Notes from Under Sky

The Luxon Wall

What happens near the speed of light?

Someone asked:

If our galaxy is travelling at the speed of light away from the big bang center and someone turned on a flashlight directly pointed at the big bang's center wouldn't the beam of light be motionless relative to the big bang's center? Conversely if it was flashed away wouldn't it be twice the speed of light. If the speed of light is the absolute limit then where is the reference point at which it is measured to?

The short answer is that you don't need a reference point, because things are worked out so that the speed of light is never anything other than c (in a vacuum, at least).

In Newtonian mechanics, speeds are additive. Therefore, if a pitcher throws a baseball at 90 miles an hour (a bowler throws a cricket ball at 145 kilometres per hour, for those of you on the other side of the pond) and he's facing forward on a train travelling at 60 miles an hour (100 kph), then the net speed of the ball, relative to the ground, is 90+60 or 150 miles an hour (245 kph). All well and good and sensible.

However, at very high speeds, Newtonian physics breaks down. One tenet of relativity is that the speed of any light is always c. Therefore, speeds cannot strictly be additive. If you shine a light on a 60 mph train, the forward light beam doesn't travel at c plus 60 mph; it can only go at c.

This also works for objects travelling at under the speed of light, too. If you're on a train (called, say, the Ryan Express) travelling at half the speed of light, and you throw a baseball forward at half the speed of light (sign that boy up!), the baseball doesn't have a net speed of c/2 + c/2 = c (and therefore infinite mass). It travels at four-fifths of the speed of light.

In general, if you have two speeds s1 and s2 (expressed as fractions of c), anytime you think you ought to add them, what you get instead is

     s1 + s2
    1 + s1*s2

So in the above example, we get

    0.5 + 0.5
    --------- = 0.8
    1 + 0.25

The reason that this doesn't bother us for ordinary trains and baseballs is that these everyday speeds are so incredibly small relative to the speed of light that the product ss2 is minuscule. Thus the denominator is practically equal to 1, and speeds are just about additive. It's only when you get to appreciable fractions of c that relativity begins rearing its complicated head.

A special case is that if the speed s2 is the speed of light (i.e., equal to 1), then we just get

     s1 + 1
    -------- = 1
    1 + s1*1

meaning that no matter how fast your train is travelling, your light beam continues to move forward at c, or backward at c for that matter. Therefore, no reference point is needed. Light (including radio waves, gamma rays, X-rays, etc) travels at c relative to whatever frame of reference, provided you are measuring using a clock and ruler that are stationary in that frame of reference—in fact, that is part of what "frame of reference" means.

You might argue (and quite reasonably, too) that Einstein just "guessed" that the speed of light was always c. He didn't prove it. Which is right, I suppose. However, that beginning principle—that the speed of light is a universal constant—leads to a whole bunch of observable predictions that Newtonian physics doesn't lead to, and anytime there has been a conflict between the two, relativity has been upheld. So we have almost unbreakable confidence that the speed of light is in fact a universal constant.

Relativity doesn't technically forbid anything from travelling beyond the speed of light. It just prevents anything with so-called "proper mass" (otherwise known as "rest mass") like baseballs and trains from travelling precisely at the speed of light. Only massless particles like photons can travel at the speed of light (which makes sense since photons are light quanta). We used to think that neutrinos travelled at the speed of light, too, but since it now appears that at least one and possibly all three varieties of neutrino have some proper mass, they cannot travel exactly at the speed of light. Pretty darn close, though. Gravitons, if they are ever discovered, might I think travel at the speed of light, but it's been a while since I consulted any reference on them.

So there could exist a world of objects travelling at 2c, or 5c, or 42c. But it's unclear how they and we might interact, if at all, and Isaac Asimov once hypothesized in one of his essays that they and we are in fact separated by what he called the "luxon wall"—the objects travelling precisely at c—and ne'er the twain shall meet. It sounds plausible to me. :)

Incidentally, we are not travelling at any speed relative to a "big bang center"; the center of the big bang—insofar as that phrase has any meaning at all—is not in the observable universe anymore than the center of a beach ball is on the beach ball surface itself. But that's a cosmology question for another time.

Copyright (c) 2000 Brian Tung