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My views on Cosmology and Physics

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Book by David Michalets

Review of Einstein's 1920 Book on Relativity  (from Translation)

An (original) line precedes original content from the source.

A (remark) line precedes my remark from my review of the preceding original content.

My remark applies to only this section of the original.

Section II. of 35



ON the basis of the physical interpretation of  distance which has been indicated, we are  also in a position to establish the  distance between two points on a rigid body by means of measurements. For this purpose we require a "distance" (rod S) which is to be used once and for all, and which we employ as a standard measure.
If, now, A and B are two points on a rigid body, we can construct the line joining them according to the rules of geometry; then, starting from A, we can mark off the distance S time after time until we reach B. The number of these operations required is the numerical measure of the distance AB. This is the basis of all  masurement of length.

Every description of the scene of an event or of the position of an object in space is based on the specification of the point on a rigid body (body of reference) with which that event or object coin1 Here we have assumed that there is nothing left over, i.e. that the measurement gives a whole number. This difficulty is got over by the use of divided measuring-rods, the introduction of which does not demand any fundamentally new method.

This applies not only to scientific description, but also to everyday life. If I analyse the place specification "Trafalgar Square, London,"

I arrive at the following result. The earth is the rigid body to which the specification of place refers; "Trafalgar Square, London" is a welldefined point, to which a name has been assigned, and with which the event coincides in space.
This primitive method of place specification deals only with places on the surface of rigid bodies, and is dependent on the existence of points on this surface which are distinguishable from each other. But we can free ourselves from both of these limitations without altering the nature of our specification of position. If, for instance, a cloud is hovering over Trafalgar Square, then we can determine its position relative to the surface of the earth by erecting a pole perpendicularly on the Square, so that it reaches the cloud. The length of the pole measured with the standard measuring-rod, combined with the specification of the position of the foot of the pole, supplies us with a complete place specification. On the basis I have chosen this as being more familiar to the English reader than the "Potsdamer Platz, Berlin," which is referred to in the original. (R. W. L.)
It is not necessary here to investigate further the significance of the expression "coincidence in space." This conception is sufficiently obvious to ensure that  differences of opinion are scarcely likely to arise as to its applicability in practice.

of this illustration, we are able to see the manner in which a refinement of the conception of position has been developed.
(a) We imagine the rigid body, to which the place specification is referred, supplemented in such a manner that the object whose position we require is reached by the completed rigid body.
(b) In locating the position of the object, we make use of a number (here the length of the pole measured with the measuring-rod) instead of designated points of reference.
(c) We speak of the height of the cloud even when the pole which reaches the cloud has not been erected. By means of optical observations of the cloud from different positions on the ground, and taking into account the properties of the propagation of light, we determine the length of the pole we should have required in order to reach the cloud.
From this consideration we see that it will be advantageous if, in the description of position, it should be possible by means of numerical measures to make ourselves independent of the existence of marked positions (possessing names) on the rigid body of reference. In the physics of measurement this is attained by the application of the Cartesian system of co-ordinates.
This consists of three plane surfaces perpendicular to each other and rigidly attached to a rigid body. Referred to a system of co-ordinates, the scene of any event will be determined (for the main part) by the specification of the lengths of the three  erpendiculars or co-ordinates (x, y, z) which can be dropped from the scene of the event to those three plane surfaces. The lengths of these three perpendiculars can be determined by a series of manipulations with rigid measuringrods performed according to the rules and methods laid down by Euclidean geometry.
In practice, the rigid surfaces which constitute the system of co-ordinates are generally not available; furthermore, the magnitudes of the coordinates are not actually determined by constructions with rigid rods, but by indirect means.
If the results of physics and astronomy are to maintain their clearness, the physical meaning of specifications of position must always be sought in accordance with the above considerations.

We thus obtain the following result: 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.
A refinement and modification of these views does not become necessary until we come to deal with the general theory of relativity, treated in the second part of this book.


In this doubt of Euclidean gemetry, Einstein describes measuring the height of a cloud using a measuring rod.

Since that time, a ceilometer was developed. This device generates a light beam. The angle when the beam reflects off the cloud enables the calculation of the cloud height, using Euclidean geometry.

Now, Trafalgar Square has a measured latitude and longitude. We defined a simple coordinate system having 2 circular dimensions of latitude and longitude, in degrees.

The reference point for this coordinate system is the center of the Earth. This is an observer independent  coordinate system. Each accounts for the shift of their current location compared to the common, physical reference point, at the center of the Earth.

The accuracy of a distance from Earth's center determines the accuracy of dstance calculations, through changes in degrees of latitude or longitude.This calculation has roots in Euclidean geometry with  2 perpendicular planes.
 Measuring a distance between 2 points does not require a measuring rod.

Einstein makes the statement that  "Every description of events in space involves the use of a rigid body to which such events have to be referred."

We live on a globe we call Earth. Our perception of the sky is an apparent globe around us, though the distance to the stars cannot be directly perceived.

The ancients could not handle an apparent "no limit" for distances beyond the visible stars. Therefore, the the stars were in a firmament, a globe  at some distance, above and around our globe. Beyond the visible stars, there was a black surface, the outer edge of the universe.

The Earth's rotation enabled the concept of an equator of the Earth,  with opposing poles of rotation.

When measuring the position of objects in the night sky, a simple 2-dimension coordinate system of 2 perpendicular planes was developed, based on Euclidean geometry. They can define for any object a left/right position and an up/down position. Since the sky appears as a sphere, both of these 2 dimensions are roughly in degrees.

The horizontal plane, for left/right  is called Right Ascension, RA. Rather than using 360 degrees, its range is 0 to 24 hours, with + or - from the reference. Therefore there are 15 degrees in each hour of RA.

The vertical plane, for up/down, is called Declination. Its units are in degrees  with +90 at the North celestial pole, and -90 at the South celestial pole.

The reference point for this coordinate system is the center of the Earth. This is an observer independent  coordinate system. Each accounts for the shift of their current location compared to the common, physical reference point, the center of the Earth.

Though the ancients did not measure actual positions of stars using numerical coordinates, they definitely recorded their patterns. Constellations were named to help remember their patterns. The ancients watched and noted the movement of the planets through these constellations.

Those who have read Worlds in Collision by Immanuel Velikovsky, know the history of the ancients assigning mythical gods to the physical planets.

I must remark that celestial measurements are never done in a simple Euclidean geometry of 3 linear dimensions.

On Earth, all physical locations are dsecribed by latitude, longitude and elevation.

Beyond the Earth, all  physical locations are defined, relative to Earth, by RA, declination, and distance from Earth.

Unfortunately, measuring the precise distance to very distant objects is nearly impossible, so can precisely measure only their position on the celestial sphere, and lacking the extra dimension of its distance from Earth

It is impossible to define a coordinate system for the universe which is not dependent on the Earth, which serves as the common physical reference point for all observers using that system.

The requirement for an oberver independent coordinate system is the definition of a fixed physical point, which all observers can use for their measurements.

Regardless of whether you agree with Newton's absolute space, the universe has no fixed point in space which can be used by all observers, to anchor their coordinate system of however many dimensions.

The background of the universe has no features. Newton callled it "always similar and immovable."

Please do not claim the non-existent CMB is a feature which has been measured. It wasn't.

We must use the Earth as our reference point when measuring objects in the universe.

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last change 05/07/2022