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Sunday, September 20, 2015

The Sun Orbits Around the Earth

sun and earth

One commonSee, for example, here for the usually much more astute Ilya Somin embracing this fallacy. trope of reporting on the scientific illiteracy of Americans goes something like this:

When surveys ask American adults to pick between the statements (A) the earth orbits around the sun and (B) the sun orbits around the earth, a large minority of about 25% pick statement B, rather than the correct statement A. This proves how shockingly ignorant many Americans are of scientific issues.

That conclusion may very well be true, but the argument proves no such thing; rather, it is merely sneering of the semi-educated at the honestly ignorant.

The reason is that statements A and B are observationally indistinguishable under most accepted theories of physics, including both the Galilean relativity of Newtonian physics and the Einsteinian relativity of modern physics.Admittedly, there was a brief interregnum when most physicists did not believe in some form of relativity. It lasted about fifty years from the time Maxwell's equations became accepted as the accurate and complete description of electromagnetic phenomena to the time Einstein's (and Lorentz's) version of relativity became accepted. Prior to Maxwell, Newtonian mechanics and gravity was invariant under Galilean relativity; indeed that is their characteristic feature. Maxwell's equations were not invariant under Galilean transformations; hence they could only be true with respect to one specific frame of reference, the one of the so-called luminiferous æther. However, Maxwell's equation are are invariant under Einsteinian relativity (and so, of course, are Einsteinian mechanics and gravity). None of this matters for purpose of the post's question. Only relative, not absolute, motion can be observed. In other words, there can exist no experiment which disproved statement A, but not B, or vice versa. They are equivalents, not opposites.

Indeed, most physical calculations are performed in laboratory frame in which the earth in not only fixed, but it does not even rotate on its axis. One can only imagine the glee at those Stupid, Ignorant Physicists—they don't even know that the Earth spins!—that these reporters would experience if they learned of this common practice.

Some will respond along the lines of But did history not have the great debate between the heliocentric and geocentric factions? And did that not establish statement A and disprove statement B?

Indeed, there was such a debate, but that is a misunderstanding of its content. There never was a dispute between statements A and B. The informed, then as now, always knew that they were equivalent. Rather, the debate was between heliocentricists who believed that the other planets orbited around the sun in roughly circular orbits and geocentricists who believed that they orbited around the earth in roughly circular orbits. It was that debate that the heliocentricists won.

Another response will be But the sun is much bigger than the earth!

Indeed that is so and was well-known even to the ancients even though, due to the weakness of their experimental evidence, they vastly underestimated the actual degree of disparity in size (in fact, about a factor of one million, rather than the ancients' estimate of about twenty).

But that is also a different question. Whether the earth or the sun is bigger is entirely distinct from which object orbits around what.

Thus, if you are ever asked does the earth orbit around the sun or does the sun orbit around the earth the only correct answer is Yes.An alert reader points out that one really should first inquire whether the or in the question is the inclusive and/or or the exclusive either or. Only in the former case is the answer Yes; in the latter it is of course No.