Editor's analysis · 30 October 2026

The Rydberg constant and time dilation

The argument below gives R(v)/R(0) = (2 − β²)β³, which equals Einstein's time-dilation factor β multiplied by (1 − v⁴/c⁴). The two agree to order (v/c)², so the experiments of 1995 could not tell them apart, as Aspden said. Fast-ion experiments now can: lithium ions at 34% of the speed of light match time dilation to ±2.3 parts in 10⁹ (Botermann et al. 2014), where this formula predicts a 2.6% shift. The earlier version in Physics Unified (1980) predicts 0.8%. Both are excluded. An aether theory need not fail this test: Lorentz's aether electrodynamics gives time dilation exactly.

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Aether Science Papers: Part I: The Creative Vacuum
Pages 41-47

Copyright © 1996 Harold Aspden

ATOMIC SPECTRA AND THE MOVING ATOM

Energy deployed in electrodynamic interactions is physically separate from the electric field and cannot be recovered fast enough to affect photon emission. An atom moving at speed u then has a spectral redshift proportional to 2β2-β3, where β is (1-u2/c2)1/2, identical to relativistic time dilation, apart from minor differences of order (u/c)4, but the latter put the relativistic interpretation in doubt.

The Australian Defence Science and Technology Organisation based on a study by their Electronics and Surveillance Research Laboratory has recently issued a report [1*] which urges an aether-based treatment of space and time measurement.

That report does not, however, contribute any new insight into the physical processes which regulate the time keeping of the atomic clock in motion through space. It assumes that clocks are slowed by the factor β of (1-u2/c2)1/2 and that the momentum of a particle of mass m takes the form mu/β, where u is the velocity of the clock in the aether frame. The argument then develops from these assumptions using non-relativistic doctrine.

However, in the debate between relativity and aether, the fundamental question concerning the time-keeping of an atomic clock is not the issue of whether time itself is speed-dependent, since 'time' has no feature which can be said to have a speed, but the effect of motion on the clock 'mechanism'. In the case of the atomic clock the issue is whether the electrodynamic interaction between the nucleus and the electrons in an atom is dependent upon the translational motion of the atom at that speed u relative to the aether or the observer at rest.

There is the equally important question concerning how energy deployed in the field surrounding the atom can be collected in a package fast enough to be shed as a photon, which is the signature of the action we see as defining frequency and which we interpret as time. Note that a photon emitted by an atom changing between specific energy states can hardly be something that waits for the atom to recover its field energy and then stores the energy about to be released until it has all been collected and packaged for emission. That would need another secondary theory to determine the delay time, the storage mechanism and the nature of the ultimate trigger permitting its release. This confronts us with an impossible task, bearing in mind that the deployment of the atom's field energy in its ground state is spread over an indefinite range and supposedly affected by field retardation in the ever-changing positions of the atomic electrons.

The answer to the first question is that we do not know from our laboratory experiments on charge interactions how two discrete electric charges in motion relative to the laboratory frame interact in force terms, because all our experiments smear at least one of those motions into a circuital current form. As to the second question, the easiest answer, and the only logical answer for a physicist impressed by the sharpness of frequency of spectral lines, is to say that the motion-related distributed field energy just cannot be redeployed fast enough to affect the emitted photon. The energy component attributable to the electrodynamic interaction is not part of the photon emission. It must be energy that is lost by adding entropy to the field environment, the so-called 'zero-point field', but energy which no doubt can somehow be regenerated, repackaged and shed back to matter-form as part of a process of thermal equilibrium prevailing in atomic matter at a steady mean temperature.

There are many researchers who are now looking to the aether as a way forward in explaining certain energy anomalies that are creeping into their experiments and this makes the issue raised by Edgar [1*] topical. The reason is that it seems that energy can become divorced from a specific atomic connection and stored in the aether pending gradual recovery from a quantum-electrodynamic field coupling between atomic electrons and the aether, and in this one sees a link with the problem of the atomic clock.

The object here is to show that the above answer to the second question, when taken in conjunction with the facts of experiment concerning the atomic clock, can lead us towards an answer to the first question. It shows us how to avoid the problem of that 'smearing' action by verifying that the component electrodynamic force action between two charges as attributable to their translational motion at a common velocity u is, contrary to the Lorentz force law, at all times the same and is directed along a line drawn between the two charges.

In atomic theory one of the primary inconsistencies is the notion of a quantized unit of angular momentum, having regard to the fact that mass can vary as a function of β. We find that electric charge is quantized and this would suggest quantization of magnetic moment rather than angular momentum. To bring reconciliation the logical step is to realise that the mass added by motion is seated in the materialization of a kind of 'ghost' particle system. This is that of the fleeting and transient statistical presence of pairs of oppositely charged leptons which can be said to have mass-energy accounting for the kinetic energy of the source charge.

Separate from the kinetic energy of the individual charges, the electrodynamic action between charges in motion then becomes a collective action seated in a local reference frame defined by that 'ghost' world. It involves field energy which one could say is 'mutual kinetic energy' but which, unlike the kinetic energy of a discrete charge, cannot itself contribute to mass, because it has no overall motion relative to the governing frame and so cannot augment the lepton population.

The Bohr theory of the atom affords the easiest presentation by which to bring these factors into perspective in determining how the translational motion of an atom might affect its spectral emission.

The Bohr theory assumes a conserved angular momentum for the atomic electrons when there is no spectral emission or event affecting the energy state of the electron. In Newtonian mechanics a conserved angular momentum is the consequence of a centrally-directed force and energy conservation. It makes sense therefore to regard the atom as conforming with both the Bohr and Newtonian conditions between such events and to assume that the regulating quantization of charge velocity moment occurs as a kind of reset action at times of energy transition. Implicit in this is the underlying requirement of that centrally-directed force, by which any electrodynamic action between the atomic nucleus and an electron must act along the line joining those particles, as does the force of gravity.

If these assumptions are correct, then we should be able to derive a satisfactory explanation for the observed electrodynamic redshift of the spectrum of the moving atom without making assumptions about time dilation.

The magnetic field energy associated with the electrodynamic force cannot be recovered from the surrounding field fast enough to contribute to the frequency characteristic of an emitted photon. However, the related electrodynamic force action does prevail in the periods between such emission. The radius of the orbital component of electron motion in the atom is affected by that and so depends on the translational motion of the atom, with a consequent modification of the Coulomb interaction energy as between nucleus and electron.

As is well known from the Bohr theory of the atom, the energy shed in emitting a photon is determined as the change of the Coulomb interaction energy as offset by half this amount owing to the corresponding change of the kinetic energy of the electron. If, however, the electrodynamic interaction causes the Coulomb attraction to be offset by a factor (u/c)2, then the force which determines the orbital radius of electron motion changes in proportion to β2. The result of this is to adjust the energy state governing the photon to relate to the Coulomb interaction energy as offset by a factor β2/2. However, note that the Rydberg constant, as derived by Bohr theory, is proportional to (Ze2)(Ze2me), where Z is atomic number, e electron charge and me electron mass. The first Ze2 term in brackets corresponds to the energy of the charge interaction but the second such term is really the result of calculating the electron's distance from the atomic nucleus. This latter distance is changed in proportion to β2 owing to the electrodynamic forces and further in proportion to β owing to the centrifugal effect of the increase in mass me with speed u.

The net result of these β2-dependent modifications is to change the Rydberg term in proportion to [2-β2](β3), which is 2β2-β5. This corresponds to a reduction of emission spectrum frequencies with increasing speed u of the atom.

Now, when this is compared with the relativistic time dilation factor β we find that the differences only appear in the fourth and higher order terms in (u/c). These are too small, given the flow speeds of atoms used in experimental tests for the findings to be capable of interpretation as proof of the time dilation hypothesis. Such evidence of slight discrepancy, as has been reported for the relativistic formulation, gives support for this author's proposition that aether-based electrodynamic principles offer the true explanation.

Indeed, there is an underlying and compelling argument in favour of the interpretation based on the non-relativistic case, because if the u-dependence of the atom's time keeping were based on the Lorentzian formulation of eletrodynamic force, which is consistent with relativistic formulation, the β2 term introduced above would become time-dependent during the period taken for the electrons to move around their orbits and its effective mean value would be much reduced. Yet, it is the assumption that the electrodynamic force between electron and atomic nucleus is a direct interaction force along the line joining them, as required for compliance with a gravitational action, and is constant for action between charges sharing a common motion component u, that results in a redshift in accordance with experimental observation.

As the author has shown elsewhere, for example in reference [2*], the known empirical data governing electrodynamic action results in the relevant force law, because two interacting charges cannot develop a turning couple by their mutual interaction and because their interaction with ever-present charge activity in the background field environment can permit energy exchanges with that environment. Such energy exchanges are, in the general case, associated with out-of-balance linear force actions. The law derived by admitting such imbalance of action and reaction nevertheless assures full balance of action and reaction for the specific case where the two interacting charges have no relative motion.

This is evident from reference [2*], where it is shown that, since the Neumann potential contains the total energy we associate with the electrodynamic interaction, any force component not represented by this potential must either do no work or do work in such a way that the relative velocity of the two charges is not affected. The Neumann potential component of the resulting force law has a symmetry owing to its (v.v')r form by which the force acts along the charge separation vector r.

It would seem, therefore, that when such electrodynamic force action is applied to the atom there is a strong case for regarding the spectral redshift from atoms in rapid translational motion transverse to the observer's line of sight as being not an indication of relativistic time dilation but rather evidence contributing to the empirical data which determines the true law of electrodynamics. The form of law so determined is compatible with the action of gravitation and so this is a step forward in the quest to resolve the long-standing problem of unifying electrodynamics and gravitation. The so-called theory of 'field unification' may not, in the end, be a theory concerning 'fields' as such, but rather a theory in which energy and force are seen as separable from the 'field' at times when there is spontaneous release of energy quanta.

The development of the theory of retardation governing actions between electric charge in relative motion and particularly the separation of the Coulomb action from the electrodynamic action has been addressed by this author in a recently published review paper [3*]. The detailed analysis and presentation in that paper are wholly consistent with the new theme presented above.

Finally, it is noted that the assumption is often made that the enhanced lifetime of the mu-meson with speed is evidence of time dilation. This is not a valid assumption. As seen by an observer at rest in the lepton-pair creation frame which characterizes the applicable reference frame in electrodynamics, the mu-meson has a mass enhanced by speed and attributable to transient pair creation of mu-mesons. The chance of total decay of this mu-meson complex is reduced by the increase in the mu-meson population, the measure of chance and the overall mass incremented by speed being in inverse proportion. If mass increases in proportion to 1/β, so the lifetime of a lepton subject to natural decay is proportional also to 1/β, because the chance of decay has reduced in proportion to β.

Since we have above seen the Lorentz force law come under challenge even though it is unaffected by transformation between inertial frames and this is generally seen as its supporting feature as based on relativity, a note is added below as an Appendix to justify this challenge.

Appendix

If the Lorentz force formula holds in one inertial frame it will, as Edgar [1*] shows, hold in all such frames, given the assumption that momentum is conserved as between lossless colliding particles. Implicit in this, however, is the assumption concerning momentum that we are dealing in mass only and this overlooks the fact that the Lorentz force is concerned with electric charge.

Conservation of angular momentum about a centre of motion is solely a consequence of motion of mass under the action of a centrally-directed force, given that energy is conserved. When two electric charges come together in a collision they are subject to mutual force action before they collide and the electrodynamic component of this action is determined by energy which is a function of the square of their relative charge velocities, v'-v. This energy together with kinetic energy and electrostatic Coulomb interaction energy is conserved and one can adduce from this that, since the energy is the same before and after collision, but there has been a redeployment, the two mathematical solutions of (v'-v)2 apply to the two respective states. In other words, the relative velocity of the two charges after impact is -1 times the relative velocity before impact.

In Newtonian mechanics, which do not concern electric charge, this circumstance of lossless collisions was derived as Newton's Rule from the assumption of conservation of linear momentum. However, the physics is that of particles which are in their underlying structure nebulous entities of electric charge. By approaching the problem from the electrodynamic aspect one then sees how Newton's Rule takes priority over the momentum conservation principle and in fact we can see that momentum is conserved solely because we have an electrodynamic action between two colliding particles and no net energy transfer to or from that two-particle system in the process.

In the real world, however, there are numerous systems of charge in motion and there is inevitably an ongoing exchange of energy between those systems. The physics of the notional two-body problem do not govern the electrodynamic interactions of a system of electrical charge in motion. However, from the physics applicable to electrodynamic actions between two charges if generalized to permit energy exchanges with surrounding charges, one can derive the solutions to problems in mechanics relating to force action between two bodies, each comprising a neutral cluster of many charges.

The heart of the problem which besets the Lorentz force law is that it does not, in the general case, satisfy Newton's Third Law but it is accepted because it satisfies the transformation rules which suit relativistic doctrine. The electrodynamic law derived in reference [2*] gives results identical to those based on Lorentz law when applied to closed circuit interactions. Contrary to the Lorentz situation, it also gives the correct form of the law of gravity, even with the planetary perihelion refinements [4*], when applied to charge systems sharing a universal jitter motion, the causal physical basis of Heisenberg's Principle of Uncertainty. The 'universal' factor is one for which a component of motion shared by all charge is a common velocity u, as used in the above analysis. The electrodynamic force of mutual attraction acting directly between the charges in the atom, has a gravitational counterpart for mutual actions between atoms, but in the latter case the charges involved are those of an overall-electrically-neutral virtual charge population that keeps the dynamic balance with that common jitter motion of matter.

We need, therefore, to question the current acceptance of the time dilation hypothesis by reexamining the electrodynamic interactions within the atom.

References


[1*] R.S. Edgar, 'Field Analysis and Potential Theory: Part 3', DSTO Report RR-0017, Australian Government Defence Science and Technology Organisation, December 1994.
[2*] H. Aspden, 'A New Perspective on the Law of Electrodynamics', Physics Letters, 111A, pp. 22-24 (1985).
[3*] H. Aspden, 'Retardation in the Coulomb Potential', Physics Essays, 8, pp. 9-28 (1995).
[4*] H. Aspden, 'Physics Unified', (1980), Chapter 2, Sabberton, P.O. Box 35, Southampton, England.

In connection with the above paper the following referee statement was provided with the letter of rejection received from Physics Letters:
"Manuscript Ho738:
Atomic Spectra and the Moving Atom, by H. Aspden

The paper is very nicely written but I do not think it is physics, more science fiction. The author is clearly very open minded about the foundations of his subject, being willing, apparently, to jettison relativity, quantum mechanics, even conventional classical electrodynamics. However, since these theories are accepted by almost everyone else, he must provide very strong arguments, which should be explicitly mathematical and include convincing detailed sample calculations, before a physics journal such as Physics Letters A should publish the ideas. I insist on the need for mathematical formulation of the ideas because it is all too easy to be carried away in a verbal phantasy which has only the lexicon of physics but none of its tight logical structure."

The accompanying letter on behalf of Physics Letters A was dated 26 September 1995 and signed by Professor P. R. Holland of the School of Interdisciplinary Sciences at the University of the West of England in Bristol. It read:
"Please find enclosed the response from the referee(s) on your paper. We regret that on the basis of the referee's report your paper is not suitable for publication in Physics Letters A. We must therefore unfortunately decline it. Thank you for submitting your work to our journal."

I note that I did enclose with the submitted paper copies of the two references to my prior published papers in Physics Letters and in Physics Essays that I identified in the submitted paper. Both had that 'explicitly mathematical content' and, indeed, I deem the analytical account presented in the submitted paper as being quite explicit in a mathematical sense, especially as the logic of the few equations used in the Bohr Theory of the Hydrogen atom is so elementary and so well known.

So, there you have it! Physicists are so well satisfied with their theory of relativity and its 'tight logical structure' that they would rather stay looking for their Holy Grail, their hoped-for Unified Field Theory, without listening to someone who points his finger directly at the weakness in what they adopt as their logical picture of the moving atom. They have failed to see that the electrodynamic force as between two discrete charges in motion reveals itself very clearly in the radiation spectrum emitted by a moving hydrogen atom as having a form wholly consistent with that of the force of gravity in that it acts directly along the line drawn between the two charges. Yet, when this is drawn to their attention, by inferring that the spectral redshift is the signature of an electrodynamic effect, rather than being a 'time dilation' phenomenon, they choose to regard the argument and the evidence as 'science fiction'.

Can you wonder, therefore, why this author has now resorted to experimental investigation aimed at extracting energy from the aether that the learned professors of physics say is an illusion?