[Name] Albert Einstein (Jewish theoretical physicist)

The Collected Works of Einstein was edited according to the opinions of Fan Dainian, Zhao Zhongli and Xu.

As we all know, Maxwell electrodynamics-now generally understood-will cause some asymmetry when applied to moving objects, and this asymmetry does not seem to be inherent in the phenomenon. For example, imagine an electrodynamic interaction between a magnet and a conductor. Here, the observable phenomenon is only related to the relative motion of the guide rail and the magnet, but according to the usual view, whether this object is moving or that object is completely different. If the magnet is moving and the conductor is stationary, then an electric field with certain energy will appear near the magnet, and current will be generated where all parts of the conductor are located. However, if the magnet is stationary and the conductor is moving, then there is no electric field near the magnet, but there is electromotive force in the conductor. Although this electromotive force itself is not equal to energy, it-assuming that the relative motion in the two cases considered here is equal-will cause a current, the magnitude and route of which are the same as those generated by electricity in the previous case.

Blocking such an example and the failure of the experiment trying to prove the movement of the earth relative to "smooth coal" have caused a conjecture: the concept of absolute rest does not conform to the characteristics of phenomena not only in mechanics, but also in electrodynamics. On the contrary, it should be considered that all coordinate systems suitable for mechanical equations are also suitable for the above electrodynamics and optical laws, which has been proved for the first-order trace. We upgrade this conjecture (whose content will be called "relativity principle" later) to a postulate, and introduce another postulate that seems incompatible with it on the surface: light always propagates at a certain speed c in vacuum space, regardless of the motion state of the emitter. Starting from these two postulates, according to Maxwell's static body theory, it is enough to get a simple and contradictory dynamic body electrodynamics. The formulation of "optical ether" will prove to be redundant, because according to the viewpoint to be expounded here, it is neither necessary to introduce an "absolute static space" with special properties nor to specify a velocity vector for each point in the vacuum space where the electromagnetic process takes place.

The theory to be explained here-like other electrodynamics-is based on the kinematics of rigid bodies, because any such theory is about the relationship between rigid bodies (coordinate systems), clocks and electromagnetic processes. Inadequate consideration of this situation is the root of the difficulties that must be overcome in dynamic electrodynamics at present.

Moving part

1, the definition of simultaneity

There is a coordinate system in which Newton's mechanical equations are valid. In order to make our expression more rigorous, and to literally distinguish this coordinate system from other coordinate systems to be introduced later, we call it "static system".

If a particle is stationary relative to this coordinate system, its position relative to the latter can be determined by rigid measuring rod according to the method of Aureli geometry, and can be expressed by Cartesian coordinates.

If we want to describe the motion of a particle, we will give its coordinate values as a function of time. Now we must remember that such a mathematical description has physical significance only after we know exactly what "time" means here. We should take into account that all our judgments that work all the time are always about simultaneous events. For example, when I say "that train arrived here at 7 o'clock", it probably means "the short hand of my watch points to 7, which is the same event as the arrival of the train."

Some people may think that it is possible to overcome all the difficulties in defining "time" by replacing "time" with "the position of the short hand of my watch". In fact, if the problem is only to define a time where this table is located, then such a definition is enough; However, if the problem is to connect a series of events in different places in time, or-the result is still the same-to determine the time when those events occurred far away from this table, then this definition is not enough.

Of course, we may be satisfied with measuring the time of an event in the following way, that is, let the observer be at the coordinate origin of the watch. When every light signal indicating the occurrence of an event reaches the observer through an empty space, he will correspond the position of the hour hand with the time when the light arrives. But this correspondence has a disadvantage, as we already know from experience, which is related to the position of the observer and the table. Through the following consideration, we get a much more practical judgment method.

If a clock is placed at point A in space, the observer at point A can determine the time of events near it by finding out the position of the hour hand that appears at the same time as these events. If a clock is placed at point B in space, we will add "This is the same as the clock placed at point A". Then, the observer at point B can also find the time of the event near point B. However, if there is no further regulation, it is impossible to compare the events at A with those at B in time. So far, we have only defined "time A" and "time B", but not the time shared by A and B. Only when we define that the time required for light to travel from A to B is equal to the time required for light to travel from B to A, can we define the time of A and B, which is set at "time A" tA, and a beam of light is emitted from A to B. It reflects from B to A, and at "time A" T'A returns to A ...

tB-tA=t'A-t'B

Then by definition, these two clocks are synchronized.

We assume that this definition of synchronicity can be non-contradictory, and it also applies to no matter how many points, so the following two relationships are generally valid:

1. If the clock at B is synchronized with the clock at A, the clock at A is synchronized with the clock at B. ..

2. If the clock at A is synchronized with the clock at B and the clock at C, then the two clocks at B and C are also synchronized with each other.

In this way, with the help of some (hypothetical) physical experience, we define what synchronization means for clocks that are stationary in different places, thus clearly obtaining the definitions of "simultaneity" and "time". The "time" of an event means that the stationary clock at the place where the event occurred is synchronized with the event, and that the clock is synchronized with a specific stationary clock, and all time measurements are synchronized with the specific clock.

According to experience, we also put the following values

2|AB|/(t'A-tA)=c

As a cosmological constant (the speed of light in a vacuum).

The key is that we use a clock that is stationary in a stationary coordinate system to define time. Because it belongs to the static coordinate system, we call the time defined in this way "static time".

2 On the relativity of length and connecting line

The following considerations are based on the principle of relativity and the principle of invariance of light speed, and we define them as follows.

1. The laws followed by the state changes of physical systems have nothing to do with which of the two coordinate systems moving at a uniform speed is used to describe these state changes.

2. Any light moves at a certain speed c in the "stationary" coordinate system, no matter whether it is emitted by a stationary or moving object. From this, it is obtained that

Light speed = distance/time interval of optical path

The "time interval" here is understood as defined in 1.

Setting a static rigid rod; Measure its length with the same static measuring rod. Let's now assume that the axis of this rod is placed on the X axis of the stationary coordinate system, and then let this rod move in parallel at a uniform speed along the X axis (speed is V). Now let's check the length of this moving rod and assume that its length is determined by the following two operations:

A) The observer moves with the measuring rod and the rod to be measured given above, and directly measures the length of the rod through the overlapping of the measuring rod and the rod, just as the measuring rod, the observer and the measuring rod are stationary.

B) With the help of some static clocks placed in the static system and running synchronously according to 1, the observer can find out which two points in the static system are at the beginning and end of the pole to be measured at a certain moment t ... The distance between these two points measured with the used measuring rod is static in this case and also a length, which we can call "the length of the rod".

The length obtained by operation a) can be called "the length of the rod in the power system". According to the principle of relativity, it must be equal to the length l of the stationary rod.

The length obtained by operation b) can be called "the length of the (moving) rod in a stationary system". We should determine this length according to our two principles, and we will find that it is different from L.

Commonly used kinematics tacitly assumes that the lengths measured by the above two operations are completely equal, or in other words, a moving rigid body can be completely replaced by the same object at a certain position in the geometric relationship at time t.

In addition, we assume that there is a clock synchronized with the static clock at both ends of the pole (A and B), that is, the time reported by these clocks at any time is consistent with their "static time"; Therefore, these clocks are also "synchronized in a static system".

Let's further assume that each clock has a moving observer, and they apply the rule of synchronous operation of two clocks established in 1 to these two clocks. There is a beam of light from a at time tA, reflected from b at time t b, and returned t' a at time t' a. Considering the principle that the speed of light is constant, we get:

TB-tA=rAB/(c-v) and t'A-tB=rAB/(c+v).

Here rAB stands for the length of the moving rod-measured in a static system. Therefore, the observer who moves with the moving rod will find that the two clocks are not synchronized, while the observer in the static system will claim that the two clocks are synchronized.

Therefore, we can't give the concept of simultaneity any absolute meaning; Two events, from one coordinate system, are simultaneous, but from another coordinate system that moves relative to this coordinate system, they can no longer be considered as simultaneous events.