Thought-Experiments in Honor of John Wheeler
About 20 years ago I ran into John Wheeler at a Baltimore hotel. “Tell me,” he asked, “how do you hold up half the ghost of a photon?” His question was a typically Wheelerish: intriguing, enigmatic, pithy, and provocative. I soon discovered it referred to an outlandish thought-experiment designed to probe the conceptual foundations of quantum mechanics.
Imagine, Wheeler mused, a photon source on a distant quasar, billions of light years away. Suppose the quasar were gravitationally lensed by an intervening massive galaxy, producing a double image when viewed from Earth (several such cases are known to astronomers). Then this arrangement will constitute a sort of cosmic interferometer. A given photon is presented with two possible paths to Earth, and in accordance with the weird requirements of quantum mechanics, it may in some sense take both routes, even though an observer on Earth would detect only a single photon. Wheeler expressed this by saying that the photon is a sort of ghost during its transit from quasar to Earth (in another famous metaphor, he described this indeterminate phase as “a great smoky dragon”). Hence “half a ghost” takes each path. Wheeler envisaged doing an interferometry experiment, but realized that the path lengths might differ, so the “ghosts” would reach Earth at different times. How might one of them be stored to allow the other one time to arrive? Would an optical fiber do the trick?
Like many of Wheeler’s thought experiments, he had taken the germ of an idea and carried to the ultimate extreme, in order to present the conceptual issue as starkly as possible. “Science advances more by the clash of ideas than the steady accumulation of facts,” I once heard him pronounce. In this case the germ of the idea was what became known as the delayed choice experiment. Niels Bohr had long before made explicit that quantum nonlocality and the theory of relativity were uneasy bedfellows, although technically compatible. Physicists had become used to the idea that a measurement made at spatial location A has instantaneous physical implications for the situation at a different location B, in spite of the fact that no direct physical influence could pass between A and B in the time available. Events that are simultaneous in space have ambiguous time order, and Wheeler seized this point to devise a nonlocality thought experiment that would appear to reach not only across space, but back in time too.
He conceived of an adaptation of the normal Young’s two-slit interference experiment in which the observer may choose, for any given photon, whether to sneak a look at the path the photon was taking, or whether to not look. The consequences of such a choice had been debated by Bohr and Einstein in the 1930’s. Today, the agreed position is that when the observer decides to not look, the photons create an interference pattern on the image screen. If the observer looks at “which path” the photon takes, then the interference pattern is destroyed. Wheeler’s refinement was to point out that a decision on “to look or not to look” can be delayed until after the photon has transited the slit system, and just before it arrives at the image screen. In effect, the observer could, at the last minute, decide to “look back” and see from which slit the photon had come. Wheeler proposed a simple way to do this.
The delayed choice experiment does not allow us to change the past or send signals backward in time. However, it startlingly demonstrates how the actions of an observer now can help determine the nature of reality that was—in the past. Since the photon has already transited the slit system when the decision is made, the photon cannot itself have decided whether to follow one path, the other path, or both paths. Which state of affairs was in fact the case (in the past) is determined by the observer (in the future). By casting this weird set-up in terms of quasars, Wheeler emphasized the fact that quantum observations made today can have a hand in determining the nature of reality that was—billions of years ago. Such ideas led to his famous notion of the “participatory universe” in which observers—minds, if you like—are inextricably tied to the concretization of the physical universe emerging from quantum fuzziness over cosmological durations. I should also point out that within a few years the delayed choice experiment was carried out (on a laboratory, not a cosmic, scale) by Carroll Alley, and was further developed by Marlan Scully and other into the famous “quantum eraser” experiments in which the choice is not only delayed, but the observer can change his or her mind afterward!
The following paper by Freeman Dyson of the Institute for Advanced Study in Princeton briefly introduces new quantum thought experiments. One of these is a simple attempt to beat Heisenberg’s uncertainty principle by seeking to acquire simultaneous information about both the position and momentum of a quantum particle. The set-up is a pair of posts placed a known distance apart, and the proposal is to time how long a particle takes to pass between them. This can be used to compute the speed, hence momentum, of the particle. However, because the location of the posts may be known with arbitrary precision, position information is also available. Dyson then concludes that a quantum description cannot be applied to past events.
Dirac considered a similar situation when discussing why the eigenvalues of the velocity operator for an electron are +c or -c. If we try to pin down the electron at one post, we know its position precisely. Hence, according to Heisenberg’s uncertainty principle, its momentum is infinitely uncertain. In nonrelativistic physics this would imply infinite speed, but Dirac’s relativistic wave equation replaced that with the speed of light, c, corresponding to infinite momentum. So when we time the electron between two posts, it seems to travel at the speed of light.
However, that was not the last word on the subject. In the 1980s attention was given to the whole problem of how to measure time and time intervals in quantum mechanics. The difficulty here is that time is not an operator, but a parameter. Analyzing the measurement of time in quantum mechanics ought, for consistency, to involve the use of quantum clocks, themselves subject to uncertainty. If a simple model quantum clock is used to measure the time of flight of a quantum particle between two posts, it turns out that so long as attention is restricted to the time difference, sensible values for the speed are obtained. That is, the expectation values can lie anywhere in the range from +c to -c, depending on the momentum eigenstate chosen. However, this thought experiment cannot tell us anything about the absolute time of passage of the particle. Attempts to acquire that information would return us to Dirac’s scenario.
The new thought experiment of Dyson neatly links back to Wheeler’s delayed choice experiment, the participatory universe, and the way in which quantum potentiality becomes transformed into physical actuality.
The subject of this lecture is a set of four thought-experiments that are intended to set limits to the scope of quantum mechanics. Each of the experiments explores a situation where the hypothesis that quantum mechanics can describe everything that happens leads to an absurdity. The conclusion that I draw from these examples is that quantum mechanics cannot be a complete description of nature.
Two of the thought-experiments, the cat in a cage proposed by Schrodinger, and the evaporating black hole proposed by Hawking, are well known. The other two, so far as I know, are novel. The novel experiments are very simple. One consists of an electron traveling through two counters separated by an accurately known distance. The velocity of the electron is measured using a time-of-flight technique, and its position is measured as it passes through the counters. The measurements can be so accurate that the Heisenberg uncertainly relation between position and momentum is violated. The other novel experiment is a variant form of the old Einstein clock-in-a-box experiment, in which the energy of a photon emitted from the box is measured by weighing the box before and after the emission, while the time of emission is measured by the clock. The experiment is changed by putting the clock outside the box instead of inside, so that the time of emission of the photon is measured after it leaves the box. With this new arrangement, the measurements can be so accurate that the uncertainty relation between time and energy is violated.
Bohr would not have been disturbed for a moment by these thought-experiments. They only violate the uncertainty principle by violating the rules that Bohr laid down for a legitimate use of quantum mechanics. Bohr’s rules say that the quantum-mechanical description can only be used to predict probabilities of different outcomes of an experiment, not to describe what happened after the experiment is finished. The thought-experiments merely confirm that this restriction of the use of quantum mechanics is necessary. Although Bohr would say that the two experiments confirm the correctness of his interpretation of quantum mechanics, Einstein might also claim that they justify his distrust. They prove in a simple and convincing fashion the contention of Einstein that quantum mechanics is not a complete description of nature. Perhaps Einstein would be happy to learn that his box is still alive and well after seventy years, and still making trouble for believers in quantum mechanics.
I deduce two general conclusions from these thought-experiments. First, statements about the past cannot in general be made in quantum-mechanical language. We can describe a uranium nucleus by a wave-function including an outgoing alpha-particle wave which determines the probability that the nucleus will decay tomorrow. But we cannot describe by means of a wave-function the statement, “This nucleus decayed yesterday at 9 a.m. Greenwich time.” As a general rule, knowledge about the past can only be expressed in classical terms. My second general conclusion is that the “role of the observer” in quantum mechanics is solely to make the distinction between past and future. The role of the observer is not to cause an abrupt “reduction of the wave-packet,” with the state of the system jumping discontinuously at the instant when it is observed. This picture of the observer interrupting the course of natural events is unnecessary and misleading. What really happens is that the quantum-mechanical description of an event ceases to be meaningful as the observer changes the point of reference from before the event to after it. We do not need a human observer to make quantum mechanics work. All we need is a point of reference, to separate past from future, to separate what has happened from what may happen, to separate facts from probabilities.