I wrote the other day about the embarrassment that Muslims feel at the actions of terrorists and that physicists feel at the actions of faculty protesters. But in fact the pope too must feel some embarrassment at the actions of some of his self-anointed efenders. At the same time that terrorists were twisting his words to justify their actions, there were those who stepped up to defend the pope by saying, "he was right to call Muslims irrational", although he did not call Muslims irrational. Now that activist faculty members are twisting his words in order to justify their actions, Benedict XVI has his defenders arguing, "he was right to condemn Galileo", although he did not condemn Galileo. Never mind what he actually said. It turns out that the internet is full of geocentrists (Who knew?), and they are quick to crown themselves with the papal tiara.
Most of these Galileophobes of the blogosphere are basing their condemnation of heliocentrism on arguments largely identical to those of Ernst Bloch,
as quoted by then Cardinal Ratzinger in 1990:
According to Bloch, the heliocentric system – just like the geocentric – is based upon presuppositions that can’t be empirically demonstrated. Among these, an important role is played by the affirmation of the existence of an absolute space; that’s an opinion that, in any event, has been cancelled by the Theory of Relativity. Bloch writes, in his own words: ‘From the moment that, with the abolition of the presupposition of an empty and immobile space, movement is no longer produced towards something, but there’s only a relative movement of bodies among themselves, and therefore the measurement of that [movement] depends to a great extent on the choice of a body to serve as a point of reference, in this case is it not merely the complexity of calculations that renders the [geocentric] hypothesis impractical? Then as now, one can suppose the earth to be fixed and the sun as mobile.” What is missing from this argument is that it was Galileo himself who first proposed the Principle of Relativity, that there is no such thing as absolute motion, but "there’s only a relative movement of bodies among themselves, and therefore the measurement of that [movement] depends to a great extent on the choice of a body to serve as a point of reference". It is precisely relative movement that is a Galilean invariant, that is, a quantity that is the same regardless of your frame of reference. And it is this Galilean invariant that means that the earth revolves around the sun, and not vice versa, both in the sun's frame of reference and in every other inertial frame of reference as well.
To see an example of this, first consider this proof that the earth rotates on its axis, and that it is not stationary with the universe revolving around it every 24 hours. Abe and Bill are both on ships on opposite sides of the world on the equator. As Abe watches the sunrise, Bill is on the other side of the world watching it set. At that moment, due to the spin of the earth, Abe, sitting peacefully on the deck of his ship, is actually heading toward the sun at 1000 miles per hour. Likewise, Bill is moving away from the sun at 1000 miles an hour. The magnitude of their relative motion, the motion relative to each other, is thus 2000 miles per hour.
"Ah", but Abe says, "you are saying this from a geocentro-centric point of view. Your reference frame is the center of the earth. From my point of view, I am not moving at all. It is the sun which is moving toward me at 1000 mph, and my buddy Bill is moving away from the sun at 2000 mph." And Abe is precisely right. But what Abe and I both agree on is that the relative motion between him and Bill has a magnitude of 2000 mph. There is no getting around it, their relative motion is a Galilean invariant. The fact that Abe and Bill, both standing stock still on the surface of the earth, have a relative motion of 2000 mph is a sure sign that the earth is rotating, and it is rotating in every Galilean reference frame.
The same thing applies mutatis mutandis to the earth's revolution around the sun. "One can suppose the earth to be fixed and the sun as mobile", says Bloch, but can you really? I tell the geocentrist that he is moving 30 km/s around a stationary sun. "Not at all", says the geocentrist. "I am stationary. It is the sun that is moving 30 km/s."
Fine, in his inertial reference frame he is not moving, and the sun is. But in six months, in that same frame, he will be moving 60 km/s, and in the same direction as the sun, which will still be moving 30 km/s! In what sense, then, can the geocentrist continue to assert that he is not moving? Sure, he can construct reference frames where the earth is stationary for one instant every year, but he cannot escape the fact that the motion of the earth in January relative to the earth in July is 60 km/s. The relative motion of the sun in January to the sun in July, on the other hand, is negligibly small.
"But wait", says the Galileophobe, "Galileo believed in absolute space and absolute time. Einstein's Special Theory of Relativity (ESTR) did away with all that. Those Galilean invariants aren't invariant at all. The Galilean Principle of Relativity (GPR) is completely wrong"
Actually, at speeds characteristic of the solar system, those Galilean invariants really are very nearly invariant, and GPR is true. But let's cut our Galileophobe a break, and pretend that we are whipping by the solar system in a spaceship at 90% the speed of light. (In that case, GPR really doesn't work.) And as why fly by, we are trying to ascertain whether the sun goes around the earth, or the earth the sun.
Since GPR doesn't work, we cannot rely on the Galilean invariant, the relative motion of the earth in January and July, to answer our question. We can, however, rely on Lorentz invariants. One example of a Lorentz invariant is the 4 dimensional momentum of the earth in January relative to that of the earth in July. Like the relative velocity in GPR, this Lorentz invariant is constant in all inertial reference frames in ESTR. It is quite analogous to relative velocity in GPR, right down to indicating that the earth is rotating about its axis in every ESTR reference frame, and that it is revolving around the sun, and not vice versa, in every ESTR reference frame.
In a sense, Bloch and like-minded bloggers have internalized the Principle of Relativity too well, better than GPR, or ESTR for that matter, can hold. GPR and ESTR hold for translational motion, but not for rotation or revolution, as has been demonstrated by a straightforward application of these theories themselves. The reason for this is that translational motion is qualitatively different from rotation and revolution in its very definition. Unlike translational motion, rotation and revolution always imply acceleration.