Asymmetry in Electromagnetism and the Theory of Relativity

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ether, that light propagates in (after all, light is an electromagnetic phenomenon), and that medium is at rest, then there would be valid grounds for arguing for some kind of absolute rest in terms of the medium. However, immediately after the example of the magnet and the conductor, Einstein continues “examples of this sort along with the unsuccessful attempts to discover any motion of the earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest.” (pp. 37) This justifies the raising of the conjecture, namely that the principle of relativity is universally valid, to the status of a postulate.

With two new postulates - 1. The law of physics hold true for all the frames of reference and 2. The velocity of light through the vacuum is constant in all frames of reference, Einstein begins to unravel his theory. However, another complexity to define time came along. In a perfect world where a “signal” of saying what time it is at a specific point in a frame of reference could travel instantaneously, we could perhaps had an absolute time where signals could be sent simultaneously saying what time it was etc. However there is no such thing to send signals with infinite speed. Light is the fastest thing that can travel but it has a definite finite speed. The notion of time is only gotten through observation (and change) and light is the thing that can be observed with the greatest speed. This insight helps Einstein to remedy this difficulty of time. Using light signals simultaneity is described for different frame of references and the clocks (which give us time with respect to a particular frame of reference) are synchronized accordingly. The insight here is that the time might be different for different frames of reference.

One easy thought experiment can be ascertained when time we might be experiencing on Earth might be different itself, compared to some other frame of reference. Say, a guy G is on the earth and the earth is moving with its average orbital speed of 30000 m/s to his right. There are two clocks in two directions, clock A on the right and clock B on the left, equidistant from the guy G. The guy G says that the clocks are simultaneous, i.e. they show the exact same time to him. Now looking with respect to some other frame of reference, we see that the earth is moving with velocity 30000m/s to the right. So, we clearly observe, because of the constancy of speed of light, the light has to travel a lesser distance from the clock A to guy G than from clock B to the guy. Hence, it would take lesser time for the light signal to reach from clock A to G than from clock B to G. Hence the clock on the left, B, has to be “ahead” of that of the right, A, when looked at from a different frame of reference.

Now with this insight he proceed to provide equations for transformations (also known as Lorentz transformations) of spatial coordinates and time from a stationary frame of reference to one moving with a uniform translatory motion. He also has to prove the non contradiction of the constancy of the speed of light in all frames of reference to the principle of relativity. This apparent contradiction came from the argument considered from the stationary frame of reference when light signal is emitted in a moving frame with velocity v, you would expect the velocity of light to be added to the velocity of the emitting frame. However, using the Lorentz transformation, Einstein proves that there is no contradiction as such and constancy of speed speed of light is held true for all frames of references. As Einstein mentions, “of course this is not surprising, since the equations of the Lorentz transformation were derived conformably to this point of view.”

After treating basic kitematics in terms of the principle of relativity, he proceeds to the electrodynamic part. Here, he begins with the Maxwell-Hertz equations given in terms of variables x,y,z, and t and X,Y, and Z for electric field and L, M, and N for magnetic field in x, y and z directions respectively. Then, using the Lorentz transformation and lots of chain rules of differentiation and algebraic manipulation, he transforms those equations for a moving frame of reference which is moving in a uniform velocity given in terms of their own spatial and temporal coordinates ,,,and by the bottom of page 52. Now the components of the moving frame of reference can be expressed exactly in terms of how it was expressed for the stationary frame of reference - After all, from the perspective of the moving frame, they are at rest. On top of 53, Einstein thus, rewrites those equations using new set of variables X’, Y’ Z’, L’, M’ and N’ derived in terms of ,,,and . Now he can effectively equate the coordinates expressing the moving frame of reference in terms of the stationary on pp. 52 with the allocated new variables of the moving system on pp.53 to arrive at the transformation of the electric and magnetic field from stationary to a moving frame of reference at the top of pp. 54.

Next Einstein, after defining a point charge of electricity of magnitude “one”, goes on to say how classical electrodynamics and principle of relativity would approach the phenomenon of a point charge moving uniformly in an electromagnetic field. As we discussed the Lorentz force earlier, according to the old way, there acts upon the particle in motion in electromagnetic field “in addition to the electric force, an ‘electromotive force’, which … is equal to the vector product of the velocity of the charge and the magnetic force divided by the speed of light”or E+1/c(v B) (Note that here the charge on the particle, q =1). In the new way of expression, the force acting upon the moving point charge “is equal to the electric force which is present at the locality of the charge” and this electric force is ascertained by “transformation of the [initial] field to a system of coordinates at rest relatively to the electric charge.” Instead of complication of electric force plus some other cross product of velocity with magnetic force, we simply have a new electric field which is described in a moving frame of reference, with the velocity the same as the particle, transformed using Lorentz transformation and the electric force that this particle gets is because of this moving transformed field. Similar considerations can be made of the magnetic field as well.

Next, Einstein claims that “asymmetry mentioned in the introduction, .., now disappears.” If the asymmetry was tied, in case of the magnet and the conductor problem, to there being different explanations for the same observable phenomena, it has now disappeared. In the case described by Einstein in the previous paragraph, since there is no preferential

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