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Books by David Michalets

Einstein's Mistakes

With Forces and Light

5 Theory of Relativity

This is section 5 of 12 in the web-book.

Einstein's Theory of Relativity was the result of a number of scientists.

5.1 Its origin

Albert Einstein published the theory of special relativity in 1905, building on many theoretical results and empirical findings obtained by Albert A. Michelson, Hendrik Lorentz, Henri Poincaré and others. Max Planck, Hermann Minkowski and others did subsequent work.

Einstein developed general relativity between 1907 and 1915, with contributions by many others after 1915. The final form of general relativity was published in 1916.

The term "theory of relativity" was based on the expression "relative theory" (German: Relativtheorie) used in 1906 by Planck, who emphasized how the theory uses the principle of relativity. In the discussion section of the same paper, Alfred Bucherer used for the first time the expression "theory of relativity" (German: Relativitätstheorie). [Reference:

https://en.wikipedia.org/wiki/Theory_of_relativity#Development_and_acceptance

]

5.2 Gerneral description

The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to other forces of nature. It applies to the cosmological and astrophysical realm, including astronomy.

The theory transformed theoretical physics and astronomy during the 20th century, superseding a 200-year-old theory of mechanics created primarily by Isaac Newton. It introduced concepts including spacetime as a unified entity of space and time, relativity of simultaneity, kinematic and gravitational time dilation, and length contraction. In the field of physics, relativity improved the science of elementary particles and their fundamental interactions, along with ushering in the nuclear age. With relativity, cosmology and astrophysics predicted extraordinary astronomical phenomena such as neutron stars, black holes, and gravitational waves. [Reference:

https://en.wikipedia.org/wiki/Theory_of_relativity


]
Observation:

There are many claims in the general description. They are addressed in several subsequent sections.


5.3 Minkowski Space

Minkowski Space was a predecessor to relativity.

Minkowski space is closely associated with Einstein's theories of special relativity and general relativity and is the most common mathematical structure on which special relativity is formulated. While the individual components in Euclidean space and time may differ due to length contraction and time dilation, in Minkowski spacetime, all frames of reference will agree on the total distance in spacetime between events.
Because it treats time differently than it treats the 3 spatial dimensions, Minkowski space differs from four-dimensional Euclidean space.

[Reference:

https://en.wikipedia.org/wiki/Minkowski_space


]

Observation:

Einstein is often given credit for the fusion of space and time.

Minkowski treated time as reversible, as shown in his light-cone diagram.

https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Minkowski_diagram_-_causality.svg/384px-Minkowski_diagram_-_causality.svg.png


The caption for the image:

Fig 4-6 Past and future relative to the origin. For the grey areas a corresponding temporal classification is not possible.
Straight lines passing the origin which are steeper than both photon world lines correspond with objects moving more slowly than the speed of light. If this applies to an object, then it applies from the viewpoint of all observers, because the world lines of these photons are the angle bisectors for any inertial reference frame.
Therefore, any point above the origin and between the world lines of both photons can be reached with a speed smaller than that of the light and can have a cause-and-effect relationship with the origin.
This area is the absolute future, because any event there happens later compared to the event represented by the origin regardless of the observer, which is obvious graphically from the Minkowski diagram in Fig 4-6.

Following the same argument the range below the origin and between the photon world lines is the absolute past relative to the origin. Any event there belongs definitely to the past and can be the cause of an effect at the origin.

The relationship between any such pairs of event is called timelike, because they have a time distance greater than zero for all observers. A straight line connecting these two events is always the time axis of a possible observer for whom they happen at the same place. Two events which can be connected just with the speed of light are called lightlike.

In principle a further dimension of space can be added to the Minkowski diagram leading to a three-dimensional representation. In this case the ranges of future and past become cones with apexes touching each other at the origin. They are called light cones.

(end caption)

Here is more from the topic [same reference] regarding this Fig 4-6.

Straight lines passing the origin which are steeper than both photon world lines correspond with objects moving more slowly than the speed of light. If this applies to an object, then it applies from the viewpoint of all observers, because the world lines of these photons are the angle bisectors for any inertial reference frame. Therefore, any point above the origin and between the world lines of both photons can be reached with a speed smaller than that of the light and can have a cause-and-effect relationship with the origin. This area is the absolute future, because any event there happens later compared to the event represented by the origin regardless of the observer, which is obvious graphically from the Minkowski diagram in Fig 4-6.

Following the same argument the range below the origin and between the photon world lines is the absolute past relative to the origin. Any event there belongs definitely to the past and can be the cause of an effect at the origin.

The relationship between any such pairs of event is called timelike, because they have a time distance greater than zero for all observers. A straight line connecting these two events is always the time axis of a possible observer for whom they happen at the same place. Two events which can be connected just with the speed of light are called lightlike.

Observation:

Minkowski is plotting time with x, but for consistent units, a variable named ct is used (time multiplied by the constant c).

It is important to note Minkowski influenced the development of relativity.

The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.

—Hermann Minkowski, 1908, 1909

Though Minkowski took an important step for physics, Albert Einstein saw its limitation:

At a time when Minkowski was giving the geometrical interpretation of special relativity by extending the Euclidean three-space to a quasi-Euclidean four-space that included time, Einstein was already aware that this is not valid, because it excludes the phenomenon of gravitation. [Reference:

https://en.wikipedia.org/wiki/Minkowski_space  ]

Observation:

Einstein integrated gravitation into the quasi-Euclidean four-space.  Here is a long excerpt.

Some scientists and philosophers of science were critical of Newton's definitions of absolute space and time. Ernst Mach (1883) argued that absolute time and space are essentially metaphysical concepts and thus scientifically meaningless, and suggested that only relative motion between material bodies is a useful concept in physics.


Mach argued that even effects that according to Newton depend on accelerated motion with respect to absolute space, such as rotation, could be described purely with reference to material bodies, and that the inertial effects cited by Newton in support of absolute space might instead be related purely to acceleration with respect to the fixed stars.

In 1907 Minkowski named four predecessors who contributed to the formulation of the relativity principle: Lorentz, Einstein, Poincaré and Planck. And in his famous lecture Space and Time (1908) he mentioned Voigt, Lorentz and Einstein. Minkowski himself considered Einstein's theory as a generalization of Lorentz's and credited Einstein for completely stating the relativity of time.

Einstein (1908) tried – as a preliminary in the framework of special relativity – also to include accelerated frames within the relativity principle. In the course of this attempt he recognized that for any single moment of acceleration of a body one can define an inertial reference frame in which the accelerated body is temporarily at rest. It follows that in accelerated frames defined in this way, the application of the constancy of the speed of light to define simultaneity is restricted to small localities. However, the equivalence principle that was used by Einstein in the course of that investigation, which expresses the equality of inertial and gravitational mass and the equivalence of accelerated frames and homogeneous gravitational fields, transcended the limits of special relativity and resulted in the formulation of general relativity.

Eventually, Einstein (1912) recognized the importance of Minkowski's geometric spacetime model and used it as the basis for his work on the foundations of general relativity.

Acceptance of special relativity

Planck, in 1909, compared the implications of the modern relativity principle — he particularly referred to the relativity of time – with the revolution by the Copernican system. An important factor in the adoption of special relativity by physicists was its development by Minkowski into a spacetime theory. Consequently, by about 1911, most theoretical physicists accepted special relativity. [Reference:

https://en.wikipedia.org/wiki/History_of_special_relativity  ]

My observations:

First:

Physicists at the time were determined to get relative time, to replace Newton's absolute time, which cannot be affected by the observer.
The phrase "simultaneity is restricted to small localities" reveals another concern with time.

Both the electric force and the gravity force are simultaneous between the 2 participants but each force decreases by the inverse square of the distance between them.

In reality, the 2 fundamental forces cannot be restricted to a "small locality."

Second:

One must note Einstein's work with the "equivalence of accelerated frames and homogeneous gravitational fields" brought with it "a new treatment of gravity, replacing the understanding of the force at that time (1912)."

This "new treatment" is simply wrong. The replacement of our "understanding of the force" was a mistake.

The unstated goal of some physicists "at that time (1912)" was replacing Newtonian physics with the possible flexibility of relative space and time.

There was no evidence space-time was better than Newton's force. The dubious evidence was provided from Eddington, by photographs taken during a total solar eclipse in 1919.

There is a section Eddington Experiment, because it was pivotal for the acceptance of relativity.

That result in 1919 was sufficient for the 4-dimensions of space-time becoming a fundamental concept of physics.

The perceived "homogenous field" can arise only in the combination of a number of tiny masses near a much larger mass, like the drop of a feather and iron ball in a vacuum. This free-fall acceleration behavior was famously demonstrated on Earth and on the Moon.

Free-fall acceleration is a very limited context of gravity.  The much larger mass has only the illusion of no motion. Perhaps Einstein accepted the illusion because space-time curvature cannot affect the other mass. For example, all the planets in the solar system are not in free fall acceleration in the gravitational fields of all other planets. It is a mistake basing a replacement of the real force of gravity on this context of a particular behavior.
There are descriptions of Einstein's thought experiments. I cannot know if they are fabricated stories.

If Einstein truly used only free-fall acceleration to develop his theory, then the theory matches his understanding of the requirements for spacetime. Unfortunately for his theory, he missed the complete set of behaviors observed with gravity.

An observer having any mass, must interact with any other mass by inverse square of distance, as explained by Newton, and as widely accepted, before space-time, like when predicting Neptune.

Space-time enables the moving observer to never affect another mass. This is simply violating Newton's force and replacing it with an incorrect interpretation.

I will take liberties here when putting relativity into simpler terms.


The special observer is moving, so in relativity their motion is described by the combination of 4 variables at each instant, in this "quasi-Euclidean four-space"

The 4 are: dx, dy, dz, dct, where "d" represents the "delta" or change in coordinate in that Euclidean dimension.

The math requires the same units among all the participants; km is the standard for a linear dimension value.  Since the units for time are unlike the spatial dimensions, the time value is multiplied by the constant c, to get km as units. This product is shown as ct, and its value in the set of 4 is dct.

This observer can measure the direction to another mass to get a vector to the source of that object's gravitational field.

Relativity is background independent, so no coordinates in real, physical, or absolute space are available, for the observer or for any object they observe.

Every distance or location measurement is relative to the moving observer's current position.

Space-time is simply the mechanism for the application of the tensor equations affecting the path of the special, moving observer by using this set of changes in 4 coordinates per unit of time.

Space-time has no application other than supporting the equations of relativity.

This is the only context where this "union of the two [space and time] will preserve an independent reality."

My observation:

The complete phrase after "this union" has an add choice of words. Newton defined absolute space and time as independent of an observer.  Newton defined an "independent universe, or reality.

Perhaps, spacetime is independent of reality, when confined to the observer's reference frame.

Space-time is defined for the special moving observer whose motion has no effect on any other mass or charge, during the motion. 

Since space-time does not identify an effect between the observer's and another's charge, space-time implicitly ignores any mutual interaction between the observer and the rest of the universe which will have mass and could have a charge.
Of course, other masses must react to the moving observer's mass, but relativity identifies none.

An ocean tide changing with phases of the Moon is strictly a behavior from the force of gravity between masses. That narrow behavior by a force cannot be explained by space-time which tries to mimic another narrow behavior of gravity, free-fall acceleration in only a gravitational field. A tide cannot be characterized as a free-fall acceleration toward the Moon.

This independent reality" is useless, beyond a game of an odd, alternate reality, where literally nothing happens to whatever you pass during your motion.

This certainly a wrong form of independence for physics, where any motion is always driven by external forces. The forces from mass or charge are always mutual, though reduced by inverse-square of distance. Thus, any body in motion must affect others, though it could be too weak to measure.

Space-time is wrong; Newton's force of gravity is correct.

I must make a comment about absolute time and the observer's time.

If an observer ever questions their personal time, like for possible time dilation, they can always "look out the window" to check the current, correct absolute time.

The "window" reference is from Einstein's famous thought experiment on a hypothetical train, using a hypothetical light clock, and there is another observer outside the train.
I heard this phrase of "look out the window" from someone else in a YouTube video, long ago, but it still resonates with me.

Our version of Newton's absolute time is driven by an atomic clock, and cannot be affected by anyone, certainly not by someone in a train using a light clock.

Space-time prevents "looking out the window" when restricted to a time value which can be manipulated during the special observer's motion, because it is 1 of the 4 parameters.

Newton could not envision someone altering the normal progression of time's increments, so it was simply called absolute time.

For consistency among all observers, one should not be able to change the absolute time that all share.

5.4 summary of section

Einstein did not understand thar the gravitational field is a behavior observed on or near the Earth.

The free-fall acceleration It is not a behavior with celestial objects. In the context of an initial  distance between bodies, Newton's force of gravity must be applied.

This is an instantaneous, mutual force between 2 masses, diminishing by the inverse-square of their mutual distance.

By using only a gravitational field from the other body to affect the path of the special observer, Einstein makes 3 significant mistakes:

1) the other body, though having mass, is unaffected by the mass of the special observer; this is a mistake,

2) when the special observer has an electrical charge, the path of the special observer must be affected by a magnetic field in its path, instantaneously; ignoring this combination for the Lorentz force is a mistake.

Go to Table of Contents, to read a specific section.

last change 01/25/2022