The relativity of motion, Article by Albert Einstein from 1905
"On the electrodynamics of bodies in motion."

So that there is no misunderstanding about the quality of the source, we quote the excerpts from the article on which we rely. We skipped passages like this: [.] You can find them in the French translation. We've added a few diagrams for clarity. Our remarks are in italics. You can discuss and dispute them.

Introduction

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.

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Maxwell uses Faraday's equation when moving a magnet in front of a wire and Ampere's theorem when moving the wire in front of the magnet. The difference in the results is less than the first order, obviously, magnet or wire move at a few hundred meters per second while electromagnetic waves travel at 300 million meters per second.

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[.]In mechanics, but also in electrodynamics, no property of the observed facts corresponds to the concept of absolute rest [.] In the text that follows, we elevate this conjecture to the rank of a postulate (which we will henceforth call the "principle of relativity") and 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.

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Making the speed of electromagnetic waves a constant, the same in all frames of reference, is one thing, but seeing it at the same speed when we are in a different frame of reference?

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These two postulates are entirely sufficient to form a simple and coherent theory of the electrodynamics of bodies in motion [.] the introduction of a "luminiferous ether" is superfluous,[.]

I. KINEMATIC PART

§ 1. . Definition of simultaneity

[.] If we want to describe the motion of a material point, the values of its coordinates must be expressed as a function of time. [.] Our conceptions, in which time plays a role, always relate to simultaneous events. For example, if we say "a train arrives here at 7 a.m.", it means "that the little hand of my watch that points exactly to the 7 and that the arrival of the train are simultaneous events".
[.]
However, in order to estimate events chronologically, we can obtain satisfaction by supposing that an observer, placed at the origin of the coordinate system with the clock, associates a luminous signal — testifying to the event to be estimated and the ray of light that comes to him through space — to the corresponding position of the hands of the clock. However, such an association has a flaw: it depends on the position of the observer observing the clock, as experience dictates. We can get a much more practical result in the following way.

However, in order to estimate events chronologically, we can obtain satisfaction by supposing that an observer, placed at the origin of the coordinate system with the clock, associates a luminous signal — testifying to the event to be estimated and the ray of light that comes to him through space — to the corresponding position of the hands of the clock. However, such an association has a flaw: it depends on the position of the observer observing the clock, as experience dictates. We can get a much more practical result in the following way.

If an observer is placed at A with a clock, he can assign a time to events near A by observing the position of the hands of the clock, which are simultaneous with the event. If a clock is also placed in B [.] an observer in B can chronologically estimate the events that occur in the vicinity of B. [.] A common time can be defined, if we posit by definition that the "time" required by light to go from A to B is equivalent to the "time" taken by light to go from B to A. For example, a ray of light starts from A at "time A", tA, in the direction of B, is reflected from B at "time B", tB, and returns to A at "time A", t'A. By definition, the two clocks are synchronized if

We assume that this definition of synchronism is possible without causing inconsistency, no matter how many points. Consequently, the following relations are true:

1. S1. If the clock in B is synchronized with the clock in A, then the clock in A is synchronized with the clock in B.

2. 2. If the clock in A is synchronized with both the clock in B and the clock in C, then the clocks in B and C are synchronized

So, with the help of some physical (thought) experiments, we have established what we mean when we talk about clocks at rest in different places, and synchronized with each other; and we have consequently established a definition of "simultaneity" and "time". The "time" of an event is the simultaneous indication of a quiescent clock located at the location of the event, which is synchronized with a certain quiescent clock in all cases of time-determination.

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). We have just defined time using a clock at rest in a stationary system. Since it exists in its own right in a stationary system, we call time thus defined "stationary system time".

§ 2. On the relativity of lengths and times

The following reflections are based on the principle of relativity and the principle of the constancy of the speed of light, both of which we define as follows:

1. The laws by which the state of physical systems is transformed are independent of how these changes are related to two coordinate systems (systems that are in uniform rectilinear motion with respect to each other).

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Einstein tells us that what is being measured (changes reported in a system of different coordinates) do not account for the observed reality

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2. Each light ray travels in a "stationary" coordinate system at the same velocity V, the velocity being independent of the condition that this luminous ray is emitted by a body at rest or in motion. Therefore

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Light is an electromagnetic wave, the speed of the waves does not depend on the speed of the object that produces them but on the characteristics of their support. An airplane can catch up with the sound it produces. Einstein said that the speed of light is the same in all stationary systems, regardless of their speed (seen from another moving frame of reference). The question "what is the speed of light seen in this other frame of reference?

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speed = Light path/ time interval

où where "time interval" is to be understood as defined in § 1.

Let us have a rigid rod at rest; it is of a length L when measured by a ruler at rest. We assume that the axis of the rod merges with the x-axis of the stationary system. Let the rod be given a uniform velocity v, parallel to the x-axis and in the increasing direction of the x. How long is the length of the moving rod? It can be obtained in two ways:

a) 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 rod and the rod are at rest.

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Here we are in the case of paragraph 1

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b) The observer determines at which points in the stationary system the ends of the rod to be measured at time t are located, using the clocks placed in the stationary system [.]

According to the principle of relativity, the length found by operation a), [.] is equal to the length L of the rod in the stationary system.
The length found by operation b) can be called the "length of the rod (moving) in the stationary system". This length differs from L.[.]

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We understand: << the length found by operation a), [.] is equal to the length L of the rod in its stationary system. The length found by operation b) is the length of the rod seen in motion from the observer's frame of reference that is stationary for him. >>

We made a diagram with the rod in the k frame of reference. The observer is in the frame of reference K that we have shifted for better readability, he observes the rod in the frame of reference k that he sees moving relative to him at the speed v. The k and K frames of reference will be seen in paragraph 3

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In the kinematics generally used, it is implicitly assumed that the lengths defined by these two operations are equal [.] Let us further imagine that there are two observers at the two clocks moving with them, and that these observers apply the criterion of synchronism in § 1 to the two clocks.
      At time tA, a ray of light goes from A, is reflected by B at time tB, and arrives at A at time t'A. Taking into account the principle of the constancy of the speed of light, we have:

Einstein uses V for the speed of light
         

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On the outward journey the point B moves away at the speed v, resulting in a speed = V -v (Einstein wrote it). On the way back, point A approaches and the speed is then V + c. For Einstein, the speed of light in one frame of reference is V, but seen from another frame of reference with a speed of -v, the light moves away at a slower speed (V-v) and approaches at a higher speed (V+v). At this stage, the additivity of Galileo's velocities is not called into question.
The opinion of physicists specializing in the field would be welcome. The public believed that in a frame of reference seen in rapid motion, time expands, while Einstein explains that for the traveler who rests in this frame of reference, time is unchanged.

We have a hypothesis about the aether from Einstein's 1921 paper "The Aether and the Theory of Relativity." 15 years later, Einstein gave up on the ether and asked never to say the word again. But pulled herself together and wrote that "removing a word doesn't solve a problem." The absence of ether poses a problem. He had not been able to attribute to it any movement so that it would be immobile in all the frames of reference. All the frames of reference of celestial bodies are in free fall and that matter falls at the same speed whatever its mass, even a mass so low that it would currently be undetectable. That's what general relativity says!

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rAB is the length of the moving rod, measured in the stationary system. As a result, observers who move with the moving rod will not assert that the clocks are synchronized, even though observers in the stationary system will testify that the clocks are synchronized.

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The phrase "observers who move with the rod in motion will not claim that the clocks are synchronized" surprises us.

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We conclude that we cannot attach absolute meaning to the concept of simultaneity. Therefore, two events that are simultaneous when observed from a system will not be simultaneous when observed from a moving system relative to the first.

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At this stage, we do not claim to have understood everything. The following paragraph 3 reinforces our understanding of the process.

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

Let us place, in the "stationary" system, two coordinate systems,[.]. Let us make the x-axis of each of the systems coincide and parallel the y-axes and z-axes. Let us have a rigid ruler and a number of clocks in each system, the rods and clocks in each being identical.

Let be an initial point of one of the systems (k) animated by a (constant) velocity v in the increasing direction of the x-axis of the other system, a stationary system (K), and the velocity being also communicated to the axes, rods and clocks in the system. Any time t of the stationary system K corresponds to a certain position of the axes of the moving system. For the sake of symmetry, we can say that the motion of k is such that the axes of the system in motion at time t (by t, we mean time in the stationary system) are parallel to the axes of the stationary system.

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Things are becoming clearer

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Suppose that space is measured by the stationary ruler placed in the stationary system K, just as by the moving ruler placed in the moving system k, so we have the coordinates x, y, z, and ξ, η, ζ, respectively. In addition, let us measure the time t at each point of the stationary system by means of the clocks which are placed in the stationary system, using the method of light signals described in § 1. Let also be the time τ in the moving system which is known for each point of the moving system (in which there are clocks that are at rest in the moving system) [.] For each of the sets of x, y, z, t values that completely indicate the position and time of the event in the stationary system, there is a set of values ξ, η, ζ, τ in the k system. Now, the problem is to find the system of equations that connects these values.

First, it is obvious that, based on the homogeneity property that we attribute to time and space, the equations must be linear. If we set x' = x - vt,

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The point x' at the speed -v in the frame of reference k that moves at + v with respect to K is stationary in K and allows the data from k to be transferred to K

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Then it is obvious that for a point at rest in the system k, there is a system of values x', y, z independent of time. First, let τ be the function of x', y, z, t. For this purpose, we must express in equations the fact that τ is none other than the time given by the clocks at rest in the system k which must be synchronized according to the method described in § 1. 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 from this place at time τ1 to the origin of the coordinates, where it arrives 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 this point we will not detail Einsteins' calculations that lead to Lorentz transformations, they are in Einstein's article that you can consult on the website of the University of Quebec in Chicoutimi:

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Sorry we are cherching the english version

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http://classiques.uqac.ca/classiques/einstein_albert/Electrodynamique/Electrodynamique.html
http://classiques.uqac.ca/classiques/einstein_albert/Electrodynamique/Electrodynamique.pdf


However, we want to draw your attention to the reason why Einstein finds the same result, his rigid rod in motion is the arm of the interferometer of the Michelson and Morley which moves at 30 km/s with respect to the reference frame of the ether and which does not detect any movement. By decreeing that the speed of light is the same in all inertial frames of reference, Einstein demonstrates that the hypothetical contraction of matter does not exist and is only an illusion. It's the way we observe an electron's electric field that we see it transform from a spherical at rest to an ellipsoid contracted in the direction of motion as a function of the electron's velocity.

By using Lorentz transformations, we maintain an ambiguity. They should be called the Einstein transformations finalized by Henry Poincaré from the identical Lorentz transformations but conceived on an error in the interpretation of the observed deformations. Yes, it's too long, but it would remove the ambiguity of the contraction of matter and confirm that it is an "optical illusion"





September 23, 2024, to be continued.

Albert Einstein


Isaac Newton


Galilée