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[Phys-l] Tutorial on the Time Symmetric Quantum Model (Quite Long ) Prt 3




cont..
However, what is important here in terms of the TSQM is that each path
(called a history) can be modeled as a particle traveling in both time directions.
That is every path is a superposition of time reversed paths. This was
demonstrated by Sinha and Sorkin in a very interesting paper. In this paper it was
shown that the classical path probabilities can be calculated by multiplying
the time reversed amplitudes for each path. Using this
formalism, Sinha and Sorkin generate the correct probabilities for the
Bohmiam version of the EPR experiment. ( Bohm formulated an EPR experiment using
spin states of particles)
So how can we have particles that travel back in time? Actually this is not
at all controversial in QT. It is already accepted that anti matter particles
are particles traveling backward in time. But antimatter particles are not
sufficient for a full time symmetric model. We must now look more closely at
the Dirac equation and resurrect two additional particle states slain by the
great Pauli.
The Dirac equation is the result of uniting special Relativity and Quantum
mechanics in terms of fermion (Matter) states.(There are other relativistic
equations, the Klein Gordon for spin 0 bosons and the Proca Equation for spin 1
bosons for which the rest of this also applies.) This equation predicted
four possible particle states. (Though they weren’t described this way until
Feynman’s QED theory) These are
1) Particles with positive energy going in the future.
2) Particles with negative energy going into the past
3) Particles with positive energy going into the past
4) Particles with negative energy going into the future.
Particles state 1 is of course ordinary particles. But what about the other
particle states? Particle state 2 is logically equivalent to positive energy
particles going into the future but with reversed charges. This state
represents anti matter and we know anti matter exist. But what about particle states
3 and 4? There is no way to interpret these states in any sensible way, or
is there.
The problem with particle states 3 and 4 is that they can not be
reinterpreted into positive energy states. And Pauli clearly demonstrated that negative
energy particles would be senseless in Quantum field theory. For one thing in
a point well beyond the technical level of this essay multiple particle
Hilbert space ( Fock Space) would generate negative probabilities depending on
even or odd particle number. Also negative particles allow violation of basic
thermodynamics allowing perpetual motion devices. They would cause normal
particles to unavoidably accelerate to near light speed in all cases something we
obviously don’t see. So particle states 3 and 4 make no sense. Right? Well
maybe they do.
First of all many of the weird effects predicted for negative energy
particles assume they couple to normal particles in terms of the known forces in
Quantum Field theory. But in fact more detailed models of negative energy
particles (there are various papers on this) indicate that they do not couple to
normal matter states in QFT. In addition these strange negative states are
already implied in interaction theory. Remember we said that particles experience
forces by exchanging other virtual particles.
It is easy to see how this works for repulsive forces. An electron for
example emits a photon and gains momentum opposite to the direction of the emitted
particle. But how could it gain momentum in the direction in the same
direction as the emitted photon? This would mean that the emitted photon had
momentum opposite in direction from its travel. Well this is exactly true of
particle states 3 and 4. Particle states 3 and 4 must “exist” as virtual
particles.
We are now ready to go back to the idea of time symmetric paths. We now have
the needed particle states to describe both real and virtual particle paths.

Virtual particle paths are used to describe interactions between real
particles.
For repulsive forces we have superposition of states 1 and 2
For attractive forces we have superpositions of states 3 and 4
For matter paths we have superposition of states 1 and 3
For Antimatter paths we have superposition of states 2 and 4.
Notice that every path is a superposition of an advanced (time reversed) and
retarded (non time reversed) particle state.
Retarded states 1&4
Advanced States 2&3
So how does this explain EPR? Well using the time symmetric path formalism
we don’t need any instantaneous effects due a measurement event. Rather the
measurement of particle A is connected to the particle creation event at time
zero by the advanced portion of the particle path from the pair creation to
its measurement at measurement device A. No faster than light signaling is
required.
So the astute reader of this would now ask the question, if this story is
true why do we only see positive energy particles? The answer is that it is
enormously improbable. And it is improbable for the same reason that the room
you are in doesn’t have every air molecule leave the room in their collective
random motion.
We “see” particles only when a measurement event occurs. This seeing is due
to the process we call Decoherence. Decoherence is when a quantum states
becomes entangled with the immense number of quantum states in the measurement
device. Any macro measurement device will have an arrow of time which is
dependent on the thermodynamic arrow of time. All measurement events involve a
direction of time.
More formally in Decoherence theory there are three requirements of a
Decoherence functional. They are
Hermiticity – only real value observables.
Positivity - all measurement events correlates to the macro arrow of time.
Normalization- The complete set of measurement events corresponds to
classical reality.
I hope this essay explains in, as non technical language as possible and
without invoking any mathematics the proposal concerning negative energy states.
Of course understanding the points here may be still be challenging due the
many new terms and ideas introduced. Also no claim is made here for any
rigor in this presentation. Finally the complete set of ideas is mine so it
shouldn’t be inferred that that there is complete agreement with me on all these
points by anyone mentioned.
Bob Zannelli