**QUANTUM TIME TRAVEL **by *John G. Cramer*

The territory of time travel has, from the days of H. G. Wells to the mid-1980’s, been the exclusive province of writers of science fiction and fantasy. SF critics have even argued that time travel stories are so scientifically unlikely that they should be considered fantasy, not science fiction.

In the last few years, however, a few theoretical physicists have been muscling in on the time travel game. The first assault was mounted by a group of general relativity theorists led by Kip Thorne of CalTech. Thorne’s group demonstrated how space-time wormholes could be stabilized and used for trans-time communication and time travel. See my Alternate View columns in [*Analog*-June’89] and [*Analog*-May’90] for references and discussions of this work.) This column describes the latest physics foray into the time travel business, which has come from the direction of quantum mechanics.

Yakir Aharonov and his group at the University of South Carolina have for a number of years been “testing the envelope” of quantum mechanics. Their work has involved probing and poking at the foundations of orthodox quantum mechanics in search of weaknesses, soft spots, and unexpected predictions. The latest of these is contained in a paper entitled “Superposition of Time Evolutions of Quantum System and a Quantum Time Translation Machine” by Y. Aharonov, J. Anandan, S. Popescu, and L. Vaidman (AAPV) that was published in the June 18, 1990 issue of *Physical Review Letters*. In essence, the AAPV paper describes how an aspect of quantum mechanics called *state superposition* can be used to translate objects inside a closed and isolated system into the future or the past. The paper, in other words, describes how, in theory, to build a quantum mechanical time machine.

To understand what Prof. Aharonov and his colleagues are proposing, we have to delve a bit into quantum mechanical superposition. To take a simple example, consider a half-silvered mirror. This is a piece of glass that has had just enough reflective material so that exactly half the light striking it at 45deg. incidence goes straight through the glass and the other half bounces from the reflective surface at a right angle. If a single photon of light encounters this half-silvered mirror, there is a 50% chance that it will be transmitted (pass through) and a 50% chance that it will be reflected.

One would think that the photon must do one thing or the other, but quantum mechanics tells us that it can do *both*. This can be verified experimentally. If we provide some extra mirrors to make two paths so that, after travelling some distance, a photon that was transmitted comes back to the same path as a photon that was reflected, we can observe “quantum interference”. The quantum mechanical wave describing the transmitted photon adds or subtracts from the wave for the reflected photon. If they subtract completely, the photon waves on the two paths cancel each other and no photons can be observed at the exit. If they add, the photons waves on the two paths help each other and can be observed. The two quantum states of the particle, “photon reflected” and “photon transmitted”, are superimposed, with definite observable consequences. Quantum superposition is not limited to photons, which are somewhat special because they have no rest mass. It works equally well for massive particles and has been demonstrated using very slow neutrons, for example.

The mathematics of state superposition is special because quantum mechanics describes each state function as a complex variable that has a real part and an “imaginary” part (that behaves like the square root of -1). Each state has its own quantum mechanical “phase”, the angle in the complex plane that its complex state function makes with the real number axis. The result of superimposing several states is determined by the quantum phases of the states. Some combinations of phases produce cancellation while others produce reinforcement.

The point of departure of the AAPV calculation from standard quantum mechanics is that it applies the principle of superposition to the *time evolutions* of a group of similar quantum states. This is not normally done in quantum mechanics, but it should be OK. It seems to be consistent with both the formalism of the theory and its usual interpretation, provided the states are isolated from measurement and outside interaction while evolving.

The application of superposition in this way, however, has unexpected and surprising consequences. Superposition can be considered the quantum mechanical form of averaging. Common sense tells us that when several values are averaged, the resulting average value must fall within the range of variations of the averaged values. AAPV, however, demonstrate that in superimposing a group of carefully prepared time-evolving states, they can produce a measured result that is far larger (or smaller) than the value that would have resulted from any of the states taken separately. This is a consequence of the fact that in quantum mechanics the “averaged” states are *complex* (real plus imaginary) space-time functions with *complex* weighting factors (not real functions with real weighting factors).

The AAPV paper illustrates this point with an example. They consider a superposition of a number of time-evolving states that differ from one another because of the size of the force that is acting to produce the change with time. The authors show that the effective force which results from the superposition of a set of time-evolving states may occasionally, under the right conditions, be far larger than any of the individual forces acting within the individual states. If ten thousand such states are superimposed, a force amplification of 100 is in principle possible through this process. The down side of the procedure, however, is that with the superposition of ten thousand identical systems, only one of these experiences this amplified force. Or, to put it another way, the 100-fold amplified force is observed only about once in 10,000 tries. This makes the effect observable, at least in principle, but it may not be particularly useful as a force amplifier.

The AAPV paper goes on to consider the application of this new quantum principle to time translation. The states they consider evolve with different elapsed times due to the time dilation effects of a gravitational field in general relativity. They arrange each superimposed system within a hollow massive shell with a quantum-uncertain radius, so that it experiences time dilation but no other gravitational effects (acceleration, tidal forces, etc.). They show that the superposition of a group of these time-evolving systems can result in a net time displacement which is quite different (positive or negative) from the elapsed time experienced by the external observer of the system. Thus, the system inside the shell had been translated forward or backward in time with respect to the observer.

The AAVP authors are careful to point out that the gravitation time translation device which they describe is a thought experiment only and is not feasible in today’s physics laboratory. They also emphasize the probabilistic aspect of the time translation. Since the weightings that produce a large time translation occur only rarely and at random, they point out that “for any significantly long time journey in time the probability to obtain this outcome is extremely small.”

For SF readers and writers, the question raised by this new result of quantum mechanics is the relation between the AAPV “time translation machine” and the familiar “time machines” and other devices of SF literature. It is not, for several reasons, a conventional SF time machine. The AAVP machine cannot be used to materialize a traveller or a message in some arbitrary point in the past or the future. What it does is modify the way a system within the machine experiences the passage of time. We could place a system in the AAVP machine, run it, and with some probability remove a system that has experienced a large positive time displacement. This could speed up the decay of a long-lived radioactive source from many years to a few seconds, suggesting a radical new way of dealing with radioactive waste. A barrel of wine or scotch might also be “aged” to increase its value and quality.

If we could select for zero time displacement, this would in effect produce a “stasis field” of the kind Larry Niven has used in his fiction. We could freeze the internal system with no time change for the period it was isolated, while time in the external world moved forward at the usual rate.

But perhaps the most interesting use of the AAVP machine would be to produce negative time displacements. It is not difficult to advance the time evolution of a system it we are patient. We have only to wait while it evolves or ages. But reversing its time evolution is not within our capabilities. The second law of thermodynamics, the inexorable increase in the entropy of a system with time, prevents such reversals. Yet the AAVP machine appears to offer the possibility of doing just that. A system, placed in an AAVP machine selected for negative time displacement, would evolve in reverse and grow younger. An aged experimental mouse, placed in a negative time displacement AAVP device, should grow younger. A clock should run backwards. A dead mouse (or person) might even be resurrected.

Another possibility worth considering is backwards-in-time communication. Communicating forward in time is no real problem. Office file cabinets are full of forward-in-time communications. But backwards-in-time communication, or foreseeing the future, is something that we don’t know how to do, (except in the National Enquirer). But suppose that we use a large number of very small identical systems which are capable of containing an encoded message in their structure. Chain-like protein molecules would serve for this purpose. We encode them with a blank message, place them in the AAVP machine, and set it to select for large positive (future) time displacement. After operation on all the systems, we scan them and then place them in cold storage for a time, after which we systematically modify all of them to contain an encoded message to be sent to the past. Most of the systems have not undergone any change in the machine. But a few have undergone a large positive time displacement. These few should contain the future message *before* to was encoded into the group, and could be decoded in the past, before the systems were changed. Thus, a message might be sent to the past using this peculiar aspect of quantum mechanics.

Can the AAVP effect really be demonstrated in the laboratory? Can it be used to freeze, advance, and reverse time? Can it raise the dead? Can it be used to communicate with the past? I would have to say that I’m not sure. The AAVP paper is very new, and it has not been completely to the full scrutiny and criticism of the physics community. There may be holes in the logic of the paper or additional effects that must be considered in stating the implications of its mathematics.

What is clear is that its implications are quite remarkable. The AAVP work serves to remind us once again of the intrinsic weirdness of quantum mechanics, and shows us that there are aspects of its weirdness that we do not yet fully understand or appreciate.