Closing Remarks

1

First and foremost, this entire discussion of relativity represents my own learning process, which started in ‘relative’ ignorance and in some eyes may not have progressed that far. However, it would appear that the scope of relativity might be described in terms of the Pareto 80/20 rule in that it appears that 80% of relativity can be generally understood with an approximate 20% effort. However, the remaining effort, which mainly lies in the area of the mathematics of general relativity, appears to have the potential to consume a lifetime of learning, let alone another 80%. In many respects, the issue of complexity returns to one of the key themes of this website as articulated by William Clifford:

“It is wrong always, everywhere, and for anyone, to believe anything on insufficient evidence`

However, in truth, it is very difficult for anybody to evaluate all the detailed evidence of theoretical physics and, as such; we are inevitably forced to rely on the weight of authority of mainstream science, wherever that lies, or have no opinion at all. This said; it is clear that the development of relativity was hailed as one of the scientific achievements of the 20th century, which has caused a profound change in the way science now describes the universe and its perception of time and space.

So, in the case of relativity, should we simply assume that the weight of authority is overwhelming?

Let us consider this question separately in terms of special relativity and then general relativity. Special relativity has been shown to correctly predict the behaviour of objects in motion in the presence of a constant or zero gravitational field, as well as those in a rotating frame of reference. However, by this admission, it is not capable of accurately describing motion in varying or strong gravitational fields; where it is essentially replaced by general relativity. However, exceptions also occur at the very small scale of quantum physics, where it is believed to lead to inconsistency due to the effects of quantum gravity. However, as a broad generalisation, special relativity is now accepted as a mainstream science, verified to some degree by experimental results, at least, on a macroscopic scale and in the absence of any strong gravitational fields. To date, the efforts of potentially thousands of amateur physicists to devise thought-experiments that lead to genuine logical paradoxes have all been refuted on examination by experts. Possibly the most famous of the thought-experiments is known as the twin paradox, which was outlined in some detail in an earlier discussion. However, while it was agreed that the relative age of each twin was not a paradox, many of the suggested descriptions of how and where time dilation takes place on-route did not always appear to provide a satisfactory explanation, e.g. simultaneity gap analysis. In this context, it was felt that there was a tendency in many references to simply forward the idea that special relativity demanded symmetrical time dilation between two inertial frames of reference separated by velocity [v], irrespective of any initial conditions.

But what is meant by symmetrical time dilation?

Conceptually, you can describe a situation where 2 apparently inertial frames of reference pass each other with some constant velocity [v] which is approaching the speed of light [c]. By the logic of special relativity, both can claim that time in the other frame of reference is running slower. However, signalling analysis of the twin paradox seems to suggest that some caveats must be attached to this interpretation, for while time does appear to be relative it is not paradoxical in sense that both twins cannot end up younger than the other. In a subsequent discussion, the twin paradox was extended and described as the triplet paradox. In this extension, 2 of the 3 triplets undertake an identical journey, except their paths are reversed, such that they eventually pass each other at near light velocity [c]. Signalling analysis of this case suggested that the relative time in each of the moving frames ticked at the same rate throughout the entire journey, although slower than that of their stay-at-home sibling. This model was then extended again, where the triplets were replaced by galaxies that were receding away from each other at near light speed [c], which then raised the following question:

Is the aging of the universe the same everywhere?

This question was raised based on the cosmological observation that different parts of the universe end up receding away from each other at relativistic velocities. However, given the scope of this discussion can be reviewed by following the link to the triplet paradox; it will not be replicated at this point. Applying special relativity to a cosmological model also raised the issue as to whether the universe does have a ‘preferred’ frame of reference in terms of the ‘Cosmic Microwave Background Radiation (CMBR)’. Again, the questions this discussion raised can be reviews by following the link above. So while there are websites that will cite all the experimental evidence supporting special relativity, see inset right by way of an example, it is still suggested that some of the wider implications may still require some further consideration, if we are to stay true to Clifford axiom above.

But what, if any, conclusions might be drawn about general relativity?

When Einstein first presented his general theory of relativity, in 1915, there was no empirical evidence to support its theoretical foundation. Later, it was shown to correctly account for the anomalous precession of the perihelion of Mercury and, to some extent, it satisfied the requirement to unify Newton's law of universal gravitation with special relativity. Subsequently, in 1919, it was shown that light did indeed appear to bend in gravitational fields in line with the predictions of general relativity, but it was only in 1959 that a program of precision tests was started to try to verify general relativity against more exacting tests. The net result of these tests still appears to support the theory, while also putting severe limitations on any opposing theory. At this point, one might also expect the weight of observation from cosmology and astrophysics to also be cited in support of general relativity and while this evidence is not being refuted, the scope of evidence under this heading needs to be examined more closely and will be the focus of the cosmology section.

But what of the logic examined in all the previous discussions of general relativity?

Well, in truth, these discussions were more about understanding the implications of general relativity rather than challenging its underlying assumptions and mathematical principles. However, it was felt that the basic model, as illustrated below, did provide a simple way of consolidating some of the key implications of both special and general relativity in a way that could be readily understood.

Falling Towards the Event Horizon?

2

By and large, this model is predicated on the same assumptions that underpin the Schwarzschild metric, but highlights the basic effects of velocity and gravity on spacetime. We may also reference some of the tests above as representative of the verification of the relativistic effects on time and space. However, even this simple model leads to situations that extend far beyond the verification testing cited above, as we explored the extreme situation of a free-falling observer plunging towards the event horizon of a black hole. In this context, the argument forwarded under the heading of ‘Gullstrand-Painlevé coordinatesthat suggested the event horizon was only a 'coordinate singularity' did not really seem totally convincing, as it appear to simply ignore the relative time of the distant observer [A]. Of course, this issue alone cannot refute all the evidence in support of general relativity, but it may suggest that there are still issues that are beyond relativity to explain and certainly beyond its ability to verify at this stage. As such, there may still be grounds on which to ask whether there is truly sufficient evidence to elevate relativity from its status of 'theory' to 'accepted fact'. In this context, there is a sense that much of general relativity can quickly be subsumed into the mechanical manipulation of mathematical expressions that have little to no correlation to any known physical reality. As such, this mathematical process might be likened to a software program, which may be equally susceptible to the adage:

Garbage In, Garbage Out

Of course, those completely familiar with all the mathematical complexities of general relativity may have good grounds to refute any such suggestion.