Consider as an example the field of gravity of the earth. If you are in a free falling lift the field of gravity is disappeared for you. Another example is a free falling airplane. The passengers move in a weightless space.

An observer on the surface of the earth will say that the lift (with his passengers) and the airplane are falling. The cause is for him the field of gravitation of the earth.

The field of gravity exist (for the observer on the surface of the earth) and it exist not (for an observer in a free falling lift).

On the opposite site we feel a force in a verhicle which accelarates (a car, a airplane), it presses us into the seat. The same would be done by a field of gravitation, if it suddenly will occur.

The resulting idea is the following: the field of gravitation disappeares through changes in the state of move (a free falling lift) or it appeares through acceleration (a car, an airplane, a rocket). One distinguishes between fields of gravitation caused through matter (real fields) and such fields that are caused through accelaration (fields of inertia).

The real fields are much more complicated then the inertial ones. As an example the field of gravitation of the earth is spherical symmetric. There exist no move in the 3 dimensional space which can cause a 3 spherical symmetric field of gravitation (the field of an rotating disc is 2 dimensional). The spherical symmetric field disappears only for very small objects, otherwise the tide forces work. If the tide forces are big enough they destroy the object.

On this way the rings of the planet Jupiter may be created. A moon which has approached the planet could be teared to pieces throught the tide forces.

The field of gravity caused by acceleration results from the **inertia
of matte**r, the field of gravity of the earth from
the **heavy
matter**.

The heavy matter can be measured by the force that works on it on the surface of the earth through gravity. On a matter of 1 kg works a gravity force of 9.81 Newton (this is an average value, on the poles of the earth the field of gravity is a little bit smaller then on the equator of the earth).

The inertia matter can be measured if the friction can be neglected (as an example consider a waggon with a magnet below hanging over a magnetic track). The force needed to give the waggon a certain acceleration will be measured. With the result the inertia matter can be calculated (using the Newton formula F = m * a, m is the inertia matter, a is the acceleration caused by F, F is the force).

One of the foundations of General Relativity is the statement that heavy matter and inertial matter are equivalent (these different kind of matter are distinguished only through a numerical constant, so the quotient of heavy matter and inertial matter is always the same).

If this statement is not true General Relativity fails.

Consider two stones, one has the double quantity of heavy matter as the other, that means that the stone with the bigger heavy matter gets as twice a force from the gravity field as the other one.

It they fall down from a tower both stones reach the bottom of
the
tower
at the same time (the friction with air can be neglicted). The
stone
with
the bigger heavy matter has as twice inertia matter as the other
one.

In the General Theory of Relativity one works often with transformations of coordinates. First a simple system is used (a system where gravity disappears, like the interior of a free falling lift). In this simple system the laws of nature are formulated. The result is then transformed into a general coordinate system (which may describe the gravity field of the earth). It's a change in the sight of view from which phenomenons are considered.

On this way one obtains laws of movement in an arbitrary field of gravity. The form of the laws allows a geometric interpretation: a matter moving in a field of gravitation moves in a 4 dimensional curved space time.

The force of gravity can be explained as a result of this curvature.

For the purpose to describe the relation between the field of
gravity
and the matter causing it one needs the **Einstein
field equations**. Matter and energy are
considered to be
equivalent following the equation E = m * c^{2 }
.
Here
m is the heavy matter, c the velocity of light and E the energy.
After
this equation each matter contains a certain quantum of energy.

Matter and energy both cause gravity.

If the matter insite a limited space exceeds an allowed maximum the curvature of spacetime can be closed. The result is a black hole.

It is interesting that the matter causing a black hole may have a distance greater then 0 from each other. If a lot of stars approach each other the whole quantity can cause a black hole. It is not clear today if the whole energy of the universe is great enough to close the universe. In this case we live insite a black hole.

**Special Relativity** is a special case
of
the general theory, it excludes gravitation. This doesn't mean
that
matter
is not considered insite the theory, but in the focus of
interest is
only
the inert matter.

Special relativity says that matter grows with velocity. This phenomenon can be observed using particle accelerators. With the growth of the particle's velocity it is more and more difficult to hold the particles on its track (which is usually a circle). In this context only the inert matter is important. Calculating the necessary energy to hold them on their track shows that the matter of the particles must grow. This is in correspondence with the predictions of Special Relativity.

Consider instead of particles an outer space rocket. If it is accelarated to a great velocity its matter grows.

This situation should be considered in greater detail.

The matter of the rocket grows for an observer on the earth but not for a passenger insite the rocket. He would also measure a bigger matter for the observer remaining on the earth as this one would measure for himself (for the passenger insite the rocket the observer on the earth moves away).

For the observer on the earth the rocket can never reach the velocity of light, otherwise its matter would grow to infinity.

The result is that matter in movement always gives a greater quantity than the same matter in rest and that matter in movement is always under the limit of the velocity of light.

Elementary particles like photons which move with the velocity of light have no rest mass, so they can always only exist in movement.

If the rocket is accelarated (maybe through the discharge of fuel) its velocity grows, but remains always under the limit of the velocity of light. This is valid for the passenger in the rocket and for the observer remaining on the earth.

The observer on the earth would say that
the
clocks
insite the rocket go slower than his own ones. This effect is
called **time
delation**.

The observer in the rocket underlies the
effect
of **space contraction**.
It works dynamically (increasing) as long as the rocket
accelerates and
it is fixed if the rocket moves with a constant velocity.

Space contraction says that the distance between the earth and the goal of the rocket for itspassenger will be smaller then for the observer remaining on the earth. This is valid for each velocity of the rocket. So the passenger in the rocket needs fewer time to travel along a certain fraction of the whole distance as it will be expected by the remaining observer on the earth.

As a consequence for the passenger insite the rocket the time interval until he reaches his goal is smaller as the observer remaining on the earth will assume.

If the passenger returns with his rocket so he has lost fewer time than his partner remaining on the earth, but he also has had fewer times to make life experiences.

This effect can be very extreme, it is limited by the amount of fuel that can be taken away with the rocket and through the acceleration that is possible for a human.

For the observer remaining on the earth the distance the rocket has to cover doesn't shrink. He got the impression that the clocks insite the rocket go slower then his own ones (time dilation).

For this penomenon exists experimental evidence. Elementary particles which move quickly have a longer life time as the same particles remaining in rest (many elementary particles have only a certain lifetime, after that they are disintegrated into its constituent parts). The observation is that this particles having a great velocity cover a greater distance as it is expected.