Einstein’s Relativity

ReferenceA Logical Approach to Theoretical Physics

The null results from Michelson-Morley’s experiment in 1887 initiated a line of research that eventually led to Einstein’s theory of Special Relativity. The expected difference between the speed of light in the direction of movement through the presumed aether, and the speed at right angles, was found not to exist. The special relativity then ruled out a stationary aether.

The difference between the universal motion of light and Earth shall be constant because the difference between their densities is constant. This explains the null result of Michelson-Morley’s experiment.

One may object to the above reasoning by saying, “The earth is orbiting the sun. Therefore, it is constantly accelerating in the radial direction towards the sun, but not in the tangential direction. So, there must be a slight difference in speed in the two directions.”

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Michael-Morley’s Experiment

We may calculate this accuracy required of Michael-Morley’s experiment as follows:

1.    From de Broglie’s relationship the frequency of Earth is about 8 x 1070. The frequency of visible light is about 8 x 1014. Therefore, the ratio of their frequency is of the order of 1056

2.     This means that earth is 1056 times as dense as light.

3.     Then the intrinsic speed of earth is 1056 times slower than the speed of light. Even if we take density to be proportional to the square of speed, the intrinsic speed of Earth shall still be 1028 times slower.

4.     Therefore, the intrinsic speed of earth is about (3 x 108 meters/sec) times (10-28), or of the order of 10-20 m/s.

5.     Then, under best of the scenarios, the Michelson-Morley’s experiment is required to detect a velocity difference of the order of 10-20 m/s.

Michelson-Morley’s experiment was unable to detect the difference in speed of the order of 10-20 m/s. It, therefore, gave a null result. According to Wikipedia, modern experiments indicate that the two-way speed of light is isotropic (the same in every direction) to within 6 nanometres per second.

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The Speed of Light

The null results from Michelson-Morley’s experiment led to the formulation of the Lorentz transformation. Einstein derived the same formulation from the principles of relativity. These principles required that the speed of light be the same in all inertial frames of reference.

From Wikipedia,

In 1905 Einstein postulated from the outset that the speed of light in vacuum, measured by a non-accelerating observer, is independent of the motion of the source or observer. Using this and the principle of relativity as a basis he derived the special theory of relativity, in which the speed of light in vacuum c featured as a fundamental constant, also appearing in contexts unrelated to light. This made the concept of the stationary aether (to which Lorentz and Poincaré still adhered) useless and revolutionized the concepts of space and time.

The speed of light provides the basis of universal motion just like Newton’s fixed stars. The fixed stars may be approximated as infinite density and zero motion; whereas, light may be approximated as zero density and infinite motion. Both work as the basis for universal motion because the scale of universal motion is inverse of the scale of density (see The Universal Frame of Reference).

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The Theory of Relativity

The theory of relativity essentially converts local motion (relative to earth) to universal motion before doing math. That is why it gives more accurate results for Mercury’s orbit (see Newtonian Relativity). It does so through the use of Lorentz Transformation.

The Lorentz transformation reduces to Galilean transformation when ‘c’ is infinite. The speed of light is practically infinite compared to the motion in material domain. This means that Lorentz transformation is essentially “Galilean transformation with a correction factor for using local motion”.  The Newton’s laws of motion remain completely valid because they were originally designed for the universal frame of reference.

Lorentz transformation looks at the characteristics of space and time from the viewpoint of the invariant speed of light. Space and time actually represent the “extents” and “duration” of the substance respectively. Thus, space-time relates to the intrinsic properties (density and intrinsic motion) of substance.

The theory of relativity is applying the universal frame of reference in looking at the density and intrinsic motion of substance in the material domain.

We shall be looking at the mathematics of Lorentz transformation in the next chapter.

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Comments

  • vinaire  On October 13, 2019 at 3:22 PM

    The fastest possible speed is infinite. Einstein practically treated ‘c’ as having an infinite value because nothing can be greater than c (infinity). If two light rays approach each other at c (infinity), their relative velocity is also c (infinity). In other words, if you add two infinities, the sum would be infinite.

    We must use a finite value for ‘c’ for math to work. When ‘c’ is given a value of infinity, the Lorentz transformation reduces to Galilean transformation. The reason the Lorentz transformation of SR works is because ‘c’ is practically infinite relative to material velocities.

    Universal Motion

    Newton’s Laws of Motion, and the Galilean transformation, apply to motion relative to fixed stars. The fixed stars are assumed to have an intrinsic motion of zero. The intrinsic motion is a characteristic that is inherent to the substance and it does not depend on anything outside of the moving body. We refer to intrinsic motion as universal motion because it is the same throughout the universe like other intrinsic properties, such as, mass.

    Therefore, the fixed stars provide the zero of a scale, relative to which we can measure intrinsic or universal motion.

    Local Motion

    In contrast to universal motion we have local motion, which is measured relative to a local body, such as, the Earth or the Sun. Working with local motion is like working with unlike quantities that require conversion to like quantities before adding and subtracting. Therefore, local motion must be converted to universal motion before Galilean transformation can be applied, especially if the densities of the moving bodies are different.

    Lorentz Transformation

    The Lorentz transformation essentially converts local motion (relative to earth) to universal motion before doing math. That is why it gives more accurate results for Mercury’s orbit. But accuracy can be greater if math can be worked out for an infinite value of ‘c’.

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