Notes on Relativity and Cosmology - Physics Department, UCSB

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174 CHAPTER 7. RELATIVITY AND THE GRAVITATIONAL FIELD 7.2.3 Gravity, Light, Time, and all that In the previous subsection we argued that light is in fact affected by gravity. In particular, when light travels upwards though a gravitational field, it looses just as much energy as would a massive object. Now, what happens to light when it looses energy? Well, it happens that light comes in little packages called ‘photons.’ This was only beginning to be understood when Einstein started thinking about gravity, but it is now well established and it will be a convenient crutch for us to use in assembling our own understanding of gravity. The amount of energy in a beam of light depends on how many photons are in the beam, and on how much energy each photon has separately. You can see that there are two ways for a beam of light to loose energy. It can either actually loose photons, or each photon separately can loose energy. As the light travels up through the gravitational field, it should loose energy continuously. Loosing photons would not be a continuous, gradual process – it would happen in little discrete steps, one step each time a photon was lost. So, it is more likely that light looses energy in a gravitational field by each photon separately loosing energy. How does this work? As we mentioned in section (6.5.1), the energy of a single photon depends on something called the frequency of the light. The frequency is just a measure of how fast the wave oscillates. The energy E is in fact proportional to the frequency f, through something called “Plank’s constant” (h). In other words, E = hf for a photon. So, as it travels upwards in our gravitational field, this means that our light wave must loose energy by changing frequency and oscillating more slowly. It may please you to know that, long after this effect was suggested by Einstein, it was measured experimentally. The experiment was done by Pound and Rebke at Harvard in 1959. Now, a light wave is a bunch of wave crests and wave troughs that chase each other around through spacetime. Let’s draw a spacetime diagram showing the motion of, say, a bunch of the wave crests. Note that, if the wave oscillates more slowly at the top, then the wave crests must be farther apart at the top than at the bottom.
7.2. SOME OBSERVATIONS 175 up Bottom Top But.... isn’t each wave crest supposed to move at the same speed c in a vacuum? It looks like the speed of light gets faster and faster as time passes! Perhaps we have done something wrong? By the way, do you remember any time before when we saw light doing weird stuff??? Hmmmm.... something is definitely funny in the diagram above. Nothing is really changing with time, so each crest should act the same as the one before and move at the same speed, at least when the wave is at the same place. Let’s choose to draw this speed as a 45 o line as usual. In that case, our diagram must look like the one below. However, we know both from our argument above and from Pound and Rebke’s experiment that the time between the wave crests is larger at the top. So, what looks like the same separation must actually represent a greater proper time at the top. Bottom Top 2 sec 1 sec up constant distance This may seem very odd. Should we believe that time passes at a faster rate
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Notes on Relativit
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26 CHAPTER 1. SPACE, TIME, AND NEWT
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Notes on Relativity and Cosmology - Physics Department, UCSB

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