Superluminal Velocities

Tachyons are theoretical particles that travel with superluminal velocities. In fact, they not only can exceed the speed of light, they can have infinite velocities, or even travel backward in time.

Of course, they always move through space when they are traveling. Therefore, a single tachyon is incapable of transporting information directly into an observer’s absolute past. But two observers utilizing beams of tachyons can accomplish the task. All they have to do is transmit and receive the modulated beams to and from one another.

The technique is the basically same as that for time travel using a hyperspace jump. The first observer would send a beam of modulated tachyons toward the second. Whether the beam traveled forward, backward, or instantaneously through time does not really matter, although things would be easier to accomplish if backward moving tachyons were available. But even with forward moving tachyons, the signal would reach the second observer faster than the speed of light. That observer could then accelerate away form the first, creating a backwards shift in time large enough for his own tachyons to reach the first observer before the original message was transmitted.

With just a little cooperation between the two observers, they could really play havoc with the principle of causality. Like the hyperspace time-traveler, these superluminal information-brokers could create numerous time paradox experiments. For example, they could send a message into the past and receive it in time to change their minds and not send the message. But if they change their minds and don’t send the message, they never could have received it. But they already have received it (before they changed their minds), so they must have sent it sometime in the future. But in that case, do they really have a choice? Are they destined to send the message regardless of how hard they try not to? Etc. Etc.

The only way that the theory of relativity can avoid such time paradoxes is to incorporate into its framework the principle of causality in addition to the principle of relativity. Since the ability to transmit information faster than the speed of light can produce situations that violate the principle of causality, the theory of relativity asserts that information cannot be transmitted at superluminal velocities.

In general, information can be transported by physical process, including a traveling person, a moving object, and/or transmitted beams of particles or waves. Therefore, we conclude that nothing physical can travel faster than the speed of light.

Therefore, if tachyons do exist, they are not physical. They cannot be observed experimentally. Nor can they be used to transmit information.

Nevertheless, there are numerous known examples of non-physical quantities that can and do travel faster than light. Most of these things are abstract concepts manufactured in the minds of observers to simplify the description of a given phenomenon. As predicted by relativity, all such examples are capable of instantaneous velocities and direction reversal by simply switching from one reference frame to another. And, of course, none of them can be used to transmit information.

Examples of such quantities are: (1) the cutting junction of a large pair of scissors, (2) the curl of the waves breaking on the shore, (3) the spot of glowing phosphor on the face of a CRT, oscilloscope, or television tube, (4) the motion of distant objects when viewed from an accelerating reference frame, (5) the appearance of objects approaching the observer at the speeds close to that of light, and (6) the collapse of quantum mechanical wave functions when a measurements are made.

Further Study:

See Tipler pp. 56-58 for more information on superluminal speeds.

Questions:

Q1. Backward moving tachyons

Why would backward moving tachyons be more useful for time communication than forward moving tachyons?

Q2. If faster than light travel ever becomes possible, according to special relativity which of the following automatically also become possible? (A) Infinite speeds. (B) Time travel into the past. (C) Multiple universes. (D) Two of these. (E) Three of these.
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Problems:

P1. Superluminal Velocity of a Distant Star

A spaceship leaves the earth and accelerates to a speed of 0.9 c in one year of earth time. Before accelerating, the pilot sees a star ahead of him 1000 light years away. (a) After accelerating, what would he say was the distance to the star? (b) Approximately how much would the pilot age while accelerating? (c) What is the approximate average velocity of the star relative to the pilot? (d) How is this possible if the speed of light is the ultimate speed.

P2. Superluminal Velocity of a Signal Change

A radio beam travels through empty space at the speed of light. If it takes sunlight 6 minutes to get to Venus, 8 minutes to get to Earth, and 12 minutes to get to Mars; if Venus, Earth, and Mars are all three lined up with the sun; and if a radio beam initially aimed at Venus is quickly redirected toward Mars; (a) how much time elapses before Venus no longer receives the signal? (b) How much time elapses before Mars begins to receive the signal? (c) How long does it take for the signal to switch from Venus reception to Mars reception? (d) What is the distance in light minutes between Venus and Mars? (e) What is the velocity of the switch in the signal? (f) How is this possible if information cannot be transmitted faster than the speed of light?

Tachyons – Hypothetical particles that can only travel faster than the speed of light.
Proper Frame – The frame of reference in which a tachyons has an infinite speed.

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