The Train Revisited

To see the impact of Einstein's second postulate, let's go back and look at our train illustration again. This time, however, we'll take a much faster train, and instead of a baseball, our "thrown object" will be light. If thinking of light as an "object" bothers you, just remember that light travels in the form of small particles called "photons". (Maybe quantum physics will be my next project. :-) Anyway, Dave shines his flashlight forward in the train, hurling photons forward with a speed of about 300,000,000 meters per second (m/s) as predicted by Maxwell's equations and verified experimentally. The train moves at 100,000,000 m/s, as Nolan looks on.

Now we've already been through this situation. The photons move at a speed of 300,000,000 m/s relative to Dave, while Dave moves at a speed of 100,000,000 m/s relative to Nolan. So to calculate the speed of the photons relative to Nolan, we have only to add these numbers. The speed of the photons relative to Nolan is 400,000,000 m/s.

And there lies the problem. This directly contradicts Einstein's second postulate, which says that the speed of light in Nolan's frame must be the same as in Dave's frame: 300,000,000 m/s. So which is wrong: the "common sense" (Galilean) relativity that we deduced a couple pages ago, or Einstein's postulates? Well, scientific experiments (many scientific experiments) back up Einstein, so let's assume he's right and let's try to figure out what could be wrong with common sense relativity.

Remember that the decision to add the velocities came fairly simply. After one second, a photon has moved 300,000,000 meters ahead of Dave, and Dave has moved 100,000,000 meters ahead of Nolan. So the photon must move 400,000,000 meters ahead of Nolan during that second. There are only two ways that this can possibly not be 400,000,000 m/s:

  1. The 300,000,000 meters, relative to Dave, is not really 300,000,000 meters relative to Nolan.
  2. One second for Dave is not one second for Nolan.
As strange as each of these possibilities may sound, they are, in fact, both correct.
Space and time
Dave's relativity page
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