Einstein abandoned absolute time and fixed space so that the speed of light could be the same for everybody observing it, as Maxwell's Laws said it would be.
Here is where that becomes a problem. If you walk up an escalator, you reach the top faster than if you were walking up a non-moving stairway.
In the diagram at the left, v is how fast you are walking, u is the velocity of the escalator, and V is how fast you are "really" going, determined by someone standing on the floor below. It seems pretty obvious that V=u+v.
Not so if you are a pulse of light that someone has projected upward along the escalator. That pulse of light has to have the velocity of light (a number called 'c' that is equal to 186,000mi/sec), both with respect to the escalator and with respect to the observer on the floor.
That's what the Lorentz transformation is all about. It was designed by Lorentz so that when you add the escalator's velocity, u, to the speed of light 'c' along the escalator, you still get 'c' as seen from the floor below.
This may not seem worth discussing, because the speed of light is so great, that, whether you add the speed of the escalator to it or not would seem to make very little difference.
But imagine (just imagine!) an escalator moving at half the speed of light (½'c'). Wouldn't then the pulse of light shown in the picture at the right have to be approaching the top of the escalator at 1½ times 'c'?
No, because Maxwell's Law about the propagation of light says light always travels at "the speed of light;" that means 'c.'
If you find that hard to accept, then you will find the story of relativity an intriguing revelation of how that comes about.
The Lorentz transformation is the mathematical way of treating velocities so that the speed of light will always come out to be equal to 'c.'
This transformation gives unanticipated results not only if the projectile is a pulse of light, but for any object whose speed is right up there close to the speed of light, 'c.'
How about a rocket travelling at 100,000mi/hr. Inside the rocket, a bullet is fired at a speed of 50,000mi/hr. You would expect the bullet to be travelling at 150,000mi/hr from the point of view of someone standing still in space outside the rocket.
Not so. That bullet in the rocket as seen from outside the rocket has a total speed of only 131,000mi/hr.
In this short chapter you will learn to solve questions like this, and even more important, you will learn how Einstein's solution to Maxwell's conundrum brought this fact to light, so to speak!
Onward to Chap 14: Simultaneity
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