Lecture XII Short lecture on Many Worlds & Decoherence Philosophy of Physics Lecture XII Short lecture on Many Worlds & Decoherence

First, a short lecture on some topics in QM that we did not have time to discuss. Then a short test. The test covers the material since the exam. It does not cover this lecture.

Other Courses PHY 491   Interpretations of Quantum Mechanics (Usually taught by Prof. John Sipe) His blurb: Review of conventional, textbook quantum mechanics. Formal measurement theory and wave function collapse; quantum states and nonseparability, violation of local causality, Bell theorems, quantum tricks, decoherence and the emergence of classical behaviour. Hidden variables, deBroglie-Bohm theory and generalizations, many-worlds interpretation and other theories of beables. Consistent histories approach of Omnes and Gell-Mann and Hartle; nature of True and Reliable statements. Prerequisite: QM (fairly advanced)

We will look at two popular approaches to the measurement problem. Many worlds Decoherence Recall what the measurement problem is: How does the (macroscopic) measuring device “collapse” the wave function of the (microscopic) entity?

Many Worlds Analogy: coin tossing A tossed coin has two possible outcomes. Suppose heads and tails both came up. How is this possible? By having the universe split in two; in one heads is the result and in the other tails. Everything that is physically possible (in QM) would be actual. All possible futures come true. The so-called “many worlds” interpretation of QM is like this.

Basic Idea Everett (1957), Wheeler, DeWitt, Deutsch, Wallace. When a quantum system is in a state of superposition, a measurement does not result in a single eigenvalue, but rather in every eigenvalue that is possible for that measurement. (This is a denial of the projection postulate. There is NO collapse of the wave function.) Eg. Suppose a photon is in a superposition of up and down in the x-direction. It is measured by an appropriately oriented Polaroid filter. The universe splits into two distinct universes with the photon having spin up in one and spin down in the other. The two universes are otherwise identical.

Schrödinger's Cat. The universe splits into two: one contains a live cat, the other a dead cat. Since we are part of the universe, duplicates of us are being created in every split.

Virtues of the Theory Takes the formalism as it is (ie, doesn't have to add “hidden variables” or somehow modify the theory). (Champions of the theory often exaggerate this virtue.) Everett said he was inspired by Spinoza. (I’m not sure why.) Minds/consciousness are not necessary. By measurement, all that is meant is, for example, that a photon is in the appropriate relation to a Polaroid filter. No micro-macro distinction. QM applies to everything.

There is no “collapse” of the wave function There is no “collapse” of the wave function. (But we can still use the projection postulate, since we are merely applying it to the universe we happen to find ourselves in.) The universe as a whole (each universe, that is) has a state function ψ. (This is not possible on any theory such as Bohr’s or Wigner’s which needs an outside observer.) Thus, popular with cosmologists.

Problems No new empirical content. (But if it solves a major conceptual problem, then this should not count too heavily against it. The same could be said, eg, about hidden variable theories.) An ontological extravaganza. To get an idea of how many universes there might be, consider a photon passing through a string of 10 filters, oriented vertically, then horizontally, then vertically, and so on.

At the first filter, the universe splits into two, with a spin up photon in one universe and a spin down in the other. The next filter then brings about another split in each of the two universes, and so on. Thus, we have 2 x 2 x...x 2 = 210 = 1024 distinct universes. Some people estimate that since the big bang there may well have been more than 10100,000,000,000 different universes created.

The probability problem. Probabilities play a central role in QM, yet the many worlds view seems to ignore them. All possible outcomes happen, so what is the difference between a pair of outcomes where one has probability 0.9 and the other 0.1. Both are realized. The different probabilities don't seem to matter. In other words, it fails to agree with or to explain the Born Rule. The basis problem. According to the many worlds theory, the universe splits into different universes corresponding to the different eigenstates of the quantum system. However, a representation in Hilbert space is somewhat arbitrary; a different eigenbasis would do as well. But it seems absurd that the universe would split in a way that depended on our arbitrary choice in representing it.

In spite of these problems, many worlds has lots of champions. Debate continues.

Decoherence Basic Idea QM applies to both the micro- and macro-world. Superpositions are, in principle, everywhere. Yet, the interference effects of superposition do no appear on a macroscopic level.

Macro-objects such as measuring devices consist of a huge number of parts and are subject to a huge number of environmental factors. This complexity leads to a collapse of the wave function very quickly. (There is a loss of coherence in the wave function because of the environment; hence “decoherence.”) Thus, Schrödinger's cat (unlike a photon) is in a state of superposition for such a small time that there are no observable physical effects. Main proponents: Zeh, Zurek, Omnès; the view is related to “consistent histories” of Griffiths, Gell-Mann & Hartle.

Details A macroscopic object (a Geiger counter, Schrödinger’s cat, etc.) is constantly subject to many influences, eg, the air, the vibrating ground, its own internal activity, and so on. It cannot be easily isolated from the environment (unlike elementary particles). If a macro-measuring device is in a state of superposition, then the different states of the superposition will interact with the environment in different ways. (They will, eg, have different interaction energies.)

Thus, the different states in the superposition will evolve at different rates and in an irregular way. Thus, there is no noticeable difference between this superposition and a “mixture.” For all practical purposes, we can call it a mixture. Roughly, in a mixture the state is definite, but we are merely ignorant of what the state is. (There are subtleties, but this will do.) If we toss a coin, but don't look at the outcome, the state is a definite heads or a definite tails, a mixture, not a superposition of both. How long does this influence of the environment take to put a macro-system into an eigenstate? Typically, something on the order of 10-45 seconds.

The virtues of this view are clear: Issues The virtues of this view are clear: QM applies to both big and small measuring does not require consciousness the von Neumann infinite regress of measuring devices does not happen. But does it really solve the measurement problem? Does our inability to distinguish for all practical purposes between the fluctuating superposition state and a mixture mean that they are the same?

Decoherence has become a new orthodoxy Decoherence has become a new orthodoxy. But it is still an open question how well it solves the measurement problem. Moreover, it has nothing to say about the other great interpretive problem of QM -- the problem of distant correlations.

Things we did not cover GRW (spontaneous collapse) Bohmian mechanics (nonlocal hidden variables) Wave function realism (reality = configuration space) QFT and String Theory (anything new philosophically?) Quantum gravity (problem of joining QM and GR) Quantum computing and quantum cryptography And lots more. If you go on in this field, there is tons of work to be done in both physics and philosophy.

Good luck on the test If you want it back, go to the Philosophy Department (170 St. George, 4th floor) and ask Eric, the person who handles the undergraduate affairs. Ready in 2 weeks Good luck with the rest of the term Happy holidays