The Theory of Observational Relativity Serial Report 1: A New Theory with Significant Discoveries

3.1 Three important concepts of OR

Observation is to perceive the objective world and obtain information about the objective world.

As depicted in Figure 1, the information about the observed object P must be transmitted by a certain observation medium at a certain speed from the observed object P to observer O, so that observer O can perceive the observed object P.

However, physicists, including Newton and Einstein, do not seem to be aware of the problems involved in their spacetime models or theoretical systems:

To clarify the role or status of observation and observation media in spacetime models and theoretical systems of physics, the theory of OR has coined three important concepts related to observation.

Železnikar employed Informon to refer to an information entity and analogized it with an electron.²¹

In theory, all forms of matter motion, not just light or photons, can serve as observation media to transmit information about observed objects to observers.

All matter waves, including sound, light, electric, water, seismic, and gravitational waves, can serve as information waves, and all matter particles, including photons, electrons, neutrons, protons, atoms, molecules, and even rocks, can serve as information.

Nature is equipped with various observation agents for humans and animals--including those listed in Table 1. The ear is the acoustic observation agent OA (v_S) and the eye is the optical observation agent OA(c). Human perception of the objective world may employ different observation agents. All spacetime models and theoretical systems of human physics, including Galileo’s doctrine, Newton’s mechanics, and Einstein’s theory of relativity, imply their respective specific observation agents.

3.2 The observational locality of mankind

Locality or the principle of locality plays an important role in modern physics. Newton and Einstein believed that there was no action at a distance in the universe.

Einstein’s concept of locality is linked to his hypothesis of the invariance of light speed: matter cannot move faster than light can. In 1935, based on his concept of locality from the ILS, Einstein and his colleagues Podolsky and Rosen conceived a famous thought experiment called the EPR Paradox²² to question the completeness of quantum mechanics.

However, an increasing number of EPR experiments have shown^23,24 that quantum entanglements do exist in the physical world. This indicates that there are forms of matter motion that exceed the speed of light in the physical world. However, this does not mean that there is spooky action at a distance in the universe.

Under the principle of physical observability, locality or the principle of locality is beyond doubt.

The Principle of Physical Observability (PPO)^12–15: In short, infinite physical quantities are unobservable, and the universe has no infinite physical quantity.

In fact, the principle of locality is just a logical inference from the principle of physical observability: the speed of any form of matter motion must be finite or limited, and it takes time for both matter and information to cross space. However, this does not imply that the speed of light cannot be surpassed, but that there is no matter motion with infinite speed in the universe.

Because the speed of matter motion is limited, the transmission speed of observed information must also be limited. This can be expressed as a principle:

The Principle of Observational Locality (POL)^12–15: According to the principle of locality, the information-wave speed η of a realistic observation agent OA(η) must be finite or limited (η < ∞), and it takes time for the information wave of OA(η) to cross space.

The principle of observational locality means that all realistic observation agents must have the observational locality ∀OA(η) η < ∞.

Human perception of the objective world is restricted by the observational locality: when you hear a bird chirping as it flies across the sky, it is no longer in the place where it was chirping; when you see its image, it is no longer in the place where it was flying.

The theory of OR has discovered that all relativistic effects are observational effects and apparent phenomena, the root and essence of which lie in the observational locality (η < ∞) of the observation agent OA(η).

3.3 The principle of general correspondence

In 1920, Bohr formally established the principle of correspondence, commonly known as the Bohr Correspondence Principle.²⁵ The basic idea of the Bohr correspondence principle can be traced back to 1913. Based on the basic idea of his correspondence principle, Bohr established an atomic model and theory.^26–28

The Basic Idea of Bohr correspondence principle: That there must be an intrinsic relationship between quantum mechanics and classical mechanics, and under certain conditions, quantum mechanics and classical mechanics can be transformed into each other.

Various interpretations of the Bohr correspondence principle have been proposed in the literature. The two limiting forms were the most common.

Actually, Galilean relativity principle is also a type of correspondence principle.

The basic idea of Galilean relativity principle: Spacetime is symmetrical, and therefore, all observers are equal or have equal rights; in other words, a physical law or spacetime model must take the same form in different reference frames.^29,30

The principle of relativity implies an intrinsic corresponding relationship between different reference frames: a physical law or a spacetime model of physics in different reference frames has the same form or structure, which is Isomorphic or Isomorphically Consistent, and possesses the corresponding relationship of isomorphic consistency.

Galileo’s principle of relativity implies the equality of observers of different reference frames, whereas Bohr’s principle of correspondence implies the equality of observers of different observation agents, including the optical agent OA(c) and idealized agent OA_∞.

Now, the theory of OR further clarifies that All Observation Agents are Equal.

The Principle of General Correspondence (PGC)^12–15: Spacetime is symmetrical; therefore, all observers, regardless of reference frames or observation agents, are equal or have equal rights, and the same physical law or spacetime model must take the same form in different reference frames with different observation agents, being isomorphic or isomorphically consistent, possessing the corresponding relationship of isomorphic consistency.

Based on the PGC principle, the theoretical systems of different observation agents OA(η₁) and OA(η₂) can be isomorphically and uniformly transformed into each other by following the PGC logical paths, as follows:

PGC logical path 1:

Based on the PGC principle, by directly replacing η₁ of OA(η₁) with η₂ of OA(η₂), the observed physical quantities of OA(η₁) are correspondingly transformed into the observed physical quantities of OA(η₂), and the physical models of OA(η₁) are isomorphically and uniformly transformed into the physical models of OA(η₂).

PGC logic path 2:

First, based on the PGC principle, transform the axiom system of the theoretical system of OA(η₁) isomorphically and uniformly into that of OA(η₂). Second, based on the transformed axiom system, following or analogizing the logic of the theoretical system of OA(η₁), we can deduce the theoretical system of OA(η₂) that is bound to isomorphically consistent with that of OA(η₁).

This is the fundamental idea of the PGC principle: One physical world, One logical system.

The PGC principle was originally a logical shortcut developed by the theory of OR specifically for the theory of GOR. It is a universal logical law for physics, providing an important ideological foundation and guiding principles for the development of new theories and the unification of old theories in physics as well as for testing the logical consistency of theoretical systems in physics.

4.1 IOR: Axiom system and logical deduction

Einstein’s theory of special relativity has two major logical premises: the second one is the principle of relativity and the third one is the principle of the invariance of light speed. However, little is known about the first one: the principle of simplicity. These Three Principles constitute the axiom system of Einstein’s special relativity. However, only the principle of invariance of light speed is indispensable, whereas the principles of simplicity relativity are only two auxiliary logic premises.

Until now, however, the principle of the invariance of light speed as the logical premise of Einstein’s theory of special relativity remains merely a specious hypothesis. Einstein’s theory of special relativity, based on the principle of the invariance of light speed, has led to numerous misconceptions in physics regarding the relativistic effects of inertial spacetime and inertial motion, including the invariance of light speed and the effects of time dilation and length contraction.

The theory of IOR is founded on a more basic axiom system and the logical deduction of IOR is rooted in more basic logical premises.

4.1.1 The axiom system of IOR

Compared to Einstein’s special relativity, the theory of Inertially Observational Relativity (IOR) has more basic logical premises and a more basic axiom system.

IOR Axiom System^12–15

The First: The Principle of Physical Observability

The Second: The Conditions of Wave-Particle Duality

The Third: The Definition of Time

The definition of time is the fundamental and indispensable logical premise of OR, both IOR and GOR, whereas the principle of physical observability and the conditions of wave-particle duality are only auxiliary logical premises of IOR.

Time is the most basic physical quantity. To some extent, the definition of OR time could be regarded as the first principle or the most basic logical premise.

4.1.2 The logical deduction of IOR

As depicted in Figures 1 and 2, based on the axiom system of IOR, starting from the definition of OR time as the first principle, OR came into deducing the inertial-spacetime transformation, attempting to build a theoretical model that could give photons the rest mass.

Figure 2. The Standard Clock: Proper Time τ and Observed Time t.

(1) Standard clock: Let a periodic signal source T_P be the observed object P, define the intrinsic period T_o and intrinsic frequency f_o of P or T_P as the basic units for measuring time; if P is stationary in free spacetime S_F, then T_P is the standard clock. (2) Intrinsic time (proper time) τ: According to the definition of OR time, it is the time observed by the intrinsic observer O_o of P or by the idealized agent OA_∞ -- Einstein called it the standard time; (3) Observational or observed time t: Constrained by the observational locality of the realistic observation agent OA(η) (0 < η < ∞), the observed time t of a realistic observer O is not the objective and real time τ (proper time) -- Einstein called it the coordinate time.

From the definition of OR time to the invariance of the time-frequency ratio, and from the invariance of time-frequency ratio to the time and space transformations of IOR, the logical deduction and theoretical derivation of IOR have produced an interesting logical conclusion^12–15 (omitting the lengthy logical deduction of IOR): Λ = η!

This means that the so-called Ultimate Speed Λ of the universe is actually the speed η at which the observation medium transmits the observed information, which depends on the observation medium of the observation agent OA(η), which is not necessarily light.

Thus, the theory of OR has discovered that there is no invariant and insurmountable ultimate speed in the objective physical world. The ultimate speed of the universe was only an observational limitation for the observers. When bats perceive the physical world with air ultrasound, the speed of air ultrasound will be the ultimate speed that bats cannot surpass observationally; when Einstein observed the physical world with light, the speed of light would be the ultimate speed that Einstein could not surpass observationally.

The theory of IOR has proven an important theorem:

The Invariance of Information-Wave Speeds --∀u∈(-η, η) η ⊕ u = η. ^12–15

In theory, all matter motion or matter waves, not just light or electromagnetic interaction, can serve as observation media or information waves to transmit information about observed objects to observers.

Thus, the author of OR seemed to understand why the Lorentz transformation and Einstein theory of relativity are linked to the speed of light c: it turns out that the invariance of light speed is only a special case of the invariance of information-wave speeds, which could be effective and valid only if the observer observes the physical world through light, and Einstein’s theory of relativity is just a theory of humans perceiving the objective physical world through light, that is, a product of optical observation and what Hawking called a partial theory.

Thus, the theory of IOR has discovered that the speed of light is not really invariant.

Based on the definition of OR time under the general observation agent OA(η) (0 < η < ∞; η→∞), while proving the theorem of the invariance of time-frequency ratio, the theory of IOR derives the differential form of the inertial spacetime-transformation equation:

By setting the initial conditions for Equation (1), one can obtain the algebraic form of the transformation equation of OR inertial spacetime, which can be referred to as the general Lorentz transformation that not only generalizes the Lorentz transformation, but also generalizes the Galilean transformation, unifying the two great spacetime transformations of human physics.

As the Lorentz transformation represents Einstein’s theory of special relativity, the general Lorentz transformation represents the theory of IOR.

As Einstein theoretically deduced the entire theoretical system of special relativity based on the invariance of light speed and the Lorentz transformation,⁸ OR theoretically deduces the entire theoretical system of IOR based on the invariance of information-wave speeds and the general Lorentz transformation.^12–15

Finally, the entire theoretical system of IOR has generalized and unified Newton’s inertial mechanics and Einstein’s special relativity, and integrates de Broglie’s theory of matter waves, moving towards the unification of relativity theory and quantum theory (see Chapter 6 of the 1^st volume IOR in^12–15).

4.2 GOR: Axiom system and logical deduction

Einstein’s theory of general relativity also possesses Three Principles: (1) equivalence, (2) general covariance, and (3) invariance of light speed. However, it is strange that physicists are fond of discussing the equivalence principle and the covariance principle, yet they often forget the principle of the invariance of light speed. In fact, the principles of equivalence and general covariance are only two auxiliary logical premises of Einstein’s general relativity, whereas the principle of the invariance of light speed is its fundamental and indispensable logical premise.

The speciousness of the principle of the invariance of light speed has been further amplified in Einstein’s theory of general relativity, leading to numerous misconceptions about the relativistic effects of gravitational spacetime and gravitational interaction, including the relativistic effect of spacetime curvature and Einstein’s prediction of gravitational waves. Based on Einstein’s theory of general relativity, modern physics has developed a few of more specious doctrines, including the Big Bang.

The theory of GOR is founded on a more basic axiom system, and the logical deduction of GOR is rooted in more basic logical premises.

4.2.1 The axiom system of GOR

Based on the principle of general correspondence (PGC), the theory of Gravitationally Observational Relativity (GOR) can be deduced by following either PGC logical path 1 or PGC logical path 2.

Compared to PGC logical path 1, deducing the theory of GOR by following PGC logical path 2 is more helpful for us to understand Einstein’s theory of general relativity, recognize the root and essence of gravitational relativistic phenomena, such as Einstein’s spacetime curvature, and elucidate the logical thought of GOR.

Under the PGC principle, following PGC logical path 2, the theory of OR transforms the three principles of Einstein’s general relativity into the three principles of GOR.

GOR axiom system

The First: The Principle of GOR equivalence

The Second: The Principle of GOR covariance

The Third: The Principle of the Invariance of Information-Wave Speeds

This constitutes the axiom system of GOR.

In the axiom system of GOR, the principles of equivalence and covariance proposed by Einstein remain valid. Furthermore, they acquire a more universal significance under the PGC principle: the observers could not only be those in different reference frames but also those in different observation agents. Under the PGC principle, Einstein’s principle of the invariance of light speed is transformed into the principle of the invariance of information wave speeds, where the information wave speed η of the general observation agent OA(η) replaces the speed of light c in the optical observation agent OA(c).

It should be noted that the principle of the invariance of information wave speeds was originally a logical consequence of IOR, that is, the theorem of the Invariance of information-wave speeds. This implies that the theory of IOR is the foundation of GOR. In other words, the axiom system of IOR is also that of GOR; whereas the axiom system of GOR, in essence, just adds two auxiliary logical premises, the principles of GOR equivalence and GOR covariance, to the axiom system of IOR.

Therefore, for the of theory GOR, only the principle of the invariance of information wave speeds is fundamental and indispensable. Overall, only the definition of OR time is the fundamental and indispensable logical premise for the theory of OR, including IOR and GOR.

4.2.2 The logical deduction of GOR

Now, one can understand that under the PGC principle, through PGC logical path 2, based on the three principles of GOR, following or analogizing the logic of Einstein’s general relativity, OR must be able to deduce the theory of GOR of the general observation agent OA(η) (0 < η < ∞; η→∞), and ultimately, to establish the entire theoretical system of GOR that must be isomorphically consistent with Einstein’s theory of general relativity.

Under the PGC principle, combining PGC logical path 1 and PGC logical path 2, OR extends the theory of IOR from inertial spacetime to gravitational spacetime and Einstein’s theory of general relativity from the optical agent OA(c) to the general agent OA(η). Thus, the theory of GOR can be established.

However, both PGC logical paths 1 and 2 are logical shortcuts based on the PGC principle.

It’s worth noting that taking shortcuts comes at a cost.

It is because of those logical shortcuts paved by Einstein specially his theory of relativity that, until today, we still cannot understand why the speed of light is invariant and why spacetime is curved. Similarly, simply and directly applying the PGC principle may lead us to miss the correct understanding of the root and essence of gravitational relativistic phenomena.

Therefore, the logical deduction of GOR does not follow Einstein’s logic of general relativity. In particular, the theory of GOR has abandoned Einstein’s logic of weak-field approximation designed specifically for his theory of general relativity, that is, the so-called weak-field approximation. While applying the PGC principle, the theory of OR strives to deduce the theory of GOR from the most basic physical concepts and logical premises, thereby elucidating the root and essence of gravitational relativistic effects or phenomena.

GOR basic way of logical deduction^12–15

Step 1: Starting from the three principles of GOR;

Step 2: Analogizing the logic of Einstein’s theory of general relativity;

Step 3: Taking advantage of the GOR logical way of idealized convergence.

First, by analogizing the logic of Einstein’s spacetime theory of general relativity, OR deduces the corresponding spacetime models of GOR and derives the GOR measuring formula of gravitational spacetime.

The measurement of GOR standard time dτ:

The measurement of GOR physical space dl:

Then, by analogizing the logic of Einstein’s gravitational field equation and motion equation of general theory and taking advantage of the GOR logical way of idealized convergence, OR deduces the gravitational field equation and motion equation of GOR.

GOR gravitational-field equation:

GOR gravitational-motion equation:

The Einstein field equation represents Einstein’s theory of general relativity, whereas the GOR field equation represents the theory of GOR.

Einstein deduced the entire theoretical system of his general theory based on the invariance of light speed as well as his gravitational-field equation and gravitational-motion equation.⁹ OR deduces the entire theoretical system of GOR based on the invariance of information-wave speeds, as well as the GOR gravitational-field equation and gravitational-motion equation.^12–15

It should be pointed out that there is still one unaddressed issue: how does the theory of OR calibrate the coefficient κ_GOR(η) of GOR field equation?

4.2.3 The GOR idealized convergence vs Einstein’s weak-field approximation

Einstein was adept at constructing logical shortcuts leading to the grand edifices of physics: to reach his theory of special relativity, Einstein designed the principle of the invariance of light speed; to reach his theory of general relativity, Einstein designed the principles of equivalence and general covariance.

In general relativity, to calibrate the coefficient κ_E of his field equation, Einstein needed to match his gravitational field equation with Newton’s law of universal gravitation, in the form of Poisson equation. To this end, Einstein specifically constructed a logical shortcut: the way of weak-field approximation.

Einstein’s weak-field approximation not only implies the hypothesis of weak-field approximation but also a set of five hypothetical logical premises:

Taking advantage of his weak-field approximation, Einstein successfully calibrated the coefficient of his field equation: κ_E = 8πG/c⁴ where G is the gravitational constant in Newton’s law of universal gravitation.

Thus, we mistakenly thought that Newton’s theory of universal gravitation was only an approximation of Einstein’s theory of general relativity under low-speed and weak-field conditions.

However, why is Einstein’s field-equation coefficient κ_E associated with the speed of light c?

The theory of OR has revealed that Einstein’s theory of general relativity is also a theory of the optical observation agent OA(c), and there is no direct correspondence between Einstein’s field equation for the optical agent OA(c) and Newton’s law of universal gravitation for the idealized agent OA_∞. Einstein’s logic of weak-field approximation misled the physics.

To calibrate the coefficient κ_GOR, the GOR gravitational-field equation must also be matched with Newton’s law of universal gravitation in the form of Poisson equation. However, as a gravitational theory of the general observation agent OA(η) (0 < η < ∞; η→∞), the theory of GOR does not require Einstein’s weak-field approximation.

The theory of GOR has proven an important theorem:

The theorem of cartesian spacetime -- h _μν →0 as η→∞.^12–15

The theorem of Cartesian spacetime clarifies that the curved metric h_μν of gravitational spacetime is zero under the idealized observation scene of OA_∞ (η→∞). This suggests that the objective and real gravitational spacetime is flat rather than curved. The so-called spacetime curvature is only an observational effect and an apparent phenomenon caused by the observational locality (η < ∞) of the realistic observation agent OA(η).

Thus, the theory of GOR has discovered that space-time is not really curved.

The correspondence between the gravitational field equation of GOR and Newton’s law of universal gravitation does not require the so-called logic of weak-field approximation, but the logic of idealized convergence.

The GOR logical way of idealized convergence^12–15: Let the information-wave speed η of the observation agent OA(η) be sufficiently large; then, the gravitational spacetime tends to be flat, and it holds true that

In particular, as η→∞, g_μν→η_μν, where η_μν is the Minkowski metric, η_μν=diag(+1,-1,-1,-1).

It can be proven^12–15 that under the GOR logic of idealized convergence, the five conditions in Einstein’s weak-field approximation must be satisfied.

Thus, the corresponding relationship between the GOR field equation and Poisson equation of Newton’s law of universal gravitation is no longer approximate but logical in a strict sense.

Taking advantage of the GOR logical method of idealized convergence, as the information-wave speed η of the observation agent OA(η) is sufficiently large, the GOR gravitational field equation is reduced to

By comparing Equation (8) with the Poisson equation ∇²χ = 4πGρ of Newton’s universal gravitation law, the GOR field-equation coefficient κ_GOR can be calibrated as

The calibration of the GOR field-equation coefficient marks the formal establishment of the theory of GOR, that is, Gravitationally Observational Relativity or General Observational Relativity.

Finally, the entire theoretical system of GOR has generalized and unified Newton’s theory of universal gravitation and Einstein’s theory of general relativity.

4.3 The different logical paths to OR

The theory of OR, both IOR and GOR, is the product of logic and theory, is rooted in the definition of OR time, and has a more basic axiom system than both Newton’s classical mechanics and Einstein’s relativity theory. It is based on more basic logical premises that the theory of OR has acquired a broader perspective, so that it has uncovered the root and essence of relativistic phenomena and has generalized and unified Newton’s classical mechanics and Einstein’s relativity theory.

If one cannot understand the logical deduction of OR based on the axiom system of OR, one can choose the following concise logical paths. The fact that different logical paths lead to the identical theory of OR can confirm the theory of OR and may be helpful for readers to understand the theory of OR.

4.3.1 From time definition to OR

As stated previously, in the axiom system of OR, only the definition of OR time is a fundamental and indispensable logical premise.

The principle of physical observability is implicitly taken as the logical premise underlying all theoretical systems in physics, including the Galilean doctrine, Newtonian mechanics, Einstein relativity theory, and quantum theory. Hence, the principle of physical observability can be regarded as a fundamental principle universally followed by all the theoretical systems in physics. Meanwhile, the conditions of wave-particle duality in the axiom system of OR can be substituted by the principle of simplicity or the principle of relativity.

Even if one cannot understand the OR conditions of wave-particle duality, based on the definition of OR time and the principle of relativity, or based on the definition of OR time and the principle of simplicity, one might also prove the theorem of the invariance of information-wave speeds (see Secs. 3.2.4-5 in Chapter 3 of the 1^st volume IOR in^12–15), derive the general Lorentz transformation, that is, the OR spacetime transformation, and establish the entire theoretical system of OR, including IOR and GOR.

4.3.2 From observational limit to OR

Perhaps one could not understand the definition of OR time and the invariance of time-frequency ratio. However, one must understand that the speed of moving objects that bats can observe with their ears cannot exceed the air ultrasonic speed of 340 m/s, the speed of moving objects that dolphins can observe with their ears cannot exceed the water ultrasonic speed of 1450 m/s, and the speed of moving objects that humans can observe with their eyes cannot exceed the light speed of 3×10⁸ m/s.

This is what OR calls Observational Limit. Different observation agents have different observational limits.

One could express it as a principle.

The Principle of Observational Limit (POL): For an observation system (P, M(η),O) or an observation agent OA(η), the information wave speed η of OA(η), that is, the speed of the observation medium M(η) transmitting the information on the observed object P, is the observational upper limit of observer O armed with OA(η):|u|, ≤η where u is the moving speed of P that can be perceived or observed by observer O.

The principle of observational limit is equivalent to the principle of observational locality.

Because the speed η of medium M transmitting information cannot exceed observationally by observer O with OA(η), the information-wave speed η of OA(η) must exhibit invariance relative to observer O.

Thus, based on the POL principle, one might also prove the theorem of invariance of information-wave speeds, and by following the logic of Einstein relativity theory, establish the entire theoretical system of OR, including IOR and GOR.

4.3.3 From the invariance of information-wave speeds to OR

More simply, one can directly express the invariance of the information-wave speeds as a basic principle of physics.

In the Michelson-Morley experiment,³ the speed of light exhibited a sort of invariant phenomenon. Based on the Michelson-Morley experiment, Einstein proposed the principle of the invariance of light speed and consequently established his theory of relativity, including special⁸ and general.⁹ To date, the mainstream school of physics still believes that the Michelson-Morley experiment is the empirical basis for the principle of the invariance of light speed.

However, as clarified in Sec. 7.2.2, the Michelson-Morley experiment does not support the principle of the invariance of light speed proposed by Einstein but supports the theorem of the invariance of information-wave speeds proven by the theory of OR.

Thus, one has every reason to express the invariance of information wave speeds as a principle: The Principle of the Invariance of Information-Wave Speeds.

Thus, based on the principle of the invariance of information-wave speeds and following Einstein’s logic of relativity theory, one might also deduce the entire theoretical system of OR, including IOR and GOR.

4.3.4 Following PGC logical path 1 to OR

PGC logical path 1 based on the PGC principle is the simplest and most direct way to extend Einstein’s theory of relativity, both special and general, from the optical agent OA(c) to the general observation agent OA(η) (0 < η < ∞; η→∞).

By following PGC logical path 1, directly replacing the speed of light c in all the principles or axioms, as well as all the theoretical models or formulae of Einstein’s theory of relativity (both special and general) with the information wave speed η of the general observation agent OA(η) (0 < η < ∞; η→∞), one might also acquire the entire theoretical system of OR, including IOR and GOR.

Now, one must understand that Einstein’s theory of relativity, both special and general, is the theory of the optical agent OA(c), that is, only a special case of OR. One must be able to predict that, as η→c, the entire theoretical system of OR strictly reduces to Einstein’s theory of relativity: IOR strictly reduces to Einstein’s special relativity (see extended data Table A1), and GOR strictly reduces to Einstein’s general relativity (see extended data Table A2).

However, one might not be able to foresee and understand that (see Section 5 and Appendix A in this article): as η→∞, the entire theoretical system of OR strictly reduces to Galileo-Newtonian classical mechanics -- IOR strictly reduces to Galileo-Newtonian inertial mechanics (see extended data Table A1); GOR strictly reduces to Newton’s theory of universal gravitation (see extended data Table A2).

Perhaps, this would give one some insights into OR.

5.1 The unity of Newton and Einstein in IOR

See Extended data Table A1 in Appendix A demonstrates the unification of Galileo-Newtonian inertial mechanics and Einstein’s theory of special relativity in the theory of IOR: as η→c, the theory of IOR strictly reduces to Einstein’s theory of special relativity; as η→∞, the theory of IOR strictly reduces to Galileo-Newtonian inertial mechanics.

The following basic relations in IOR are demonstrated as a few typical examples in which the corresponding relations in Einstein’s theory of special relativity and Galileo-Newtonian mechanics are familiar to everyone:

5.1.1 The IOR factor of spacetime transformation

The IOR factor Γ(η, v) = 1/√(1- v²/η²) (Equation 2) is the OR factor of inertial spacetime transformation under the general observation agent OA(η), also called the inertially-relativistic factor. The larger the value of Γ, the more significant the inertially relativistic effects exhibited by the observed object P in inertial spacetime.

The IOR factor Γ(η, v) of spacetime transformation can be decomposed in terms of the Taylor series:

In Einstein special relativity, the inertially spacetime-transformation factor γ = 1/√(1- v²/c²) can be referred to as the Lorentz factor,^5–8 where the speed of light c is an invariant and the value of γ depends on the speed v of P. Based on this, Einstein believed that the relativistic effects of inertial spacetime were real natural phenomena, and the root and essence were decided by matter motion.

However, the IOR factor Γ = Γ(η,v) indicates that the value of Γ depends on the information wave speed η of OA(η). Given that the moving speed v of P, the larger the value of η, the weaker the inertially relativistic effects exhibited by P would be If η is infinite, the inertial spacetime would have no relativistic phenomena. Thus, the theory of IOR discovered that the relativistic effects of matter motion in inertial spacetime are not objective and real physical reality but rather observational effects and apparent phenomena caused by the observational locality (η < ∞) of the observation agent OA(η).

The IOR factor of spacetime transformation generalizes both the Lorentz factor and Galilean factor, unifying them within the theory of IOR.

As η→c, OA(η)→OA(c), the IOR factor Γ(η, v) strictly converges to the Lorentz factor γ = Γ(c,v):

It is thus clear that the Lorentz factor γ = Γ(c,v) is relativistic because of the optical observation agent OA(c) with the observational locality of c < ∞. Thus, the optical agent OA(c) and Einstein special relativity present inertially relativistic effects, that is, observational effects.

As η→∞, OA(η)→OA_∞, the IOR factor Γ(η, v) strictly converges to the Galilean factor Γ_∞ = Γ(∞,v):

It is thus clear that the Galilean factor Γ_∞ ≡ 1 is non-relativistic because of the idealized observation agent OA_∞ with no observational locality (η→∞). Thus, the idealized agent OA_∞ and Galileo-Newtonian inertial mechanics present the objective and real inertial spacetime.

So, OA_∞ might be referred to as the God’s Eye.

5.1.2 The IOR spacetime transformation

As shown in Equation (1), the transformation equation of IOR inertial spacetime deduced based on the definition of OR time was originally in a differential form. Integrating it, its algebraic form can be obtained, which is called the general Lorentz transformation:

As the Lorentz transformation represents Einstein’s theory of special relativity, the general Lorentz transformation represents the theory of IOR.

The general Lorentz transformation generalizes both the Lorentz transformation and Galilean transformation, unifying them within the theory of IOR.

As η→c, OA(η)→OA(c), Γ(η, v)→Γ(c,v) = γ, and the spacetime transformation of IOR strictly converges to the Lorentz transformation:

As η→∞, OA(η)→OA_∞, Γ(η, v)→Γ_∞ ≡ 1, and the spacetime transformation of IOR strictly converge to the Galilean transformation:

The IOR 4d spacetime transformation equation (Equation (13)), in which space and time are originally interdependent, splits into two independent equations: (1) the 3d space equation {x = x′ + vt′; y = y′; z = z′}, which is exactly the Galilean transformation; and (2) the 1d time equation t = t′ = τ where different observers O and O′ have the same observed time (t = t′), that is, the objective and real time τ.

This suggests that, in the objective and real physical world, space and time are independent of each other, just like Newton’s statement³¹: space exists immutably and time flows silently.

5.1.3 The IOR law of speed addition

Originally, human physics believed in Galileo’s law of speed addition. However, after the establishment of Einstein special relativity, human physics came to believe in Einstein’s relativistic law of speed addition.

The theory of IOR also deduces the relativistic law of speed addition based on the differential form (Equation (1)) of IOR spacetime transformation, one can directly derive the IOR speed-addition formula:

The IOR relativistic law of speed addition generalizes Einstein’s relativistic law of speed addition and Galileo’s classical law of speed addition, unifying them within the theory of IOR.

As η→c, OA(η)→OA(c), the IOR law of speed addition strictly converges to Einstein’s speed addition:

As η→∞ OA(η)→OA_∞, the IOR law of speed addition strictly converges to Galileo’s speed addition:

As a physical model of the idealized observation agent OA_∞, Galileo’s law of speed addition is the true natural law in line with human reason and intuition.

5.1.4 The IOR observed mass

In Einstein special relativity, matter in inertial space-time has two types of mass: the rest mass m_o and the moving mass m (referred to as relativistic mass). According to Einstein’s mass-speed relation, m = m_o/√(1- v²/c²).

The theory of IOR deduces the relativistic mass-speed relation of the general observation agent OA(η):

However, according to Equation (19), the IOR mass m = m(η) depends on the observation agent OA(η) and information wave speed η of OA(η). This suggests that the so-called relativistic mass, both the IOR m(η) and Einstein m(c), is actually a sort of observational or observed mass containing observational effects and is not entirely objective and real.

The IOR mass-speed relation generalizes Einstein’s relativistic inertial mass and Newton’s classical inertial mass, unifying them within the theory of IOR.

As η→c, OA(η)→OA(c), the IOR mass-speed relation strictly converges to Einstein’s mass-speed relation:

The concept of Inertial Mass originated in Newtons. According to the IOR definition of inertial mass observed with OA(η) in Equation (19), Newton’s inertial mass m_I should be the IOR-observed mass m_∞ = m(∞) as η→∞, that is, the IOR mass observed with OA_∞:

Equation (Equation (21)) has important enlightening significance: Newton’s inertia mass m_I is exactly Einstein’s rest mass m_o. According to Equation (21), the so-called rest mass m_o is the mass observed with the idealized agent OA_∞, that is, the objective and real mass of matter, and is equal to Newton’s classical mass m_∞ and Newton’s inertial mass m_I.

It turns out that mass is mass: m_o = m_∞ = m_I.

5.1.5 The IOR observed momentum

In his special relativity, Einstein defined the momentum, p of a material particle as the product of its relativistic mass, m and speed, v: p = mv. In the theory of IOR, the momentum p of the observed object P is defined as the product of the relativistic mass m and speed v of P:

The momentum formula of IOR generalizes Einstein’s and Newton’s momentum formulas, unifying them within the theory of IOR.

As η→c, OA(η)→OA(c), the IOR-observed momentum p = p(η) strictly converges to Einstein’s relativistic momentum p = p(c):

In Newton’s inertial mechanics, the momentum of a material particle is defined as the product of the inertial mass m_I or classical mass m_∞ and moving speed v: p_∞ = m_Iv = m_∞v, that is Newton’s classical momentum.

As η→∞, OA(η)→OA_∞, m_o = m_∞ = m_I, the IOR-observed momentum p = p(η) strictly converges to Newton’s classical momentum p_∞ = p(∞):

5.1.6 The IOR observed energy

People always take delight in discussing Einstein’s mass-energy relation, that is, the famous Einstein formula E = mc². However, the theory of OR discovers that E = mc² is only an integral constant in Einstein’s derivation of the kinetic-energy formula and does not represent the objective and real energy of matter. Einstein’s rest energy, E_o = m_oc² is also an integral constant and is not an objective physical existence. What has physical significance is only the kinetic energy of the observed object P: K = E-E_o.

The theory of IOR also involves two integral constants during the derivation of the kinetic energy formula: (1) E = mη² and (2) E_o = m_oη². It is worth noting that E = mη² generalizes Einstein’s formula E = mc²; E_o = m_oη² generalizes Einstein’s rest energy E_o = m_oc².

In the inertial spacetime of IOR, the only energy formula with objective and real physical significance is the kinetic energy formula of IOR:

The kinetic-energy formula K = K(η) of IOR generalizes Einstein’s relativistic kinetic-energy formula and Newton’s classical kinetic-energy formula, unifying them within the theory of IOR.

As η→c, OA(η)→OA(c), the IOR-observed kinetic energy K = K(η) strictly converges to Einstein’s relativistic kinetic energy K = K(c):

In Newton’s inertial mechanics, a matter particle has neither the mass energy E nor the rest energy E_o, but only kinetic energy: K = m_Iv²/2 = m_∞v²/2.

Actually, as η→∞, The IOR mass energy E = mη²→∞ and the IOR rest energy E_o = m_oη²→∞. According to the principle of physical observability, both E and E_o are unobservable. In other words, neither the mass energy E nor the rest energy E_o is the objective physical existence.

However, as η→∞, OA(η)→OA_∞, the IOR-observed kinetic energy K = K(η) strictly converges to Newton’s classical kinetic energy K = K(∞)=K_∞:

Section 5.1 demonstrates that the theory of IOR is logically consistent with Einstein’s theory of special relativity and Galileo-Newtonian inertial mechanics. This from one aspect confirms that the theory of IOR is logically self-consistent and theoretically correct. For details, see Chapter 8 of the 1^st volume IOR, of OR.^12–15

5.2 The uinity of Newton and Einstein in GOR

See Extended data Table A2 in Appendix A demonstrates the unification of Newton’s theory of universal gravitation and Einstein’s theory of general relativity in the theory of GOR: as η→c, the theory of GOR strictly reduces to Einstein’s theory of general relativity; as η→∞, the theory of GOR strictly reduces to Newton’s theory of universal gravitation.

The following basic relations in the theory of GOR are demonstrated as a few typical examples, in which the corresponding relations in Einstein’s theory of general relativity and Newton’s theory of universal gravitation are familiar to everyone.

5.2.1 The GOR factor of spacetime transformation

The GOR factor of spacetime transformation is the OR factor of gravitational spacetime transformation under the general observation agent OA(η):

The GOR factor Γ = Γ(η,v,χ) is also referred to as the relativistic gravitational factor; the larger the value of Γ, the more significant the relativistic or observational effects of P exhibited in gravitational spacetime, which can be decomposed in terms of the Taylor series:

In Einstein’s general relativity, the gravitational space-time-transformation factor is γ = 1/√(1- v²/c²+2χ/c²)⁹ or γ = 1/√(1 + 2χ/c²) without considering the moving speed v of P. Because the speed of light c is an invariant, the value of γ depends on the gravitational potential χ. Based on this, Einstein believed that the relativistic effects of gravitational spacetime were real natural phenomena and that the root and essence of gravitational-relativistic effects were determined by gravitational interaction.

However, the IOR factor Γ = Γ(η,χ) indicates that, in essence, the value of Γ depends on the information-wave speed η of OA(η). Given the gravitational potential χ where P is located, the larger the value of η, the weaker the gravitationally relativistic effects exhibited by P would be; if η is infinite, the gravitational spacetime would have no relativistic phenomena. Thus, the theory of GOR discovered that the relativistic effects of matter interaction in gravitational spacetime are not the objective and real physical reality, but rather the observational effects and apparent phenomena caused by the observational locality (η < ∞) of the observation agent OA(η).

The GOR factor of spacetime transformation generalizes both Einstein’s relativistic gravitational factor and Newton’s classical gravitational factor, that is, the Galilean factor, unifying them within the theory of GOR.

As η→c, OA(η)→OA(c), the GOR factor Γ(η, v,χ) strictly converges to Einstein’s factor of gravitational-spacetime transformation γ = Γ(c,v,χ):

It is thus clear that Einstein’s factor γ = Γ(c,v,χ) of gravitational-spacetime transformation is relativistic because of the optical observation agent OA(c) with the observational locality of c<∞. Thus, the optical agent OA(c) and Einstein theory of general relativity present the observational effects of gravitational interaction and gravitational spacetime.

As η→∞ OA(η)→OA_∞, the GOR factor Γ(η, v,χ) strictly converges to Newton’s factor of the gravitational space–time transformation Γ = Γ(∞,v,χ):

This is exactly the Galilean factor: Γ_∞ ≡ 1.

It is thus clear that Newton’s factor Γ_∞ ≡ 1 of gravitational-spacetime transformation is non-relativistic because of the idealized observation agent OA_∞ with no observational locality (η→∞). Thus, the idealized agent OA_∞ and Newton’s theory of universal gravitation represent the objective and real gravitational spacetime.

So, OA_∞ might be referred to as the God’s Eye.

5.2.2 The GOR metric equations of spacetime

To remove the influence of gravitational relativistic effects on the measurement of gravitational spacetime, that is, to remove the observational effects of the optical agent OA(c), Einstein established formulae for determining the standard time dτ and physical space dl in his theory of general relativity. For the general observation agent OA(η), by following Einstein’s logic, the theory of GOR derives the formulae (Equation (3) and Equation (4)) to determine the standard time dτ and physical space dl.

The GOR metric equations of the standard time dτ (Equation (3)) and physical space dl (Equation (4))generalize and unify Einstein’s metric relations of relativistic spacetime and Newton’s metric equations of classical spacetime.

As η→c, OA(η)→OA(c), the GOR metric equation of the standard time (Equation (3)) strictly converges to Einstein’s metric equation of the standard time dτ:

As η→c, OA(η)→OA(c), the GOR metric equation of physical space (Equation (4)) strictly converges to Einstein’s metric equation of physical space:

As η→∞, OA(η)→OA_∞, the GOR metric equation of the standard time (Equation (3)) strictly converges to Newton’s classical time dt_∞ = dτ:

It is thus clear that as the idealized observed time of OA_∞, Newton’s classical time dt_∞ is exactly the standard time dτ, that is, the objective and real proper time.

As η→∞, OA(η)→OA_∞, the metric of gravitational spacetime converges to the Minkowski metric η_μν = diag(+1,-1,-1,-1), the metric of physical space γ_ik(η)→ diag(1,1,1), and the GOR metric equation of physical space (Equation (4)) strictly converges to Newton’s classical space:

It is thus clear that as the idealized observed space of OA_∞, Newton’s classical space dl_∞ is exactly the Cartesian space, that is, the objective and real physical space.

5.2.3 The GOR gravitational-field equation

As Einstein’s gravitational field equation represents Einstein’s theory of general relativity and Newton’s gravitational field equation represents Newton’s theory of universal gravitation, the GOR gravitational field equation (Equation (5)) represents the theory of GOR.

The GOR gravitational field equation (Equation (5)), which extends Einstein’s gravitational field equation from the optical agent OA(c) to the general observation agent OA(η), not only generalizes Einstein’s gravitational field equation, but also generalizes Newton’s gravitational field equation, unifying them within the theory of GOR.

As η→c, OA(η)→OA(c), the GOR gravitational field equation (Equation (5)) strictly converges to Einstein’s gravitational field equation:

By defining the extended Newtonian gravitational potential χ_μν, the GOR field equation can be rewritten as:

where η is the information-wave speed of the general observation agent OA(η), η_μν=diag(+1,-1,-1,-1) is Minkowski metric; ∇ is the 3d partial differential operator, Δ=∇² is Laplace operator, and $\square$ the general d’ Alembert operator defined in OR, i.e., the second-order partial differential operator of the general observation agent OA(η).

As η→∞ OA(η)→OA_∞, the GOR gravitational field equation (Equation (5)) strictly converges to Newton’s gravitational field equation, that is, the Poisson equation of Newton’s law of universal gravitation:

5.2.4 The GOR gravitational-motion equation

Einstein once thought that his theory of general relativity should consist of two fundamental equations: the first is a gravitational-field equation that describes how gravitational spacetime is curved; the second is a gravitational-motion equation that describes how an object moves in curved gravitational spacetime.

Subsequently, Einstein et al.³² and Fock³³ independently proved that Einstein field equation and Einstein motion equation are equivalent.

However, this does not deny the independent value of Einstein field equation or Einstein motion equation. The calibration of Einstein’s field-equation coefficient κ_GOR not only needs the gravitational-field equation but also needs the gravitational-motion equation.⁹

The GOR gravitational field equation and the GOR gravitational motion equation more clearly demonstrate the equivalence between the field equation and the motion equation in gravitational space–time. Similarly, the calibration of the GOR field-equation coefficient κ_GOR not only needs the GOR gravitational-field equation but also needs the GOR gravitational-motion equation.^12–15

The GOR gravitational motion equation (Equation (6)), which extends Einstein’s gravitational field equation from the optical agent OA(c) to the general observation agent OA(η), not only generalizes Einstein’s gravitational field equation, but also generalizes Newton’s gravitational field equation, unifying them within the theory of GOR.

As η→c, OA(η)→OA(c), the GOR gravitational motion equation (Equation (6)) strictly converges to Einstein’s gravitational motion equation:

As η→∞, OA(η)→OA_∞, and as in the Galilean transformation, the GOR 4d motion equation (Equation (6)), in which space and time are originally interdependent, splits into two independent equations of space and time:

5.2.5 The GOR observed mass

Based on the GOR relativistic factor Γ = Γ(η,v,χ) (Equation (28)), we obtain the general mass-speed relation:

Based on the GOR mass-speed relation (Equation (42)) under the general observation agent OA(η), the theory of OR defines the following two concepts for matter mass.

OA(η) observed inertial mass m _I (η):

OA(η) observed gravitational mass m _G (η):

The GOR observed inertial mass in Equation (43) generalizes Einstein’s relativistic inertial mass and Newton’s classical inertial mass, and the GOR observed gravitational as in Equation (44) generalizes Einstein’s relativistic gravitational mass and Newton’s classical gravitational mass.

Thus, the GOR observed-mass relations (Equation (43) and Equation (44)) unifies Einstein’s relativistic mass and Newton’s classical mass.

As η→c, OA(η)→OA(c), the OR inertial mass m_I(η) (Equation (43)) observed with OA(η) strictly converges to the inertial mass m_I(c) observed with Einstein’s OA(c):

As η→c, OA(η)→OA(c), the OR gravitational mass m_G(η) (Equation (44)) observed with OA(η) strictly converges to the gravitational mass m_G(c) observed with OA(c):

As η→∞, OA(η)→OA_∞, the OR inertial mass m_I(η) (Equation (43)) observed with OA(η) strictly converges to the inertial mass m_I(∞) observed with Newton’s OA_∞:

The concept of Gravitational Mass originated from Newton. Intuitively, it is believed that Newton’s gravitational mass m_G should be equal to Newton’s inertial mass m_I, that is, m_G = m_I, and may also be referred to as Newtonian classical mass, labeled as m_∞.

As η→∞, OA(η)→OA_∞, the OR gravitational mass m_G(η) (Equation (44)) observed with OA(η) strictly converges to the gravitational mass m_G(∞) observed with OA_∞:

Like Equation (21), Equation (48) also has important enlightening significance. Combining Equation (21) and Equation (48), the theory of OR has discovered that

5.2.6 The GOR observed energy

In gravitational space–time, the observed object P has both the kinetic energy K and the potential energy V, and the total energy H = K+V of P must be conserved.

Based on the GOR mass-speed relation (Equation (42)), under the general observation agent OA(η), the theory of OR defines the following two concepts for matter energy.

OA(η) Observed Kinetic Energy K(η):

OA(η) Observed Potential Energy V(η):

Thus, the total energy of the observed object P moving in the GOR gravitational spacetime is

The GOR-observed kinetic energy formula (Equation (49)) generalizes Einstein’s relativistic kinetic energy and Newton’s classical kinetic energy. The GOR-observed potential energy formula (Equation (50)) generalizes Einstein’s relativistic potential energy and Newton’s classical potential energy. Thus, the GOR-observed mass relations (Equation (49) and Equation (50)) unifies Einstein’s relativistic energy and Newton’s classical energy.

As η→c, OA(η)→OA(c), the OR kinetic energy K(η) (Equation (49)) observed with OA(η) strictly converges to the kinetic energy K(c) observed with Einstein’s OA(c):

As η→c, OA(η)→OA(c), the OR potential energy V(η) (Equation (50)) observed with OA(η) strictly converges to the potential energy K(c) observed with OA(c):

Naturally, as η→c, the total energy H(η) (Equation (51)) of the observed object P moving in the GOR gravitational spacetime observed by the general observation agent OA(η) strictly converges to the total energy H(c) of P observed by Einstein’s optical agent OA(c):

You might be a bit surprised that, as η→∞, OA(η)→ OA_∞, the OR kinetic energy K(η) (Equation (49)) observed with OA(η) strictly converges to Newton’s classical kinetic energy K_∞ = K(∞) observed with Newton’s OA_∞:

Equation (55) is exactly Newton’s classical kinetic energy formula K_∞ = m_∞v²/2.

You might be a bit surprised that as η→∞, OA(η)→ OA_∞, the OR potential energy V(η) (Equation (50)) observed with OA(η) converges strictly to Newton’s classical potential energy V_∞ = V(∞), observed with Newton’s OA_∞:

Equation (Equation (56)) is exactly Newton’s classical potential energy formula, V_∞ = -GMm_∞/r.

Naturally, as η→∞, the total energy H(η) (Equation (51)) of the observed object P moving in the GOR gravitational spacetime observed by the general observation agent OA(η) strictly converges to the total energy H_∞ = H(∞) of P observed by Newton’s idealized agent OA_∞:

5.2.7 The GOR celestial-motion equation

Based on the GOR field equation (Equation (5)) and GOR motion equation (Equation (6)), the theory of GOR establishes an observational model of the celestial two-body system (M, m) under the general observation agent OA(η):

The GOR celestial-motion equation (Equation (58)) generalizes and unifies Einstein’s celestial-motion equation for OA(c), and Newton’s celestial-motion equation for OA_∞.

As η→c, OA(η)→OA(c), the GOR celestial-motion equation (Equation (58)) under OA(η) strictly converges to Einstein’s celestial-motion equation under OA(c):

It is worth noting that compared to Newton’s celestial-motion equation, Einstein’s celestial-motion equation (Equation (59)) has an additional item: 3h_Ku²/c², that is, the orbital precession term. With it, Einstein predicted the orbit precession of Mercury: Mercury’s perihelion would precess 43.03″ every 100 years.

However, it is puzzling that astronomical observation data indicate that Mercury’s perihelion actually precesses 5600.73 arcseconds every 100 years, of which Einstein’s predicted value is less than 8‰. Why did Einstein not predict the remaining 99.2%?

The GOR celestial-motion equation (Equation (58)) also has an orbital precession term, 3h_Ku²/η². However, the GOR celestial-motion equation indicates that such orbital precession depends on the observation agent OA(η) and the information-wave speed η of OA(η), which is an observational effect or apparent phenomenon caused by the observational locality (η < ∞) of OA(η). The Mercury’s data of 5600.73 arcseconds is sourced from the optical astronomical observation, and the observation agent is naturally the optical agent OA(c). If the data of 5600.73 arcseconds does indeed contain the 43.03″ predicted by Einstein, then it just means that the Mercury’s data does indeed record the observational effects and apparent phenomena of the optical agent OA(c) caused by the observational locality (c < ∞) of OA(c).

Thus, Mercury’s astronomical observation data do not support Einstein’s theory of general relativity but rather support the theory of GOR.

As η→∞, OA(η)→OA_∞, the GOR celestial-motion equation (Equation (58)) under OA(η) strictly converges to Newton’s celestial-motion equation under OA_∞:

This is exactly Newton’s classical celestial-motion equation in the form of Binet equation.

Section 5.2 demonstrates that the theory of GOR is logically consistent with Einstein’s theory of general relativity and Newton’s theory of universal gravitation. This from one aspect confirms that the theory of GOR is logically self-consistent and theoretically correct. For details, see Chapter 20 of the 2^st volume GOR of OR.^12–15

Section 5 indicates that Einstein’s theory of relativity, both special and general, is that of optical observation with the optical agent OA(c); Galileo’s doctrine and Newton’s mechanics are theories of idealized observation with the idealized agent OA_∞.

Section 5 and Tables A1 and A2 in Appendix A (refer to extended data) tell us that the theory of OR has not only generalized Einstein theory of relativity but also has generalized Newtonian mechanics, ultimately unifying Newtonian mechanics and Einstein theory of relativity in the same theoretical system under the same axiom system.

It is thus clear that logically, the theory of OR is not only isomorphically consistent with Einstein’s relativity theory, but is also isomorphically consistent with Newton’s classical mechanics. This confirms the logical self-consistency and theoretical correctness of OR.

6.1 OR justifying Galileo and Newton

OR Clearing Galileo’s Name

The Galilean transformation is not an approximation of the Lorentz transformation, but rather a natural law of the physical world, whereas the Lorentz transformation is only a model of optical observation, presenting us with an optical mapping of spacetime transformation. Galileo’s law of speed addition is not an approximation of Einstein’s relation of relativistic speed addition, but a natural law of speed addition, whereas Einstein’s relation of speed addition is only a law of optical observation, not entirely objective and real.

OR clearing Newton’s name

Newton’s mechanics is not an approximation of Einstein’s theory of relativity, but rather a true portrayal of the physical world, representing the objective and real natural world. Einstein’s theory of relativity, both special and general, is that of optical observation, only presenting us with an optical image of the physical world that could be effective and valid only under the optical agent OA(c).

6.2 The significant discoveries of OR

The theory of OR has discovered that mankind’s perception of the objective world not only depends on but is also restricted by observation; all theoretical systems in physics, including Galileo’s doctrine, Newton’s mechanics, Einstein’s relativity theory, and even quantum theory, must be branded with observations.

Einstein’s theory of relativity, both special and general, is the theory of optical observation that is effective and valid only in optical observation armed with the optical agent OA(c). The information-wave speed of OA(c) that transmits the observed information is the speed of light c which is limited. Therefore, the optical observation agent OA(c) has the observational locality of c < ∞ such that matter motion and gravitational interaction exhibit relativistic effects in Einstein’s observational space–time.

Galileo’s doctrine and Newton’s mechanics are theories of idealized observation armed with the idealized agent OA_∞. The information-wave speed of OA_∞ transmitting observed information is idealized as infinite; therefore, the OA_∞ has no observational locality and might be referred to as the God’s Eye. Therefore, Galileo’s doctrine and Newton’s mechanics represent the objective and real physical world.

However, in reality, there is no idealized observation agent OA_∞. The objective and real natural world can only be touched by human reason.

The theory of OR has discovered that, in essence, all relativistic effects or relativistic phenomena of matter motion and matter interactions presented in spacetime are observational effects and apparent phenomena rooted in the observation locality of the human observation agent OA(η) (η < ∞).

Therefore, the speed of light is not really invariant, and spacetime is not really curved.

The theory of OR has discovered that, in essence, all quantum effects or quantum uncertainties presented in microscopic spacetime are observational effects rooted in the observational perturbation of the human observation agent OA(η) (h_η > 0: h_ηη ≡ hc) (see Chapter 6 of the 1^st volume IOR in^12–15).

Heisenberg’s uncertainty³⁴ is only the observational perturbation effect of the information (photons) of the optical agent OA(c) on observed objects.

6.3 OR and the big puzzles in physics

The theory of OR has listed 15 big puzzles in modern physics^12–15: BP-01–15. The interpretations of these big puzzles made by the mainstream school of physics are well known and are mostly based on Einstein’s perspective of the optical observation agent OA(c). Based on the theory of OR, we now have a broader perspective from the general observation agent OA(η) (0 < η < ∞; η→∞) to re-examine these big puzzles. Perhaps, we will have new discoveries and insights.

Below is a brief overview of the interpretations of some of these big puzzles based on OR. For details, see Chapter 9 of the 1^st volume IOR and Chapter 21 of the 2^nd volume GOR in The Theory of Observational Relativity: The Unity of Newton and Einstein.^12–15

BP-02: On photon mass

Photons have their own rest mass m_o, which is the objective and real mass of matter. According to the theoretical calculation of OR, a photon with frequency f weighs m_o = m = hf/c².

BP-04: On planck constant

The Planck constant h is the energy-frequency ratio of photons, or to be more exact, is the energy-frequency ratio of the information of the optical agent OA(c), whereas the energy-frequency ratio of the informons of the general observation agent OA(η) can be called the general Planck constant and denoted as h_η: h_η = hc/η.

BP-06: On uncertainty principle

In the theory of OR, Heisenberg’s principle of uncertainty or σ_xσ_p ≥ ħ/2 is just a special case of the principle of general uncertainty: σ_xσ_p ≥ ħ_η/2.

BP-07: On De Broglie wave

De Broglie wave is not the inherent wave of matter, but rather the information wave of the optical agent OA(c).

BP-10: On mercury precession

Based on his general relativity, Einstein predicted that Mercury’s perihelion would precess 43″ every 100 years. However, Einstein’s prediction is not the objective and real precession of Mercury but rather the observational effect and apparent phenomenon of the optical agent OA(c).

BP-13: On gravitational waves

The gravitational waves predicted by Einstein based on his theory of general relativity are not objective and real gravitational radiation but the information wave of the optical agent OA(c). The speed κ of gravitational waves is definitely not the speed c of light.

LIGO, the Laser Interferometer Gravitational-Wave Observatory in the United States, claimed that they had detected gravitational waves coming from deep space,^35,36 and that the speed κ of gravitational waves determined by LIGO was exactly the speed c of light.³⁷ However, the gravitational-radiation signals detected by LIGO do not originate from the distant deep space of the universe, but rather from electromagnetic matter systems, such as gamma-ray bursts or X-rays, which carry their own gravitational fields, pass over the earth, and invade the space around the LIGO detector at close quarters. It was not that the speed of gravitational radiation was the speed of light but rather that the gravitational fields of these electromagnetic matter systems moved at the speed of light with their electromagnetic systems.

The theory of OR does not doubt the existence of gravitational waves or gravitation. In the theory of OR, Gravitational Wave is regarded as the equivalent concept of Gravity or Gravitational Radiation.

According to Laplace’s theoretical calculation, the speed κ of gravitational radiation is much higher than the speed c of light: κ > 7 × 10⁶c, ³⁸ whereas Flandern’s calculation is κ = 2 × 10¹⁰c.³⁹ This is reasonable; otherwise, it would be difficult for us to imagine how photons could be acted upon by gravitational radiation, or as Flanders put it, the universe would lose its existing stable structure.

If the speed κ of gravitational radiation is equal to the speed c of light, how can gravitational waves or gravitons escape from black holes and interact gravitationally with external celestial bodies?

BP-14: On black holes

The theory of OR cannot deny the existence of black holes. The theory of GOR and Newton’s theory of universal gravitation can also be used to deduce the theory of black holes. However, the black hole theory in modern physics is derived from Einstein’s theory of general relativity, which is only that of the optical agent OA(c), and cannot represent the objective and real physical existence of massive celestial bodies or black holes.

Based on the theory of OR or GOR, from the perspective of the general observation agent OA(η), blackhole scholars, including Hawking, will definitely find that black holes differ from what they imagined.

BP-15: On the big bang

Similar to the theory of black holes, the theory of Big Bang in modern physics is also a product of the so-called Modern General Relativity which is based on Einstein’s general relativity from the perspective of the optical observation agent OA(c). Therefore, the so-called Big Bang could only be an optical illusion or mirage and not the objective or real physical reality.

Cosmological redshift does not imply that the universe is expanding, nor does it imply that the universe has experienced a Big Bang.

According to the theory of OR or GOR, spacetime is not really curved. Therefore, spacetime will never curl up to the singularity of the Big Bang.

So, the universe did not undergo the Big Bang.

The interpretations of OR for big puzzles in modern physics are not necessarily correct. These are only for readers and physicists to examine, thus promoting our understanding of these big puzzles in physics.

7.1 Is the theory of OR right?

The theory of OR, both IOR and GOR, is logically concise and easy to understand.

As demonstrated in Section 5 and Tables A1 and A2 in Appendix A- (refer to extended data), the theory of OR is isomorphically consistent with Einstein’s relativity theory and Newton’s classical mechanics. As a theory of the general observation agent OA(η) (0 < η < ∞; η→∞), the theory of OR has generalized Newton’s classical mechanics of the idealized agent OA_∞ and Einstein’s relativity theory of the optical agent OA(c), unifying the two great theoretical systems of human physics in the same theoretical system under the same axiom system.

This isomorphic consistency, as well as generalization and unification, confirms the logical self-consistency and theoretical validity of the theory of OR, including IOR and GOR, from one aspect.

The theory of OR has uncovered the essence of the relativistic phenomena of matter motion and matter interactions presented in spacetime. This seemingly fulfills Hawking’s statement that we are beginning to know the mind of God.

Perhaps you cannot understand the logical deduction of OR based on the definition of OR time as the first principle. In this regard, Sec. 4.3 specifically depicts for readers the different logical paths that could also lead to the theory of OR. Different logical paths could lead to the same theory of OR, which from one more aspect confirms the logical self-consistency and theoretical validity of the theory of OR.

In particular, Sec. 4.3.4 describes PGC logic path 1, leading to the theory of OR. You only need to replace the light speed c of the optical agent OA(c) in Einstein’s relativity theory with the information-wave speed η of the general observation agent OA(η), and you could directly obtain the entire theoretical system of OR including IOR and GOR. Thus, you could certainly predict the isomorphic consistency between the theory of OR and Einstein’s relativity theory, and the generalization of OR for Einstein’s relativity theory, including special and general.

However, you might not be able to understand the isomorphic consistency between the theory of OR and Galileo-Newtonian mechanics, and the generalization of OR for Galileo-Newtonian mechanics.

Actually, it is unexpected for the theory of OR to generalize and unify Galileo-Newtonian mechanics and Einstein relativity theory. This further confirms the logical self-consistency and theoretical validity of the theory of OR, including IOR and GOR.

7.2 Does the theory of or have empirical basis?

Einstein’s theory of relativity, both special and general, is revered as the Bible of human physics because it possesses empirical evidences, supported by most observations and experiments.

So, what about the theory of OR?

7.2.1 Why do observations and experiments mostly support Einstein?

The theory of OR repeatedly emphasizes that Galileo’s doctrine and Newton’s mechanics are theories of idealized observation, which is the true portrayal of the objective physical world. Einstein’s theory of relativity, both special and general, is that of optical observation that presents us with only an optical image of the physical world and is not entirely objective and real.

Now that Galileo is more right than Lorentz and Newton is more right than Einstein, why do human observations and experiments mostly tend to support Einstein?

The reason for this is simple: human observations and experiments mostly use the optical observation system, that is, the optical agent OA(c), and thus they naturally tend to support Einstein.

However, this does not mean that Einstein was more right than Newton. This simply means that Einstein relativity theory is just that of optical observation.

It is not so much that these observations and experiments support Einstein but rather support the theory of OR. With advancements in science and technology, mankind will master superluminal observation techniques, invent superluminal observation agents, and observe the more objective and real physical world. At that time, human observations and experiments will be more inclined to support Galileo and Newton.

7.2.2 Is the theory of OR supported by observations or experiments?

In fact, an observation or experiment that supports Einstein’s relativity theory must be a support for the theory of OR, such as the Michelson-Morley experiment. An observation or experiment that supports Galileo’s doctrine or Newton’s mechanics must also be a support for the theory of OR, such as the Galilean transformation and Galileo’s principle of speed addition.

Therefore, to some extent, the theory of OR has been supported by all observations and experiments to date.

Indeed, in the Michelson-Morley experiment,³ the speed of light appeared invariant. However, the theory of OR finds that this is only an apparent phenomenon.

In the Michelson-Morley experiment, light or photons serve as both the observed object of Michelson and Morley and the observation medium transmitting the observed information for Michelson and Morley. In other words, the observation agent OA(η) of Michelson and Morley is the optical agent OA(c), and naturally, the information-wave speed η of OA(c) is the speed of light c.

It is thus clear that in the Michelson-Morley experiment, the invariance of light speed is only a phenomenon, whereas the invariance of information-wave speeds is the essence.

Therefore, the Michelson-Morley experiment does not support the hypothesis of the invariance of light speed and Einstein’s theory of relativity, but rather supports the theorem of the invariance of information-wave speeds and the theory of OR.

Originally, mankind believed in Galileo’s principle of speed addition, which is a direct inference of the Galilean transformation.

Relative to the observer on the platform, the speed u of a passenger on the train is equal to the speed v of the train plus the speed u′ of the passenger walking on the train⁴¹: u = u′ + v, that is, Galileo’s principle of speed addition.

However, after Einstein’s special theory, people have turned to believe that Galileo’s speed addition is simply an approximation of Einstein’s speed addition in the case of macroscopic low speeds.

The theory of OR has discovered that Einstein’s speed addition is the product of the optical agent OA(c) and optical observation. The optical agent OA(c) has the observational locality of c < ∞, presenting observational effects and apparent phenomena. Thus, Einstein’s speed addition is not entirely objective and real.

According to the theory of OR, the higher the information-wave speed η of the observation agent OA(η) or the lower the moving speed v of the observed object, the weaker the observational effects and apparent phenomena of OA(η) become, and our observations would be closer to the objective physical reality observed by the idealized agent OA_∞.

In daily life, that is, in the case of macroscopic low speeds, the speed addition observed by people conforms to Galileo’s principle of speed addition. This confirms the logical conclusion of OR: Galileo’s principle of speed addition is the product of the idealized agent OA_∞, which is the objective and true natural law of speed addition.

Thus, it is clear that daily human observations, human common sense, and human rationality are more in line with the idealized observation of the idealized agent OA_∞, supporting Galileo’s principle of speed addition. This demonstrates that Galileo’s principle of speed addition and daily human observations supports the theory of OR.

8.1 The theoretical significance of OR

Hawking remarked that¹ human physics was increasingly fragmented and divided into increasingly partial theories; the ultimate goal of physics and physicists was to unify them.

The theory of OR, as a new physics theory, is based on more basic logical premises and has a broader perspective. Therefore, it has uncovered the root and essence of relativistic effects in macroscopic spacetime, unifying Newton’s classical mechanics and Einstein’s relativity theory in the same theoretical system under the same axiom system; also, it has uncovered the root and essence of quantum effects in microscopic spacetime, marching towards the unification of relativity theory and quantum theory.

This undoubtedly has great theoretical significance.

Naturally, the theory of OR is far from the ultimate theory. In fact, as the theory of OR points out, due to the observational locality, mankind will never be able to reach the realm of absolute truth.

So, there is no the so-called ultimate theory in physics.

In a sense, however, OR is a complete theory–that is, a triumph of human reason–in Hawking’s words.

The theory of OR will inject fresh blood and new ideas into human physics. According to the theory of OR, mankind needs to reshape its view of nature.

8.2 The practical significance of OR

Einstein’s theory of relativity, as a special case in the theory of OR with the optical agent OA(c), has practical applications such as the GPS positioning system. In addition to the OR of the optical agent OA(c), both the OR of the subluminal agent OA(η) (η < c) and the OR of the superluminal agent OA(η) (η > c) possess potential values for practical applications.

8.2.1 Optical OR: for GPS system

The best-known application of Einstein relativity theory as a special case of OR with the optical agent OA(c) is for the GPS positioning system to determine and calibrate the time of GPS satellites.

In a GPS system, satellites orbit the earth at a speed (v) of over 7.9 k/s in the gravitational field (χ); therefore, both inertial and gravitational relativistic effects must be considered. Thus, the determination and calibration of GPS time have employed Einstein’s theory of relativity: dτ = dt(c)√(1- v²/c² + 2χ/c²), where the speed c of light or electromagnetic radiation is the information wave speed c of the optical agent OA(c).

In GPS systems, satellites communicate with each other via radio signals. Naturally, its observation agent is the optical agent OA(c), and the determination and calibration of GPS time must rely on the theory of OR with the optical agent OA(c), that is, Einstein’s theory of relativity. Therefore, the GPS system is an applied example of the theory of OR in the case of the optical agent OA(c).

The practical applications of OR are not limited to the optical agent OA(c). According to the theory of OR, Einstein relativity theory would inevitably become invalid under the non-optical observation agent OA(η) (η ≠ c). In this case, we would have to adopt the theory of OR with non-optical agents: either subluminal (η < c) or superluminal (η > c).

8.2.2 Subluminal OR: for the multi-robot system operating collaboratively in deep sea

In the future, the deep sea will become an important exploration area for humankind.

China’s Jiaolong robot has already been able to dive 10,000 m underwater. As multiple robots work collaboratively in the deep sea, they will face the same problems as GPS satellites: how to calibrate time and how to determine space.

Underwater communication systems cannot use light or electromagnetic waves. Underwater robots, like dolphins, must use underwater ultrasonic waves as the observation medium, employing the dolphin agent OA (v_U): η = v_U ≈ 1450 m/s, which is much lower than the speed of light c. Particularly, the ratio of the underwater robot’s speed to underwater ultrasound is much greater than the ratio of the GPS satellites’ speed to the speed of light, and the gravitational field in the deep sea is much stronger than that of the GPS satellites. Therefore, the dolphin agent OA (v_U) must have more significant relativistic effects than the optical agent OA(c).

Thus, the collaborative operation of multiple robots in the deep sea requires the subluminal theory of OR with the dolphin agent OA (v_U) listed in Table 1.

This is a potential application of subluminal OR.

8.2.3 Superluminal OR: for gravitational wave astronomy

As shown by an increasing number of quantum entanglement experiments,^23,24 the physical world does have superluminal forms of matter motion. In the future, with the development of science and technology, superluminal observation agents (η > c) will be developed. Therefore, mankind must use the superluminal theory of OR.

LIGO’s exploration^35,36 of gravitational waves has led to a new concept⁴²: Gravitational Wave Astronomy. Of course, as the theory of OR has clarified, the speed κ of real gravitational waves is more in line with the calculations of Laplace³⁸ and Flandern,³⁹ much higher than the speed of light (κ >> c) -- It is definitely not the speed of light envisioned by Einstein and LIGO.

To develop gravitational wave astronomy in the true sense, physics requires the superluminal theory of OR and gravitational agent OA(κ) which employs gravitational radiation as the observation medium.

To this end, the primary task of experimental physics is to measure and determine the speed κ of gravitational radiation or waves.

With the help of the superluminal theory of OR and superluminal agents, mankind will “see” or observe a more objective and real physical world.

This is a potential application of superluminal OR.

8.3 The guiding significance of OR: for experimental physics

The theory of OR states that what we perceive or observe may not necessarily be the objective physical reality. Phenomena may not necessarily be the essence.

However, experimental physicists always believe that observation represents reality and that phenomena represent the essence. Such observationalist views on nature have misled human physics.

The theory of OR has important guiding significance for experimental physics.

Owing to the current level of science and technology, our observations and experiments mostly rely on the optical agent, OA(c). Therefore, most of observations and experiments support Einstein’s theory. In many cases, experimental physicists are not sure or not concerned about what their observation agents are or who is transmitting the observed information to them.

According to the theory of OR, an experimental physicist conducting a physical experiment must first give a definite answer to the following questions: what the observation agent OA(η) for his experiment is, and what the information wave speed η of OA(η) is.

In theory of OR, the OR factor of spacetime transformation Γ(η) = 1/√(1- v²/η² + 2χ/η²) can be decomposed into Γ_∞ and ΔΓ (η): Γ(η) = Γ_∞+ΔΓ(η), where Γ_∞ ≡ 1 is the Galilean factor representing the objective physical reality; ΔΓ(η) is the relativistic factor representing the pure observational effects and apparent phenomena exhibited in observations and experiments, depending on the information wave speed η of OA(η), rooted from the observational locality (η < ∞) of OA(η). Therefore, to determine the objective and real physical quantities of observed objects, experimental physicists must remove ΔΓ(η) from Γ(η).

If experimental physicists introduce the observation-agent concept of OR into experimental physics, they will definitely obtain new discoveries.