SHORTCUT TO ALICE LAW
February 24, 2018
1) Let’s discuss a signal transmitter whose wavelength is λ0 and frequency is
f0 . Here, we have the following equation: c = λ0 .
2) If a signal emitted from the transmitter is moving towards a frame in motion, signal wavelength will, because of the Doppler Effect, go through a change as much as
λ1 = λ0 (c±v)/c. Here, ±v value is the approaching (-v) or moving-away (+v) speed of the moving frame relative to the transmitter.
3) Wave speed equation is as follows:
WAVE SPEED = WAVE FREQUENCY x WAVELENGTH
4) Therefore, the speed of the wave that a transmitter sends to a target in motion relative to the its reference system is as follows;
Outgoing Wave Speed = c' =
f0 . λ0 . (c±v)/c =
f0 . λ1
(So, it is always different from c)
c'= f0 . λ0 (c±v)/c
c = λ0 . f0
Based on  and , we can present the speed of a signal sent to a target that is in motion relative to the reference system of the transmitter as indicated below ;
c' = c±v
5) What will be the speed of the incoming signal that comes towards the arrival target relative the reference system of the arrival target?
Relative to the reference system of the transmitter, as the speed of the signal it emits is c' = c±v and the speed of the frame which is the arrival target of the signal is ±v; relative to the reference system of the arrival target, the approaching speed of the signal that comes towards it is;
Incoming Wave Speed = c±v - (±v) = c
(So, it is always constant.)
The speed of a signal going towards a target in motion has not been measured so far. In the near future, science of Physics is going to carry out this measurement and lead itself towards the right direction.