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When I was young, I was fascinated by elevators: When you went up, everything else
seemed to go down. When you go down, the world goes up.
When I got older, I got used to the notion that the world isn't really going up or down,
but that the only one that was moving was me.
Yet, it is somewhat a mistake to ignore what we see. The truth is that: going forward,
for example in a train, does not affect the earh too much. But the earth is moving relative
to the people inside! That's the basis of relativity.
Sound simple. Someone moving at relative speed to someone else, would look to the other one,
as if he was moving in opposite direction and in the same speed, and that is as complicated
as it gets.
But something did not fit. You see, the knowledge gained during the last decades of the 19th
century, gave more than a hint to the possibility that light does not adhere to relativity.
Everyone, moving fast or slow, seemd to be having essentially the same speed of light.
It seemd benign, but look at that: This craft travels at speeds close to the speed of light.
What you just saw, was two simultaneous lightning strikes at the forefront and back of the craft
Now, you can see the light from both events coming towards the person in the middle, as
he is moving toward the light from the front, and the light from the back have to chase
him. So, he will see the lighting from the front first. So far so good.
However, and pay close attention to this: Relative to him, the light comes at the same
speed, and takes the same time to reach him from both directions. So for him, seeing the
front lightning strikes before the one in the back, means the front striked first!
Something is very wrong. Or is it?
The greatness of Einstein was that he managed to understand it is possible to reconcile
Relativity with the notion of unchanging speed of light. He did that by adding something
to the Theory of Relativity: Time. Time, he said, is relative. Simultaneity is
relative. And that's not all:
Let's take a look at the length of the craft: We'll assume we can estimate the distance
between the lightings in the photo. As we've seen earlier, relative to the person inside,
and the craft, the front meets point A first, and the rear meets B a little later. So from
inside, length A to B seems to be shorter. This is what's called length contraction.
The factor by which the contraction occurs is called the Lorentz Factor.
The Lorentz factor stays close to 1 for most velocities but rise fast when approaching
the speed of light.
In almost the same way, it can be shown that a moving clock will tick slower than a stationary
one, and by the same factor.
The general rules of relativistic location and time have been summerised by equations
called "The Lorantz equations". These equations have some other interesting implications.
For example, if someone throws a ball in a moving car, it’s reasonable to assume
that we can sum that speed, and the speed of the car, and that will be the speed of
the ball relative to the outside world. The Lorentz equations tell us it will actually
be slower. Never over the speed of light in vacuum, by the way.
But the most famous implication stems from the derived equation for energy:
What we get is "Energy equal to the lorentz factor, multiplied by mass, and the speed
of light squared". While fast things have a lot of energy, when they're standing still
(lorentz factor of 1), they do have some energy... quite a lot actually.
It seems that everything has energy just by having mass. Releasing or capturing energy,
by the way, changes the mass.
While these predictions of his theory seem weird at best, and are definitly not apparent
on our day-to-day experiences, they have been tested innumerable number of times. Clocks
really do tick slower at different speeds, lengths do change, and so on.
Time is relative. And everything that stems from it is, well, weird...
But real.