by T L Hurst
Thought Experiment continued...
Whilst, in the time taken for the time signal "10:00:02.00" to reach Carol, she "moves" 1 light second away from the transmitter, and that time signal is 1 second later than the one Betty receives (when they are adjacent). This is so even though Alice travelled at 0.2c for 5 seconds, whilst Carol travelled at 0.33c for 3 seconds. The effect is referred to hereafter as the "velocity effect", and it suggests that:
- The magnitude of the difference in the time signals received (in seconds) is equal to the distance "moved" by the observer (in light seconds) between the time that the time signal is emitted and when it is received.
- A velocity towards the transmitter causes the observer to receive an earlier time signal than that received by a "stationary" observer (who is co-located when the time signals are received).
- A velocity away from the transmitter causes the observer to receive a later time signal than that received by a "stationary" observer (who is co-located when the time signals are received).
Note: You may have noticed that the Doppler effect has not been mentioned. The Doppler effect and the "velocity effect" are related, as, for light, both are products of the relative velocity of the source and the observer. However, the Doppler effect deals with the shift in frequency observed in the signals, whereas the "velocity effect" focuses on the timing of the receipt of the signals.
The Velocity Effect Model
The scenario we wish to model is where the speed of light is constant with respect to the target. The relationships between macro objects conform to Newtonian relativity. I.e. All motion is relative, and there is no time dilation or distance contraction. The following diagram describes the scenario. For convenience, the graphic displays the scenario as viewed from the rest frame of the transmitter, and velocities are generally given with respect to the transmitter: