Theory of relativity for dummies: The content simply explained

When one thinks of the theory of relativity, the formula E = mc² usually comes to mind. This practical tip will tell you what this formula is all about and what you should know about "relativity".

The theory of relativity simply explained

The theory of relativity deals with space, time and gravitation and was a real milestone in physics. Many things like warp drive and time travel made a little bit more possible. It is composed of two theories.

1. The special theory of relativity. It explains the behavior of time and space from the perspective of observers.
2. The general theory of relativity. It describes gravity as the curvature of time and space, which is created by large masses such as stars.

Explanation

In physics, a reference system is called a spatio-temporal structure, which is required to describe location-dependent processes exactly. An inertial system is a reference system in which force-free particles rest or traverse straight paths at constant speed. For example, time passes more slowly in one inertial system than in another.

• According to Einstein's special theory of relativity, all inertial systems are equal in nature. If time passes faster in one system than in another, both properties apply. Time flies faster and at the same time normally.
• However, one must note that no system, object or particle can be faster than light. At 299792.458 km / s, the speed of light (c) is an upper limit for speeds. Unfortunately, flying a spaceship at "twice the speed of light" in some sci-fi films is not possible.

E = mc² - that means the formula

Almost everyone knows them, but nobody knows how to actually use them: we are talking about the famous formula E = mc². With this the energy can be calculated depending on the relative mass.

• According to Einstein, energy and mass (e.g. with particles) are equivalent.
• The total energy (E) can be calculated using the formula E = mc² with m = m ': √ (1 - v²: c²). In this case m 'is the mass at rest. However, the formula cannot be applied to "classical" physics, but only applies to relativistic physics.

The theory of relativity: what are time dilation and length contraction?

Depending on the speed (of an object), the time (which passes relative to the observer) or the length (of the object) can be influenced. Time and length depend on the speed.

• The faster an object moves in space, the slower time passes relative to a resting observer. Even in the vicinity of large crowds, time passes more slowly. You can find more detailed information in our article on "Time dilation".
• When an object moves at high speed in space, its length (in the direction of speed) is also compressed. Here too you will find a separate article dealing with length contraction.

Curvature of space and time: Large masses in space

Finally, we would like to dedicate ourselves to the large masses in space (such as a planet).

• As you already know from our article on time dilation, time passes more slowly near large masses.
• Large masses, such as a star, bend space (and time). You can think of this phenomenon as a large cloth that "bends" down when you put something heavy on it, such as a watermelon. Space-time is curved similarly. This means that light is also deflected by large masses.

Einstein's Theory of Relativity: You should be able to use these formulas

Many different formulas are used in relativistic physics. We'll show you the most important ones you should know.

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• The formula for the relative time is ∆t '= ∆t: √ (1 - v²: c²). In this example we would like to calculate how many seconds pass in a system that moves at 200000 km / s: ∆t '= 5s: √ (1 - (200000000 m / s) ²: (299792458 m / s) ² ) ≈ 6.712 s. This means that while 5 seconds pass in an accelerated system, around 7 seconds pass in a stationary system! At the speed of light there would be a 0 in the denominator. This would result in ∞.
• The formula for length contraction is l = l '⋅ √ (1 - v²: c²). The relative length depends on the basic length and the speed. At the speed of light, the length would be 0!
• You also know the formula E = mc² with m = m ': √ (1 - v²: c²) from this article.
• Finally, there is the formula for the relativistic Doppler effect (for professionals). You will notice the Doppler effect when, for example, a police car with a siren drives past you. This phenomenon can be applied analogously to relativistic physics: the frequency depends on the speed. If the transmitter and receiver of electromagnetic waves (eg light) move away from each other, the frequency is changed. The following applies: f '= f ⋅ √ ((1 - v: c): (1 + v: c))
• If you master these basic formulas, you can already solve many relativistic problems.