14 Mechanism of length contraction and magnetic phenomena (straight line)
The time dilation effect in relativity is well organized. It is well-formulated and conceptually well-documented, and has proven to be very robust in experimental terms. However, length contraction is not so. The mechanism by which length contraction occurs is unknown even if everything else is aside. So here we have to think about the mechanism of length contraction.
Three expected mechanisms of length contraction
There are three ball-like particles arranged side by side. It's still inactive. Therefore, they did not change the length at all. Let's assume that they are the same and the spacing between them is constant. Now let's see what happens when these particles run fast.
The picture and contents below are referenced at http://www.alternativephysics.org/book/LengthContraction.htm.
There are three ways to predict the length contraction mechanism.
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| Fig. 1 Stationary particles |
When particles run at relativistic speeds, length contraction will occur in one of three ways:
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| Fig. 2 Three Mechanisms of Length contraction |
In Process A, the distance between particles does not change, but only the particles shrink. In Process B, both the distance and the particle shrank based on the first front particles. In Process C, the particles shrank together to the space based on the first front particles.
We used the first front particle as a reference. However, it may be based on the middle particle, or it may be based on the back particle. Let's skip the others and look at the first front particle.
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| Fig.3 Nine (3X3) mechanisms of length contraction |
When do you think length contraction takes place? Through the process A, B, and C? Or do you think it happens with other mechanisms? Or do you think you do not need to look at these things? In fact, any of the above mechanisms will result in fatal problems. Relativistic electromagnetics has been described in connection with this. I will talk about it from now on.
The specific mechanism of magnetic phenomena
It is early known that electric force and magnetic force are one. However, the detailed mechanism of how the magnetic force is generated is unknown. Under these circumstances, there is a pioneer who came up with a specific mechanism for the cause of magnetic forces. It was Edward M. Purcell.
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| Fig. 4 Purcell, 1952 Nobel prize |
Purcell noticed the length contraction of the theory of relativity to account for magnetic force. Purcell noted the following equation in Lorentz force:
There is a v in the above expression. This v generally means the speed of charge. Charge is actually flowing from the wire. Purcell explains the mechanism of magnetic force using the effect of length contraction by the speed of charge. Purcell's description is as follows.
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Fig. 5 Observed wires from proton's point of view |
The negative charge on the wire is moving to the right at vo speed, and the test charge is moving at v speed. From the point of view of the test charge, it is as follows.
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| Fig. 6 Observed wires from test charge's point of view |
In my opinion, these explanations have fatal weaknesses. The number of positive charges moving to the left is greater than the negative charge moving to the right. Purcell did not explicitly draw this from his book, but in the above video it is fully explained. Below is one of those scenes.
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| Fig. 7 More (+) particles than (-) particles |
There are more positive charges (16) moving to the left than negative charges (8). Purcell knew in advance that this would happen. So he assumed an infinite lead. He explained the mechanism of magnetism and explained that there is no problem even assuming infinite conductance.
The law of conservation of charge and interpretation of Purcell
There are many conservation laws in nature. The laws of conservation of mass, the laws of conservation of energy, and the laws of conservation of momentum. In the field of electromagnetism, there is a law of conservation of charge.... If it is possible to introduce Purcell's infinite conduct, what is the law of conservation of charge? Can we ignore the law of conservation of charge?
In general, the mechanism plays a slightly different role than the experiment. The mechanism should explain the detailed process in which the phenomenon occurs. It should be explained in detail without any leaps of logic, so that it can be easily understood by anyone, using common sense or theoretically.
The charge density increases as the charge flows. This phenomenon is explained numerically. As the speed of charge increases, the charge density increases as follows. λo is the charge density when it is relatively stationary, and λ is the charge density when moving at the speed of v.
If you look at the shape of the expression, it looks the same as the time dilation expression or the mass increase expression. When we write down the shape of the equation, it is closer to the shape of the length expansion than the expression of the length contraction.
Anyway, the theory should be tested thoroughly by experiment. And there is something that is essential before experimental validation. There should be no internal logical deficiencies or contradictions within the theory. If there is a serious contradiction in the theory, it should not be published as a theory.
The theoretical expression is completed by writing the equation, but it is not easy to describe the detailed mechanism. The mechanism proposed by Purcell is shown below.
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| Fig. 8 Core of Purcell Mechanism |
In Purcell's mechanism, the number of particles increases as shown in the above figure. There is also a theoretical equation about magnetic force, and experimental facts exist. Then it is time for human interpretation to intervene. Is the mechanism proposed by Purcell above convincing? This is a triple error. It violates three important laws: the law of conservation of mass, the law of conservation of charge, and the causality.
Purcell has an important meaning in that it has attempted relativistic interpretation on the origin of magnetic force. When no one can think of a mechanism for the generation of magnetic force, it is his merit that has tried to explain the mechanism of magnetic force. However, it is difficult to get persuasive by assuming infinite conduction or by not following some conservation laws. We have a good alternative. There is a good way to clear all the flaws by Purcell.
Mechanism interpreted by length expansion theory
This problem, like any other problem, can be interpreted easily if it is interpreted as a length expansion. You do not need to assume infinite wires and you do not have to violate the law of conservation of charge. The increase in charge density is easy to understand. The process is as follows.
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| Fig. 9 The increase in charge density, which is interpreted as the length expansion |
Most of the theoretical development process is the same as Purcell. However, the shape of the relatively moving charge does not contract, but rather expands. If the amount of charge density is large, the test charge is naturally repelled by the repulsive force, and everything is explained without any inconsistency.
This interpretation precisely matches
(1) the equation (λ = γλo),
(2) you do not need to assume an infinite wire, and
(3) you do not need to violate the law of conservation of charge.
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Fig. 10 Mechanism interpreted as length expansion |
If you draw a picture, it will look like this. There is no contradiction.
I will introduce a circular current in the following post. At circular currents, Purcell's logic falls into an extremely contradictory situation. The length contraction is paradoxical and cannot be explained at all, but the circular current is also easily interpreted by the theory of length expansion. As you could well expect.
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