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
NNTP-Posting-Host: unixg.ubc.ca

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.

|According to Ramsay:

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

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. 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.

|#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.

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.

|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.

[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,->

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.

|<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.

Keith Ramsay         "But I really think that frequent posters such as 
ramsay@unixg.ubc.ca  myself, Dale, Scott, McIrvin and others are not 
                     crackpots; we are simply loudmouths."
Newsgroups: sci.physics