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Relativity

Shadow areas to illuminate.
It seems that a lot of things have been forgotten

  Welcome - Einstein's relativity - The ether - Galileo's relativity - Waves - References 



   

A short history of relativity

We will be brief but complete. The first to be trapped by this principle was the great Aristotle himself.

Don't laugh, he is one of the greatest scientists of his time, his teacher, Plato, had nicknamed him "intelligence", he was the tutor of Alexander the Great, which says a lot about his notoriety and whose exploits of his student are partly due to him. He has demonstrated very intelligently that the Earth is stationary, and therefore that the Sun and the planets revolve around it. Aristotle was trapped by the relativity of motion, a principle he did not know.

Demonstration of the immobility of the Earth.

It's very simple, if an object falls from the edge of a table, it falls at the foot of the table, proof that the Earth and the table did not move during its fall. In the same way, you throw a stone in the air, vertically and you have to move out of the way so that it does not fall on your head, proof that you and the Earth have remained motionless during the vertical movement of the stone.

Aristotle's other mistake will be to say that heavy bodies fall faster than light bodies and to classify his five elements from the heaviest, earth to the lightest, ether, passing through water, air and fire. In any case, these elements did not make sense, as chemists would show over time.

     


The Earth revolves around the Sun

About 1800 years later, Nicolaus Copernicus was the first to present a model in 1513 where the Earth and the planets revolve around the Sun convincingly enough to be accepted.

Giordano Bruno, a powerful and observant mind, noticed that an object that fell from the top of the mast of a boat moving in a good breeze, fell at the foot of the mast and not at the back of the boat which continued to move forward during the fall. He realized that this undermined Aristotle's demonstration of the Earth's immobility.


This discovery and his ideas about an infinite universe as well as his vision of religion led the Roman Catholic Apostolic Church to condemn him to be burned alive in 1600. In the name of a god who would be the father of us all and would love us all as his children!

For his part, Johannes Kepler took up the work of Copernicus, benefited from the very precise measurements of the position of the planets made by Tycho Brahe before his death and led to elliptical orbits around 1609.

The fall of the bodies

For his part, Galileo was interested in the fall of bodies, Aristotle had adopted the generally accepted idea that heavy bodies fell faster than light bodies. To get to the bottom of this, Galileo rolled marbles of different masses on an inclined plane that slowed the speed of the fall enough for it to be observed. By placing the bells activated by the passage of the marbles along the path, Galileo verified that they were accelerating and that in order for the sounds produced to be spaced by the same amount of time measured by an oscillating pendulum, the bells had to be pushed further and further apart.

Galileo and his students verified that if the marble travels one unit of distance first, for one unit of time, it travels 3 for the next unit and then five for the next unit, which gives for units 1, 2, 3 the progression 1, 4, 9. It is a uniformly accelerated movement whose distance traveled is proportional to the square of the elapsed time.


Inclined plane visible at the Galileo Galilei Museum in Florence
https://florencesite.fr/musee_galilee.html


Galilean relativity

Giordano Bruno's observation interested him but he couldn't reuse it without risking the stake, so he placed himself in the captain's cabin and noted that everything happens in the same way, whether the boat is stationary or running: the flies fly in the same way without getting stuck to the aft bulkhead, The water is dripping vertically, it is impossible to know if the boat is moving forward or not without looking out the window.

"Movement is like nothing". The fact that a falling object continues to move horizontally at the same speed, he describes a parabola, led him to state the principle of relativity:

    A body moving in a straight line at a constant speed keeps this direction and speed indefinitely in the absence of any external force or friction
Galileo made another advance, the additivity of speeds. A small drawing is better than a long speech.



Einstein and relativity

In 1905, the Wonderful Year, Einstein published four important articles. The first concerns photoelectric phenomena with the creation of a particle of light that has energy and frequency but no mass; the second is about Brownian motion explained with Newtonian mechanics; then the founding article of relativity entitled "On the electrodynamics of bodies in motion". The last article will be the demonstration that the famous formula E = mc² is conserved during the transformations of the changes of reference frames of relativity. These transformations are identical to those of Lorentz Poincaré, we will see why.

The article on relativity was rejected by the scientific community. The reasons for this rejection had nothing to do with the person of Albert Einstein since his three other papers were well received and his thesis that he passed in 1906 which gave the size of the molecules and made it possible to calculate the Avogadro number was also appreciated. Of course, there were people with bad intentions or who hated Einstein who took advantage of the situation

Galilean relativity applied to electromagnetic phenomena

In his article entitled "On the Electrodynamics of Bodies in Motion", Einstein posits two postulates. The first, that Galilean relativity applies to electromagnetic phenomena. He points to the fact that when you move a magnet in front of an electrically conductive wire, you get the same result as when you move the wire in front of the magnet at the same speed. But he acknowledges that this contradicts Maxwell's equations which use Faraday's equation when moving the magnet and Ampere's equation when moving the wire (coil is more efficient). He states that the deviations of these equations are undetectable at the first order. Maxwell's equations are still not called into question and if it is true that the differences depending on the object we are moving are undetectable, it is due to the difference between a motion of a few tens of meters per second for the object being moved, compared to three hundred million meters per second for the speed of electromagnetic waves.

This situation may be surprising, but it surprised us. To avoid any misunderstanding, here is the version translated into French that respects the original one in German:
    "It is known that if we apply Maxwell's electrodynamics, as we conceive it today, to bodies in motion, we are led to an asymmetry which does not agree with the phenomena observed. For example, let's analyze the mutual influence of a magnet and a conductor. The phenomenon observed in this case depends solely on the relative motion of the conductor and the magnet, whereas according to the usual conceptions, a distinction must be made between cases in which one or the other of the bodies is in motion. »
He posits a second postulate:
    "and let us introduce another postulate — which at first glance is incompatible with the first — that light propagates in empty space, at a speed V independent of the state of motion of the emitting body"

The speed of waves is independent of the speed of the objects that produce it, an aircraft can catch up with the sound it produces and even exceed it, but it depends on the characteristics of the medium that propagates them. Einstein in the wake of this eliminates the ether, the medium that fixes the speed of electromagnetic waves and which a priori would prevent these waves from having the same speed in all reference frames. We say a priori because we have a hypothesis on this question. A hypothesis that at first glance seems absurd, but which is made possible by general relativity itself. Having found no one to listen to us, we thought it important to clear the ground of misunderstandings about this exceptional theory. You should begin to understand the reasons why it was criticized even by the greatest physicists of the time.

Our goal is to consolidate it with regard to this speed of light, which would be the same everywhere, which would contradict the relativity of its motion if there were no other condition to be fulfilled.

§1 Definition of simultaneity.



It uses synchronized clocks at both ends. An observer emits a ray of light from point A at time tA, which is reflected at point B at time tB and which returns to A at time t'A. Observers check the immobility of clocks that have not moved during the measurement and find a value


In accordance with the experiment, we will therefore make the assumption that the magnitude is a universal constant (the speed of light in empty space).
Einstein uses V for the speed of light, c will be used later



§2 On the relativity of lengths and times

    a) The observer with the measuring rod moves with the measuring rod and measures its length by superimposing the ruler on the rod, as if the observer, the measuring ruler and the rod are at rest
    b) The observer determines at which points in the stationary system are the ends of the rod to be measured at time t, using the clocks placed in the stationary system
Case b requires that the observer is no longer in the frame of reference of the moving rod where he was stationary in relation to the rod to be measured, but is now in another frame of reference that moves in relation to the previous one at the speed -v which makes him see the rod in its frame of reference moving at the speed + v



Here Albert Einsteins' explanations are a little tricky to follow. We have made a diagram. The observer is in the frame of reference K and the rod in k in motion at the speed v
From K we see the light at the speed V chase the point B which moves away at the speed v. the light ray takes longer to reach B Einstein writes on the return the point A approaches at the speed v and therefore:

               


where rAB is the length of the moving rod, measured in the stationary system. (K)

font-size=2>Translator's note: Here, the term "time" refers interchangeably to "time in the stationary system" and "position of the hands of a moving clock" located at the position in question

§3 Theory of the transformation of coordinates and time from one stationary system to another in uniform relative motion

Be careful, for non-physicists and especially non-mathematicians, things are getting serious. We will do our best:

Einstein takes up the case of paragraph 2 where we have dissociated the two frames of reference for greater clarity. We will present the way in which Einstein establishes his equation linking the coordinates of the two frames of reference and use variations that tend to 0 for the calculations, calculations that we will not detail and which lead to the same transformations as those of Lorentz.

Let us measure the space with the ruler and clocks of the stationary system K, with coordinates x, y, z and time t, those of the ruler in the coordinate system k moving at the speed v which will be x, y, z and time t to differentiate them

If we set x' = x - vt, then for a point at rest in the system k, there is a time-independent system of values x', y, z.

We translate that there is a point x' of K which at time t coincides with x of k with respect to which it moves at the speed -v, x' is stationary in K. This point will be used to transport the coordinates of k into K.

Let be a ray of light sent at time τ0 from the origin of the system k along the x-axis in the increasing direction of x' and which is reflected at the point B at time τ1 towards the origin of the coordinates, where it arrives at A at time τ2.


So, we have        


If we introduce as a condition that τ is a function of the coordinates, and apply the principle of the constancy of the speed of light in the stationary system, we have

At time t, we have time t0 at position x=0, y=0, and z=0. The time font face="Symbol">t2 is measured at the time t2 and t2



Continuing the calculations, which we will not detail here, he finds the same transformations as Lorentz, finalized by Henri Poincaré. There is no plagiarism since he does not use the displacement of the Earth at 30km/s in the reference frame of the ether which he does not need. He uses the postulate that light propagates in empty space, at a speed V independent of the state of motion of the emitting body.

We promised to explain why Albert Einstein finds the same values as Lorentz. It's very simple, you just have to draw the arm of the interferometer which is parallel to the movement of the Earth, and which is made up of a rigid rod AB equipped with a semi-reflective mirror inclined at 45° in A and a mirror that reflects light in B.

A ray of light is sent parallel to the rod AB, at A it splits in two, and while the ray perpendicular to AB will bounce off a mirror located at the distance AB, the undeflected ray goes to B, from where it is reflected to A.

It should be noted that the interferometer arm parallel to the Earth's displacement leads to the same measurements and transformation to explain the lack of detection of the Earth's motion in relation to the supposed reference frame of the ether.



We find the same motion proposed by Einstein for the rigid bar AB and therefore the same equation as Einstein's for which the interferometer must not detect any variation. Hat.

General relativity

We won't go into detail about general relativity, we wouldn't be able to, but we will examine how Einstein discovered the path to follow and why it is generalized Galilean relativity.

Einstein said that he had the "happiest idea of his life"5 in 1907, when he realized that in free fall, we do not feel our own weight, we do not feel subject to any force, we float in the void and the objects that accompany us are immobile in relation to us.

No physics experiment carried out in this frame of reference distinguishes this state from that of an inertial frame of reference far from any gravitational field. This makes free fall a relative movement that cannot be detected in the absence of external landmarks



Newton's "cannon" allows us to understand free fall: the shell is in free fall, its speed allows it to travel through a parabola before falling to the ground. At a high speed it is satellited and at the escape velocity, it escapes the Earth's gravitation.

Einstein places himself in the position of the observer. Seen from Earth, we see the celestial bodies revolving around us.

Incidentally, he justifies Aristotle's error, in the free-falling frame of reference of the Earth he could not detect its motion by a local experiment.

He makes another discovery apparently related to the operation of elevators. When going up, when starting you feel slightly packed, it's due to the acceleration of the cabin. On the descent on the other hand at the beginning we are lighter, it is still due to the acceleration of the cabin but which at this moment is negative in relation to the Earth's gravitation and suddenly decreases it.

Einstein deduced that acceleration was equivalent to gravitation


Acceleration and gravitation are equivalent


Conclusion

General relativity has not said its last word. It will probably be completed with current discoveries, its equation will probably be refined, but the principle will remain correct.

It has a particular characteristic that we have discovered that would allow us to formulate a bold, bold but simple hypothesis that is relatively easy to verify. It also has the great advantage of being able to be formulated using only what Albert Einstein wrote. This hypothesis is rightfully his.

It is up to you to decide whether you want to know her or not. We have published a book which explains this hypothesis and the means of verifying it with experiments. If you could buy this book and talk about it to friends, physicists if possible, in order to make known this hypothesis which seems absurd at first glance and which uses the word ether to which for a moment, from 1920 to 1936, Einstein considered existence and then abandoned for lack of having or attributing to it a motion that agrees with relativity. Overcoming the hurdle of the word ether will be the most difficult, I speak from experience. In the end, it is general relativity that explains the mysterious motion of the ether and at the same time makes it compatible with relativity but can ultimately be explained in a simple way. Thanks in advance.



https://librairie.bod.fr/lether-quantique-dalbert-robert-j-9782322521401


https://librairie.bod.fr/the-ether-of-albert-einstein-robert-jobard-9782322455959





Albert Einstein


Isaac Newton


Galilée

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