People in the same "frame" measure how long something takes to happen. Their clocks keep the same time. But in another "frame" their clocks move at a different rate. The reason this happens is as follows. No matter how an observer is moving, if he measures the speed of the light coming from that star it will always be the same number.
Imagine an astronaut were all alone in a different universe. It just has an astronaut and a spaceship. Is he moving? Is he standing still? Those questions do not mean anything. Why? Because when we say we are moving we mean that we can measure our distance from something else at various times. If the numbers get bigger we are moving away. If the numbers get smaller we are moving closer. To have movement you must have at least two things. An airplane can be moving at several hundred kilometers per hour, but passengers say, "I am just sitting here."
Suppose some people are on a spaceship and they want to make an accurate clock. At one end they put a mirror, and at the other end they put a simple machine. It shoots one short burst of light toward the mirror and then waits. The light hits the mirror and bounces back. When it hits a light detector on the machine, the machine says, "Count = 1," it simultaneously shoots another short burst of light toward the mirror, and when that light comes back the machine says, "Count = 2." They decide that a certain number of bounces will be defined as a second, and they make the machine change the seconds counter every time it has detected that number of bounces. Every time it changes the seconds counter it also flashes a light out through a porthole under the machine. So somebody outside can see the light flashing every second.
Every grade school child learns the formula d=rt (distance equals rate multiplied by time). We know the speed of light, and we can easily measure the distance between the machine and the mirror and multiple that to give the distance the light travels. So we have both d and r, and we can easily calculate t. The people on the spaceship compare their new "light clock" with their various wrist watches and other clocks, and they are satisfied that they can measure time well using their new light clock.
Now this spaceship happens to be going very fast. They see a flash from the clock on the space ship, and then they see another flash. Only the flashes do not come a second apart. They come at a slower rate. Light always goes at the same speed, d = rt. That is why the clock on the spaceship is not flashing once a second for the outside observer.
Special relativity also relates energy with mass, in Albert Einstein's E=mc formula.
E=mc, also called the "mass-energy equivalence", is one of the things that Einstein is most famous for. It is a famous equation in physics and math that shows what happens when mass changes to energy or energy changes to mass. The "E" in the equation stands for energy. Energy is a number which you give to objects depending on how much they can change other things. For instance, a brick hanging over an egg can put enough energy onto the egg to break it. A feather hanging over an egg does not have enough energy to hurt the egg.
There are three basic forms of energy: potential energy, kinetic energy, and rest energy. Two of these forms of energy can be seen in the examples given above, and in the example of a pendulum.
A cannonball hangs on a rope from an iron ring. A horse pulls the cannonball to the right side. When the cannonball is released it will move back and forth as diagrammed. It would do that forever except that the movement of the rope in the ring and rubbing in other places causes friction, and the friction takes away a little energy all the time. If we ignore the losses due to friction, then the energy provided by the horse is given to the cannonball as potential energy. (It has energy because it is up high and can fall down.) As the cannonball swings down it gains more and more speed, so the nearer the bottom it gets the faster it is going and the harder it would hit you if you stood in front of it. Then it slows down as its kinetic energy is changed back into potential energy. "Kinetic energy" just means the energy something has because it is moving. "Potential energy" just means the energy something has because it is in some higher position than something else.
When energy moves from one form to another, the amount of energy always remains the same. It cannot be made or destroyed. This rule is called the "conservation law of energy". For example, when you throw a ball, the energy is transferred from your hand to the ball as you release it. But the energy that was in your hand, and now the energy that is in the ball, is the same number. For a long time, people thought that the conservation of energy was all there was to talk about.
When energy transforms into mass, the amount of energy does not remain the same. When mass transforms into energy, the amount of energy also does not remain the same. However, the amount of matter and energy remains the same. Energy turns into mass and mass turns into energy in a way that is defined by Einstein's equation, E = mc.
The "m" in Einstein's equation stands for mass. Mass is the amount of matter there is in some body. If you knew the number of protons and neutrons in a piece of matter such as a brick, then you could calculate its total mass as the sum of the masses of all the protons and of all the neutrons. (Electrons are so small that they are almost negligible.) Masses pull on each other, and a very large mass such as that of the Earth pulls very hard on things nearby. You would weigh much more on Jupiter than on Earth because Jupiter is so huge. You would weigh much less on the Moon because it is only about one-sixth the mass of Earth. Weight is related to the mass of the brick (or the person) and the mass of whatever is pulling it down on a spring scale – which may be smaller than the smallest moon in the solar system or larger than the Sun.
Mass, not weight, can be transformed into energy. Another way of expressing this idea is to say that matter can be transformed into energy. Units of mass are used to measure the amount of matter in something. The mass or the amount of matter in something determines how much energy that thing could be changed into.
Energy can also be transformed into mass. If you were pushing a baby buggy at a slow walk and found it easy to push, but pushed it at a fast walk and found it harder to move, then you would wonder what was wrong with the baby buggy. Then if you tried to run and found that moving the buggy at any faster speed was like pushing against a brick wall, you would be very surprised. The truth is that when something is moved then its mass is increased. Human beings ordinarily do not notice this increase in mass because at the speed humans ordinarily move the increase in mass in almost nothing.
As speeds get closer to the speed of light, then the changes in mass become impossible not to notice. The basic experience we all share in daily life is that the harder we push something like a car the faster we can get it going. But when something we are pushing is already going at some large part of the speed of light we find that it keeps gaining mass, so it gets harder and harder to get it going faster. It is impossible to make any mass go at the speed of light because to do so would take infinite energy.