Another approach to relativity 17/12/2022
Pascal DUBOIS
Keywords: special relativity; general relativity; gravitation; gravitational field; energy; mass; equivalence; invariance; clock; synchronisation; limiting speed; time dilation; photon; frequency; spectral shift; curvature; Mercury; Einstein; Schwarzschild metric; Pound and Rebka; Shapiro.
In the theory of special relativity, the principle of relativity (invariance of the laws of physics when changing a Galilean reference frame) and the universality of the speed of light (independence from the reference frame and the speed of the source) imply that the clocks of two reference frames in relative motion appear to be out of sync. Apart from this desynchronisation, the equations for changing coordinates (Lorentz formulae) show a dilation of durations and a contraction of distances from one reference frame to the other.
Several physical phenomena, such as the delay of clocks in motion or the increase in the lifetime of atmospheric muons compared with muons at rest, are in agreement with the predictions of the theory and give reality to time dilation, according to the commonly accepted interpretation. It is implied that the systems under consideration are not affected by their rectilinear and uniform motion: in particular, clocks continue to deliver the same unit of time.
From our point of view, this phenomenon of time dilation constitutes a real point of contradiction, since observers of one reference frame are justified in maintaining that time really does pass more slowly in any reference frame in rectilinear and uniform motion compared with their own reference frame.
For its part, the theory of general relativity uses a curvature of spacetime, produced by the distribution of energy, to account for gravitation. In this way, it fully explains phenomena such as the advance of Mercury's perihelion or the curvature of light rays close to the sun, which can be observed during eclipses.
The starting point for this paper is the search for an answer to the following question: without calling into question the principle of relativity, is it possible to construct an alternative, noncontradictory theory that does not involve distortions of space and time?
After a reminder of the synchronisation of clocks in Galilean reference frames and the establishment of the equations for changing coordinates between reference frames within the framework of special relativity, we examine the notion of event and propose an alternative analysis that is consistent with an absence of dilation of space and time. The change of coordinates is no longer onetoone.
On the basis of the principle of equivalence between mass and energy and the fundamental law of (relativistic) dynamics, we propose a second analysis that supports the previous one. It leads us to question the principle of invariance of mass at rest, which is accepted in the theory of special relativity as it is in classical mechanics.
We present an alternative to this principle: the energy imparted to a particle (in a given reference frame) to set it in motion is conserved in the reference frame where the particle is at rest. The invariant is no longer the mass at rest, but the total energy of the particle. This hypothesis is consistent with the absence of dilation of space and time.
The phenomena mentioned above then appear to be the consequence, not of time dilation, but of the variation in energy at rest from one frame of reference to another. Since the atoms in the clock that is set in motion have greater energy than those in the clock that remains stationary, these two clocks no longer deliver the same unit of time[1].
One chapter is devoted to the consideration of luminous phenomena, comparing the new approach we are proposing with that of special relativity.
The hypothesis of noninvariance of rest mass naturally leads us to consider that gravitation can have an influence on it: the gravitational shift of clocks is interpreted as a consequence of the variation in the rest energy of atoms as a function of their distance from the gravitational source. This implies that gravitation and acceleration cannot be considered to be completely equivalent.
We show that this hypothesis makes it possible, in the case of weak gravitational fields, to formulate simple laws while remaining within the framework of dynamics without spacetime deformation :

the variation in the potential energy of a particle, with zero or nonzero mass, is proportional to its total energy;

the variation in total energy of a particle is equal to the inverse of the variation in potential energy plus the work of external forces, if any;

the rest energy of a particle of nonzero mass varies with its distance from the source. In the absence of external forces, the variation in energy associated with rest energy and the variation in energy associated with momentum are each equal and opposite to half the variation in potential energy;

the fundamental law of dynamics can be applied to determine the relationship between the variation in the momentum of a particle of nonzero mass and the corresponding variation in energy under the effect of the gravitational field;

particles of zero mass are slowed down as they pass through the gravitational field.
With these laws, the physical phenomena that have been experimentally verified are correctly explained, including the Shapiro effect. There is a difference with the theory of general relativity in the evaluation of the gravitational spectral shift, but the result of the Pound and Rebka experiment is still explained.
In conclusion, the note explains the similarities and differences with the theory of general relativity by referring to the Schwarzschild metric.
One conclusion, valid for both special and general relativity, could be as follows: the postulate of invariance of mass at rest forces us to deform space and time in order to simulate the energy variations taken into account in the new approach proposed.
A gravitational field model justifying the laws proposed for weakfield gravitation is presented in a separate note entitled "Gravitational Field, Fundamental Principle of Dynamics and Quantum Mechanics". This model also makes it possible to take into account a problem that is not limited to two bodies and to envisage an extension of the laws outside the weak field.
There is, of course, a fundamental question that may call into question our current representations of matter and energy: since we accept that particles of the same type can have different rest energies, what does this difference in energy physically correspond to?
[1] at least for an atomic clock