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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
вЂў But what is quantum mechanics (QM)?
вЂў Theory needed to predict behavior of very
small particles such as atoms, electrons,
photons, and other subatomic particles.
вЂў QM works very well but what it actually tells
us about reality is very unclear
вЂў An interpretation is intended to make clear
what the theory tells us about reality
The biggest quantum puzzle:
вЂў The вЂ�measurement problemвЂ™
вЂў The probability rule for outcomes of
measurements
The Measurement Problem
вЂў A quantum system is described by a quantum
state:
вЂ�QвЂ™
Measuring a quantum system
вЂў Suppose we want to find out where a
вЂ�particle,вЂ™ such an electron, is?
вЂў The electron gets created in some state вЂ�QвЂ™
вЂў It could be in different positions a, b, c
вЂў Quantum theory just gives us probabilities for
those positions: Prob(a|Q) or Prob(b|Q) or
Prob(c|Q)вЂ¦.but no answer for why we only
see 1 of them
Quantum superpositions
вЂў The preceding is known as a вЂ�superpositionвЂ™ of
different possible outcomes a, b, c:
вЂ�QвЂ™ ( measurement) в†’
вЂ�aвЂ™ + вЂ�bвЂ™ + вЂ�cвЂ™
вЂ�SchrodingerвЂ™s CatвЂ™
вЂў Erwin Schrodinger: pointed out this can get
ridiculous: Take an unstable radioactive atom
in the quantum state
вЂ�decayedвЂ™ + вЂ�undecayedвЂ™
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 вЂњquantum state of the entire systemвЂќ is:
{вЂ�decayedвЂ™ вЂ�geiger counter triggeredвЂ™ вЂ�broken vialвЂ™ вЂ�dead catвЂ™ }
+
{вЂ�undecayedвЂ™ вЂ�geiger counter untriggeredвЂ™ вЂ�intact vialвЂ™ вЂ�live catвЂ™}
i.e., the cat is in a вЂ�superpositionвЂ™ of alive and dead!
But we never see cats in superpositions, or anything else for that
matter
the usual (inadequate) way of thinking
вЂў says that the quantum state вЂ�collapsesвЂ™ to a
particular result (takes on a particular result)
upon measurement , but
вЂў cannot account for how or why a
вЂ�measurementвЂ™ is completed
вЂў depends on an вЂ�observerвЂ™, but
вЂў cannot define what an вЂ�observationвЂ™ is
transactional interpretation (TI)
вЂў defines вЂ�measurementвЂ™ (or any process resulting
in a definite outcome)
вЂў вЂ�measurementвЂ™ occurs upon
absorption/annihilation of the quantum state
вЂў absorption not taken into account in вЂ�standardвЂ™
qm
вЂў why not? because itвЂ™s really a relativistic process
(remember E=mc2 ? high energies/speeds)
quick and dirty relativistic qm
вЂў quantum states of particles are created via
action of вЂ�creation operatorsвЂ™ on the вЂ�vacuum
stateвЂ™ , вЂ�0вЂ™:
в�є вЂ�0вЂ™ = вЂ�QвЂ™
вЂў quantum states destroyed via action of
вЂ�destruction operatorsвЂ™ on the вЂ�quantum stateвЂ™
вЂ�QвЂ™:
вЂ�QвЂ™ = вЂ�0вЂ™
ordinary nonrelativistic qm:
вЂў typically takes creation (emission of a
quantum particle) for granted and ignores
destruction; and assumes energy is always
positive
вЂў TI: must take destruction (вЂ�absorptionвЂ™) of
quantum states into account to understand
measurement
вЂў but also: emission and absorption involve
both positive and negative energies
вЂ�offer wavesвЂ™ and вЂ�confirmation wavesвЂ™
вЂў in TI, the usual quantum state is called an вЂ�offer
waveвЂ™ (OW)
вЂў the negative energy component from the
absorberвЂ™s response to the offer wave is called a
вЂ�confirmation waveвЂ™ (CW)
вЂў the interaction of OW and CW is like a
вЂ�handshakeвЂ™ that occurs outside spacetime. It sets
up possible вЂ�transactionsвЂ™: 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 вЂ�handshakeвЂ™; one of these
вЂ�winsвЂ™ the competition and a photon is
transferred from the emitter to that
absorber in spacetime.
Spacetime: вЂ�tip of the icebergвЂ™
the TI picture
TIвЂ™s solution to the вЂ�catвЂ™ problem
вЂў quantum absorbers in the geiger counter
respond to the unstable atomвЂ™s offer wave by
generating confirmation waves
вЂў 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
вЂў the account is not observer-dependent
however:
вЂў it is still fundamentally uncertain as to
whether a given transaction will occur or not
вЂў quantum mechanics suggests that nature is
indeterministic at a fundamental level
вЂў But it gives us a way to calculate the
probabilities that various outcome will occur.
returning to the electron example
вЂў the electron emitted in state Q is вЂ�measuredвЂ™
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
вЂў The probabilities вЂњQ(x)Q*(x)вЂќ express the
interaction of the offer wave Q(x) and the
confirmation wave Q*(x)
Conclusion: TI provides the best
explanation for quantum theory
вЂў Allows us to give a definite answer for how and
why a definite outcome occurs; a cat is not in a
вЂ�superpositionвЂ™ of alive and dead
вЂў Provides a physical explanation for the probability
formula for outcomes
вЂў Gives a rigorous account of the measurement
process
вЂ“ does not require reference to an outside observer to
explain why there are definite outcomes in QM
вЂ“ (if a tree falls in the forest it does make a sound,
period.)
Stay tunedвЂ¦
```
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