Category Archives: Science

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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By vinaire | Also posted in Einstein | Comments (0)

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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By vinaire | Also posted in Einstein | Comments (0)

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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By vinaire | Also posted in Einstein | Comments (0)

Einstein 1920 (II) System of Co-ordinates

January 2, 2019 – 8:31 AM

Reference: Einstein’s 1920 Book

Section II (Part 1)
The System of Co-ordinates

Please see Section II at the link above.

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Summary

In reality, the body of reference is the rigid body with the point with which the position of an object or an event coincides. A length is correct only when it is measured directly with the use of a rigid rod of standard length.

Distance to locations that are far from the body of reference can be determined by means of optical observations according to the rules and methods laid down by Euclidean geometry, and taking into account the properties of the propagation of light.

We may apply the Cartesian system of co-ordinates to describe a position in space. Such a system shall consists of three rigid plane surfaces perpendicular to each other and rigidly attached to the body of reference. Perpendiculars can be dropped from that position to those three plane surfaces to describe it by means of three coordinates.

The measurements are generally made by indirect means as described above. However, the physical meaning of specifications of position must always be sought.

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Comments

“Every description of events in space involves the use of a rigid body to which such events have to be referred. The resulting relationship takes for granted that the laws of Euclidean geometry hold for ‘distances’, the ‘distance’ being represented physically by means of the convention of two marks on a rigid body.” ~Einstein

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By vinaire | Also posted in Einstein | Comments (0)

Einstein 1920 (I) Geometrical Propositions

January 2, 2019 – 7:12 AM

Reference: Einstein’s 1920 Book

Section I (Part 1)
Physical Meaning of Geometrical Propositions

Please see Section I at the link above.

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Summary

We all believe in the propositions of Euclid’s geometry with total certainty. But what is meant by the assertion that these propositions are true?

If we look closely, we note that geometry is not concerned with the relation of the ideas involved in it to objects of experience, but only with the logical connection of these ideas among themselves.

Geometrical ideas correspond to more or less exact objects in nature. This prevents geometry from attaining largest possible logical unity of structure.

When we consider the geometrical points to always correspond to points on a practically rigid body, then the rigidity of measuring instruments, such as, ruler and compass, also becomes significant. We can then treat geometry as a branch of physics.

In this sense, we find that the conviction of the “truth” of the Euclidean propositions is founded exclusively on rather incomplete experience.

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Comments

The axioms and logic used in Euclidean geometry are idealistic rather than realistic. The distances measured in space do not maintain their exactness as geometry supposes them to. Therefore, when we use geometry to calculate distances in space, we are doing that based on incomplete experience.

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By vinaire | Also posted in Einstein | Comments (2)