SR clock hypothesis
Under special relativity, the clock hypothesis states that the acceleration of a body has no effect on its rate of timeflow. This hypothesis is in disagreement with the Principle of Equivalence and with the general principle of relativity, but seems to have been implemented after 1960, as a way of defending special relativity against the GPoR.
Special relativity's requirement for the hypothesis
Special relativity and the equivalence principle (and, in fact, Newtonian theory) agree that a clock circling an observer wrt the background stars should age more slowly.
- " the circling clock is moving at right angles to the observer, and is therefore seen to be red-shifted. Since this redshift continues indefinitely, we have to conclude that the clock is physically ageing more slowly, in a manner that can be established objectively by experiment. "
- " if we switch from the equations of special relativity to those of Newtonian mechanics, NM predicts a nominally stronger transverse redshift, due to aberration redshift. While this would not normally considered evidence of real time-dilation, the circling object should nominally be seen to be redder under NM than SR, when viewed seen from any angle. If the the SR argument is taken as valid, and the NM argument predicts redder shifts, then it would seem to also generate a time-dilation effect. " (see caveat)
Equivalence principle argument
- " According to Mach's principle, and the GPoR, asymmetrical effects associated with rotation and acceleration can be interpreted as the result of a special class of gravitational field. If the observer and clock are both attached to a rotating disc, then with respect to the disc, there appears to be an outward-acting gravitational field – if the disc has radial grooves carved into it, and we place a ball bearing into one of the grooves, the bell will accelerate outwards as if it is freefalling in a gravitational field, and the perimeter clock attached to the disc will feel stresses and strains as if its anchoring is physically preventing the clock from falling in the field. Light travelling across this apparent gradient should undergo a change in energy (Michell 1783), which has to be interpreted as a gravitational time-dilation effect (Einstein 1911). The circling clock therefore has to age more slowly by a factor that depends on the geeforces that it experiences.
Until 1960, it was believed that the SR and EP arguments were equivalent - both predicted the same qualitative result to the available experimental accuracy. However further geometrical analysis showed that the two descriptions were not dual but competing, and one or other of them had to be wrong.
At this point, we decided to choose to believe that SR was correct and the GPoR was wrong.
SR clock hypothesis argument
If we start by presuming the validity of special relativity, we can argue:
- " under special relativity, we can calculate the correct behaviour of the circling clock by assuming flat spacetime and velocity-dependent time dilation. The EP argument is not dual to the SR argument. Since the SR argument is fundamental, and explains the full measured effect, there is no remaining residual effect to be explained by the EP. Conclusion: the EP and GPoR do not apply in this situation, and we know as an experimentally-verified fact that the acceleration of the circling clock has no detectable effect on its physical clockrate. it's perfectly okay to use special relativity in rotating-body problems"
Alternative EP-based argument
However, if we start by presuming the validity of the GPoR, we can argue the opposite position:
- " under the GPoR, we can calculate the correct behaviour of the circling clock by assuming an apparent radial gravitational field and gravitational time dilation. The SR argument is not dual to the GPoR argument. Since the GPoR is fundamental, and explains the full measured effect, there is no remaining residual effect to be explained by the special theory. Conclusion: SR is not fundamental theory. It produces an alternative "quick and dirty" method of calculating an inherently curved-spacetime effect while assuming flat spacetime. Although special relativity can be used as an "engineering theory" for rotating-body problems, it is not theoretically correct to use it in these situations as more than a 'stop-gap' theory. "
We can see from the above that although the experimental case for the clock hypothesis being "proven" is sometimes presented as being overwhelming, the opposite argument is similarly (if not more) overwhelming. Regardless of whether we believe that it is the GPoR or SR that cannot be wrong, the ensuing chain of logic will seem to reassure us that our initial choice was correct.
Since the GPoR appears to invalidate SR in this case, and the GPoR arguments are arguably more fundamental than those of SR, if we require SR not to be invalidated, we require the SR clock hypothesis as a way of eliminating the opposing viewpoint.
In defence of the hypothesis, we can point out that the word "hypothesis" is clearly part of its name, and that since it appears to be required to prevent SR's invalidation, and therefore seems to be required within SR. We can say that it is entirely reasonable to present it as an "SR hypothesis", and leave the question open as to whether or not it might be an SR-specific hypothesis.
What we must not do, though, is present the clock hypothesis as something that is known to be supported by fact, or as a hypothesis based on any general principles. The basis of the hypothesis is theological - it is required within the theory, as an add-in, to head off arguments discovered after the theory was designed, which would otherwise lead to the theory's invalidation.