There seem to be two alternative views on what would happen if an atomic clock on a fast moving train were viewed by an external observer: the astronomical and the relativistic. There may now be a third view: electromagnetic interaction.
Suppose the train were travelling at a constant speed which is a significant fraction of the speed of light, and the observer were standing on the platform past which the line ran. Suppose the train had an atomic clock, which was located such that it could be seen by the observer as the train approached, passed and receded into the distance. Suppose finally that the train had no width, so that light travelled directly to the observer down the line or *x* -axis.

What would be the wavelength of light seen by the observer at every stage of the process? For comparison there would be an identical atomic clock standing on the platform to which the observer could refer.

**1. The Astronomical View**

In astronomy the view seems to be quite straightforward. The colour of light emitted by the train clock would be seen by the observer to be shifted towards the blue end of the spectrum because of the velocity of the train, when compared with the colour of light from the platform clock. The decrease of wavelength would then depend on the velocity of the train relative to the velocity of light.

At the point at which the clock was immediately abreast of the observer, the wavelength of light from the train clock would be the same as the observer would see from the platform clock.

As the train receded, the opposite would happen. The wavelength would increase i.e. the colour would be shifted towards the red end of the spectrum, and the increase of wavelength would depend on the velocity of the train away from the observer, relative to the velocity of light.

As noted elsewhere, this is the standard Doppler explanation, but it does imply that the clock on the train can catch up with or pull away from the wavefront of the light which it has emitted, contrary to measurements made on Earth and the premise of the Special Theory. The Doppler explanation is discussed further in Paper III.

**2. The Relativistic View**

In the Special Theory of Relativity the velocity of light is constant, irrespective of the velocity of the source emitting the light or the observer receiving the light. The consequence of the Special Theory is that on the train described above, time slows and dimensions change along the axis of travel, the *x* -axis. Along the other two axes, the *y* and *z*, which are perpendicular to the *x* -axis and each other, there is no change. (There is also an increase in mass, which is not relevant to the argument because the frequency of light which an atom emits when an electron drops from shell to shell does not involve changes in mass).

Atoms and the frequencies of their emissions are homogeneous through time. They are the same everywhere and at all times. With an atomic clock both distance and time reduce to a number of wavecrests. Number is also homogeneous through time.

As far as an atom is concerned, the number of wavecrests emitted in a wavetrain in any direction *x*, *y*, or *z*, must be identical and their timing must be simultaneous, whatever is considered to have happened to elapsed time and distance. There are arguments about the meaning of simultaneity in a relativistic world, but these apply to the problems of observation rather than the atomic clock emitting the light, which in this regard is rather like a single event.

If time and distance change, it must mean that the wavecrests are closer together or further apart, though how this could be known is open to question, because it cannot be measured. There is nothing in between wavecrests.

There are two separate parts of the discussion: what happens to light on the train, and what appears to the observer to happen on the train i.e. what is the wavelength of light when it actually reaches him.

Time and length are increased in the direction of travel away from the observer, and diminished in the opposite direction, according to the Lorentz transformation. Thus as the train approaches the observer, the wavecrests are closer both in time and space. It seems to follow that when they leave the train the same number of wavecrests will still be closer as they travel at the constant speed of light. As a result they will be blueshifted when they reach the observer, compared with the platform clock.

When the train is abreast of the observer, he will see the same wavelength of light as emitted by the identical platform clock, because time and distance do not change in the directions of the *y* and* z* axes.

As the train draws away from him, time and length are increased because the velocity of the train with respect to the observer has changed sign, in this case negative to positive. The light reaching the observer as he watches the train recede will be redshifted.

The effect in total will therefore be a shift from blue to zero to red.