The essence of the three relativistic theories, that of Galileo, Einstein’s special theory and his general theory, points the way towards a final theory of total relativity, currently unattainable.
Albert Einstein caused a scientific revolution that made it possible to explain the universe, space and time, as an absolute, finite, but at the same time unlimited and curved whole. Even great physicists have had difficulty understanding this. More than a century later, we continue to try to explain it to society.
The essence of the three relativistic theories, that of Galileo, Einstein’s special theory and his general theory, points the way towards a final theory of total relativity, currently unattainable.
Galileo came first
Galileo Galilei (1564-1642) was the first to formulate the principle of relativity, or covariance. He did it in 1632, in his book Dialogue on the two greatest systems of the world. On the second day of dialogues, Filippo Salviati proposes:
“Lock yourself with a friend in the main cabin, under the deck of a rather large ship; and catch flies, butterflies and other flying animals. Hang a bottle so that it is emptied, drop by drop, into a large container below. Make the boat go at the speed you prefer, always the same, without veering to one side or the other. You will see the drops always fall into the container, without deviating towards the stern, even if the boat moved forward while the drops were still in the air. The butterflies and flies will continue their usual flight, as if they never tire of maintaining the speed of the ship, no matter how fast it goes; and it will never happen that they gather at the stern.”
Galileo states that there is a universal law for uniform motion (in a straight line, at constant speed). The law is the same everywhere, whether it is Madrid, Buenos Aires, the Moon or Mars. Either at rest or mounted on a train, ship or rocket moving at a constant speed. In the absence of an external force influencing the system, it will remain the same indefinitely. They are known as inertial reference systems.
If the law is universal, why do we talk about relativity?
The key is that the description of the same reality is different depending on the frame of reference adopted. Seen from the ship, it is the sea around and the port from which it set sail that moves.
Therefore, the law of motion (the mathematical equation) is universal, but its solution (the description of reality) is different in each reference system (initial conditions). Hence the term “relativity”.
The Galilean is the simplest of all relativistic theories. Jean-Marc Lévy-Leblond formulated it similarly to Einstein’s special relativity. However, there was one loose end, apparently small but essential: Galileo’s equations do not work at the speed of light (c), not even at speeds close to it.
Unlikely phenomena
In one of his four fundamental works of 1905 (the year that bears his name). Annus mirabilis), Einstein published his theory of special relativity. Starting from the principle of relativity (from Galileo) and the constancy of c (corroborated by Michelson and Morley’s experiment), he obtained the Lorentz and Poincaré transformations. These had been in use for almost twenty years, but Einstein reformulated them and proved their meaning by interpreting them as simple changes in the reference frame of his special theory. Both return to Galilean transformations, when the speed is much less than c. From there everything fits together, without the space having to be filled with ether.
The consequences derived from the theory of special relativity are extraordinary, difficult to digest for those of us who always move at speeds that are insignificant compared to the speed of light. Unlikely phenomena appear: the simultaneity of two events is relative, time expands, durations shorten… These are phenomena that occur at speeds close to that of light, and which have been confirmed in a multitude of laboratory experiments carried out with elementary particles, in photonics and which have practical applications in everyday life, such as GPS signals.
Although the most extraordinary consequence of the theory of special relativity is the equivalence between mass and energy: E=mc². Einstein stated that the laws of conservation of energy and mass were “one and the same law” .
“The happiest idea of my life”
The general theory of relativity contains only one further postulate: the equivalence principle. Einstein formulated it one day when he had what he called “the happiest idea of my entire life”.
This happened in 1907, while he was working at the Patent Office in Bern. Suddenly, he was startled to think what would have happened if he, at that very moment, had fallen on his feet from the roof of his house. As long as he fell, no gravitational field would exist for him. If you had an object in your hand, a coin or an apple, and you let it go, it wouldn’t fall at your feet, it would remain next to your hand, without separating you from it: you wouldn’t feel… any gravity!
Conclusion: the force of gravity is not special, it is like any other mechanical force that accelerates an object (Einstein, 1907)
The theory of general relativity is based on this principle of equivalence, as simple as the two previous ones of special relativity. And it’s gone!
Of course, it still took Einstein ten long years to formulate the corresponding equations.
The temporal dimension comes into play
When we delve deeper into special relativity, time appears as the fourth dimension of a space-time that transcends the Newtonian conception. This idea, due to Hermann Minkowski, becomes fundamental in the theory of general relativity, in which the very geometry of space-time is influenced by the presence of matter.
His “happy idea” allowed Einstein to understand that gravity can change into pure geometry and express itself in terms of deformation of the fabric of space-time: gravity translates into curvature of space-time.
Einstein successfully predicted the deflection of light from distant stars as it passed near the Sun during the eclipse of May 1919. Furthermore, the existence of black holes, lenses and gravitational waves, the experimental verification of which had to wait many years later.
Today they constitute essential tools for understanding our universe: its origin, its evolution, its future.
What remains to be done
Einstein immediately recognized that his theory was approximate, incomplete. He predicted that others will improve it soon, which has not yet happened, although attempts are being made. General relativity works very well up to very high energies; He did it, precisely, in the collisions of black holes of thirty solar masses. But at even higher energies, capable of folding space-time into layers, difficulties are expected.
Einstein failed to realize Ernst Mach’s principle of total relativity, which includes the most general possible transformations of space-time coordinates. The definitive equations should contain all possible movements and not just those linked to a constant velocity (Galileo) or acceleration (Einstein).
So far, the essentials. From here, an entire universe to explore with these fabulous tools.
Emilio Elizalde, Senior Research Professor, Theoretical Physics and Cosmology, Institute of Space Sciences (ICE – CSIC)
This article was originally published on The Conversation. Read the original.
2024-01-10 13:52:00
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