In an earlier post I wrote about how light moves at a single universal speed. Not only has this been well observed experimentally, it forms the foundation for the theories of special and general relativity, which are also well supported by experiment. Often, relativity is summarized as “nothing can travel faster than light.” Which raises the interesting question, what about gravity?
Light Matters
The inherent speed of light is built into the very nature of what light is. Since the fundamental leptons and quarks that comprise matter have electric charge, they are also subject to the fundamental nature of light speed. All the strange aspects of time dilation and warped gravity work in such a way that the speed of light is always preserved.
Time in a Bottle
In an earlier post I talked about how certain kinds of dark matter might be detectable by the global positioning system (GPS). Part of the reason for that is due to the fact that GPS satellites have extremely precise clocks in them. So precise that the relativistic effects of gravity and relative motion have a measurable effect on the rate at which their clocks tick. This led some readers to ask just how gravity can affect the flow of time. It all has to due with Einstein’s theory of relativity.
A Matter of Principle
Imagine taking a bucket of water and spinning it. As you rotate the bucket, the water would fling outward a bit, so that the surface of the water is concave. Compare that to a bucket of water that isn’t spinning, so that the water is flat. If both buckets are perfectly smooth and symmetrical, and the water is perfectly calm, the only difference you would see is that one bucket has concave water and the other has flat. But why are they different?
Sphere of Influence
Suppose you were to flash a light where you are at this moment. The light would speed away from you at about 300,000 kilometers per second, which is known as the speed of light. In general you could point the light in any direction, so flash of light would in general be an expanding sphere of light.
Wandering Stars
One of the consequences of general relativity is that light can be deflected by nearby masses. Mass curves space, and this curvature causes light to bend slightly. It was first observed during a total eclipse in 1919. The effect is extremely small unless the light passes close to a large mass, so gravitational lensing (as it is typically known) is usually only noticed with objects such as lensed galaxies, or specific tests of general relativity. But even though the effect is small as you get further from a mass, it isn’t zero. As our astronomical measurements become more precise, the effects of gravity are starting to become something we can’t ignore.
Flight Delay
It’s a well known law of physics that the speed of light (in a vacuum) is always the same, regardless of your frame of reference (essentially your vantage point). But this isn’t entirely true. It actually depends on how you define “speed”.
In the Red
If you toss a ball into the air, it will slow down as it rises. The Earth’s gravity pulls on the ball as it moves upward, causing it to slow down until it comes to a momentary stop at its highest point. Then it will begin to move downward, speeding up as it does. Suppose, then, that you were to shine a flashlight upward. What would happen? You might argue that gravity would pull on the photons, causing them to slow down, but we know that light has a constant speed, and can’t slow down. You might argue that since photons are massless gravity doesn’t affect them, but we know that the Earth’s mass, like any other mass, can cause light to change directions. So neither of these can be the answer. The real answer is pretty interesting, and it turns out to be one of the tests of Einstein’s theory of relativity.
Secular and Periodic
More general relativity today. This time a bit on how to calculate the perihelion advance of Mercury in general relativity. When you derive the central force equation for relativistic gravity you find there is an extra term not seen in Newton’s gravity. The extra term is small, but enough to make Mercury’s orbit (any orbit really, but we typically use Mercury as an example) deviate slightly from an ellipse. Since the deviation is small, you can make some broad approximations, get an approximate solution for Mercury’s orbit, then determine the perihelion advance for one orbit.