# Relatively Speaking

While writing yesterday’s post and double-checking the barycenter equation, I came across a marvelous statement that the earth doesn’t rotate around where the earth-sun barycenter is now, but where it was about eight minutes ago. It would take that long for light to travel the distance from the barycenter to earth (though, due to all the stuff in the way, it can take a photon thousands of years to reach the surface). But though gravity, like X-Rays and neutrinos, isn’t blocked by all that stuff, it still doesn’t act instantly. And it turns out that the speed of light in a vacuum is the limit. That means yesterday, when the earth was about 1.521 x 108 km from the barycenter, it would take about 8 minutes, 27.35 seconds, for light to travel that same distance through nothing. Since the speed of light in a vacuum is the limit, it takes that long for the earth to respond to shifts in the barycenter. If the sun were to abruptly vanish, we wouldn’t know of it until about 8 minutes later.

That there’s a limit to how an object can react to changes in gravity might seem odd, just as the idea that nothing can travel faster than the speed of light might seem strange, and it is. It’s counter-intuitive to everything we experience. If we’re on a train traveling 60 miles an hour and walk at 2 miles per hour toward the front, someone outside the train would measure our speed as 62 miles per hour, though we would only measure it as 2. But if we were to shine a flashlight toward the front, both us and someone outside the train would measure it as the speed of light through air. Yes, that can happen, and scientists, in a way, discovered that before Einstein’s Special Theory of Relativity.

Back when science was first studying electromagnetic waves, they faced a huge question: what are the waves traveling through? Every wave then known had to have some medium to travel through. So, to account for this, a substance called aether was theorized. To work it would have to be incredible stuff, having no effect on matter while being stronger than metal, and fill all of space.

Since light is an electromagnetic wave, it, too, would have to travel through aether, and that meant it should be possible to detect the earth’s motion through it by comparing the speed of light in the direction of the earth’s rotation to the speed of light from pole to pole. As the earth turned, the speed of light should vary through the aether “wind,” just as if you can feel a light breeze if you’re walking into it, but might not notice it if you’re walking in the same direction. So two scientists, Michaelson and Morley, built an instrument that floated on a pool of mercury and split a beam of light, sending one in one direction and the other in one 90º to it. To measure the difference they recombined the beams. A difference in speed would show up as interference patterns. But when they tried it, they made a startling discovery: they could not detect any difference in the speed of the light! Whether there was aether or not, that strongly implied that the earth was standing perfectly still – unless something else was going on.

That something else turned out to be Relativity. In 1905, Einstein published his theory of Special Relativity, which held that the speed of light was the same regardless of whether an object was moving or not. So if you measured a beam of light in the direction of the earth’s rotation against one perpendicular to it, both would be the same, and the earth would look like it was standing still.

Yes, that’s weird. But that’s what happens. Because the implications of this means there are even weirder effects, and we can test them. Such as time dilation. Let’s say our train is moving close to the speed of light. We shine our flashlight toward the front of the train. We would think that the beam of light is traveling at the speed of light plus the speed of the train. So, for an outside observer to measure the same speed for the beam of light, time on the train would have to seem like it has slowed down. We see this effect in cosmic rays, some of which shouldn’t last long enough to reach the earth’s surface, but are moving so fast that time seems to slow down for them.

Why don’t we see this at slower speeds? Because you really have to be moving to get into noticeable relativistic effects. Though, with equipment today, it’s possible to measure smaller-scale changes. Such as placing two atomic clocks on planes and flying them in different directions around the earth, or even comparing one that’s higher than another. The effect is tiny, but it’s there, and it agrees with General Relativity.

There’s other neat effects, like objects appearing shortened, or light shifting colors, or gravitational lenses, where the gravity of a galaxy can act as a lens to light behind it. But the main one that came to mind with the Aphelion post was the limit to the action of gravity. The speed of light in a vacuum is the limit for all sorts of things in our universe, including gravity. And the implications of that limit are some very weird effects, indeed.