*Ramsay - the point is there is only one phase difference phi - or rather
one with a small dispersion much less than 2pi. This is very unlike the
case of a 2-slit arrangement in which your point would be correct. If I
tried to used a standard 2-slit with screen in transmitter the device would
not work because of the sum over all phases 0 to 2pi. In contrast, the MZ
has a sharp phase.*

|According to Ramsay:

I'd be careful attributing to me claims about an experiment which we
haven't discussed yet!

*? - I have bee ndiscussing an experiment what have you been discussing?*


Let me suggest that in the future, we try to limit our use of
"argument by analogy" between different experiments since it seems not
to be helpful, in either direction.

|Note that the relative phase shift of the beam splitter is not frozen in
|stone like the Ten Commandments but adjusts itself globally to the
boundary
|conditions or "total experimental arrangement" - in this case the setting
|on the variable phase plate.

Who's the supplier of your optical equipment? :-) You're implying that
the sort of interaction that the beam splitter has with photons
passing through it varies somehow, without giving a reasonable
physical basis for it.

*Look at Bohm's quantum potential approach to QM for a clear example of
nonlocal influences which is implicit in Copenhagen interpretation if you
read Bohr.  You are thinking locally I mean classically Ramsay not quantum
mechanically. But the main thing is that I have shown that the standard
formalism allows quantum conneciton commuication.*

Beam splitters have optical properties (index
of refraction, reflectivity, etc.), which determine the relative phase
shift. If you claim that it changes, you'll have to explain why its
optical properties have changed.

*because of nonlocal quantum action at a distance - especially clear in
Bohm's formulation*


|#4 Now insert a half-waveplate in the o-space path. The unitary operator
|U(o:1/2) only acts locally and unitarily in the o-path because that is
|physically where the plate is. There is no half-wave plate in the e-path.
|Ramsay seems to get confused on this, falsely applying the unitary
operator to the entire state - which is wrong standard quantum mechanics
(SQM).

No, Sarfatti. Remember that you yourself described the experiment
having the operators act on the state of the photon (the "whole
thing"), until it turned out to contradict your "indistinguishability"
claim about photons in the two paths.

*I did nothing of the sort Ramsay. You are totally distorting what I
claimed. You might have thought I claimed it because of defects in my
notation but I have always been clear that the different pieces of physical
apparatus act locally - dynamics is local, connection is nonlocal. That is
ordinary forces are local but quantum actions are not! They are distinct!*

Standard quantum mechanics talks about transformations of the state,
and asserts that the operators producing them are unitary (until
measurement, of course). Where does it say, "but in some cases you
have to break the state space into pieces; the operator acts
unitarily, but only on each piece"? I think this is just your invention.

*Ramsay you are being incredibly thick-headed over something very simple
and obvious. Do you mean to say that a half wave-plate stuck into the o-
beam of a doubly refracting crystal will not only rotate the plane of
polarization of the o beam but also of the e-beam.  Well that would be
something if true! It is not true. But my predicted fringe shift at the
receiver end I think is true.*

|Preamble:Ramsay's remarks about summing over phi are clearly wrong as he
|has not conceptually distinguished between a 2-slit experiment and a Mach-
|Zehnder experiment.

This is inaccurate; I am aware of the difference.

*If you arem you are not being conmsistent.*

[diagrams and description]
|The initial "entangled" (i.e. quantum-connected) photon-pair state is:
|
||a,b> = {|a,e>|a,+>|b,+> + |a,o>|a,->|b,->}/sqrt2
|
|local unitary action of both phi-meter in e-path and 1/2 wave plate in o
|path of photon a is "polarization disentanglement":
|
||a,b> -> {e^iphi|a,e>|a,+>|b,+> + |a,o>|a,+>|b,->}/sqrt2
|
|       = |a,+>{e^iphi|a,e>|b,+> + |a,o>|b,->}/sqrt2 = |a,b>'

I trust you will agree that, more generally, the action of this
optical apparatus upon a pair state

   |a,b> = z1 |a,e,+>|b,+> + z2 |a,o,->|b,+>
          +z3 |a,e,+>|b,-> + z4 |a,o,->|b,->

*NO I don't agree. That is totally wrong physics. It ain't quantum
mechanics! Show me one physical way to do what you have written. Just
because you wrote it mathematically does not mean there is a real physical
procedure to implement it. If there is, show it!*

with |z1|^2+|z2|^2+|z3|^2+|z4|^2=1, takes it to

   |a,b'> = e^{i*phi} z1 |a,e,+>|b,+> + z2 |a,o,+>|b,+>
          +e^{i*phi} z3 |a,e,+>|b,-> + z4 |a,o,+>|b,->.

|The recombination at counter 1 induces
|
||a,b>' -> |a,+>|1>{e^iphi|b,+> + |b,->}/sqrt2 = |a,b>'''

I still see no reason to believe this, and moreover, I see no natural
way to extend such a transformation to the entire state space (which
makes sense, that is). Unless it is defined on the whole state space,
it is not a well-defined operator.

*Ramsay, this is nonsense. It ain't standard quantum mechanics.  Every
physical process between measurements can be described by a unitary
transformation of the initial state |i> into a final state |f>. That simply
means <i|i> = <f|f> = 1. True, one can write an operator U that can act on
any state you can mathematically construct. But the rsult of that action
will be different for different inputs. I am only interested in a
particular kind of input state passed through a particular apparatus
described by a particular apparatus. Other inputs may or may not be of
interest. Also you are not free to choose z1,z2,z3,z4 arbitrarily for the
input state because of conservation laws of parity, angular momentum in em
interaction as well as conservation of probability. So the "whole space" is
really irrelevant to the physics!*

|<a,b|a,b> = '<a,b|a,b>' = '''<a,b|a,b>''' = 1
|
|so these transformations are unitary.

This also has to hold true for the action upon all the other vectors
of the state-space, or it isn't really unitary.

*Bull tweedle!*