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# Special theory of relativity

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Special Theory of Relativity (or Special relativity) is the formal theory elaborated by Albert Einstein in 1905 in order to draw all the physical consequences of Galilean relativity and the principle according to which the speed of light in a vacuum has the same value in all Galilean (or inertial) reference systems, which was implicitly stated in Maxwell’s equations (but interpreted quite differently until then, with Newton’s “absolute space” and the ether).

Galilean relativity states, in modern language, that any experience made in an inertial reference system is perfectly identical in any other inertial reference system. Having become the “principle of relativity”, its statement will then be modified by Einstein to be extended to non-inertial references: from “restricted”, relativity will become “general”, and will deal furthermore with gravitation, which was not present in the special relativity .

The theory of special relativity has established new formulas to move from one Galilean reference to another. The corresponding equations lead to predictions of phenomena that run counter to common sense (but none of these predictions have been invalidated by experience), one of the most surprising being the slowing down of clocks in motion, which made it possible to design the thought experiment often called twins paradox. This phenomenon is sometimes used in science fiction.

Special relativity has also had an impact in philosophy by eliminating any possibility of existence of absolute time and durations in the universe as a whole (Newton). Following Henri Poincaré, it forced philosophers to ask the question of time and space differently.

#### History

In Newtonian mechanics, the speeds are added during a change of reference: these are the transformations of Galileo. For example, if a rocket moving away from the Earth at a speed of 7 km/ s fires a cannonball forward at a speed of 1 km/s from the rocket, the speed of the projectile seen from Earth will be 8 km/s; if the cannon is pulled backwards, its observed speed from Earth will be 6 km/s.

At the end of the nineteenth century, James Clerk Maxwell established the equations governing electromagnetic waves, including light waves. According to this theory, the speed of light should depend only on the electrical and magnetic properties of the medium, which posed a problem in the case where this medium is the vacuum because it suggests an independence of the speed of light compared to the reference frame of the measuring instrument: if a light beam is emitted from the rocket forwards or backwards, the speed of the light measured with respect to the Earth will be the same, unlike the ball. The hypothesis of the ether, the medium of propagation of light, therefore a rather natural hypothesis, was to remove for light this property and render its propagation compatible with Galilean relativity. In 1887, an experiment was conducted by Michelson and Morley to measure the speed of the Earth with respect to this ether: an experiment similar to that of the rocket mentioned above, and where the Earth itself holds the role of the rocket . They wanted to measure this speed by highlighting the difference in speed of light between different possible propagation directions. Not having detected a significant difference, the result of this experiment proved difficult to interpret, so much so that their authors went so far as to imagine an unexplained contraction of the measuring instruments in certain directions: the special relativity will justify that afterwards.

(Albert Einstein and Hendrik Lorentz, 1921.)

Formulas of transformation to pass from one observer to another were established by Hendrik Lorentz before 1904; they were equations of compatibility whose meaning was unclear to the author. Other physicists, such as Woldemar Voigt (1887), had a similar approach earlier. Henri Poincaré published articles to find an interpretation, shortly before Albert Einstein. The contribution of other scientists in the emergence of the theory of special relativity has been the subject of controversy, particularly in the 2000s.

In 1905, in his article entitled O the Electrodynamics of Moving Bodies, Albert Einstein introduced relativity as follows:

• Ether is an arbitrary notion that is not useful for the expression of the theory of relativity.
• The speed of light in vacuum is equal to c in all inertial reference systems. It does not depend on the movement of the source or the observer.
• The laws of physics respect the principle of relativity.

The resulting Lorentz equations are consistent with physical reality. They have unintended consequences. Thus an observer attributes to a moving body a length shorter than the length attributed to the same body at rest, and the duration of the phenomena which affect the moving body is increased with respect to this “same” duration measured by immobile observers by relation to this body.

Einstein also rewrote the formulas that define momentum and kinetic energy so as to make their expression invariant in a Lorentz transformation.

Time and the three space coordinates playing inseparable roles in Lorentz’s equations, Hermann Minkowski interpreted them in a four-dimensional space-time. Note, however, that time and space remain of different natures and can not be assimilated to each other. For example we can turn around in space while it is impossible in time.

In 1912, Lorentz and Einstein were nominated for a joint Nobel Prize for their work on theory. The recommendation was from Wien, winner of 1911, who states that “although Lorentz must be considered the first to have found the mathematical content of the principle of relativity, Einstein succeeded in reducing it to a simple principle. We should therefore consider the merit of the two researchers as comparable”. Einstein never received a Nobel Prize for relativity, this prize being, in principle, never granted for a pure theory. The committee waited for an experimental confirmation. By the time it came up, Einstein had moved on to other important work.

Einstein will finally be awarded the Nobel Prize in physics in 1921 “for his contributions to theoretical physics, and especially for his discovery of the law of the photoelectric effect”.

1. ##### Special theory of relativity – Dictionaries
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