Will on special relativity

Clifford M. Will is one of the foremost authorities on the testing and classification of gravitational theories, and one of the main architects of the PPN (Parameterised Post Newtonian) system for evaluating gravitational models.

His popular book, "Was Einstein Right: Putting General Relativity to the Test" gives an engaging account of the history of GR testing, and is a recommended source for anyone interested in the subject. Will comes across as pleasant, humorous, cheerful, highly-informed, open-minded, and very, very credible. However, in the Appendix to the book, "Special Relativity: Beyond a Shadow of a Doubt", scientific rationality appears to be put on hold and replaced by "cheerleading":

"IT IS DIFFICULT to imagine life without special relativity. Just think of all the phenomena or features of our world in which special relativity plays a role."

Will then lists:

1. "Atomic energy" (SR's prediction of $E=mc^2$)
2. "Chemistry, the basis of life itself" (the success of a combination of QM and SR in describing atomic interactions)
3. "Evolution of the species" (the amount of mutation-inducing high-energy particles that reach ground level when cosmic rays strike the upper atmosphere)
4. "The US National Budget" (the high cost of the Superconducting Super Collider (SSC), due to the difficulty of accelerating particles closer and closer to the speed of light)
"Special relativity is so much a part not only of physics but of everyday life, that it is no longer appropriate to view it as the special "theory" of relativity. it is a fact, as basic to the world as the existence of atoms or the quantum theory of matter. ..."

Critical analysis

 “ The muon ... would decay long before reaching sea level ... if it weren't for the time dilation of special relativity ” — C.M.Will 1986

The problem with Will's list is that one item is debatable, three appear to have little or no significance (because the results are exactly the same as we'd predict under Newtonian theory), and for one of those three, where Will says outright that the thing wouldn't happen if SR wasn't right - the math disagrees with him.

• Will Point 1: Yes, SR generates the $E=mc^2$ relationships, just as Einstein said. But if we replace the SR content with C19th "Newtonian" shift relationships, Einstein's generic argument still gives exactly the same outcome (with slightly simpler working). "Historically" speaking, $E=mc^2$ is an SR result, but mathematically and theoretically it's also an NM result.
• Will Point 2: Evaluating claim #2 is obviously more difficult. SR is a classical theory, and QM predicts "nonclassical" behaviours that do not exist in SR or in an SR-based general theory. However, the alternative to SR, a relativistic acoustic metric, appears to be dual with quantum mechanics, and does predict effects such as Hawking radiation, that would have been liable to be considered non-classical in 1986. So where Will says that the welding together of special relativity with the quantum theory has led to a total understanding of chemistry, it might be that the success of quantum electrodynamics may largely be due to QM providing all the missing mechanisms that SR fails to predict, and that if we had a better classical model, it might simply agree with QM "as-is", with no "welding" required.
• Will Point 3: Muons: If we calculate the penetration depth of a muon before decay using NM and SR, starting from agreed inputs such as energy and momentum, and an agreed rest-frame decay time, we find that the particles decay at precisely the same height regardless of which theory we use. In Point 1, Will implies that a relationship might be unique to SR, but here he actually states it. And he's wrong.
• Will Point 4: Particle accelerators: The SR and NM Doppler relationships both predict that the coupling efficiency of a set of particle accelerator coils drops towards zero as $v$ goes to $c_{BACKGROUND}$. With both sets of equations, the recession redshifted and transverse redshifted signals reduce to an energy and frequency of zero at $v=c$ (SR transverse redshift, NM aberration redshift). So the classic "SR" particle accelerator lightspeed limit is also the "NM" particle accelerator lightspeed limit – at least, for direct acceleration.

While it's doubtless very satisfying to make grand statements about how one's favourite theory is proven beyond a doubt by particle accelerators, atomic energy, evolution of the species and "the basis of life itself", three out of four of the above statements suggest that perhaps the significance "sanity-checks" that we'd expect to see in a scientific analysis of experimental results still hadn't been done in the case of SR as late as 1986. Without at least an attempt at scientific objectivity, these sorts of statements are like a football fan's insistence that their team is definitely the best in the world, or a preacher claiming that they have proof that God exists "because otherwise the Sun wouldn't shine". If we claim exclusive ownership of effects for a theory without looking to see if the same outcomes result if the theory is wrong, then this is not just bad science – it is not science at all.

Notes

Admittedly, we can't be expected to compare a theory's results against everything ... but one might expect that it at least be compared against the previous theory, especially when that theory is as famous as Newtonian mechanics. For this to appear still not to have happened as late as the 1980s seems odd.

References

• Clifford M. Will, Was Einstein Right?: Putting General Relativity to the Test (OUP, 1986), Appendix ISBN 0192822039