Below are five tables that summarize basic formulas of Special Relativity. If you want to try them out, fill in the data fields and click the "calculate" button.
Those five formulas are intimately bound. If you would take only one of them into consideration then you could easily demonstrate that special relativity is a nonsense. But if you are using them altogether then everything becomes fluent and perfectly logical.
The speed of light is represented by the symbol c. That's 299,792,458 m/s (in vacuum).
Let's consider a rocket. When the rocket stands still compared to you, it has a length of l_{0}. (It may be immobile next to you or parked far away...) When it will be traveling at speed v compared to you, you will see that it now has a shorter length of l. (The diameter of the rocket did not change.) In other words: when the rocket was at rest compared to you, it had a length of l_{0}. Now that it shears at a high speed v compared to you, you will see or measure that it has a shorter length, of l. Yet a person aboard the rocket will still claim it has a length of l_{0}, because that person stands still compared to the rocket.
If an hourglass lasts t_{0} second when it is in your hand (or anywhere else, but immobile compared to you), then when it is aboard a rocket that travels at speed v compared to you, you will see that it lasts longer: t seconds. Yet for any person aboard the rocket, it still lasts t_{0} second.
You put two clocks a distance d apart along a rocket's body. If the rocket now travels at a speed v compared to you and everybody onboard the rocket says that the clocks are synchronized, then you will see that the clocks are not synchronized. The forward clock is t seconds back.
If a rocket travels at a speed v compared to you and a snooker ball is made to roll on the rocket's flour towards the front and the passengers inside the rocket say that the ball rolls with a speed v_{m} compared to them, then v_{s} is the speed of the ball compared to you.
If an object has a mass m_{0} when it is motionless compared to you, then it will have an increased mass m when it moves at a speed v compared to you.
Galilean Relativity states the following:
Whatever steady speed a closed laboratory moves at, any experiment you do inside the laboratory will give the same result. So you will never be able to determine at what steady speed that laboratory moves, just by doing experiments inside the laboratory.
Whatever place you put a closed laboratory, any experiment you do inside the laboratory will give the same result. So you will never be able to determine where the laboratory is, just by doing experiments inside the laboratory.
Whatever direction you turn a closed laboratory in, any experiment you do inside the laboratory will give the same result. So you will never be able to determine what direction the door of the laboratory is directed towards, just by doing experiments inside the laboratory.
Special Relativity adds the following:
Any laboratory, moving at any constant speed towards any constant direction, measuring the speed of some light produced by itself or by any other laboratory moving at any speed and in any direction, will always measure that the speed of that light is 299,792,458 m/s.
In order to keep this rule true, the Universe squeezes every objects. And changes the speed of every clock.
General Relativity adds the following:
A little and closed laboratory cannot know whether it is placed aboard an accelerating rocket, sitting on the surface of a planet or placed on the edge of a huge rotating wheel.
This implies once more that objects are squeezed and that the speed of clocks changes. For example, clocks on Earth run a little slower than clocks on the Moon. Even space itself is bend and curved...
General Relativity is shipped with an impressive calculation system. It can compute out just any situation: accelerating or turning laboratories, electromagnetic or gravitational fields, encounters with big masses... Yet it can be quite difficult to handle.
That statement of objects, clocks and space being squeezed by the Universe is just a way to express the reality. There are other ways round to describe the reality; other points of view, that come out with the same physical results. Be open to them.
Maybe you conclude that the Universe simply cannot behave like a Tex Avery cartoon and that the content of texts like this one must be erroneous. First of all, in a Tex Avery cartoon the characters squeeze and expand at random. While in the Universe, it happens a very accurate, mathematic and reproducible way. Second, this all has been tested out thoroughly. From the faintest atomic phenomenon up to stars, till now everything obeys the formulas of Relativity. (Yet there seems to be a problem with the universe as a whole. It seems to expand in a way that may be not compatible with General Relativity.)