--Difficult Conundrum?--  

                                Since the first publication of the last blog "Further Considerations", on August 3, I have been pleased to learn that there are other writers who at least believe the subject of alternate theories to Relativity is worthy of being addressed.  Some of these do so critically (1.), and there are even at least a few who, inspite of the apparently large amounts of evidence claimed for relativity by its exponents, remain favorable to one or other alternate view. (2.)  These theories, as far as I can tell, generally fall into two categories; first, those which involve 'a luminiferous ether', and second, 'emission theories' (1.), which include one theory Albert Einstein is said himself to have considered before he came up with his Special Theory of Relativity. (3.)  Theories in the first category I think are generally viewed by most scientists as improbable given the Michelsen-Morley experiments and those related to it; while the second category; in which, if I understand it, the velocity of light would change as it entered one or another medium, are viewed as improbable largely because this would not necessarily effect the speed of light in a vacuum, and because light waves which changed velocity would collide with one another causing jumbled interference patterns. (3.)                                                                            I have not however been able to find any reference to any theory that as far as I can tell seems to resemble the theory which I introduced in the first blog at this site.  In that theory, intended for a 'Hypothetical Cosmos', a light source would emit light waves in a continuous range of velocities, with each light wave being visible only to an observer who's velocity differed from that of the light wave by the constant c predicted by Maxwell's theory for the speed of light in a vacuum. (4.) This theory might perhaps be called reception theory; but I have decided to refer to it in terms of a specific principle, "Special Galilean Invariance" which would hold in the type of hypothetical universe alluded to.  Proponents of alternate theories to Relativity presumably believe such theories are permissible, while critics of them presumably hold to the 'two postulates of Relativity' (5.), and the 'mass-energy equation'.  Since the theory I propose is both an alternate theory and upholds the last two, I might hope to gain at least some sympathy from both camps!                                                                                     I have said that I am not, however claiming that our universe is necessarily such a hypothetical universe as I described, and I am still not claiming that, though I also do not exclude the possibility altogether.  While I admit that the apparent wealth of evidence for the Theory of Special Relativity does, indeed look favorable for it, that does not to me eliminate any possibility of an alternate theory being true.  The theory of epicycles appeared at one time to do a very good job of explaining the positions of the planets in the sky, indeed any tiny discrepancies were only known to a small elite, but this did not make it impossible for Kepler to overturn the whole 'contraption' and show that a much simpler description of planets in elliptical orbits obtained.                                                                       The precise timing needed for the G.P.S. (Global Positioning Satellite) system is often brought up as an apparent proof of the theory of Relativity. (1.)  However the satellites in this system all reside in an accelerated frame of reference which differs from that of the earths surface.  This difference in accelerated reference frames results first from the fact that the force of gravity experienced by the satellites is different from that experienced on the surface of the earth as they are at a higher altitude; and secondly from the fact that in orbit they experience a centrifugal force which roughly counteracts even this reduced force of gravity.  As such the time dilation involved might tend to conform, at least approximately, to the predictions made by the theory of General Relativity, but might have less to say about the theory of Special Relativity, which deals with pure inertial frames of reference.  The G.P.S. satellites are clearly not in pure inertial reference frames, so one would have to disentangle the contributions made by each of the two relativity theories, to determine the exact contribution of each.                                                                                                                                                                As stated in the first blog, "Hypothetical Cosmos, Preliminary Analyses", I do not exclude the possibility that some kind of 'general relativistic principle' might hold in an S.G.I. (Special Galilean Invariant) universe, as defined there.  The precise form which such a principle might take in a universe of this type is difficult to articulate, but one would assume it likely would predict a time dilation close to that which can be derived from the 'classical red shift', namely:  T=t(1+Gm/rcc), (6.) for T=(time elapsed on a clock removed from the gravity field), t=(time elapsed on a clock at a distance r from the center of gravity), m=(mass of the source of gravity), G=(the universal constant of gravity), or: t2=t1(1+ah/cc), (6.) for the time elapsed on clock 2 at a height h above clock 1 in a vehicle undergoing constant acceleration a. (6.)  The first equation is also close to the value predicted by the "Schwartzschild solution" to the equations of General Relativity. (7.)                                        Since the design of the G.P.S. system is classified, I can not, of course examine exactly how it works; nor can many others.  It can only be examined by a relatively small group of individuals authorized to operate it, and their main concern has perhaps not been to worry about exactly how it works, but to get it to work; and to keep it working.  One must imagine that when the system was first implemented, it didn't work as well as at present.  Over time and with practice, one imagines, the system was re-calibrated and fine tuned until it was verified that it was achieving a high level of success.  It is then conceivable, that even the designers of the system, and possibly no one, knows exactly how it works, though they perhaps imagine that they know.  It might only be known partly from experience that designed and calibrated as it is at present, it gives a very high accuracy.  It could even be that having initially been programed to take into account predicted relativistic effects, the absence of which caused unforeseen discrepancies, the same effects were somehow re-programed into the system in the opposite direction; so that the two effects finally cancelled each other out and the system worked!  I'll admit this is all pure speculation, but I don't see any need to refrain from that, since once and awhile that may lead to truth.                                                                                                                          Close examination of some texts on physics do not necessarily encourage easy acceptance of the theory of General Relativity.  "Fundamental Formulas of Physics"' edited by Donald H. Menzel, considered by many to be an authoritative reference on physics, gives on page 216 the presumably empirically correct value for the "deviation of a light ray" owing to a gravity source as "2E"; "E=2/p", where p is the distance to a "straight line parallel to the y-axis".  However this value is obtained here from a clearly faulty process, step "1.6.14". Following his recommended procedure beginning with "1.6.11", one more likely obtains the value E={(pp+8)^1/2}/2.  The value he gives for the perihelion of Mercury on page 215 appears to result from another questionable step, "1.6.9".                 

                                                                         October 3, 2017                                                                                                I'll have to confess, there are also some situations in Special Relativity which have me confused.  A case in point is one I just came across, shown in the diagram below.  This situation involves two spaceships, marked e) and f) traveling with high velocity v close to the speed of light; one directly behind the other in their line of motion; with a distance d' measured between them in F1, the frame of reference of the second two spaceships, marked g) and h).  This second pair of spaceships are also arrayed one behind the other along a line parallel and right next to that of the first pair of spaceships; and they measure a distance d=d'/{(1-vv/cc)^1/2}>d', between themselves.                                     At time t1=0, spaceship e) arrives just beside spaceship g), when spaceship g) emits a brief light pulse forward in e)'s line of motion.  As f) followed by e) are both moving with high velocity v through F1, spaceship f) eventually reaches stationary spaceship h).  For reasons that will be made clear later, we assume the light pulse has not yet overtaken spaceships f) and h) at this time. (Otherwise it might have been observed by these two spaceships by this time).  This light pulse could however have been observed at this time by two additional spaceships (not included in the diagram), one moving with velocity v at point q between e) and f), and the other stationary at point p located a distance L behind  h) on the line g)--h) which happen to pass by one another at this same time t2 when the light wave reaches point p a distance L from h).                                                                                           In the frame of reference of the moving spaceships e) and f): F2, according to Special Relativity, the times, as well as the distances d and d' would be reversed; h) should first be observed passing by f), moving to the left of the page at time T1, and only later should g) pass by e) going in the same direction at time T2>T1.  (Note that t2-t1=T2-T1).  However in F2, the light pulse is only emitted at this later point in time, so it presumably can't exist anywhere in this reference frame before this, which explains why the light pulse could not yet have reached f) and h) at t2; since it would then have already reached them at time T1 in F2, before it would have been emitted at later time T2!  The light wave can then, of course, not reach the point p which in F2 is a short distance L' from h) until a later time T3>T2 at the precise moment when the points p and q would coincide in F2.                                 Now, however, consider the order of events.  In F1 the emission of the light wave occurs at t1, followed later at time t2 by the simultaneous meetings of the spaceships f) and h) and that of the points p and q.  In F2 however, the meeting of the spaceships f) and h) comes first at T1, followed by the emission of the light pulse later at time T2; with the  meeting of the points p and q (and of the un-diagramed spaceships at each of these points) taking place still later at time T3>T2.  So not only is the order of the meetings of spaceships e)-g) and f)-h) reversed in the two frames of reference; but the order of the three meetings e)-g), f)-h), and p-q are completely jumbled; with two simultaneous events in F1 shoved in F2 to either temporal side of an event which in F1 preceded both, in time as well as in space!  Granted all of this may be possible; but it is hard to deny that it is also bewildering.

 

                                                                    --Notes--

        (1.)   See "Why we believe in Special Relativity: Experimental support for Einstein's Theory" by John S. Reid, Department of Physics, University of Aberdeen                                                                         (2.)   A Dissident View of Relativity Theory" by William H. Cantrell, Ph.D     www.infinite-energy.com/iemagazine/issue59/adissidentview.html                                                                                (3.)   en.wikipedia.org/wiki/Emission_theory                                                                                                (4.)   See Haber-Schaim, U. Cross, T.B. Dodge, T.H. Walter, J.A. "PSSC Physics Forth Edition" p.-544. 

        (5.)   See Einstein, Albert and Infeld, Leopold "The Evolution of Physics from Early 

Concepts to Relativity and Quanta", pp.-156,157.  

        (6.)   See Feynman, Richard, "Six Not So Easy Pieces" pp.-131-137, for derivations of these two formulas.    

        (7.)   See Menzel, Donald H. "Fundamental Formulas of Physics", p.-217.