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The Cosmic Microwave Background temperature fluctuations from the 5-year Wilkinson Microwave Anisotropy Probe data seen over the full sky. Could Earth be in one of its two centers?

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The struggle, so violent in the early days of science,
between the views of Ptolemy and Copernicus would then
be quite meaningless. Either CS [Coordinate System]
could be used with equal justification.
The two sentences, ‘the sun is at rest and the earth moves’ or ‘the sun moves and the earth is at rest,’
would simply mean two different conventions concerning two different CS.

Albert Einstein

I. Introduction – About Geocentric and Heliocentric systems

People used to think the Earth as the center of the solar system. That model is called “geocentric”. It was supported by Aristotle and first widely promoted by Ptolemy. That was the story until the 16th century “revolution”. It was then that Copernicus, actually copying and promoting an old idea of an ancient Greek astonomer (Aristarchus), proposed that the Sun should be promoted to the center of the solar system. Since then most people think that the Sun being at the center of the solar system is the “truth”. That couldn’t be more far from the truth, since as I am going to show in “Chapter II – Nothing wrong with Changing Coordinate Systems”, it is completely valid to use any coordinate system you want in order to formulate physical laws. What is more, not many people know that even though scientific data showed that the Earth is at a priviledged centric position in the universe, cosmologists in the days of Hubble chose simply not to “accept” that data based on philosophical grounds, see “Chapter III – Heliocentric system is based on dogmas and not data”.

What this article does NOT

This article does not attempt to “prove” or “disprove” any hypothesis about the cosmological systems used.  This article just presents two different models of the universe and shows that heliocentric model is not the only model to be taken into consideration. It simply states some facts so as to show that choosing a Coordinate System (CS) is open to discussion and no single model holds some kind of self-proved “ultimate validity”, scientifically speaking. All established scientists accept that changing a reference system does not mean anything as far as the scientific valitity of the model is concerned.  New geocentic theories are promoted by well known cosmologists (see George Ellis), that show that a geocentric model could be more simple than a heliocentric one. The scientific papers mentioned in this article can be found by everyone on the Internet or in academic resources (respective sites are cited). Common terms (like “reference system” or “epicycle”) are presented based on Wikipedia articles.

II. Nothing wrong with Changing Coordinate Systems

Physics uses coordinate systems as reference when studying systems. A frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer. The need to distinguish between the various meanings of “frame of reference” has led to a variety of terms. For example, sometimes the type of coordinate system is attached as a modifier, as in Cartesian frame of reference. Sometimes the state of motion is emphasized, as in rotating frame of reference. [1]

A Simple example of changing Coordinate Systems

Below I cite a simple example of changing systems of referece (coordinate systems) in a case where two cars are running in a road.These two cars moving at different but constant velocities observed from stationary inertial frame S attached to the road and moving inertial frame S’ attached to the first car.

At some particular moment, they are separated by 200 meters. The car in front is traveling at 22 meters per second and the car behind is traveling at 30 meters per second. If we want to find out how long it will take the second car to catch up with the first, there are three obvious “frames of reference” that we could choose.

First, we could observe the two cars from the side of the road. We define our “frame of reference” S as follows. We stand on the side of the road and start a stop-clock at the exact moment that the second car passes us, which happens to be when they are a distance d = 200 m apart. Since neither of the cars are accelerating, we can determine their positions by the following formulas, where x1(t) is the position in meters of car one after time t seconds and x2(t) is the position of car two after time t.

 x_1(t)= d + v_1 t = 200 +  22t ; quad x_2(t)= v_2 t = 30t

Notice that these formulas predict at t = 0 s the first car is 200 m down the road and the second car is right beside us, as expected. We want to find the time at which x1 = x2.
Therefore we set x1 = x2 and solve for t, that is:

200 + 22 t = 30t quad8t = 200 quadt = 25 quad mathrm{seconds}

Alternatively, we could choose a frame of reference S’ situated in the first car. In this case, the first car is stationary and the second car is approaching from behind at a speed of v2 − v1 = 8 m / s. In order to catch up to the first car, it will take a time of d /( v2 − v1) = 200 / 8 s, that is, 25 seconds, as before. Note how much easier the problem becomes by choosing a suitable frame of reference.

The third possible frame of reference would be attached to the second car. That example resembles the case just discussed, except the second car is stationary and the first car moves backward towards it at 8 m/s.

It would have been possible to choose a rotating, accelerating frame of reference, moving in a complicated manner, but this would have served to complicate the problem unnecessarily. It is also necessary to note that one is able to convert measurements made in one coordinate system to another. For example, suppose that your watch is running five minutes fast compared to the local standard time. If you know that this is the case, when somebody asks you what time it is, you are able to deduct five minutes from the time displayed on your watch in order to obtain the correct time. The measurements that an observer makes about a system depend therefore on the observer’s frame of reference (you might say that the bus arrived at 5 past three, when in fact it arrived at three).

Difference between geocentric and heliocentric frames of referece

So as a conslusion, we find thatchanging the coordinate system (frame of reference) is a choice we have to make and that choice does not affect the “validity” of the scientific analysis of the system under investigation.  There is no difference between the goecentric and the heliocentric system in terms of “scientific validity”. We can choose any frame of reference and still be able to formulate physical laws and make correct predictions. That is why ancient Greeks were able to predict with such precision solar eclipses decades or even centruries before they happened.

What is interesting to note is that the geocentric (Ptolemaic) model of the solar system is still of interest to planetarium makers, as, for technical reasons, a Ptolemaic-type motion for the planet light apparatus has some advantages over a Copernican-type motion. The celestial sphere, still used for teaching purposes and sometimes for navigation, is also based on a geocentric system. [2]

The “elegance” principle

Many people advocate that the heliocentric model is more “valid” because it is more “elegant” than the geocentric one, since the latter has to make use of epicycles to fully describe the planetary motions. That could not be more far from the truth. The model of Copernicus also uses epicycles.In the Ptolemaic system of astronomy, the epicycle (literally: on the circle in Greek) was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. It was designed by Apollonius of Perga at the end of the 3rd century BC. In particular it explained the retrograde motion of the five planets known at the time. Secondarily, it also explained changes in the apparent distances of the planets from Earth.
When Copernicus transformed Earth-based observations to heliocentric coordinates [3], he was confronted with an entirely new problem. The Sun-centered positions displayed a cyclical motion with respect to time but without retrograde loops in the case of the outer planets. In principle, the heliocentric motion was simpler but with new subtleties due to the yet-to-be-discovered elliptical shape of the orbits. Another complication was caused by a problem that Copernicus never solved: correctly accounting for the motion of the Earth in the coordinate transformation. In keeping with past practice, Copernicus used the deferent/epicycle model in his theory but his epicycles were small and were called “epicyclets”.

In the Ptolemaic system the models for each of the planets were different and that was the case with Copernicus’ initial planetary models. As he worked through the mathematics, however, Copernicus discovered that his models could be combined in a unified system. Furthermore, if they were scaled so that Earth’s orbit was the same in all of them, the ordering of the planets we recognize today literally fell out of the math. Mercury orbited closest to the Sun and the rest of the planets fell into place in order outward, arranged in distance by their periods of revolution.
Whether or not Copernicus’ models were simpler than Ptolemy’s is moot. Copernicus eliminated Ptolemy’s somewhat-maligned equant but at a cost of additional epicycles. Various 16th-century books based on Ptolemy and Copernicus use about equal numbers of epicycles. The idea that Copernicus used only 34 circles in his system comes from his own statement in a preliminary unpublished sketch called the Commentariolus. By the time he published De revolutionibus orbium coelestium, he had added more circles. Counting the total number is difficult, but estimates are that he created a system just as complicated, or even more so. The popular total of about 80 circles for the Ptolemaic system seems to have appeared in 1898. It may have been inspired by the non-Ptolemaic system of Girolamo Fracastoro, who used either 77 or 79 orbs in his system inspired by Eudoxus of Cnidus. [3]

Copernicus’ theory was at least as accurate as Ptolemy’s but never achieved the stature and recognition of Ptolemy’s theory. In scarcely more than a hundred years, Copernicus would be overcome by events set in motion by Johannes Kepler and Galileo Galilei. Copernicus’ work provided explanations for phenomena like retrograde motion, but really didn’t prove that the planets actually orbited the Sun.

The first planetary model without any epicycles was that of Ibn Bajjah (Avempace) in 12th century Andalusian Spain, but epicycles were not eliminated in Europe until the 17th century, when Johannes Kepler’s model of elliptical orbits gradually replaced Copernicus’ model based on perfect circles.

Newtonian or Classical Mechanics eliminated the need for deferent/epicycle methods altogether and produced theories many times more powerful. By treating the Sun and planets as point masses and using Newton’s law of universal gravitation, equations of motion were derived that could be solved by various means to compute predictions of planetary orbital velocities and positions. Simple two-body problems, for example, can be solved analytically. More-complex n-body problems require numerical methods for solution.
The power of Newtonian mechanics to solve problems in orbital mechanics is illustrated by the discovery of Neptune. Analysis of observed perturbations in the orbit of Uranus produced estimates of the suspected planet’s position within a degree of where it was found. This could not have been accomplished with deferent/epicycle methods.

Important Questions that arise

The main question that arises from all the above is simple: how can we “know” what is the more “scientifically valid” coordinate system to use? Does the simplicity of a model indicate its correctness? The simple answer is that no coordinate system is more valid than any other, since chosing a reference system does not have any effect on the essense of the physical laws and the system’s behaviour. However it is true that if a model requires n equations to describe the system under analysis and another model requires (n + 100) equations to accomplish the same thing, the first model “looks” more “correct”. Nature is simple in essense and the more simple a theory the more “true” it “must” be. However new discoveries in the field of cosmology have questioned the heliocentric system exactly on the basis of “simplicity” and “elegance”, to which it was based to overthrow the geocentric model. In particular,  the current model of cosmology has reached some serious problems that cannot surpass without “inventing” new terms. We now must use “dark energy” and “dark matter” to explain how galaxies move. Some new geocentric cosmological models deem the use of “dark energy” and “dark matter” unneccessary, as the well known coslologist George Ellis has shown (see Chapter IV – Modern Cosmology and Earth Positioning). Does that mean that according to new data the most “correct” model is the geocentric one?

III. Heliocentric system is based on dogmas and not data

Exact sciences like physics have many limitations, often disregarded by their “followers” (i.e. people who think that measuring, evidence-based exact science is all, then we forget the basis of our science. When we forget that we use axioms (and that if we use other axioms we will reach completely different conclusions) then those axioms turn into dogmas. And dogmatism, in any form, is not a good thing…

…Such a condition would imply that we occupy a unique position in the universe, analogous, in a sense, to the ancient conception of a central Earth…This hypothesis cannot be disproved, but it is unwelcome and would only be accepted as a last resort in order to save the phenomena. Therefore we disregard this possibility…. the unwelcome position of a favored location must be avoided at all costs…. such a favored position is intolerable…Therefore, in order to restore homogeneity, and to escape the horror of a unique position…must be compensated by spatial curvature. There seems to be no other escape” [4] (Hubble, The Observational Approach to Cosmology)

The famous astronomer Edwin Hubble published on 1937 a study on the cosmological model of the universe, under the title “The Observational Approach to Cosmology”. In the data published in that study it was evident that Earth apperared like having a “unique” position in the cosmos, i.e. that it was in the center or very close to it. However Hubble chose not to accept that unique position based on philosophical propositions (principles) that be believed in.

In particular and even though the nebula distribution showed that Earth should be in a center position, he discarded that idea based on the “principle” that we are not unique (so it is illogical to say that we are in a priviledged center position in the Universe). In order to accomodate that “principle” he added some corrective factors to his equations! As simple as that! No hard data, no scientific analysis – a plain philosophical choice was the basis of the choice of heliocentricity over geocentricity!

Excerpt from “The Observational Approach to Cosmology”

One of the parts of the Hubble’s research where he makes those “philosophical” choices is cited below (source: http://nedwww.ipac.caltech.edu/level5/Sept04/Hubble/Hubble3_6.html) [emphasis added by me]:

The departures from uniformity are positive; the numbers of nebulae increase faster than the volume of space through which they are scattered. Thus the density of the nebular distribution increases outwards, symmetrically in all directions, leaving the observer in a unique position. Such a favoured position, of course, is intolerable; moreover, it represents a discrepancy with the theory, because the theory postulates homogeneity. Therefore, in order to restore homogeneity, and to escape the horror of a unique position, the departures from uniformity, which are introduced by the recession factors, must be compensated by the second term representing effects of spatial curvature.

Plate VI – Remote clusters studied by Hubble
[Source: http://nedwww.ipac.caltech.edu/level5/Sept04/Hubble/Hubble2_12.html%5D

There seems to be no other escape. Observations demonstrate that

Equation

Relativistic cosmology requires that

Therefore,

The curvature of space is demonstrated and measured by the postulated recession of the nebulae. To the observer the procedure seems artificial. He has counted the nebulae to various limits, applied only the corrections that are necessarily required (energy-corrections), and derived the quite plausible result of uniform distribution. Now, in testing the relativistic theory, he introduces a new postulate, namely, recession of the nebulae, and it leads to discrepancies. Therefore, he adds still another postulate, namely, spatial curvature, in order to compensate the discrepancies introduced by the first. The accumulation of assumptions is uneconomical, and the justification must be sought in the general background of knowledge. The outstanding argument is the fact that velocity-shifts remain the only permissible interpretation of red-shifts that is known at the present time. [4]

[End of excerpt from "The Observational Approach to Cosmology"]

The full text of the abovementioned reserach paper by Hubble can be found online at The Observational Approach to Cosmology archived at the respective site of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology (CalTech), under contract with the National Aeronautics and Space Administration (NASA).

Cosmology has not proved or disproved any model

So it is evident that astronomy has not proven or disproven geocentrism. In fact astronomy has provided a lot of evidence that supports geocentrism. Cosmology has created models, based on many unproven assumptions, that would make the observations of astronomy reject geocentrism. But if we took alternate assumptions, then those same observations would support geocentrism.

Two of those assumptions are:

1. Isotropy- the universe looks the same in any direction (and from any place)

2. Homogeneity- The make-up of the universe is more or less the same everywhere.

These two points taken together are called the Cosmological Principle. Since it is a “principle”, this means that pretty much all cosmologists, astronomers, etc. will make this assumption. Wikipedia simplifies that Cosmological Principle “on a large scale the universe is pretty much the same everywhere”. What does Wikipedia call on for support?

Observed isotropy of the cosmic microwave background radiation (CMB), combined with the Copernican principle

In cosmology, the Copernican Principle, named after Nicolaus Copernicus, states the Earth is not in a central, specially favoured position. More recently, the principle is generalised to the simple statement that humans are not privileged observers. In this sense, it is equivalent to the mediocrity principle, with significant implications in the philosophy of science. [5]

Many of the above point towards Milne’s metaphysical views, which were based in positivism, most especially in operationalism: only those objects whose properties could be directly revealed by some observational procedure, or operation, were to be counted among the real. His ‘cosmological principle’, namely, that every cosmologist in the universe should look out upon the same cosmos, was the prime example of such thinking. Later, Bondi would found Steady-state Cosmology on an even more general version of Milne’s principle, which he called the ‘perfect cosmological principle.’ Dingle is here arguing against the view, Milne’s view, that authentic science may be rationalist in epistemology (scientific knowledge is founded in pure theoretical reasoning apart from sense perception), and hypothetico-deductive in method (general principles are justified by their deductively implying correct observations). According to Milne’s principle, every observer in the universe should get the same world picture, that is, should make precisely the same observations of the universe at the same moment as any other observer. [6] Uniformity over spatial slices is guaranted by Milne’s invoking of the principle. Yet Milne’s universe evolves, it changes its form over time. Hence it has no temporal uniformity. Bondi felt that this raised the possibility that physics itself might change over time. Because of this risk, Bondi generalized Milne’s cosmological principle into what he called the perfect cosmological principle [=PCP]. According to this principle, all observers at all places and at all times will look out upon the same unchanging, unevolving, universe. Such a universe is a universe in a steady-state—hence the name. Although the principle (and the theory which results from it—steady state cosmology) is, as McVittie remarked, “much more restrictive than general relativity”; [7] it is this very restrictiveness which satisfies Bondi’s Popperian wishes:  For the correct argument has always been that the steady state model was the one that could be disproved most easily by observation, Therefore, it should take precedence over other less disprovable ones until it has been disproved. [8] But PCP and the theory which it engendered were exactly as described: eminently falsifiable. No matter the extent of Dingle et al’s disdain, Steady State theory stayed right out in front, ready for whatever empirical observations might be slung at it. As Bondi said “Show me some fossils from an evolving universe, and I’ll give it up.” In 1965, the fossils arrived, courtesy of the observations of the 3° K remnant microwave radiation. And Bondi, true to his philosophy, gave it up. [9]

Stephen Hawking says about these principles that “…all this evidence that the universe looks the same whichever direction we look in might seem to suggest there is something special about our place in the universe. In particular, it might seem that if we observe all other galaxies to be moving away from us, then we must be at the center of the universe.” [10]
He does provide and alternative view, though, as he continues: “There is, however, an alternate explanation: the universe might look the same in every direction as seen from any other galaxy, too. This, as we have seen, was Friedmann’s second assumption. We have no scientific evidence for, or against, this assumption.

We believe it only on grounds of modesty: it would be most remarkable if the universe looked the same in every direction around us, but not around other points in the universe.” [10]

We always keep in mind that the now used heliocentric model is not based purely on scientific data but also on philosophical propositions. That is not something “wrong” on its own. Everyone uses such assumptions when talking, thinking, writing scientific papers. What is “wrong” is trying to persuade people that what you say is the “only truth” that is acceptable by science…

IV. Modern cosmology and Earth positioning

Some modern cosmologists have presented data that make the thesis of an Earth-centric system more plausible. One of them is the well-known and well-established astronomer George Ellis.  George F. R. Ellis is the Distinguished Professor of Complex Systems in the Department of Mathematics and Applied Mathematics at the University of Cape Town in South Africa. He co-authored The Large Scale Structure of Space-Time with University of Cambridge physicist Stephen Hawking, published in 1973, and is considered one of the world’s leading theorists in cosmology. From 1989 to 1992 he served as President of the International Society on General Relativity and Gravitation.
Ellis has proposed that we live on a planet that is near one of the two centers the universe has and – according to his calculations – that geocentric model removes the need to “invent” terms like “dark energy” or “dark matter” to explain how galaxies in the cosmos move.

People need to be aware that there is a range of models that could explain the observations,” [...] “For instance, I can construct you a spherically symmetrical universe with Earth at its center, and you cannot disprove it based on observations.” [...] “You can only exclude it on philosophical grounds. In my view there is absolutely nothing wrong in that. What I want to bring into the open is the fact that we are using philosophical criteria in choosing our models. A lot of cosmology tries to hide that.” [11]

George Ellis, Mathematics
Department, University of Cape Town

In particular George Ellis proposed a “semi-geocentric” model universe that contains a naked singularity as a recycling mechanism, which he claims gives almost as good a description of the real universe as the conventional model. [12][13][14] In an article in Nature [15] Ellis proposes that the universe is like a cylinder-shaped universe with two “centers”, with the Earth is located on one side and a naked singularity on the other.

The two-centered universe proposed by Ellis, with our Galaxy near one of the centers.
(a) Space-time diagram of the Universe (two spatial dimensions suppressed). It is a cylinder, with a timelike singularity at the other center. Our past light cone is shown.
(b) Space section of the Universe (one spatial dimension suppressed). The singularity lies behind a fireball, which is like a supermassive star “over there.”
[Source: http://nedwww.ipac.caltech.edu/level5/Sept01/Ellis/Ellis5_2.html%5D

There is no cosmic inflation – the galaxies are arranged very unevenly, with a great deal of material crowded round the singularity, and very little near the Earth. The effect of such a distribution of matter is to produce a red shift of light that, at the Earth, has the same characteristics as if the galaxies were receding. [16] In particular, the Universe seems to be expanding ever faster — a phenomenon generally ascribed to the influence of ‘dark energy’. But Ellis suggests that the observed acceleration be a trick of the light in an inhomogeneous Universe and if we accept his geocentric model, we could do away with dark energy by imagining that we lived at the center of a spherical [15] inhomogeneity.

Possible objections to the model of Ellis

Possible objections to that model do exist, as there are objections to the standard cosmological model or any other model as well. In discussions [17] many people believe that such a model requires “believing” in some other anthropic principles that have not yet been proved. However the fact is that no matter what model you chose, you will make your choice based on philosophical grounds since science cannot tell the difference between a “correct” universe cosmological model and an “incorrect” one…
Moreover, modern cosmological models describe that the Big Bang happened at a singularity, or in other words: it happened at what was at then “everywhere”. That point the created the universe inflation we observe now. So in that way we are all now at the universe “center”.

VI. Conclusions – Where do we stand after all?

George Ellis in his paper “Cosmological Models” [18]states that(1) The Newtonian theory of cosmology is not yet adequately resolved.Newtonian theory is only a good theory of gravitation when it is a good approximation to General Relativity; obtaining this limit in non-linear cosmological situations raises a series of questions and issues that still need clarifying, particularly relating to boundary conditions in realistic Newtonian cosmological models.

(2) We have some understanding of how the evolution of families of inhomogeneous models relates to that of families of higher symmetry models. It has been indicated that a skeleton of higher symmetry models seems to guide the evolution of lower symmetry models in the state space (the space of cosmological space-times). This relation needs further elucidation. Also, anisotropic and  inhomogeneous inflationary models  [note: inhomogenity is closely related to the cosmological model proposed by Ellis] are relatively little explored and problems remain.

(3) It must be noted that it was Kepler and his idea of elliptical orbits which eliminated the need for epicycles – and not the heliocentric system idea by itself. Some people (wrongly) claim that the heliocentric model is more “correct” (whatever that means) because it is more simple than geocentric model. But is an ellipsis more “simple” than a circle? And what about the explanation of us seeing all galaxies getting away from us (Hubble) or the elimination of the need for dark energy if we consider Earth at the center (Ellis)? Does that mean that the geocentric model is in general more simple in explaining the observations? Even simple words like “simple” could be hard and complicated to define after all… And what about the fact that we are here (at Earth) looking at planets going around us? Is it really more “simple” to think that we stand somewhere else?!?!? If you are in a car and see other cars running, do you make your observations as if you were in *another* car? Would it be logical to do something like that?

In another of his papers, Ellis has postulated the following principle: Scientific exploration can tell us much about the  universe but not about its ultimate nature, or even much about some of its major geometrical and physical  characteristics. Some of this uncertainty may be resolved, but much will remain. Cosmological theory should acknowledge this uncertainty. [19]

Taking into account all of the above, we must be very careful when we speak as scientists or when we read as intelligent beings. When formulating / reading a theory we must clearly state / know what are the preassumptions that we make and the axioms or propositions that we use. [20]