Tachyons

William Lane Craig

This rejoinder to theological fatalism, which seems to me altogether correct, has some disturbing consequences when we turn to philosophy of science to investigate the possibility of tachyons and of time travel. When Albert Einstein proposed his Special Theory of Relativity in 1905, he conceived of the speed of light c as a limiting velocity such that transmission of energy from point to point in space-time at superluminal velocities is impossible: "velocities greater that that of light," he concludes, "have no possibility of existence." ⁽³⁾ This is because the mass of a particle would become infinitely large as its velocity approaches c. The speed of light was therefore conceived to be an inviolable barrier for particle velocities. In the second half of the century, however, physicists such as Olexa-Myron Bilaniuk, V. K. Deshpande, E. C. George Sudarshan, and Gerald Feinberg realized that Einstein's conclusion was overdrawn ⁽⁴⁾. Although his equations prohibited the acceleration of particles traveling at subluminal velocities to or beyond c, they did not preclude the existence of particles whose velocities are always greater than or equal to c. After all, photons and neutrinos both travel with a velocity equal to c without ever having been accelerated from a subluminal speed to luminal velocity. So why could there not exist particles that travel at superluminal velocities without ever having been accelerated from speeds less than or equal to c? In this case the speed of light remains an inviolable barrier, but that does not preclude the existence of particles on the other side of the barrier. Feinberg dubbed such particles tachyons, from taciV (swift), and the experimental search for these exotic entities was on.

And, indeed, if tachyons do exist, they are exotic. Apart from other oddities, the equations for energy and momentum for such particles reveal that tachyons would accelerate as they lose energy. Conversely, whenever energy was imparted to a tachyon, it would decelerate. This leads to one of the most peculiar characteristics of tachyons: their prima facie possession of negative energy. Let an observer at rest in a reference frame S observe a tachyon traveling with a velocity v relative to him. This same particle will travel with a different velocity u relative to another observer in a reference frame S1 which is moving with respect to S with a velocity w. When the product vw exceeds c2, the tachyon will possess negative energy relative to S1. More peculiar still, such particles will seem to travel backward in time. To the observer in S1 the negative-energy particle would appear to be absorbed first and emitted later.

The implications of such behavior were noticed by Richard Tolman as early as 1917 in what has come to be known as Tolman's Paradox, namely, that communication with the past is possible ⁽⁵⁾. Let an observer O in a reference frame S send out a burst of infinitely fast tachyons at t1 to an observer O1 in a reference frame S1 which is receding from S at the uniform velocity w. The reception of the tachyon signal in S1 triggers a similar burst of tachyons back to O which travel with an infinite velocity relative to S1. The relativity equations dictate that the second signal arrives in S at a time t0 before the burst of tachyons is sent at t1. But, since the signal from O1 to S was triggered by the signal from O to S1, it follows that the effect (O's reception of O1's signal) precedes the cause (O's sending his signal to O1) in S, or, in other words, tachyons furnish the mechanism for backward causation.

This implication alone was enough to warrant the rejection of the possibility of tachyons in the minds of many physicists ⁽⁶⁾. Proponents of tachyons felt at first constrained to explain away Tolman's paradox with its attendant backward causation by means of a "reinterpretation principle." "It is precisely by putting together the two quizzical concepts of 'negative- energy' particles traveling backward in time that the resolution of the difficulty is found," stated Bilaniuk and Sudarshan; "A 'negative- energy' particle that has been absorbed first and emitted later is nothing else but a positive-energy particle emitted first and absorbed later, a perfectly normal situation.⁽⁷⁾" By interpreting any negative-energy particle moving backward in time as a positive-energy particle moving forward in time, one may thereby eliminate the occurrence of an effect before its cause. In our previous case, for example, O1 will naturally regard the tachyon beam received from S as actually a signal that he is himself sending to S1. O1 and O will regard these beams as spontaneous emissions from their own tachyon transmitters rather than as receptions from another reference frame.

Now, at face value, the reinterpretation principle sounds merely like the endorsement of what can only be characterized as a fantastic delusion. If O's tachyon signal really does trigger O1's transmitter to send a return signal, then it is simply irrelevant whether O or O1 believes that no backward causation has occurred. Perhaps the best face to put on Bilaniuk and Sudarshan's remarks is to interpret them as claiming that the causal relation is itself relative to reference frames; that is to say, there is no absolute causal directionality in the same way that there is no absolute simultaneity according to Special Relativity. The world-line of the tachyon burst simply exists (tenselessly) between space-time points in S and S1, and whether the tachyons are moving from S to S1 or vice versa is observer-dependent, as is also which event is conceived to be the cause and which the effect. Unfortunately, it has been shown that, even on this understanding, backward causation cannot be precluded ⁽⁸⁾.  More to the point, however, the notion that causal directionality is relative to reference frames seems clearly untenable. In their engaging discussion of a tachyonic antitelephone, Benford, Book, and Newcomb point out that causal directionality is independent of temporal considerations and is therefore not susceptible to arbitrary reinterpretation:

For example, let A be William Shakespeare and B Francis Bacon, and let V1 [the outgoing tachyonic velocity] be negative. If Shakespeare types out Hamlet on his tachyon transmitter, Bacon receives the transmission at some earlier time. But no amount of reinterpretation will make Bacon the author of Hamlet. It is Shakespeare, not Bacon, who exercises control over the content of the message (265) ⁽⁹⁾.
Thus, "the direction of information transfer is necessarily a relativistic invariant. An author's signature, for example, would always constitute an invariant indication of the source" (loc. cit.). The reinterpretation principle is thus seen to be essentially an exercise in self-delusion: causal directionality is invariant across reference frames, and to interpret events as related otherwise than as they are is only self-deception.

In light of these facts, proponents of tachyons began to reassess whether backward causation was after all so objectionable or paradoxical ⁽¹⁰⁾. Some writers argued that the problem entailed by permitting tachyonic backward causation is fatalism. Feinberg, for example, called this the "most serious qualitative objection" to tachyons; the transmission of signals into the past of a single observer "is in apparent conflict with the natural view that one is free to decide whether or not to carry out an experiment up until the time that one actually does so. ⁽¹¹⁾" The objection seems to be that one could, for example, call oneself in the past on a tachyonic antitelephone and then, after receiving the call, decide not to place it after all. Our discussion of theological fatalism, however, makes the flaw in the reasoning clear: the fact that one has received a call from oneself entails not that one is not free to refrain from placing the call, but only that one will not in fact refrain from placing it ⁽¹²⁾. If one were to refrain from placing the call, then one would not have received it in the first place. Thus, no fatalistic paradox is generated by the existence of negative-energy tachyons.

But, although objections to tachyons based on fatalism are unimpressive, a more substantive objection appears to arise when one considers cases in which tachyonic backward causation would entail the existence of what Paul Fitzgerald has called a "logically pernicious self-inhibitor" ("Retrocausality," 534/5). Benford, Book, and Newcomb invite us, for example, to envisage a situation in which observers A and B enter into the following agreement : A will send at 3:00 a tachyonic message to reach B at 2:00 if and only if he does not receive a message from B at 1:00. B will send at 2:00 a message to reach A at 1:00 if and only if he receives a message from A at 2:00. Therefore, the exchange of messages takes place if and only if it does not take place. They conclude that "Unless some truly radical solution is found to this paradox, we must conclude that tachyon experiments [such as those being currently carried out] can only yield negative results" (265). John Earman points out that such paradoxes do not depend on human agency, but may be constructed solely with machines. Thus, the reinterpretation principle is irrelevant. A contradiction is generated by asking whether a certain event occurs; we find that it occurs if and only if it does not occur ⁽¹³⁾. Although the tachyon event might be interpreted differently by different observers, this difference is totally irrelevant to the contradictory nature of the conclusion.

Now, it is not the existence of tachyons as such, admits Earman, that entails the possibility of a logically pernicious self-inhibitor; rather it is the whole situation which is impossible, and this includes assumptions concerning the possibility of controlling tachyon beams, of detecting them, and so forth. By giving up one or some of these other assumptions, one may impose consistency conditions on hypothetical cases so that the paradox cannot arise. Thus, Fitzgerald maintains that we must conclude only that tachyons cannot be controlled in all ways required for the self-inhibitor to function ⁽¹⁴⁾. When asked why such machines fail, he responds that it may be either for empirical reasons involving constructibility or controllability or owing to a fortuitous set of accidents each time one tries to experiment. The difficulty with the attempt to impose consistency conditions based on considerations of constructibility and controllability, however, Earman explains, is that we have good reason to believe that such devices are possible. The assertion that such experiments cannot be carried out is, therefore, "brazen," since the experiments involve "only operations which we know to be possible in our world. ⁽¹⁵⁾" Since such devices as are required for these experiments are apparently nomologically possible, it follows that tachyons are nomologically impossible and therefore do not exist. The threat of fortuitous accidents' preventing such experimentation seems utterly implausible, Fitzgerald himself confesses, for we should then have to posit a lawlike regularity of accidents to prevent the functioning of a machine which should be constructible if tachyons exist ("Tachyons," 428). Hence, the conclusion of the foregoing analysis would seem to be that, given the nomological possibility of tachyon emitters and detectors, one cannot avoid the paradoxes by denying assumptions concerning such devices, but is led instead to denying the possibility of the existence of tachyons. Although this reasoning has, to my knowledge, gone unchallenged in the tachyon literature, there is, within the body of literature on the possibility of time travel, a significant challenge to the modal validity of inferring that tachyons are impossible from the nomological possibility of such devices, a challenge akin to the argument against theological fatalism. Let us therefore turn to that discussion.

⁽³⁾ "Elektrodynamik bewegter Körper," Annalen der Physik, XVII (1905): 891-921.

⁽⁴⁾ Bilaniuk, Deshpande, Sudarshan, "Meta Relativity," American Journal of Physics, XXX (1962): 718ff; Gerald Feinberg, "Possibility of Faster-than-light Particles," Physical Review, CLIX (1967): 1089-1105.

⁽⁵⁾ The Theory of Relativity of Motion (Berkeley: University of California Press, 1917), pp. 54/5. Actually Tolman's paradox results not only when infinite velocities are involved, but for all velocities greater than c²/w, where w is the relative velocity of two observers.

⁽⁶⁾ See Bilaniuk et al., "More about Tachyons," Physics Today (December 1969), p. 49; David Bohm, The Special Theory of Relativity (New York: W. A. Benjamin, 1965), p. 158; F. A. E. Pirani, "Noncausal Behavior of Classical Tachyons," Physical Review, D 1 (1970): 3224.

⁽⁷⁾ Bilaniuk and Sudarshan, "Particles beyond the Light Barrier," Physics Today (May 1969): 47; Gerald Feinberg, op. cit., p. 1091.

⁽⁸⁾ See Bilaniuk et al., "More about Tachyons," pp. 48-50; G. A. Benford, D. L. Book, and W. A. Newcomb, "The Tachyonic Antitelephone," Physical Review, D 2 (1970): 263-265 [this is the same Newcomb of the famous Newcomb's paradox]; Pirani, op. cit., p. 3224; Paul Fitzgerald, "Tachyons, Backwards Causation, and Freedom," in PSA, 1970, Roger C. Buck and Robert S. Cohen eds. Boston Studies in the Philosophy of Science, VIII (Boston: Reidel, 1971), pp. 421-423; T. Chapman, Time: a Philosophical Analysis, Synthese Library (Boston: Reidel, 1982), pp. 23-25.

⁽⁹⁾ Cf. Fitzgerald, "Tachyons," pp. 421-423.

⁽¹⁰⁾ Roger G. Newton, "Causality Effects of Particles that Travel Faster Than Light," Physical Review, CLII (1967): 1274. Interestingly, Newton acknowledges his debt to Michael Scriven on the score of causal directionality and time and appeals to tachyons to show the possibility of precognition experiments. See also Paul L. Csonka, "Advanced Effects in Particle Physics, I," Physical Review, CLXXX (1969): 1266-1281; Bilaniuk et al., "More about Tachyons," p. 52.

⁽¹¹⁾ Op. cit., p. 1092. Cf. Chapman, Time, p. 23, who asserts that, after receiving a return signal which he will trigger, the observer may decide not to send his signal after all; in this case the standard objection to backward causation applies.

⁽¹²⁾ Cf. Fitzgerald, "Tachyons, Backwards Causation, and Freedom," pp. 428-434; and, "On Retrocausality," Philosophia, IV (1974): 543. Suppose, he says, I receive a tachyon message from the future that a man I am about to shoot will be at a banquet two days hence. Is it therefore not within my power to kill him? Not at all, responds Fitzgerald; I have both the ability and opportunity to do so, so that I could kill him; but were I to do so, I would not have this reliable message from the future that he is alive. The point is that ignorance is not a necessary condition of an action's being within one's power. Fitzgerald's analysis is flawed, however, when he proceeds to argue that, in the case in which one does not try to perform the action precisely because one believes the tachyon message, then one's freedom is limited by the message from the future. For anything, he claims, which prevents a person's doing what he wants is to a limit on his freedom. Fitzgerald fails to see, however, that in this case what one wants to do is changed by the message; it does not therefore prevent one from doing what one wants to do. It merely changes one's motivation. As Fitzgerald goes on to observe, this can arise without messages from the future at all. Suppose before I pull the trigger someone rushes up and informs me that my intended victim is my beloved, long-lost uncle. Suddenly, my motivation is changed, and I no longer want to kill him, but would we say that my informer has limited my freedom in conveying his report to me?

⁽¹³⁾ "Implications of Causal Propagation outside the Null Cone," Australasian Journal of Philosophy, I, (1972): 254. Thus, the escape route suggested by DeWitt, that information sent into the past is wiped from the observer's memory, is unavailing (Bikaniuk, et al., "Tachyons," p. 50).

⁽¹⁴⁾ "Tachyons," p. 427; and "Retrocausality," p. 435.

⁽¹⁵⁾ Earman, "Causal Progagation," pp. 234/5. Assuming that the apparatus will work as it is supposed to, a typical experiment will involve the following elements: (1) a tachyon source that can be amplitude modulated, (2) a tachyon detector, (3) a velocity filter giving a monoenergetic beam. Proposed devices for each of these are used in tachyon research. (Benford et al., "Antitelephone," p. 263; cf. Bilanuik and Sudarshan, "Particles," pp. 50/1; et al., "Tachyons," p.52.)