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2 Some Philosophical Comments



Название2 Some Philosophical Comments
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2.2. Some Philosophical Comments.

揂bsoluteand 揜elativeare a pair of antithetical and interdependent concepts. 揜elativewould be meaningless, if there were no 揂bsoluteand, vice versa, 揂bsolutewould not exist without many 揜elatives 揂bsoluteinvolves many 揜elativesand the 揜elativesunderlie the 揂bsolute One cannot say 揂ll things are relative The 揂llitself bears a tone of 揂bsolute

Endless time is both absolute and relative. It is absolute in terms of the universal time-synchronism µ §. It is relative because all events are ordered by timing: 揃efore 揂fteror 揝imultaneous Moreover, the absolute time-synchronism µ § can be directly deduced from the relativity principle (See .2).

Boundless space is both absolute and relative. It is absolute because the length is absolutely constant with regard to any reference system:

µ §.

It is absolute also because the boundless and vacuous space exists independently and permanently by itself, no matter it is being sensed or not. It is relative because all bodies are relatively located: 揕eft vs Right 揂bove vs Below 揃efore vs Behind It is relative also because the values of a body抯 coordinates depend upon the selection of a reference system.

Matter is both absolute and relative. It is absolute in terms of a body抯 absolutely constant static inertial eigenmass and non-potential gravitational eigenmass. But, it is also relative because the value of a body抯 moving mass depends upon the body抯 relative velocity (which in turn depends upon the selection of a reference system) and the value of a body抯 gravitational mass depends upon the potential experienced by the body (which in turn depends upon the distance between the body and the gravitational center).

揝pace 揟imeand 揗atterare three 揂bsolutes Exactly, the three 揂bsolutesconstitute the absolute system of units (CGS), from which all units of mechanical quantities are derived. The three are independent from each other. Matter does not cause any space-time warp. Matter, static or moving, and space have no influence on the universal time-synchronism. Space and time are not material. 揝pace 揟imeand 揗atterexist and count by themselves separately and independently.

It is unfair to criticize the Newtonian mechanics for its absolute and non-material space-time. The only shortcoming in the Newtonian mechanics is its ignorance of relative moving mass aside from absolute static eigenmass, which renders it non-relativistic. But, the Newtonian mechanics remains completely valid in cases of subjective self-assessment and must be used, for example, by cosmonauts. Referring to himself, everybody is his own absolute reference system. So, there exist countless absolute reference systems.


The boundless universe exists endlessly over time and does not have 揝ingularityanywhere at any moment because there is no such so-called 揕orentz factoras µ § at all, which can lead to infinity or even imaginary quantities when µ §. 揂ll physical laws fail at the Singularity which is currently a rather popular saying in the physics community, is a sheer nonsense.

Appendix A. Analysis of the Lorentz and Galilean Transformations

. Constant Speed of Light Violates the Relativity Principle.By use of the transmission of two successive electromagnetic signals between two relatively moving bodies 揂and 揃 we can demonstrate that the postulate of constant speed of light violates the principle of relativity.

.1. Acceptance of the Postulate of Constant Speed of Light.

Suppose 揃is moving away from 揂

At a moment of µ §, when the distance between 揂and 揃is µ §, 揂sends the first signal toward 揃 Signal-I spends time µ § to reach the moving 揃at a moment of µ §, when the distance from 揂to 揃has become µ §, so that µ § and µ §. On the other hand, signal-I passes the distance µ § with the constant speed of light µ § and spends time µ § to reach 揃so that µ § or µ §.

At the moment µ §, when the distance between 揃and 揂is still µ §, 揃instantly sends the received signal-I back to 揂 Signal-I passes the same distance with the constant speed and spends time µ §to reach 揂at a moment of µ §.

At a moment of µ §, when the distance between 揂and 揃has become µ §, 揂sends the second signal toward 揃 The interval between the two signals is µ §. Signal-II spends time µ § to reach the moving 揃at a moment of µ § so that µ §.The distance passed by signal-II from 揂to 揃has become µ § so that µ §. On the other hand, signal-II passes the distance µ § with the constant speed of light µ § and spends time µ § to reach 揃so that µ § or µ §.

At the moment µ §, when the distance between 揃and 揂is still µ §, 揃instantly sends the received signal-II back to 揂 Signal-II passes the same distance µ § with the constant speed µ § and spends time µ § to reach 揂at a moment of µ §.

The interval between the two signals sent by 揂is µ §. The interval between the same two signals received by 揃is: µ §.

Since µ §, µ § and µ §, so µ §. Therefore,

µ §.

The interval between the two signals changes from µ § at 揂to µ § at 揃 The ratio of the change is: µ §.

Since 揃reflects the two signals instantly back to 揂 so the two incoming signalsinterval µ § is exactly the two outgoing signalsinterval µ §. Therefore, µ §. On the other hand, the reflected signal-I and signal-II reach 揂at the moment of µ § and the moment of µ § respectively. Therefore, the interval between the two reflected signals received by 揂is: µ §.

Since µ § and µ §, so we have:

µ §.

The ratio of the change of the interval between the same two signals sent by 揃and received by 揂is:

µ §

According to the principle of relativity, the two relatively moving bodies 揂and 揃are on equal terms and none of them is privileged. µ § violates the relativity principle and testifies against the postulate of constant speed of light.

Moreover, µ § reveals that, due to the postulate of constant µ §, the so-called Lorentz factor µ § 搒neaksinto the µ § based E-L Transformation.

.2. Rejection of the Postulate of Constant Speed of Light.

At a moment of µ §, when the distance between 揂and 揃is µ §, 揂sends the first signal toward 揃 Signal-I spends time µ § to reach the moving 揃at a moment of µ §, when the distance from 揂to 揃has become µ §, so that µ § and µ §. On the other hand, signal-I passes the distance µ § with the speed of light µ § and spends time µ § to reach 揃so that µ § or µ §.

At the moment of µ §, when the distance between 揃and 揂is still , 揃instantly sends the received signal-II back to 揂 Since 揃is moving away from 揂 so the signal sent from 揃to 揂has speed µ § with regard to 揂 The signal-I passes the same distance µ § and spends time µ § to arrive back to 揂at a moment of µ §. Since µ § and µ §, so we have µ §. Therefore, µ §.

At a moment of µ §, when the distance between 揂and 揃has become µ §, 揂sends the second signal toward 揃 The interval between the two signals at 揂is µ §. The signal-II spends time µ § to pass a distance of µ § to reach 揃at a moment of µ § so that µ § and µ §. On the other hand, the signal-II sent from 揂to 揃has the speed µ § to cover the distance µ § so that it spends time µ §to reach 揃 Therefore, µ § or µ §.

At the moment of µ §, when the distance between 揃and 揂is still µ §, 揃instantly sends the received signal-II back to 揂at the speed µ §, not µ §, because 揃is moving away from 揂with a speed µ §. The signal-II passes the same distance and spends time µ § to reach 揂at a moment of µ §.

The interval between the two signals sent by 揂is . The interval between the same two signals received by 揃is µ §.

Since µ §, µ § and µ §, so µ §. Therefore,

µ §.

The interval between the two signals changes from µ § at Ato µ § at 揃 The ratio of the change is: µ §.

Since 揃reflects the two signals instantly back to 揂 so the two incoming signalsinterval µ § is exactly the two outgoing signalsinterval µ §. Therefore, µ §. On the other hand, the reflected signal-I and signal-II reach 揂at the moment of µ § and the moment of µ § respectively. Therefore, the interval between the two reflected signals received by 揂from 揃is: µ §.

Since µ §, µ §, µ §, so µ §. On the other hand, µ §, µ §, so we have: µ § and µ §.

Therefore, µ §.

Finally, because of µ § or µ §, we have µ §.

Therefore, µ §.

The principle of relativity is observed and the Lorentz factor has no way to 搒neakinto our relativity theory which is based on variable speed of light.

. Invariant Transformation between Two Reference Systems.

.1. Invariance of Transformation Equations Themselves.

Strict compliance with the principle of relativity demands that the forward and the reverse transformations have identical forms not only for a group of transformation equations as a whole but also for every individual trasformation equation in the group.

.1.1. Galilean Transformation.

The group of forward transformation equations is:

µ §

µ §

µ §

µ §

Due to the universal time-synchronism µ § and the relative motion抯 µ §, from the forward trasformation equation µ § can directly get its invariant reverse transformation equation µ §. So, the whole group of equations and every individual equation in the group have invariant reverse transformations respectively.

.1.2. Lorentz Transformation.

The group of forward transformation equations is:

µ §

µ §

µ §

µ §

First of all, the forward transformation equation µ §alone leads to a reverse transfomation µ §, the form of which violates the invariance demanded by the relativity principle. Secondly, the forword time-transformation µ § alone gives a reverse transformation µ § which violates the relativity principle抯 demand, too. Thirdly, the solution from the combination of the above two 搗iolatorsµ § gives µ §. The denominator in the second equation抯 parenthesis is µ §, not µ §. That is why, in order to make the group of reverse transformation equations invariant, it was necessary for Einstein to introduce a third 搗iolatorof the relativity principle — the postulate of constant speed of light µ §.

.2. Invariant Transformation of Spherical Wave Equation of Light.

Spherical wave equation of light in the µ §-system and the µ §-system are:

(1)

(2)

.2.1. Galilean Transformation.

The group of Galilean Transformation equations is:

µ §

µ §

µ § (3)

µ §

µ §

It can do the invariant forward transformation from (1) to (2). The first four equations in the group (3) have their own invariant reverse equations respectively. So, to achieve the invariant reverse transformation from (2) back to (1), it is necessary to examine whether an invariant reverse velocity-transformation equation can be deduced. Actually, due to µ § and µ §, we can get from (3):

µ § or µ §.

Thus, we get an invariant reverse velocity-transformation equation µ §. An identical reverse transformation group does exist: µ §

µ §

µ § (4)

µ §

µ §

(4) can invariantly transform (2) back to (1). Therefore, the Galilean Transformastion (4) completely complies with the principle of relativity.

.2.2. Interdependence of Lorentz抯 and Einstein抯 Postulates.

The group of E-L Transformation equations is:

µ §

µ §

µ § (5)

µ §

µ §

It can do invariant forward transformation from (1) to (2). As we have proven in .1.2., in order to get an identical reverse transformation group of equations, it is necessary for Einstein to add his µ § postulate to Lorentz抯 postulate of µ §. The two postulates, both of them violate the principle of relativity, are interdependent upon and indispensable for each other.

Suppose Einstein抯 µ § is coupled with Galilean µ §so that the forward transformation equations become: µ §

µ §

µ §

µ §

Placing them into (1), we can get from µ §:

µ § or µ §.

Therefore, the forward transformation group becomes:

µ §

µ §

µ § (6)

µ §

µ §

which can invariantly transform (1) into (2).

To do the reverse transformation from (2) back into (1), we must first deduce an identical reverse transformation group from (6). Unfortunately, placing µ §, µ § and µ § into µ §, we get µ § or µ §.

Taking µ § into consideration, we have µ §. Finally, the reverse time-transformation equation is µ §, which is totally different from the forward time-transformation equation.

Obviously, Einstein抯 µ § alone without Lorentz抯 µ §cannot do the invariant reverse transformation of the spherical wave equation back from (2) to (1).

Now, let抯 examine if Lorentz抯 µ § alone without Einstein抯 µ § can do the invariant transformation between (1) and (2). In this case, the forward transformation equations are:

µ §

µ §

µ §

µ §

Placing them into (1), we can get from µ §:

µ §

or µ § or µ §.

Because of µ § and µ §, we have:

µ §.

Thus, in order to be able to transform (1) invariantly into (2), the forward transformation group must be:

µ §

(7)

µ §

Unfortunately, an identical reverse velocity-transformation equation µ § cannot be deduced. Obviously, Lorentz抯 µ § alone without Einstein抯 is unable to make an invariant reverse transformation from (2) back to (1).

To sum up, either Einstein抯 or Lorentz抯 µ § cannot survive alone. They are interdependent and must go together to constitute the E-L Transformation. Einstein claims that his E-L Transformation relies only on two principles — the principle of relativity and the principle of constant speed of light. It is not true. Actually, his E-L Transformation relies on two postulates, his and Lorentz抯 µ §, and one principle — the principle of relativity.

. Lorentz抯 Length-Contraction Postulate Causes Wrong Formula of Aberration.

From the E-L Transformation (5), which contains both µ § and µ §, we can directly obtain: µ §.

From the above transformation group (7), which contains only Lorentz抯 postulate µ § without Einstein抯 , we also can directly obtain:

µ §.

Since and , so in both cases we haveµ § which is Einstein抯 wrong formula of aberration.

From the Galilean Transformation (3), which contains µ §, we can directly obtain:

µ §.

From the above transformation group (6), which contains only Einstein抯 without Lorentz抯 µ §, we also can directly obtain:

µ §.

So, in both cases we always obtain µ § which is our correct formula of aberration, regardless of whether or is involved.

In short, Lorentz抯 always causes Einstein抯 wrong formula of aberration., regardless of whether the transformation involves or . Therefore, it is Lorentz抯 wrong postulate µ § to blame for having misled Einstein to his wrong formula of aberration.

Appendix B. Angular Deflection of Light in the Sun抯 Gravitational Field

Suppose a body (or a photon) has static inertial mass µ § and non-potential gravitational mass µ §. The body passes over the sun抯 surface tangentially with velocity µ §. The sun抯 radius is µ §[µ §] and its gravitational mass is µ §[kg]].

In polar coordinates, µ §, where µ § and µ § are the radial and tangential components of µ §. Hence, µ § and µ §.


Let抯 first analyze the issue in the Newtonian framework: kinetic energy µ §, potential energy µ §, gravitational constant µ §[mµ §kgµ §sµ §]. The angular momentum and the total energy are: µ § (1)

µ § (2)

At the point of tangency µ §(µ §), the body has µ § and µ §. The conservation of angular momentum and energy can be expressed as:

µ § (3)

µ § (4)

From (1): µ § so that µ §. Let µ §, so µ § and µ §. Placing them into (2), we obtatin:

µ §.

Taking (3) and (4) into consideration, we have µ § and µ §. So,

µ §.

Therefore,

µ §.

Since µ §, so µ §. As µ §, we have:

µ §.

It can be seen from the above figure, the angular deflection on the sun抯 right side is µ §. So, µ § and µ §. Since µ §, so µ §. The total angular deflection on both sides of the sun is: µ §[radian]µ §拻. However, astronomic observation gives µ §拻. The discrepancy stems from that the observation is our relative assessment of the phenomenon whereas the Newtonian mechanics, particularly its kinetic energy µ §, is non-relativistic.

An observer (subject) must use our new relativistic mechanics to deal with his relative assessment of a body抯 (object抯) motion. In our new relativistic mechanics, we have moving mass µ §, momentum µ § and angular momentum µ §.

In a closed energy-conservative system with the sun at the center, we must use our relative kinetic energy µ § given by formula (47): µ §

or µ §

At the point of tangency µ §, where µ § and µ §, we have:

µ § and µ §.

On the other hand, the potential energy is µ §, where µ § is the 損otential gravitational massof the body. At the distance of µ § from the sun抯 center, the gravitational acceleration is µ §. Therefore, µ §.

Since µ § at any point of the trajectory, so µ §. Hence, µ § and µ §. Passing over the sun抯 surface and flying to µ §, any body ought to lose the sun抯 second escape velocity which is only about µ §. So, µ § and µ § anywhere on the entire trajectory. Thus, µ §. At the point of tangency µ §, we have: µ §.

In the framework of new relativistic mechanics, the laws of conservation of angular momentum and energy can be expressed as:

µ § (1

µ § (2

At the point of tangency µ §, we have: µ § (3

µ § (4

From (1, we have µ §, so µ §. Let µ §, we have:

µ § and µ §.

Placing them into (2, we obtain: µ §,

where µ §, µ §, µ §.

Therefore, µ §.

From (3 and (4: µ §, µ § and µ §.

So, µ §, µ §, µ §.

Hence, µ §.

Since µ §, we can obtain:

µ §µ §.

Therefore, µ §. As µ §, then µ §. Because of µ §, we have: µ §.

Finally, we get: µ §[radian].

Total angular deflection on both sides of the sun is µ §[radian]µ §拻 which matches the astronomic observation.Our new relativistic mechanics has proven that the angular deflection is irrelevant to a body抯 eigenmass and photons behave as any ponderable bodies under the sun抯 gravitational attraction. In short, the gravitational attraction is a mechanical phenomenon. It does not warp the space-time. Einstein抯 geometrical interpretation of the gravity is unnecessary if not wrong. The force of gravitational attraction is a mechnical quantity and can be interpreted within the mechanical domain.

Appendix C. The Perihelion Motion of Mercury

In 1915, Einstein published a paper on the 揈xplanation of the Perihelion Motion of Murcury from the General Theory of Relativity He writes: 揑 find an important confirmation of this most fundamental theory of relativity, showing that it explains qualitatively and quantitatively the secular rotation of the orbit of Mercury.We will show that his explanation is a complete failure and, in contrast, our new relativistic mechanics can precisely calculate the perihelion motion of Mercury.

. The Failure of the Newtonian Mechanics.

It抯 well known that the Newtonian mechanics cannot explain a planet抯 perihelion motion. In order to compare the three mechnics (Newtonian, Einstein抯, New relativistic), however, we first study why the Newtonian mechanics fails.

Suppose a planet moves with velocity µ § around the sun. In polar coordinates (µ §) with the sun at the origin, we have µ §, where µ § and µ § are radial and tangential components of µ § respectively. According to the Newtonian mechnics, the planet抯 kinetic energy is µ §, potential enegy is µ § and angular momentum is µ §, where µ § is the sun抯 mass and µ § is the gravitational constant. The conservative orbital energy µ § and angular momentum µ § are:

µ § (1.1)

µ § (1.2)

From (1.2): µ §, so µ §. Let µ §, we have:

µ § and µ §. Therefore, from (1.1) we obtain:

µ §. (1.3)

At the aphelion (µ §) and the perihelion (µ §) the velocities are completely tangential µ § and µ §. Therefore, the conservative orbital energy and angular momentum are:

µ § (1.4)

µ § (1.5)

From (1.4) and (1.5), we have:

µ § or µ §. (1.6)

We also have: µ § or µ §.

Thus, µ § or µ § (1.7)

Placing (1.6) and (1.7) into (1.3), we obtain: . Let µ § and µ § so that µ §, we have:

µ § (1.8)

Finally, µ §.

Moving from the aphelion to the perielion and back from the perihelion to the aphelion, the planet抯 orbit is a strict ellipse without the perihelion motion: µ §. The Newtonian mechanics fails, because: (1) It is non-relativistic so that its kinetic energy µ § cannot be used by an observer (subject) to relatively assess the motion of a planet (object); (2) It does not recognize the variable 損otential gravitational massand deems a body抯 gravitational mass constant.

. Questioning Einstein抯 Explanation.

In his 1915 paper Einstein gave the following formula for calculating the perihelion motion:

µ § (2.1)

where µ § is the perihelion motion per one round of orbit, µ § the orbital period, µ § the orbit抯 semimajor axis, µ § the orbit抯 eccentricity and µ § the speed of light.

For Mercury: µ §[earth day]µ §[s], µ §[cm], µ §. With these data, (2.1) gives Mercury抯 perihelion motion per mercury-year as µ §[radian]. For every 100 earth-year Mercury makes about 415.28 orbital rounds, so its perihelion motion per 100 earth-year is:

µ §[radian]µ §拻

which matches the astronomic observation, and Einstein declared his success.

Einstein抯 formula (2.1) comes from his formula:

µ § (2.2)

where µ § is the angle described by the radius-vector between perihelion and aphelion, µ § and µ § are the reciprocal values of the perihelion and aphelion radius-vectors µ § and µ § respectively.

According to Einstein, his (2.2) comes from:

µ § (2.3)

or, upon expansion of µ §, he obtained approximately:

µ § (2.4)

Einstein claimed that the integration yields his formula (2.2). This is a grave blunder! Actually, a correct integration should be as follows:

µ §

µ §

µ §

µ §.

So, µ §

µ §.

Therefore, the correct integration of (2.4) yields:

µ §.

Mercury抯 µ §[m] and µ §[m], µ §. Since the sun抯 gravitational mass µ §[kg] and the gravitational constant µ §[mµ §kgµ §sµ §], so µ §[m] and µ §[radian] or µ §拻 per 100 earth-year. It is far from the astronomical observation.

Einstein抯 (2.4) is an approximation from his (2.3), which in turn originates from the following equation obtained by him from his general theory of relativity:

µ §. (2.5)

Einstein wrote: “µ § and µ § signify the roots of the equation µ § and closely correspond to the neighboring roots of the equation that arises from this one by the omission of the last term This means that his (2.5) can be approximately expressed as:

µ §. (2.6)

Then, Einstein wrote: 揟hus, it can be established with the precision demanded of us that”

µ §. (2.3)

This is again a questionable approximation, which requires:

µ §

or µ §.

This is impossible, unless µ §. However, µ §[m]µ §. Moreover, if µ §, then (2.3) and (2.6) would be degenerated into the Newtonian formula (1.8) and the orbit would be strictly elliptic without perihelion.

To check Einstein抯 calculation, we have done a computerized digital integration directly from his (2.6). The result is µ § or µ §[radian] or µ §拻 per 100 earth-year. The perihelion motion is negative in the backward direction!

Moreover, Einstein抯 formula (2.1) is dubious, according to which the perihelion motion µ § even when µ §. However, if a planet moves along a circular orbit (µ §) with neither perihelion nor aphelion, how can its orbit have any perihelion motion µ §?

Mercury抯 orbit is not a strict ellipse. That抯 why it has perihelion motion. However, Einstein makes multiple approximations by use of the following relationships among elliptic orbit抯 parameters:

µ §, µ §, µ §.

The approximations cause the eccentricity µ § to appear in his (2.1). Actually, his (2.2) becomes µ § and he approximately obtained µ §. Since an elliptic orbit抯 period is µ §, so µ §. This final elliptic approximation led him to his formula (2.1) µ § with the irrational appearance of the eccentricity in it.

For every round of its orbit (µ §, Mercury抯 perihelion motion is just about µ §拻. To deal with such a fine quantity, it does not allow Einstein to do so many arbitrary approximations.

To sum up, Einstein抯 general theory of relativity cannot explain Mercury抯 perihelion motion. He has tried to narrow the gap between his theory and the reality by one wrong integration and many arbitrary approximations. His formula (2.1) is a fabrication tailored specially for Mercury. That is why (2.1) fails to explain the perihelion motions for Earth and Mars. Einstein was unfair to blame 搕he small eccentricities of the orbits of these planetsfor his failure.

. Explanation from the Galilean Relativistic Mechanics.

We study a planet抯 orbital motion in a reference system with the sun at its origin. According to our Galilean relativistic mechanics, a body moving with velocity µ § has moving mass µ §.

In relation to the sun, a planet has relative kinetic energy: µ §. At the distance µ §, its potential energy is µ §, where µ § is its 損otential gravitational mass µ § is its 搉on-potential gravitational mass µ § is the sun抯 gravitational mass and µ § is the gravitational acceleration. Since µ §, so we have:

µ §, where µ §.

Therefore, the planet抯 orbital conservative energy can be expressed as:

µ §

or µ §. (3.1)

A planet抯 angular momentum is µ §, where µ §. So, we have:

µ § or µ §. (3.2)

Placing (3.2) into (3.1), we get:

µ § or µ §. (3.3)

On the other hand, since µ § and µ § so that we have:

µ §. (3.4)

From (3.2) and (3.4) we obtain: µ §

or µ §. (3.5)

Eliminating µ § by use of (3.3), we get: µ §

or µ §.

Let µ § so that µ §. The above equation becomes:

µ §

or µ §.

Therefore, we have: µ § (3.6)

where µ § and µ §.

For a computerized digital integration of (3.6), we need to know the expressions of conservative quantities µ § and µ §. At the apogee and the perigee, the velocity has only tangential components µ § and µ § respectively. The conservation of angular momentum can be expressed as:

µ § or µ §

or µ §.

Due to µ § and µ §, if we denote µ § and µ §, then we have:

µ § (3.7)

or µ § (3.8)

On the other hand, from (3.1) we have the conservative quantity µ § at the apogee and the perigee as: µ § (3.9)

From (3.9) we have: µ §. (3.10)

Placing (3.10) into (3.7), we can obtain:

µ §

or µ §µ §.

Solving this equation, we obtain:

µ §µ §

where µ §[m], Mercury抯 µ §[m] and µ §[m] for Mercury. So, is known. Therefore, from (3.8) and (3.9) we can calculate:

µ § and µ §.

Finally, the computerized digital integration of (3.6) yields µ §. So, the perihelion motion of Mercury is µ §[radian]µ §拻 per one orbital round. In 100 earth-year Mercury makes 415.28 rounds. Its perihelion motion is µ §拻 µ §拻.

The result matches the astronomic observation. Our new relativistic explains the perihelion motion of Mercury correctly.

Appendix D. Black Hole and Dark Matter

Simple astronautical mechanics tells us: if a celestial body with radius µ § and gravitational mass µ §, then in case of µ § any body (including photon) with outgoing velocity µ § cannot escape. This celestial body is a black hole and µ § is the Schwarzschild radius.

A spherold with radius µ § has volume µ §. With gravitational mass of µ §, the spheroid has an average density of µ §. From µ § and µ § we can obtain µ §. Therefore, we can have the relationship between a black hole抯 radius µ § and its average density µ §:

µ § [m] µ § µ § µ § µ §

µ § [kg/mµ §] µ § µ § µ § µ §

Obviously, it is unnecessary for black holes to have high density. A gigantic spheroid with matters of very low density can be a black hole. For example, a spheroid with a radius of one billion kilometers (µ §[m]) but small density (µ §[kg/mµ §] which is thinner than water) can form a black hole. A water spheroid (µ §[kg/mµ §]) with a radius of µ §[km] can be a 搘et black hole

There may exist two kinds of dark matter. We can抰 see black holes. We also can抰 see matters moving away from us with super-light speed. But, we can sense their existence because the gravitational force transfers much faster than the electromagnetic force.

Current popular cosmology deems that the gravitational attraction causes all matters to collapse to a 揝igularity of Universe The universe experineces a process of contraction to none. Then, a 揃ig Banggives the universe a birth from none. Unable to characrize the sigularity clearly and convincingly, the physics community has to declare 揂ll physical laws fail at the singularity

Our theory does not involve the Lorentz factor µ §. There can抰 be infinitely large gravitational attraction to cause the universe to collapse to a singularity. The universe is endles and boundless. 揥arp space-time 揟ime Tunnel 揥orm Hole 揝tring Theoryare all dubious concepts.


Some Notes for You to Catch the Essence of the Above Lengthy Paper

Einstein's theory of relativity contains so many fundamental and fatal mistakes that I could not have my paper 獸undamental Revision of Einstein's Theory of Relativitywritten shorter. The following notes may help you go through my lengthy paper patiently and catch its essence easier.

A Grave Century-Old Misunderstanding

About the Invariant Transformation of Maxwell抯 Electromagnetic Field Equations*

Invariant transformation of Maxwell抯 electromagnetic field equations was used by Einstein to justify his Lorentz Transformation (LT), which is the corner-stone of his relativity theory. Actually, however, a careful analysis proves that his LT cannot invariantly transform Maxwell抯 field equations.

In a vacuum without free electric charge and conduction current, Maxwell抯 field equations are:

µ §, µ §

µ §, µ §

µ §, µ §

µ §, µ §

First, his LT cannot invariantly transform µ § and µ §, which were omitted (intentionally or inadvertently?) by Einstein, into µ § and µ §.

Secondly, Maxwell抯 electromagnetic field equations do not describe electromagnetic wave抯 propagation and have nothing to do with the speed of light µ §, although µ §allows us to write the remaining six equations as: µ §, µ §

µ §, µ §

µ §, µ §

Here, µ §is just a constant coefficient and not subject to transformation.

In his 1905 and 1907 papers, however, Einstein ignored µ § and µ §, and erroneously wrote:

µ §, µ §

µ §, µ §

µ §, µ §

µ § are the electric intensities (unitµ §), µ § are the magnetic intensities (unitµ §), µ § is magnetic permeability (unitµ §), µ § is dielectric constant (unitµ §). The incompatibility of units between two sides of the above equations reveals that Einstein抯 version of Maxwell抯 field equations was incorrectly written and misled readers and himself to believe that µ § in the field equations is not a constant coefficient but the real speed of light subject to transformation.

Thirdly, Einstein claimed that his LT can invariantly transform his version of all the above six equations from the µ §-system into the µ §-system:

µ §, µ §

µ §, µ §

µ §, µ §

where µ §, µ §

µ §, µ §

µ §, µ §

Electric field intensity µ § and magnetic field intensity µ § have different units. How can their components be added to or subtracted from each other?

Worst of all, his LT can only satisfy the two equations of µ § and µ §, which are longitudinal along the µ §-direction of the relative motion µ §, but cannot invariantly transform other four transverse equations of µ §,µ §,µ §,µ §. Without thoroughly examining all the six equations, Einstein hastily declared that his LT could invariantly transform all his wrong-written equations.

About the Invariant Transformation of Electromagnetic Wave Equations*

Electromagnetic wave equations can easily be deduced from Maxwell抯 field equantions. In theµ §-direction, for example, the second order partial derivatives of µ § give:

µ § and µ §.

In vectorial form, the 3-dimensional electromagnetic wave equations can be concisely expressed as:

µ § and µ §

where µ §. They represent a spherical electromagnetic wave radiated at velocity µ § from a source fixed to the µ §-system抯 origin and µ § is measured in the µ §-system.

The relativity principle demands the wave equations be invariant in the µ §-system:

µ § and µ §

where µ § is measured in the µ §-system, in which the source of radiation is moving at velocity µ § along the µ §-axis.

Einstein's LT cannot invariantly transform the wave equations. In the µ §-direction, for example, due to Einstein抯 µ §, µ § and µ §, his LT leads to:

µ § and µ §.

No invariance can be realized unless there is no relative motion (a trivial case of µ § and µ §). Similarly, for the wave equations in the µ §- and the µ §-directions, his LT cannot realize invariant transformation either.

A Fast-moving Nuclear Bomb Is Less Powerful Than a Static One?**

Einstein抯 special relativity theory (SRT) gained him a world-wide reputation mainly because his famous formula µ § had put the theoretical foundation for building nulear weapons.

Assuming µ § so that µ § and by use of his LT between two relatively moving reference systems µ § and µ §, Einstein obtained an energy-transformation formula:

µ § or µ §

Then, he suggested that the extra energy µ § came from the kinetic energy µ §of mass µ § so that µ § or µ §. Finally, he obtained:

µ §. (A)

Here, µ § is the lost mass (mass-defect) due to nuclear reaction.

Upon expanding µ § into a power series, the above equation (A) becomes:

µ §.

In case of µ §, the two reference systems µ § and µ § coincide and the source of radiation (nuclear bomb) is at rest in both systems so that µ §. This is Einstein抯 famous formula of the mass-energy equivalence for a static body (a static nuclear bomb). If a nuclear bomb carried by a missile moves at large µ § so that high orders of µ § are not negligible, then his formula (A) directly gives:

µ § µ §; µ § µ §; µ § µ §.

As µ § increases, the efficiency of the mass-energy conversion decreases. This would mean that a fast-moving nuclear bomb is less powerful than a static one! However, a reasonable intuition tells us the contrary: A moving nuclear bomb must be more powerful because its defected mass has certain kinetic energy which must contribute certain additional amount of energy to the bomb's total output of energy.

There are many other mistakes in Einstein's SRT.* But, let's turn to his General Relativity Theory (GRT).

Einstein's General Relativity Theory Is Misleading

Einstein's GRT became famous due to his explanations of three astronomic observations: the perihelion motion of Mercury, the sunlight's red shift and the deflection of light by the sun's gravity. Actually, Einstein failed to explain Mercury's perihelion motion. His GRT can only approximately explain the sunlight's red shift and the deflection of light by the sun because the sun's gravity is weak.**

Einstein抯 Explanation of Mercury's Perihelion Motion Is a Sheer Fabrication***

Started with multiple arbitrary approximations, Einstein obtained:

µ §.

Einstein claimed that the integration gave: µ §. (A)

This is a grave mathematical blunder! Actually, a correct integration yields:

µ §

or µ §. (B)

In case of Mercury, µ §[m], µ §[m] and µ §[m]. The correct integration results in µ §拻 per 100 earth-year. It is far diffrent from the astronomical observation of 44拻 per 100 earth-year. Yet, with his wrong integration, Einstein claimed that his GRT successfully explained Mercury's perihelion motion of 44拻 per 100 earth-year. Actually, he hit the mark by a fluke!

Next, from his wrong formula (A) Einstein obtained the following formula for calculating a planet's perihelion motion: µ § (C)

where µ § is the perihelion motion per one round of orbit, µ § the orbital period, µ § the orbit抯 semimajor axis, µ § the orbit抯 eccentricity and µ § the speed of light.

According to Einstein抯 formula (C), if a planet moves along a circular orbit (µ §) with neither perihelion nor aphelion, it still has perihelion motion µ §, which is absurd!

Mercury抯 orbit is not a strict ellipse. That抯 why it has perihelion motion. However, Einstein again made multiple arbitrary approximations by use of the following relationships among parameters of an elliptic orbit:

µ §, µ §, µ §, µ §, µ §.

This way he obtained his wrong formula (C) from his wrong formula (A) :

µ §.

Obviously, Einstein抯 GRT cannot explain Mercury抯 perihelion motion. He had tried to narrow the gap between his GRT and the astronomic reality by one wrong integration and multiple arbitrary approximations. His formula (C) is a sheer fabrication tailored specially for Mercury. That is why his fabricated formula (C) failed to explain the perihelion motions of other planets such as Earth and Mars.

Black Hole *

If a celestial body with radius µ § has gravitational mass µ §, then the gravitational potential µ § on its surface is µ §, where µ § is the gravitational constant. If the gravitational potential at its surface is as strong as µ § so that µ §, then µ §. This is exactly the Schwarzschild Radius for a body to be a black hole, from which photons with speed µ § cannot escape.

Einstein deduced a frequency-transformation formula in gravitational field µ §. According to his formula, the gravitational potential must at least be as strong as µ § or µ § to form a black hole (µ §), which requires µ § because of µ § and violates Schwarzschild.s black hole radius criterium µ §. Other words, Einstein's GRT mistakenly demands that the gravitational potential on a celestial body's surface be at least as strong as µ §. Schwarzschild's µ § is not enough.

To sum up, the gravitational attraction is a mechanical force-interaction and all the three astronomic observations can be precisely calculated in the framework of mechanical interpretation.* Einstein's geometrical interpretation of gravity with the so-called 搒pace-time warp攊s misleading. Space and time are independent of each other. There is no such thing as the Minkowski four-dimensional space-time continuum.

Einstein's Lorentz Transformation——The Ill-Root

Einstein's relativity theory went wrong because it grew from an ill-root—his Lorentz Transformatio. His LT is wrong because its starting block—his postulate of constant speed of light—is wrong.

In my lengthy paper, I have provided many ways to prove that not only Einstein's postulate of constant speed of light µ § alone but also his LT as a whole violate the principle of relativity.**

Moreover, Einstein' did not tell the truth in saying that, in addition to the principle of relativity, his LT is based only on one postulate µ § which was thus raised by him from a postulate to a principle. The truth is that his LT has to rely on two postulates. Without Lorentz's length-contraction postulate µ §, he would not have been able to obtain his LT.*** Both µ § and µ § together violate the principle of relativity and thus constitute the ill-root of Einstein's LT.

Originally, Lorentz's LT was wrong because of Lorentz's postulate of µ §. Einstein added another wrong postulate of µ § and made Einstein's LT double-wrong!

Furthermore, Einstein's LT contains inherent self-contracdiction. Let's check his Time-Transformation Equation µ § in his LT.****


In case of a relative motion with velocity µ § in an arbitrary direction µ § between two reference systems µ § and µ §, Einstein抯 time-transformation equation µ § can be written as:

µ §, where µ §.

The µ §-system抯 relative motion in the µ §-direction can be resolved into two independent relative motions along the µ §-system抯 µ § and µ §axes respectively with µ § and µ §. This is similar to a wagon carrying a lift. The wagon moves in the µ §-direction and simultaneously the lift on the wagon moves upward in the µ §-direction. The combined motion is in the µ §-direction.

A clock fixed to the µ §-system抯 origin µ § shows time µ §. Another clock fixed to the wagon and moving with velocity µ § shows time:

µ §, where µ §.

A third clock fixed to the lift, which is moving with velocity µ § with reagard to the wagon, shows time:

µ §, where µ §.

Since a superposition of these two motions is equivalent to a single relative motion in the µ §-direction, so the resultant time µ § must be the same time µ § directly transformed from the µ §-system抯 time µ §. Hence, there must be µ §. Yet, a detailed calculation results in µ §, which is absurd!

Relativity Theory Based on Galilean Transformation

It is not enough just to prove where and why Einstein's relativity theory went wrong. It is necessary to develop a correct relativity theory to replace Einstein's wrong SRT and GRT. Everywhere in my lenghty paper, along with finding out Einstein's errors caused by his LT, I give detaild analysis to justify that the classical Galilean Transformation (GT) is the solid foundation for developing a correct relativity theory. The GT-based new relativity theory relies solely on the principle of relativity without any additional postulate and can rectify all the mistakes in Einstein's SRT and GRT such as: The invariant trasformations of electromagnetic field equations and wave equations; The Doppler effect, abberation and red shift; The mass-energy equivalence formula for moving bodies, The perihelion motion of planets; The sunlight's red shift and the deflection of light by the sun; The black hole; etc.

One of the most important findings is the formula of moving mass:

µ §

whereas Einstein's formula is µ §, which rules out µ § and demands photon's µ §.

揜elativisticvs 揘on-Relativistic”

Suppose 揂and 揃are at rest. 揂has static eigenmass µ §. At certain moment, 揂feels being pushed by some external force and his accelerometer shows µ §, while 揃feels no external action and his accelerometer remians µ §. 揂starts departing from 揃

Let抯 first analyze A抯 self-assessment. 揂deems that he is always static with regard to himself and has constant eigenmass µ §. 揂can use his accelerometer抯 µ §-readings to calculate the kinetic energy he has acquired due to the external force抯 action: µ §. Having been accelerated from µ § to µ §, 揂assesses his acquired kinetic energy as µ §, which is Newtonian.

So, the Newtonian mechanics can be used for 搉on-relative self-assessment because it holds mass µ § absolutely constant and does not recognize variable moving mass µ §. That is why the Newtonian mechanics is 搉on-relativistic

Let抯 now analyze how 揃assesses 揂 which is a 搑elative assessmentof 揂(object) by 揃(subject). 揃deems that 揂 moving at velocity µ §, has varying moving mass µ §. 揃can use the µ §-readings, dispatched by 揂to 揃or measured by 揃himself through external ballistic telemetry, to calculate the kinetic energy acquired by 揂 Accelerated from µ § to µ §, 揂with variable moving mass µ § has acquired kinetic energy:

µ §,

The essential difference between non-relativistic mechanics and relativistic mechanics lies in that: the former recognizes only constant static eigenmass and thus can only be used for a subject抯 non-relative self-assessment of itself, whereas the latter recognizes variable moving mass and thus can be used by a subject to assess a relatively moving object.

Newtonian mechanics is non-relativistic and applicable to any cases of subjective self-assessment. It is wrong to say that Newtonian mechanics is inapplicable to cases concerning high velocity (µ §). For any subjective self-assessment, the Newtonian mechanics is always precise. Astronauts launched by a rocket carrier, for example, must always use non-relativistic Newtonian mechanics to subjectively calculate their own velocity and acquired kinetic energy, no matter how high velocity they have reached. The rocket-carrier's lauching pad is the origin of their reference system. This is so-called 揝elf-Independent Inertial Navigation攚ell known in the astronautic community.

We (subjects) must always use GT-based relativistic mechanics to study relatively moving bodies (objects), regardless of the speed of moving bodies. Einstein抯 LT-based relativistic mechanics is wrong and misleads people to believe that the speed µ § of relative motion is a determinant factor: µ § is non-relativistic; µ § is relativistic.

On the other hand, it is also wrong to say that the Newtonian mechanics, which is non-relativistic, is only approximately applicable to cases with slow-moving bodies. In the quantum mechanics, for example, we (subjects) study relatively moving partcles (objects) so that the quantum mechanics is always relativistic.

In short, 揝elf-assessmentis non-relativistic. 揜elative assessmentis relativistic. 揜elativisticor 搉on-relativisticis not determined by the speed of relative motion.

The de Broglie Matter Wave*

A moving particle抯 matter wave has wavelength µ § and frequency µ §, here µ §and µ § are the moving particle抯 momentum and energy respectively. What energy does µ § represent? Classical quantum mechanics has so far been unable to answer this question clearly and definitely.

Newtonian µ § and µ § lead to µ § and separate a moving particle from its own matter wave. This is because Newtonian mechanics is non-relativistic and not applicable to the quantum mechanics, with which we (subjects) study relatively moving particles (objects).

Einstein抯 µ § and µ § lead to µ §. Obviously, Einstein抯 LT-based relativistic mechanics is not compatible with the de Broglie matter wave theory either.

Classical quantum mechanics has to assume a moving particle as a wave packet composed of infinite number of plane waves and to use the non-relativistic Newtonian kinetic energy µ § to prove that a wave packet's group velocity µ § in order to bypass the awkward µ §. Unfortunately, however, wave packets are destined to expand, while partcles never 揻atten up Why? The physics community has so far been shying away from answering this puzzling question.

The GT-based new relativistic mechanics can solve this old puzzle. If a moving particle抯 velocity is µ §, then its matter wave抯 phase velocity must be µ §, too. Otherwise, the particle would be separated from its own matter wave and the separation would be farther and farther over time. Hence, µ § or µ §. Since µ §, so µ §. This is exactly the physical quantity kinetic energy possessed by a moving particle抯 moving mass, which is discovered by the GT-based new relativistic mechanics.**

µ § is precisely correct for any particle moving with any speed (from µ § to µ §). This discovery will cause significant breakthroughs in the quantum mechanics.


Grand Unification of Relativity Theory and Quantum Theory

It is well known that Einstein's LT-based SRT and GRT are inconsistent with one another. For example, the speed of light µ § in his LT-based SRT is constant whereas it is variable in his LT-based GRT. However, the GT-based SRT in the inertial field and the GT-based GRT in the gravitational field are completely consistent.***

The contradiction between the quantum theory and the LT-based Einsteinian relativity theory is also commonly known in the physics community. The GT-based Galilean relativistic mechanics serves the quantum theory perfectly with a great revision of the classical quantum mechanics. For details, please see the author抯 next paper: 揜evision of Classical Quantum Mechanics


Some Philosophical Comments

揂bsoluteand 揜elativeare a pair of antithetical and interdependent concepts. 揜elativewould be meaningless, if there were no 揂bsoluteand, vice versa, 揂bsolutewould not exist without 揜elatives The 揂bsoluteinvolves 揜elativesand the 揜elativesunderlie the 揂bsolute We cannot say 揂ll things are relative The 揂llitself bears a tone of 揂bsolute

Everybody is absolute to itself and everybody is its own absolute reference system. There are countless bodies and each of them is its own absolute reference system so that there are countless absolute reference systems.

There can be countless bodies moving with different speeds. Each of them is a relative refrence system so that there are countless relative refernce systems, too.

Endless time is both absolute and relative. It is absolute in terms of the universal time-synchronism µ §. It is relative because all events are ordered by timing: 揃efore 揂fteror 揝imultaneous

Boundless space is both absolute and relative. It is absolute because the length is absolutely constant with regard to any reference system:

µ §.

It is absolute also because the boundless and vacuous space exists independently and permanently by itself, no matter it is being sensed or not. It is relative because all bodies are relatively located: 揕eft vs Right 揂bove vs Below 揃efore vs Behind It is relative also because the values of a body抯 coordinates depend upon the selection of a reference system.

Matter is both absolute and relative. It is absolute in terms of a body抯 absolutely constant static eigenmass. But, it is also relative because the value of a body抯 moving mass depends upon the body抯 relative speed, which in turn depends upon the selection of a reference system.

揝pace 揟imeand 揗atterare three 揂bsolutes Exactly, the three 揂bsolutesconstitute the absolute system of units (CGS), from which all units of mechanical quantities are derived. The three are independent from each other. Matter does not cause any space-time warp. Matter, static or moving, and space have no influence on the universal time-synchronism. Space and time are not material. 揝pace 揟imeand 揗atterexist and count by themselves separately and independently.

It is unfair to criticize the Newtonian mechanics for its absolute space-time. The only shortcoming in the Newtonian mechanics is its ignorance of relative moving mass aside from absolute static eigenmass, which renders it non-relativistic. But, the Newtonian mechanics remains completely valid in cases of subjective self-assessment and must be used, for example, by astronaut in their self-independent navigation..

The boundless universe exists endlessly over time and does not have 揝ingularityanywhere at any moment because there is no Einstein's µ §, which can lead to infinity or even imaginary quantities when µ §. Unable to evade the awkward infinity, mainstream physicists say: 揂ll physical laws are invalid at the Singularity which is a sheer nonsense.

* For details, please refer to in my paper.

* For details, please refer to in my paper.

** For details, please refer to in my paper.

* For details, please refer to , and in my paper about the Doppler effect, the abberation and the red shift.

** For details, please refer to 1.6, 1.7 and Appendix B in my paper.

*** For details, please refer to of Appendix C in my paper.

* For details, please refer to 1.8 and Appendix D in my paper.

* For details, please refer to 1.6 and Appendix B in my paper.

** For details, please refer to , Appendix A in my paper.

*** For details, please refer to .2.2 of Appendix A in my paper.

**** For details, please refer to .4 in my paper.

* For details, please refer to .4 in my paper.

** For details, please refer to .2 in my paper.

*** For details, please refer to 1.1, 1.2 and especially1.2 in my paper.





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