Category Archives: Einstein

Einstein 1920 (XXXII) The Structure of Space

June 8, 2019 – 8:01 PM

Reference: Einstein’s 1920 Book

Section XXXII (Part 3)
The Structure of Space According to the General Theory of Relativity

Please see Section XXXII at the link above.

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Summary

The geometrical properties of space are not independent of matter. The matter is almost at rest; whereas, light has a tremendous velocity of transmission. They both contribute to the geometrical property of space.

The presence of gravitational fields around matter tells us that the geometry of the universe is not exactly Euclidean. But it is conceivable that our universe differs only slightly from a Euclidean one, because matter is only a very small part of it.

The detailed distribution of matter is not uniform in this universe. The real universe will deviate in individual parts from the spherical, but it will be necessarily finite.

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Final Comments

The space has substantiality, which gives it a measure of consistency. When the consistency is extremely small, the space appears as fluid energy that has a very high velocity. When the consistency is extremely large, the space appears as rigid matter that has a very low velocity. In between, the space appears as the gravitational field of variable consistency and velocity. The velocity has an inverse relationship with consistency. It is the balance of inherent motion of matter floating in a sea of energy that is perceived as the phenomenon of Gravity.

The spectrum of energy/matter based on the property of consistency suggests a vortex type pattern, which is seen repeated in nature at all scales. For example, the atoms display this pattern where the electrons form a vortex, at the center of which there is an extremely dense and small spinning nucleus. The “gravitational field” at this level appears as charge.

At the level of the solar system, planets revolve, as if they are caught up in a vortex of gravity, at the center which is a massive and spinning sun. In their turn, the spinning planets form the center of smaller vortices of gravity in which their moons are caught up.

On a much larger cosmic scale, we have solar or star systems that are caught up in a vortex of gravity which appears as a galaxy. At the center of the galaxy is an extremely dense and small spinning black hole.

All these vortices at different scales seem to be overlapping and producing a very complex pattern in which the inherent motions of the heavenly bodies balance each other in a cosmic dance. We may thus visualize the universe having a “solid” spinning center made up uncountable number of galaxies with a great periphery of curving light far away of unimaginable proportions.

This “vortex universe” is devoid of solid masses in about 99% of its volume; but that volume is filled with palpable energy. The universe may be considered to be finite yet unbounded because it seems to curve upon itself.

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Einstein 1920 (XXXI) The Possibility of a “Finite” and Yet “Unbounded” Universe

June 8, 2019 – 4:59 PM

Reference: Einstein’s 1920 Book

Section XXXI (Part 3)
The Possibility of a “Finite” and Yet “Unbounded” Universe

Please see Section XXXI at the link above.

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Summary

A universe can be without bounds (infinite) from the perspective of its dimensions, but from a higher dimension it can be seen to be finite.

If the ratio of the circumference of a circle to its diameter is determined very accurately, and it is less than π, then that circle is drawn on a spherical surface.

Riemann discovered a three-dimensional analogy of a two-dimensional spherical surface. That means an object moving in a straight line in any direction will ultimately reach its starting point. Such a space is finite but it has no bounds.

Thus, closed spaces without limits are conceivable. From amongst these, the spherical space (and the elliptical) excels in its simplicity, since all points on it are equivalent. This is the approach taken by the general theory of relativity.

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Final Comments

Our space has the property of consistency beyond just having a location. Because of this consistency the space has a curvature. The smaller is the consistency, the larger is the curvature. Even light does not travel in straight lines but has a curvature on a cosmic scale; therefore, it will never escape this universe. This universe can therefore be viewed as unbound but finite in nature.

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Einstein 1920 (XXX) Cosmological Difficulties of Newton’s Theory

June 1, 2019 – 9:11 PM

Reference: Einstein’s 1920 Book

Section XXX (Part 3)
Cosmological Difficulties of Newton’s Theory

Please see Section XXX at the link above.

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Summary

The universe appears to be homogenous on a cosmic scale. But this view is not in harmony with the theory of Newton, according to which the stellar universe ought to be a finite island in the infinite ocean of space.

It is thought that light would be escaping this island universe without ever returning and this shall violate the law of conservation of energy; but this is not certain.

As a result a modification is suggested to Newton’s law of gravitation that would limit the size of gravitational fields, and make universe appear not to be centered. But we do not know if the universe is centered or not. The real problem is that we have no law of gravity that has a firm theoretical foundation.

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Final Comments

Einstein is looking at the problem of not having a strong empirical or theoretical foundation for Newton’s Law of Gravity.

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Einstein 1920 (XXIX) The Solution of the Problem of Gravitation

June 1, 2019 – 6:59 PM

Reference: Einstein’s 1920 Book

Section XXIX (Part 2)
The Solution of the Problem of Gravitation on the Basis of the General Principle of Relativity

Please see Section XXIX at the link above.

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Summary

In the Galilean domain of the special theory of relativity there is no gravitational field, and “isolated” material points move uniformly and in straight lines.

In the random Gaussian domain of the general theory of relativity, the influence of gravitational fields on the behavior of measuring-rods, clocks and freely-moving material points can be studied simply by mathematical transformations. With this mathematical device, we investigate the space-time behavior of the gravitational field, which was derived from the Galilean special case, and formulate that behavior into a law.

We then generalize this law for all gravitational fields by taking into consideration the conservation laws and the general postulate of relativity. We then determine the influence of the gravitational field on the course of all those processes which take place according to known laws when a gravitational field is absent. The theory of gravitation derived in this way from the general postulate of relativity has already explained a result of observation in astronomy, against which classical mechanics is powerless.

The Newtonian Theory can be derived as a special case from this general theory of gravitation. The deviations from Newtonian theory can also be calculated, which, otherwise, are difficult to observe because of their smallness. For example, the general theory of relativity accurately predicts the delicate rotation of the ellipse of mercury as observed. But it also predicts the rotation of the ellipse of all other planets, which is too small to observe.

The general theory of relativity has been confirmed further, by phenomenon, such as, the curvature of light rays by the gravitational field of the sun.

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Final Comments

In an abstract sense, Time reflects endurance of Space. The Gaussian coordinates express time as a variable at each location of space. If the endurance of a location is infinite it has no motion. It is totally rigid. If a location has no endurance it is all motion. It is totally flexible. In short, the lesser is the endurance the greater is the motion. 

In a practical sense, time introduces a gradient of motion among locations, which introduces acceleration and force. This is sensed as if space has substance. Thus, space-time-substance become covariants.

With no time, there is no gradient of motion, no acceleration, no force, and nothing is sensed. As time comes about, so does the sense of substance. With greater variations in time, there is greater acceleration and force built up in space. When the gradient of variation in time is small, the space is sensed as the electromagnetic radiation, such as, light. When the gradient of variation in time is very large, the space is sensed as rigid matter.

The gradient of time comes about in terms of vibrations. The gradient is small when vibrations are small. The gradient is large when the vibrations are large. Matter has much higher vibrations than electromagnetic radiation or light.

The Gaussian coordinates thus produce space that can be sensed. This is the basis of a gravitational field.

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Einstein 1920 (XXVIII) Exact Formulation of the General Principle of Relativity

May 31, 2019 – 9:17 AM

Reference: Einstein’s 1920 Book

Section XXVIII (Part 2)
Exact Formulation of the General Principle of Relativity

Please see Section XXVIII at the link above.

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Summary

In the general theory of relativity, the rigid reference bodies are replaced by the Gaussian coordinate systems.

In special theory of relativity, we replace the space-time variables of a Galilean reference-body by the space-time variables of a new reference body that makes use of Lorentz transformation. In general theory of relativity, we replace one Gaussian coordinate system by another, while the equations which express the general laws of nature pass over into equations of the same form.

In a way we are replacing the reference systems of material bodies with limited range of flexibility by reference system of gravitational field with infinite range of flexibility. Special kind of gravitational fields may appear as being attached to material bodies.

In gravitational fields there are no such things as rigid bodies with Euclidean properties. The physical sense of space and time also becomes very different from that in the special theory of relativity.

The rigid reference-bodies of the special theory of relativity are replaced by non-rigid reference-bodies of gravitational field in the general theory of relativity. In a gravitational field, the variations in rigidity are continuous without limitation just like the motion. Therefore, the term “reference-body” may be replaced by the term “reference-mollusk.” The “mollusk” gives a certain comprehensibleness is the (really unqualified) formal retention of the separate existence of the space co-ordinate.

The general theory of relativity thus assigns certain rigidity to space coordinates, from almost no rigidity in case of light to a high order of rigidity in case of matter.

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Final Comments

The gravitational field as represented by Gaussian coordinates is like space with some substantiality. In other words, space has a consistency that varies from one location to the next. As the consistency increases, the space becomes more concentrated and it starts to appear as the electromagnetic radiation. Near infinite consistency turns space into matter with the characteristics of inertia. Within an atom, the increasing consistency appears as the electronic and the nuclear regions.

As the concentration of “substantial” space increases, boundaries between spaces of different consistencies become more visible. Thus come about the appearance of discrete particles within the continuous medium of space.

As consistency increases the velocity decreases, and that seems to provide a model of a vortex of decreasing radius. This radius finally becomes so small that the velocity of concentrated space turns into spin of solid particles at the bottom of the vortex.

This Vortex Model may apply to spinning atoms and also to the spinning planets with their gravitational fields.

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