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The Transactional Interpretation:

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The Transactional Interpretation:
an introduction
В©2012 R. E. Kastner
The Transactional Interpretation is an
interpretation of quantum mechanics
• But what is quantum mechanics (QM)?
• Theory needed to predict behavior of very
small particles such as atoms, electrons,
photons, and other subatomic particles.
• QM works very well but what it actually tells
us about reality is very unclear
• An interpretation is intended to make clear
what the theory tells us about reality
The biggest quantum puzzle:
• The �measurement problem’
• The probability rule for outcomes of
measurements
The Measurement Problem
• A quantum system is described by a quantum
state:
�Q’
Measuring a quantum system
• Suppose we want to find out where a
�particle,’ such an electron, is?
• The electron gets created in some state �Q’
• It could be in different positions a, b, c
• Quantum theory just gives us probabilities for
those positions: Prob(a|Q) or Prob(b|Q) or
Prob(c|Q)….but no answer for why we only
see 1 of them
Quantum superpositions
• The preceding is known as a �superposition’ of
different possible outcomes a, b, c:
�Q’ ( measurement) →
�a’ + �b’ + �c’
�Schrodinger’s Cat’
• Erwin Schrodinger: pointed out this can get
ridiculous: Take an unstable radioactive atom
in the quantum state
�decayed’ + �undecayed’
and put it in a box with a geiger counter, vial of
poison gas, and a cat. Close the box and wait 1
hour. If the atom decays, it sets off the geiger
counter which beaks the vial of gas and kills the
cat :(
in the usual way of thinking:
The “quantum state of the entire system” is:
{�decayed’ �geiger counter triggered’ �broken vial’ �dead cat’ }
+
{�undecayed’ �geiger counter untriggered’ �intact vial’ �live cat’}
i.e., the cat is in a �superposition’ of alive and dead!
But we never see cats in superpositions, or anything else for that
matter
the usual (inadequate) way of thinking
• says that the quantum state �collapses’ to a
particular result (takes on a particular result)
upon measurement , but
• cannot account for how or why a
�measurement’ is completed
• depends on an �observer’, but
• cannot define what an �observation’ is
transactional interpretation (TI)
• defines �measurement’ (or any process resulting
in a definite outcome)
• �measurement’ occurs upon
absorption/annihilation of the quantum state
• absorption not taken into account in �standard’
qm
• why not? because it’s really a relativistic process
(remember E=mc2 ? high energies/speeds)
quick and dirty relativistic qm
• quantum states of particles are created via
action of �creation operators’ on the �vacuum
state’ , �0’:
� �0’ = �Q’
• quantum states destroyed via action of
�destruction operators’ on the �quantum state’
�Q’:
�Q’ = �0’
ordinary nonrelativistic qm:
• typically takes creation (emission of a
quantum particle) for granted and ignores
destruction; and assumes energy is always
positive
• TI: must take destruction (�absorption’) of
quantum states into account to understand
measurement
• but also: emission and absorption involve
both positive and negative energies
�offer waves’ and �confirmation waves’
• in TI, the usual quantum state is called an �offer
wave’ (OW)
• the negative energy component from the
absorber’s response to the offer wave is called a
�confirmation wave’ (CW)
• the interaction of OW and CW is like a
�handshake’ that occurs outside spacetime. It sets
up possible �transactions’: real transfers of energy
-- and one of these is actualized in spacetime.
Example: a laser
photon OW are created in the laser and
propagate outside spacetime to interact
with absorbers making up the detector.
Each available absorber responds with
its own CW. OW and CWs interact in a
competing �handshake’; one of these
�wins’ the competition and a photon is
transferred from the emitter to that
absorber in spacetime.
Spacetime: �tip of the iceberg’
the TI picture
TI’s solution to the �cat’ problem
• quantum absorbers in the geiger counter
respond to the unstable atom’s offer wave by
generating confirmation waves
• a transaction may occur during the time the
box is closed. If it does occur, the cat dies, if it
does not occur, the cat lives
• the account is not observer-dependent
however:
• it is still fundamentally uncertain as to
whether a given transaction will occur or not
• quantum mechanics suggests that nature is
indeterministic at a fundamental level
• But it gives us a way to calculate the
probabilities that various outcome will occur.
returning to the electron example
• the electron emitted in state Q is �measured’
to find out where it is:
в—Џa
в—Џb
в—Џc
QM tells us that the probabilities are given by:
Q(a)Q*(a)
Q(b)Q*(b)
Q(c)Q*(c)
(where the star is the complex conjugate)
but the standard theory has no reason for the
mathematical form of the quantity Q(x)Q*(x)
TI gives an answer
• The probabilities “Q(x)Q*(x)” express the
interaction of the offer wave Q(x) and the
confirmation wave Q*(x)
Conclusion: TI provides the best
explanation for quantum theory
• Allows us to give a definite answer for how and
why a definite outcome occurs; a cat is not in a
�superposition’ of alive and dead
• Provides a physical explanation for the probability
formula for outcomes
• Gives a rigorous account of the measurement
process
– does not require reference to an outside observer to
explain why there are definite outcomes in QM
– (if a tree falls in the forest it does make a sound,
period.)
Stay tuned…
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