From: sarfatti@well.sf.ca.us (Jack Sarfatti)
Subject: Beyond Quantum Mechanics?
Organization: Whole Earth 'Lectronic Link
Date: Sun, 22 Nov 1992 04:01:03 GMT


Sarfatti Lectures in Super Physics (Lecture 3)

*Announcement: Beyond Quantum Mechanics?

A new law of physics? The design of the detectors in the future
retroactively post-determine the nature of the pair state from the source.
There is no transformation |a,b> - > |a,b>' in the course of time which
Ramsay et-al object to. There is only |a,b>' from the very beginning due to
real quantum action at a distance backwards in time - a kind of Wheeler-
Feynman model without an abosorber boundary condtion. But this model can be
tested easily - the prediction of "Sarfatti Mechanics" is receiver
polarization of sin2@cos(phi).

Note Sarfatti Mechanics = Quantum Mechanics + Hutzpah!


#8 Mach-Zehnder interferometer revisited with parallel |t> and |r> kets
works as well as with orthogonal ones!.

---->\\---------\
|a>  |    |t>   |
     |          - phase plate (phi)
     |          |
     \----------\\----- |tr+rt> = |I1> interferogram 1
          |r>   |
                |
                |
                 |tt+rr> = |I2> interferogram 2

Fig.8A MZI (parallel ket?)

can we get anything sensible if we assume

|t> = e^i@|r>

|a> = (1/sqrt2)[|t> + |r>] = (1/sqrt2)|r>[e^i@ + 1]

<a|a> = 1 implies @ = pi/2 so that

|a> = (1/sqrt2)|r>[1 + i] since |(1/sqrt2)[1 + i]|^2 = 1.

Note in general:

|a> = |t><t|a> + |r><r|a>

if <t|r> = 0, then <a|a> = 1 implies

|<t|a>|^2 + |<r|a>|^2 = 1.

On the other hand, if

|t> = e^i@|r>

|a> = [e^i@<t|a> + <r|a>]|r>

||e^i@<t|a> + <r|a>|^2 = 1

this can be satisfied if

|<t|a>|^2 + |<r|a>|^2 = 1

as before for orthogonal kets <t|r> = 0

but now we have an extra constraint in the parallel case

@ + arg<t|a> - arg<r|a> = pi/2

so that the relative phase between the two "parallel" kets |t> and |r> must
adjust itself for every particular superposition.  Is this too big a price
to pay? Let's continue.

So far no problem with parallel path kets of the MZ interferometer. What
about the second beam splitter?

Again, in general (look at Fig.8a):

|a> = (1/2)[|t><t|a> + |r><r|a>] = |1><1|a> + |2><2|a>

|t> = |1><1|t> + |2><2|t>

|r> = |1><1|r> + |2><2|r>

|a> = (1/sqrt2){[|1><1|t> + |2><2|t>]<t|a> + [|1><1|r> + |2><2|r>]<r|a>}

= (1/sqrt2){|1>[<1|t><t|a> + <1|r><r|a>] + |2>[<2|t><t|a> + <2|r><r|a>]}

If <1|2> = 0 as will be so for separate counters, then

<1|a> = (1/sqrt2)[<1|t><t|a> + <1|r><r|a>]

<2|a> = (1/sqrt2)[<2|t><t|a> + <2|r><r|a>]

If |t> = e^i@|r>

<1|a> = sqrt2<1|t><t|a>

<2|a> = sqrt2<2|t><t|a>

therefore,

2|<t|a>|^2 [|<1|t>|^2 + |<2|t>|^2] = 1

For half-silvered beam splitters

|<1|t>| = |<2|t>| = |<t|a>| = 1/sqrt2

and every thing about the moduli of the complex numbers appears to be self-
consistent so far.

<1|a> = sqrt2<1|t><t|a>

e^iarg<1|a> = e^i(arg<1|t> + arg<t|a>)

arg<1|a> = arg<1|t> + arg<t|a>

<2|a> = sqrt2<2|t><t|a>

e^iarg<2|a> = e^i(arg<1|t> + arg<t|a>)

arg<1|a> = arg<2|t> + arg<t|a>

So everything seems fine with the phases.

*It appears that a self-consistent quantum mechanics of the MZ
interferometer with parallel kets from the first beam splitter and
orthogonal kets from the second (since there are two counters) is self-
consistent. We also found self-consistency with the 2-slit experiment.




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