![]() |
||||||||||||||||||||||||||
Response by Sam Cox to "Cosmodynamics" by Bruce Jimerson (U.S.A.)Hello! Quite some time ago, Bruce Jimerson wrote me a letter expressing interest in, and a certain fascination with the Einsteinian Hyperspherical Universe paper. He suggested that I look at certain concept discussions in his paper. I have, and can say the paper makes very interesting scientific reading. Like any good scientist, Bruce is very methodical and organized. A point by point discussion of Bruce's, quite comprehensive work would be too lengthy for this setting, but I do want to discuss certain very important conceptual and theoretical ideas relating to his paper. Research people using descriptive EHU material will find some very important concepts of The Einsteinian Hyperspherical Universe discussed in this response. First lets look at something easily accessible to everyone, Bruce's abstract. It is very well written, and gives a brief overview of his paper. The following statement is significant: "In a dilating spherical geometry, Newtonian laws and Einsteinian Equivalence lead to surprisingly simple explanations of the observed forces." I want to discuss this first, because a combination of Einsteinain Equivalence and Newton's laws is common in alternative cosmological concepts. I found similar concepts in Dr. Vankov's paper and Dr. Crawford's paper....and in a somewhat more generalized way, in Mr. Neese's and Mr. Fido's papers as well. I mention Dr. Crawford again, because, depending on the way this kind of theory is conceptually organized, it can very closely approximate reality. Newton's concept of gravity also closely matches the reality we observe in our frame of reference, however, as I said in my response to Mr. Homann, little things REALLY matter. We will discuss just how fundamentally little experimental deviations can affect the nature of reality toward the end of this response, but readers of my work describing the 7-Dimensional (and up) Einsteinian Hyperspherical Universe posted on this site ALREADY have a pretty good idea! I want to honestly say that I have serious theoretical reservations about mixing classical with Einsteinian concepts over cosmological distances. I'm very much a purist. While I realize that there is absolutely nothing wrong with using Newtonian dynamics and Euclidean space at non-relativistic (relative) speeds, and scales not too far out in the universe, I feel that Newton and Euclid were fundamentally wrong conceptually about the nature of the cosmic reality. The concepts are fine when evaluating a single frame of reference, (NASA uses Newtonian formulae in its computers which calculate spacecraft trajectories) but just cannot work when we attempt to use them to describe reality in our incredibly vast universe. A member of our English Department here at the college, while appreciating my writing very much, has criticized my use of clichés! Be that as it may, here goes another one! Lets not try to put a square peg in a round hole. I like clichés because they sell. They are warm and familiar. They help us to see concepts in a simple light, and if not blatantly misused, I think they sometimes fit in writing like, well, a round peg in a round hole- which is what happens in Cosmology when we combine Einsteinian equivalence with General Relativity. Dave Butterfield and Bruce Jimerson share many of the same ideas about space, but Dave, in this matter of space, is pretty Einsteinain, insofar as the geometry of space goes anyway. Dave wrote me about the possibility of massed space. I told him what I told our readers; that I do not believe space itself is a massed quantity. In the Einsteinain model, Matter and energy are massed quantities and space and time are not. (Are space and time found in the formula E=mc2?) While singularity can permeate, and even displace space and scale in an Einsteinain Hyperspherical Universe, space and scale themselves are defined by the relative presence of matter and energy. However, I also told Dave that the "neck" of space at 10-33 Centimeters is NOT a geometric point, and the universe, while vast, is not infinite either. If Dave wishes to investigate the possibility of massed space, such an endeavor, while heterodox to GR, constitutes a legitimate area of scientific study. Mass is conserved in each "hemisphere" of the 7- Dimensional Einsteinian Hyperspherical Universe. Each "hemisphere" contains 50% of the mass of the universe forever. Time, order and space likewise are conserved items in an eternal Einsteinain Hyperspherical Universe. While the total space of the universe remains static in General Relativity, the universe below the speed of light is internally dynamic, with the linked momentum of space, time and energy giving us our perception of movement in what to us is a dynamic universe. Space is the stage of reality, but I can say quite definitely that in any GR universe, Matter is definitely not passive. As I said, it is a basic fact of life in GR, that energy, space and time are eternally linked to each other in a multitude of possible proportions, at different, eternal coordinates of the universe. No ingredient of the universe is passive. In the Einsteinian Universe, by definition, neither space/time nor energy can exist without the others, and I'm afraid many important scientists forget this fact! Space without energy and time is an impossibility in a General Relativity universe- it cannot exist without them. Later in this response, I will reconcile this reality of the Einsteinian Hyperspherical Universe with certain theoretical problems and potential entropy difficulties. We will see how, and why, in an Einsteinain Hyperspherical Universe, Life is crucial to existence, not only by the intelligent observation of everything, everywhere, and by eternally existing, but in the role of a servo mechanism, anticipating and gradually correcting problems as eternity rolls! I was interested in Bruce's "Pseudo-space" outside the "Big Bang". As I just asserted, no such "potential" or pseudo-space exists in an Einsteinian Hyperspherical Universe. Beyond the singularity of the "big bang" is a "black hole". 360 degrees of EVERYWHERE becomes NOWHERE. Our only access to the "other side" is to proceed in a linear but opposite direction into the sub microscopic, through the neck of scale at 10-33 Centimeters and out, into the other side of space/time. As we look into space, from that frame of reference, we "see" not a "big bang" but a monster "black hole". The polarity of our atoms is reversed. Electrons are Positrons. Protons are Antiprotons and Neutrons are Antineutrons. Times flow seems normal to us, but broken eggs come together on the floor and jump into our hands. The flow of time returns in a single but CIRCULAR motion to its place of origin- the "black hole" of the other side. Like space and energy, time passes us in a linear, but seemingly reversed direction. Gravity pulls down, but the world lines of objects constantly defy it! We realize once and for all what a fictitious force gravity truly is! The mass of one "hemisphere" of the 7-Dimensional Hypersphere perfectly balances the other and prevents the universe from falling out of existence. The universe/antiverse systems "float" on each other at the sub microscopic multidimensional interface of a "sea" of froth. Like the sea of our Earth, this "mat", or better, interface of quantum fluctuations has waves and troughs. Near the two poles of the hypersphere, this sub microscopic "sea" whips into spray, and gathers like a huge tide to overwhelm space and time, which move into momentary nothingness with it. The "Big Bang" is hot and real, but there are two, not one. Half the universe always exists, while the other half is born in its arms...at a distant scale. Like a bonfire 20 miles away, the "Big Bang" seems insignificant to the rest of the universe, except that the patterns of entropy reverse...in a timeline, "bean shaped" singularity at the other pole of reality. Life never ceases. Each coordinate is preserved forever, yet from each frame of reference, a perfect mechanical explanation...a VERY REAL explanation of the dynamic processes involved exists. Quantum Mechanics works because it describes from OUR REFERENCE FRAME the very real relativistic changes which occur as our frame of reference with particles at relativistic velocities and energies in the universe, changes. We see these changes in terms of probabilities, yet from an eternal frame of reference, it can be seen that what we see (our own existence for example) as near impossibility is in fact certainty, certainty in an eternal Einsteinian Hyperspherical Universe! A four dimensional universe in General Relativity is analogous to a motorcycle on a one way road to eternity. General Relativity in 4-D, like our motorcycle on a one way road, works, but the cycle can fall over easily if we change only a few dynamic conditions, for example, slow down, or make a sudden turn at high speed. Also, since the road is one way, goes in one direction, and is the only road, there is no way to return home. The seven dimensional universe, by comparison, is like a four wheeled sports car, on a two way road to eternity. It is very stable and dynamically light years improved over the four dimensional model. The two way road permits a "turnaround" and return home. There are other important reasons why the 7-D model makes more sense too. If the reader is curious, he or she can read "The Einsteinian Hyperspherical Universe" posted on this web site, but briefly, as I just implied, a 4-D universe in GR explains nothing about where the universe comes from, it leaves the First Law of Thermodynamics hanging over a precipice, it has no mechanism to prevent the collapse of the universe from an engineering standpoint, and the symmetry problems are awful! Out of respect for Dr. Crawford, and to gain perspective on Bruce Jimerson's concept, lets see how the "motorcycle universe" and the "sports car universe" compare in a static frame of reference! As the motorcycle (4-D universe) slows up it becomes increasingly unstable. When it stops, it falls over...it is unstable. To support it, we need a kick-stand ...the kick-stand of classical Euclidean space. When we "park" our 7-D "sports car" universe and view it from a static perspective, it is perfectly stable; we can wash it and wax it. It has inherent dimensional stability, stability built in. The only problem with a parked car, is that we can't use it! It does not and cannot perform the function for which it was designed - to take us somewhere! If our sports car is to be useful, we must get inside it and go somewhere. Our universe is analogous. We can picture it from a static frame of reference, but we must get inside and go along for the ride to truly experience it. People who ignore the symmetry problems of a 4-D universe are conceptually- and in practical reality- on thin ice...really thin ice. Mirror images are an unsound concept, just as circular orbits, or a perfectly spherical Earth are unsound concepts. In fact the Einsteinian Hyperspherical Universe in reality may be more like the Einsteinian "Hyperspherical" Ladyfinger Banana! (perhaps not that distorted, but I'm sure the reader gets the idea. Even singularity can be distorted, as I implied in my discussion of "hairy" singularity!) Yet, who can visualize a living 1/2 of a person in traumatic hemi-section, or half a Sun, or for that matter, half a universe? When rounding a curve in our car, would we DARE assert that everything on the other side of that curve doesn't exist, just because we can't see it right now, and haven't seen it before? Of course, not every living, (or non-living) thing is symmetrical, certainly not from every frame of reference! Viewing a human being from either the front or the back, we are bilaterally symmetrical. If we draw a line (construct a plane surface) down the middle, we have two ROUGHLY similar halves. We have one of body parts in the middle, mouth, nose and navel, while we have two eyes, breasts, arms and legs. Imperfect symmetry is referred to by topologists as chirality. The Earth looks round from far in space, but on closer inspection it is not perfectly round and it has rough mountains on its surface. The plane of symmetry in the human body is a chiral area. Although such surfaces seem asymmetrical, they play a very important role in the universe! A fish has a two chambered heart. A human has a four chambered heart. The plane of symmetry is, from the viewpoint of the concept of Organic Evolution, a dynamic area, just as the chiral surface of the Earth is the abode of life! The 4-dimensional body is created from a tiny point (an egg), and then this plane of symmetry, which has no thickness! Over history, the fish heart developed a partition on the plane of symmetry, first between Auricles, creating the Amphibian heart. Then an incomplete wall formed between the two sides of the ventricle creating the Reptilian heart. In some reptiles, birds and mammals the partitioning of the heart was completed to form two attached, yet separate organs. While the heart was created, along the plane of symmetry, the circulatory systems of living things changed as well so as to create a more efficient, separate pulmonary and systemic circulation pattern. In Biology, we understand the limitations of the concept, but we say: "Ontogeny recapitulates Phylogeny". The development, short term of the young from egg to adult is somewhat similar to the development of a species over geological time. Here, interestingly, we have two different "kinds" of time...each linked to a different kind of consciousness! Living things as we know them are open, seeding, sub-universes. They start from a seed, grow, die and fall apart- all the while reproducing other similar universes to replace themselves. Yet, because of the nature of the universe, each living thing is an eternal stone in the cathedral of the sky, with its own time and space coordinates. It is intermittently, over 100 Billion years, born and reborn, forever. Yes, living things die, or better change, but they, like the universe itself, are preserved. If we rotate the human body only 90 degrees and view it from the side, it is no longer symmetrical in the same way. We have a front side and a back side...very different! Particles and photons are analogous. The asymmetry front and back, in the case of a human being is a reflection of the very real arrow of time, and the survival demands of our frame of reference. Walking "backwards" may seem funny, but I wish to remind our readers that in the antiverse, our backside and the past are (presumably) not dangerous, so our configuration there would hardly seem to be a matter of concern! Yet, if eyes are not needed in the antiverse, how do we "see"? Consciousness in the Antiverse, could not be experienced the same way we experience it in the universe. Unanswered too is the role of changing consciousness. Consciousness DOES change, but why and for what purpose? Permit me to make one metaphysical reflection. This universe is beautiful, so, in all good conscience we have no right to expect the other side to be any less so...though it might, like living in our own universe, take "some getting used to". Thomas Edison's last words when he briefly awoke from a coma were: "My, it IS beautiful over there!". Our universe has fundamental symmetries, of a variety of kinds, and when laws of thermodynamics, and basic concepts of engineering are at risk, I and all scientists should definitely take a close look at the demands of symmetry- and consider whether seemingly counterintuitive models might in fact, be the best representations of reality! Basic topological concepts are not really hard to understand! If we look at a piece of paper from the side, we see little or nothing. The same piece of paper turned towards us looks like the broad side of a barn! A basic understanding of what happens at singularity is no farther away than a simple Mobius Strip! We can look at a videotape or a CD-ROM and understand the essential idea of the eternal Einsteinian Hyperspherical Universe. Yet the Einsteinain Hperspherical Universe is not JUST a concept!! IT IS THE MOST EXPERIMENTALLY VERIFIED MODEL OF REALITY IN THE HISTORY OF THE WORLD! Albert Einstein was named "person of the 20th Century" for very good reasons! Why, in these discussions do I say 7-D AND UP (universe)? Am I the "Oracle at Delphi"? No. Increasing dimensions give increasing degrees of freedom in the construction of new realities, and, as important they give ever increasing stability to the universe. A huge (though not infinite) number of dimensions gives "Rock of Gibraltar" stability and IS A REFLECTION OF THE ETERNAL NATURE OF "The Einsteinian Hyperspherical Universe! This fact also implies that what we see and perceive is but the tip of a gigantic iceberg. (note: another 4-D projection). A good question for perceptive people who read this material is: "OK , it's vast, but not infinite. We wouldn't and couldn't exist, as we are, if the universe was infinite. I know, and I can understand that fact! Yet, somewhere isn't this universe lacking something in the entropy department? Not much, but eternity makes a big difference! This is the catch 22 of any finite universe, however vast and perfectly engineered- and it does open the door to the idea of an umbilical cord to infinity. The fact that light in the antiversal hemisphere can create in the universe, and influence events, however slightly by what we call "coincidence", is another subtle clue to the fact that control is indeed being exercised over events- however slowly, and that even the EHU has a need for entropy adjustments. The $64,000 question is; "Does the door to infinity in the Einsteinian Hyperspherical Universe open inward or outward?" Our readers may recall I have affirmed over and over again that there is NO OUTSIDE of the Einsteinian Hyperspherical Universe. By DEFINITION, outside the EHU is impossible. This leaves inside the universe, but how can infinity be found inside a finite universe? I considered this problem theoretically serious, and speculated about an entropy adjustment "umbilical cord" in my Einsteinian Hyperspherical Universe paper. In my original response to Dr. Nanduri, I felt confident enough about the need for an outside connection with infinity, I said that Dr. Nanduri's concept of a "self-contained universe" while very Einsteinian, was somewhat less than Divine! Yet on further consideration of the GR model, I am forced to agree with Dr. Nanduri that if Einstein is correct, infinity MUST BE FOUND INSIDE, NOT OUTSIDE A SELF-CONTAINED AND FINITE COSMOS. This connection, necessary to complete the theoretical concept of the Einsteinian Hyperspherical Universe, must link the eternal, and in that sense, infinite existence of the GR universe with a dimensional structure approaching the infinitely complex. An astronomer I respect very much, has a fine web site in which he has a question and answer section, for the public to ask questions...which by the way are very good questions indeed. One question was; "Do Photons have mass"? His answer was no. My guess is that he answered this question in the negative to avoid having to develop some of the most counterintuitive of Einsteinian ideas, such as I have developed on this site. However, by definition, Photons embody energy and energy has mass. A negative answer in effect is a denial of the Einsteinian principle of the equivalence of matter and energy...E=mc2. If we refuse to deal with that reality, we cannot go one step further toward understanding what is really happening in this universe of ours. Neither I, nor most scientists would assert that Photons individually have any more than the tiniest mass, but they do, in the SR, GR and QM model at least, have mass, and are not mass less. In fact, the concept of massed energy being equivalent to matter in a fixed proportion is the cornerstone of the universe! In the response to Dr. Crawford, I expressed amazement at the resolution and definition of the universe, down to an hourglass neck parameter (an absolute Planck Horizon) of 10-33 Centimeter. I tied this to the number of atoms in the universe, 1080 and asserted that the number of frames of reference in the universe is greater than 10100...much greater. I also said that if photons were used as a frame of reference base in the universe, and for a number of reasons this approach is favored, the number of frames of reference in the universe would be trillions on trillions of times larger. Our well engineered, eternal universe in 7-Dimensions and up needs very little entropy adjustment. However, indications are that it needs some. How can this adjustment come from within a finite universe? Many of our readers have heard of servo mechanisms. These are intelligently engineered systems designed to control energy or matter flow, defeat chaos and automatically prevent increased entropy (disorder) in a system. I designed a water system here in Pohnpei. If pump 1 fails, pump 2, 3, or 4 take over automatically. If power fails completely, check valves sense the dropping water pressure, open and keep the water coming from storage tanks on the hill. If power fails on one side of the road, the other side carries the load. Even a cut or broken pipe will not stop water supply to most of the system. Cars are built with oil and air filters, and special devices to protect close tolerance machinery from the carelessness of the ignorant. They are also built to protect occupants in a collision. Spacecraft have many redundant systems. Such careful conceptualizing brought the Apollo 13 astronauts home safely after a major disaster far from the earth. What our universe needs (and has) to make entropy adjustments is a servo mechanism based on infinity. This servo mechanism is LIFE. Life is embodied both in free electromagnetic energy and compacted matter based forms, and pervades the universe, making adjustments, anticipating problems and constructing defenses against increasing entropy (disorder), much as the Dutch people build and maintain dikes to keep out the raging North Sea. The famous scientist, Stephen Hawking, made a comment about Biology at the White House Millennium Conference with American President Bill Clinton, and was good-naturedly rebuffed by a Biologist who pondered his credentials to discuss Biology! Yet Biology, and the existence of life is the solution to the entropy problems of a closed, finite and eternal universe as defined in General Relativity! Life as a servo mechanism is an essential ingredient in the concept of Einstein, not only bringing the universe into being by observing it, but by making things happen and exercising a conscious and tenacious will to live against the tendency toward chaos. Concepts of "Good" and "evil", construction and destruction are closely tied to the unrelenting struggle against chaos and darkness in the universe. Now lets return to the infinity inward concept. Life finds its embodiment in light and its compacted forms. Frames of reference in the universe are based on Photons! Elsewhere in my reviews, I said that mathematically, GR admits values of 0 to infinity, and the universe continues forever. The AMOUNTS of space, time, and energy, though vast, are finite. These finite parameters are necessary to permit life to exist. Even a slight change in the mass of the universe, for example, would preclude life. (This is why a stellar black hole, in no way can be considered a separate universe....it is only a part of a greater, though finite, whole). Yet the universe exists eternally. This fact combined with a near infinite Photon based, frame of reference system, in which possibilities become so vast as to approximate infinity, coupled with the servo mechanism of life, makes the Einsteinain Hyperspherical Universe complete within itself. General Relativity is, as we will see shortly, logically rigid and very precise in its predictions. This makes it possible to conceptualize and describe it quite accurately, despite its complexity. Visualizing GR is an important first step toward understanding- and using it. I would like to see the Einsteinian Hyperspherical Universe "nailed down" conceptually within the next several years, in fact this "Cosmology Review" project in cooperation with the University of North Carolina is an ambitious first step. I am really happy with the research being posted on the Internet, and the articles appearing in wide circulation publications relating to the conceptualizations of GR posted on this web site. The material posted here is not copyrighted. It may be downloaded and used in any way the reader sees fit, for the Einsteinian Hyperspherical Universe is the property of the people of the world. To the best of my knowledge, Einstein never attempted to copyright the Theory of Relativity! I imagine a Unified Field Theory to be based on a function, perhaps some logarithmic relationship relating space, matter, universal scale, photon mass, and relative proximity to base microscopic singularity mass with the observed "forces". Push/pull forces would possibly relate to slight asymmetries in the configuration of superimposed, but topologically separated matter/antimatter pairs. I would be interested (and I know Dr. Natarajan would be interested) to know what people in the future find out atomic "particles" really are, and how they attain and maintain "structure". Recent discoveries regarding quarks are a good beginning. Magnetism is, I would think, our best hope for technological breakthroughs in GR. By 2025, I believe the experimental verification process of GR will be 99.9% complete, and if anything substantial lies beyond, we will have found it. By 2050, perhaps earlier, engineers may be building our first practical high-technology based on the GR concept. By the 22nd century, the planet Earth may be so different, we would hardly recognize it. Yet the largest gains we will accrue as a result of Einstein will be, I feel, in the area of the philosophical, spiritual and metaphysical. By 2200 AD the people of the world will TRULY appreciate why Albert Einstein was named the most influential person of the 20th century! Bruce's paper is very interesting! I wish I had the time and space here to speak to every aspect of his concepts, on a point by point basis. I have, however, made an attempt to touch on some of his major points as they compare and contrast with the Einsteinain Hyperspherical Universe. As the reader can see, the Einsteinain Hyperspherical Universe is truly comprehensive and specific. Its logical system is VERY precise, with no room for "fudging". I was recently looking at work on the predictions of General Relativity, compared with recent observations of the precession of the orbits of Mercury, Venus, the Earth and the Asteroid Icarus, as well as the other planets. The latest data on this experiment, a powerful confirmation of General Relativity, first publicized in 1915 and since refined with advanced spacecraft, are as follows, with comments by a thoroughly awed scientist, KS Brown, http://www.seanet.com/~ksbrown : "More recently, efforts have been made to explain some or all of Mercury's precession by oblateness in the shape of the sun. In 1966 Dicke and Goldenberg reported that the sun's polar axis is shorter than its equatorial axes by about 50 parts per million. If true that would account for 3.4" per century, so the unexplained part would be only 39.6", significantly different from GR's prediction of 43". The Brans-Dicke theory of gravity can account for 39.6" precisely by adjusting "w", which is a free parameter of the theory. However, Dicke's and Goldenberg's solar oblateness data was contradicted by a number of other heliometric measurements, all of which showed that the solar axes differ by no more than about 4 parts per million. In addition, the sun doesn't appear to rotate nearly fast enough to be as oblate as Dicke and Goldenberg thought, so their results could only be right if the interior of the sun is spinning about 25 times faster than the visible exterior, which is highly implausible. The current consensus is that the Sun is not nearly oblate enough to upset the agreement between Mercury's observed precession and the predictions of GR. This is all the more impressive considering that, in contrast to the Brans-Dicke and other alternative theories, GR has almost no "freedom" to adjust its predictions. It's is highly constrained by its own logic, so it's remarkable that it continues to survive experimental challenges. By the way, it may be worth noting that Mercury isn't the only object in the solar system that exhibits anomalous precession. The effect is most noticeable for objects near the Sun with highly elliptical orbits, but it can be seen even in the nearly circular orbits of Venus and Earth, although the discrepancy isn't nearly so large as for Mercury. In addition, the asteroid Icarus is ideal for studying this effect, because it has an extremely elliptical orbit and periodically passes very close to the Sun. Here's a table showing the anomalous precession of four objects in the inner solar system, based on direct observations:
The large tolerances for Venus and Earth are mainly due to the fact that their orbits are so nearly circular, making it difficult to precisely determine the axes of their elliptical orbits. Incidentally, Icarus periodically crosses the Earth's path, and has actually passed within a million kilometers of us - less than 3 times the distance to the Moon. It's about 1 mile in diameter, and may eventually collide with the Earth - reason enough to keep an eye on that precession! Sam's note: The author then proceeds into a detailed, and very interesting description of the mathematical aspects of this prediction by GR and concludes with the following comments and table: . As noted above, the gravitational radius of our Sun is 1.475 kilometers, so based on the elements of the planetary orbits we can construct the following table of relativistic precession.
The observed precession of 43.1 ± 0.5 arc seconds per century for the planet Mercury is in close agreement with the theory. We noted in Chapter 5.8 how Einstein proudly concluded his presentation of the vacuum field equations in his 1916 paper on general relativity by pointing out that they explained the anomalous precession of Mercury. He returned to this subject at the end of the paper, giving the precession formula and closing his masterpiece with the words: "Calculation gives for the planet Mercury a rotation of the orbit of 43" per century, corresponding exactly to the astronomical observation (Leverrier); for the astronomers have discovered in the motion of the perihelion of this planet, after allowing for disturbances by the other planets, an inexplicable remainder of this magnitude." (Albert Einstein) We mentioned previously that the small eccentricities of Venus and Earth make it difficult to determine their lines of apsides with precision, but modern measurement techniques (including the use of interplanetary space probes and radar ranging) and computerized analysis of the data have enabled the fitting of the entire solar system to a parameterized post-Newtonian (PPN) model that encompasses a fairly wide range of theories (including general relativity). Once the parameters of this model have been fit to all the available data for the Sun and planets, the model can then be used to compute the "best observational fit" for the precessions of the individual planets based on the PPN formalism. This gives precessions (in excess of the Newtonian predictions) of 43.1, 8.65, 3.85, and 1.36 arc seconds per century for the four inner planets respectively, in remarkable agreement with the predictions of general relativity....end quote of Mr. Browns comments but Sam has a couple of footnotes! "Cosmology Review" readers with a penchant for mathematics and topology will find a number of topics quite appropriate to the Einsteinian Hyperspherical Universe on Mr. Browns "math pages". I especially suggest "Mobius Transformations of the Night Sky". Also the perceptive reader will note a GR prediction of 3.85, but an observed precession of the Earths orbit of 5.0 arc seconds per century, an acceptable but much more significant deviation from the GR predictions than that of the other solar system bodies mentioned. The very slight eccentricity of the Earths orbit is, I feel, only a partial explanation for this observation. I wrote the editor of "Cosmology Review" and alerted him to the possibility that the moon was omitted in the calculations! Sir Isaac Newton complained that the dynamics of the Earth/Moon system were so complex, and had so many terms they gave him a headache. A quick calculation including the mass of the moon gave Sam a GR prediction figure of 4.4 arc seconds per century for the system, but this figure is probably on the low side. GR is SO PRECISE, I can say with certainty that when someone with an appropriate computer recalculates the figures, the GR prediction for the Earth/Moon system will be as close to the observed figures as those of the other planets and asteroids! The Einsteinian Hyperspherical Universe is truly, "Aaron's Rod", an almost magical vision of the universe, best portrayed in a multitude of dimensions. The above is only one set of recent data on one famous experiment. Other completely different experiments have tested this theory with results good to as many as 17 places- not the limit of General Relativity, but the limits of precision of our instruments! Look at the majestic cosmos, and yourself, in a mirror...and ponder! Sincerely, Samuel A. Cox; College of Micronesia, April 21, 2000 |
||||||||||||||||||||||||||
| Appendix B | ||||||
© 2000 Samuel Cox |
||||||