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Geocentricity 101: A beginner’s Course
Geocentricity 101, Part I: Basic Principles
Geocentricity 101, Part II: Basic Physics
Geocentricity 101, Part III: Scriptural and Church Position

Mark Wyatt

Mach’s principle makes explicit reference to “distant stars.”–i.e., objects infinitely far away. It then picks out a preferred reference frame by demanding stationarity with respect to these.

A priori, there is no reason to postulate the existence of such objects (in fact, until recently, it was reasonable to believe that the universe might have a finite volume, and therefore, a finite “maximal” diameter).

The equivalence principle is essentially a statemetn that there is no such thing as absolute acceleration–acceleration and four dimensional curvature are interchangeable concepts (speaking very loosely, find a coordinate system where F/m is the same as the Christoffel symbols). Hence, in GR, there are only equivalence classes of inertial reference frames (i.e., sets of frames which do not accelerate with respect to each other), rather than an absolute notion of inertial/non-inertial. That is, unless you invoke something like Mach’s principle, or a Geocentric principle, or a Heliocentric principle.

Even though things LOOK the same, you CAN tell the difference between 1) the stars spinning about you, and 2) your body spinning at the same angular rate.

So Mach’s Principle is not part of GR (even though it motivated Einstein).

And inertial reference frames have a preferred place in the theory in the sense that they are all connected by the modern version of the Equivalence Principle in a way that accelerated frames are not.

Hence, the Earth revolves around the Sun, because the former’s acceleration well exceeds the latter’s.

Geocentrism, as advocated by creationists or other religiously fundamental people, is certainly wrong.

How, you may ask? What is going on is that you can do a change of reference frame to a geocentric one, and by relativity the math must still work out. I readily admit that. I do not understand all the math involved, but I will take it for granted that it works out, and that physically, geocentrism is just as valid as, say, heliocentrism.

But note the words “just as valid”. Also, by relativity, it cannot be any more valid; geocentrism is just another change of frame (although to a non-inertial one).

What geocentrists are saying is that geocentrism is the one, true frame. Creationists must say that because that is what is says in the bible. Now pay attention here, because this is the important bit: to say geocentrism isn’t wrong, you have to accept the premise that any frame of reference is just as valid as any other. But to claim that geocentrism is correct, you have to ignore that very same premise.

Geocentrism as the One True Way is therefore self-contradictory. It doesn’t work.

This metric, however, looks very awful in the neighborhood of the black hole horizon. For a sufficently large mass black hole, however, you can show that a local observer doesn’t really observe any significant effects as (s)he crosses the r = 2M threshold.

In the Schwarzchild coordinates, this seems extremely puzzling, but switching to a coordinate system in which the time coordinate is (roughly) given by the proper time elapsed by a family of geodesically infalling observers (or null light rays), it can be shown that the singular behavior of the metric at the horizon completely evaporates. The price? The loss of the convenient interpretation of the metric components near infinity.

So, my point is, what coordinate system is best depends on what type of calculation you are doing…

In a reference frame with simpler motion w.r.t. to distant stars or to the CMB, the Sun’s reference frame wins out over the Earth’s reference frame.

I have been thinking abou writing about this a while ago, when I got a phone call with exactly this question (sitting in an astronomy department makes you get all kinds of phone-calls), but I then forgot about it. Over at Cosmic Variance, they have done i

As you should know, the Coriolis forces that we usually measure, such as with Foucault’s Pendulum, are due to the once-per-sidereal-day *rotation* of the reference frame that is fixed with respect to the Earth’s surface, not (to first approximation) the once-per-year *orbit* of the Earth around the sun.

If we were to do experiments in a non-rotating frame which was fixed with respect to the center of mass of the Earth, we could presumably also measure its departures from being inertial, but they would be substantially smaller than the effect of rotation with respect to the fixed stars seen by Foucault’s pendulum.