Light Experiment
The Velocity of Light Experiment
This thought experiment is based on the assumption that the velocity of light is constant with respect to the target, rather than the accepted assumption that it is constant in all frames of reference. The latter assumption leads to time dilation, which does not arise in this scenario.
In a region of space far away from other material objects there is a radio transmitter and two girls, Alice and Betty. The transmitter emits a hundred time signals per second. At 10:00:00 the transmitter sends the time "10:00:00.00".
Alice and Betty each have a device capable of displaying the time signals as they are received. Each girl also has a synchronized clock co-located with them. Note: As there is no time dilation in this scenario, the clocks always indicate the same time as the transmitter. Betty is at rest with respect to the transmitter and 4 light seconds distant from it. So the time displayed on her device is always 4 seconds behind the actual time (as displayed on her clock).
So at 10:00:00 Betty's device displays "09:59:56.00". Whilst at 10:00:00 Alice is 5 light seconds distant from the transmitter and approaching it at 0.2c (i.e. one fifth of the velocity of light). At this moment, the time signal displayed on Alice's device is not known.
In 5 seconds time (at 10:00:05) Betty's device will display the time signal "10:00:01.00". Meanwhile, during the 5 seconds. Alice will have travelled 1 light second and be adjacent to Betty. You might therefore expect that at 10:00:05 she too would receive the time signal "10:00:01.00". However, in Alice's rest frame, she is stationary and the transmitter is approaching her at 0.2c. At 10:00:00, when it is 5 light seconds distant from her, the transmitter emits the time signal "10:00:00.00" and continues on its way. The time signal approaches her at the velocity of light, so Alice will receive the time signal "10:00:00.00" at 10:00:05.
So at 10:00:05, even though they are adjacent, Betty receives the time signal "10:00:01.00" and Alice receives the time signal "10:00:00.00".
Furthermore, Alice, will see Betty's device displaying "10:00:01.00", and Betty will see Alice's device displaying "10:00:00.00". Also, as five seconds have passed since the time signal "10:00:00.00" was transmitted, both their clocks will display "10:00:05.00". So there is no discrepancy in how much time has actually passed for Alice and Betty (as indicated by their clocks), but the time signals received on adjacent devices from a distant transmitter differ by 1 second.
Let's now re-run the experiment, starting again at 10:00:00. This time, moments before they are adjacent, both girls move sideways such that at 10:00:05 each is at the exact position occupied by the other in the first experiment.
The small transverse movements should have no effect on when the girls receive the time signals, so Betty's device will still show "10:00:01" whilst Alice's will show "10:00:00". The girls are at the exact positions occupied by each other in the first run, yet each still receives the time signals according to their own relationship to the transmitter.
Similarly, we may add a third observer, Carol, who is travelling at 1/3 c away from the transmitter.
If at 10:00:02 Carol is 3 light seconds distant from the transmitter then, at 10:00:05 she too will be co-located with Alice and Betty, and her device will show "10:00:02.00".
Furthermore, if we assume that the girls could see the transmitter; at 10:00:05 Alice would see it as being 5 light seconds distant, Betty would see it as being 4 light seconds distant, and Carol would see it as being 3 light seconds distant. Is there an actual difference in the distance? No. The girls see the transmitter as being at different distances because they are seeing it where it was (with respect to themselves) when the light that each receives was emitted. So even though the actual physical relationships are unaffected, the apparent relationships to a distant object can, and will, differ.
Conclusion
It is apparent that, in the time taken for the time signal "10:00:00.00" to reach Alice, she "moves" 1 light second towards the transmitter, and that time signal is 1 second earlier than the one Betty receives (when they are adjacent). 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.
This suggests that:
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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.
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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).
This effect is referred to hereafter as the "velocity of light effect".
Note: You may have noticed that the Doppler effect has not been mentioned. The Doppler effect and the "velocity of light" 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 of light effect" focuses on the timing of the receipt of the signals.
