# What is a stone in simple terms

## Relativity in simple terms

### 1. Light, matter and energy

We know from experience that all straight and uniform speeds only make sense relative to other bodies. For example, the speed of a car we overtake is slower relative to us than that of the oncoming vehicles. But we also know that light always flies past us at the same speed, regardless of whether it is coming towards us or overtaking us. The speed of light is therefore one of the fundamental constants. That was exactly Einstein's great realization! In this chapter we show that the mass of a body therefore increases with increasing speed so much that no body can move faster than light. At the same time, however, the body's energy increases with speed. This leads directly to the famous equation \ (E = mc ^ {2} \), which expresses that mass and energy are two sides of the same coin. We also show that light is pure energy that moves restlessly, has mass, and can turn into matter.

### 2. Light, time, mass and length

Since the speed of light is absolute, lengths, time and mass are relative: their size depends on the speed relative to the observer. Moving clocks go slower and moving lengths shorten in the direction of movement. In addition, the statement “at the same time” has no absolute meaning for events that take place in different places: It depends on the relative speed of the clock and the observer. We deduce from this how the mass of a moving body increases with increasing speed, and how to correctly add speeds.

### 3. Light, electricity and magnetism

We saw in the first two chapters that the theory of relativity gives us many new insights into how light, time, space, mass, energy and other quantities are related. Einstein's achievement thus consisted in rethinking fundamental concepts such as “space” and “time”, “length” or “simultaneity”, concepts which the famous philosopher Immanuel Kant still thought their meaning was in human brain designed from the outset so that we can understand the world at all. But Einstein's theory did not come about in a vacuum: the blueprint for the theory was already there! It was and still is the theory of moving electrical charges, namely electrodynamics. The reason for this is very simple: While mass, time or length all depend on the relative speed to the observer, the electric charge just like the speed of light does not depend on it, so it is absolute. We show this with a thought experiment in which an electric current flows through a wire and thus creates a magnetic field. In fact, it was precisely this thought experiment that was the starting point for Einstein's special theory of relativity.

### 4. Acceleration and inertia

The first three chapters dealt with the influence of linear, uniform movement on space, time and mass. This part of the theory of relativity is the so-called special theory of relativity. However, in order to get to a certain speed, or to change the direction of the speed, we have to accelerate. The simplest case is the rotational movement, where the value of the speed remains the same and only the direction of the

Speed changes. In this case, the school geometry is no longer correct because lengths depend on the direction in

shrink to different degrees. Clocks react even more strangely, which is expressed in the famous twin paradox that we

discuss in detail. When we accelerate, lengths in space change as a function of time due to the changing speed, and space becomes spacetime. For example, the term “shortest connection between two points in space” from school geometry no longer makes sense.

### 5. Inertia and gravity

We know that astronauts are floating in a spacecraft orbiting the earth, so there is no force acting on them. In this chapter we show that in fact gravity is not a force that attracts us. But why then do objects fly around the earth on curved orbits? The reason is that gravity bends spacetime around any heavy mass. It is crucial that all sufficiently small and light masses fall freely in the same way if they are not hindered by air resistance or the like. In other words: all types of matter react equally to gravity. This is the so-called equivalence principle, with the help of which we study the curvature of spacetime.

### 6. The principle of equivalence in action

In this chapter we apply the equivalence principle introduced in the previous chapter: We want to find out how exactly gravity bends space-time in the vicinity of spherical objects such as stars or planets. We go to a place far enough away from the sphere and let ourselves fall free from there. While we are falling freely towards the ball, no force is acting on us because of the principle of equivalence. Nevertheless, we are falling faster and faster towards the ball. This rate of fall determines by what proportion of the clocks lying on the sphere, or rods on the sphere shorten, relative to a far enough distant, stationary observer. In other words, as soon as we consider this rate of fall in Chap. 8 with the help of the Einstein equation of gravity, we will know the curvature of space-time around such a heavy sphere.

### 7. How mass creates gravity

How does mass bend spacetime? In other words: How does mass create gravity? The famous one provides the answer

Einstein equation of gravity, which we explain in simple terms. This is possible because nature is that

has chosen the simplest conceivable law of gravitation. Essentially, gravity shrinks a given volume.

We explain in detail how this law of gravitation is compatible with the special theory of relativity. But mass

not only generates gravity, but also reacts to gravity, as the principle of equivalence shows us. We show,

that these two natural laws are in harmony with each other, and that is why the general theory of relativity

really delivers the simplest conceivable theory of gravity.

### 8. Solution of the Einstein equation of gravitation

We saw in the previous chapter that the Einstein equation of gravity determines how mass creates gravity. In this chapter we get to know the most famous solution of the Einstein equation of gravity, namely the Schwarzschild solution. It shows us how space-time bends in the vicinity of a spherical mass such as a star or a planet. To do this, we calculate the speed of fall of a test mass that falls freely from a resting place far enough away from the sphere. This and the results of the previous chapters enable us to express the curvature of spacetime around a spherical mass in simple terms. We also see how Newton's law of gravitation results as an approximation.

### 9. Application of general relativity

We present the classic effects that can be explained with the help of the general theory of relativity: We show, among other things, the angle at which a ray of light curves as it sweeps past the edge of the sun. We will see that we not only need the curvature of space near the sun, but also the curvature of spacetime, since otherwise we would only get half of the observed value. We also show that the curvature of spacetime slowly rotates the orbits of the planets around the sun. We calculate this so-called perihelion rotation without complicated mathematics. We also show that there can be black holes and how big and heavy they have to be. Finally, we apply the Einstein equation of gravity to space as a whole and see why there must have been a Big Bang. But we also show that we do not yet understand how the curved spacetime influences the smallest structures in space, i.e. the elementary particles.

### 10. Appendix

We carry out several calculations from the main part in detail here.

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