The Transactional Interpretation: an introduction ©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=mc 2 ? 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: ● a ● b ● c 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…