Evaluating special relativity

As detailed here, the theory of special relativity contains the following components:

Everything is relative, or all observers are equivalent

The constancy of the speed of light

The use of the Lorentz transformation

Physical laws are the same in different inertial frames.

Not all of these stand up to modern scrutiny, and not all have been retained in practice.

## Absolute rest

The cosmic microwave background radiation or CMBR exists at microwave frequencies and is anisotropic, meaning not the same in every direction. This has allowed us to calculate how the Earth would have to alter its motion in order to bring this into balance. This in turn allows astronomers to ascribe a velocity to the Earth and its solar system relative to that background. This motion, as you will find it easy to confirm, is almost a million miles an hour in a direction just south of the constellation Leo.

Whatever this CMBR is, it certainly has this property ‘corresponding to the idea of absolute rest’, and suggests that – as far as we are able – we have discovered ‘the absolute motion of the Earth’. More accurately, and in the parlance of relativity, there is a ‘preferred frame’ in the local universe, and the CMBR is one of the modern observations that requires us to re-examine important earlier conclusions.

## Everything is relative

As detailed here, special relativity was a response to the failure to find or describe a background medium or ether. Its huge advantage over the competing position of Lorentz was that it provided a theoretical justification for the lack of such a background, and a mathematical and intellectual means of living without it.

It stated therefore that, when you and I are in relative motion, and both of us are inertial, then I can consider myself at rest and you in motion, and you take a different view, that you are stationary. As a particular example of this, I see your clock running slow and you see my clock running slow. Who is stationary, who in motion and whose clock runs slow are all relative.

The twin paradox occurs if both clocks are brought back together, because then we must agree on which clock is ahead and which behind. Critics of critics point out, quite correctly, that this cannot occur with the inertial motion described in special relativity, as it would require at least some non-inertial motion to achieve this.

It could certainly occur with orbital motion, considered inertial in general relativity, but, curiously, the paradox has, as far as I can tell, not been discussed for this situation.

The clocks in planes experiment of Hafele and Keating, when analysed with caution, illuminates these points.

## Clocks in planes

The clocks in planes experiment, discussed here, examined the timekeeping of clocks due to their motion. Certain aspects of this observation are incompatible with the theory that it is claimed to validate.

Firstly, the motion was in no sense inertial. None was in straight-line unaccelerated motion, none was free from the effects of gravitation, and all could experience the effect of gravitation and a countering force.

Secondly, there are points in their calculation where they add velocities in a way of which Newton would have approved (the way we normally use away from advanced physics), but that was anathema to both Einstein and Lorentz.

Third, they then applied the Lorentz transformation in non-inertial situations for which it had not been considered appropriate in Einstein 1905. As justification for this they cited the work of Geoffrey Builder in a paper entitled ‘Ether and relativity’ (Australian. J. Phys. 11, 279, 1958), that contained the early statement ‘There is therefore no alternative to the ether hypothesis’.

In their references, they chose not to give the paper’s title.

Fourth, the results were not relative. Observers all agree that the westward flying clock ran fast due to its velocity and the eastward flying clock ran slow.

And fifth, they identified a preferred frame of reference for determining clock timekeeping, namely the non-rotating, orbiting Earth. There is no justification for this in Einstein 1905 or in Builder, but this conclusion has subsequently been adopted by a number of textbooks and websites.

There is justification in gravitational relativity (Einstein, 1915 & 1916) for using this frame of reference for the gravitational effect (as there is in Newton, 1687), but not for the velocity effect. This appears therefore to be an entirely unscientific conflation, adopted carelessly by physics generally.

## The fastest ticking clock

The results of Hafele and Keating show (above) that motion does affect the timekeeping of clocks, in a non-relativistic fashion, and this indicates that frames of reference are not equivalent for timekeeping.

The mathematical attraction of the Lorentz transformation is that it is perfectly suited to the ideas of special relativity, in that it provides results that show no preferred frame. However, it then requires that we add velocities in a complicated way.

Hafele and Keating, as part of their calculation, add velocities in the manner of Newton, and this is not compatible with relativity. This appears to be an oversight, rather than a conscious choice of theory.

This allows them to settle on a specific preferred frame of reference, whereas one of the lessons of Lorentzian addition of velocities is that you cannot find a preferred frame by calculation. This is what makes the formula central to relativity.

The lesson from the observations of Hafele and Keating, on the other hand, is that we can, in principle and in practice, find a preferred frame by observation.

We know, therefore, that there is a frame of reference in which clocks tick faster than those in the earthbound laboratory. We assume that there is a frame of reference in which clocks tick faster than those in the westbound plane, because it would be bizarre to have found the fastest-ticking frame by happenstance. Physics assumes that the fast frame, as we might call it, is the non-rotating but orbiting Earth. There is mathematical justification for this conclusion in Hafele and Keating, but the maths is wrong and the theory (taken from Builder) unsupportive of this conclusion, as well as being non-relativistic.

Since we routinely send atomic clocks into space for purposes of timekeeping, we could easily test this poorly reasoned conclusion, and at the same time search for a faster frame for clocks. Simple and potentially revolutionary!

## Preferred frames

One of the key predictions of general relativity is considered to be the advance of perihelion of Mercury, yet the way we know that the axis of its elliptical orbit is slowly changing its orientation is by observing it against a background frame. Textbook authors in gravitational relativity are generally very clear about this:

‘As far as the cosmic background radiation is concerned the distant galaxies provide a preferred frame, something that is anathema to special relativity or classical mechanics. In modern cosmology a preferred frame emerges naturally (the comoving frame) for universes whose behaviour is consistent with general relativity.’^{i}

And ‘the very accurate determination of the orbits of the planets proves them to be rotating ellipses, and this rotation is verified by observations made in a frame of reference defined relative to the distant stars, although no such stars enter into the calculation.’^{ii}

General relativity therefore contradicts this element of special relativity.

## Constancy of light speed

Michelson in 1887 found that light speed was constant, and didn’t vary, relative to us, as we orbited with the Earth. In 1905, after considerable discussion between Poincaré and Lorentz, this was enshrined as a principle, and we became used to calculating from light speed rather than calculating light speed from other observations.

For gravitational effects, specifically the bending and delay of light and radio signals passing the Sun, we find it much more convenient to revert to pre-1905 practice and consider the speed of light to vary depending upon the local gravitational field. In this view, light travels slower the closer it is to the Sun, and this is called gravitational lensing.

Key observations related to general relativity therefore contradict this element of special relativity.

## Evaluation

Most of what is distinctive and special about special relativity has been quietly abandoned.

In calculations of advance of perihelion, in applications of the Lorentz transformation to timekeeping of clocks, and in determining the motion of the solar system through the heavens, we are perfectly happy to identify preferred frames, and even frames of reference that have ‘properties corresponding to the idea of absolute rest’. In practice, therefore, physics has little use for the suggestion that everything is relative, or that all observers are equivalent.

Physics instead acts according to the belief that the use of the Lorentz transformation is universally applicable, and not restricted to inertial frames, and that the observed timekeeping of clocks is not relative.

For gravitational effects, the constancy of the speed of light is routinely abandoned in the most important ‘relativistic’ calculations, those of light bending and delay.

The Lorentz transformation is still used, and is the theoretical basis for the observation that physical laws are the same in different inertial frames. These two aspects of the original theory survive and are still respected, including by this author.

It is perhaps useful to note that the Lorentz transformation can be derived from a great variety of different starting assumptions, as is explained here, and this may be why it survives when the conceptual aspects of special relativity have been largely abandoned.

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i. Ian. R. Kenyon, General Relativity (Oxford Science Publications, 1990) page 3

ii. C.W. Kilmister, General Theory of Relativity (Pergamon Press, 1973) page 39