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Last Updated December 6, 2003
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Gravity and the Speed of Light
So, what relates the speed of light to gravity? The explanation deals with a frame of reference. For this illustration, we'll use a 3-dimensional frame including the x (horizontal), y (vertical), and t (time) dimensions. So, no depth. Now, imagine that a beam of light must travel from one side of this frame to the other. Traversing this distance will take time (t). Light, which always travels in a straight line relative to itself, will follow a straight path from one side of the frame to the other.
In this frame, the dotted line represents the beam of light. As mentioned above, it travels in a straight line. Now, we will place this frame in a gravitational field. What effects does gravity cause? It exerts am attractive force on objects, causing them to accelerate. So, when we place this frame in a gravitational field, it will accelerate. Now, imagine what will happen to the beam of light if the frame is accelerated downward. It will curve, like so.
In this example, the top frame is t1, and the bottom frame is t2, denoting the different times that each frame exists in. So, you see that, once the frame is accelerated downward over a time (t), the beam of light will appear curved to us. Now, you may ask, "Why does the light have to curve? The frame is just moving down, so wouldn't it make a straight line from its origin to the target?" The answer is no. Remember that the frame is accelerating, so its velocity is constantly changing. This means that the light will curve. Again, you may ask why. Well, let's say the light took 10 seconds to cross the frame, and that the frame was being accelerated downward at a rate of 1g (Earth's gravitational pull, equal to 9.8m/s2. We'll say 10m/s2 just for simplicity). Now, let's divide the time into 1s intervals, and the frame has an initial velocity of 0m/s. At t = 1s, the velocity of the frame will be 10m/s, and the light will have traveled 1/10 of the distance of the frame, sloping downward a distance of 5m by d = (1/2)at2, in a straight line, since we're taking intervals of 1s. Now, at t = 2s, the light will have traveled 1/5 of the distance of the frame, but it will have deviated by 20m from its original position on the y axis, not another 5m. As you keep going on, the light's deviation keep increasing. With this in mind, realize that if we divide the time into an infinite number of intervals, we will get infinitesimally small deviations (this is the principle behind a derivative in Calculus, that a curve can be divided up into an infinite number of infinitesimally-small but sloping straight lines). So, with infinitesimally small and increasing deviations, we will get a curve.
So, now you know the relationship between light and gravity. Gravity causes acceleration and light bends in an accelerating frame of reference. So, gravity must bend light, and it does. This is experimentally verified. There is a theoretical quantum mechanical explanation, as well. I'll make it short. Remember the photon, and how it was the mediating particle in any interactions involving electromagnetic forces? Well, gravity's mediating particle (which hasn't been confirmed to exist, but gravity's effects on the quantum scale have been observed just recently) is the graviton. Quantum mechanics predict that gravitons, like photons, will travel at c. Thus, gravity propogates at the speed of light. This is more evidence of a connection between the speed of light and gravity.
