Theory of relativity

Theory of Relativity . It is the theoretical framework that explains the behavior of the universe at a macro level, that is, at the level of galaxies , planets , star or solar systems and other celestial bodies . Any theory of motion that attempts to explain how speeds (and related phenomena) appear to vary from one observer to another would be a Theory of Relativity.

History

At the end of the 19th century, the scientific community knew that there was much to create and invent, applying the various physical principles discovered, such as electricity, magnetism and mechanics, but they were convinced that there was almost nothing new left to explain, nature had been discovered in its entirety and now they only had to begin to apply that knowledge to human activities for their own benefit and well-being.

Until then, the foundations of physics were two great columns built by two of the greatest scientists in science. One was the theory of mechanics, where all the knowledge of kinematics and dynamics from Aristotle to Galileo was condensed into a single theory, known today as Classical Mechanics , or Newtonian Mechanics . The other column supported the other half of physics, referring to the magnetic and electrical effects known since the Greeks to the latest advances of Oersted, Faraday and Lenz. All this technical information was unified in the Theory of Electromagnetism of the brilliant English scientist James Maxwell .

But in reality something was wrong, because some new questions or unknown physical effects were appearing, and it was thought that by “polishing” the concepts of the moment a little they could be easily explained, so they were almost underestimated by many of the researchers of that time.

Theories

Yo

Absolute, true, mathematical time, in itself and by its own nature, flows in an equable manner and without any relation to anything external, and is also known by the name of duration; relative, apparent, and common time is a sensible and external measure (whether exact or inequable) of duration by means of motion, and is currently used instead of true time; examples of it are the hour, the day, the month, the year.

II

Absolute space, by its very nature and without any relation to anything external, always remains similar and immovable. Relative space is a movable dimension or measure of absolute spaces, which our senses determine according to their position with respect to bodies and which is commonly taken as immovable space; such is the dimension of an underground, aerial or celestial space, determined through its position with respect to the earth. Absolute space and relative space are equal in form and magnitude; but they do not always coincide numerically. For when, for example, the earth moves, any space in our air, which relatively and with respect to the earth always remains the same, will at a given moment occupy a certain part of the absolute space through which the air passes; at another moment it will occupy a different part of the same; and so, understood in an absolute sense, it will be continually modified.

III

It is the part of space which a body occupies, and according to space it may be absolute or relative. This part of space, not the situation or the external surface of the body. For the places of equal solids are always equal, while their surfaces, by reason of their dissimilar figures, are often unequal. In the proper sense, positions do not possess quantity, nor are they so much the places themselves as the properties of the places. The motion of the whole and the sum of the motions of the parts are all one; that is, the translation of the whole out of its place and the sum of the translations of the parts out of their places is the same thing; and, consequently, the place of the whole is the same as the sum of the places of the parts, and for this reason it is an internal and inherent property of the body as a whole.

IV

Absolute motion is the translation of a body from one absolute place to another, and relative motion is the translation from one relative place to another. Thus, in a ship under full sail, the relative place of a body is that part of the ship which the body possesses, or that part of the cavity which the body fills, and which therefore moves with the ship; and relative rest is the permanence of a body in the same part of the ship, or of its cavity. On the other hand, real, absolute rest is the permanence of the body in the same part of that immovable space in which the ship, its cavity, and all that it contains move. Hence if the earth is really at rest, then the body, which is at relative rest with respect to the ship, will really and absolutely move with the same velocity as the ship on the earth.

But if the earth also moves, the true and absolute motion of the body will be due partly to the true motion of the earth in immovable space, and partly to the relative motion of the ship on the earth; and if the body also moves relative to the ship, its true motion will arise partly from the true motion of the earth in immovable space, and partly from the relative motions both of the ship on the earth and of the body on the ship; and from these relative motions will arise the relative motion of the body on the earth. So that if that part of the earth on which the ship is situated is really moving eastwards with a velocity of 10,010 parts, while the ship itself, under full sail and in a very strong wind, is driven westwards with a velocity expressed by 10 of those parts, and if a sailor walks on the ship towards the east with one part of that velocity, then the sailor is really moving in immovable space towards the east with a velocity of 10,001 parts; but relatively, with respect to the earth, towards the West with a speed of nine of said parts.

Just as the order of the parts of time is immutable, so is the order of the parts of space. If we move these parts from their places, we have moved them (if we may say so) out of themselves. For times and spaces are, as it were, the places both of themselves and of all other things. All things are placed in time according to an order of succession, and in space according to an order of situation. They are places by their very essence or nature, and it would be absurd for the primary place of things to be movable. These, therefore, are the absolute places, and the only absolute movements are translations from these places.

The parts of space cannot be seen, nor distinguished from one another, by our senses; so we use sensible measures of them instead. So that from the positions and distances from any body considered as immovable we define all places, and then, relative to these places, we estimate all motions, considering the bodies as transferred from one of these places to another. And so, instead of absolute places and motions, we use relative places and motions; which is no inconvenience in ordinary matters; but in philosophical disquisitions we must abstract from our senses and consider things in themselves, distinguishing them from what are only sensible measures of them. For it may be that there is no body which is really at rest, and to which the places and motions of all the others can be referred.

Need

he theory became necessary when certain anomalies in the universe could not be explained on the basis of Newtonian mechanics or classical physics. It has some antecedents such as the Lorenz transformations, the fact that the speed of light does not change in any frame of reference, the fact that Mercury deviated from the orbit predicted by Kepler and Newton without the existence of another body attracting it other than the Sun, to name a few.

Proposal

The theory was proposed by Albert Einstein in 1905 and received with applause from some and skepticism from others. It consists of two parts, the one published in 1905 known as the Special or Restricted Theory of Relativity that analyzes only inertial reference frames (points or observation frames that move at a constant speed) and the General Theory of Relativity that studies inertial and non-inertial frames (whose speed changes over time).

Examples

According to the laws of motion first set out in detail by Isaac Newton around 1680-89, two or more motions add up according to the rules of elementary arithmetic. Suppose a train is passing us at 20 kilometres per hour and a child throws a ball from the train at 20 kilometres per hour in the direction of the train’s motion. For the child, who is moving along with the train, the ball is moving at 20 kilometres per hour. But for us, the motion of the train and the motion of the ball add up, so the ball will move at the speed of 40 kilometres per hour.

As we can see, we cannot speak of the ball’s speed alone. What counts is its speed relative to a particular observer. Any theory of motion that attempts to explain how speeds (and related phenomena) appear to vary from one observer to another would be a “theory of relativity.”

Einstein’s theory of relativity was born from the following fact: what works for balls dropped from a train does not work for light. In principle, light could be made to travel either with or against the Earth’s motion. In the former case, it would appear to travel faster than in the latter (in the same way that an airplane travels faster relative to the ground when it has a tailwind than when it has a headwind). However, very careful measurements showed that the speed of light never varied, whatever the nature of the motion of the source emitting the light.

Suppose that when the speed of light is measured in a vacuum, it always comes out to the same value (about 299,793 kilometers per second), under any circumstances. How can we arrange the laws of the universe to explain this? Einstein found that in order to explain the constancy of the speed of light, a series of unexpected phenomena had to be accepted.

He found that objects had to shorten in the direction of motion, the more so the greater their speed, until finally reaching zero length at the limit of the speed of light; that the mass of moving objects had to increase with speed, until becoming infinite at the limit of the speed of light; that the passage of time in a moving object became increasingly slower as the speed increased, until it stopped at this limit; that mass was equivalent to a certain amount of energy and vice versa.

He elaborated all this in 1905 in the form of the “special theory of relativity”, which dealt with bodies with constant speed. In 1915 he drew even more subtle consequences for objects with variable speed, including a description of the behaviour of gravitational effects. This was the “general theory of relativity”.

The changes predicted by Einstein are only noticeable at high velocities. Such velocities have been observed among subatomic particles, and the changes predicted by Einstein have indeed occurred, and with great accuracy. Furthermore, if Einstein’s theory of relativity were incorrect, particle accelerators would not work, atomic bombs would not explode, and certain astronomical observations would be impossible.

Special Theory of Relativity

Yo

The speed of light is a constant, meaning that no matter what frame of reference is used, the speed of light does not change. There are also other constants: the electric charge and the phase of a wave.

II

There is a fourth dimension: time, therefore the universe is within what is now called a chronotope, that is, a space-time, this makes there exist a constant apart from the previous ones: the distance between any two points in the universe does not vary in space-time, for this to occur then if two points move away, time and space are distorted, keeping space-time constant.

III

Mass and energy are equivalent, from which comes the equation E=mc2 which we would translate as the energy of a body (at rest) is equivalent to the mass of the body times the speed of light raised to the second power.

IV

The Lorentz transformations, which were a mathematical curiosity since practically all mathematicians and physicists knew them but did not know exactly what to use them for, were used by Einstein instead of the Galileo transformations (used by Newton) to explain relative motion and with them obtain that the mass, length of an object and time change with speed, explaining the distortion of space-time in other words. As Galileo’s transformations are a particular case of the Lorentz transformations we could affirm that Newton’s mechanics is a particular case of relativistic mechanics (or the theory of relativity).

V

An observer cannot distinguish whether his frame of reference is moving or stationary unless an acceleration occurs. Sixth: The laws of the universe apply equally in any inertial frame. The General Theory of Relativity: Extends the conditions of special relativity to frames where there are accelerations (where the speed changes). In these conditions the first consideration is that an accelerating frame works like a gravitational system, that is, the acceleration of the frame works like the acceleration of gravity to the point that an observer could not distinguish between a gravitational or accelerated frame. This principle has a limited application because no object can remain in acceleration infinitely.

These limitations also imply certain truths, for example when one says that the center of the universe is the Earth (that is to say that the Earth does not move) it is implicitly admitted that it does move with respect to other bodies, therefore no frame of reference is immobile. After more than 100 years of being proposed, the theory of relativity is the most accepted in explaining what happens in the universe because there is a great amount of evidence that confirms it, such as the existence of black holes, the curvature of space around massive bodies such as the Sun or planets and many others. However, it is also becoming evident that some revisions must be made to the theory that will lead to new theories.

VI

According to special relativity, very strange things happen when an object moves at nearly the speed of light. Time slows down, the length of an object decreases, and the mass of the moving object increases. If two observers are in relative motion with respect to each other, they can disagree about whether two events occur at the same time. According to Einstein’s famous equation, E=mc2 , mass and energy transform into each other. Einstein introduced the special theory of relativity in 1905.

The general theory of relativity postulates that the “shape” of space can be bent near large objects with a lot of gravity. In fact, according to relativity, gravity is more a curvature of space than a force. Even light rays bend when they pass near a massive object. This is why black holes can “suck in” light that passes near them.

Postulates

  • First postulate: All inertial reference systems are physically equivalent, or in other words, the laws of Physics take the same form in all inertial reference systems.
  • Second postulate: The speed of light in vacuum always has the constant value c in all inertial reference systems, that is, it does not depend on the speed of the motion of the source.

Mathematical explanation

When the light on your watch takes, for example, 1 sec. to go up and down, you will observe that the light on the other ship will take longer to travel that triangular path. When you do the calculations, you will observe that this time is extended by a factor of gamma (which is greater than 1) with respect to your own time. This factor will be greater and greater the higher the speed of the ship. Assuming that v=0.8c (80% of c), the time on the other ship will increase by 66% with respect to yours, therefore, you will measure: 1.66 sec. When the speed reaches the speed of light, gamma will be infinite.

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