Flogging a Pink Unicorn

Why Modern Geocentrism is Intellectual Blancmange

Alec MacAndrew

In the pantheon of bizarre anti-intellectual, anti-science, religiously inspired ideas even geocentrism (the idea that the earth is the unmoving centre of the universe) still exists. All forms of geocentrism are rejected by all serious scientists; its modern proponents are scientifically ignorant, religiously motivated cranks such as the self-appointed Roman Catholic apologist, Robert Sungenis (1).  (Robert Sungenis is also a Young Earth Creationist with all the science-denying obfuscating counter-Enlightenment baggage that goes along with that discredited notion). Sungenis's geocentric nonsense is, I hasten to add, peculiarly his, and is not officially sanctioned by any institutional body of the Catholic Church. Indeed I get the impression that Sungenis is something of a embarrassment to the Church. Here is a summary of the arguments that demonstrate that modern geocentrism (2) is not a tenable hypothesis for a reasonable person with a moderate knowledge of modern physics. Please note that I am not seeking to prove the truth of heliocentrism or any-other-centrism, but merely to show why geocentrism is not tenable.

The whole argument can be summarised in one sentence, so if you can't be bothered to read the whole article, just read the next sentence:

I’ll also argue that the promotion of geocentrism is unnecessary for salvation, is contrary to reason, and represents a major source of scandal, calling ridicule down on the Church and the Faithful

In Newtonian mechanics, geocentrism cannot be true for many physical reasons

Newtonian mechanics works within Euclidean geometry, which, for our purposes, we can summarise as a three dimensional spatial geometry based on an absolute space. Euclidean space is absolute and independent of matter or energy, which exist within Euclidean space without, in any way, affecting it. In addition, Newtonian mechanics relies on an additional dimension of absolute time.

Note that the concept of the equivalence of reference frames exists in Newtonian mechanics. It is a mistake to think that the idea that reference frames are equivalent is a new finding of Special or General Relativity. Indeed, the concept of relativity and the equivalence of reference frames was first understood by the great scientist, Galileo, whose name is given to the mathematical expressions used to transform between reference frames in Euclidean geometry - these expressions are called Galilean transformations after him.

Galilean relativity states that relative motions of systems of bodies are the same no matter what inertial reference frame they are in, where an inertial reference frame is one in which the motion of a body not subject to forces is in a straight line and uniform and where the acceleration of bodies is proportional to applied forces. In Newtonian mechanics inertial reference frames move uniformly and rectilinearly with respect to one another.

Newton used this property of Galilean relativity in his calculations of planetary motion. It follows from the definitions of inertial frames and their equivalence that the centre of mass of an isolated system of bodies is at rest in an inertial frame. Newton reasonably approximated the solar system as an isolated system of bodies (this is not strictly true, but the forces and influence of the rest of the universe on relative motions within the solar system are vanishingly small on the scale of years). Within this reference frame, he then calculated the accelerations that would result from the gravitational forces between the bodies. Newton rejected the notion of geocentrism and heliocentrism (neither of which were ever to make an appearance in physics again); instead it is the centre of mass of the system of bodies (in this case the solar system), that is at rest with respect to the reference frame - all the other bodies (including the sun) experience accelerations and are not therefore at rest in the inertial frame. The sun, of course, is vastly more massive than every other body in the solar system, and so its centre is nearly at the centre of mass of the solar system and nearly stationary with respect to it, but not quite. So heliocentrism, within the solar system, can be seen as a close approximation to the Newtonian case. All of this is true whether we observe this from an inertial frame at rest with respect to the solar system or the fixed stars, as we can transform between them using the Galilean transformation.

It is unreasonable to hold that the earth is the unmoving centre of the universe according to Newtonian physics, in which there is an absolute space. The arguments against geocentrism in a Newtonian universe are overwhelming and have been rehearsed many times. I do not intend to go into them in detail, but I list some of them below:

1. Satellites are launched to the east because the earth's rotation boosts the velocity of the satellite and helps it to achieve orbital velocity - the earth is used as a sling shot
2. Satellite launch sites are as close to the equator as nationally possible for the same reason as 1.
3. Points at rest or in uniform motion in inertial frames of reference (which in Galilean relativity are frames of reference in which a point not under the influence of applied force continues in rectilinear and uniform motion), have no unresolved forces
4. The earth has obvious unresolved forces
   (Items 3 and 4 have relevance in Riemannian geometry too)
5. Foucault's pendulum demonstrates the existence of unresolved forces at the surface of the earth
6. Weather systems always rotate counter clockwise in the northern hemisphere and vice versa in the southern hemisphere owing to the coriolis force of rotation
7. Oblate earth - the earth has a greater girth at the equator than across the poles owing to the centrifugal force of the earth's diurnal rotation
8. Parallax in the star fields as a consequence of earth's rotation round the centre of gravity of the solar system
9. Red shift in the star field as a result of ditto
10. A star field with a radius of 14 billion light years and a mass 3x10^27 times that of the earth rotating around the earth once a day and wobbling with a amplitude of 186 million miles at an angle of 23.5 degrees annually is an untenable dynamical system in Newtonian mechanics
11. Systematic forces which explain the dynamics of retrograde planetary motion are not available in a Newtonian gravitational system

Interestingly, there is a serious sense in Newtonian mechanics that refutes the idea of not just the earth, but any body being the unmoving centre of the universe. Even if we accept, for the sake of argument, that the universe is spatially finite, and we accept that there is a point in absolute space that corresponds to its centre of mass, no object with finite mass and finite spatial extent can be permanently at rest with respect to that point, because all objects with finite mass and spatial extent necessarily experience accelerations caused by the gravitational forces resulting from the presence of other bodies of finite mass in the universe, accretions of matter and other Newtonian interactions, in addition to tidal gravitational forces (ie forces resulting from gravitational gradients within the finite spatial extent of the body) and they therefore cannot be permanently at rest in any given Newtonian inertial frame.



Geocentrism is meaningless in General Relativity

Geocentrism, indeed any-centrism, is meaningless in the formulation of GR that accurately describes the universe structure. So let's see what that is.

First of all, solutions to Maxwell's electromagnetic equations yielded an expression which showed that the speed of propagation of electromagnetic energy (light) is constant irrespective of the frame in which you measure it. So now we have a phenomenon that disobeys the principle of Galilean relativity. The solution to this conundrum is Einstein's special relativity. The inconsistencies between constant c, the speed of light in vacuo and Galilean relativity are resolved by giving up the idea that length and time are independent of reference frame. The Galilean transformation is replaced by the Lorentzian transformation and Newtonian spacetime by Minkowski spacetime. We have to give up the concept of simultaneity - events that appear simultaneous in one reference frame do not appear simultaneous in another, so we also lose the concept of absolute time.

Einstein then developed his insight that the force of gravitational attraction is indistinguishable and no different in principle from the force of acceleration.

The Einstein equivalence principle states that in a local inertial reference frame the outcome of any non-gravitational experiment is independent of the velocity of the frame or its position in spacetime and that the laws of nature are those of special relativity. This does NOT mean that rotation is the same as being static nor does it deny the special status of inertial reference frames; in fact, EEP holds only in inertial reference frames

The consequence of this is that in General Relativity (GR), spacetime is not flat as it is in Newtonian mechanics or Special Relativity, but is curved. Moreover, the curvature is determined by the presence of mass. We now have to work in non-Euclidean geometry, with no absolute flat co-ordinate system. In order to calculate the dynamic behaviour of masses we have the complex problem that the presence of the mass curves spacetime in such a way as to create what we observe as the gravitational force (although in GR we shouldn't think of gravity as a force) between them, but also influences the geometry of space and time in their locality. We have to work in Riemannian geometry using tensor analysis, the details of which are way beyond the scope of this article.

The Einstein field equation is the generalised formulation of gravitational physics and one of the reasons that it is expressed in terms of tensors is that doing so allows a co-ordinate free description. It is important that no co-ordinate system is deemed to have precedence, as it is possible, in any such preferred system, to re-introduce the discarded notion of gravitational force. So GR is formalised in a co-ordinate free manner.

From a cosmological perspective, there have been various attempted solutions of the Einstein field equation, the most successful of which, the Friedmann-Robertson-Walker solution closely reflects the observed universe. In the FRW metric, the universe is homogeneous and isotropic, that is, from any point it looks the same in all directions and its properties at all points are the same.

In a homogeneous universe the curvature of space time is invariant with position and determined by the energy density of the universe. Locally however, spacetime is curved by the presence of massive objects.

Now what about the proposition that the earth is the unmoving centre of the universe? Well, GR states that the effect of a force resisting gravity and the effect of a force accelerating a reference frame are identical and indistinguishable. In GR, spacetime geometry is determined by the distribution of matter/energy in the universe (there is no absolute space) and the spacetime geometry influences the flow of matter/energy. It is therefore utterly meaningless to talk about a spatial centre for the universe because in GR, space has no absolute meaning.

Mach’s principle states that inertia is not absolute but depends on matter in the universe. Matter/energy there determines inertia here. There is no such thing as absolute rotation in the universe independent of the distribution of matter, and no absolute space. The closest we can get to a definition of absolute rotation is rotation with respect to the average distribution of matter in the universe: the distant stars; or rotation with respect to a local inertial frame (which is, in fact, very closely aligned to the star field, although this alignment can be slightly perturbed by the influence of large nearby masses)

General covariance applies in all inertial frames of reference. It is extremely misleading, and a characteristic error of geocentrists to claim that in GR, all reference frames are equivalent. They are not. Let's do a thought experiment. Let’s imagine we are in a spacecraft, with blacked out windows, that is rotating so that the centrifugal force creates an artificial gravity – we are pinned against the walls of the craft by this force. We then employ the steering motors of the spacecraft to manoeuvre the craft so that all forces that we can measure within the craft disappear. We open the window blinds and what do we see? The craft is not rotating with respect to the stars. The craft is now at rest within what we call a local inertial frame of reference, one in which there are no measurable residual forces due to linear accelerations. According to Mach, matter/energy there determines inertia here, so the inertial frame aligns closely with the star field (with local perturbations due to large nearby rotating masses - a phenomenon known as frame dragging).

In GR, an inertial frame is defined as a frame in free-fall in which an object at rest experiences no forces. The equivalence principle applies only in inertial frames. The surface of the earth is absolutely not an inertial frame in GR, because if you are standing on the surface of the earth you experience a force due to the local curvature of spacetime (gravity) as well as coriolis and centrifugal forces. Such forces do not appear in an inertial frame.

Now we have seen that talking about a centre of the universe in GR (or at least as far as the Friedmann- Robertson-Walker metric solution to the Einstein field equation goes) is meaningless, but is it meaningless to talk about absolute rotation? Well when astronomers and cosmologists talk about rotation in the universe they do so with respect to local inertial frames (which we have seen are very closely aligned to the distant stars), or with respect to the star field itself. So in GR, the formal conclusion is that it is meaningless to posit absolute rotation independent of matter in the universe, but that inertial frames are special (in that they uniquely represent conditions with no detectable residual forces), they align with the star field according to Mach’s principle, and if absolute rotation means anything at all, it means being in a non-inertial reference frame rotating with respect to the stars; in such a frame forces are detectable. The Earth’s surface is just such a non-inertial frame: by this definition it rotates. (3), (4), (5)

What about translation? To the extent that we claim that an object is moving or is stationary, we need to define that movement with reference to something. Although in relativity, preferred inertial frames are rejected, the Cosmic Microwave Background (the afterglow of the Big Bang) is taken as a special reference, and is interpreted as the rest frame of the universe. Measurements of the dipole of the Cosmic Microwave Background power spectrum show that the solar system is moving with respect to the CMB at a velocity of 368 km/s and the galaxy and Local Group of galaxies at a velocity of 600km/s, (6), (7).

To summarise this section, in General Relativity the concept of the centre of the universe has no meaning. Furthermore, to the extent that any reference frames are special, inertial frames and the rest frame of the CMB have that distinction. The earth's surface is not at rest in an inertial frame and the earth has a significant velocity with respect to the CMB and so there is no sense in which we can say that earth is stationary in the centre of the universe.

Apples are not Frogs

Geocentrists also confuse kinematic transformations with dynamic transformations. Just because a kinematic transformation is possible does not mean that the physics cannot distinguish between the two reference frames. Here's a simple example. A flea leaps off the surface of the earth. Now there is nothing wrong with describing that event kinematically in a reference frame stationary with respect to the flea. In such a reference frame the earth accelerates away from the flea rapidly to a maximum velocity at the point where the flea loses contact with the earth. Thereafter, the earth continues to move away from the flea but more and more slowly until the earth stops and begins to accelerate back towards the flea. The earth eventually hits the flea at about the same speed that they originally parted. The earth then slows down and stops. (The event can be described from an earth frame of reference simply by swapping the words flea and earth)

From a dynamic point of view the reference frames are not equivalent. A point in the flea's reference frame will experience forces associated with the flea's rapid acceleration and deceleration. A point in the earth's reference frame will experience almost zero force as the acceleration of the earth's frame due to the flea's antics is very very very tiny. Dynamically it is not correct to say that the earth leapt off the flea. (Strictly speaking, the reference frame that experiences zero acceleration and zero force as a result of this experiment is one in which the centre of gravity of the flea and the earth is at rest.)

Similarly, it is not dynamically correct to say, as you must if you hold that the earth is the unmoving centre of the universe in an absolute space, that the impact of a large meteorite on the earth causes an absolute acceleration of the entire universe.

Geocentrism harms the church and the faith

Geocentrism is either wrong or meaningless depending on whether you are working in Newtonian mechanics or GR. A belief in geocentrism doesn't harm one's ability to get to heaven any more than a belief in young earth creationism, a literal belief in Noah's flood or a belief in Santa Claus or pink unicorns (except to the extent that we suppress our reason, we are suppressing one of the important faculties that distinguishes us from other animals).

But neither is holding to the plain error of geocentrism any help to the faithful. Frankly, most people don't care. The majority of people who come across Sungenis's bunkum will see it as that. But since Sungenis represents himself as a master apologist for the Catholic Church, then it's the Catholic Church that gets smeared with the buffoonery. It's certain that Sungenis causes scandal and damages the Church’s reputation amongst the faithful and unbelievers because of his insistence on this scientifically wrong and theologically unimportant point. It is appalling science, poor apologetics and abysmal evangelism.

He can't hope to convince scientists, because the geocentric idea is scientific candy-floss, uninteresting and meaningless in modern cosmology, promoted only by acolytes who themselves lack any fundamental scientific understanding.

Summary

To summarise, in order for the ‘centre of the universe’ to have meaning, we need an absolute space. In such a space, Newtonian mechanics (plus special relativity) applies, and there are many compelling reasons in that system which show that the earth cannot be the unmoving centre. In order to refute these reasons, Sungenis calls on General Relativity, but in General Relativity talk of a centre is meaningless (Sungenis also vehemently denies the propositions of General Relativity so logically he shouldn’t use it; he wants to have his cake and eat it). In an absolute space (Euclidean-Newtonian) model the earth cannot be at the centre and in a GR model there is no centre. Sungenis is caught in a fundamental logical inconsistency.

Here endeth the flogging of the pink unicorn.

References

1. For a Wikipedia article on Robert Sungenis go here: http://en.wikipedia.org/wiki/Robert_Sungenis

2. http://en.wikipedia.org/wiki/Modern_geocentrism

3. Ciufolini and Wheeler, Gravitation and Inertia, Princeton University Press, 1993

4. Penrose, The Road to Reality, Jonathan Cape, 2004

5. Feynman, Lectures on Gravitation, Penguin Books, 1999

6. See for example: http://pdg.lbl.gov/2004/reviews/microwaverpp.pdf

7. Bennett et al, First Year Wilkinson Microwave Anisotropy Probe(WMAP) Observations: Preliminary Maps and Basic Results, accepted by the Astrophysical Journal, available on line here:

http://lambda.gsfc.nasa.gov/product/map/dr1/pub_papers/firstyear/basic/wmap_basic_results.pdf

© 2006