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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