The Transactional Interpretation of Quantum Mechanics
Today I have the privilege to host a guest blog post by Ruth
E. Kastner (@rekastner http://transactionalinterpretation.org/
) who is an expert in the Transactional Interpretation of Quantum Mechanics. She
recently published a book on this topic.
Part 1: Introduction
The
Transactional Interpretation of Quantum Mechanics (‘TI’ for short) was proposed
by John G. Cramer in the 1980s (Cramer’s comprehensive 1986 presentation is here). The distinguishing feature of TI is its ability to ‘read off’ the Born Rule
for the probabilities of measurement results from the basic formalism. How does
it do this? By including the solutions of the advanced (negative energy/time
reversed) Schrödinger Equation, as well as the retarded solutions of the usual
Schrödinger Equation.
TI is based
on the Wheeler-Feynman time-symmetric theory of classical electromagnetism
(Wheeler and Feynman 1945, 1949). In this theory, a charge emits a
time-symmetric field having equal components retarded and advanced radiation,
while any absorber responds to that radiation by generating its own
time-symmetric field. The responding field is exactly out of phase with the
stimulating field. This results in the cancellation of all fields except the
one between the emitter and the absorber—that field is built up to full
strength, thereby transporting energy from the emitter to the absorber. (See
below.)
The
Wheeler-Feynman theory accounted nicely for ‘radiative damping,’ or loss of
energy by a radiating charge. This could only be accounted for in the
traditional theory (which assumes only a retarded field is radiated) by
assuming an ad hoc sourceless ‘free
field’. Wheeler and Feynman’s original
motivation in developing this ‘direct action’ theory was to eliminate the field
as an independently existing entity, to solve the problem of self-action in the
classical theory – in which a charge interacted with its own field, resulting
in infinite energies. They lost interest in it when they found that some degree
of self-action was needed to account for relativistic effects (such as the Lamb
shift). However, the direct action picture can still be used, and in fact
Davies developed a direct-action picture of quantum electrodynamics in the
1970s (Davies 1970, 1971, 1972).[1]
The
transactional interpretation is an application of the direct action picture to
quantum systems. It departs from the Wheeler-Feynman (WF) classical picture in
the fact that, instead of being a continuous quantity, energy can only be
delivered in discrete packets (quanta). The usual retarded quantum states, such
as |Y>, are called offer waves (OW) and the advanced states, <F|,
are called confirmation waves
(CW). Since TI deals with quantized energy and momentum, many absorbers may
respond with CWs to an emitter’s OW, but (for a one-quantum OW) only one of the
responding absorbers can actually receive the energy. But this quantized
version of the WF picture allows for a very nice resolution of the notorious
‘problem of measurement’: namely, it allows one to ‘read off’ the heretofore
mysterious ‘Process 1’ of John Von Neumann’s theory of measurement, which also contains the Born Rule. We’ll now see how this works.
To review,
‘Process 1’ is the transition of a quantum system from a pure state to a mixed
state upon measurement, i.e.:
The coefficients |cn|2 are the
probabilities given by the Born Rule for each of the outcomes yn.
Von Neumann noted that this transformation is acausal and
fundamentally irreversible, yet he was unable to explain it in physical terms,
and treated this transition as fundamentally dependent on an observing
consciousness. However, if we take into account the advanced responses of
absorbers, then for an OW described by |Y>,
we have for a collection of numbered absorbers:
In the above diagram, an initial offer wave from emitter E passes through some measuring
apparatus that separates it into components áyn|Yñ |y nñ, each reaching a different absorber n. Each absorber responds with an
advanced (adjoint) confirmation áyn| áY|y nñ. In TI, these OW/CW encounters are called incipient transactions. They are
described in probabilistic terms by the product of the OW and CW, which gives a
weighted projection operator: áyn|YñáY|ynñ |y nñáy n | = |cn|2 |y nñáy n |. If we add all the
incipient transactions, we clearly have the density operator representation of
‘Process 1”:
Thus, by including the advanced responses of absorbers, we
have a physical account of measurement as well as a natural explanation of the
Born Rule and Von Neumann’s ‘Process 1’. The response of absorbers is what
creates the irreversible act of measurement and breaks the linearity of the
basic deterministic propagation of the quantum state. Since the conserved
physical quantities can only be delivered to one absorber, there is an
indeterministic collapse into one of the outcomes y k with
a probability given by the weight |ck|2 of the associated projection operator |y kñáy k |. This is called an actualized transaction, and it consists
in the delivery of energy, etc., to one absorber. I see this is a form of
spontaneous symmetry breaking (this is discussed in Chapter 4 of my book).
I have been
developing the transactional picture in two specific ways: (1) investigating
what kind of ontology underlies the offers and confirmations, especially when
these are multi-quantum states: and (2) extending TI explicitly into the
relativistic domain to give a more detailed account of emission and absorption,
both of which are inherently relativistic processes. Both emission and
absorption play crucial roles in defining the measurement process. Only the transactional picture, in which
absorption contributes advanced states, provides a physical basis for what is
otherwise an ad hoc mathematical
recipe (Von Neumann’s ‘process 1’ and the accompanying Born Rule). In Part 2, I
will discuss my recent developments of TI. Further information and discussion
is available at my website (http://transactionalinterpretation.org/
).
References
Cramer J. G. (1986). ``The
Transactional Interpretation of Quantum Mechanics.'' Reviews
of Modern Physics 58, 647-688.
Davies, P. C. W.
(1970). “A quantum theory of Wheeler-Feynman Electrodynamics,” Proc. Cam. Phil. Soc. 68, 751.
___________(1971).”Extension of
Wheeler-Feynman Quantum Theory to the Relativistic Domain
I.
____________(1972).”Extension of Wheeler-Feynman Quantum
Theory to the Relativistic Domain II. Emission Processes,” J. Phys. A: Gen. Phys. 5, 1025-1036.
Kastner, R. E
(2012). The Transactional Interpretation
of Quantum Mechanics: The Reality of Possibility. Cambridge : Cambridge University
Wheeler,
J.A. and R. P. Feynman, "Classical
Electrodynamics in Terms of Direct Interparticle Action," Reviews of
Modern Physics, 21, 425–433 (1949).
[1]
Meanwhile, the infinities resulting from self-action are being ‘tamed’ by
renormalization techniques.
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