# Special Relativity after 100 Years

### Article

### John Geohegan

#### Volume 29.5, September / October 2005

Special relativity has been phenomenally successful, but its nonintuitive nature has made it difficult for us to absorb Einstein’s central message about time and simultaneity.

One hundred years after Albert Einstein gave us the theory of special relativity, we have made good progress in applying the equations he gave us, but we have difficulty absorbing his central message about time and simultaneity. Time and again, his predictions have been tested; the Global Positioning System simply wouldn’t give us good results unless Einstein’s equations were hidden in the little handheld GPS instruments used by hunters and hikers to find their way in the woods. Special relativity has been combined with quantum physics to produce quantum electrodynamics, the most accurate physical theory ever devised. Shortly after Einstein finished his famous paper, he used it to derive the famous equation E=mc^{2}, showing that when a body radiates energy, it loses mass.

So what’s the problem? Well, we haven’t yet absorbed his message that “we cannot ascribe *absolute* meaning to the concept of simultaneity; instead, two events that are simultaneous when observed from some particular coordinate system can no longer be considered simultaneous when observed from a system that is moving relative to that system” (Einstein 1905, 130). As long as we think there’s such a thing as “a point in time” or events that can be described as universally simultaneous, we will be faced with misconceptions such as “moving clocks run slow” and “moving objects shrink in the direction of motion.” The following simple thought experiment shows how such misconceptions can arise.

Imagine two identical space ships, A and B, far out in space, away from any large gravitating bodies, traveling away from each other at a high velocity. Neither one is accelerating, no engines are operating, and the occupants of each ship consider their ship to be motionless while the other ship is moving rapidly away. The two ships have just passed each other, almost colliding, and at their closest positions, they have synchronized their identical clocks at 12:00. The clocks each cause a bright blue light on the outer hull of their respective ships to flash each hour, and the ships are separating so rapidly that the passengers on each see the blue light of the other shifted to half its frequency, into the infrared. This is the famous red shift caused by the Doppler effect, in this case a shift of 100 percent. The same shift means that the light signals sent out by A at 1:00, 2:00, and 3:00 according to A’s clock will be received by B at 2:00, 4:00, and 6:00 according to B’s clock. Similarly, A will receive signals from B at 2:00, 4:00, and 6:00 according to A’s clock.

Now, consider the signal sent by A at 1:00 according to its own clock. B will receive it at 2:00 according to B’s clock, and it will be reflected back to A along with B’s 2:00 signal to be received by A at 4:00 according to A’s clock. A will receive the reflected signal as deep in the infrared, one-fourth the frequency it had when it was sent out. The crew of A can now calculate that this signal, which was sent out at 1:00 and returned at 4:00, must have been reflected at 2:30, halfway between 1:00 and 4:00, because it traveled an equal distance each way. If they learn that B’s clock read 2:00 at the time of reflection, they *may* think B’s clock must have been thirty minutes slow. The situation is exactly parallel; B will receive its 1:00 signal return at 4:00 and its crew *may* conclude that A’s clock was thirty minutes slow.

As simple as the above description may be, it’s worth reviewing to see the following points:

- A and B are equally justified in considering themselves to be at rest. This is in accordance with Einstein’s postulate that all inertial systems are equivalent.
- Both A and B consider light to travel away from the space ship at the same velocity as it returns. This reflects Einstein’s postulate that the speed of light is the same in all inertial reference frames.
- A and B observe the same red shift in the light coming from the other spaceship.
- Sending and receiving a reflected signal shows how a distant event on a moving body can be timed.
- Lack of agreement over the time of reflection is shown to occur even though all clocks are working perfectly. This lack of agreement isn’t normally seen, because we don’t usually deal with such high velocities (in this case, three-fifths the velocity of light) or super-accurate clocks. Disagreement could be avoided by A and B refusing to judge what happened at a distant point as “simultaneous” with the ticking of their own clocks.

To measure the length of a moving object, it is necessary to measure the distance to both its front and rear ends *at the same time*. Without being able to agree on what’s simultaneous, different observers will measure different lengths of moving objects. This effect is called the Lorentz-Fitzgerald contraction, in recognition of the two scientists who concluded that moving objects are physically shortened in their direction of motion. This was before Einstein explained the same effect as a result of the relativity of simultaneity.

Another common misunderstanding concerns the so-called “clock paradox” (or “twin paradox”—see the sidebar on page 35), which says that if B’s clock is transported to be compared with A’s, it will show that less time has elapsed than will A’s. This is not a paradox, because the two clocks have no longer had identical experiences. Specifically, B’s clock will have been accelerated so that it could be returned to A’s position. The behavior of clocks has been accurately tested, and Einstein’s equations have been verified. More troublesome, though, is trying to understand what “really” happens to B’s clock, or more accurately, what we “really” mean by time. We have an intuitive concept of time that resists accurate definition, and we have seen that the timing of a moving clock by sending light signals back and forth gives nonintuitive answers in experiments involving high speeds and very accurate clocks. Our intuitions work perfectly well with everyday clocks and everyday velocities, so it’s a slow process trying to give up the idea of absolute simultaneity.

Perhaps the best approach belongs to Stephen Hawking: “I take the positivist viewpoint that a physical theory is just a mathematical model and that it is meaningless to ask whether it corresponds to reality. All that one can ask is that its predictions should be in agreement with observation” (Hawking and Penrose 1996). We have the model that gives accurate predictions. Perhaps a new concept of time will gradually work itself into our collective intuition as more and more practical applications of special relativity are realized.

## References

- Bondi, Hermann. 1962, 1964. Relativity and Common Sense. New York: Dover Publications. Chapters VII, VIII, and IX are recommended for learning the method of tracing light beams on simple space-time diagrams.
- Darwin, C.G. 1957. The clock paradox in relativity. Nature 180 (November), 976—977. This is the ultimate short-and-sweet explanation of the clock paradox.
- Einstein, Albert. 1905. On the electrodynamics of moving bodies. In John Stachel (ed.). 1998. Einstein’s Miraculous Year: Five Papers that Changed the Face of Physics. Princeton, New Jersey: Princeton University Press. This is a recent translation of Einstein’s famous paper.
- Einstein, Albert. 1961 [1916]. Relativity: The Special and General Theory, 15th edition. New York: Crown Publishers. Pp. 21—27. These pages clearly show that simultaneity is not an absolute.
- Hawking, Stephen and Roger Penrose. 1996. The Nature of Space and Time. Princeton, New Jersey: Princeton University Press. Pp. 3—4.