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

"On the electrodynamics of bodies in motion."

[.]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.

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,[.]

[.]

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".

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).

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

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.

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 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*

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:

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!

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.

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.

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.

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,

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:

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