If you were moving at the speed of light and you shined a flashlight in the direction you're moving the light would just barely come out of the flashlight and then stop? understand? But according to Lorentz invariation light travels at light speed regardless of the speed of the source of the light. Moving through the conductive grid or ether of space doesn't change the speed of light. but light doesn't travel at different speeds in relation to the movement of the observer through space time.
Relativity arbitrarily sets ε = ½. When ε = ½ this means light takes an equal amount of time to go from A to B as it does from B to A hence the ½ (each journey is 1/2 the total time of a round trip journey). Einstein arbitrarily set this value in his theory and he acknowledged as much. He did it because it simplified the math and made a very useful convention (Einstein Synchronization Convention).
We can't definitively find the one-way speed of anything as it depends on choice of ε. We can choose ANY valid ε we wish which amounts to changing the one-way speed of light both ways but preserving the two-way speed of light (by any possible perspective we could choose we can definitively measure the two-way speed of light). Even using Einstein's Synchronization light moves (or at least seems to move) at values other than c relative to objects moving relative to you if you set ε = ½ for your own reference frame (Einstein Synchronization). This is because Einstein's Synchronization always chooses the local observer (you) as having light isotropic (moving the same speed c in all directions). Relativity chooses this methodology because it can and it greatly simplifies calculations. However, we could run all the math for a different ε which means the one-way speed of light isn't c and everything would be just fine.
It seems completely weird that we can't definitively set the one-way speed of anything but this is because Relativity is a local theory and we only know what "now" is definitively in one location. Trying to measure the one-way speed of light requires us to know what now is in two different spatially separated locations. We don't know what now is elsewhere because we can't send signals instantaneously from one location to another and infinitely many planes of simultaneity exist. This is a complex and very subtle topic.
The way in which distant clocks are synchronized can have an effect on all time-related measurements over distance, such as speed or acceleration measurements. In isotropy experiments, simultaneity conventions are often not explicitly stated but are implicitly present in the way coordinates are defined or in the laws of physics employed.
Although the average speed over a two-way path can be measured, the one-way speed in one direction or the other is undefined (and not simply unknown), unless one can define what is "the same time" in two different locations. To measure the time that the light has taken to travel from one place to another it is necessary to know the start and finish times as measured on the same time scale. This requires either two synchronized clocks, one at the start and one at the finish, or some means of sending a signal instantaneously from the start to the finish. No instantaneous means of transmitting information is known. Thus the measured value of the average one-way speed is dependent on the method used to synchronize the start and finish clocks. This is a matter of convention. The Lorentz transformation is defined such that the one-way speed of light will be measured to be independent of the inertial frame chosen.
We do know the two-way speed of light is exactly c independent of our choice of ε. We also know the two-way speed of anything is independent of our choice of ε.
When we emit light in the forward direction away from us after changing our velocity to almost the speed of light that light will STILL move at the maximum speed possible away from us. The two-way speed of light will still be c. It sounds weird but because of time dilation, space contraction, and relativistic aberration we can't definitively know the one-way speed of anything. We simply choose ε = ½ at almost an instinctive level and Einstein used it to streamline the math.
Define v- as:
v- = c/(1 - κ) (1 - (f’/f)²) / (1 + (f’/f)²)
Define v+ as:
v+ = c/(1 + κ) (1 - (f’/f)²) / (1 + (f’/f)²)
f' is the observed frequency sent from another frame (think of a cop's radar gun)
f is the frequency of that same radar gun if it were local (in your lab not moving relative to you)
k can be anything 0 to 1
c is the two-way speed of light
v- is the velocity of something in one direction
v+ is the velocity of something in the other direction
v t = x → x / v = t
t round trip = x/v = 1/2( x/v- + x/v+) (half the trip is in one direction and half is in the other)
x/v = 1/2 ( x/c (1 - κ) + x/c (1 + κ)) (1 + (f’/f)²) / (1 - (f’/f)²)
x/v = x/c (1 + (f’/f)²) / (1 - (f’/f)²)
v = c (1 - (f’/f)²) / (1 + (f’/f)²)
v/c = (1 - (f’/f)²) / (1 + (f’/f)²)
Which rearranged equals:
f'/f = (1 - v/c) / √(1- (v/c)²)
The above is the Relativistic Doppler Shift Equation.
Let f'/f go to zero in the two original equations
v- = c/(1 - κ)
v+ = c/(1 + κ)
As viewed from other reference frame which think the time is dilated and space is contracted we have
v'- = c/(1 - κ) γκ^2 = c/(1 - κ) (1 - κ^2) = c/(1 - κ) (1 - κ) (1 + κ) = c (1 + κ)
v'+ = c/(1 + κ) γκ^2 = c/(1 + κ) (1 - κ^2) = c/(1 + κ) (1 - κ) (1 + κ) = c (1 - κ)
We definitely assume these values when we set ε = 1/2 relative to our own reference frame (which means κ = 0). κ ≠ 0 relative to other reference frames (at least as it appears) from our point of view when we choose ε = 1/2.
For example if something is moving 20% the speed of light relative to us and we assume ε = 1/2 for our own reference frame then light moves at:
v'- = c (1 + .2) = 1.2c
v'- = c (1 +- .2) = .8c
The above two are completely in compliance with Einstein's Relativity where we always set ε = 1/2 for our own reference frame. The whole subject of one-way speeds and simultaneity is very subtle and confusing.
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