by Fred Vaughan
I'm tired of Old;
Let's quit this game.
Let's play something else
Like Doctor.
The author and patient at home.
Memoir of a Non-Irish Non-Jew, 99 pages (paperback $999,999.99) by Richard May
What is our identity, if we awaken in the moment?
Memoir of a non-Irish non-Jew isn't about being Irish and Jewish or non-Irish and non-Jewish. It is about the chase of tracking down one's ancestral origins, whatever they may be, and the delightfully quirky unexpected discoveries that await you along the way, no matter what your family origins. "You are a link in the chain of your blood. Be proud of it, it is an honor to be this link," G. I. Gurdjieff. But it's also about learning not to identify with the achievements and failing of one's ancestors or even with one's own carefully crafted persona. "What do I have in common with the Jews? I don't even have anything in common with myself, " Franz Kafka. Who are we? Remembering with awareness of various levels of irony the response of Bodhidharma, the Indian monk who brought Buddhism from India to China, to King Wu's question, "Who are you?" — "I don't know"! What is our identity, if we awaken in the moment from the stories of our lives and the dreams of our culture?
http://www.lulu.com/content/803771
Paradise Emporium -- a collection, 247 pages - $9.48
by CL Frost
This newly released collection by a versatile, highly
skilled writer and artist includes short stories in the science
fiction, fantasy, magical realism and speculative genres. Among
these is the short story from which the collection derives its
title as well as many fine poems and a huge assortment of visual
artistry that also covers a wide variety of genres.
http://www.lulu.com/browse/book_view.php?fCID=561988
World of Villages: A Six-Year Journey Through Africa and Asia,
499 pages - out of print, but used copies are
readily available at very reasonable prices.
by Brian Schwartz.
The author traveled with, and stayed among, the native villagers
everywhere he traveled throughout Africa, Asia, and Indonesia
getting to know the strange behaviors of strange peoples.
Published in 1986 by Random House ISBN: 0517558157
Also published as Travels Through the Third World by
Macmillan ISBN: 0283992123
Brian Schwartz also wrote China Off the Beaten Track
- How to do it on your
own, published by St. Martin's Press ©1983 Library of
Congress # 82-61428. Copies of this book are also readily
available.
Aberrations of Relativity, 201 pages - $15.00
by Fred Vaughan
This is a collection of articles that emphasize one the most observable
aspects of relative motion, i. e., aberration effects. There are many
informative diagrams and illustrations with many new insights. What the
author calls "observational relativity" is defined in this book as a
possible alternative to Einstein's special theory.
The reader will gain valuable insights into all aspects of relativity
including why Einstein considered it necessary to embrace time dilation
and length contraction in his special theory, and why that might very
well not have been necessary.
The book is written for the intelligent (maybe very intelligent) layman,
with little in the way of advanced mathematics required to fully
comprehend the discussions.
http://www.lulu.com/content/572819
In Proust's Footsteps, 99 pages (hardcover $22.40)
by Maria Claudia Faverio
"In Proust's Footsteps" is Maria's fifth poetry book after "Entropy",
"Behind the Mask", "Metaphors instead of Formulas", and her "Selected
Poems" collection. Maria is a committed, award-winning poet whose books
are highly recommended by the Poetic Genius Society. Maria is also the
current editor for poetry and prose of the International Society for
Philosophical Enquiry.
http://www.lulu.com/content/430375
Learn about this talented Australian author, poet, and artist as well as her many creations of prose, poetry, classical music CDs, puzzle books, fairy tales, and artistic images at the following site: http://www.lulu.com/mycreations.
NATAN, 108 pages - $13.69
by Albert Frank and Muriel Hustin
Nath is a genius, Tanguy an idiot. Any such extremes disturb people. In
recognition of this fact, a pharmaceutical corporation is undertaking
experiment with a new drug, ?normality pills?, that would move them both
toward the norm. It is decided to put them in contact using e-mail
exchanges. Those responsible for the experiment will monitor the
exchanges. So a deep friendship evolves between two individuals who
normally would never have even met. Their dialogue is moving right up to
the terrifying conclusion. One of the themes of the narrative is the
loneliness of the extremes.
http://www.lulu.com/content/71060
Losing Faith in Faith: From Preacher To Atheist, 342 pages - $25.00
by Dan Barker
After 19 years of evangelical preaching, missionizing, evangelism and
Christian songwriting, Dan Barker "threw out the bathwater and
discovered there is no baby there." Barker describes the intellectual
and psychological struggle required to move from fundamentalism to
freethought. Sections on biblical morality, the historicity of Jesus,
bible contradictions, the unbelievable resurrection, and much more. This
book is an arsenal for skeptics and a direct challenge to believers.
http://ffrf.org/shop/books/details.php?cat=fbooks&ID=FB5
The Magic of Ed Rehmus, 192 pages - $15.00
by Ed Rehmus (edited by Fred Vaughan)
This collection of creations by Edward Rehmus includes essays, artwork,
poetry, linguistic studies, comics, and puzzles. The style of Ed
Rehmus' prose is reminiscent of H. L. Mencken in his hay day. As a
friend said of Ed in eulogy, "He went for the bones of what he was
considering and the stormy winds could make off with the sails if that
was a consequence!" On his own behalf Ed had said, "What indolence and
what prodigality to trust to usage that which ought always to be
spontaneous, creative and conscious: speech!"
http://www.lulu.com/content/476575 - regular price.
" No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury, except in cases arising in the land or naval forces, or in the Militia, when in actual service in time of War or public danger; nor shall any person be subject for the same offense to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation."
... "'defence' of Lie's behaviour by referring to the close relationship between genius and madness really created a generally accepted explanation which has survived up to the present. By this act of 'defence' Klein did his old friend an incredible injustice."1
by Fred Vaughan
We all know what it means to "take the fifth". It ain't good!
There have been many attempts to reduce the number, modify the structure, and alter the phraseology of Euclid's postulates, but it has been found that for plane projective geometry they are by and large very sound as initially presented. However, there seems to have been little effort to determine whether there might be a different postulate more appropriate that the fifth for modification to provide compatibility with the formalism of relativity and our current view of the universe.
That one of Euclid's postulates upon which he based The Elements of his geometry might be flawed, or worse yet, unnecessary is, of course, an integral part of present day establishmentarian mathematics and physics. The Fifth Postulate, that through any point only one line can be drawn parallel to any other has been unanimously selected as the culpable postulate invalidated by the current understanding of relativity and cosmology at larger scales of our universe.
Long before that mathematicians began exploring alternative geometrical possibilities deriving from the elimination of this assumption after repeatedly failing to reduce it to a provable theorem. This was before there was any inkling that we might actually live in such an alternative universe.2 Gauss actually attempted measurements employing light signals to determine based on such empirical evidence whether that might be the case, however. But with the advent of Einstein's relativity, bold conjectures of a combined spacetime exhibiting strange geometrical properties have been totally accepted by the scientific community, so that alternative-fifth-postulate-geometries thrive; notwithstanding this feeding frenzy on the Fifth, Postulate convincing evidence that another of Euclid's postulates is invalid continues to be denied.
Relativity provides the analytic work of pioneering mathematicians a context of immediate relevance and it should not be surprising that their work would have been re-evaluated with renewed interest. These former discoveries concerning viable geometries not requiring Euclid's Fifth Postulate revitalized mathematical physics.
One must note that even in the general theory of relativity, physical experiments are always considered as being conducted within locally-Lorentz reference frames. What this means is that even though an observer may experience wild gyrations of acceleration due to gravitation or his own rocket engines, at each moment in time it is only his instantaneous velocity relative to what is being observed that is pertinent to the geometry of his current observations. This is where one must begin if the objective is to map observations between oneself and other observers in relative motion. So the Lorentz geometry of special relativity would seem to be the local geometry of choice. This has been thought to involve a flat spacetime, but it is hardly without distortion as the author has discussed elsewhere. In particular relativistic aberration distorts the directions of objects in one frame of reference relative to where those objects are to be seen in the other. The coordinate axes of the other observer are not immune to this distortion
Let us look at Euclid's five postulates and attempt to determine for ourselves which one seems most likely to be at odds with such observational inferences made from Lorentz reference frames. Here are all five postulates3:
- Only one straight line can be drawn between any two points.
- A finite straight line can be extended indefinitely.
- Only one circle of a given radius can be centered at a given point.
- Through a point at a distance from a given line there is only one line that can be drawn through the point that is perpendicular to the given line.
- Through a point at a distance from a given line there is only one line that can be drawn that is parallel to the given line. 4
In lieu of the apparent directional distortions of the three perpendiculars that constitute the spatial axes of Lorentz reference frames of various observers in relative motion, one can but wonder why there has been this preoccupation with the Fifth Postulate anyway? What we have found is that each of all possible coincident observers with unique relative velocities would witness all other observers' perpendicular directions to be misaligned with regard to their own. Parallel lines of sight in one frame of reference would remain parallel for the others although they would in concert be pointing off in other directions.
So it seems self-evident that to make sense of the coordination of the geometrical observations and constructions between relatively moving observers, we must reject the Fourth Postulate! It seems to the author that we may even need a new theory of perpendiculars. But his elder sister did nickname him "Perpendicular" — Perpy for short — so maybe such stigmata warps ones sense of geometrical rectitude.
On that charge I think I will claim my Fifth Amendment right.
1 Written by Marius Lie's friend and collaborator Friedrich Engel at his death. The quote is provided gratuitously as being of possible interest to this audience.
2 Robert Bonola, Non-Euclidean Geometry, Dover, New York (1955), originally published 1914. Supplements within this book contain "The Theory of Parallels" by Nicholas Lobachevski, and "The Science of Absolute Space" by John Bolyai. The book also provides a context for the pioneering efforts of such names as Gerolamo Saccheri (1667-1733), Johann Lambert (1728-1777), Adrien Legendre (1752-1833), Wolfgang Bolyai (1775-1856), Friedrich Wachter (1792-1817), Bernhard Thibaut (1776-1832), Karl Gauss (1777-1855, Ferdinand Schweikart (1780-1859), Franz Taurinus (1794-1874), Nicholas Lobachevski (1793-1856), John Bolyai (1802-1860), B. Riemann (1826-1866), Ludwig Helmholtz (1821-1894), and Marius Lie (1842-1899).
3 This version involves only a slight rephrasing of those given by Sir Thomas Heath in The Elements of Euclid. Changes parallel Playfair's rephrasing of the Fifth Postulate.
4 In 1795, John Playfair (1748-1819) offered an alternative version of the originally translated postulate involving interior angles, which was: That if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the straight lines, if produced indefinitely, will meet on that side on which the angles are less that two right angles. This alternative version, of course, gives rise to the identical geometry of Euclid. It is Playfair's version of the Fifth Postulate that most often appears in discussions
by Fred Vaughan
There is something very compelling about a logarithmic functional form for the distance-redshift relation in observational cosmology. In fact, it is so compelling as to seem logically necessary as the form of that relationship — whether that fact is generally acknowledged or not, which of course…it is not.
To adequately understand this, let us look at what is involved in light being redshifted along a propagation path between emission and observation. Suppose there is an observer at point A for which a telescope on earth would suffice as an instance. And suppose that there is an ensemble of atoms in a star in a distant galaxy that we will refer to as point C that emit light at a specific wavelength associated with the spectra of a particular element. These atoms emit photons of light that can ultimately be observed by the telescope at A. If there is a distance-related redshift in the spacetime where all this takes place, then the wavelength of the light λAobserved at A will be related to the emission wavelength λCemitted at location C according to the redshift definition:
ZAC = ( λA − λC ) / λCThis is true no matter what the separation between A and C or anything else. It's just a definition. For physical reasons ZACmust be a continuously increasing function of the separation AC. So, let us define the redshift-related parameter ζ(d) as a continuous function of the separation d = AC as follows:
ζ(d) = ZAC + 1 = λA / λC
Since ζ(d) applies to for any separation, we should be able to place an observer at any point B along the light path from C to A, where d1= AB and d2 = BC, with the observed radiation exhibiting redshifts as follows:
&zeta(d1) = λA / λB and &zeta(d2) = λB / λCTherefore, over the total distance for which d = d1 + d2 the following relation must apply:
ζ(d1 + d2) = ζ(d1) . ζ(d2),And as a necessary consequence of this relation, we must have that:
ζ(d) = e αd = e α ( d1 + d2 ).And, of course, the inverse functionality must be:
d(ζ) = ln (ζ)
The "standard model" embraces a broad class of disparate alternatives loosely associated by adherence to Hubble's hypothesis and one form or another of Einstein's theory of general relativity. The Einstein — de Sitter model is but one of the simpler of these alternatives that exhibits a "flat" spacetime, because of which it is frequently discussed for didactic purposes, although it is generally disparaged as a somewhat naïve candidate for serious consideration. This short shrift seems ill-advised to the author in light of the interesting fact that a key feature of the Einstein — de Sitter model (unlike the others that are considered more viable) is that the distance-redshift relation is given by the logarithmic form.
Although the Einstein — de Sitter model is virtually never considered a viable contender by current cosmologists for the ultimate acceptance, its logarithmic form of the distance-redshift relation is generally used for convenience in analyzing associated phenomena because it so closely fits the actual data as distances to observed objects increase. Strange isn't it?
The preceding discussion explains the situation depicted in the figure below.
It is worth considering what would be implied by a relationship other than one involving the logarithm: What is involved is whether or not homogeneity applies to this relationship.
The seeming improbability of, but nonetheless presumed, failure of the logic we have described above is what has contributed so substantially to presumptions of the supposed evolution of developments in our universe. But if one decouples redshifting as an observed phenomenon (whatever its cause) from constraints imposed by whatever causes it according to one cosmological theory or other, then the logarithmic relationship to distance continues to make logical sense as we have shown above. We will be told, of course, that to presume that distances could be linearly additive if space itself is nonlinearly distorted would itself be an improbability. But would it? Even along a curved path the distance along that path is linearly additive as the basis for the integration of distance along infinitesimal line segments.
In the next figure we have drawn a situation similar to that shown in figure 1 except that space is such that line of sight distance is curved along a light path through space. In this case, in addition to observers A and B, we have observer B capable of emitting light from a separate source at the moment of his observation of the light from C which is set to resonate at precisely the same frequency (wavelength) as the radiation he observes. Let us analyze the possibilities here.
As before, we must now have that ζ(d1) = λA / λBand ζ(d2) = λB1 / λC. This would seem to apply by reason of the definition of redshift, if the source of the radiation of wavelength λB1is indeed set up to equal that of λB. This can be verified by the digital communication from B to A independent of the redshift impact on that link if A's antenna is properly tunable. Then as long as there is a general formula applicable throughout space and time relating redshift and distance,
d ← f(Z+1) and Z+1 ← ζ(r)If the peculiar functionality of the inverses f(x) and ζ(y) were independent of position in spacetime (i. e., if spacetime is indeed homogeneous), then the logarithmic/exponential relationships must apply. It is the ad hoc denial of this cosmological principle that had reigned supreme since Copernicus that empowers the standard model with the freedom to deny an otherwise logical premise.
by Richard May in response to Fred Vaughan
Fred wrote, "If one pokes an active hornets nest something will happen."
Fred,
The hornets will greet you with cake and flowers and view you as their liberator!
The Creator made hornets as lovers of freedom. Hornets should have a Western style democracy. If a hornet tries to sting you, it's part of Al Qaeda.
Don't misunderestimate hornets! Lovers of freedom should invade hornets nests everywhere. A surge of nest pokers is vital to our national interest or the hornets will attack the Homeland!
If you see a mad dog, kick it!
You just don't make any sense, Fred!
"W"-Tzu
"Veritas Our president is a Christian? So was Adolf Hitler. What can be said to our young people, now that psychopathic personalities, which is to say persons without consciences, without senses of pity or shame, have taken all the money in the treasuries of our government and corporations, and made it all their own?"
&mdash Kurt Vonnegut
by Fred Vaughan
I was born here, as were all of the previous five generations in my family. I believe that every one of my progenitors considered themselves most fortunate to be American. I do. Of course one must assume that they were indeed proud to be Americans as well, just as I had been until Election 2000. The illusion of democratic difference died then, and the corpse is beginning to stink. Like Kurt Vonnegut I have become quite a disillusioned old curmudgeon.
There is still much to be happy for. Our standard of living is still high - not the highest in the world anymore, but still high. We still have constitutional rights - although nowhere near as many as we had a very few years ago. We still have freedom of speech - more or less - as this will hopefully demonstrate, but nowhere near as much as we once had, and our "freedom of the press" has become freedom of the administration and its corporate backers to propagandize the populace.
But I am ashamed of the rape of democracy by organized voter fraud, manipulated propaganda, and the projection of lies such as, "Why vote, they're all equally bad!" Anyone who believes that has not really thought about it. Would Al Gore have lied to get us into a stupid and unconscionable war with 'collateral damage' running to a million lives? Would John Kerry? Would either of those candidates who by almost any valid accounting actually won the last two elections have condoned torture or systematic destruction of the constitution? Would they have unconscionably provided tax cuts to the top 1% which depleted the treasury at a time when hundreds of billions were being appropriated for a war initiated because of administration lies just to give the excuse of our not having enough resources to care for our sick, our poor, our aged? Would they have ignored the victims of Katrina? Would they have ignored global warming? Would they have sold our freedom of the press to our largest corporations for campaign donations who then goad us into the wars that maintain their "World Trade"?
Today we still mourn the deaths of those students and faculty massacred at Virginia Tech. Our president says we will get over it — without gun control legislation just as we do the other 30,000 fatalities from gun violence in the United States each year! Just as he thinks we will get over Katrina — even without there having been a conscionable FEMA response. In the last week 30 Americans died in Iraq, and I suppose we will get over them too just as we have gotten over the 3,000 before them. We will get over the 200 innocent lives lost to collateral damage by bombs in Baghdad today just as we have gotten over the million before them — collateral damage to Bush's "just cause".
Here is a tribute to Kurt Vonnegut who had the courage to say it how it is:
His book is "Cat's cradle", not "Ice Nine"!
The Way the World Ends!
by Fred Vaughan
"I've got a question, Ray. Everyone knows your opinions about miracles and that it's all physics, so what I want to know is how your good fortune can be reconciled with statistical probabilities. What you have experienced seems impossible to me, Ray!"
"It's the wrong use of the telescope again, Tim."
Tim listened and laughed. "How can that be? Where's the telescope?"
"Well, you're asking about the probability of an event after it has already occurred, aren't you? So probability and statistics don't apply. Statistics has to be directed the other way. Let's say I flip a fair coin one hundred times and get one hundred heads in a row. How would one square that with statistics? Isn't that the essence of your question?"
"Yes! That is the question, Ray! How is it you could flip one hundred heads in a row?" Tim affirmed.
"Well, what if I had flipped a head and a tail alternating until I had fifty heads and fifty tails? Would that bother you as much?" Ray asked.
"No, of course not! That's fifty-fifty, right on the law of averages!" Tim said.
"Well, you're using your telescope incorrectly then, because both cases — a hundred heads in a row, and a sequence of head-then-tail fifty times in a row — have exactly the same likelihood. The only reason you think the one case more likely is because it's similar to a kazillion other cases that are also fifty-fifty. But whatever combination of heads and tails that you get after a hundred flips of that coin will be exactly the same likelihood as the hundred heads, Tim. You flip a coin a hundred times and whatever sequence of heads and tails that you get will have been exactly that unlikely. But a lot of them are disguised."
" Disguised? You've got to be kidding me, Ray!" Tim was not convinced.
"Nope. I'm not." Ray seemed to be done with that discussion.
Tim came back with, "Wait, Ray! That makes no sense! This kind of thing just doesn't happen!"
Ray seemed somewhat tired as he replied, "Your key phrase there was 'kind of thing', Tim. Classes of situations like flipping fifty heads in one hundred flips of a fair coin are the 'kind of thing' that are phenomenally more likely than flipping all heads or all tails. But what you're missing here is that each one of those situations like, head-tail-tail-tail-head-head-tail-head… etc., is no more likely than flipping all heads. There are just more situations that comprise the class involving fifty heads. There are kazillions of them like I said. Does ten-to-the-twenty-ninth have any meaning for you, Tim? Remember! Whenever something actually happens, it is a single situation not a class of them. Everything is unlikely, Tim. Everything! When you flip your coin a hundred times, whatever you come up with will have defied odds of ten-to-the-thirty-first-to-one! But don't doubt for a second whether what happened actually happened, or if it defied the laws of physics, just because of that or you'll be legally insane. Something happens! It has to."
Tim looked as baffled as an ostrich blinking at a bright sun.
Ray knew he had been a pompous asshole. He had indeed been phenomenally lucky. He had to admit that much. Wasn't 'fair' coin defined as one for which one hundred heads in a row does not happen? What about each subsequent flip of that coin along the way? Any one of those coming up tails would have terminated the phenomena of Ray Bonn. Ray Bonn was not some metaphysical being standing back behind a protective glass watching the coin flipping; he was the coin flipping. He was the outcome of all the contingent coin tosses; anything else was an instance of that most major of logical fallacies, looking down the wrong end of telescopes.
"…how shall they believe in him of whom they
have not heard?
and how shall they hear without a preacher?"
— Romans 10:14
by Fred Vaughan
In "Death of a Salesman" by Arthur Miller there is an illusion nurtured by Willy that a man can be "worth more dead than alive."1 Obsessions with destiny can play such tricks on a person. In the end, however — but before Willy's suicide — there is a summing up: "Pop!" his son says, "I'm a dime a dozen, and so are you!" Repudiating him with, "I am not a dime a dozen! I am Willy Loman," does nothing to substantiate an imagined reality in which the salesman Willy Loman has profound significance. But the Willy Lomans of the world, and perhaps even Arthur Millers, cast short shadows in comparison to men for whom the appellation "tragedy" applies. There is neither singular tragic flaw to precipitate demise nor great ideas hanging in the balance with their life or death. So the terms "tragedy," "death," and "salesman" to which I refer in the title pertain very little to the play of the similar name. Miller argued that although Willy is indeed a "little man" he is worthy of the pathos we usually reserve for tragic heroes such as Oedipus Rex. His argument was that any character willing to sacrifice his life to secure a sense of personal dignity invokes the sense of tragedy. So who knows, it could be, although I tend to doubt it. Nonetheless, I had something else in mind.
There must certainly be many cases throughout history in which ideas of extreme import have been lost for no other reason than the death of a chief proponent although a full accounting of the overwhelming loss due to such events is well beyond any conceivable effort at historical reconstruction. Certainly the most complete instantiations of such carnage have by their very effectiveness destroyed all evidence of the ideas that were lost. We only occasionally get glimpses that such situations may actually occur because a meme has managed by some accident of fate to frustrate the procedure and escape into the world at large before the death of its initial advocate. We find even in such cases in which complete premature annihilation of an idea was unsuccessful, sad commentary with regard to the surviving culture unilaterally pardoning past sins whereby counter culture has been illegitimately destroyed. Furthermore, desecrated ideas do not reoccur in the interim as they are purported to be capable of doing in cultural fairy tales that promote the concept of "inevitability" of all great ideas. They are gone — it is possible that most truly great ideas have vanished forever! The context of history changes such that an unformulated idea would never occur to anyone else after its time had passed. Even "immortal" gods, perceived rationally by many as simply the products of human intellectual exercise, are vulnerable to extinction with their adherents. St. Paul knew this. And H. L. Mencken named one hundred seventy one "immortal" gods that have long since succumbed to the nether world, in conclusion quipping: "All were theoretically omnipotent, omniscient, and immortal. And all are dead."2 Preemptive violence employed against their human hosts in preventing unwanted meme epidemics one must conclude to have been spectacularly successful in every area of intellectual endeavor including philosophy, science, mathematics, music, religion, and, of course, politics. The effectiveness of accidental death or ruthless intrigue on all sides of every issue has been truly appalling and there is little reason to doubt that nascent ideas will be vicariously assassinated well into the future. It's happening right now. Machiavellian techniques apply not just to politics, but sadly, to every area of human intellectual endeavor.
Proponents of tired paradigms inaugurated before the eldest living human was old enough to propound the previous paradigm, still melodramatically cite Thomas Kuhn's popularized notion that a paradigm can only become universally accepted when death finally takes all those who upheld the previous paradigm to illegitimately criticize opponents.3 It's a dumb argument. Establishmentarian ideas debated into the ground have not died on account of the deaths of their proponents! There was full knowledge of their inner workings as a part of the debate that accompanied their demise. And long after the last proponent has been ushered to the nether region, stories survive of the victory of the new paradigm that will be extolled until it is in turn replaced, and in extolling its success, the defeated ideas survive as leitmotif against which it can be praised. Only fragile newborn ideas, unheard outside an inner circle, are truly vulnerable to death whether by natural disease, accident, or inquisition of one or few of their intellectual hosts. It is in this defenseless phase of private discovery and investigation prior to joining the public debate where destiny balances precariously on a fragile human fulcrum.
In his American classic, Robert Pirsig suggested that philosophical ideas propounded by the sophists in pre-Parmenidean Greece may have been systematically destroyed by antagonists and that what must once have been a heated debate turned into a unilateral attack on "sophistry" as mere rhetoric.4 With no sophist alive to set the record straight these accusations held for millennia, so sophists' alternative philosophical structure disappeared from the face of the earth, the minds of mankind. That is, of course, unless Pirsig actually did recapture from extracted roots of words and innuendos in accusations some of the original intent in his revitalized concept of Quality as preeminent over subsequent Westernized Aristotelian classifications.
In an earlier attempt at imitating the style of Jorge Luis Borges5I intimated that science perfunctorily expunges concepts from its registry as a part of a normal retroactive redaction, such that records of the life work of the hapless characters Woran von Geht and Friedrich Spielen had already been expurgated from journals: "The considerable volume of their contributions… more recent translations…have mercifully omitted…" However, beyond the facetious novelty in that account, a real danger exists of very similar expurgation processes. Nearly a century ago two of the most brilliant prospects for salvaging physics from the doldrums of academia vied with their alternative fixes to then current dilemmas. As protege of Poincaré, Walter Ritz had developed alternatives to the already gilded dogmas surrounding Maxwell's wave equations of electricity and magnetism. He was able to avoid the problems of having to throw away legitimate solutions to theoretically justified equations just because they ignobly refused to apply to the "real" world. Ritz's theory also competed honorably with Einstein's relativity for a time, accounting for many of the experiments because of the accepted factuality of what he pointed out with regard to the phenomenon of extinction of light by lenses, mirrors, and indeed by any material medium. Some years later Wilhelm de Sitter promoted Einstein's special relativity in preference to Ritz's using illegitimate arguments with regard to the non-existence of ghost images of binary stars.6 I sometimes wondered why so brilliant a physicist as Walter Ritz would not have rebutted such feeble arguments and thus have kept the debate alive. I finally realized why that was. Walter Ritz had long since been dispatched to the nether world! Earlier he and Albert Einstein had also argued at length about the origin of irreversibility in physics, an argument that had gone on for some time. At length the editor of the journal Physikalische Zeitschrift seems to have suggested that the two formulate their respective positions, sign an agreement to differ and get on with it.7 So they did that in 1909 and the debate ended. But of course, as too few know, the primary reason that the debate had ended was because Walter Ritz died two months after the agreement to disagree was published. Hence also, of course, de Sitter's subsequent claim in 1913 with regard to relativity would go unchallenged. Later in life Einstein recapitulated the arguments with regard to irreversibility to Wheeler and Feynman as stimulation to their development of absorption theory8and seemed to have somewhat altered his own position on issues including the debate with Ritz.9 But Einstein is dead too and most physicists have accepted his previously formulated position that complexity with the associated need for probabilistic solutions must, in itself, produce irreversibility without a microscopic counterpart. Cramer alone, who also challenged the "Copenhagen Interpretation" with his "Transaction Interpretation" of quantum mechanics, seems to maintain the standard propounded by Ritz.10 But sadly, although "a formula, a phrase remains, — …the best is lost" as Edna St. Vincent Millay sadly bemoaned.11 To my knowledge, no one has been able to reconstruct Ritz's electromagnetic theory.
In mathematics there is Evariste Galois, without whose willingness to write down the ideas of group theory the night before his duel over the dignity of a whore, we would not now have one of the major branches of mathematics. But, of course, if he had gotten a good night's sleep, practiced with his pistols, or better yet, just capitulated with regard to his lust, all of mathematics might be much more sophisticated than it is. In music there was Mozart, perhaps murdered or at least driven to deadly abstraction by an opponent of his abilities.
If salesmanship and religion don't seem to fit in the same sentence, read Roger Rueff's play "Hospitality Suite,"12or see the movie based on it, "The Big Kahuna" with Kevin Spacey and Danny De Vito. With regard to religious ideas it should be noted that although Judaism, Christianity (for a time), and Islam (during the odd crusade) were repeatedly under attack, these were always after their associated memes had leaked out into society at large and were, therefore, ineffective beyond the associated slaughter of humans. Zoroastrianism, on the other hand, like so many religious ideas before and after it in cultures throughout the world including previously cited immortal gods, did not fare so well. It was destroyed most effectively by the more or less total destruction of Persians who held to the doctrine of good versus evil to the bloody end. Perhaps current administrative decisions by the U. S. may in some way revitalize this notion that lacks so much in subtlety by its vain attempt to destroy all those infected by the offending idea of the Western world being evil. Ethnic groups everywhere and always have seemed to annihilate without compunction anyone holding opposing religious ideas for the greater glory of their own gods, their own culture, their own ideas.
In the political arena, character and literal assassination has been the norm that seems to have picked up momentum over the last quarter century. The tragic deaths and subsequent annihilation of character of key liberals by the resurgent American conservative movement has been motivated in large part by an agenda that cared primarily for the destruction of liberal political ideas to which cause these people's lives had no moral standing. In contrast, by elevating the stature of a chief proponent of terrorism and attempting to destroy his person but failing, his ideas may be emboldened like flames in a wind that has just failed to extinguish a fire. Creating public martyrs has the opposite effect of secret assassinations. So, although it is not surprising that bin Laden should find himself under attack by the most powerful nation ever to rule the world, it is indeed surprising that there would be so little awareness by Americans of the phase of this particular epidemic of anti-American sentiment. It seems well past the stage at which the incineration of any affected person or even of a small group of people could be effective in the eradication of the viral meme. The idea that the Western world is consumed by its own power and glory is out there! That notion and the associated hatred of Americans have been out there for some time with only the most naïve caught unaware on September 11, 2001. Now the idea is being reinforced by ill-conceived attempts to destroy it. It would seem that it should have been, and should still be, obvious that that idea must be debated openly to portray the proper perspective. Having resorted to prehistoric methods of idea extinction, too late in any case, the approach can only confirm by its success or failure what we desperately want to believe to be an invalid idea. How do we now convince anyone of its illegitimacy? Certainly Afghanis nor Iraqis (nor any other of the billions of Muslims) will buy the idea that we do not, and will not, continue flaunting military and economic might throughout the middle East and entire world until we have utterly destroyed all cultures but our own. That is an idea worthy of our consideration -- something to think about.
The death of a "salesman" of any idea by any method whatsoever is akin to killing the messenger. Certainly terrorists instrumental in massive killing are not merely killing salesmen. They must be brought to a justice that may involve their own deaths no less or more so than other perpetrators of heinous crimes. But let it be known that even in such cases capital punishment is constitutionally administered in consequence of those plans or actions involving the killing of human beings and not for nurturing ideas. For one thing (and it is, in fact, a major thing) to act otherwise is immoral by virtually any standard in any society. Those who treat human life as subsidiary to, or as mere attributes of, material symbols of an idea (or of an idea itself) are grossly immoral. Ideas must warrant victory and arguments should be won or lost based on relative merits of the competing ideas, not by "kill ratios" reminiscent of Viet Nam. Pursuing ideological arguments with human slaughter, however effective, by definition disqualifies participants from victory in any war alleged to pit good versus evil. Once both sides have reverted to such tactics, what is left is a bloody crusade of "us" versus "them!"
1 Arthur Miller, Death of a Salesman, Penguin, USA (1998)
2 H. L. Mencken, "Memorial Service," Prejudices (a selection), Vintage, New York, 143-147 (1958)
3 Thomas Kuhn, The Structure of Scientific Revolution, University of Chicago Press, Chicago (1962)
4 Robert Pirsig, Zen and the Art of Motorcycle Maintenance,
5 See for example, Jorge Luis Borges, Labyrinths, New Directions Pub Corp., New York (1964)
6 R. Fred Vaughan, "Special Relativity: An Experimental Error," Gift of Fire, 31, 6-15 (July 1988).
7 Walter Ritz and Albert Einstein , "On the Current State of the Radiation Problem," Physikalische Zeitschrift, 10, 323-324 (1909).
8 John Wheeler and Richard Feynman, "Interaction with the Absorber as the Mechanism of Radiation," Review of Modern Physics, 17, 157 (1945).
9 Abraham Pais, Subtle is the Lord — The Science and Life of Albert Einstein, Oxford, 467 & 484 (1982).
10 John Cramer, "Velocity Reversal and the Arrows of Time," Foundations of Physics, 18, 1205 (1988).
11 Edna St. Vincent Millay, "Dirge Without Music," Collected lyrics, Washington Square, New York, 172 (1959).
12 Roger Rueff's play "Hospitality Suite" does not seem to be available in print.
by Fred Vaughan
There seem always to be these nearly insurmountable epistemological traps and barriers to overcome. We seem always to be peering down the wrong end of telescopes, until very occasionally by some accident of fate, we run off yelling "Eureka! Eureka!" like demented hippies in the backwoods of California. Our various highly evolved linguistic and mathematical skills get applied primarily to justifying the particular inanity that happens to be in vogue — never with actually changing paradigms. There seem always to be mathematical mappings of what is known of the unknowable depths of our universe to the shallow waters of our intellectual wading preference, but the veracity of such mappings are warranted no more than formal propriety justifies aphorisms depicted in poesy.
Consider what we know of our universe with regard to its composition as a very diffuse but impure hydrogenous plasma. Yes, as surely as to a first approximation we ourselves are mere bags of salt water, the universe is a hydrogenous plasma, both being pretty damn good approximations! With only this much firmly in our grasp, we must resist urges to charge off like rabid string theorists to find the big end of some telescope, waving at cameras and grabbing microphones as they go!
How diffuse? About 10-25 grams per cubic meter. So in sifting through a cubic meter or so of universal debris at random you might find an odd proton, an electron to neutralize the concoction, and by-product neutrinos all whizzing about at significant fractions of the speed of light. The most obvious decomposition of this plasma being that apparently on large scales everywhere in the universe it is 76 percent hydrogen nuclei and 24 percent helium nuclei (by mass such that there are about twelve hydrogen nuclei per each helium) with mere traces of other isotopes.
At high temperatures helium nuclei are formed from hydrogen nuclei by nuclear fusion. (Of course at even higher temperatures protons which comprise the nucleus of hydrogen can be created from neutrons, and positrons, with neutrinos and associated "opposites" dashing about, but let us ignore third tier observations.) All nuclear reactions are reversible with equilibrium percentages of each product determined by temperature. Those of us who still accept the conservation of energy — notice that most cosmologists do not — insist that if the 24 percent helium did indeed derive from primordially pure hydrogen plasma, then the energy released would not be totally lost. This caveat holds to the extent that the universe is a closed system, which it would seem to this author to be by definition. This radiant energy, however thermalized, must therefore still be present somewhere in the universe.
Now if you go through the calculations, and they are very straight-forward, you will find that the amount of radiation energy released per cubic centimeter is precisely the amount of energy invested in the microwave background radiation. All fashionable cosmological theories take this to be a mere coincidence. They tell us that the facts of annihilation associated with an unknowable primordial imbalance in matter and antimatter right after a miracle happened resulted in that glut of energy which today is viewed as some sort of perversely understood "fact" of the universe supposedly in reality being only 3 degrees Kelvin rather than the many orders of magnitude higher temperatures observed everywhere we look! According to these theories the energy balance coincidence is just a strange happenstance of our being here now rather than somewhere somewhat similar a billion years ago or hence! With such a perspective my confusion might have been avoided. But I don't have it!
So how "bright" should it be if this coincidental amount of radiation that we all agree is actually out there is actually out there? Well, let's think about that: On average every hundred cubic meters or so of the universe contains evidence of these reactions having taken place. From our observation point the intensity from each reaction is diminished as 1/r2 where r is the distance to each occurrence. We arrive at Olbers paradox with the number of cubic meters increasing as the square of the distance, r2. Thus, we get to the crux of the paradox when we combine these two effects for the entire universe. But of course modern cosmology resolves such difficulties by demanding a finite universe of radius Ro = 1/Ho where Ho is Hubble's constant. So we end up with a modest(?) intensity given by:
So a finite universe and a justifying Bang are made for each other. But if the redshift-distance relation is accepted as mere fact rather than some grandiose deduction from conjecture, to the accuracy of precise observations the relation is characterized by r = Ro ln (z+1), which theorists will tell you corresponds to an "Einstein-de Sitter Universe." Here we have distance given by the natural log of redshift, z, plus one, all divided by Hubble's constant. The effect of redshift is to reduce the frequency of radiation, thereby reducing its intensity by the factor 1/(z+1) = e− r/Ro. So that in an infinite universe we would have:
Thus, identical facts can be used to justify opposite theories if you're into that.
Of course cosmology involves a mass of observations concerning a broad scope of concepts, all of which must be understood in such a way that they agree before any comprehensive theory will ever even approach some sort of validity. But, as with the preceding, there seem to be more ways of looking at each fact than initially meets the eye. Einstein's gravitation equations don't address the obvious possibilities of gravitational energy suffering the depredation by redshifting while being propagated. Why not? Nor, of course, should "Newton's iron sphere theorem" be taken as having any relevance once one realizes that the metaphor does not hold for a closed universe for which there is no inside-outside surface. Here too, therefore, observed gravitational effects of finite universes cosmologists favor can be matched or bettered by virtually identical ones involving indefinite extension.
Are these mere cosmic coincidences? I don't think so.
by Fred Vaughan
After the peaceful breakup of the Soviet Union and the Israeli - Palestinian resolution quite a few years ago now, I was reminded of the stupidity of concepts such as manifest destiny; fifty-four-forty-or-fight; the Little Big Horn; the Promised Land; the Bay of Pigs; the taking of Europe by Cromagnons from Neanderthals; Catholic Croatia, Serbian and Muslim Bosnian hatreds; Somalia; the genocidal war in Rwanda; the Sudan; now Afghanistan and Iraq, etc.. All involved an absurd but universal notion that "This land is my land!" and anyone else is an interloper. Having been (or supposing that it was their destiny to be!) in control of a particular hunk of land at a particular time since their racial memory began constituted in all such cases a perpetuated sacred responsibility to re-take the land whenever there was the slightest provocation or vulnerability of the current occupant at whatever cost is required in terms of human life. All these persistent grudges have guaranteed generations of genocide and poverty, especially in the "old world" where many still extent races of men have at one time or another been born into more or less legitimate control of some appreciable piece of soil. And why? Even as I propose to doubt the inevitability of such chaos it almost seems even to me to be the only reasonable conduct of history. But of course even the apparent reasonability of this insanity springs from my racial memory and the fact that we have not yet broken our umbilical with "Mother Earth," our linkage with "Land of Israel," "This land is my land from sea to shining sea," etc.. We limit our "ethnicity" to encompass only a limited group by our religion, color, political ties, etc. but then we glue this label onto the land even though the land may be shared by many groups. Ultimately (one might hope!) our vision could be improved to include all associated people and all indigenous species of the region. From religious protectorates associated with "The Land" sprang governments to control (optimistically for their own survival) the people that occupied the land.
Governments are born of a particular people but have always been instituted as being over all the people in a region and are, thereby, bounded artificially by that region rather than that people that is their legitimate bound, but the land does not obey laws, the requirement for all encompassing laws throughout a region can only be to assure the security of the government of the one people from internal attack at the hands of the disenfranchised peoples, not in any inclusive sense of wanting everyone to be equal sharers of the bounty of the region or to protect all from outside attack. Governments implicitly condone an ethnic "purging" of the land by occupation. Oh, yes, the disenfranchised whether they remain or flee as refugees still (and then to an even greater and much fantasized degree) "love" their homelands, only giving up control of them in desperation, hoping and scheming to someday "take" them back. Islam raises this to another level: Any region once occupied by Muslims must be secured and retaken if lost by the Mother of All Battles -- Jahad!
But individuals only inhabit the land for a generation and collectively such mortals constitute a people. So why can only one ethnic group peacefully occupy any hunk of land at any one time? Why do we so naturally focus on such narrow windows of geography and history? Why don't we squint our eyes temporally to blur our historic vision as we do our spatial vision when we look at a piece of art to perceive the layout independent of the details. Why is continuous sequential control over contiguous square miles throughout historically short periods so profoundly more glorious than contemporaneous control of non-contiguous (or even non-geometrical) areas throughout a much larger interval? (The Jews accomplished this feat amazingly well until it appeared obvious that real estate itself was also important. Did ownership itself distort that vision?) On large enough time scales interrupted control is simply contemporaneous control like timesharing in a multitasking computer system where the multitasking allows several jobs to share resources during the same appreciable interval on the same computer even though on a microscopic scale each was only individually in control of the machine (or "a" machine on an interconnected network) during separated short intervals of time. Why can human beings who have mastered such multitasking schemes not "get it"?.
Radio and TV signals and starlight all pass through every infinitesimal region of our atmosphere at the very same time without solely possessing it (although, of course, the property rights of waveband regions are being bitterly contested just as claim jumper grabbed at mining rights, but again, only by money grubbing interests and governments). In fact there are on the order of 10 billion times more quanta of light than matter in our universe and they crisscross every cubic centimeter of all space with none demanding ownership to pass.
Looking West from the back porch on the house on "my" farm of 27 years, I "loved" the land, not just my farm land but the whole setting as far as the eye could see to the Olympic mountains. My neighbor to the North looked South and "loved" the land, not just his land, but my land as far as his eye can see to Mount Rainier. In a very real sense, we "own" our own perspectives -- all of it! -- and sometimes confuse that for all the land we see, like Lot in the Old testament. Clearly, Lot did not actually own the "well-watered plains of Jordan" he had claimed -- probably much to the chagrin of his wife!
We raised race horses on our farm until a few years back, controlling their destinies in the long haul, but on a day-to-day basis, they had their own hierarchy. We could not change it other than get rid of a horse if it became too destructive like God might have sent a lightning bolt or turned Lot's wife into a pillar of salt to effect a similar correction process in Old Testament days. Or we could banish them to a remote paddock or send them to the track as a God might have sent a man to war, or sell them as slave owners sold their slaves "down river".
Then there were the cats! A tom always ruled our farm with an iron clawed paw; he might originate as the most docile of kittens loved by our children, sleep for virtually three years like a curled up caterpillar as did "Patches The Horrible," but then one day his "destiny" would dawn upon him and the most feared force in the barn cat kingdom would begin a reign of terror without precedent. We could never do anything much about this carnage other than get rid of the aggressor when the carnage irritated us too badly! (Not a bad idea!) Then there were the pigeons, the mice, not to mention the flies, the frogs, and -- us! These stratified kingdoms co-inhabited the same twenty some odd acres for many years. There were disastrous interactions on occasion, as when a horse kicked a person or stepped on a cat, or a person started a vehicle with a cat hiding near the fan belt, or as when Patches bit through my rubber boot when I had attempted to break up a cat fight by stepping into a whirl of fur. But by most any accounting these were pretty minor events in the affairs of the respective kingdoms. But of course we fed the cats including those who couldn't or wouldn't eat the mice and rats (and pigeons!) that ate the oats that the horses should have eaten. And the horses won the races that provided the money to feed their dams and everybody else on the whole damn farm. And it all worked pretty well.
In the United States we have First, Second and even Third World nations. Why can't we acknowledge"..., [these many] nation[s], under God [sic.], indivisible, with liberty and justice for all..."? Let them all exist on the same soil with their own legitimate governments, even unique forms of governments. The United Nations or some hierarchy of nations should be able to accommodate the similarity of mailing addresses and monitor and control the interactions. But in this country at this time it is popular to hate welfare (even?) worse than foreign aid, but they are really the same thing, especially now in our age of the Small World where we search for bin Laden. The war in Iraq is costing the US $9 billion per month according to the nonpartisan government accounting office. In short, the cost of the senseless war in Iraq and paying the interest on the increasing national debt required to support it dwarfs welfare, but a "Christian Nation -- under God" cannot afford help the less fortunate?
I felt very congratulatory to the Israelis and Palestinians on their Peace Accord even though they were each no doubt as oblivious to the sense they were making as the cats and horses on our farm ...
... that we have now sold, after having dispersed the last of our horses, with one of the conditions of sale having been that we "get rid of the cats." That's commerce … and the price we pay for it.
Sadly, since the Palestinian Peace accord Rabin was assassinated by one of his own people for his role in bringing about a new order. Bus bombs and human bombs, and Israeli assassinations and increased occupation continue to appall us all in destroying the peace process. The Serbs and Croats wrecked havoc in the Balkans but were eventually stopped after the genocide. Genocide has killed millions in Africa in the last decade alone. Sunnis killed Shiites in Iraq under Saddam because it was "their land" even though they were out numbered. Now both Sunnis and Shiites slaughter each other in total civil war carnage because (no matter who gets the oil underneath it that is protected by US troops) each side believes Iraq to be "their land". Thousands die every moth in Iraq; just today the news is that 105 have died Baghdad alone.
And it will continue to happen. It has to happen. It will happen to us … unless we learn that "The Promised Land" is not dirt.
Rejecting Action at a Distance Resolves Precession of the Perihelion of Mercury without Requiring General Relativity
by Fred Vaughan
"…What would happen if the Earth were suddenly dropped into place, at its proper distance from the Sun? How would the Sun 'know' that the earth was there? How would the Earth respond to the presence of the Sun?…But the Sun would not 'know' that the Earth had arrived until there had been time (Faraday had no way of guessing how much time) for the Earth's gravitational influence to travel across space… and reach the Sun."1
the author encounters the
gravity of the physical world
Newton's action at a distance involving instantaneous transmittal of forces was problematic from the first. If one is to eliminate action at a distance from the classical equations acknowledging that it takes time for forces of interaction to be transmitted between objects but retaining Newton's other concepts of a centrally directed gravitational force, one is faced with a dilemma — the elliptical orbits will precess. But once this has been taken into account by the gravitational force, general relativity is not required because the precession implied by removing action at a distance accounts for observations without further emendation.
Much of the simplicity that Newton was able to incorporate into his laws of nature might seem necessarily to have become obfuscated if action-at-a-distance does not apply, however. We encounter, for example, the situation of the "central"force being directed, not along the line of centers of two massive objects, but offset at an angle in a direction to which there would seem to be no source for a force. If the transmittal speed of the potential energy that drives the force is equal to that of light in a vacuum, then the angle of relativistic aberration determined by the relative velocity of the objects would determine the "line of sight"to where each object would appear. This then would serve also as the realized direction any associated force. This has the merit, of course, of both objects experiencing the force to and from the direction at which the other object appears, even if not where it is. But the framework in which this is true is not an inertial coordinate frame; it is an accelerating frame of reference - at least with respect to the location of the center of mass of the two objects as it is usually accounted. Newton's laws of motion had, of course, been accepted as applying exclusively with respect to such inertial frames of reference.
Determining the center of mass of the two relatively moving massive objects is problematic from the start. Without action-at-a-distance, wherever there is relative motion there will be alternative perspectives caused by the direction from which the light (or force in this case) arrives, which will be in the direction to which the object had been located when the light (force) was emitted — not to where it is located when it arrives. This "aberration" will result in assessments of the center of mass being at variance. Look at the system of two equally massive objects depicted in figure 1. Since the minimum separation of their two straight line trajectories as drawn from a third perspective of an observer C half way between them (defined so as to provide symmetry) is non-zero, aberration distorts their assignment of a center of mass to the system (i. e., CMA, CMB, and CMC) as shown. About which of these points will the objects orbit?
In figure 2 we have drawn the circular orbit of radius R of what could be a planet p about a star S. Of course, the planet would be moving at the astronomically high speed of 0.449 times the speed of light, c to produce this much aberration. The darkened circle S is drawn where we conceptually envision the star to "be" and S' is drawn where it would appear from the vantage of the planet in its path about the star (assumed to be much more massive than the planet so the center of mass of the system is approximately that of the center of the star). The planet's orbital speed was merely chosen in this case to accommodate the planet completing one orbit in exactly 14 times the length of time it takes the force field to travel from the star to the planet so it could be easily visualized. (However, if the realities of actual planets being unable to achieve viable orbits at distances compatible with this speed is a drawback to the reader in understanding what is at issue here, then assume the integer 14,000, or 140,000, or an irrational number for that matter; it really makes no difference to the point of this article.) So if we evaluate the status of the situation 14 (or 140,000) consecutive times during the course of an orbit as shown, we see that in a reference frame stationary with respect to the center of mass, the orbit of the planet whether about the actual star or about the apparent star is the same! See panels a and b of figure 3. However, in the latter case (panel b) the orbit is out of phase by one fourteenth (or one hundred and forty thousandths) of the orbital period such that p1 is to S as p2 is to S2', etc.. (Also S as well as p orbits S' in this case.) This relationship of pi being to S as pi+1 is to S', etc. will be the same no matter what the relationship of the speeds v and c as long as the separation of pi and pi+1 is R v/c, but if c is not an integral multiple of v, there will be a change in the phase shift from one orbit to the next that is proportional to the residue.
Whether the actual star S (which is not seen from the planet) or the apparent star S' (that is seen) is envisioned as orbiting also (at the radius R v/c) about the center of the planet's orbit may seem of little import since the planet's path will be the same in either case. Of course, there are major epistemological differences in these perspectives. One tends to care little whether mere ephemeral conceptual constructs gyrate in strange ways to accommodate mathematical models, but for an actual star to orbit a void point other than the center of mass of the system from the perspective of comoving surrounding systems might seem to involve some travesty of thought. It is, after all, only in the accelerated frame of the ephemera that the unseen but "actual"star orbits. However, it is only in that frame of reference that our familiar concept of an inverse square law force "actually"applies. So, after all these mental gyrations, where are we? Maybe this just seems to work because we are dealing with a circular orbit here rather than the more general conic elliptical orbits. How would this alternative to action-at-a-distance play out with an elliptical orbit?
The answer is that the elliptical orbit (as seen from the comoving surrounds of the star) would involve the precession of an otherwise stationary closed elliptical orbit, whereas the elliptical orbit solution about the appearance of the aberrant star for which the central force equations apply would not precess. And this brings us to the famous test of Einstein's general theory of relativity with regard to the precession of the perihelion of Mercury by 41 seconds of arc in a century, which is unaccounted for in Newtonian mechanics. We are repeatedly reminded that the phenomenon is finally resolved by general relativity with the determination having been made by Schwartzchild of the appropriate gravitational metric tensor from which to determine the Ricci tensor, Ricci scalar, and stress-energy tensor from which the result can supposedly be computed. Needless to say, "That ain't necessarily easy for neophytes!"It is much easier, in fact, to merely acknowledge that it takes time for forces of nature to travelthrough space and determine the relative locations of the interacting bodies at appropriate times as shown above. That makes sense!
In looking up the data on the precession of Mercury's perihelion to check out the viability of all this, I ran across a very learned article published in arXiv.org:physics/0510086, January 20, 1906 by Jaume Giné on the internet1, which exhaustively describes the history of such efforts as mine and extols the efforts of a German school teacher named Paul Gerber who in 1898 proposed just such an approach. It resulted in accounting for only 14 seconds of arc and not the entire 41. However in analyzing those results Giné was able to show that using the round trip time instead of the one way force interaction time as suggested by the collaboration of Wheeler and Feynman on absorber theory in 1945, that the entire phenomenon is thereby completely accounted. See figure 4 taken from the reference.
In the diagram of figure 4 the retardation parameter τ is equal to what we would have referred to as R v/c2 above. And the fact that the two pie-shaped segments differ in the second panel in figuring the round trip delay is that the orbit is not assumed to be circular as we did for didactic purposes in figure 1. In Giné's article he does not associate retarded potentials directly with the special relativistic aberration phenomena, but this association is inevitable.
To update my own analyses as Jaume Giné did for Paul Gerber, the relationship would have to be made between pi being to S as pi+2 is to S', etc.. What this says in interaction terms is that the force "signal"sent out by S is in response to a complementary force signal received from p, so that the force received by p from S will be in response to where p was located two intervals back. It should be obvious that this makes sense once action-at-a-distance is done away with.
So, although I feel somewhat "scooped" (albeit narrowly by only one hundred and eight years), it is refreshing to know that, however rare, perspicacity has always lurked around every corner. And there is some, however, vestigial memory of the right answers to real problems.
1 John Gribbon, The Scientist, Random House, New York, 2002, p. 423. In reference to a presentation made by Michael Faraday to the Royal Institution on 19 January 1844.
1 http://www.citebase.org/cgi-bin/fulltext?format=application/pdf&identifier=oai:arXiv.org:physics/0510086
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