The Fall of Special Relativity and The Absoluteness of Space and Time

Rongqing Dai

Abstract

The special theory of relativity is wrong because its two postulates are logically defective. In this writing, through thought experiments and logical discussion, we will see how the first postulate would infer the violation of the 2^nd law of thermodynamics and how the second postulate would lead to logically impossible results. Some historical paths leading to those postulates will be reviewed, and the famous Sagnac experiment will be discussed to demonstrate how history has taken a confusing detour in getting the truth about the relativity. Accordingly, this writing concludes that the speed of light in vacuum is not a constant to all observers but needs to obey the Galilean rule of speed addition. The postulate of the constant speed of light in vacuum to all observers would be replaced by a revised postulate of speed of light in vacuum, and thus the speed of light in vacuum should no longer be assumed to be the limit of energy (information) propagation. For the first time in history, a definite and correct explanation to the result of the Michelson-Morley experiment will be provided based on the revised postulate of speed of light in vacuum. The notion of relativity of simultaneity would be abandoned; consequently, space and time will be considered independent from each other in the absolute sense. However, we are not going back to the old rigid Newtonian space and time, but rather entering a new era of the soft absolute space and time that would conform to the general theory of relativity. Accordingly, the notion of spacetime still remains valid in correlating the space and time of all events, especially in calculating the gravitational impact on the curvature of spacetime, i.e. the space warping together with the change of tempo rate under the impact of gravity.

Keywords: Special Relativity, Principle of Relativity, Speed of Light, Thought Experiment, Simultaneity, Absolute Space and Time

1. Introduction

Although it is said that Newton was the first person who explicitly brought up the issue of the absoluteness of space and time in his masterpiece Philosophiæ Naturalis Principia Mathematica [[1]], if we carefully review all the antique uses of the notions of space and time we might find that ancient people never seemed to assert or deny the absoluteness of space and time (because it was just natural to them) until the time of Newton and Leibniz when the need of more precise kinematic description of motions occurred. Even when Galileo proposed his version of kinematic principle of relativity, he did not have the need to worry about the absoluteness of space and time.

For a long time, the contention against the notion of absolute space and time mainly remained at philosophical realm when sagacious people like Leibniz, Berkley, Mach, and others struggled with their difficulty of imagining the abstract meanings of absolute space and time, or the difficulty of perceiving the absolute space and time without any material references. An important reason for the issue of absolute space to remain unsettled was that even the proponents of the absolute space such as Newton could not convincingly identify with clear philosophical term the absolute frame of reference in the universe while all things are found to move with each other, especially after Earth, Sun, and later Milky Way were denied as the center of universe one after another. As for the notion of absolute time, the main trouble for the relativists to accept it is the difficulty for them to perceive the time without counting on the referential series of events. Correspondingly, the notion of inertial coordinate system, i.e. a preferred set of frames of reference that move uniformly with respect to one another, was employed as the basic selection of the frame of reference, instead of directly invoking the absolute space and time in calculation.

The biggest rebuff in history against the notion of absolute space and time happened when Einstein proposed the relativity of simultaneity, and consequently, the notion of absolute space and time was completely abandoned (together with the luminiferous aether) by the scientific community for more than a century until the special relativity is proved wrong because of the defects of its two postulates. In this writing we will discuss why the special theory of relativity is wrong and thus the notion of the absolute space and time is the best we have so far concerning space and time.

2. The Troublesome First Postulate of Special Relativity

The first postulate of the special theory of relativity states that all inertial coordinate systems are equivalent in describing natural laws [[2], [3]] (it was then extended to any Gaussian coordinate system or simply any system by Einstein [[4]] for the general theory of relativity). This postulate, together with the postulate that the speed of light in vacuum is constant to all observers, is the foundation of the special theory of relativity. However, as we will see in this section and the following section 3, both postulates would logically entail impossible outcomes and thus both of them are logically incorrect.

In order to appreciate the meaning of the equivalence of describing natural laws, we need first to be clear about how natural processes are supposed to be observed in any coordinate system or frame of reference in physics. In the study of physics, a coordinate system or a frame of reference would normally extend to infinity from negative to positive, and all locations in the universe that are covered by its coordinates are supposed instantly observable by any observer that is stationed with the system (i.e. the observer is moving with the system). This stipulation is important for the special theory of relativity because of the claim made by the first postulate that physical laws are all the same in any inertial system, e.g. we cannot say that an observer O that is moving with system K (e.g. the Sun), no matter where he locates in K, has more authority than an observer O’ that is moving with system K’ (e.g. the Earth), no matter where he locates in K’, about the laws concerning some physical processes happening in K.

Closely related to the above mentioned stipulation, the most important knowledge about relativity is that it claims not to be mere mathematical expressions, but rather the reflection of the reality of real physical processes observed in any inertial system. Accordingly, even if a physical process happens in a body attached to a coordinate system K, according to the special theory of relativity, the same process observed (or estimated) by an observer O’ in a body attached to coordinate system K’ moving relatively to K is as real as an observer O attached to K in the sense that none of them is more favored in explaining the physical nature of the process. This is the requirement of the first postulate of the special theory of relativity.

2.1. The Consequence of Applying FitzGerald–Lorentz Contraction and Einstein E = mc² Together

FitzGerald [[5]] in 1889 and Lorentz [[6]] in 1892 independently proposed the hypothesis that all bodies are contracted in the direction of their motion by a factor of (1 – v²/c²)^1/2 so that we have

L’ = L(1 – v²/c²)^1/2                                                      (1),

where L is the length along the moving direction in the coordinate system K moving with the objects and L’ is the length along the same direction but in the coordinate system K’ moving relative to the objects at speed v. Equation (1) was subsequently called FitzGerald–Lorentz contraction hypothesis, and in 1905, Einstein published his famous formula

∆E = ∆mc²                                                                       (2)

The FitzGerald–Lorentz contraction hypothesis (1) is a composing part of the famous Lorentz transformations, and the Lorentz transformations and the Einstein energy-inertia relationship (2)have become two most important icons of the special theory of relativity.

Equation (2) excludes the possibility of a mass deduction due to the motion, while equation (1) leads to a volume deduction due to the motion. Therefore, the combination of equation (1) and equation (2) would logically lead to the following conclusion:

[The density of the moving object increases as the result of its motion.]       (*)

The above statement (*) is very troublesome because it indicates that the motion of a body could actually change the physical properties (e.g. density) of another independent body, which is utterly in contradiction to our daily experience.

In the above example of moving object, to an observer O moving with the object, the energy, mass, volume of the object all take the rest values. It is only to observers O’ that is in movement at the speed v relative to the object would observe that the density of the object would increase because of its movement. However, according to the first postulate of the special theory of relativity, i.e. the principle of relativity, we know the following:

1) The relative movement between the object and the observer O’ could be caused by the movement of the observer O’ starting from his original stationary status with respect to the object;

2) To observer O’, the change of density is not a mere mathematical game, but rather physically real, and anyone who is at rest with respect to the object does not have more authority over the physical status of the object than observer O’; or we may say that the physical status of the object observed by O’ would not be determined by the observation of anyone who is at rest with respect to the object, but only determined by O’.

If the above relativistic conclusion could be true, then the whole world would be in a complete mess. For a solid object, the change of density would mean the change of the arrangement of molecules in the object, and for fluids, the change of density could entail the change of pressure, temperature, and even chemical compositions, as will be demonstrated through thought experiments later in this writing.

2.2. The Troublesome First Postulate of Special Relativity

From the above discussion we might see that the combination of the FitzGerald-Lorentz contraction hypothesis and Einstein energy-inertia relationship (2) would lead to absurd conclusions as illustrated by the above statement (*). However, this would happen only if we accept the first postulate of special relativity.

Humans make astronomic observations mainly to help us to better understand the universe and to predict cosmological impacts upon our planet, and we do not expect that our observation would impact the physical processes on other celestial bodies. However, the physical realness demanded by the principle of relativity, i.e. the first postulate of special relativity, tells us two very special things: 1) the physical processes we observed on the celestial bodies that are in movement relative to us are not the same as what observers on those celestial bodies would see due to the relative speed v between us; 2) what we observed on those celestial bodies are not less real than what observers on those celestial bodies would see as long as we could have good enough apparatus since all frames of reference are of equal rights in describing physical laws in the universe.

If any one of the above two relativistic statements is invalid, then the whole framework of the special theory of relativity would collapse. The first batch of consequences of denying the correctness of the above two relativistic statements would be that the length contraction and time dilation are not real, which would utterly eradicate the value of special relativity.

However, if we accept the first postulate of special relativity, then as discussed above, when we apply both FitzGerald–Lorentz contraction hypothesis and Einstein energy-inertia relationship to a moving object, we would say things as absurd as the above statement (*).

2.2.1. The increase of complexity that would change the mathematical nature of things

In 1889, Heaviside [[11]] showed that based on Maxwell’s equations the electric field surrounding a spherical distribution of charge should cease to have spherical shape but instead be of the so-called Heaviside ellipsoid once the charge is in motion relative to the luminiferous aether. In response to this, FitzGerald [5] in 1889 and Lorentz [6] in 1892 independently proposed the hypothesis that all bodies are contracted in the direction of their motion relative to the ether by a factor (1 – v²/c²)^1/2, which was subsequently called FitzGerald–Lorentz contraction hypothesis.

Now we know, as will be discussed soon below and also as suggested by Jefimenko [[12]] decades ago, the FitzGerald–Lorentz contraction should have never actually happened anywhere in the universe. Nevertheless, as a mathematical formulation, the FitzGerald–Lorentz contraction hypothesis could still be very well adopted as a mathematical means to help solving the Maxwell’s equation of electromagnetic wave.

However, when that mathematical expedient is extended from the electrodynamics to the classic mechanics to replace Newtonian mechanics, a simple mathematical common-sense error was committed: while it is reasonable to assume that the postulated contraction of the scale of the electromagnetic wave in the direction of motion would not affect the physics in the other two perpendicular directions, when the same assumption is applied to a macroscopic moving object, it would be immediately problematic due to the inevitable violation of the 2^nd Law of Thermodynamics.

A macroscopic object, no matter in what form of matter, would be composed of a large number of microscopic particles. When the scale in one direction decreases accompanied by the increase of mass, two types of things would happen: 1) the interactions of the particles would increase because of the increase of the density; 2) the positional arrangement and random movements in the other two directions would be changed, and when the object is in solid state the Poisson’s ratio of change in those directions would not be zero. Any claim that the above two types of things would not happen is against the 2^nd Law of Thermodynamics.

We might better appreciate the abovementioned two consequences of the hypothesized FitzGerald-Lorentz contraction with the following two thought experiments.

Experiment one: Permanent plastic change of a cuboid of plasticine

Suppose we have a cuboid of plasticine with a longitudinal length of L and sectional area of A in a frame of reference K and there is an observer O’ in a frame of reference K’ that is moving at speed v relative to K in the direction parallel to L. Now according to FitzGerald–Lorentz contraction hypothesis (1) and Einstein energy-inertia relationship (2), we would have a volume reduction A∆L and a mass augmentation of ∆m, and thus a density increment of

 ∆ρ = (∆Lm+L∆m)/AL²                                (3)

where both ∆Land ∆m are positive. However, according to the theory of solid mechanics, the deformation of a solid in one dimension would also cause the deformation of the solid in the other two dimensions [[13],[14]]; but in the case of a cuboid of plasticine, the non-relativistic deformation in the other two dimensions would be permanent and would not disappear even though the length in the moving direction could be assumed to restore to the original L after the relative motion stops according to special relativity. If this irreversible change could happen, the universe would be in mess.

Experiment two: Melting wax

Suppose we have an insulated box filled with air consisting of molecular nitrogen and oxygen only [[15]] at 38˚C and also containing a wax bar that will melt at 40˚C. Now a spaceship at a distance away is launched and a while later it reaches the speed about 18% of the speed of light c. Then according to the special theory of relativity, the astronaut O’ in the spaceship who is knowledgeable of the insulated box would estimate that the density of the box and everything inside would have increased more than 1.6% due to the reduction of the volume and the addition of mass, and thus the temperature within the box should have adiabatically risen to exceed 40˚C, which means that the wax bar is melting. Since the melting of wax is thermodynamically irreversible, the melted wax in the insulated box “observed” by the astronaut O’ will never come back to its original intact state again. Then the astronaut returns to the launch site and go to check the insulated box after he has landed. When he opens the box, if the wax is melted as he “observed” in space according to the special theory of relativity, then the whole universe would be in a complete mess. But fortunately, as we can say with confidence, the wax in the insulated box would not melt simply because of the motion of some irrelevant spaceship faraway.

2.2.2. Remark

Given that the mathematical complexity created by large number of particles (compared to the single moving source of electromagnetic wave) and the physical challenge prescribed by the 2^nd law of thermodynamics had been a common knowledge for a long time at the turn of 20^th century, when the principle of relativity was proposed and accepted as the first postulate of special relativity, unfortunately, we have to say that the mistake of extending the mathematical expedient of assuming the scale change for electromagnetic waves in the direction of motion to the assumed physical reality of general macroscopic material objects is philosophically quite obvious. Hence, it is quite puzzling when thinking about its happening to a group of top elite scientists in human history.

It is important to notice that in each of the above two examples, the observer O’ does not have direct connection with the observed object which could justify a cause and effect relationship, and thus O’ and the observed object could be just two randomly moving objects in the universe.

2.2.3. The end of twin paradox

Originated from the comment about the delay of the moving clock made by Einstein in his 1905 landmark paper “On the Electrodynamics of Moving Bodies”, the most critical connotation of the famous twin paradox is indeed not who might live longer between the separate twins, but rather the claim that the natural processes in two independently moving systems are related by their relative movements through mathematical relations, the Lorentz transformations. While many believe that they could provide a reasonable solution to the twin paradox and thus show that the twin travelled with spaceship can live longer and some others would say the opposite, the absurdity of the above statement (*) would put an end mark on the debate because the assertion of the meaningfulness of the twin paradox would lead to absurd results similar to the deformation of the cuboid plasticine and the melting wax discussed above.

2.3. The Congenitally Insufficient Historical Path to the Principle of Relativity

The historical cause which gave birth to the first postulate of special relativity as the extension of the Galilean principle of relativity is itself defective. As we will see in the next section, the desire to have Maxwell equation look the same in all inertial frame of reference was clearly the reason for instating the principle of relativity for the special theory of relativity. It just semantically sounds bizarre that a principle of relativity demands an absolute look of the form of some theoretical formulation as well as it results in all frames of reference that are moving relative to each other. We do not really have a sound logic for demanding so at all.

3. The Problematic Second Postulate of Special Relativity

The constancy of the speed of light in empty space to all observers was proposed by Einstein in 1905 [[16]] as the second postulate for the special theory of relativity. Since then the concept of the constancy of the speed of light in vacuum to all observers has become one of the fundamental elements of modern physics and become the reason why the speed of light in vacuum is no longer a measurable quantity but instead a defined value. However, as would be demonstrated by the thought experiment presented in this section, under certain particular condition, the postulate of the constant speed of light in vacuum could lead to logically impossible conclusions.

3.1. The Logical Threads Leading to the Constancy of Speed of Light

Although Einstein proposed the constancy of the speed of light in vacuum to all observers as a postulate together with the above discussed first postulate [2, 3], both of them were the outcome of a long collective journey started from Maxwell to Voigt, Heaviside, Lorentz, Poincaré, Michelson-Morley, Abraham and many others.

First, in 1865 Maxwell [[17], [18]] published his wave function for electromagnetic waves in vacuum as

∂²A/∂t² = v_ph²∆A                                       (4)

where A is either the electric field E or the magnetic field B,

and

v_ph = 1/(√(ε˳µ˳))                                                                 (5)

is the phase velocity of electromagnetic waves, and ε_o is permittivity in vacuum and μ_o is permeability in vacuum.

When Maxwell calculated speed of light using (5) with the values of ε_o andμ_o known to him, he found that it matched the recent measured speed of light in vacuum at that time very well and thus believed that light be electromagnetic waves and equation (5) be the formula for the speed of light in vacuum c.

In 1887, Voigt [[19]] “accidentally” claimed that (4) (and correspondingly (5)) should maintain its form upon transformation into a moving system. In the same year, Michelson and Morley [[20], [21]] carried out an experiment attempting to detect the “world aether”, which was thought to be the invisible medium occupying the entire universe and transmitting electromagnetic effects and radiation. In spite of the great sensitivity of their apparatus, no aether was detected. In 1889, Heaviside [11] showed that based on Maxwell’s equations the electric field surrounding a spherical distribution of charge should cease to have spherical symmetry once the charge is in motion relative to the luminiferous aether. In response to the result of the Michelson and Morley experiment and the discussion of Heaviside, with the mindset similar to Voigt, Fitzgerald [5] in 1889 and Lorentz [6] in 1892 independently proposed the hypothesis that all bodies are contracted in the direction of their motion relative to the ether by a factor (1 – v²/c²)^1/2, which was subsequently called FitzGerald–Lorentz contraction hypothesis. After that, with the same desire of making the Maxwell equation invariant between inertial systems, Larmor [[22]] proposed the time dilation in addition to the FitzGerald–Lorentz contraction, and independently, Lorentz [[23]] proposed the notion of local time to incorporate the time dilation into his length contraction formula, which was later named as Lorentz transformations by Poincare [[24]] in 1905, from which a constant speed of light in vacuum to all observers is a definite solution.

The above historical discourse clearly shows two intertwined logical threads leading the two postulates made by Einstein in1905 for special relativity.

First, a peculiar aesthetical fondness drove scientists to demand that the Maxwell equations should look the same in all inertial frames of reference; this is undoubtedly the origin for the first postulate, i.e. the principle of relativity, which could be deemed as an extension of the Galileo’s principle of relativity [[25]]. This peculiar relativistic requirement inspired scientists to propose the contraction of length and dilation of time as the basic nature of space and time, resulting in the Lorentz transformations according to which the calculation of the speed of light in vacuum would always give the same invariant result. Hence, both the principle of relativity and the constancy of the speed of light in vacuum as two postulates of the special theory of relativity were naturally entailed by the theoretical efforts of making Maxwell equations invariant in an absolute sense at the end of 19^th century and the dawn of 20^th century.

Second, the failed Michelson and Morley experiment of searching for aether served as a confirmation to many that the speed of light in vacuum had to be a constant. Even if Maxwell equation looks the same in all inertial frames of reference, the need of a media for the light to propagate might become an important reason for people to think that the actual speed of light could change with respect to the observers of different velocities. As a comparison, the formula for the speed of shallow water waves is√(hg), which does not involve the frame of reference and conforms to the principle of relativity, but the speed of water waves are not independent of the selected frame of reference. This is because water is a movable medium, and thus the speed of water waves might not only be superposed by the speed of the water flow but also be altered by the observer’s speed relative to the medium. At the end of 19^th century and the dawn of 20^th century, the medium for light to propagate was believed to be the luminiferous aether. Therefore, the believed missing of aether shown by the failed Michelson-Morley experiment seemed to eliminate the last necessary condition for applying Galilean addition of velocity to light in vacuum for the physicists at that time.

Therefore, the above two logical threads seemed to naturally lead to the two postulates of the special theory of relativity. Einstein’s main contribution to this was to explicitly express them as two premises of a consistent theory and use them to re-derive the Lorentz transformations, from which to work out the relativistic simultaneity and the energy-inertia relationship for the special theory of relativity.

Nevertheless, as we will discuss below through a thought experiment and the review of the Sagnac experiment, we could see that the second postulate is logically as wrong as the first postulate as we have discussed in the previous section. Later we will also see that the use of Michelson-Morley experiment as a reason to affirm the constancy of speed of light in vacuum is not logically sound.

3.2. A Thought Experiment to Invalidate the Second Postulate

Figure 1 illustrates the set up of the thought experiment. There are two parallel thick light beams A and B in the vast interstellar empty space. A long slender empty chamber is moving towards the beams A and B in the direction perpendicular to A and B at a speed of V = 3c/5. The length of the empty chamber L = 1c, where 1 represents 1 second to make up the dimension and c is the speed of light, which is supposed to be a constant in vacuum to all observers according to the second postulate of the special theory of relativity and is currently defined (see [16]) as 299792458 m/s = 299792.458 km/s, and the distance between beam A and beam B equals L = 1c as well. Suppose no gravitational field is near the scene so that we do not need to consider any external gravitational influence.

Figure 1 Schematic of the thought experiment of the paradox of light speed.

All above data are the values known to the observers in the moving chamber. To them there would be no ambiguity that both the length of the chamber and the distance between beam A and beam B are equal to 1c, and no simultaneity issue involved in this because the observers in the moving chamber do not need to talk to each other instantly but only need to make journey logs and they can exchange the logs afterward any time later. They can do calculations based on their logs just the same as physicists on this earth planet could do calculations based on historical data. Since on the same moving frame of reference, the tempo rate is considered fixed without any relativistic variation (i.e. the space-time coordinate system on the same moving frame of reference extends to infinity), as long as the clocks on the moving chamber are of high enough precision, and any possible errors could be theoretically calibrated, then there would not be any confusion to the observers in the moving chamber about the distance between beam A and beam B from reading the working logs afterward, let alone the length of their own vehicle.

3.2.1. Values for observers outside the moving chamber

It is not necessary to involve any external observer for the sake of this thought experiment, but if we are interested in knowing the relevant length and time recorded by external observers in the outer space anyway, then we need to apply the Lorentz transformations as long as the constancy of the speed of light in vacuum is assumed to be correct.

Let’s assume some massless virtual intelligent beings sitting in the beams A and B. In their coordinate system, the length of the moving chamber according to the Lorentz transformations would be L’ = L/γ where γ = 1/√(1- V²/c² ) and 1- V ²/c² = 16/25 which makes γ = 5/4 and L’ = 4L/5 = 4c/5. They knew beforehand that the chamber was coming to them and thus they adjusted their distance to be of the same length as L’ so that the distance between A and B in the coordinate system that is fixed with A and B would also be 4c/5, which is corresponding to 1c in the coordinate system moving with the chamber.

3.2.2. Two Scenarios Leading to Logical Impossibilities

Let’s consider two scenarios. Scenario 1 is shown in (a) of Figure 1 in which there is a small hole at the rear of the empty chamber and a laser beam is shot from the head of the chamber towards the small hole at the rear when the head of the chamber just touches beam B. One second later, the laser beam would arrive at the rear hole because the length of the chamber equals 1c; in the meantime, since the speed of the laser beam relative to beam A is also c because of the constancy of the speed of light, and the distance between beam A and the shooting spot of the laser beam (i.e. the head of the moving chamber) also equals 1c when the laser beam was shot, the laser beam should hit the beam A at the same time as it arrives at the small rear hole. However, this is impossible because at that moment the distance between beam A and the rear hole of the chamber would be D = 3c/5 ×1≈ 179875 km.

Now let’s consider the second scenario as shown in (b) of Figure 1, in which there is a small hole at the head of the empty chamber and a laser beam is shot from the rear of the chamber towards that small hole when the rear of the chamber just about to leave beam A. One second later, the laser beam would arrive at the hole at the head of the chamber; in the meantime, since the speed of the laser beam relative to beam B is also c, and the distance between beam B and the shooting spot of the laser beam also equals 1c when the laser beam was shot, the laser beam should hit the beam B at the same time as it arrives at the front hole. However, this is impossible because at that moment beam B would shine on the body of the chamber at a distance of 179875 km away from its head.

Now if the observers on the moving chamber assume that in the first scenario, the laser beam should not arrive at the rear hole and beam A at the same time because of the relative velocity V = 3c/5, then they would be literally subtracting V from c in the relative velocity between the laser beam and beam A, which would invalidate the constancy of the speed of light in vacuum to all observers; if they assume that in the second scenario, the laser beam should pass beam B before it hits the small hole at the head of the chamber, then they would be literally adding a velocity V to c in the relative velocity between the laser beam and beam B, which would violate the constancy of the speed of light in vacuum to all observers as well.

Now let’s check what the virtual observers sitting in beam A and beam B might find. Due to the fact that their distance equals the length of the moving chamber, when the virtual massless observers at B find the head of the moving chamber they would know that its tail must be at the position of A without the need to communicate with the virtual massless observers at A. For the first scenario, when a laser beam is shot from the head of the moving chamber towards the rear of the chamber, the massless virtual observers at B would know this event instantly since they are on the exactly same spot of the shooter and they would know that it would take t = 4c/5 ÷ c = 4/5 seconds to reach beam A, and by invoking the constancy of the speed of light in vacuum, they also know that it would take t = 4c/5 ÷ c = 4/5 seconds to reach the rear of the chamber as well, and thus they would conclude that the laser beam would hit the rear of the chamber and beam A at the same time. However, this expected event would not be observed by massless virtual observers at A since after 4/5 seconds, the distance between the rear of the moving chamber and beam A would be 179875 ×4/5 = 143900 km in their coordinate system. Similarly, for the second scenario, massless virtual observers at B would not witness what massless virtual observers at A would expect to happen according to the second postulate of special relativity. Therefore, in their weekly meeting afterward, they would find out that their expectations based on the constancy of the speed of light in vacuum to all observers do not hold valid based on their observations.

3.2.3. The conclusion

Therefore, starting from the constancy of the speed of light in vacuum to all observers we will reach some logically impossible results as demonstrated in the above thought experiment, which tells that as the second postulate of the special relativity, the constancy of the speed of light in vacuum to all observers is logically incorrect.

3.2.4. Replacement of the kinematic special relativity with dynamic analysis

Due to the dire requirement of moving at a relativistic speed, all experimental verifications of length contraction and time dilation are in fact indirect, no matter how much it might look like direct or might be claimed to be direct. It might sound easier to directly test time dilation than length contraction because time dilation might elongate the life span of something, which can be measured based on the irreversible record of the permanent change of the status of existence. However, the relative easiness might be more semantic than physical because if the recorded change of the expected life span of a moving object is unequivocally caused by relativistic effect, then the change of its expected travelling distance before the life span is over would be the true trustworthy length contraction in the moving system.

On the other hand, as discussed in the previous section, the FitzGerald-Lorentz contraction should have never really happened in the universe. In 1998, Jefimenko [12] demonstrated with examples that it is potentially possible to explain any announced apparent length contraction or time dilation by taking into consideration the detailed physical causes involved during the moving processes without the need of invoking the relativistic kinematic relations. As a matter of fact, the mathematical origin of the Lorentz factor is the so called Heaviside ellipsoid [[26]] that is caused by the deformation of the electromagnetic distribution on a moving body, which was the reason for scientists [[27]] to propose length contraction and time dilation in order to keep the Maxwell equations in the same form for all moving inertial frames of reference; thus, naturally, we could see it in the non relativistic formula of calculating electromagnetic force by Heaviside [[28]].

3.2.5. More about the thought experiment

The number 3c/5 in the above thought experiment is arbitrarily selected to make a scale of relativistic significance, and also to offer the ease for applying the Lorentz transformations since 3c/5 would give a clean rational number 5/4 for the Lorentz factor γ in the Lorentz transformations. Besides, unlike some famous thought experiments (e.g. the Schrödinger’s cat) that cannot be materialized, the above thought experiment of moving chamber can be materialized with realistic values for the length and velocity in our earth environment (e.g. a laser beam shot in a slender vessel moving in a big vacuum chamber set up on the ground) as long as the measurements of time could be taken up to high enough precision.

Both the observers in the moving chamber and the massless virtual observers in beam A and beam B do not need to have any real time chat with their pals. They only need to record what they do and what they see, and then they could exchange information with each other on their weekly online staff meeting afterward.

The use of laser beam in the thought experiment is to create a sense of focused straight path for over about 300000 km distance so that it would be psychologically easier for the readers to perceive the experiment. It would not be logically different if the laser beam is substituted with a single photon since there is no medium to influence the motion of the photon in the vacuum. We even do not need to assume that a laser beam or a photon is “shot” from the ends; even if some photon accidentally travels the described path for whatever reason (e.g. a gamma ray from far away just randomly get into the chamber along the described path), it will not change the nature of the logical outcome of this thought experiment. Similarly, the attribute of “small” applied to the holes as well as “slender” to the chamber are also used in an attempt to highlight the needed directional straightness of the path of the beam or photon from one end to the other perpendicular to beam A and beam B. It would not change the nature of this thought experiment by replacing the “holes” with open ends or widening the chamber to a great width. The universe is big enough for our thought experiment. As for beam A and beam B, they are just used as position markers to make it easy for readers to imagine the scene. We might just replace them with virtual empty pillars and assume some virtual beings on the positions of beam A and beam B when the rear and head of the chamber are spatially coinciding with those positions. With this set up we would not have the so-called simultaneity issue in the experiment. The key idea of this thought experiment is to test the postulate that the speed of light would be the same relative to the holes on the chamber and some spatial positions that are moving relative to the chamber, by examining the supposed positional overlapping according to the said postulate.

3.3. Sagnac Experiment

In 1913 French physicist Georges Sagnac conducted an experiment which substantially challenged the second postulate of the special theory of relativity. During the experiment, a beam of light is split into two beams which are made to follow the same path but in opposite directions, and on return to the point of entry the two light beams are allowed to exit the ring and undergo interference as recorded by an interferometer. When Sagnac [[29],[30]] let the table on which the light paths were established to rotate slowly (1 to 2 revolutions per second), he recorded the difference between the paths of those two beams, which was a clear indication that the speed of light relative to the observers obeys the classic Galilean rule of superposition. The mechanism of the Sagnac experiment has been named as Sagnac effect and found applications in many areas. Because of its incredible precision, devices built with Sagnac effect are capable of detecting and measuring extremely small amounts of absolute rotation. Today such devices are routinely used in guidance and navigation systems for commercial airliners, nautical ships, spacecraft, and in many other applications, and are capable of detecting rotation rates as slight as 0.00001 degree per hour [[31]].

However, the physical revelation of the Sagnac experiment has been surprisingly misinterpreted for the past more than a century period of time to be a typical example of the correctness of relativity. As the basic knowledge that has been taught around the world in physics class that when the motion is slow there is no difference between classic mechanics and relativity, and thus the result of Sagnac experiment should be very well explained within the domain of classic mechanics [[32]]: the speed of light relative to the observer equals the speed of light in empty space stationary to the observer plus or minus the speed between the source and the observer, as calculated by Sagnac, based on the fact that if the time for light to travel two different paths of the same length with the same starting point in opposite directions, then the speeds of light are not the same to the end observer. Any effort of interpreting the Sagnac effect beyond the classic mechanics by invoking principles of relativity, no matter the special or general theory, would be in conflict to the basic understanding of the significance of relativity.

In fact, the most hilarious part of the practice of misinterpreting the Sagnac effect is that the relativistic derivations of Sagnac effect would normally share such a commonplace of first admitting that the speed of light of those light beams in opposite directions equal to c – v and c + v, and then managing to prove that the constant speed of light in vacuum makes sense in Sagnac experiment by applying the Lorentz transformations, as we see in [31] when the author even admits that devices made of Sagnac effect are capable of detecting rotation rates as slight as 0.00001 degree per hour. Obviously, these people do not seem to realize that by assuming the speed of light of those light beams in opposite directions to be c – v and c + v, they already defy the constancy of the speed of light in vacuum to all observers and thus deny the value of special relativity. This is a typical example how things could go wrong for a long time (more than a century) after people collectively losing the capacity of thinking in philosophically correct ways.

3.3.1. The influence of Sagnac’s goal and claim upon the misinterpretation

Respecting truth and denying untruth should always be the ultimate principle for scientific explorations and thus humans do not have any excuse for making collective mistakes such as misinterpreting the outcome of Sagnac experiment for more than one hundred years. Nevertheless, it might also be meaningful for us to notice the distractive effect of Sagnac’s goal for his experiment and correspondingly his claim of what his experiment proved.

Sagnac was trying to prove the existence of the luminiferous aether and claimed that he succeeded in doing so while the connection between his results and the existence of aether was not soundly convincing. As we could see from the above discussions, the need to assume the velocities of light to be c + v and c – v by the relativistic scholars has already proved that the constancy of speed of light in vacuum is wrong, and this is in perfect accordance with the revised postulate of speed of light in vacuum as will be introduced in next section. That is to say, the result of Sagnac experiment could be well explained without the need of the superfluous notion of aether that is attached to extra unneeded attributes. However, more than one hundred years ago, when the scientific focus was still not completely off the topic whether space was filled with the luminiferous aether, Sagnac’s goal of searching for aether and his claim of having found it could practically play a role of distracting the attention of scientists and caused them to ignore the fact that Sagnac experiment had offered a good example that speed of light in vacuum is not constant to all. 

But on the other hand, humans should not use any excuse to shed off the collective responsibility for such a long-lasting mistake, just like that a failed student cannot blame some intentional distractions of tricky questions in a test. We need to introspect about our worldwide culture in the scientific community to find more profound social cultural causes behind this phenomenon. By doing so we might identify a more general cause for this: people often defend something simply because the big name of the thing makes them feel that they should defend it instead of that they really understand what they are defending. This mindset of placing social benefits above truth is against the fundamental principle of philosophy that values truth above utilitarian needs.

3.4. Comparison between Sagnac Experiment and the above Thought Experiment

Although the Sagnac experiment and my thought experiment manifest the same principle of calculating the speed of light in vacuum by applying the Galilean rule of superposition, they differ from each other significantly in the following essential aspects:

1) Different goals

Sagnac’s goal is to prove the existence of aether, and my goal is to prove that there is a problem with the postulate of the constancy of the speed of light in vacuum to all observers.

2) Different forms and degrees of complexities of design

The difference in the goal as mentioned above leads another two important differences: a) a big difference in the form of design and the corresponding complexity. Sagnac’s goal is constructive, and constructive goals often require complex means to achieve; Sagnac not only needs complex experimental devices, but also sophisticated mathematical calculations to prove his claim. On the other hand, my goal is just to overturn an existing postulate and thus the simpler the better. b) as discussed above the goal of proving aether might practically play a role of distracting the attention of others when public focus was not completely off the topic of aether yet in Sagnac’s days.

3) Very different effects

The more complex a theoretical system, the easier it is to be attacked, even if the reason for the attack itself is extremely absurd, as long as it can be accepted by the public. This is one of the reasons why Sagnac’s experiment, despite of having found many applications worldwide, is misinterpreted by scholars all over the world as opposite to the true manifestation of the result of the experiment for more than a century. On the other hand, because of the simplicity of the form and conclusion of my thought experiment, no one can deny it with a logically correct reason at all.

4. Revised Postulate of Speed of Light in Vacuum and Rule of Speed Addition

While both the above thought experiment of moving chamber and the Sagnac experiment would negate the second postulate of the special theory of relativity, what has actually been falsified is the claim of “constancy of speed of light to all observers”. Here the critical words that have been proved wrong are “to all observers”. Neither the above thought experiment of moving chamber nor the physical experiment of Sagnac could be considered as the proof to negate the Maxwell formula (5) for the calculation of the speed of light in vacuum. In fact, we do have the need for the Maxwell formula (5) after we invalidate the second postulate of the special theory of relativity. This is because of two basic reasons:

a) Formula (5) was developed based on many empirically rooted precedent works on earth planet as an inertial system, including the works of Ørsted [[33]], Ampère[[34]], Faraday[[35]], Ohm[[36]], and many other precedent works, and

b) Formula (5) fits the past measurements of speed of light in vacuum quite well.

But in the meantime, we do not have an unchallengeable logical reason to guarantee the complete correctness of formula (5) either. Consequently, even if we remove the adscititious assertion of “constant to all observers”, as long as we want to use formula (5) to calculate the speed of light in vacuum, we need to deem that use as a postulate, which can be formally stated as:

The speed of light is constant in vacuum that is not attached to any specific material object and is always the same to the source of the light in vacuum. The value of this constant speed of light is given by the Maxwell formula c = 1/√(ε˳µ˳), where ε_o is permittivity in vacuum and μ_o is permeability in vacuum.

We might call the above statement as the revised postulate of speed of light in vacuum to differentiate it from the postulate of constancy of speed of light in vacuum to all observers as the second postulate of the special theory of relativity. In fact, this revised postulate is a replacement of both the first and second postulates of the special theory of relativity while the differences it makes compared to those two postulates are quite subtle instead of obvious. Its difference from the first postulate is that it would not require the Maxwell wave function take the same form in all moving coordinate systems but it still requires that the Maxwell wave function take the same form in all source coordinate systems; its difference from the second postulate is that it would not require that the speed of light in vacuum calculated by the Maxwell formula is constant to all observers but still requires that the speed of light calculate by the Maxwell formula is constant in vacuum that is not attached to any specific material object.

The difference between the revised postulate and the second postulate of special relativity might be easier to comprehend since it reflects the logic revealed by both the thought experiment of above section 3 and the result of the Sagnac experiment. The difference between the revised postulate and the first postulate of special relativity might be more philosophically intricate and thus more difficult to comprehend. What we are facing here is the different applications of the logical symmetry. Unless there is a cosmic center or a single privileged coordinate (which we do not seem to have), we do not have any reason to assume that the Maxwell wave equation would look different for different source coordinate systems — this is a very sound application of the logical symmetry, and accordingly we could comfortably require that the speed of light in vacuum would be same for all sources of light in vacuum; however, the first postulate of special relativity takes one more step further to demand that the Maxwell wave equation should take the same form for all moving coordinate systems, which is not supported by the logical symmetry since there could be clear reasons (e.g. the Heaviside’s ellipsoid) for things not to be so, and thus it is not natural but very artificial.

4.1. Inertial Coordinate Systems as the Preferred Coordinate Systems

While the revised postulate of speed of light in vacuum does not involve any coordinate system, we would still need the concept of inertial motions as established since Galileo’s time, of which all systems are moving with regard to each other at constant speeds. We would still call all the coordinate systems that are doing inertial motions without the impact of gravity as inertial coordinate systems.

If we insist on having a special (or preferred) coordinate system for the notion of absolute space and time to sooth our imagination and thus to make ourselves more comfortable, then we might envision a coordinate system of absolute space and time anywhere in the universe, which would entail a continuous set of infinitely many coordinate systems of absolute space and time that are at rest with each other.

However, as shown in the Appendix I of this writing, when applying the revised postulate of speed of light in vacuum, we only need to have the relative velocity between the source and the target of a light beam to work out the Galilean rule of speed addition, and thus the speed of light between two objects would be determined by equation (A4); hence, with the revised postulate of speed of light in vacuum, we can apply the Galilean rule of speed addition to calculate the real speed of light between the source and target without the need to know the absolute velocities of the source and target in vacuum.

Further, this tells us that there is no kinematic difference between any two inertial coordinate systems in terms of calculating the real speed of light between the source and target. Since the notion of absolute space and time demands the sense of stillness, any coordinate system that is considered as a preferred coordinate system of the absolute space and time cannot move with accelerations, which entails that all inertial coordinate systems are preferred coordinate systems of absolute space and time. This reassures the correctness of the Galilean principle of relativity, although we have to banish the principle of relativity as the first postulate of special relativity. This would further infer that the speed of light in vacuum between two moving objects is the same to all inertial coordinate systems. This sounds a lot like the second postulate of special relativity, but it differs from the latter in that the speed of light between two objects varies with the relative speed between those two objects.

4.1.1. The straight line motion of light in inertial systems

Since all inertial coordinate systems are equivalent in terms of representing the absolute space and time, from the empirically confirmed rectilinear propagation of light as discovered by Pierre de Fermat [37] it would be naturally to conclude that light propagates rectilinearly in all inertial systems.

4.2. Limit of the Speed of Energy (Information) Propagation

Because of the essential role of the Lorentz factor γ = 1/√(1- v²/c² ) in the special theory of relativity, for an object moving at speed v the energy-inertial relationship (2) is often extended to the following form:

E = γmc²                                              (6)

Since γ goes to infinity when v = c, we have the famous relativistic assertion that the speed of energy (information) propagation cannot exceed the speed of light c.

Now since Lorentz transformations are no longer considered as valid reflection of the real physics in nature, (6) would no longer be considered as a valid relationship between energy and inertial of a moving object although relationship (2) remains valid because of its non-relativistic nature as discussed above. Accordingly, we can no longer claim that the speed of energy (information) propagation cannot exceed the speed of light c.

With the revised postulate of speed of light in vacuum now we know the following:

1) If we still stay with the existing popular assumption that objects with nonzero masses have to move at speed below the speed of light c in vacuum calculated by the Maxwell formula (5), when the information is transferred in the form of light, if the relative speed between the target and source is close to the speed of light c in vacuum, then according to equation (A4), the speed of the propagation of information would be close to 2c.

 2) Now since we are no longer restricted by the Lorentz factor γ in equation (6), theoretically we might even have objects of nonzero mass to move at or faster than the speed of light c relative to each other. For example, if object A moves at 0.8c relative to object B, and object C moves at 0.8c relative to object B, then by applying Galilean rule of speed addition we would know that object C moves at 1.6c relative to object A if their velocities are in the same direction.

3) Because of the reason said in 2), when the information is transferred in the form of light, the speed of the propagation of information could go much beyond 2c.

Given the above considerations, we should expect that the speed of a particle that is said to be 0.99c as calculated with equation (6) based on the supposed energy of that particle would  actually be 3.489645c (see Appendix II). Now this question arises: what are the actual speeds of the particles in those thousands of accelerators across the world? The answer is: we do not really know. We could not find any record of direct measurements of the speed and energy of the particle in all those accelerators except for the values that were calculated using the theory of special relativity based on the energy consumed by the accelerators. The reason for this is understandable: when the particle moves near the speed of light to orbit the accelerator tens of thousands of rounds per second, it is technically more difficult to measure the speed of the particle in the accelerator chamber than measure the speed of light due to the restriction of the Heisenberg uncertainty principle.

That is to say that we do not really have a solid base to draw the conclusion that the particles in those accelerators have never moved faster than light although physicists working with the accelerators all seem to believe so based on their passion with the special theory of relativity.

Now what if one day some lab in the world claims that they have somehow managed to measure the speeds of those extremely fast moving particles and found that they could never be faster than the speed of light? Well, although the chance for this to happen does not seem to be realistic at this stage, even if it happens, as long as we intelligent humans still believe that logic is a consistent whole, we should not even assume that the data from those accelerators could prove the physical significance of the Lorentz transformations beyond mathematical expediency after we have seen many negative examples disproving the physical realness of the Lorentz transformations in other circumstances. We should rather investigate what could have caused that kind of ostensible anomaly as Jefimenko did with those examples of apparent length contraction and time dilation which never physically happened in nature [12].

4.3. Solution to the Failed Michelson-Morley experiment

As mentioned earlier, the missing of aether shown by the failed Michelson-Morley experiment seemed to eliminate the last necessary condition for applying Galilean addition of velocity to light in vacuum, and thus many believed that it was the straw that broke the camel’s back because they thought that the missing aether was the proof that the speed of light should be constant in vacuum to all observers.

But the above logic of confirming the constancy of the speed of light in vacuum using the failed Michelson-Morley experiment is hilariously ill-founded. From (A4) we could clearly see that the reason why the Michelson-Morley experiment failed is because with their experimental set up, ∆v_ab = 0, and thus in theory we should have c_ab = c; of course, since earth is not in pure inertial motion but with slight acceleration, with high precision Michelson-Morley style experiments, we might still detect the tiny ∆v_ab caused by the acceleration of earth. Therefore, the failed Michelson-Morley experiment could in fact be a strong support of the revised postulate of speed of light in vacuum which is used to replace the second postulate of special relativity after we phase out the latter.

5. The Misleading Diagnosis for the Apparently Longer Lifespan of the Muon

In this section let’s look into a famous claim among the so-called experimental testing of time dilation that the apparent elongated lifespan of muons travelling through the atmosphere is the result of time dilation. The theory normally goes like this [[38]]:

The emergence of the muons is caused by the collision of cosmic rays with the upper atmosphere, after which the muons reach Earth. Suppose T is the lifespan of muon measured in the earth inertial frame S, and T’₀ is the lifespan of muon according to the proper time of a clock in the inertial frame S’ comoving with the muon, corresponding with the mean decay time of the muon in its proper frame, then because of time dilation we have

 T = γT’₀ > T’₀,                                                (7)

where γ = 1/√(1- V²/c² ), from which the relativistic scholars conclude: the reason why the muon can pass through the thickness of earth atmosphere within its supposedly very short lifespan is because when observing from the earth inertial frame S its lifespan become longer thus it can move farther with the same value of the supposed lifespan at the same relative speed v.

Then when stepping from S into S’, the relativistic scholars would use time dilation no more but shift to length contraction as follows

 L = L’₀ /γ < L’₀,                                              (8)

where L’₀ is the proper distance in S’ that muon could travel within its lifespan, and L is the distance that muon can travel in S when calculated in S’, from which the relativistic scholars conclude: the reason why the muon can pass through the thickness of earth atmosphere within its supposedly very short lifespan is because when observing from muon’s inertial frame S’, the earth atmosphere becomes thinner thus muon needs shorter time to pass through it at the same relative speed v.

Here we should take heed of the typical asymmetric uses of the Lorentz transformations: time dilation is cited when the discussion is based on the observation from S while length contraction is cited when the discussion is based on the observation from S’.

This asymmetric uses of Lorentz transformations in S and S’ when explaining the seemingly longer lifespan of the muon is not accidental but due to inevitable causes:

If they continue to use time dilation when stepping into S’, since the relative speed v would not change with the Lorentz transformation, we would have

L = vT = vT’₀/γ = L’₀ /γ < L’₀                                           (9)

Although (8) and (9) look exactly the same, they actually read very differently because with (8) we are focusing on the relativistic change of spatial span while with (9) we are focusing on the relativistic change of temporal duration. More specifically, (8) reads as “the thickness of the earth atmosphere in S that the muon needs to pass through becomes thinner when observing from S’”, but (9) reads as “the distance L that the muon can travel in S within its lifespan is shorter than the distance L’₀ that the muon can travel in its own frame S’ within its lifespan”.

Obviously, the effect indicated by (9) would logically cancel out the effect indicated by (8): even though now the muon only needs to travel a shorter distance in order to pass through the earth atmosphere, it would also die within a shorter distance therefore it might still not be able to pass through that shorter distance.

Here the catch that causes this confliction is that the speed v of the muon and the lifespan T’₀ of the muon in S’ are two constants for the analysis. Therefore, when we make observation from S, we might conclude that the muon can travel a longer distance at the same speed v because the earthly observed lifespan is longer than T’₀, but when we make observation from S’, we would find that a shorter period of time T in S would be corresponding to T’₀ in S’ according to Lorentz transformation for time dilation, which entails that the muon would only travel a shorter distance in S within its lifespan T’₀. Obviously, these two conclusions contradict each other.

This need of asymmetric treatment due to the difficulty of symmetric treatment is a common problem with special relativity. In fact, if we cite length contraction instead of time dilation when observing from S, it would right away lead to the opposite conclusion of a longer lifespan for a moving muon: we might find that when observed in S whatever distance the muon travels would become shorter and thus the muon would die within a shorter distance than calculated in S’.

5.1. A simple and reasonable explanation to the muon lifespan issue Given that air density is much higher in the lower atmosphere than the  upper atmosphere while cosmic rays are constantly penetrating the atmosphere with high magnetic rigidity [[39]], the assumption that muons in the atmosphere are solely created at the upper atmosphere is logically unsound. This is because the increase of air density near the ground compared to the upper boundary of atmosphere is tremendous while the reduction of cosmic rays due to the influence of earth magnetic field is only a small portion as pointed out in [39], and thus there would be more chances for the cosmic ray to create muons in the region with higher air density.

6. The Problem of Relativity of Simultaneity and Relativistic Chronology

Although it seems that we can derive relativity of simultaneity from Lorentz transformations, in fact, one needs the notion of relativity of simultaneity to fortify the position of Lorentz transformations in the special theory of relativity. This is because if the simultaneity is of absolute nature then Lorentz time dilation would be only a mathematical trick without any physical significance. For this reason, Einstein obviously felt the necessity of establishing the notion of the relativity of simultaneity through the famous train thought experiment [[4]]. One interesting part of the train experiment is that Einstein first established the notion of the relativity of simultaneity by taking into consideration of the impact of the train speed v upon the discrepancy between the observations of the observer stationary to the rail embankment and the observer stationary to the moving train, but then use the constancy of the speed of light to deny the influence of the movement of the train upon the speed of light. While this is a legitimate technique of discourse, it does remind us that the constancy of speed light would be in trouble without the concept of the relativity of simultaneity. On the other hand, from the train experiment of Einstein we might see that the notion of the relativity of simultaneity is constructed on top of the troublesome first postulate of the special theory of relativity. Without the principle of relativity, one cannot assume the equal rights to judge the simultaneity of the two flashes of lightning in Einstein’s thought experiment.

Further, more importantly, the relativity of simultaneity is constructed on top a peculiar light-seeing-based philosophy, which lies at the core of special relativity. It claims that the happening of event P is meaningful to event Q only when the (imaginary) light emanating from the spot of P could reach the spot of Q according to the speed of light in vacuum c; vice versa. According to this special logic, to anyone in the spot of Q, P never happens until the light emanating from the spot of P could reach the spot of Q. If event P and event Q cannot “see” each other, they are considered as irrelevant in the universe. Both relativistic simultaneity and relativistic causality are established on top of this peculiar philosophy of determining the mutual reality of things. We might call this philosophy as relativistic chronological logic because it determines how a relativistic scholar should think of the sequential influence between things, including how to determine simultaneity and causality.

It is this relativistic chronological logic that makes the special relativity different from simply the mathematical framework of Lorentz transformations.

The most astounding application of the relativistic chronological logic could be found in cosmology where we often hear people claim that it is meaningless to even talk about the happening of a cosmological event before we can virtually see it (according to the calculation based on speed of light).

This would lead to the hilarious conclusion that the explosion X of a celestial body of 1000 light-year away 999 years ago happened later than the explosion Y of a celestial body of 5 light-year away 5 years ago, despite that the relativistic cosmologists would still study the explosion X as 994 years earlier than the explosion Y because they know that if they do not do so, the whole cosmological causality chain network would be messed up so that it would be impossible for them to correctly study the cosmological history and dynamics.

Obviously, the light-seeing-based relativistic chronology creates a cracked logical framework that cannot be consistent with itself or with the logical and semantic systems of the general culture. As a matter of fact, even from the most utilitarian point of view, the abovementioned relativistic causality view is problematic because even before the observer sees the light from a cosmological event, physical events within each celestial body and interactions between all celestial bodies never cease to happen, which is not determined by whether it is possible for an observer to see anything of them at all. On the contrary, only if the observer respects the objective happenings before he could see them he could possibly understand them correctly.

6.1. Separation of Space and Time

Once we invalidate the notion of relativistic simultaneity, the next logical move would be to break up the so-called spacetime and thus separate space from time, since we could no longer admit that the advance of time would be affected by spatial changes. This would undoubtedly be the most serious impact of phasing out special relativity upon modern physics since the notion of a holistic spacetime has become part of the gene of theoretical physics especially the general theory of relativity. Nevertheless, the notion of spacetime would still has its own right in reminding us of the correlation of space and time for events evolving in the universe, especially when evaluating the relationship between the curvature of spacetime and gravity. For this reason, we need to carefully review some notions that have been developed through the special theory of relativity.

6.1.1. The need to reinterpret Minkowski spacetime

Minkowski spacetime is the flat spacetime including three spatial dimensions (x, y, z) and one time dimension (t) [[41]]. The time dimension could be expressed as an imaginary term ict with c being the speed of light in vacuum, so that when distance ds in the four dimensional spacetime (x, y, z, ict) is expressed using the four dimensional Pythagorean theorem as

ds² = – [dx² + dy²+ dz² + (ict)² ] = (ct)² – dx² – dy² – dz²                                        (10),

it will be an invariant based on Lorentz transformations.

Mathematically, the time dimension is still treated differently in the Minkowski spacetime (which makes it different from pure four dimensional Euclidean space), but physically, by making time changes somehow equivalent to space changes through the calculation of the spacetime distance (the geodesic distance) according to equation (10), Minkowski spacetime has helped to establish the relativistic notion of spacetime in an effort of abolishing the traditional notion of absolute time that is completely independent of the change of spatial location.

Once we come back to the notion of absolute time, time and space would no longer be considered as interchangeable, and the square of ds as expressed in (10) would not be an invariant when dx, dy, dz, and dt of real events are put into (10); it would even not always be greater than zero.

6.1.2. Demystify the infinity of non-relativistic speed of light in vacuum

Minkowski assumed two options for the speed of light in vacuum, either to be a constant c, or an infinity c, and majority of the scientific community have shared with his view. However, obviously this dichotomy is not founded with sound logical or empirical evidence. As is discussed above, the speed of light in vacuum is not a constant to all observers as assumed by the second postulate of special relativity but should obey certain rule of speed addition, and it still does not entail the infinity speed of light at all.

6.1.3. Light cone and relativistic causality

Light cone was conceived by Minkowski [[42]] to define the relativistic causality, which describes the path that a flash of light, emanating from a single event at a single point in space and a single moment in time and traveling in all directions, would take through spacetime. Behind this idea is the relativistic chronological logic as discussed earlier.

Now since the ds calculated by (10) would no longer be invariant once we come back to the notion of absolute time, the famous Minkowski relativistic light cone would no longer be meaningful as before. With the knowledge that the speed of light towards an observer would be impacted by the relative speed between the source and the observer, now we know that the Minkowski light cone would no longer provide a rigorous boundary for observable events to a general observer. Accordingly, the abovementioned relativistic causality and the corresponding philosophy of judging the moment of an event based on whether or when the event could be virtually seen by the observer should be replaced by more realistic views of causality and of relationship between events.

6.1.4. Meaning of simultaneity

Now let’s come back to Einstein’s train experiment. Once we deny the relativity of simultaneity, the question of whether the observer on the rail embankment or in the train has more rights to decide the simultaneity issue of the flashes of lightning would come to the surface.

From the above discussions, we have learned that the issue of how to balance the relative rights in judging physical significance in different frames of reference is not solely a kinematic issue, but would involve other laws about real physical processes (e.g. the thermodynamic 2^nd law). Therefore, when reviewing the issue of simultaneity, if two events physically happen in the same body of coordinate system (e.g. the coordinate system of the rail embankment in Einstein’s train experiment), an easy way to determine the simultaneity issue would be to assume a priority to that coordinate system over moving coordinate systems. But if two events happen in two systems in relative movement (e.g. if one lightning hits one spot on the rail embankment and another hits the tail of the train), then with the notion of absolute time, the observer on the rail embankment should calculate the time when the lightning hits the tail of the train by the position and speed of the train relative to the observer when he sees the lightning, as well as the speed of light; the observer on the train should do the similar for his own interest. In other words, the estimation and calculation of the time and simultaneity issue would go back to what is discussed in textbooks of classic mechanics.

6.1.5. Curvature of spacetime

Unlike the special theory of relativity, the general theory of relativity has been verified by many reported observational data; accordingly, as the foundation of the general theory of relativity, the notion of curved spacetime would be respected. Nevertheless, similar to that the meaning of the flat Minkowski spacetime would no longer be the same as with the special theory of relativity, when time is taken in the absolute sense after invalidating the relativity of simultaneity, the meaning of curvature of spacetime would also undergo certain modification.

We would respect the conclusion reached by Einstein that both space and time would be affected by the gravitational field [4,[43]]; however, after space is physically separated from time, the curvature of spacetime would not happen holistically as with the notion of relativity of simultaneity, but rather would be the resultant effect of the curvature of space and the change of the scale of time. This might make the general theory of relativity somehow sound like the Newton-Cartan theory [[44]] although they would indeed still not be the same.

We might notice that for most of the observed events, the relative speed between the source of light and earth is far from the speed of light, and thus the agreement between the observed results and the calculations from the general theory of relativity should not be impacted by the abandonment of the special theory of relativity.

7. A New Staging Stage for a Centuries Long Journey of Learning about Space and Time

After an overly long journey, we should now be able to realize that the general theory of relativity, even though not perfect and still requiring updating, was the goal for this special semiotic scaffolding project. All others, no matter how much aura has been added to it, were just the props of the middle stage to help or conduct the human mind to take a sharp veer from the absolute-space-and-time-based Newtonian mechanics to accept the otherwise hard to swallow general theory of relativity. Hence, the mission of the special theory of relativity should have been ended more than a century ago because of its own logical defects when humans entered the realm of the general theory of relativity. Unfortunately, that overdue ending of the mission of the troubled special relativity did not happen for the past more than one hundred years.

Now as we know that the special theory of relativity is incorrect, we seem to have come back to the old Newtonian absolute space and time. But the truth is that we indeed are not going back to the old rigid Newtonian space and time, but rather entering a new era of the soft absolute space and time that would conform to the general theory of relativity.

Up to this stage, we humans have finally come to a staging area after the centuries long journey from Newton to Einstein to now, and learned that space and time are neither rigidly absolute nor softly relativistic, but rather softly absolute. One thing that we need to take special heed is that in this softly absolute space and time, space and time are independently separate from each other instead of correlating with each other through Lorentz transformations as required by the special theory of relativity.

8. Conclusion

The special theory of relativity should be phased out because its two postulates are logically defective. The speed of light in vacuum is not a constant to all observers but needs to obey the Galilean rule of speed addition. The postulate of the constant speed of light in vacuum to all observers would be replaced by a revised postulate of speed of light in vacuum, and thus the speed of light c in vacuum should no longer be assumed to be the limit of energy (information) propagation. The notion of relativity of simultaneity should be abandoned. Nevertheless, what we are facing is no longer the old rigid Newtonian space and time, but rather the soft absolute space and time that would conform to the general theory of relativity.

9. Final Remark

This writing is an integration of my two previous writings “Why the First Postulate of Special Relativity Is Not Right” [[45]] and “Invalidating the Postulate of Constant Speed of Light with a Thought Experiment” [[46]]. I started the journey of invalidating the special theory of relativity with the thought experiment and presented in a short essay which was then reorganized into the longer version of [46]. Although in [46] I have already pointed out that the first postulate of special relativity is also problematic and thus should be abandoned together with the second postulate, it was later in [45] I put forth a much involved discussion on the problem of the first postulate and thus the problem of the relativity of simultaneity as presented also in this writing. But then I realized that since the overall consequence of invalidating the first postulate and the second postulate is the invalidation of the special theory of relativity as a theoretical framework, which would lead to the consequent restoration of the absolute sense of space and time (in the soft form instead of Newtonian rigid one though), I should combine [45] and [46] together as a single writing, and add some new contents that I have worked on after I posted those two articles. But since the postulate of the principle of relativity is the first postulate and the postulate of constant speed of light is the second postulate in special relativity, the order of discourse in this writing cannot follow the order of the historical course of my journey of invalidating the special theory of relativity, which leads to the arrangement of the sections in this writing. 

Appendix I. Rule of Superposition for Speed of Light in Vacuum

Suppose the source and target of a light beam are two inertial bodies so that when we project their velocities onto the virtual line connecting those two objects as v_a// and v_b// and onto the planes perpendicular to the connecting line as v_ap and v_bp as shown in Figure A1_, their relative velocity along their connecting line ∆v_ab = v_a// – v_b// = -∆v_bawould be a constant. While v_a// and v_b// are inthe same direction (or in opposite directions), v_ap and v_bp are not necessarily parallel to each other.

Figure A1. Decompositions of the velocities of the source and the target of a light beam

Now we shoot a light beam from a towards b at time t₀ and it reaches b at time t₁, and let’s call the speed of light from a to b as c_ab. During the time interval ∆t = t₁ –t₀ the distance between a and b changes from d₀ to d₁ so that ∆d = d₀ – d₁ , but we also have                                                        

d₁ =∆v_ab∆t                                                                               (A1)

d₀ = c_ab∆t                                                                                 (A2)

According to the revised postulate of speed of light in vacuum as proposed earlier, we have

∆d =c∆t                                                                                  (A3)

Therefore, we have c_ab∆t = c∆t + ∆v_ab∆t, i.e.

c_ab = c + ∆v_ab = c – ∆v_ba                                                            (A4)

Relation (A4) is the famous Galilean rule of speed addition. Now we know the following:

If v_ba = c, then c_ab = 0; if v_ba > c, then c_ab < 0; if v_ba < 0, then c_ab > c. The maximum of c_ab would be 2c.

Appendix II. The Real Value of the Apparent Speed Calculated by Lorentz Transformation

Suppose somehow we know the total energy of a particle in an accelerator to be E and its apparent speed calculated by equation (6) to be 0.99c, we would have

E = mc²/√(1-(0.99)²)                                                                                  (A5)

Now by denying the relativistic relationship, we should have

E = (1/2) mv² + mc²                                                                                   (A6)

From (A5) and (A6) we have

mc²/√(1-(0.99)²) = (1/2)mv² + mc²                                                                 (A7)

∴ v² = 2( 1/√(1-(0.99)²)  – 1)c²                                                                (A8)

∴ v = 3.489645c                                                                                  (A9)

References

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