rimey@ucbmiro.ARPA (Ken Rimey) (08/24/85)
You people don't know the Many Worlds Interpretation of Quantum Mechanics from a hole in the ground. The name of this idea, which I will shorten to "Many-Worlds", is a misnomer. Many-Worlds is no more than the idea that quantum mechanics can be applied to the universe as a whole. It is the idea that the postulates of quantum mechanics regarding the probabilistic nature of measurement can be deduced by considering the evolution in time of the closed system consisting of both the experimenter and the apparatus being measured. Consider an experiment with two outcomes A and B that are predicted to be equally probable by quantum mechanics. Philosopher X says that there is just one future, but it is impossible to determine in the present whether outcome A or outcome B will have happened in the future. Philosopher Y says that there are two futures, one for A and one for B, and contemplates the implications of irrational probabilities. None of this has anything to do with Many-Worlds. Consider the apparatus used for this two-outcome experiment, and consider the experimenter. The two, together with the rest of the universe, constitute a single closed system that, according to quantum mechanics, evolves completely deterministically. For simplicity, imagine that the universe consists solely of the apparatus and the experimenter. Furthermore, imagine that the apparatus has only three possible states, A, B, and P, where P will be its state before the experiment; and imagine that the experimenter has only three possible states: p - where he sees the apparatus in state P a - where he continuously thinks "Aha! The outcome was A" and b - where he continuously thinks "Aha! The outcome was B" The universe starts out in state Pp, and eventually evolves into state (Aa + Bb)/sqrt(2). If A and B were not equiprobable, the resulting state would instead be xAa + yBb, where x and y are complex numbers and the magnitude squared of x is the probability of outcome A. Notice that the calculation of the final state does not involve the usual postulates related to measurement. No measurement was performed on the system. Yet all the information we might want to know is apparent in the answer. The terms of the sum represent possible outcomes, and the probabilities of these outcomes can be determined from the coefficients. Notice that in our example only two of the nine possible outcomes have non-zero coefficients. Readers unfamiliar with quantum mechanics may be thinking that this sum of terms is simply a notation for listing possible alternatives for the future, or for listing possible alternative futures. No, it is really a sum, and that sum in its entirety describes the only possible future. This is because a state can be decomposed into a sum of terms in many possible ways; different decompositions correspond to different hypothetical measurements, the coefficients in that decomposition determining the probabilities for the various outcomes of that measurement. You may have noticed that, in describing a theory in which the universe is deterministic and measurement is not a fundamental idea, I sure refer to measurement and probability a lot. The point is that these ideas are involved only in the interpretation of the mathematical object that represents the state of the universe. They don't clutter up the theory of how to calculate that object. In particular, in the Many-Worlds view, wave functions don't "collapse". Many-Worlds is indistinguishable experimentally from the more popular variant of quantum mechanics that talks about wave functions collapsing. Then why is Many-Worlds interesting? Indeed, Many-Worlds is less a theory than an argument that some of the conventional postulates of quantum mechanics are not fundamental. Then why do people sometimes argue for or against it as if it were a theory to be proved or disproved? In practice, useful quantum mechanical calculations pertain only to simple systems, and certainly not to systems that contain intelligent components. Furthermore, many people find thought experiments on quantum mechanics extremely non-intuitive if they involve people, or animals - Schrodinger's cat is the classic example. Many working physicists will, if you ask them, express doubt as to whether quantum mechanics is really applicable to cats and such. The state of the universe as it has evolved since the big bang is an even more horrendous thing to imagine, and since imagining it isn't going to help you make faster integrated circuits for SDI, these physicists just smile and try to find another conversation. On the other hand, it is often suggested that quantum mechanics is incomplete. The problem is that the rules for how a system changes state when it is measured seem to be central features of quantum mechanics, and yet these rules make explicit reference to measurement, as if the observer played a distinguished role in the universe. This difficulty motivates much crackpot physics. If you believe the Many-Worlds idea, then this is not a problem, and rather than waste time on crackpot physics, you can get back to working on faster integrated circuits for SDI. Finally, allow me to show that understanding the Many-Worlds argument is at least an interesting exercise. Consider an apparatus for doing double-slit diffraction with electrons, one electron at a time of course. The electron's wave function emerges from the two slits and forms the same kind of interference pattern that light does. If you note where the electron lands on a screen, and repeat the experiment for many electrons, you can see the interference pattern - there are alternating likely and unlikely places for the electron to land. If you add apparatus for detecting which slit the electron went through, you find that the interference pattern is no longer formed. How is this understood from the Many-Worlds viewpoint? We further idealize the thought experiment and use an extension of the ABPabp notation from above. Say that if the electron is going through the left slit, it is in state A; through the right slit, state B. The detector, initially in state p, goes to state a or b according to whether the electron is in state A or B. However, after this happens, the electron evolves such that state A goes to (C+D)/sqrt(2) while B goes to (C-D)/sqrt(2). C and D are meant to represent two different positions on the screen. Say there is no detector. We start the system in state (A+B)/sqrt(2). Its state then evolves into [(C+D)/sqrt(2) + (C-D)/sqrt(2)] / sqrt(2) = C We got constructive interference for result C, and destructive for D. Now install the detector. We start the system in state p(A+B)/sqrt(2). Since pA would go to aA and pB would go to bB, this goes to (aA + bB)/sqrt(2). The detector now remains static, but the electron evolves as before yielding [a(C+D)/sqrt(2) + b(C-D)/sqrt(2)] / sqrt(2) = [aC + aD + bC - bD] / 2 The outcomes aC, aD, bC, and bD each have probability 1/4. This time C and D are both possible. The only difference is the presence of what looked like a completely non-intrusive detector. While your friends are busy debating whether the interference pattern is destroyed even if nobody looks at the detector, you can be calculating exactly how much the interference pattern is destroyed if the detector is only correct n% of the time. Ken Rimey rimey@dali.berkeley.edu