N.B. This paper was written prior to the author's being made aware of further literature that convincingly contradicts some of the cited and widely accepted evidence held to confirm the predictions of relativity.
Tom Milner-Gulland
25th February 2003
Recent papers have cast considerable doubt on the reliability of the empirical evidence to support general relativity. The aim in this paper is to present a broad-ranging critique of theory of relativity, exposing its logical inconsistencies, yet showing also how the use in the general theory of the idea of geodesic (a misnomer by this account) may have considerable potential for making predictions for increase in a body's mass with increase in velocity, even under the concept of absolute time. The focus in the main is on the relativistic conceptions of time and motion; the Einsteinian conceptions of time, relative motion and non-Euclidean geometry are rejected, to the effect that the principle of relativity can be seen to be untenable. The final section develops a novel conceptualisation of the cosmos, designed to arrive at a depiction of the conservation of energy in a macroscopic context.
That general relativity (GR), of 1916, is based upon the earlier special relativity should not necessarily mean that all its elements are untenable if special relativity (SR) is fundamentally flawed. Einstein formulated SR on the uncontested premise that momentum is invariably conserved in natural processes. The first postulate, or principle of relativity (common equivalence among all inertial reference frames, of physical processes) Brown (1967) traces to a 1902 work by Poincaré. The second postulate (common constancy among all inertial frames, of c) was inherited from the Maxwell-Lorentz theory of electromagnetism. Evidently the latter was problematic in the context of GR since, as Dingle (1972) notes, Einstein says at the beginning of his 1916 paper, ‘It will be obvious that the principle of the constancy of velocity of light in vacuo must be modified’ (p.175). Relativity can barely be understood as a congruous sequence of ideas; Essen, 1971 (p.23), remarks that ‘Einstein makes implicit assumptions that are additional to and contrary to his two initial principles’ and points out further that Einstein gives no logical reasoning in his switching between the apparent effect and the physical, in the transition between SR and GR (p.20).
An introduction to some fundamental issues and an innovatory field
One chief area of dispute, for which this account will seek to propose a solution by way of a consideration of concepts introduced in GR, resides in the possibility that a body’s mass will increase with increase velocity. Believed by many modern physicists not to hold, the mass transformation is inferred from the equation E=mc². The latter equation appears to have been posited initially by Poincaré in 1900 (Brown, 1967); why it should ever be deemed integral, as opposed to incidental to the conceptual innovation of SR, is unclear. If integral it indeed is, the issue of whether or not a mass’s energy content includes translational kinetic energy would seem pivotal. If the mass transformation holds, then physical processes can serve to distinguish between reference frames, since the gravitational attraction between masses will vary with a system’s velocity.
If photons are physical entities, the fact that relative motion between an emitter and a reflector has no effect on light’s speed when it is reflected back to its source is incongruous with kinematics. In that the fundamental constants of nature are set rigidly in a balance to which material properties must conform, this can be seen to yield issues associated with the idea of space-time geodesic. Geodesics, we shall establish, can be conceived as a conditioning that renders kinetic energy immediately forceful. This can be understood as follows. A body’s kinetic energy does not of itself have a bearing on its material constitution, yet the acquisition of any other form of energy (save gravitational field energy, which we shall deal with through the same analysis) would so affect it, through the action of force. Logically, therefore, when a body acquires kinetic energy, such energy must be represented in a magnitude of force, over and above that which it exerted initially (as through gravity), that it exerts upon all other masses in the cosmos. This effect we shall seek to investigate in the final section. However, it is significant that the energy embodied in a photon and the rate of occurrence of electron transitions (oscillation) in atoms, are bound in a relationship that is responsive to the emitting body’s acquisition of kinetic energy. It is in virtue of the prevalence of this relationship that the apparent flaw in Einstein’s conception of time has been overlooked. The confusion has evidently arisen through the fact that the fundamental constants perform the same operation of balancing energetic quantities that they would were it that the energy of a single photon was in reality kinetic energy (as is intrinsic to all material particles) and from the point of view of a receptor, the energy will increase or decrease in relation to the phenomenon that Einstein considered to be the variable flow of time.
It should be remembered that the reality of space as anything more than a synthesis of the mind, laden with metaphors in the form of observable effects, has yet to be established. In view of this, where gravity is observed to affect the properties of a photon, it should be considered to signify the action of a locally exerted force (gravity) upon all matter in the cosmos, the consequences for photon properties being a mere metaphor for the entirety of this effect. Accordingly, Brown (1967) deprives Einstein of great credit even for the idea of gravitational red shift, asserting that it follows from Mach’s principle.
In the Minkowsky idea of the space-time geodesic, which was adopted in GR, time-like geodesics of free particles are conceived to exist in a conformal relationship with the null-geodesics of light (Disalle, 1995). Fundamentally, both an increase in velocity and also an increase in strength of gravitational field exerted upon a body are associated with the dilation of the average time span between electron transitions in its atoms, the latter measure being taken in relativistic physics as the basic unit of time. Objections have been expressed by Dingle, 1972, who considers it improper to interpret particles as clocks (p.34), and Essen, 1971 (p.7, p.13), who views variations in such so-termed time as the mere changing of units employed. Dingle, echoing Brown (1967), is concerned with the 'clock paradox' in SR wherein, if motion is purely relative, two clocks can both run slower than each other (p.34). Essen articulates that the two sets of pulses emitted (and received reciprocally) by each such clock, constitute a single cycle of events (cf. p.14), and if differential ageing between individuals (as can be substituted for clocks) occurs by virtue of a change of units rather than velocity itself, ‘symmetry no longer exists and the relativity postulate is not valid’. Einstein did concede that there was a conflict with the principle of relativity (Brown, 1967) and his eventual explanation in terms of accelerations has been shown by Brown (1967) to be fallacious, as, for example, these could be made insignificant by the time span of the experiment.
A preliminary exploration some issues concerning the general theory
A broader perspective, exploring aspects of the general theory, will assist us in an appraisal of Einstein’s conception of time. By way of a consideration of a mass that is a hollow sphere situated in free space, it can be established that mass does not in itself cause motive gravitational attraction of one body to another. Vector Calculus will ascertain that for a body situated anywhere inside the hollow, the motive gravitational attraction upon it, toward any particular point on or in the shell will, if the shell is of uniform density and thickness, be annulled by a net equal and opposite force of gravitational attraction from matter in the same shell, irrespective of the shell’s thickness. However, the gravitational field of every constituent particle of the shell must nevertheless be retained in all directions in spite of such counteraction. Its representation inside the hollow will take the form of a potential that will be expressed as relative time dilation in any matter residing in the hollow. This demonstrates that gravitational acceleration is not attributable to the so-termed stretch of space-time per se, but rather to local directional change in the stretch over distance. (In this account I speak in terms of the stretch of space-time purely for the sake of convention.)
Let us consider briefly the speed of transmission of compression waves, which signify the process by which momentum is transferred, in a specified medium. All things, save so-termed atomic time dilation, being equal, such a speed must be invariant since their rate of propagation is governed by the fundamental constants of nature. We shall seek, in this account, to establish the existence of a single momentum-based time flow that is invariant and essentially Newtonian in concept. If such is a reality, the argument for a non-Euclidean space-time will be untenable, as will the basis for relativity itself.
In GR, Einstein postulated the equivalence between inertia and mass. Although ultimately he deemed rotation, gravitation and acceleration all equivalent, it remains evident that the properties of any one of these, in relation to a body subjected to it, could simply be considered an expression of the exertion of force, if so-called resultant forces such as centrifugal force are not taken to be fictitious. Ellis (1965, in Hunt and Suchting, 1969) argues that the distinguishing of a force is founded in convention and he opens enough doubt, even in Hunt and Suchting’s treatment of him, to enable such a shift in conceptual orientation. Einstein’s contribution is valuable, however, in demonstrating how the attributes of the photon (a chief influence upon which is atomic time dilation) unite the properties of gravity and relative motion. It is a point to be entertained by philosophers that ultimately in physics there is no distinction, save on a subjective level (whereby direction is apprehended), between a relative attraction of one material entity to another and a relative repulsion exerted upon it by all other material entities save that to which it is impelled, and conversely. Hence there is no privileged status to be conferred upon any specific source of impetus, save the pre-existent energetic properties of the universe. Accordingly, while gravity is a force of attraction, inertia acts in opposition to (nongravitational) accelerative forces, the difference between the two expressions of mass being in essence an observer-based phenomenon a fuller understanding of which will incorporate the net repulsive force of the totality of nongravitational energy.
An examination of the space-time geodesic
A space-time geodesic is represented in the relationship between the path (in this account, this includes changes in velocity) of a force-free body, and the local gravitational gradients that act upon it. To increase a body’s kinetic energy is to supply it with a degree of resistance towards local gravitational influences; this is one phrasing of the logical interpretation of Newton’s bucket experiment that demonstrated gyroscopic inertia. According to Mach’s principle, inertia is definable as a body’s immediate interaction with all other matter in the universe. Subsequent to the addition of kinetic energy, the inertia of a body becomes proportionally more influential with relation to its trajectory in that it will follow a closer approximation to a rectilinear course, local gravitational fields being less influential. Escape velocity is put into context here. A celestial body will be more resistant to the gravitational field of another celestial body merely by virtue of an increase in its kinetic energy, and where this is the result of a nongravitational force its geodesic will be correspondingly changed. The resistance to local gravitational fields may, then, be said to be a freely moving body’s capacity, which in many cases is to be realised by way of a deflection its path, to move counter to the ambient gravitational gradient.
Einstein says in a 1920 lecture, ‘The general theory of relativity teaches that the inertia of a given body is greater as there are more ponderable masses in proximity to it’ (1922, p.42). The issue of time dilation served to mislead Einstein into the belief that momentum is conserved by way of an increase in mass in a body when it is brought into proximity to another, and in this regard GR conflicts with empirical evidence, by which precisely the converse effect seems to occur, owing to so-termed (gravitational) self-energy. Hence the energy-mass relation is seen once more to conflict with the logic that Einstein developed in relativity. Orbiting bodies are on a geodesic; the mass-energy they possess remains constant but their velocity may vary through a translation between kinetic energy and gravitational potential (or self-) energy, hence these two forms of energy could be termed ‘geodesic energy’.
Gravity and nongravitational energy
Save that the morphology of space-time distinguishes gravitational fields from other embodiments of energy, there is a subtle flaw in the idea that a fundamental distinction exists between nongravitational and gravitational acceleration. The underlying issue is of a force’s property of being local, in that it cannot be applied with perfect uniformity throughout a body. To undergo the sensation of g-force occurring by virtue of an attached source of propulsion is to sense compression of the components of the anatomy, occurring on account of their inertia. However, were it possible to engineer a system whereby all the atoms were subjected to a nongravitational force of acceleration of uniform magnitude and direction, the effect would be indistinguishable from free fall, ignoring internal gravitational gradient. In such a scheme the idea of uniform motion is meaningful only in relative terms, and this is exhibited in the photon properties that are a consequence of the spatial relationship between emitter and receptor. Furthermore, a natural inference from the same scheme, broadly in line with Ellis’ (1965) discourse (in Hunt and Suchting, 1969), is that in neither case can any force be definitively discerned and that force is merely a concept that enables a quantitative prediction of the constitutional and thermal changes within matter that result from the relative energetic conditions of masses. A point that seems to elude many post-relativity commentators on the reality of motion, such as Miller (1936), is that one can consider motion to be absolute in so far as quantification and spatial relations are meaningful, yet, also, energy to be a more fundamental concept than either force or motion. Insofar as the passage of light is a real phenomenon, as a fundamental constant of nature the speed of light is integral to the structure of matter. Given what is known about c in relation to reference frames, this means that motion, insofar as it itself is real, is likewise.
The principle of equivalence and Einstein’s thought experiments
Einstein illustrated the equivalence between gravity and force of acceleration with a thought experiment involving an elevator in space, residing at a location remote from strong gravitational fields, which is subjected to a force of acceleration. Its contents include an observer. Einstein asserted that the effect upon the contents is indistinguishable from the effect of a gravitational field of a g-force equal to the force applied to the elevator. A development was to envisage attached to one of the inner side walls of the elevator a source of light, the beam issuing from which is parallel to the floor, passing (squarely) across the elevator’s interior. Einstein predicted that to an observer situated externally to and at rest with respect to the elevator the beam would, on reaching the far wall, appear displaced, to a minute degree, in the direction of the apparent fall of the contents, as the target wall of the elevator would have travelled a small distance in the time it takes for the light to reach it. The mathematics associated with the idea is applied with relation to regions where space-time is genuinely distorted; however, the precise role of the distortion of space-time in Einstein’s notion of equivalence remains obscure (the mass of the elevator is not incorporated in the model). Brown (1967) refutes the equivalence principle by showing that, unlike the force produced by acceleration, a source of gravity acts to converge bodies’ paths towards a point.
Another issue is that the time dilation of a body in free fall, occurring in association with both increase in velocity and increasing proximity to mass, will be not apparent in the case of the elevator as it would in a gravitational field; nor is there scope, in Einstein’s depiction, for the gravitational gradient that inevitably exerts stresses upon materials merely by virtue of their spatial extension. The latter issue strengthens the case for gravity’s having the status of a force and is overlooked in Hunt and Suchting’s (1969) contradiction of Ellis (1965) in their view that the argument turns on the gravity-inertia equality and empirical evidence for GR.
However, Brown (1967) says of the 1919 eclipse experiments, ‘This must be one of the most extraordinary self-deceptions in the whole history of science’, on account of the selectivity applied to the data. The same and subsequent experiments, that have generally been interpreted as providing confirmation of GR, have been powerfully attacked by Marmet and Couture (1999), to be given intellectual support by Strel’tsov (2001), and the other significant purported evidence for the validity of GR, the advance in the perihelion of Mercury, has been explained in an exclusively classical formulation by Marmet (1999).
Length contraction
With a little investigation, which we shall undertake shortly, we can appreciate that in actuality the beam of light in the elevator will not be observed to be displaced from the perpendicular, by either observer. In SR, not acceleration but mere velocity as a proportion of c is considered to cause the displacement of a beam of light, in the viewpoint of the observer at relative rest. This point is pivotal to the justification for applying a non-Euclidean geometry, since it is associated with the idea of length contraction. Following Lorentz, Einstein hypothesised that a train travelling at a velocity close to c will, in the viewpoint of the observer at relative rest on a platform, contract in the axis of its motion. Any light that propagates directly from one end of the carriage to the other, from a source rigidly attached to the train wall, will be observed to traverse the distance in accordance with the distance-time equation that lends him the measure of c, and no faster. To such an observer, a photon from this beam would cover the distance at a speed equal to the train’s speed added to c were it that length contraction did not occur. Einstein speculated that only by virtue of the supposed retarding effect (applying even to mental processes) of time dilation would the speed of light, as measured in the frame of the platform observer, be the same as that measured in the train traveller’s frame.
It is should be commented that atomic time dilation has been found to be an objectively recordable reality. Essen (1971) points out that at the end of a section in the discussion of the relationship between a moving and a stationary clock, and from then onward in relativity, Einstein suddenly and without reasoning ceases to qualify, with the phrase ‘viewed in A[’s reference frame]’, the fact that the travelling clock, clock B, will be running slower than a clock A in the rest frame (pp.12-13). Here Einstein evidently overlooks the basic conceptual distinction between the actual and the apparent. It will be futile in any case to claim that such a distinction is fundamental to physics, when contact-sensitive apparatus can record the spatiotemporal characteristics of an experiment as a single, potentially interdependent system of events. If a train’s physical processes are relatively retarded, to a specific factor, on account of the time dilation associated with its velocity, its wheels will be rotating at a correspondingly slower rate and the resulting deficit in the distance the train covers will correlate with fuel consumption, not relativistic concerns. The flaw in SR is evident: time dilation is a consequence of velocity, but velocity is quantified as distance divided by time. As is hinted at by Brown (1967), if processes are in any way changed in a moving body, the difference must be explained in energetic terms. Yet if time dilation is measurable – on account of the constancy of c coupled with the quantity of energy embodied by each photon released in an electron transition – in the reference frame in which it occurs as a physical process, then the principle of relativity is invalid, and in a conceptual sense relativity is a hollow theory.
Einstein justified the idea of a non-Euclidean space-time geometry by applying the concept of length contraction to a disc rotating with respect to a rest frame. The disc will, he speculated, contract in circumference in virtue of its angular velocity. He concluded that for an observer inhabiting the disc, who applies measuring rods at tangents to the perimeter, the ratio of the perimeter to the diameter will not be to the value of pi, as in Euclidean geometry, if the diameter is measured in a rest frame. Immediately, this seems to deny that the body retains its circularity or suggests that it becomes in some way deformed, but this is not considered. Under merely minimal scrutiny, it is in this thought experiment that it becomes most obvious that if length contraction, which must be reciprocal between frames in relative motion, occurs it must be a frame-dependent illusion that would have no bearing on data obtained through contact-sensitive detectors that would serve as interconnecting agents between different frames.
A series of objections to the length contraction hypothesis
Logical flaws abound in the reasoning behind the SR thought experiment. For one, it is notable that the laws of physics would not be indistinguishable between the two reference frames, contrary to the requirement of the first postulate of relativity. Although Einstein maintained that length contraction would be undetectable to the traveller regardless of its proportions, if it occurred to any significant degree the difference would in truth be apparent to the traveller, in the angle by which light reflecting from objects in the carriage will reach his eye. Furthermore, if, as Einstein seemed to believe, this difference is attributable to an actual change in the lengths of material objects, then the geometry of atomic bonding in the train will necessarily be different from that in the rest frame, despite all prerequisites associated with the geometry of electron orbitals, as would the density of the train’s constituent particles.
Moreover, in reality there would be no difference in the sequence of temporal events between frames of reference. A photon is destined exclusively for a single location and will not pass through the mind of the traveller prior to its arrival in the eye of the rest frame observer, so there is no justification for deeming critical the perception of the time interval between the emission and reception of photons. Nor is there anything (as an ether) that can travel with the motion of the train so as to govern the rate of supposed transit of light though a locality, in accordance with time flow in matter in the vicinity. Evans (1969) points out that light waves must, in any such system as Einstein describes, logically have a variable velocity along what by definition is taken to be a straight path, and ‘there is no need to invoke both a temporal and a spatial correction’. Furthermore, as Dingle (1972) appreciates, the presence of observers is irrelevant when clock readings can be photographed and the data viewed later (p.153); photoelectric detectors might be used also.
It is utterly implausible that, say, a projectile launched at the train would be retarded by the relatively slow lapse of a atomic time, such that before striking it, it becomes in some way suspended mid-flight as the train moves, until the relevant number of oscillations have occurred to render the two temporal realities congruent. Two time-separated events will be observed to occur with the same temporal interval between them, and at the same geographical location, by observers in both frames. If we amend the thought experiment involving the train, into a visualisation in which its wheels are cogwheels and the track has corresponding teeth, we can appreciate definitively that no physical length contraction can occur in the absence of the input of energy that will serve to fracture teeth. It could be envisaged, further, that the train’s wheels drive, by geared belts, the hands of clocks attached to the inside walls of the carriage. Because the train’s velocity is constant the clock cycles would be observed to repeat at the same rate for both the travelling and the platform observer and each cycle would correspond to and effectively register determinable track distances covered and, therefore, geographical locations. It also remains obscure as to why the frame-dependent contraction in a single axis, the axis of motion, should bear any relation to the local morphology of space-time.
Light at emission and reception
To assess the plausibility of the idea of light’s possessing a starting velocity, we can return to Einstein’s thought experiment involving the elevator. The language used in relativity lends photons a motion-like transit, so we can hold to this thinking in order to expose its flaws. Suppose that some of the particles emitted at the light source are atoms, among which a single such travels, not perpendicularly to the wall, but directly to the ceiling. Take it also that the elevator is, in this case, at uniform velocity. From the point of view of a rest frame observer, the atom’s kinetic energy, prior to its release, is supplied by the elevator, in addition to which it assumes a kinetic energy on release. A photon from the same source will arrive at the same destination, if it takes the same path, in a shorter time span than will the atom. Were the elevator to be accelerated, thence to acquire, once more, uniform motion, this principle would apply with regard both to the velocity prior to and also to the velocity subsequent to acceleration. Thus a photon must assume the starting speed of the elevator, as does the atom. In the case of the horizontal beam this starting speed will negate the effect of the relative displacement of the target wall. Although this conclusion conflicts with SR, such is nevertheless consistent with the apparent null result of the Michelson-Morley experiment of 1887 (though this result is cause, in itself, for further debate). The anomaly that appears, on the face of it, to characterise the passage of light is that relative recession of receptor from emitter will add to the starting velocity of a photon and conversely their relative approach would subtract from it, to the effect that c, as was shown by Römer (Brown, 1967), at reception is invariant. This thinking conforms with the idea that the emission and reception of light exhibits, by way of the constancy of c, the sense in which motion can be regarded as relative and light cannot lose or acquire speed on reflection from bodies in motion. However, Essen (1971) notes the ambiguity between velocity as a physical process and as a measured quantity (p.50). Therefore the second postulate of relativity is ambiguous even when the relativity of time is not considered. The preferable understanding from the point of view of maintaining the principle of symmetry would be that photon transfer accords to a simple distance-time equation; distance in this case being relative, as the distance of emitter relative to receiver, their velocity being superfluous (though this, it should be noted, conflicts with the well-known Sagnac effect). The conclusion must then be that the physical transit of particles of light is as much a fiction as is the reality of any system of units by which are conceived relative magnitudes – from which, circularly, physicists’ conclusions about the properties of the individual photon are ultimately made meaningful.
The acceleration of the elevator will not affect the distance-time relationship for photon transfer; equivalently, there is no difference in c merely on account of the presence of a gravitational field. Reverting to the issue of the horizontal beam, the same region, which might, were the beam from a laser, become distinguished by a scorch mark at a determinable height from the floor of the elevator, will appear illuminated for both observers. The characteristics of the photon transfer prior to reflection from this region will not feature in the rest-frame observer’s perception, because photons are not observable in transit, if transit they are declared to have; hence there is no basis for supposing the beam will appear displaced.
The characteristics of the propagation of light, in any case, strongly suggest that motion is not a property of photons. Light traverses distances with no accelerative impetus: the laws of motion do not apply. Rather than following, as such, the curvilinear path determined by Minkowsky’s null-geodesic, it seems that, as quantities of energy, photons dematerialise from one atom later to materialise in another, as presumably do all subatomic particles with rest mass, although the latter have, built into their operations, the ‘clock’ of atomic oscillation.
Whether or not space may be considered to be distorted in the vicinity of mass remains chiefly contingent upon one’s definitions. Gravity will continue to act in Euclidean rectilinear lines. A form such as a tetrahedron constructed from solid matter will retain the Euclidean relationships exhibited through its spatial extension irrespective of space-time geodesics, which evidently pertain merely to action between masses.
If the mathematical equations in GR correspond to reality, then atomic time might seem elemental to the geodesic. Irrespective, however, of the nature of the empirical data, the geodesic represents the implications for different bodies of the universality of the fundamental constants of nature. The basic relationship in question must reside in the speed of light’s being a fundamental criterion in the conservation of energy, such that one might perceive a simple triangular relationship between it, photon frequency, and the rate of photon release through electron transitions, while in contradiction to relativity an increase in velocity, so as to approach a local escape velocity, would seem, by the foregoing discussion, to be additive to what might be construed as an absolute quantity of energy possessed by a single photon on release. Indeed, Dorling (1978) regards the issue of time dilation associated with velocity to be one that, even in SR, implies absoluteness in that it gives ‘an independent criterion for identifying accelerated systems’.
Momentum-based time
It may be established that there is a fundamental distinction, not recognised in relativity, to be discerned with regard to the understanding of time. Pendulum clocks measure time with relation to the same Newtonian principles that apply to astronomical cycles. Disregarding friction, a pendulum of specified arm length will swing at a rate that is independent of the mass of its attached weight. The idea that the motion of the weight will be retarded on account of the atomic time dilation associated with its velocity is untenable. One will struggle to imagine the top of the pendulum, that has a faster ‘time’ lapse, swinging many times for every swing of the base of the pendulum, the attachment between them being a solid rod whose atoms exhibit increasingly diminishing time dilation with proximity to the vertex, as their velocity decreases. It might be considered that the arm would break, but this would require the input of an additional force that does not exist. The difference in atomic so-termed time lapse must, then, apply to matter and not space, contrary to GR. Processes sustained by momentum transcend, as a unified system of motion, atomic time lapse as though the universe were a system of integrated cogwheels. Significantly, observers function in accordance with the momentum of biochemical entities.
While increase in strength of gravitational field will increase the rate of fall of a pendulum, accelerating its cycle of ‘ticks’, it will also be associated with a slower rate of electron transitions. Neither system of units constitutes a record of the flow of universal time, the measurement of which is to be achieved most directly by reference to c in a vacuum and rigid measuring rods.
c and inertia
Contrary to the early speculations of relativists, there is no indication in the gradient by which accelerated particles apparently increase in mass that the strength of their gravitational field will increase without bound on their approaching c. The tendency among modern physicists to distinguish between gravitational mass and inertial mass, on account of these more recent findings, inevitably causes confusion with regard to the concept of inertia. The significance of a body’s possessing an intrinsic source of propulsion is to be appreciated in that energy is constrained to a specific rate of propagation and in the case of masses propelled exclusively by sources at relative rest, as this ceiling is approached, naturally the difference between the body's speed and the speed, c, at which energy apparently travels, is diminished. Critically, then, as is broadly suggested by Brown (1967), it would seem that the smaller the difference between a body’s velocity and the speed of light as measured in the frame in which the source of energetic propulsion resides, the greater its resistance towards an increase in velocity, disregarding gravitational influences. The observation that a particle’s inertia will seemingly increase without bound as it approaches the speed of light is therefore explained. This perception might, in truth, involve a misappropriation of the concept of inertia, which denotes resistance to change in motion, not necessarily to an increase in its velocity. When a retarding force is applied, the velocity will become decreased to a greater factor in relation to the velocity increase that would result from a force of equal magnitude applied in the direction of motion. The premise in relativistic physics that increase and decrease in kinetic energy are ultimately indistinguishable, the term deceleration being redundant, would appear fallacious, and shortly we shall strengthen this view with a discussion of the idea of absolute velocity.
The speed of light can be conceived as a synthesis of other fundamental constants of nature, the crucial two such being the gravitational constant and the rest mass ratio between proton and electron (which effectively governs the Planck constant). In these two constants there is embodied the threefold relationship between mass, distance and the structure of matter, and also, by way of levels of nuclear stability, the basis of such critical concerns as the average density of matter. The speed of light, being directly associated with the universal conditions governing motion, will, we can establish, be observed to vary when measured in relation to local rates of atomic time lapse while remaining constant as a measure of momentum-based time.
A proposed geodesic-based justification for the mass transformation
Minkowsky’s concept of a space-time geodesic, adopted in GR, while seemingly something of a misnomer, has great potential for expressing the nature of the relationship between rate of atomic oscillation and mechanical properties of bodies. For the sake of analysis we may envisage an evacuated sphere that has been accelerated thence to assume uniform motion. A beam of light traversing its interior will cover a greater distance than prior to its acceleration, for every unit of atomic time that passes in the sphere, owing to time dilation. In this sense the speed of light could be considered to have increased as a consequence of the acceleration. Thus if a body is given kinetic energy while in the gravitational field of another mass, it will be conditioned by a new geodesic and with such its inertia defers, to an increased degree, to the cosmos at large (as noted earlier), as would be the case were it more distant than previously from any local source of gravitation. Once it has become more distant, much of its kinetic energy will, if it follows a geodesic path, have been translated into gravitational potential energy. One can conceive an imaginary sphere surrounding the real body, demarcating an isometric contour of its gravitational field. In the case where the body is at greater velocity but situated in a stronger gravitational field, as exerted by another mass, for a beam of light to traverse this same three-dimensional contour in the same number of atomic oscillations, the imaginary sphere must expand in diameter. In other words, when a force of nongravitational acceleration is applied to a body, it increases in mass. However, as with the Lorentz transformations, this principle is not dependent on Einsteinian relativity.
The infinitesimal effect made observable
We established implicitly with the example of the hollow sphere that force of gravitational acceleration in itself represents the difference between the degree of so-termed stretch of space-time at one point and that at another, the two points being separated along a line radiating outwards from the centre of gravity of the ponderable mass. When a projectile, launched vertically, approaches its vertex, although to a ground-based observer its speed may appear to diminish, it seems it will nevertheless retain its speed as a proportion of c as measured by atomic clocks situated at different heights in its trajectory. Its speed gradient as measured by absolute time will correlate with the gradient of rate of atomic time lapse, as this corresponds to the gravitational gradient. The difference in rate of atomic oscillation will be infinitesimal between any two locations on its visually observable path; however, observers perceive but a tiny fraction of any object’s absolute velocity (the latter being a term used in astronomy to represent velocity relative to cosmic microwave radiation). The miniscule difference in stretch of space-time therefore has a great effect upon the trajectory of the projectile in the observation of the ground-based observer, who does not, for example, perceive the kinetic energy bestowed upon the projectile by the earth's spin, the rotation of the earth about the sun and so on; in short, there is a fuller trajectory that is not directly observable, which is artificially extended by the launch.
The mass-velocity equality
When a body is at escape velocity its time dilation will be weighted equally between being attributable to velocity and being attributable to gravitation. The properties of the photon and its rate of release, given the various conditions considered in relativity, are a metaphor for an equality that evidently exists between gravity and velocity in reference to atomic time dilation. The sole complication here is that the instantiation of differential magnitudes of mass and velocity (as being greater or lesser than the escape velocity at any location) of celestial bodies is inherently removed from the system of energy conservation that is manifest in photon properties, being generally attributable to imposed cosmological ‘design’. One can take escape velocity to be a metaphor (by way of the fundamental constants of nature) for the expansion of the universe (mutual ‘escaping’ of matter). It will then be evident that a body’s mass, as a self-energy, is representative of its having escaped from an original energetic whole, to which no concept of gravity would be applied. Velocity is the medium of escape, so the acquisition of velocity presupposes the acquisition of self-energy even when a body’s mass is removed from the equation. Any such ‘escape’ must imply, if only in the sense in which the photon is a metaphor for the dynamics of the separation between and mutual adhesion of matter, some ultimate notion of recession, and in order that photons embody a constant quantity of energy on reception, atoms must, as part of the metaphor, adjust their rate of oscillation. The properties of the photon exhibit the unity which the mind imposes, as an integral part of its imposition of ordering, upon the essential truths of nature, such ordering seemingly deferring to the concept of the sphere, with a kind of implicit, nonspatial centre-periphery relationship that bestows upon kinematics a geodesic context. One could argue that cosmological design (which one would naturally interpret as an external influence that develops gravitational relationships) opens the disparity between centre and periphery, since the determinants of rate of atomic oscillation are not exclusively a matter of embodiment of energy.
At the basis of the mass-velocity equality there must be some metaphysical link between matter and motion, yet a more appropriate term than space-time ought to be assigned to its spatial, mutable manifestation. At least we seem here to have found some kind of justification for an abstract notion of gravitational length contraction, albeit that it will not pertain to material objects and, furthermore, cannot be said to be an ultimate fact of nature: a beam of light is effectively condensed into higher frequencies in the presence of a gravitational field.
An argument for absolute velocity
The absoluteness of velocity is established through the notion of escape velocity, if mass is not considered to be frame-dependent. However, Miller (1936) is very typical in stating ‘if we assume that motion and rest are relative terms at best, then it is quite logical to conceive of the sun, the moon, and stars as revolving about the earth as a centre as it is to conceive of our planetary system with the planets revolving around it.’ It will be self-evident that the velocity of every planet is necessarily greater in absolute terms than the velocity of the sun, which logically will not be covering more distance per unit time than the bodies in orbit. There is no defending the notion that the sun might be conceived as being in orbit of all the planets, somehow imbuing each with a diurnal and an annual cycle. Further, the fully and long acknowledged reality of the Sagnac effect, in which the counter-rotation two different light beams, reflected into the form of a loop, accords different arrival times for each, is evidence that distance has both an absolute and a relative connotation.
The concept of the vacuum speed of light can be considered objectively by envisaging a rigid, physical structure serving as a cubic grid that is imposed upon the cosmos for the purpose of measuring absolute distances. If the kinetic energy and direction of every celestial body in the cosmos were to be ascertained on a relative basis then a scale for velocity may be derived and extended to include an absolute velocity of zero, this being the velocity of the grid. The fact that this is impracticable is irrelevant in this context. This system will not perfectly correspond to the correlation between change in a body’s geodesic and change in its kinetic energy, since when the paths of motion and axial spin of celestial bodies are taken into consideration, a projectile’s moving counter to such motion will amount to a net decrease in the absolute distance it covers per unit time. This reinforces our inference that energy, including ‘geodesic’ energy, is a more fundamental concept than motion.
An argument towards metaphysics
From the totality of the above discussion, the striking conclusion that offers itself is that a body possessing an intrinsic source of propulsion can in theory accelerate to exceed c as defined by the distance-time equation by which photon exchange occurs. To assess the concept of rest mass we should be led to contemplate the known phenomenon of the spontaneous, random emergence of particle-antiparticle pairs in a vacuum. The rest mass of any free particle, at the instant of its inception, could be considered to be its total mass minus the energy it has by virtue, not of motive gravitational attraction per se, but of what is conceived as the distortion of space-time. To elaborate, what we perceive as electromagnetic radiation must, at its foundation, be merely a medium for transmitting changes, exhibited on the basis of location, in the frequencies represented through the stimulation of atomic electrons. Miller (1936) interprets Eddington and Einstein to have held the opinion that order between events is dependent upon a mind. From this, we can develop the thesis that matter’s inherent property of seeming to filter the energy contained within the universe, thus to render energy identifiable in terms of specific frequencies at specific locations, is mind-dependent; it evidently yields the travel-time c. However, no concept of a transit of photons need enter into consideration. Energy in its unfiltered form can now be considered synonymous with the substrate, whatever it be, that underlies space-time, thus the distortion of space-time serves to supply a basic kinetic energy, by way of a velocity that is a particular fraction of c, for a free subatomic particle (should such be considered an actuality), in accordance with its rest mass. In a metaphysical line of thinking, it can be supposed that as a concomitant to the filtering effect, which might be deemed a subjectively imposed ordering, it is the spatial character of reality that yields the two phenomena of velocity and mass. In this model, singularity may constitute an outer limit of the universe, to which black holes are a conduit, as in Milner-Gulland’s (1997, p14) metaphysics; the apparent sizelessness of singularity might be taken to be the extreme case of the mind’s contracting of space in the vicinity of matter.
A theory of energy conservation through gravitational instabilities
The question remaining is of how a quantity of kinetic energy at a specified location will be represented at remote locations, in the mechanical operations that occur throughout the cosmos. Relativity offers no general system for mass-energy conservation. If the principle of the conservation of energy holds, it may be inferred that there exists a medium through which the universe’s total energy content is retained in each and every exchange of energy, it being the spatial and therefore gravitational relations between all matter distributed throughout the cosmos. Ultimately energy is represented in changes, occasioned on a local basis, to otherwise predictable paths of bodies. This is exploited in Milner-Gulland’s (1997) metaphysics, through the idea that gravitational instability issues, analogously to a wave front, from point sources, being manifest in the form of disturbances within solar systems (pp126-7). We can develop this idea.
Given that the transference of mass-energy to a body will cause the paths of other bodies to exhibit a relative directional bias toward that body, then every local embodiment of energy must serve as a distorting influence upon the path of every celestial body. It will be over a sustained period that the effect of an energetic exchange will be realised, the distortions in the geometry of local gravitational relationships being relayed successively from one body’s path to the next, gradually to be magnified in each through gravitational acceleration. The model that may be invoked is one in which orbital relationships represent a high degree of gravitational stability between two celestial bodies and the closer an orbit approximates to circularity, the more representative it is of such stability. A body that is remote from sources of gravitation might seem to defy this principle because of the weakness of its gravitational interaction with other bodies. However, it will possess a self-energy, gravitational field energy, classically conceived as gravitational potential energy. Its effect upon gravitational relationships will be disproportionate to the strength of its gravitational field since the gravitational action of a mass (upon another mass) operates as a vector quantity, and it is the balance between such quantities that renders gravitational relationships stable. So it is simply a matter of bias in one’s understanding of gravitational instability: in the latter case the effect upon spatial configurations is more immediately chaotic.
When a body’s kinetic energy is artificially increased, therefore, paths of other bodies are distorted in that, in relative terms, the carriage of their momentum becomes directionally biased, by gravity, toward the accelerated body. When its kinetic energy is then artificially decreased, such carriage must be directed less strongly towards that body, in response to the gravitational fields of the bodies to which its mass-energy has been transferred. Inertia constitutes the response of the totality of the matter in the universe to local transfers of energy, to the effect that, through the distribution of the resulting gravitational disturbances in orbital relationships and the concomitant consuming of matter by singularities, the degree of gravitational instability in the universe remains constant. Gravity, operating in isolation, would contract all geodesics to a single point, and this general force of contraction is apparent in the form of inertia. When considering the incorporation of a temporal component into this model, as it has been shown that we should no longer define units of time in the unqualified terms of atomic oscillations that are currently employed.
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