The Original Philosophy behind Special Relativity
Rongqing Dai
Abstract
This paper discusses how the logical errors of special relativity actually stemmed from a misunderstanding of the shape of the electric field around a moving electric charge, viewing it as a flaw in our understanding of the nature of space and time. Special relativity was precisely the product of the joint efforts of the physics and mathematics communities at the turn of 20th century to artificially remedy this so-called human flaw. Furthermore, this paper provides an in-depth analysis of the profound meanings of the notion of space.
Keywords: Space, Speed of Light, Principle of Relativity, Observer and Observed, Epistemology, Ontology
1. A Brief Background
By following the works of ?rsted[[1],[2]], Gauss[[3]], Faraday[[4],[5],[6]], Ampère[[7],[8]], Ohm[[9]], and others, in 1860s Maxwell[[10]] worked out his equations for electromagnetic waves in charge-free vacuum, which was then reorganized by Heaviside into the following form[[11]]
??A/?t? = c2?A (1)
where A is either the electric field E or the magnetic field B,
and
c = 1/(√(ε???) ) (2)
was later proved to be the speed of light in vacuum, and εo is permittivity in vacuum and μo is permeability in vacuum.
In 1889, Heaviside[[12],[13],[14]] showed that based on Maxwell’s equations the electric field surrounding a charge (or a spherical distribution of charge) moving through a dielectric cease to have spherical symmetry (as in the case of a fixed charge) but take the ellipsoid shape which is later called Heaviside ellipsoid. This discovery strangely unsettled the physics community at the time, which claimed that the so-called Galileo's principle of relativity about the kinematic motions[[15]] should be translated in a modern sense as the principle of relativity of all physical laws, and sparked a subsequent wave of efforts trying to turn the Heaviside ellipsoid back to a sphere by all means.
Fitzgerald[[16]] in 1889 and Lorentz[[17]] in 1892 independently proposed the hypothesis that all bodies are contracted in the direction of their motion relative to the aether 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[[18]] proposed the time dilation in addition to the FitzGerald–Lorentz contraction, and independently, Lorentz[[19]] 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[[20]] in 1905. Then by making the abovementioned modernized Galileo’s principle of relativity as the first postulate and merging the precedent length contraction and time dilation hypotheses, Einstein gave birth to the special relativity in 1905.
2. A Strange Philosophical Confusion
The above historical overview could help us to track down the philosophical origin of special relativity, which emerged in 1905, back to the Heaviside's 1889 report of the deformation of the solution curves of Maxwell's equations when the source of charge moves.
But here is the problem: Heaviside made his conclusion by “observing” the movement of the source of charge from the perspective of an observer, not from the perspective of the moving charge itself, and then Lorentz and his colleagues, however, were forcibly imposing the observer’s perspective onto the observed source itself. This way of thinking became precisely the fundamental philosophical logic behind the special and general theories of relativity developed by Einstein later. Following this philosophical view, Nobel laureate Penrose used the claim that photons do not experience time as the basis of his cosmology, the physics community debated over the so-called twin paradox for more than a hundred years and still have not stopped, and almost the entire quantum theory is based on the assertion that scientists can simply impose the observer's observation onto the observed moving subject.
But even high school students know the difference between the observer's perspective and the perspective of the observed subject in motion. This is why the physics community at the turn of the 20th century felt the need to borrow the Galileo’s principle of relativity, seemingly unaware that the so-called Galileo’s principle of relativity, proposed in 1600, merely tells that all inertial frames of reference are essentially equivalent to each other when judging kinematic motions.
2.1. The principle of relativity
The validity of the principle of relativity of Galileo is obvious since as we know that the acceleration calculated in all inertial frames of reference is the same while acceleration is the only dynamic element, or the only thing that is nonlinear for spatial variation, existing in kinematic motions, which can be dynamically calculated through Newton’s law,.
Now we also know that many physical quantities that can be described as the so-called tensors, such as temperature, force, length, time, mass, etc, are the same not only in all inertial systems but also in all reference systems. However, when all physical laws are involved, there is simply no reason for anyone to assume that two frames of references are equivalent simply because they are both inertial. In fact, the difference between the shape of the electric field around the stationary charge and the shape of the electric field around the moving charge offers an excellent example for the violation of the principle of relativity of Galileo when electricity is involved in the investigation. Very strangely the world's elite intellectuals at the turn of 20th century rejected in unison what nature revealed through Heaviside’s mathematical derivation, but were unanimously determined to tell nature how to behave through their own mathematical tricks and artificial postulates.
If the Lorentz transformation, upon which the theories of relativity are based, were merely a mathematical tool for solving Maxwell's equations, that would be perfectly fine. However, the physics community, starting with Lorentz, insisted on calling it the physical nature of spacetime itself.
With this being done, an epistemological problem was forced into a fake ontological reality. Unfortunately, the entire global physics community has followed this line of thinking to this day and has no sign of willing to stop.
But they overlooked the fact that for every observed subject, there might be countless observers. Therefore, equating one's own observation of motion with the observation of all observers is not respecting the relativity of the individual, but rather making things follow a false, absolutely identical pattern. The constancy of the speed of light in vacuum to all observers, as the combination of both length contraction and time dilation of Lorentz, is the best embodiment of this absoluteness for its complete denial of the variation of the speed of light relative to different observers.
2.1. Speed of Light in Vacuum
The essence of the speed of light in vacuum is actually quite simple: imagine placing a rod at one point in vacuum, and another rod at a different point. Let light pass through both rods and record the time taken. Dividing the distance between the rods by the recorded time we get the speed of light in vacuum. Because the speed of light is extremely fast, measuring it in reality using this method is very difficult, but it doesn't prevent us from defining and understanding the speed of light in vacuum based on this principle.
Currently, the most reliable theory we know about the speed of light in vacuum is based on the empirically rooted Maxwell's equations of electromagnetism, which themselves do not address the motion of the light source. However, in physics, we cannot always ignore the motion of the light source without reason; therefore, we need a theory of the speed of light that can handle the motion of the light source.
Special relativity, based on the Lorentz transformations, assumes that the speed of light in vacuum is constant for any observer. But this is a flawed postulate because its logical shortcomings make it seem elegant when explaining certain phenomena but look seriously wrong with a slight change in perspective.
The revised postulate of speed of light in vacuum proposed by Dai since 2022[[21]] offers a reasonably promising alternative solution and its biggest difference from the special relativity’s postulate of the constancy of the speed of light is that it denies the claim that the speed of light is constant for all observers, and instead assumes that the speed of light is constant only for its source when it is inertial.
Nevertheless, the assumption that the speed of light is constant for the inertial light source itself requires a better understanding of the nature of space itself.
3. The Complexity of the Notion of Space
The complexity of the notion of the very space that we are living in might offer one of the explanations to the abovementioned strange confusions of the community of physics at the turn of the 20th century.
When we view the universe from a static perspective, it's easy to imagine the isotropic spherical symmetry of space….Just imagine a point in an absolutely empty and boundless vacuum. We have no reason to believe it's asymmetrical in different directions…. Because there's no reason to believe it's asymmetrical, the only answer is that it is spherically symmetric in all directions. After we introduce the concept of inertial frame of reference and assume an object is moving at a constant velocity in a straight line, an observer on that uniformly moving object will also naturally assume that the surrounding space possesses the isotropic spherical symmetry, as long as there is no reason to believe the existence of any inertial frame of reference with absolute superiority in judging the reality.
However, when we introduce two inertial objects in relative motion, or, as Heaviside observed in his own inertial frame the inertial motion of a charged particle, we will face the challenge posed by the loss of spatial symmetry. When inertial frames A and B are in relative motion, broadly speaking, we might think that A and B still each possess their own spatial symmetry; however, once we assign specific physical properties to A and B, situations might arise where the spatial symmetry of A and B cannot be simultaneously satisfied. For example, Heaviside’s observation revealed that when a charged particle moves at a constant velocity in a straight line, the electromagnetic field around it no longer exhibits the spherical symmetry expected of a stationary charged particle, but rather a distribution known as the Heaviside ellipsoid.
3.1. The paradox of dynamic symmetry in space
When a solid object is thrown from an inertial system into the gravity and charge free vacuum, there will be an accelerating process before the object leaves the inertial system, and the object’s subsequent velocity is the final velocity it acquires during this acceleration. However, light is different. According to the existing physics, although a light source does consume energy to give energy to light waves or photons when emitting light, once the light leaves the source and enters the vacuum, its speed in vacuum is independent of the energy consumed by the source and is entirely determined by Maxwell's electromagnetic field equations.
The physical mechanism behind this is that a solid object needs a force to move from rest, while according to the current theory, the motion of light is caused by the induction between electric and magnetic fields; even if light is considered as particles called photons, they do not require external acceleration to achieve a finite velocity since photons have zero mass according to the existing physics..
Besides, based on our current understanding of the universe, there is no absolutely stationary center in the universe. Therefore, according to the basic principle of symmetry or the so-called Galilean principle of relativity (not the principle of relativity of the theories of relativity), the vacuum at any point is stationary relative to the inertial frame at that point----This is a paradox. For example, if two objects A and B are in relative motion, the vacuum at the location of A is stationary with respect to A, and the vacuum at the location of B is stationary with respect to B; however, all parts of the vacuum space are a unified whole with no relative motion between each other—this directly creates a logical incompatibility. It sounds a bit like assuming Jack and Bob being of the same height, and John and Bill being of the same height while Jack and John are not of the same height, but Bob and Bill are of the same height.
We can call this paradox the Paradox of Dynamic Symmetry in Space.
To resolve this paradox, a possible solution might be to assume that the vacuum is an absolutely stationary frame of reference. However, this raises another problem: if an absolutely stationary frame of reference exists, and the vacuum is that frame, then who can know which moving inertial frame is stationary relative to that absolutely stationary frame of reference? If no one knows which inertial frame is stationary relative to that vacuum frame of reference, then what does it mean by the velocity of any inertial frame relative to the vacuum?
This is both an epistemological question (i.e. one for which the answer is difficult to find) and an ontological question, because while the vacuum sounds abstract, objects moving in the universe are concrete. There is no reason to think that any inertial frame is more special than any other, so no inertial frame should be regarded as absolutely stationary; therefore, an absolutely stationary vacuum ceases to exist. However, this brings us back to the paradox we discussed earlier: the vacuum of the universe as a whole has no relative motion between itself (although the expansion of the universe claimed by modern cosmology sounds like there is relative motion between different parts of the vacuum space, that relative motion is not the same as the relative motion we are discussing here), but objects that are stationary relative to the vacuum in different locations can have relative motion between each other.
4. The Linguistic Challenge and Ontological Reality
In fact, the first challenge we encounter here is not a physical challenge, but a linguistic challenge. It is an example of how language affects people's thinking. . . . People are accustomed to using a reference object to measure and calculate the speed of another object in life. Therefore, when it comes to the speed of light in vacuum, people will naturally imagine the vacuum space as a reference system, thereby giving the vacuum space a kinematic meaning. . . . Once space is given kinematic meaning, the paradox of dynamic symmetry in space we mentioned earlier will arise.
5. The Meaning of Space
The above discussion exposes the flaw of current human understanding of space which can lead to various confusions. Therefore, it is necessary to further clarify what we mean by “space”.
5.1. Kinematic meaning of space
In its most basic sense, space is a void container that holds all the matter. However, the development of civilization, especially the development of physics, has given space many more complex meanings than a void container. One of the simplest examples is the kinematic meaning of space. The Galilean principle of relativity, that is, “there is no absolute inertial system” is actually a special kinematic meaning assigned to the notion of space. . . . The so-called inertial observing system is not just an object that makes inertial motion, but rather a frame of reference that makes inertial motion and the so-called reference system is not only an abstract coordinate system, but also the entire infinitely large spatial range covered by that abstract coordinate system.
The essence of the reference system is to measure the movement that occurs within the spatial range covered by the reference system. In order to measure motion, distance and speed must be calculated. For a reference system, the most basic distance calculation is based on the coordinates determined by the distance to the origin of the reference system, and the most basic speed calculation is to calculate the speed relative to the reference system itself. The implicit premise here is to assume that the frame of reference itself is stationary in space. The stationary state of the reference system in space is a kinematic meaning of the space, and the Galilean principle of relativity gives space another specific kinematic meaning.
From the previous discussions, we have seen that the kinematic significance of space will directly lead to the paradox of dynamic symmetry in space.
5.2. Dynamic significance of space
In addition to the kinematic meaning, with the development of physics, the word “space” also acquires complex explicit and implicit dynamic meanings. For example, the electromagnetic field is a special dynamic meaning of space. There are electric fields in the space around charged particles, which itself is a dynamic meaning of space. For an observer moving with a charged particle, the space around him has only a spherical distribution of electric field without magnetic field. However, for someone like Heaviside who was standing on the ground and observing the particle moving in space, there is not only an electric field but also a magnetic field around the particle. Similarly, when a magnet moves through the air, an electric field appears around it, but to an observer moving with the magnet, they are surrounded by a pure magnetic field.
Humans currently do not know why there is an electric field in the space around the charge or why the movement of the charge produces the so-called magnetic field. Similarly, people do not know why the movement of the magnetic field produces an electric field in the surrounding space that does not exist around the static magnetic field. Relativity scholars claim that these phenomena are caused by the relativistic nature of spacetime, but it actually has nothing to do with the deformation of space and time claimed by them at all, and thus the whole thing has nothing to do with the theories of relativity at all except for the their wishful claim. As we now know that mass cannot curve the so-called spacetime to create gravity and the string theory has also failed to prove that any curvatures of high dimensions to be responsible for other fundamental natural forces.
But on the other hand, the complex patterns of electric and magnetic fields and the existence of gravitational fields in space show us a dynamic picture of space. In addition, the theory of cosmic expansion claims that the universe is constantly expanding under the influence of dark energy, and experiments in quantum mechanics claim that energy exists in the vacuum. Quantum theory also assumes that the vacuum energy fluctuates up and down around the zero point energy, and some short-lived virtual particles pop up out of and vanish into the vacuum from time to time.
In short, the development of physics has given complex dynamic meanings to space, some of which may be reasonable and some of which may be illusory.
5.3. Linguistic challenges related to space and the need for the conceptual clarification
From the above discussions, we can see that, whether in everyday language or in scientific terminology, the word “space” has far more complex connotations than its basic meaning of “a void container”, bearing various historical imprints of civilization’s development. These complex meanings are often not consistent with each other. To avoid the complexity of historical markers interfering with our understanding of the characteristics of space, we need to make some more granulated distinctions between concepts related to space.
5.3.1. The ontological container space
Since humans developed the concept of the universe, “the universe fills the entire space” has been the basic imagination of the relationship between the universe and space. A natural inference from this premise is that “there is nothing outside the universe”. However, with the introduction of the theories of cosmic expansion and the Big Bang, this ancient idea of universe led people to equate the expansion of the universe with the expansion of space without sufficient evidence, resulting in some logical confusion in cosmological research. In response to this issue, at the end of 2025, Dai[[22]] proposed that we should conceptually separate universe from space within which it exists so as to avoid confusion in understanding space and universe caused by the traditional ambiguity throughout the history of civilization. The necessity of such conceptual refinement stems from two factors: firstly, human thinking (including scientific thinking) is largely influenced and limited by the language we use [[23]]; secondly, these refined concepts point to ontological characteristics of existence.
Moreover, the discussions above show us that, in order to better understand the essence of space, it is necessary to refine the long-used concept of space. Firstly, we can further clarify the “space” proposed by Dai in 2025 (distinguishing it from the universe) as a void vacuum devoid of any kinematic or dynamic meaning, and name it as “Ontological Container Space” (OCS). Such a completely void vacuum is neither the universe created by the Big Bang nor stationary to any coordinate system, thus eliminating the previously mentioned paradox of dynamic symmetry in space. Of course, such a void space still possesses the most fundamental elements of space—spatial points and the distance between them. The speed of light in this vacuum space is simply the distance between two points divided by the time it takes for light to pass between those two points; the so-called speed of light relative to such vacuum becomes completely meaningless. ... The space covered by any coordinate system with a stationary meaning does not belong to this OCS.
5.3.2. Physical space (or “space” for short)
The main purpose of proposing the concept of ontological container space (OCS) is to remind people of the existence and significance of this completely empty space, and to help resolve perplexities such as the paradox of dynamic symmetry in space. It is not intended to replace the term “space” used in daily life and scientific research, including physics research, since that would be unrealistic. Nevertheless, the introduction of OCS provides an effective tool for resolving related perplexities in social practice.
Meanwhile, while continuing to use the simple term “space” in daily life and scientific research, we can also give it a formal name: “Physical Space” (PS), to remind people when needed that the term “space” in everyday life actually has very complex physical connotations. It is these physical connotations that cause problems such as the paradox of dynamic symmetry in space.
5.3.3. Energy Space
The application of the term “space” by ordinary people in daily life does not actually carry complex physical connotations. However, this does not mean that related physical connotations do not exist, nor does it mean that the term “space” will not bring about perplexities such as those surrounding electromagnetic problems over the past century in specific contexts. Therefore, it is necessary to have a term for the physical connotations of space, which can be called “Energetic Space” (ES). This term primarily refers to the energy phenomena bound to space, such as electromagnetic fields, gravitational fields, and so-called dark energy and zero-point energy, etc.
5.3.4 Universe
After refining the notion “space” into ontological container space (OCS), physical space (PS), and energy space (ES), by referring to the separation of “space” and “universe” by Dai in 2025, we can say that the space occupied by the universe is a subset of the combination of OCS and ES.
First, all three-dimensional matter, including the universe, exists within the OCS. Second, according to current theories, the space occupied by the universe possesses energy; therefore, the universe exists within the ES.
The terms “space” (which we also call “physical space” here) and “universe” have been used interchangeably since ancient times. Since we retain the traditional concept of “space” for convenience, the space occupied by the universe is equal to the PS.
It is necessary to emphasize again that the refinement of these concepts here is not only for ontological reasons, but also for the consideration of linguistic influences on people’s thinking.
5.3.5 Luminiferous aether
In addition to the philosophical origin discussed above, the process of the emergence of special relativity also involved some other specific issues faced by the physics community at the end of the 19th century, one of which was the search for the so-called Luminiferous aether[[24] ]. The birth of special relativity was considered a declaration of the failure to find Luminiferous aether, although, as Dai pointed out before, there is no logical causal relationship between them at all[21].
In recent years, with the discovery of vacuum energy, the concept of aether has been brought back to the forefront of physics by some scholars. However, the original concept of aether had some meanings beyond the energy observed in quantum mechanics and cosmology today. Therefore, we should not equate the concept of energy space (ES) introduced here with aether.
5.3.6. The sizes of OCS, ES, and PS
The ontological container space OCS defined in this paper is infinitely large; the physical space PS proposed in this paper (i.e. the space commonly referred to as “space”) corresponds to the universe produced by the Big Bang, and is therefore finite in size. However, the size of the energy space ES is currently difficult to determine. This is because, based solely on current observations, we cannot yet determine whether the so-called vacuum energy (or zero-point energy, dark energy, etc) was generated with the Big Bang, whether it is inherent in the three-dimensional ontological container space as part of a higher-dimensional space, or whether it is caused by some other reasons.
6. The Motion of Light Relative to an Inertial Light Source
With the refined understanding of the meaning of space, and thus of vacuum, now we know that the speed of light determined by Maxwell’s equations is the speed of light in OCS vacuum instead of relative to OCS vacuum. However, for the sake of dynamic calculations, we need the speed not only in the abstract sense but also relative to something in the material world, while the speed of light in vacuum determined by Maxwell’s equations is independent of the motion of the light source. That is the reason why we need the revised postulate of speed of light in vacuum[21] after knowing that the constancy of speed of light in vacuum of special relativity is wrong.
This revised postulate is consistent with the empirical basis upon which Maxwell derived his electromagnetic equations. This is because Maxwell’s empirical basis corresponds to the light source stationary on the Earth while the vacuum in which the imagined light source exists is also stationary to the Earth. Under that premise, the speed in the vacuum is actually the speed relative to the Earth, and hence to the light source. Therefore, although Maxwell’s mathematical derivation does not reflect the ontological connection between the speed of the electromagnetic wave and the source of the emission of the wave, this connection actually is implicitly in the preconditions of the empirical theories he relied on.
By the way, with the revised postulate of the speed of light in vacuum, the emphasis on the “inertial motion” of the light source is crucial because, according to this new postulate, once the speed of the light source changes after the light is emitted, the speed of light relative to the light source is no longer c.
7. Final Remarks
As it is said, “a miss is as good as a mile”. The logical fallacy of special relativity actually stemmed from the fact that the leading scholars at the turn of 20th century interpreted the change in the shape of the solution curves of Maxwell’s equations, calculated by Heaviside from an observer’s perspective under the condition when the source of electric charge is moving, as a flaw in human understanding of the nature of space and time. Special relativity was precisely the product of the concerted efforts of the communities of physics and mathematics to artificially remedy this purported defect of humanity. Even more astonishing is that for over a century afterward, the mainstream of the world’s physics community unanimously accepted this clearly flawed philosophical thinking, to the point that even today, the physics community cannot escape the dominance of its consequence.
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