Herr Einstein's derivation of the "Lorentz" transformations explained.
Herr Einstein defines time as follows:
"Die letztere Zeit kann nun definiert werden, indem man durch Definition festsetzt, daß die "Zeit", welche das Licht braucht, um von A nach B zu gelangen, gleich ist der "Zeit", welche es braucht, um von B nach A zu gelangen. "
which translates into English as
"We have not defined a common "time" for A and B, for the latter cannot be defined at all unless we establish by definition that the "time" required by light to travel from A to B equals the "time" it requires to travel from B to A.
Let A and B be the end points of the train from which light is emitted, reflected and received and let us determine their common time.
Making use of Herr Einstein's equation:
and his definition of x' = x-vt which is "independent of time" (Herr Einstein's way of stating that the length of the train will not change tomorrow and is the same as it was an hour ago), we see that at frame 0 all clocks read zero, and the time for light to go from the camel's right ear (B) to a point in space off further to our left (A) is equal to the time for light to go from A to B in the camel's "stationary" (and inertial) frame of reference.
To simplify arithmetic, I have chosen the speed of light to be c = 5 units per second and the speed of the train (which is moving past the camel) to be 0.6c, or 3 units per second. These are simply choices of units, because everything should be as simple as possible, but not simpler. The train can attain this enormous speed because it is pulled by a Rocket. Now because all clocks are set to the same time, t, we can safely assume, in agreement with experience, they are synchronized, at least at the beginning of the thought experiment, which is what this is. The length of the train is 32 or 40 units, we'll see why later.
The next moment of interest is the moment when the green ray reaches the rear of the train (which is no longer at A because the train has moved):
In agreement with experience we further assume Herr Einstein's definition of time to be correct, hence 8 seconds have elapsed since the beginning of the experiment with the light travelling at 5+3 = 8 units per second in the inertial frame of reference of the train, although the red light from the back of the train, travelling at 5-3 = 2 units per second, has still to reach the locomotive. We have yet to find a common time for A and B. For the next few frames the green ray is reflected at the rear of the train and become an orange ray, chasing after the red ray until the red ray arrives at B (which is not the camel's right ear, but approximately at an ear):
During this interval, "moving" clocks run slow compared to the clock on the right, which is stationary. For the next few frames until the end of the experiment, half a "moving" clock run fast, the other half runs slow, but they do not catch up enough to match the high speed camel's clock in the "stationary" frame:
16 seconds have elapsed in the "moving" inertial frame of reference of the train (by both hands), 20 seconds have elapsed in the "stationary" inertial frame of reference of the camel. The clocks at the ends of the train (which are not at A and B) are now in agreement, in agreement with experience, because in agreement with experience we further assume they have to agree with Herr Idiot Einstein. Thus we have found a common time for A and B. The equations relating the time in the "stationary" frame and the "moving" frame are linear, Herr Einstein said so : "In the first place it is clear that the equations must be linear on account of the properties of homogeneity which we attribute to space and time." Unfortunately Herr Einstein does not tell us that in the second place it is clear the equations are not linear on account of his stupidity. The equation used to derive the cuckoo transformations:
does not contain the term c+v on the right hand side, that was put there by me because Herr Einstein was a half-arsed halfwit who thought half (an apple plus an orange) was only ever an apple, never an orange and needed a Rocket up his arse, as do his moronic disciples. To discover why the length of the train is either 32 or 40 units, that is very simple. The speed of light has to be made 5 units per second in all frames of reference, so the Herr Einstein says 40 = 8 seconds times 5 units per second to agree with the idiot Lorentz.
So, in agreement with experience, it is clear that we further assume the train shrinks when it travels at 0.6c and this is known as the Lorentz contraction. We see it pass by at 32 units, but it really is 40 units.
The camel sees the train "Lorentz contracted" to 32 units. Einstein was a camel. All we need do is discover whether he was dromedary or bactrian.
For further reading continue at http://www.androcles01.pwp.blueyonder.co.uk/Smart/Smart.htm