The Problem of Relativity

Lorentz Boost

Reference: Disturbance Theory

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Einstein regarded space as a physical reality for the following reason. From Einstein’s essay, Relativity & Problem of Space [1]:

But in this [Newton’s] theory, acceleration can only denote “acceleration with respect to space”. Newton’s space must thus be thought of as “at rest”, or at least as “unaccelerated”, in order that one can consider the acceleration, which appears in the law of motion, as being a magnitude with any meaning.

In Newton’s theory, acceleration is a motion relative to the object itself and not to other objects in space. On a smoothly flying plane, we do not feel the velocity, but the moment there is acceleration we feel it instantly in our bones. The idea of acceleration is tied closely with the concept of inertia, which is the property of all substance.

Newton defined inertia in his book “Philosophiæ Naturalis Principia Mathematica”as follows:

The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, endeavors to preserve its present state, whether it be of rest or of moving uniformly forward in a straight line.

In the cosmic background all bodies have some “uniform motion” or a drift velocity. This velocity shall be small for stars of very large inertial mass because the larger is the inertial mass the more force it takes to move it. On the same account, the drift velocity  for bodies of small inertial mass shall be large. Theoretically, a body with infinite inertia may have zero velocity; and a body with zero inertia may have infinite velocity. A finite drift velocity of a body shall mean that it has finite inertia. This shall apply to all substances whether matter or field.

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Light

Though light has a very large speed in the cosmic background, it is not infinite. Michelson-Morley’s experiment determined this speed quite accurately, but it was unable to detect any inertia for light. However, the large but finite velocity of light means that it must have finite inertia. This inertia maybe infinitesimally small but it is not zero.

Light is made up of electromagnetic cycles. Each cycle consists of dynamic interchange between electrical and magnetic fields. But there is innate resistance to the formation of these fields. The inertia of light comes from such resistance to its cycles. Permittivity (ε0) is the measure of resistance that is encountered when forming an electric field in emptiness. Permeability (μ0) is a measure of how easily a magnetic field can pass through emptiness. Therefore, the resistance to the formation of an electromagnetic cycle is (μ0ε0). This may provide a measure of inertia for light.

The relationship between this inertia and the speed of light is,

c = 1/√(μ0ε0)

We may say that the speed of light is inversely proportional to the square root of its inertia.

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The Lorentz Transformation

In physics, the Lorentz transformations are coordinate transformations between two coordinate frames that move at constant velocity relative to each other. Historically, the transformations were the result of attempts by the Dutch physicist Hendrik Lorentz and others to explain how the speed of light was observed to be independent of the reference frame.

The derivation of Lorentz transformation from purely mathematical considerations may be found at Reference from Khan Academy and Reference from Yale University.

The derivation of Lorentz transformation assumes the following.

Assumption #1: The speed of light is the same in all inertial systems.

Based on Michelson-Morley’s experiment, the speed of light of 3 x 108 meters/second was not affected by the velocity of the earth, which is 3 x 104 meters/second relative to the sun. The “v/c ratios” in this case is 1/10,000, which is of the same order of magnitude as most material bodies in the universe. Therefore, this assumption is good for a “v/c ratio” of 1/10,000 or less.

Assumption #2: The gamma “fudge” factor is the same for observers in different inertial systems.

In this cosmos, each body is drifting in space under a balance of inertial forces. These drift speeds are as different as their respective inertia. This may influence the gamma factor. But this difference may not be significant for a “v/c ratio” of 1/10,000 or less.

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Special Theory of Relativity

The special theory visualizes inertial systems to be boundless inertial “spaces” that move rigidly relative to each other. These inertial systems are equivalent for the formulation of natural laws. In other words, the natural laws are invariant with respect to the transition from one inertial system to another.

The special theory further assumes that the speed of light is a natural law. It is, therefore, invariant with respect to the transition from one inertial system to another. This allows the Lorentz transformations to be used in the special theory. According to Einstein,

The whole content of the special theory of relativity is included in the postulate: The laws of Nature are invariant with respect to the Lorentz transformations. The important thing of this requirement lies in the fact that it limits the possible natural laws in a definite manner.

The Lorentz transformations have been successful in explaining the “aberration” of the fixed stars in consequence of the annual motion of the earth; and the “Doppler effect”, i.e. the influence of the relative motion of stars on the frequency of the light. This success depends on the “v/c” ratio being within the limits of assumption of the Lorentz transformation in these cases. In other words, the validity of Lorentz transformations depends on the inertia of light being negligible compared to the inertia of matter.

Thus, the special theory produces valid results as long as the inertia of light is negligible compared to the inertia of the system under consideration.

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The Atomic Systems

The atomic systems have inertia comparable to the inertia of light. Therefore, when it comes to the application of special theory to systems of atomic dimensions, the inertia of light can no longer be considered negligible. So, the special theory of relativity does not produce valid results in such cases.

The success of the theory of relativity can be assured across the board only by reformulating it with a reference point of zero inertia instead of the velocity of light.

Such a reference point is provided by the concept of emptiness.

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Comments

  • vinaire  On December 28, 2017 at 6:39 AM

    The application of Einstein’s special theory to atomic dimensions requires a better understanding of inertia and its calculation for electromagnetic field and atomic particles that provides absolute values.

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