Imagine you are in a spaceship moving away from the earth at a velocity v. Imagine that a TV broadcast is sent to your spaceship from Earth. How would you see the broadcast?

Some mathematical preliminaries will help figure out the observed differences. In terms of the K factor . Reciprocity of K factor means . Hence,

1. A sends a signal at time T
2. B receives it at time (at event P)
3. B reflects it back to A who receives it at time
4. According to A, the signal was received by B at time q
5. Velocity of B as measured by A = distance signal traveled / time it reached B ( q)
6. The distance traveled by light =
7. Hence, velocity of B as measured by A = d/q = 

The above equation shows that the velocity of B as measured by A is necessarily less than c – and is related by a factor that depends only on time dilation (the ‘K’ factor).

How does this relative motion affect the received broadcast?

There are two ways in which the received broadcast will differ from the original source signal:

1. Frequency at which the broadcast is received (the Doppler Effect)
2. The interval between the successive ‘refreshes’ (screen refresh rate)

Frequency at which broadcast is received

Frequency is defined as the speed divided by the wavelength :

.

The wavelength is basically a distance (the distance between successive peaks)  – and this distance in the moving frame is measured to be longer than in the stationary frame (since dist  = c * Time Interval – and Time Intervals undergo dilation). Since the wavelength is measured to be longer, the frequency (inversely related to the wavelength) appears to be shorter. This is the classic Doppler effect – the frequency observed while receding from a source, is lower than the source frequency.

This means, our spaceship will have to tune to a lower frequency to receive the signal.

Screen Refresh Rate (Interval Between Successive Refreshes)

Now that you have tuned your TV to the correct frequency to receive the broadcast, there is still one more annoying thing to deal with. A television picture is nothing but successive screen refreshes (of so many frames per second). Since a second is longer in your moving spaceship than it is on earth, you will be seeing the same frame persist over a longer period of time. This will make the broadcast seem discontinuous. In order for the broadcast to seem continuous, earth’s broadcasting station will need to broadcast at a higher refresh rate. This rate is calculated by multiplying the K factor with the original refresh rate.

For e.g. – if the original refresh rate was set to be 30 frames per second – and the K factor = 1.5 (the ratio of the spaceship interval and the earth’s time interval), then the broadcasting station will need to broadcast at 45 frames per second for the broadcast to appear continuous.

Of course, a simpler solution would be to use digital video recorders – and buffer the frames as they are received. Then, just play them back at 30 frames per second from the recorded buffer. This would leave the original broadcast frequency at 30 frames per second.

Summary

If you are ever stuck on a spaceship moving away from the earth at relativistic speeds, and have arranged for your favorite TV shows to be broadcast to you from earth, you will need to have the above two calculations handy. The first one (frequency of received broadcast) determines the channel to which you will have to tune your own TV (a lower frequency than the one being broadcast – due to the doppler effect). The second phenomenon (slower screen refresh rate) is caused by time dilation – causing measured intervals on the moving spaceship to be longer than those on earth.  This can be addressed by buffering received frames and playing them back at the regular 30 frames per second.