Wednesday, February 28, 2007

Geocentrism – where’s the physics?

(The New Geocentrism, Part IV)

A response to Mr. Wyatt's comments on my previous post, "Relative claims to absolute Truth" (Part III of this series).

First some minutiae:
Mr. Wyatt is correct about the numbering of the articles. To give credit where it's due, however, it was Mary Daly (hedgemaker) and not I who wrote the original article, "The New Geocentrism."

Mr. Wyatt objects to my claim that he believes geocentrism to be obligatory, saying: “I have not stated that they still oblige, necassarily [sic].”

I am happy that Mr. Wyatt does not believe geocentrism is an article of faith. If that is the case, however, I am at a loss to understand why he considers the issue serious at all; it's just a curiosity of physics. Therefore, I would suggest that there are much more important areas to which Mr. Wyatt could contribute this time and energy. The culture war is in great need of persistence and energy, especially on the marriage and life issues fronts.

The Physics
In the following, I give Mr. Wyatt's statements in block quotes, with my responses following. Point numbers refer to the numbered points regarding the physics in my previous post, "The New Geocentrism, Part III."

Points 1-2:
Mr. Wyatt opines that the first two points of my commentary flow from my "presumptions." However, he quotes from Rosser as follows:

"...If one considers the rotating roundabout as being at rest [i.e., fix the earth], the centrifugal gravitational field assumes enormous values at large distances, and it is consistent with the theory of General Relativity for the velocities of distant bodies to exceed 3 x 10^8 m/sec under these conditions." (An Introduction to the Theory of Relativity, W. G. V. Rosser, London, Butterworths, 1964, p. 460)

What is Rosser saying here?
"If one considers the rotating roundabout as being at rest [i.e. fix the earth]..."

  1. The roundabout (earth) is rotating.

  2. We can pretend (OK "consider") it to be at rest

  3. by using a rotating coordinate system, aka a rotating frame of reference.

  4. "Under these conditions," i.e. within this rotating frame of reference, distant objects can have faster-than-light (FTL) velocities.

  5. Yeah, general relativity gives us the math to do it. (Special relativity does not allow rotating frames of reference, but general relativity does.)

That's exactly what I said in my first two points, which is to say it's the physics, not my presumptions.

Point #3:
Mr. Wyatt says:

First, if the universe is rotating, then special relativity does not apply, general relativity is required.

This is incorrect as stated. The “rules” of special relativity do apply to inertial observers viewing rotating objects, but not to rotating (and other accelerating) frames of reference. The universe as a whole is not sufficiently “flat” for special relativity to apply throughout, but that is completely independent of any rotation that might exist.

If an object were to locally overtake a star at a relative speed greater than "c", then in that case, even under general relativity, Cerenkov radiation would be locally generated, because in that case space-time would be [approximately] flat.

I assume he means, "If a star were to overtake its own light, ...." Nevertheless, it is heartening to see that he is willing to concede a couple of points here.

  1. This statement is a tacit admission that the stars are not really, actually, traveling faster than light, i.e. the light they themselves generate. They only look like they do (which is why I called it apparent motion).

  2. If we can show that objects in a local region (i.e. approximately flat space-time) would have to exceed the speed of light, we can prove that the geocentric position is tenable ONLY with a rotating frame of reference.

Let's look at a very local region of space, namely the Solar System. If Mr. Wyatt is correct in stating that the geocentric position uses a non-rotating, non-translating frame of reference -- indeed it could be called the ultimate inertial reference frame -- then special relativity applies in this local region.

A quick calculation yields the fact that an object at a distance of a mere 27.6 AU (astronomical unit = the average distance from the earth to the sun) would have to be traveling at the speed of light to circumnavigate the earth in 24 hours. Guess what? Many objects within the solar system have distances this great from the earth.

A well-known example is Pluto, formerly known as a planet, now re-christened a dwarf planet. Its average distance from the earth is approximately 39 AU, putting its average speed at about 1.4c (c is, of course, the speed of light). Further, because of its large orbital eccentricity, its minimum distance from the earth is approximately 28.6 AU, while its greatest distance is about 50 AU. Thus, Pluto's required orbital speed ranges from just over the speed of light to around 1.8c. So not only do we have FTL motion, we have accelerating and decelerating FTL motion.

An even more striking example from the many that could be given involves the famous comet Halley. At its nearest approach to earth, this comet is well under 1 AU distant (for example, in 1986 it came to within 0.42 AU of earth); however, at its greatest distance, it is about 35 AU from us. The astute reader will notice that this places its required orbital speed around the earth at much less than the speed of light when it is close to the earth, but as it moves away, it must accelerate to the speed of light and beyond. There's a word to describe this behavior: impossible.

The FTL velocity required of Pluto at all times and the acceleration / deceleration required of comet Halley from subluminal to superluminal and back again violates special relativity if the observer on earth is in an inertial frame of reference as Mr. Wyatt asserts. And we should, as he admits, see Cerenkov radiation if they really moved at FTL speeds.

Hence, the inertial frame of reference assumption must be wrong; therefore, the frame of reference for the geocentric universe is a rotating one, as Mr. Wyatt's own quote from Rosser indicates.
Bottom line: the geocentric view requires a rotating frame of reference.

Next item:

As to sciencemom's ballerina, unfortunately, general relativity has to consider the the universe rotating around the tip of her nose just as real as the ballerina rotating in a static universe, because general relativity excludes the concept of absolute space.

Yes, and thus of absolute motion. I think Mr. Wyatt has very nearly grasped Mary's point made in the original "The New Geocentrism" post, i.e. that the geocentric universe is no more "real" than the ballerina-nose-centric universe she suggests. Just for the record, I don't have a problem with the big bang theory put forward by Fr. Georges LeMaitre.

Amazing the corner that Catholics back themselves into to be "cool" to the world!

I have refrained from indulging in ad hominem arguments as they are both counter-productive and uncharitable. I would appreciate it if you showed me the same courtesy, Mr. Wyatt. We're discussing the physics, not either of our personal motivations which neither of us can know.

Point #4 (on lack of rotation of the universe):

Correct, it is difficult to rule out entirely, and just stating so does not constitute evidence.

It was not meant to be "evidence," but rather an acknowledgment of the limits of science. My point was that observational measurements cannot tell us for certain that there is no rotation, for the simple reason that measurements are only so accurate. When measuring small quantities, what looks like zero today may look like some small non-zero value next century. But read the rest of it. Direct measurements indicate that rotation is no more than 0.1 arc seconds per century. One published paper caused a great stir for claiming to have measured 10^-13 rad/yr (which is much less than 0.1 arc seconds per century).

Yet Mr. Wyatt continually refers to a "rotating universe" – one that rotates around the earth's axis once every 24 hours – as though it is a real thing and not a mathematical construct. That would be almost 5 billion times the maximum rotation indicated by measurements, and would undoubtedly result in fun alterations to the shape of the universe. A rotating universe would assume the shape of an oblate spheroid, which is not the shape of the real universe; the faster the rotation the more significant the flattening. (One can observe this effect in rotating galaxies, for example.) Even given that we cannot see the whole universe, we would still see the effect in the structure and mass distribution of the visible universe. Of course we don’t actually see any such thing.

Rotation means acceleration, and acceleration can always be measured, though uniform linear motion cannot. Rotation would also create a pattern of motion that would be seen in the CMBR (cosmic microwave background radiation). Such rapid rotation would be very readily detected.

Plus, objects in a universe that rotates around an axis would experience a centrifugal force proportional to their radial distance from the axis. Thus, objects in the “equatorial” plane of a fast-rotating universe, such as the one Mr. Wyatt suggests, would experience a significant outward acceleration; however, objects on the axis would not. This would result in a systemic anisotropy in measured redshifts: a very clear pattern of location-dependent variations. Again, no such pattern exists in real life.

Bottom line: all the evidence indicates that the universe does not rotate significantly

Besides, as I showed earlier, the geocentric position requires a rotating frame of reference. This is because the earth does rotate. The apparent “rotation of the universe” is merely the result of our living in this rotating frame of reference.

On to point #5:

Again, sciencemom misses a fundamental point. True if one stared down on the sun then one would "see" the entire universe rotating around the sun!

Mr. Wyatt has either misinterpreted or completely missed my point here. I do not believe the universe rotates around the sun, or the milky way for that matter. Mary made this quite clear at the end of part II of this series, "Up to Date Cosmology." The planets, dwarf planets, asteroids, and miscellaneous other bodies in the solar system do orbit the sun.* (Obviously moons orbit some of the planets, not the sun directly.)

[*This is an approximation because, technically, objects orbit their mutual barycenter (center of mass); however, since the sun is so much more massive than everything else in the system, the barycenter is always very close to the sun. For example, the barycenter of the Sol-Terra-Luna (sun-earth-moon) system is within the body of the sun, very close to its center. The statement about the planets and their moons employs a similar approximation.]

Since she claims this to be an inertial reference frame, and she is being precise, she must be proposing some form of milky-way-centrism! One in which the universal center corresponds to a point that sits above hte [sic] sun's orbit at least at one point in time.

The first sentence is a classic non sequitur. And as to the second, I don't recall proposing that the universe even has a physical center, let alone that it resides at #1 N. Solar Avenue.

When I spoke of an inertial reference frame, I was indeed being precise. For those who aren't sure what the term means, it refers to a non-accelerating (thus also non-rotating) frame of reference. I chose the location above the sun merely for convenience in observing the solar system. A location near the Andromeda galaxy wouldn't be nearly as opportune.

True if one stared down on the sun then one would "see" the entire universe rotating around the sun!
Rather, I think sciencemom is confusing coordinate transforms with reality, and trying to imply that the abstract mathematical concept of inertial reference frames, as applied in especially special relativity, "prove" that the universe is not rotating.

I said what I said because it is precisely what I meant. There are no coordinate transforms involved in my comments about what one would see.

And, I find a contradiction between Mr. Wyatt's two comments cited above. In the first, I am apparently trying to show that the universe rotates around the sun. Yet in the second (from the same paragraph!) I am accused of trying to show that the universe does not rotate at all. Weird. The fact is, I am trying to do neither. I am simply describing what one would see from an inertial frame of reference placed above the sun's north pole merely for viewing convenience.

Wrap-up :

as shown in great detail in Galileo Was Wrong, most of our observations and mnay [sic] experiments support a central and non-moving (rotating or translating) earth!

Again, I find a strange dichotomy between this assertion that one can "prove" a non-moving earth, and the previous assertions having to do with the fact that in general relativity there is no absolute space or motion. Further, it is physically impossible, even in classical physics, to prove non-motion for the simple reason that there is no way to detect uniform linear motion.

Science itself admits that it cannot demonstrate the rotation or translation of the earth (as independent of a counter movement of teh [sic] universe).

This is also untrue, as I believe I have amply demonstrated above when I showed that the geocentric view requires a rotating frame of reference. Besides, ring lasers can measure absolute rotation. I plan to soon post a brief article on physical evidence for the earth's rotation.

Finally Scriptures, the Fathers, and a number of popes have testified or made declarations in favor of geocentrism. None have explicitlky [sic] denied it. Why not at least consider it?

I have considered it, and find it untenable. Readers may wish to check out Mary Daly's "Up to Date Cosmology" post for more on the Church's view.

For the reasons I discussed before, and in more detail above, the geocentric system requires a rotating frame of reference. It's the physics, not my presumptions, that dictates this. All the physical evidence indicates that the universe does not rotate significantly, and that the earth does rotate.

Perhaps a simple thought experiment will clarify the situation for most of us. If we could somehow remove just the earth from the solar system, the rest of it would continue to operate pretty much as before, except for earth’s moon. However, if we could remove the sun, the solar system as a system would fall apart.

The most that can be said for the geocentric view is that "it sure looks that way from our position here on earth and we can express that idea mathematically using general relativity," but that doesn't make it Truth. This seems to me to be a classic case of "confusing coordinate transforms with reality," to borrow a phrase from Mr. Wyatt.

Back to Part III

On to Final Note


ScienceMom said...

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