Reference: A Logical Approach to Theoretical Physics
In his 1905 paper on Relativity1, Einstein starts out by pointing out the asymmetries that originate from Maxwell’s electrodynamics. He says,
It is known that Maxwell’s electrodynamics—as usually understood at the present time—when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion. For if the magnet is in motion and the conductor at rest, there arises in the neighbourhood of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated. But if the magnet is stationary and the conductor in motion, no electric field arises in the neighbourhood of the magnet. In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise—assuming equality of relative motion in the two cases discussed—to electric currents of the same path and intensity as those produced by the electric forces in the former case.
The following must be noted here:
(1) This problem arises because Maxwell’s electrodynamics has not identified the frame of reference associated with absolute rest.
Einstein then considers a solution to this problem that would not require an “absolutely stationary space”. He says,
Examples of this sort, together 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. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell’s theory for stationary bodies. The introduction of a “luminiferous ether” will prove to be superfluous inasmuch as the view here to be developed will not require an “absolutely stationary space” provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place.
The following must be noted here:
(2) The “light medium” was supposed to be the “absolutely stationary space” but no motion of earth was detected relative to it. Yet earth moved around the sun. This produced an anomaly. It suggested to Einstein that the idea of absolute rest could not be justified. Thus he rejected the idea of aether.
(3) According to the laws of mechanics, however, in a system of rotating bodies, the more massive body is closer to the common center of mass and rotates more slowly. Therefore, the speed of Sun is much slower than the speed of Earth. In short, the greater is the mass of a body, the slower is its free speed in space.
(4) A body’s natural speed, therefore, depends on its inertia. It is inherent to the body. A body with infinite inertia will be at absolute rest. As inertia decreases the natural speed increases. The speed of light is very large but finite because light has a very small amount of inertia (quantization).
(5) This is consistent with “continuum of substance” perspective. Space is the basic substance of zero quantization. The natural tendency for a pulse in space is to spread at infinite speed. All quantized radiation and material bodies are like pulses in space. This tendency to move rapidly gets resisted by inertia, and a finite natural speed results from that balance. This natural speed is absolute in nature.
(6) Einstein’s first postulate that “the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good” is logical because this universe is naturally continuous, harmonious and consistent. Otherwise, there will be no laws of science. All laws are consistent to the degree that they contain no unwarranted and unverified assumptions.
(7) Einstein’s second postulate that “light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body” is logical because inertia (quantization) of light is insignificant compared to the inertia of matter, and it can be used as the reference point of “zero”. This postulate, however, runs into difficulty with quantum mechanics only because the inertia of light is not insignificant compared to the inertia of quantum “particles”. The quantum particles are also radiation except little more quantized than light.
Einstein defines a “stationary system” in which the equations of Newtonian mechanics hold good. He then defines time objectively as “simultaneity of events” with information moving at speed of light between two events far from each other. Einstein postulates the speed of light to be constant in all systems regardless of their motions. This allows Einstein to compare relative speeds of the systems accurately as long as they are insignificant compared to the speed of light. This is true for all speeds in the material domain.
Einstein’s stipulations may be understood more clearly as follows: A completely “stationary system” shall correspond to infinite inertia. A moving system shall correspond to lesser inertia. The greater is the motion the lesser is the corresponding inertia. Einstein can measure the relative inertia of systems accurately as long as the inertia of light is so insignificant that it can act as the reference point of “zero” inertia.
Einstein considers the motion of coordinate systems attached to bodies. The inertia, space and time of the bodies depend on this motion. To keep this version of the theory simple Einstein does not consider any acceleration. That means that motion and inertia of the bodies remain constant.
Einstein imagines the following:
Let there be given a stationary rigid rod; and let its length be l as measured by a measuring-rod which is also stationary. We now imagine the axis of the rod lying along the axis of x of the stationary system of co-ordinates, and that a uniform motion of parallel translation with velocity v along the axis of x in the direction of increasing x is then imparted to the rod.
The following must be noted here:
(8) Motion cannot be imparted to an absolutely stationary system because its inertia is infinite. Therefore, Einstein’s “stationary system” is only relatively so.
(9) To impart motion, Einstein must accelerate the system somehow so it is now moving at a different velocity. Einstein is not accelerating the system overtly. So, he is adding inertia to the system in this thought experiment. This is similar to increasing the quantization of radiation.
Application of mathematics then leads Einstein to the same relationships that Lorenz had come up with earlier with a different model but with the constant speed of light.
(10) The equations obtained above essentially predict that length of the rod would shrink and its duration would increase (time delay) with increased inertia or quantization. But the math does not reveal this unless the thought experiment is evaluated properly as above.
Einstein interprets his mathematical results about length as follows.
… i.e. the greater the value of v, the greater the shortening. For v=c all moving objects—viewed from the “stationary” system—shrivel up into plane figures. For velocities greater than that of light our deliberations become meaningless; we shall, however, find in what follows, that the velocity of light in our theory plays the part, physically, of an infinitely great velocity.
It is clear that the same results hold good of bodies at rest in the “stationary” system, viewed from a system in uniform motion.
The following must be noted here:
(11) As inertia of a body increases, its natural speed decreases. So the parameter v in the equation is deceptive. It actually represents a negative velocity.
(12) Einstein is looking at matter to be stationary from the viewpoint of the speed of light. He is only considering a velocity differential from the “stationary condition of matter”. But that cannot lead to length always shrinking with velocity. Therefore, Einstein’s statement in the second paragraph above is incorrect.
Einstein interprets his mathematical results about time as follows.
If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be ½tv2/c2 second slow.
The following must be noted here:
(13) The clock must increase in inertia to move away and decrease in inertia to move toward. So the movement in a closed curve should cancel out the effect of motion on time. Therefore, Einstein’s conclusion above is incorrect.
(14) The theory of relativity becomes incompatible with Newtonian mechanics by not relating motion with inertia.
In the composition of velocities section, Einstein says,
It follows from this equation that from a composition of two velocities which are less than c, there always results a velocity less than c… It follows, further, that the velocity of light c cannot be altered by composition with a velocity less than that of light.
The following must be noted here:
(15) These conclusions are correct only if the speed of light is infinite. Since that is not the case, these conclusions by Einstein are incorrect. Thus, we see that math can be fallible when the assumptions are ignored.
In the subsequent portion of his relativity paper, Einstein is applying his new theory to several different situations in Physics. However, he is not always careful of his assumptions as in the cases cited above.
The success of the theory of relativity primarily shows up in astronomical situations where the assumption underlying this theory are justified, as explained above.
.
1“On the Electrodynamics of Moving Bodies”, by A. Einstein, June 30, 1905
.
