Category Archives: Einstein

Einstein 1920 (VII) Apparent Incompatibility

January 3, 2019 – 3:29 PM

Reference: Einstein’s 1920 Book

Section VII (Part 1)
The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity

Please see Section VII at the link above.

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Summary

From all observation, the velocity of light depends neither on its color, nor on its direction, nor on the velocity of its source. We may consider it to be constant and absolute in nature.

But, if we apply the theorem of addition employed in classical mechanics, the velocity of light must change when observed from a moving system of reference.

The view based on classical mechanics contradicts the observed fact that the velocity of light is constant. If the speed of light is a universal constant and a natural law, then, according to the principle of relativity, it should be the same for all Galilean coordinate systems irrespective of their motion.

The theoretical investigations of H. A. Lorentz on the electrodynamical and optical phenomena connected with moving bodies show that the law of the constancy of the velocity of light in vacuo is a necessary consequence.

When we consider both the law of propagation of light, and the principle of relativity to be correct, we arrive at the special theory of relativity.

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Comments

The order of magnitude for the velocity of light is so different from the velocity of material bodies that the sum of the two velocities would not be appreciably different from the velocity of light.

One may also argue that the changes in the velocity of light due to differences in colors, directions and the velocity of its source could similarly be imperceptible.

The theoretical research in electrodynamics and optics simply relates the velocity of light to electrical constants related to space, and we do not understand the nature of space.

It is true that the special theory of relativity improves upon the law of addition of the classical theory, because it takes the finite velocity of light into account. But, it is not totally satisfactory because its assumptions are not completely explained.

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Einstein 1920 (VI) Addition of Velocities

January 3, 2019 – 2:21 PM

Reference: Einstein’s 1920 Book

Section VI (Part 1)
The Theorem of the Addition of Velocities Employed in Classical Mechanics

Please see Section VI at the link above.

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Summary

In classical mechanics, we have the theorem of addition of velocities when there is a system of reference that itself is moving relative to another system of reference. But this theorem does not always hold in reality.

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Comments

When a body of reference is moving, its internal inertia also plays a part. That is why different bodies have different uniform velocities inherently. But, in material domain, the difference in inertia is so small that it is practically imperceptible.

Therefore, in most cases in the material domain the inertia can assumed to be constant. This allows velocities of the same order of magnitude to be simply added. But when the two velocities are not of the same order of magnitude, the theorem of addition cannot be applied.

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Einstein 1920 (V) Principle of Relativity

January 3, 2019 – 7:07 AM

Reference: Einstein’s 1920 Book

Section V (Part 1)
The Principle of Relativity (In the Restricted Sense)

Please see Section V at the link above.

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Summary

Uniform translation means constant velocity and direction with no rotation. If that is the case with different coordinate systems then they are all Galilean in nature, and the mechanical laws of Galilei-Newton hold good with respect to all of them.

The principle of relativity (in the restricted sense) states that the natural phenomena run their course with respect to all Galilean coordinate systems according to exactly the same general laws.

Classical mechanics affords an insufficient foundation for the physical description of natural phenomena, such as, the phenomena of electrodynamics and optics. So the validity of the principle of relativity needs to be looked at more closely. 

The principle of relativity applies with great accuracy in the domain of mechanics. It is possible that Galilean system we have chosen in this domain is “absolutely at rest,” while the systems that describe the phenomena of electrodynamics and optics are “in motion.”

The Galileian co-ordinate system of the earth is in motion relative to the Galileian co-ordinate system of the sun. One would expect anisotropic properties due to change in directions of the earth but none have been found so far. Therefore, the principle of relativity applies at least over the range of motion for the matter.

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Comments

The changes in the state of motion of various Galilean co-ordinate systems, in the material domain, do not appreciably affect the validity of the principle of relativity. In other words, the law of inertia is pretty much constant for matter in spite of differences in motion.

It is possible that there are imperceptible changes in inertia responsible for the changes in motion.

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Einstein 1920 (IV) Galileian Co-ordinates

January 2, 2019 – 8:51 PM

Reference: Einstein’s 1920 Book

Section IV (Part 1)
The Galileian System of Co-ordinates

Please see Section IV at the link above.

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Summary

The Law of Inertia basically means that in the absence of external forces, a body moves without acceleration at an inherent constant velocity in a straight line.

If we use a system of co-ordinates which is rigidly attached to the earth, then, relative to this system, every fixed star describes a circle of immense radius in the course of an astronomical day. But this is opposed to the statement of the law of inertia, since the visible fixed stars have no motion or acceleration. We, therefore, conclude that the earth is actually rotating around an axis. Thus, the law of inertia also indicates the reference-bodies, or systems of co-ordinates, permissible in mechanics.

The “Galilean system of co-ordinates” is a system of co-ordinates of which the state of motion is such that the law of inertia holds relative to it. The laws of the mechanics of Galilei-Newton can be regarded as valid only for a Galilean system of co-ordinates.

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Comments

The law of inertia is very specific about zero acceleration and the uniform velocity of the body in a straight line. However, it omits to mention anything about the magnitude of that uniform velocity.

The magnitude of the uniform velocity may depend on the mass of the body, because if the mass of the body is infinite, it cannot have inherent velocity.

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Einstein 1920 (III) Space and Time

January 2, 2019 – 9:28 AM

Reference: Einstein’s 1920 Book

Section III (Part 1)
Space and Time in Classical Mechanics

Please see Section III at the link above.

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Summary

“Space,” most likely, means a volume free of matter for a material object to exist in. The “position” of an object in that space can only be specified by referencing it from another object using the coordinate system. Thus, we always see the trajectory of a body relative to another body, and not independently.

Time is measured by the regular ticks of a clock that are standardly spaced apart. This clock is attached to the reference body. The motion of the object is determined by noting its position at every tick of the clock. The time coordinate should also take into account the time light takes in traveling  from the object to the origin point on the reference body.

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Comments

Einstein notes that the space coordinates shall be affected by the degree of rigidity of the coordinate system, and the time coordinates shall be affected by the finiteness of the velocity of light.

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