Monday, January 14, 2013

Why The Speed Of Light Is Constant

When many people first learn that the speed of light is constant — that it’s the same everywhere in the universe, and is measured the same by all observers — it all seems kind of arbitrary. It’s strange enough that the speed of light is a “cosmic speed limit,” beyond which no object can go. But, how can the speed of anything possibly be a constant value? When I’m in an airplane and I walk forward up the aisle, I am going faster than the plane itself, something that could be verified by an observer on the ground. My total speed, relative to the ground, will be the speed of the plane plus my walking speed. (Subtract the speed if I’m walking in the other direction, toward the tail.) Yet, if I measure the speed of a light beam coming from a laser aboard a plane or a spaceship, I’ll always get the same result of 186,000 miles per second, whether the beam is facing forward, backward, or sideways, or even if it’s beamed from the spaceship in any direction and measured on the ground. Why?

It actually has to be this way. A world in which the speed of light varied might be impossible logically (see below), or at least could be so messed up and incoherent that complex structures such as galaxies and intelligent life might not be possible.

Consider a thought experiment: You set up a rapidly rotating beacon in deep space, with a radio antenna on it. (Radio waves are an invisible form of light.) The antenna is transmitting a radio signal consisting of a sequence of natural numbers: 1, 2, 3, and so on. Far away from the transmitter, you tune in your receiver and wait for the beacon to start spinning and transmitting the sequence. What kind of signal will you receive?

That depends on whether the speed of light is constant or not. Let’s imagine that it isn’t. In that case, the speed of the radio signal in your direction would change according to the velocity of the transmitting antenna, as with the example of walking up the aisle of an airplane: As the beacon spins, sometimes the antenna would be coming toward you — which would “throw” the signal faster in your direction — and sometimes it would be moving away, which would subtract some miles per hour from the signal’s speed. So, parts of the signal would be traveling toward you faster than other parts. Naturally, if the speed of different portions of the signal is different, the faster portions will reach you sooner than the slower portions. This effect would worsen the farther away you are from the beacon, and the faster the beacon is spinning. You might end up receiving a steady sequence of numbers like this:

1 - 2 - 3 - 7 - 8 - 9 - 4 - 5 - 6 - 10 - 11 - 12 - 16 - 17 - 18 - 13 - 14 - 15 ...

Here, the 7 - 8 - 9 segment is arriving sooner than the 4 - 5 - 6 segment, even though it was actually transmitted later. If this were a television signal rather than a sequence of numbers, with the antenna on a large rotating disc, the program would be really messed up. A political candidate might be seen giving a concession speech, followed by a speech where he seems confident he’ll win. I’m not sure that causal impossibilities would result from incoherent information flying around the universe,* but surely the formation of large structures such as galaxies, responding gravitationally to far-away moving bodies, would be affected (if gravity would even exist in such a universe).

Now let’s consider what happens in a world where the speed of light is constant. In this case, all portions of the signal are transmitted at the same speed relative to you, even as the beacon rotates, so no portion reaches you faster than any other. The numbers arrive in the correct sequence, just as they were transmitted. However, the only way this can possibly work (as Einstein showed) is if measurements of time and distance change for various observers. For a transmitting antenna on a rotating beacon, this produces a relativistic Doppler effect — a slowing down and speeding up of the signal, almost like a vinyl record being played back off-center, something like this:

1 ---- 2 --- 3 -- 4 - 5 - 6 -- 7 ---- 8 --- 9 -- 10 - 11 - 12 -- 13 ---- 14 --- 15 ...

If the TV antenna on the disc were transmitting American Idol, you’d see the show from beginning to end without interruption — no unexpected spoiler — but the slowing down and speeding up might make it sound as if the singer and the band can’t stay on key to save their lives (which in reality happens sometimes).

As it turned out, the constant speed of light was confirmed by the Dutch astronomer Willem de Sitter in 1913, through observations of double star systems, where two stars are rotating around each other closely. He realized that if the speed of light varied as the stars advanced toward us or receded away, the orbits would appear erratic. The system might appear blurry or scrambled and incoherent, and from great distances the laws of motion would appear not to work at all. However, such was not the case in any system that de Sitter observed, and this was used as evidence to support Einstein’s special theory of relativity and the constancy of the speed of light. All observations made to date support the same conclusions.

Personally, I think that the constant speed of light is a hint that the universe is fundamentally informational (the “it from bit” hypothesis proposed by the great physicist John Wheeler). This idea says that matter/energy and spacetime emerge from a deeper layer of existence that’s based purely on information. In our universe, information in the form of light always passes from point A to point B in a coherent, sequential fashion, for every observer — it’s space and time (and even mass) that all change accordingly to suit it. There might be a lesson there.


* I haven’t been able to come up with a paradox of cause and effect, resulting just from some information traveling faster than other information. In the days when some news came by rail and some by telegraph, you might have heard that Lincoln’s assassin had been caught before you heard that Abe had been shot — but nobody went back in time to kill John Wilkes Booth. Still, I suspect there is a thought experiment that would show it couldn’t work. If you have any ideas, please comment.

1 comment:

  1. It is quite fascinating! Makes you wonder if there is a relationship of space/time and light that we don't yet understand.

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