INCOMING SIGNAL SPEED

5. INCOMING SIGNAL SPEED
THE SPEED OF LIGHT CONSTANT (c)

I am working on INCOMING signals by dividing the topic into two parts: when the two frames are moving away from each other and when they are approaching each other. We assume that the speed of frames relative to each other is “v”.

The frames are moving away from each other

First, let’s see how the event looks like from Frame A’s reference system.
Frame A thinks that it stands still and that Frame B is in motion.

The course of the event relative to Frame A’s reference system:
1.1 – Frame B sends a signal in the direction of Frame A from d₀ distance.
1.2 – Signal arrives at Frame A.

Without hesitation, we use “c” constant as the speed of the signal.
When the signal travels to Frame A, it will cover d₀ distance at c speed.
Then the travel time of the signal is

Within the travel time, Frame B covers

distance in the direction of the red arrow. The moment the signal reaches Frame A, Frame B will be in d₁ distance.

Now, let’s have a look at how the event is seen from the reference system of Frame B.
Frame B thinks that it stands still and that Frame A is in motion.

The course of the event relative to Frame B’s reference system:
2.1 – Frame A sends a signal in the direction of Frame B from d₀ distance.
2.2 – Signal arrives at Frame B.

Identical calculations apply for Frame B.
When the signal travels to Frame B, it will cover d₀ distance at c speed.
Then the travel time of the signal is

.
Within the travel time, Frame A covers

distance in the direction of the red arrow. The moment the signal reaches Frame B, Frame A will be in d₁ distance.

The frames are approaching each other

It will be some kind of a repetition, but we must analyze the event when Frame A and Frame B are approaching each other.
First, let’s have a look at how the event is seen from the reference system of Frame A. Frame A thinks that it stands still and that Frame B is approaching it.

The course of the event relative to Frame A’s reference system:
1.1 – Frame B sends a signal in the direction of Frame A from d₀ distance.
1.2 – Signal arrives at Frame A.

Without hesitation, we use “c” constant as the speed of the signal here, as well.
When the signal travels to Frame A, it will cover d₀ distance at c speed.
Then the travel time of the signal is

.
Within the time signal travels to Frame A, Frame B covers

distance in the direction of the red arrow.
The moment the signal reaches Frame A, Frame B will be in d₁ distance.

Finally, let’s have a look at how the event looks like from the reference system of Frame B.
Frame B thinks that it stands still and that Frame A is approaching it.

The course of the event relative to Frame B’s reference system:
2.1 – Frame A sends a signal in the direction of Frame B from d₀ distance.
2.2 – Signal arrives at Frame B.

Without hesitation, we use “c” constant as the speed of the signal here, as well.
When the signal travels to Frame B, it will cover d₀ distance at c speed.
Then the travel time of the signal is

.
Within the travel time, Frame A covers

distance in the direction of the red arrow. The moment the signal reaches Frame B, Frame A will be in d₁ distance.

As a result of our analysis, we make an extremely important inference. We identify a golden result to which we can always resort.

INCOMING SIGNALS

Relative to an inert reference system, the speed of an INCOMING signal (an electromagnetic wave) coming towards it is always constant and equals to “c”. This situation is independent of the speed or the movement direction of the reference system. Similarly, it is also independent of the speed or the movement direction of the source that emits the signal.

As can be seen, no matter which direction or how fast the source emitting the signal and the target of the signal move, relative to the reference system of the target of the signal, the speed of the signal coming towards the target itself is “c”. The reason why we can write this result so freely is that the answer to the question which frame, A or B, is in motion is not known. We have come to this conclusion with the help of the principles we read at the beginning.

I’d like to draw your attention to something here. We have calculated the travel time of the signal for both frames as t₀ = d₀ / c. We will make use of this time value while working on OUTGOING signals. Because of the importance of this value, I’d like to highlight it again:

Travel time of the signal

d₀ : The distance between the frames
c : The light speed constant
t₀ : Travel time of the signal

In this way, we have covered the topic of INCOMING signals. Now we will focus on OUTGOING signals.