- #1

- 27

- 0

1) In special relativity, we are amazed that a beam of light emitted by a space ship moving at .99c and measured by either a stationary observer (relative to the space ship) or by an observer on the moving ship has velocity c and not as we might expect 1.99c as would be the case were this a projectile fired from a conventional terrestrial vessel. Why is this so amazing? Do we not observe the same phenomenon when a sound is emitted by a moving train whose velocity, for the purpose of analogy, is less than the speed of sound in air? Both an observer on the train or on the platform measures the speed of sound in air as having the same velocity since the velocity of sound in air is independent of the velocity of the train. What differs for the two observers is the perceived frequency of the sound. The difference is of course the familiar Doppler effect. Similarly, the two observers of the beam of light will perceive the frequency of the emitted beam of light very differently. The stationary observer will see the light's frequency shifted due to the Doppler effect, the moving observer will not. The analogy breaks down because sound is purely a wave phenomenon and light is not. There are no “auditons” emitted by the train whistle. In fact nothing “new” is emitted by the whistle, it simply acts on the air molecules to create alternate regions of compression and rarefaction which propagate through space with wave-like properties at the speed of sound. This won’t do for light since light is an actual something moving wave-like through space. So the analogy with sound ends there and we demand that since it has a “particle-like nature” as well as a “wave-like nature” it should resemble

a projectile fired from a conventional vessel whose velocity appears different to different observers depending on their point of view.

Now we know the velocities of the light beam cannot be additive since c, and only c, is the velocity of light in a vacuum or in space and in this way it is wave-like and behaves like sound. But consider the momentum or "energy" of a photon, which for a classical projectile would differ for the two observers as expected: The observer on the ship sees the projectile’s momentum as a function of the projectile’s velocity alone, while the stationary observer measures the momentum as a function of both the velocity of the vessel and the velocity of the projectile. How does this sleight of hand trick help? Since we know the momentum/energy of a photon is proportionate to Planck’s constant times its frequency and since the frequency is shifted, according to the stationary observer, by the Doppler effect, he will measure the energy of the emitted photons as being a function of both the speed of light and the speed of the space ship while the moving observer will measure the momentum/energy of the emitted photons as being a function of the speed of light alone. So it seems once we sort out the nature of light a bit thanks to the work of professors Planck and Einstein, the predictions of special relativity regarding light's peculiar behavior with respect to observers in 2 frames of reference that are in uniform rectilinear motion are really quite similar to other more familiar terrestrial phenomena.