1960 Crisis

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The 1960 crisis in gravitational theory occurred after a paper was published by the Harwell group, on an experiment that measured the redshift on a centrifuged "clock". The group presented the result as confirming the existence of gravitational redshifts, by invoking the principle of the equivalence of inertial and gravitational effects (equivalence principle, Mach's principle).

After the paper had passed peer review and been published further study of the problem revealed that the GPoR applied to rotation problems was actually incompatible with special relativity, suggesting that one or both were wrong. After some debate behind the scenes, the community decided that losing the GPoR as a fundamental principle was the "least worst" option, as losing the GPoR as a principle only downgraded general relativity, but losing SR as an exact solution meant losing both Einstein's general theory and SR.

As a result of the crisis, it was decided that the original specifications of Einstein's general theory had been wrong, and that the GPoR should be treated as a guide rather than as a strict principle, and should be suspended whenever a collision with SR would otherwise happen.

The duality argument

" We know that special relativity and gravitational principles both predict that an object circling relative to the background stars should age more slowly: "
1. " I stand at the centre of a spinning disc, but do not rotate with it. For me, the edge of the disk its moving transversely at a speed v, and therefore undergoes SR time-dilation."
2. " I stand at the centre of a spinning disk, but rotate with the disc. For me, there is no relative motion between myself and any part of the disc, and therefore no motion-based time-dilation. However, I realise that there seems to be a radial gravitational field pulling light and matter away from the disc centre, so that the edge of the disc is "downhill" from my position, and therefore undergoes gravitational time dilation".
" These two explanations are equivalent and dual. The same effects can be described either in terms of gravitational effects (principle of equivalence), or as SR effects (Sr time dilation) depending on the chosen reference system. "

The argument fails

Geometrical analysis after the paper's publication showed that, counter to expectations, the two explanations were geometrically incompatible. Explanation #1 assumed flat spacetime, while Explanation #2 assumed curved spacetime, with the curvature being intrinsic. This meant that the curvature in Explanation #2, if it existed, had to be present for both observers, meaning that both observers could calculate the correct amount of gravitational time dilation from the situation as revealed to them by their instruments, without using special relativity. The special theory appeared to be superfluous.

Worse, the gravitational explanation seemed to be unavoidable. Einstein had already pointed out that SR's length-contraction effect meant that the geometry of a spinning disc could not be regarded as Euclidean, and, if we mapped the time dilation of different parts of the disc, we would find that particles in the disc were ageing at a rate that reduced as the radius increased. If the rate of timeflow was unambiguously varying across the disc structure, then the speed of EM signals passing though the disc should change, and light traversing the disc should be defected to the region of slowest timeflow (the outer edge), by Huyghens' principle. A physically identifiable variation in timeflow across the surface had to be associated with similarly "physical" gravitation-equivalent effects.

We also didn't have the option of dismissing the gravitational effects as a "minor" supplemental effect to SR, because we had already worked out (when we thought that the two effect were dual), that they two sets of results had the same order of magnitude in the Harwell experiment.

Catastrophe

If both effects are independently correct, then the non-rotating observer should measure the cumulative effect of both the gravitational and SR redshifts, while the rotating observer should only measure the gravitational effect (there being no relative motion between them and the disk). Unfortunately, this discrepancy is not allowed - both observers have to agree, or at least be arbitrarily close to agreement. *

Since we cannot invoke a shift due to relative motion in the rotating-observer case, since there is no motion between observer and disc, the gravitational calculation for this case has to be correct, which means that a separate additional motion shift cannot appear in the other case. Since both SR and NM require there to be a motion shift (transverse redshift, aberration redshift), we now appear to be looking at a paradox.

The unacceptable solution

The only logical relativistic solution to there being a pure gravitational shift in one case, and exactly the same gravitational shift in the other case, but also a motion shift of the same magnitude in the second case only ... with both total shift predictions then giving the same final prediction ... would seem to be for us to say that the motion shift and the gravitational shift are not cumulative, but are actually the same effect. We would then be saying that the relative motion of a transverse-moving body (and by extrapolation, the relative motion of bodies in any direction) must involve curvature, and that the shift associated with that curvature must be exactly equal to the shift calculated from the body's velocity.* This gives us a derivational route to a shift equivalence principle, which in turn leads to a gravitoelectromagnetic theory of relativity, and a relativistic acoustic metric – a whole new fourth-generation iteration of the theory of relativity built on more advanced concepts, with a different mechanism for lightspeed constancy – we get the AGR system.

However, AGR was not an option in 1960, and people who'd based their professional careers and reputations on the idea that SR and GR1916 were correct were probably not enthusiastic about th eidea of publicly decalrign that both theories appeared ot be invalidated by the GPoR, especially as there was no obvious "road map" or schedule for constructing a more advanced replacement theory

Pragmatism

Instead of taking the 1960 crisis as our cue to start work on the next generation of relativity theory, the community seems to have decided that losing Sr was not aceptable, and that if the GPoR invalidated SR, then the GPoR was wrong. Our choice of interpretations was then between:

  1. "The Newtonian concept of absolute motion is correct, and the basic concept of GR is wrong. the circling clock ticks more slowly in both cases because it is "really" circling, and the gravitational arguments do not apply."
  2. "The GPoR is a useful guide, that helped in GR's development but not a law. We use it when it is useful to us, but suspend it when it appears to be about to cause problems."

This second "pragmatic" interpretation is the one that appears to correspond to "textbook GR" from the 1960s onwards. While it avoids the "total rewrite" option for relativity theory, it leaves us in an impasse, with a general theory that is no longer really a general theory, which is internally fudged, and which cannot be reconciled with quantum mechanics.

Notes

The rotating and non-rotating cases need to be identical or arbitrarily similar. The disc-physics seen by the observer depends on (a) what happens in the body of the disk (b) what happens to the signals ans they travel to the observer's central location, (c) the physics at the central location, and (d) any additional distortional effects due to the relative rotation of the observer's body and the disc. If we make the disk arbitrarily large, we can have the edge speed of the disc approachign the speed of light, even if the observer is only rotating at one rpm, one rpDay, or one rpYear. Even in the most extreme light-dragging models, we cannot blame this arbitrarily-large clock-slowing on the arbitrarily-small distortions at the centre of the disc, or explain how the same arbitraily-small distortions can have a real physical influence on the physics of the distant rim, that becomes more powerful as the separation increases. Also, the observer canbe arbitrairyy small, so that their vanishingly-slow rotation corresponds to the radius of, say, an atom. For the effect beign described, the physics of the disc and the behaviour of the signals traversing it need ot be essentially the same regardless of whether the central observer rotates or not - the shift seen by the arbitrarily-small, arbitrarily-slowly-rotating central observer needs to be effectively the same regardless of whether or not they rotate or not. In this "generic" situation, both calculated shift results need to be the same.Shift equivalence creates a new mechanism for local lightspeed constancy - if a body recedes at v m/s, and its associated gravitational effect also has a terminal velocity of v m/s, then light-signals passign between it and the observer will automatically have a velocity of [math]c_{OBSERVER}[/math] at one end of the signal path and [math]c_{OBJECT}[/math] at the other.Note that there is no obvious technical or conceptual problem with solving the 1960 crisis with a new theory – the difficulty seems to be a social one ... much of the community doesn't seem to want a new theory.