Reawakening the Luminiferous Aether - 2
The rotation of the Sun
on its own axis can
be explained using
In the beginning, an enormous slowly-rotating cloud of mainly hydrogen gas with some helium collapsed under its gravitational self-attraction. It contained a tiny amount of iron and nickel together with lighter and heavier elements from supernovae elsewhere in the Galaxy, which eventually formed Earth. Meanwhile, the contracting solar nebula had occupied the centre of what was to become our Solar System, switching on a hot proto-Sun which spun faster as it settled down towards its present size. Gravitational energy made way for nuclear fusion energy. The planets were born from rings of encircling matter and leftover hydrogen.
In a nutshell, this is a reasonably straightforward account of how we originated about five billion years ago, some nine billion years after the formation of the Universe. As with all good theories, it covers an enormous range of explanatory power and throws in almost as many new questions as it seeks to answer en route to what the majority of scientists now believe to be certain truth.
There is, however, one fatal flaw. In any rotating cloud of gas and dust with a gravitational well at its centre, all of the higher-density dust would swirl preferentially inwards relative to the lighter gas, to form concentric vapour shells at the Sun's core. If the only pressure available had been provided by the gas surrounding every particle of dust, Earth and the other three metallic rocky planets Mercury, Venus and Mars could never have formed, and we wouldn't be here to notice the fact.
So something is wrong with this account. As far as anyone can judge by appearances it seems to be happening elsewhere in the Galaxy, but despite all the books which have been written on the subject planetary formation is unlikely to have occurred that way in our own Solar System. Looking more deeply into the question, it doesn't seem to be a matter of whether God exists or not. Instead, we're either missing some part of the physics, or the physics itself is incomplete, maybe both.
As discussed in the first part of this article, there may be a case for considering that a more inclusive and intuitive view of a theory might indicate that something else entirely could be happening. The same kind of enquiry can equally well be applied to the way in which the Sun seems to have ended up rotating far too slowly on its own axis.
As the primordial solar nebula contracted it rotated faster, and since the present Sun contains more than 99.8% of the mass of the Solar System, nearly all the angular momentum of the original nebula should have been invested in a by-now very rapid rotation on its own axis. That angular momentum is actually located in the planetary orbits, particularly Jupiter's; while the Sun, with a leisurely 27-day spin period with respect to our view of it from Earth, contains hardly any. Either that momentum was never there in the first place, or it has since been transferred from the Sun to the planets via some form of electromagnetic coupling, say.
From the viewpoint of being able to predict something interesting, it is clearly more useful to consider what might be happening now instead of a once-and-forever event long ago, so we can safely pass over the second option. We already know that in some ways our Sun fails to conform to the nuclear fusion model. One of these is the "faint young Sun" paradox, which concerns the 30% increase in solar energy output over its life to date. Both the land surfaces and the oceans of Earth should have remained snow- and ice-covered for those essential few billion years life took to get started, yet according to the fossil record they were warm enough for it to evolve successfully during that time.
As a result, there is a sensible way to open up the debate on the alternative first option, based on the possible existence of an as-yet unrecognised force which would be additional to the usual gravitational dynamics. This force hasn't just been pulled out of a hat, but is required to explain the failure of the gravitational model for the outer planetary orbits. When applied to the planets Saturn, Uranus, Neptune, and dwarf planet Pluto, that model comes up with a consistent excess of over 0.5% above the correct balance between the cubes of their mean orbital radii R and the squares of their mean orbital periods T (given by the Kepler-Newton law R3/T2 = 1). Since the four inner planets seem perfectly happy to follow the same gravitational law to a worst error of only 24 parts per million for Mars (0.002,4%), with Jupiter anomalously between the two figures, something strange is obviously going on.
Now, on cloudless occasions at some time during every day of our lives we've watched the Sun rise in the east and set in the west. At night we've seen the Moon, planets and stars rise and set in the same way. From this, even though we can't feel it happening in any form at all we infer that the Earth is ceaselessly turning relative to the rest of the Universe.
What if it isn't? Suppose something-spacetime is turning instead, carrying the rest of the observable Universe round with it under a force far stronger than the weak gravitational one? Then two forces could be simultaneously operating, a daily spacetime rotation around Earth and a yearly orbital movement of Earth around Sun. How would we be able to decide whether the other. non-gravitational force existed?
By its relativistic effect, possibly. If spacetime is revolving around a stationary Earth, it can easily be shown that at the Sun's distance from the Earth its revolution would have a very fast transverse velocity, vs say, in its direction of motion. It would be going round once in a solar day tsol of tsol = 86,400 seconds (s), at a Sun-Earth mean orbital radius Rse of close to Rse = 149.6 million kilometres (km). Since the velocity of light c is close to c = 300,000 kilometres per second (km s-1), the dimensionless ratio vs/c of transverse to light velocities would be:
vs/c = 2πRse/tsolc = 0.036,3 (3)
In other words, vs would be close to 1/27th of the velocity of light. For this kind of motion, the less well-known transverse Doppler effect should produce a small but significant time dilation of the form (1 - vs2/c2)-½, that is (a few easy trial calculations can check this) a lengthening of time the faster the revolution. For the value of vs/c given by Equation (3), this dilation is about 1.000,66.
What could obviously then occur might be a slight redshifting of the Fraunhofer absorption lines in the solar spectrum, but as far as I can tell from published data this doesn't seem to happen. To make up for that, however, the time-dilation factor does predict almost the entire amount of the Sun's rotation on its own axis. This, if you recall, is inexplicable using the rotating primordial solar nebula theory.
We can do that calculation by noting that the surface of the Sun nearest Earth is closer than the exact value of the Sun-Earth orbital radius Rse by the radius of the Sun rs itself, and so because the transverse velocity is then less it experiences a slightly lower time-dilation effect. The visible surface therefore imperceptibly advances on the hidden centre in the direction the Sun is moving, from east to west. Or alternatively, the further-away hidden centre, with a slightly larger value of time-dilation factor, lags behind the surface.
The net effect is an apparent visual rotation of the Sun on its own axis. Essentially, a tiny dimensionless time-differential ends up rotating around the Sun. This is in units of seconds per second (s s-1), an odd effect I don't think any physicist may yet have come across except perhaps in the quantum world. Using a fairly simple theoretical approach that differential, Δt say, can easily be calculated as:
Δt = 4π2Rsers / (tsolc)2 = 6.126 x 10-6 s s-1 (4)
The equatorial circumference of the Sun is for calculation purposes better given in light-seconds, as 2πrs/c, and the apparent rotational time-period τs in seconds is then simply obtained by dividing this circumference by the time-differential Δt, giving:
τs = 2πrs/ cΔt = tsol2c / 2πRse = 2.381 x 106 s (5a)
or, dividing by tsol, in solar days:
τs/tsol = tsol c/2πRse = 27.6 days (5b)
This last equation is merely the inverse value of Equation (3). Though approximate, it correctly predicts both the magnitude of the rotation period at the Sun's equator to an accuracy of about 95%, and the sense of that rotation from east to west across the Sun's face.
Have we solved the apparent paradox of a slowly-turning Sun only to end up losing the rest of the Universe, though? For, a little thought shows that anything 27 times further away than the Sun could be revolving around Earth as fast as the velocity of light itself.
Audouze, J., and Israel, G., (Eds) "Cambridge Atlas of Astronomy" (2nd Ed) [C.U.P. (1988), p.44]