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Max Concern

**Part II The incredible lightness of being in Special Relativity**

Abstract

It is shown that serious doubts must be cast upon the current causeless interpretation of special relativity by demonstrating that omissions of a material nature in the latter effectively detach the theory of special relativity from the success of its predictions. The special theory of relativity is shown to be primarily an application of Huygens’ principle legitimised by Maxwell’s equations. The absence of vitally important details in the formulation of the special theory of relativity is shown to result in the conclusions that there cannot be any physical observers present in that theory and that the light used in Einstein’s derivation of the special theory cannot be the light of common scientific experience. These two facts remove scientific support from Relativism and question the nature and meaning of the velocity in the Lorentz transformation equations. These conclusions, together with the obvious success of the theory’s predictions, and its dramatic failure to explain many physical phenomena, and the inherent dangers of thought experiments shown in Part I of this paper, have necessitated the conclusion that a unique mathematical labyrinth of unreality has been constructed that encloses and protects special relativity, supports the mathematical abstractions involved and hides the details of interactions necessary for an understanding of the Lorentz transformation equations and the interaction of particles.

The expanding sphere of light

The Lorentz transformation equations form the first foundational expression in mathematics of the relativity theory. As an alternative to Einstein’s method, the expanding sphere of light mentioned in the special relativity paper can be used as the basis for deriving the Lorentz transformation equations. In fact the derivation is simpler^{ } (Einstein et al, 1923). This expanding sphere has had a remarkable and rich history in the 200 or so years prior to the publication of Einstein’s paper. It is recognized as Huygens’ principle (Huygens, 1690), or Huygens’ construction. This is an important device for those striving to understand the physics of the "thought experiment" in special relativity.

The sphere of light and Relativity

Huygens’ principle can be regarded as a geometrical method for reconstructing the next light wave front from a prior light wave front. It imagines the emission of spherical wavelets from each point on the prior wave front, so that the envelope of these wavelets forms the next wave front. Each point in space is a non-material source of light. As unreal as it seems, it works in practice.

It is Huygens’ principle that attempts to describe the way light travels in empty space.^{ } It does this quite well in the absence of diffraction effects. The vital point is that it applies to a local space free of material bodies. There are no material bodies in Huygens’ principle. Born and Wolf (Born & Wolf; p 374, 1965) have said of Fresnel’s modifications to Huygens’ principle

"*The additional assumptions must, however, be regarded as purely a convenient way of interpreting the mathematical expressions and as being devoid of any physical significance..." *

The same can be said of Huygens’ principle itself, since more accurate results are obtained in the theory of diffraction without its aid. Its use is now limited to applications where its assumptions are approximately valid. It is by no means sufficiently powerful to predict or explain experimental results. Special relativity relies, or can be made to rely, on the same core concept so it is clear that material bodies are absent from this theory too. Indeed, it would appear that none are wanted, for their introduction results in fundamental contradictions that even the mathematical theory of relativity cannot ignore.

Non-corporeal observers

An observer is normally considered to be a material object, so whatever observers are present in this Principal of Relativity are not material objects, but they exist wherever light does. The non-existence of material observers withdraws this aspect of scientific support for the arguments of the pro-Relativism participants in the debate. It is certain that there is some unknown structure in space but to give it the nature of a pair of observers (and, when it is convenient, a pair of human observers), as is done in special relativity, is obfuscating.

Further Justification

In addition to the strong mathematical connection to Huygens’ principle, there are additional reasons for adducing the observers to be unreal or at least not corporeal. There is the strange light in special relativity. It is strange because it has so few properties. In fact the list of properties that it doesn’t have is quite long, and some conflict in a fundamental way with the properties made plain by the exacting mind of Max Planck (Planck, 1914) in his theory of radiation.

Relative wavelength

There are no requirements placed on the wavelength of the light relative to the physical size of the reflecting and emitting bodies. There are well-established fundamental requirements that place constraints on their relative magnitudes. Neither Einstein nor Lorentz considers these fundamental constraints, and they are absent from Huygens’ principle.

Mass and Momentum

There are no requirements placed on the mass of the emitters and reflectors, even though it is shown in the same paper that the light has momentum and energy. These requirements are a consequence of the principle of the conservation of momentum and energy. Light has momentum and so therefore the source should be affected by the concepts that Einstein’s paper introduces, *viz*. light pressure and continual loss of mass. So there is really no material source, because it is Huygens’ principle that is being applied.

Frequency

There are no frequency sensitive aspects of reflection, even though the light is reflected, and these should have seemed necessary from work on the photoelectric effect at least. Even without the detail of the photoelectric effect, frequency selective aspects of reflection and diffraction are universal. Neither Lorentz nor Einstein includes them, and there are none in Huygens’ principle either.

Rise and fall

There is no rise nor fall time, neither of the "ray" nor of the "spherical wave". The time resolution of emitted and received light flashes, pulses, waves, rays or call them what you will, places obvious fundamental limits on the measurement of intervals, so that the unreserved progression to infinitesimals is fundamentally compromised. The frequency of the light is ignored in the theoretical derivation by both Einstein and Lorentz, but is re-introduced by Einstein in the Doppler shift formula as if the problem never existed.

Intensity

The light intensity suffers no diminution with distance from its emitter. For example, there is no mention of, and no mathematical provision for, the inverse square law of radiation. In fact everything that characterizes the interaction of light with matter is missing, save the bare fact of reflection, and the other complexities of that process are absent too. In summary, these are just the characteristics of geometrically idealized light in a transparent medium. This is the domain of Huygens’ principle.

Matter and impact

The major characteristic of the interaction of matter with matter is absent. Here the reference is not to gravity, but to impact. For throughout the discussion in special relativity the origins often coincide in four-space, and of course they cannot if there are masses there or any material observers there. There would be a collision. This ubiquitous phenomenon, known to humans for millennium, is omitted from special relativity.

This common phenomenon is absent from general relativity too. This omission strikes those to whom it is pointed out as strange in a theory claiming the universality of relativity. But Einstein is not alone. Newton’s law does not predict that the apple will strike the ground, or that an asteroid will collide with the earth. For Newton proved mathematically that a mass behaved as though all the mass were concentrated at its centre. But we know well enough that a collision occurs in all cases before zero separation is reached, no matter what size the mass. Newton’s law of gravity may predict an infinite force at zero separation, but his predictions are wrong on three counts. Firstly a collision always occurs before the point of zero separation is reached. Secondly the force is eventually repulsive and not attractive. Thirdly the infinite force is beyond the limit of all substances to withstand, so it cannot be infinite. Maxwell’s electron currents in wires are in essence flows in space curves and these curves pass through each other with accomplished ease, exactly like the displacement current. Einstein, Maxwell and Newton use mathematical idealizations of reality that are demonstrably incorrect. Therefore the progression to infinitesimals should be qualified, especially if nothing is known of this domain.

In special relativity, trivial invariance to translations of the origin is guaranteed. Therefore the observers are everywhere as well as anywhere in each of the two inertial frames. This is of course expected from Huygens’ principle, where every point in space is a non-material source. An observer who is everywhere is an absolute in every sense, the existence of which is specifically and fundamentally rejected in special relativity. Since trivial invariance with respect to time translations is included by the equation in differentials, this mathematical thing is additionally every when, existing for all time.^{ }Although it is plain that a stronger case could be made, this absolute is reminiscent of the absolute implied by Newton’s laws, which retrospectively assigned failing of Newton’s has been criticised so much by the unquestioning supporters of relativity, and in a patronizing way by Einstein himself.

But this observer, who is now taking on some of the characteristics of a deity, must also be a material one since light signals are received. So we see that the "moving bodies" in Einstein’s theory have no distinguishing feature at any scale that enables them to be recognized as essentially different from the background mathematical space in which they are supposed to exist. Without distinguishing features the phrase "moving bodies" is meaningless. Thus there is nothing to which the all-pervasive relative velocity can be assigned, and this reveals the relative velocity (or v/c) for what it is, a parameter in need of an explanation.

Light without shadow

This highlights the dangers of an unqualified thought experiment that omits important detail. If the rules of scientific investigation have been slightly bent for the thought experiment of special relativity, one would expect that the rules of interpretation of the mathematics should be similarly flexible, but in the case of relativity no flexibility has been allowed. Special relativity is not specifically about the passage of light in a pipe through which water flows at some constant velocity, although this may perhaps have been a better scientific approach.

Special relativity is about the inertial frames of reference of two separate observers *in vacuo*, and about showing, *inter alia*, that neither of them has a preferred frame of reference over the other. In this it must fail because the observers are not material objects. They may be imagined, as one would a ghost, but they are not even mathematically real. The replacement of "observer" by "frame of reference" in an attempt to legitimise the theory does not avoid the need for observers, nor does it explain their introduction if a frame is what is meant. In any case, the observers suddenly become human again in many of the ‘counterintuitive’ paradoxes that inexplicably are the favourite of physics authors and litter their textbooks. So disproportionate a space is sometimes devoted to these paradoxes that one is lead to suspect that the repetitive generation of counter-intuitive arguments is the main aim of the authors.

The juxtaposition of these two terms has lead many mathematical physicists into the error that the use of mathematical frames alone provides the more convincing proof of the theory. The phrase "the frame of reference of the observer" contains the same false but subtle and subliminally convincing instructions to one’s mind, as does the phrase "thought experiment". Both phrases have the same mix of thought and the allusion to hard scientific or mathematical fact. In the first the mathematical foundation is unsound, and the second has been dealt with. The first is nothing other than a mathematical-scientific statement of the philosophy of group Relativism and the second is its personification.

This light has the singularly Newtonian property of travelling at constant speed. This is an idealized mathematical property of a non-material something whose existence cannot be detected without material detectors and an assumption that requires an infinite time and an infinite space to experimentally prove. No material object arrests its endless march, no distance lessens it, no material object is involved in its production, and there are no shadows at all. It does not interact with matter, and yet it must.

The entire mathematical and deductive structure of relativity would remain exactly the same if all the ‘experiments’ were carried out inside a solid block of glass, fictitious moving observers included. For none of the "laws of nature" prohibit it. Not Einstein’s, not Maxwell’s and not Newton’s. Since electromagnetic radiation, and not specifically visible light is required, even the visible transparency is not required, and the entire thought experiment could be mathematically performed inside a solid uniform rock.

Only the constancy of v and c is required, not that it have any particular value, and in any case, inside such a rock, one would never know there was such a thing as an inside and an outside, because the mathematics of the transformation and the so-called laws of nature exclude the possibility of defining it. In addition, the ratio v/c is the mathematically important fact, and not their individual magnitudes. Other things are subliminally imported from human experience; they are not contained in the mathematics, so they are not contained in the theory. If those adherents to the glory of mathematical physics have any intellectual honesty at all, they are surely bound by their own commitment to prove that mathematics can at least stand up unaided.

This clearly shows the additional danger of relying on a thought experiment is that the boundaries of the experiment are not set by the complexities of the experimental world. They are set by the thinker who stops the experiment at a time and level of interaction and abstraction that is convenient for the results desired. The real experiment contains many unknown and potentially vitally important interactions. Not just the mathematically desirable ones and those that seem to have served a non-scientific purpose for so long, but also those that would seriously challenge the assumptions of relativity and Relativism.

It should be expected that those who study physics doubt the reality of this light and the existence of the observers. It is a logical deduction that the light serves no other purpose than to act as a surrogate messenger for assumed isotropy, and the mathematical basis for this assumption should be assigned to the initial success of Huygens’ principle. A participant from the anti-Relativism side of the debate would regard the scientific and logical basis of the theory of special relativity as the spell of a conjuror, a light illuminating a façade of plausibility. With some justification, it can be described as a sleight of mind.

Implications

If it must be assumed that there are observers present in special relativity, then it is necessary to assume that they are not corporeal and exist only in the minds of the supporters of the theory. From the invariance to translation of the differential length element in four-space it is concluded that there are an infinite number of them existing throughout space-time. The fact that the light used in the thought experiment does not possess numerous fundamental, proven, experimental characteristics of the light of common scientific experience either in descriptive or mathematical form, makes it certain that it is not that light, even though it is so used by Einstein.

Accordingly, for either or both of these reasons, scientific support claimed from the theory of relativity for the philosophy of Relativism and its ideals has been and remains totally unfounded. Additionally, it follows that any discussions concerning the experiences, feelings, relationships and observations of these imaginaries, and any paradoxes arising there from, must serve purposes other than scientific. The non-scientific purposes they serve are, in effect if not by design, those of the philosophy of Relativism. These purposes are achieved through the mathematical devices of the transformation of coordinates representing frames of reference and the principle of the invariance of mathematical form.

Einstein achieved partial success using this modified form of Huygens’ principle in special relativity as the main vehicle for the analysis, but not the explanation, of some physical light phenomenon. In addition, he achieved further success with his mathematical generalization of the Faraday field into general relativity. It is as well to point out that the essential connection between special and general relativity is not based on physical phenomenon, but on a presumption of a mathematical and philosophical idealism. The blind faith in this idealism had as its direct and immediate consequence the problem of an unknown causal connection between gravity and electromagnetism. This remains unsolved to this day. Ironically, this idealism served only to separate rather than unite these phenomena. The point at which this "disconnection" occurred can be traced to specific places in the original papers of Lorentz and Einstein, and is described in the appendix to this paper.

We recall the famous statement made by Minkowski (Minkowski, 1908) echoed repeatedly and zealously by modern physicists

"*Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.*"

The words "mere shadows" aptly describe our present understanding of the physics of particle interaction in the present world-view of a multi-dimensional mathematical space, a world-view supported through mathematics by the philosophy of group Relativism.

We hope to show in a subsequent paper that the use of Maxwell’s equations already requires the presence of frames of reference that are not inertial. In other words, the inherent property of the rotation of particles must be already contained within Maxwell’s equations. This is a necessary condition for the existence of the fields they describe. Therefore Einstein’s use of these equations in inertial frames reveals an insurmountable contradiction.

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Appendix

The inclusion of mass into the programme of special relativity had to come from Newton’s laws. No other interpretation was attempted by either Lorentz or Einstein. Both Lorentz and Einstein make similar comments regarding the application of their transformation equations to all mass. In both of these quotations, the italics are taken from the references. Lorentz (Lorentz, 1904) says about the development of his "longitudinal" and "transverse" mass formulae:

"In the second place I shall propose *that the forces between uncharged particles, as well as those between such particles and electrons, are influenced by a translation in quite the same way as the electric forces in an electrostatic system*."

Einstein (Einstein, 1905) has this to say about his "transverse" and "longitudinal" mass formulae:

"We remark that these results as to the mass are also valid for ponderable material points, because a ponderable material point can be made into an electron (in our sense of the word) by the addition of an electric charge, *no matter how small*."

The neutron, whose existence was hypothesised in 1920 and eventually discovered in 1932, made absolutely no difference to the interpretation and presentation of the ideas of relativity. Quite apart from questions that should initially have been raised regarding the meaning of the phrase in italics in the above quotation from the English translation of Einstein’s paper, the neutron has no charge at all. So any argument based on the sending and receiving of light and light signals is of course inapplicable to the neutron.

So the neutron is out on a limb, so to speak. In Lorentz’s case by an axiomatic statement to do with forces, and in Einstein’s by a statement that is so vague that it amounts to the assumption that the neutron displays charge-like behaviour, a seemingly ridiculous statement about a neutral particle. All this is a consequence of an almost pathological obedience to an idealism, and using Maxwell’s equations to further these prejudices. But the fact that the electron just happens to have mass as well as charge is purely coincidental as far as Maxwell’s equations are concerned, for nowhere in the form of Maxwell’s equations used by Einstein and Lorentz is the mass of the charge carriers mentioned. Indeed, if experiments prior to these papers had shown that the neutron’s mass increased with velocity, then the introduction of Maxwell’s equations, let alone the gauge invariance of the Lorentz transformation, would have been pointless. The introduction of Maxwell’s equations, given this experimental scenario, would have necessitated a direct causal connection between a neutral mass particle that is supposed not to radiate, and a charged particle that does radiate.

As it happened, the connection between mass and charge was made by the experimentally unwarranted assumption of relativity and later "proven" by experiment, since the mass of the neutron increases with velocity. It is universally assumed that the subsequent experiments proved relativity. What the mathematical physicists failed to notice in their mathematically driven fervour is the surprising conclusion that the behaviour of the chargeless neutron must be covered by a version of Maxwell’s equations. So instead of the neutron being outside the reach of Maxwell’s equations, it must be included therein. Thus de Broglie’s matter waves would have been anticipated instead of being mathematically hypothesized in the quantum era.^{ }

The role of the neutron highlights the initial tenuous, axiomatic and experimentally groundless nature of the assumptions in relativity theory and the unfathomable unwillingness on the part of subsequent generations of devout mathematical physicists to criticise what they seem to regard as sacred concepts and texts. It may well turn out that such criticisms eventually support the conclusions reached in these early papers, but then again they may not. The lack of curiosity from modern devout mathematical physicists points to an intellectual stubbornness that is the opposite of the zeal they display when using relativity as a revolutionary tool. Yet they treat that same zeal with ridicule when it is demonstrated by others. They have become the new establishment, an exact inflexible mirror of the classical one they expended so much time and energy attempting to dismantle.

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References for Part I and Part II

Born, M., Wolf E. Principles of Optics, 3^{rd} edition, Pergamon, (London, 1965)

de BROGLIE, L. Interpretation of quantum mechanics by the double solution theory, Annales de la Fondation Louis de Broglie, Volume 12, no.4, 1987 This is an English translation by Maurice Surdin of Foundations of Quantum Mechanics Rendiconti della Scuola Internazionale di Fisica "Enrico Fermi", IL Corso, B. d'Espagnat ed. Academic Press (N.Y.1972) http://www.ensmp.fr/aflb/

Chandrasekhar, S. Ellipsoidal figures of equilibrium, Dover, (New York, 1987) http://www.nobel.se/physics/laureates/1983/ chandrasekhar-autobio.html

Elkana, Holton (Ed.) Albert Einstein, historical and cultural perspectives, Princeton University Press, (Princeton, 1982)

Einstein, A., Zur Elektrodynamik bewegter Körper, Annalen der Physik, 17, 1905. Translation into English can be found in (Einstein et al, 1952) and at http://www.fourmilab.ch/etexts/einstein/specrel/www/

Einstein, A., H. A. Lorentz, H. Weyl, H. Minkowski, The Principle of Relativity, English translation by W. Perret and G. B. Jeffery, with notes by A. Sommerfeld, Dover reprint of 1923 (New York, 1952)

Huygens C., Traité de la Lumière, (Leyden, 1690) http://www.univ-lille1.fr/culture/archives/ lna/35/txt/Huygens.html

Lorentz, H. A., Electromagnetic phenomena in a system moving with any velocity less than that of light, Proceedings of the Academy of Sciences of Amsterdam, 6, 1904

Minkowski, H., Space and Time, Address delivered at the 80^{th} Assembly of German Natural Scientists and Physicians, at Cologne, 21 September 1908. Translation into English can be found in (Einstein et al, 1952).

Planck, M., The Theory of Heat Radiation, especially Chapter 1. 1914. Authorized English translation by Morton Masius, Dover reprint (New York, 1991).

Rindler, W., Introduction to special relativity, Clarendon Press (Oxford, 1982)

Ryckman, T. A., "Early Philosophical Interpretations of General Relativity", The Stanford Encyclopaedia of Philosophy (Winter 2001 Edition), Edward N. Zalta (ed.), URL = http://plato.stanford.edu/archives/win2001/entries/genrel-early/

Swoyer, C., "Relativism",* **The Stanford Encyclopaedia of Philosophy (Spring 2003 Edition)**,* Edward N. Zalta (ed.) http://plato.stanford.edu/archives/spr2003/entries/relativism/