Steven Rado :
 

Aether Resistance and the Lorentz Transformation
 
 
     From the very inception of classical theoretical physics there existed a built in duality in the fundamental concept of Space.
     Galileoís Principle of Inertia and Newtonís Mechanics required Space to be empty and perfectly frictionless. Eternal uniform motion  can only exist in a featureless empty void. -- However, this fundamental assumption, lead to the mysteries of the ëaction at a distance forcesí like gravity, electricity, magnetism and others and to the enigma of the transmission of light throughout the Universe.
     Thus, Descartes, Huygens and others invented another Space, filled with the Aether; a gaseous substance of supermundane order of magnitude which was suppose to be the conveyer of those phenomena and explain away the problems that the featureless empty space created.
     Like tree-leaves are carried on circles in the eddies of a running spring, in this universal medium, the planets could be floating on their orbits in the immense rotation of the Solar Vortex. In higher orders, the Milky-way and billions of other Galaxies could be local twisters in the all-pervading cosmic Aether. Light, in this gaseous medium was thought to be minuscular compression waves propagated throughout the Universe just like the sound-waves in air. -- But then, how can the Galileo-Newton mechanics work in this Aether-filled Universe ?
     The duality of Space has sharpened by the introduction of two controversial theories of light; Huygensí wave theory needed an Aether, Newtonís corpuscular theory needed the empty space. The great debate seemed to be settled with the victory of the Aether, when Thomas Young proved by his double slit interference experiment that light consists of precisely calculable wavelengths and frequencies just like sound.
     Thus, Huygensí simple principle of wave propagation became the basic explanatory method of all phenomena of wave-optics: reflection, refraction, diffraction, interference, etc. -- Adding to the strength of the Aether hypothesis, Faraday and Maxwell developed the theory of electromagnetism, based on the assumption of a similar mechanical fluid. Hence, the mysteries of the ëaction at a distance forcesí of electricity and magnetism were replaced by dynamic flow-patterns, stresses and strains in a luminiferous Aether.
     In a parallel but isolated evolution Earthly and Celestial mechanics also developed to an ever more sophisticated level, but there was no progress in resolving the duality of the controversial concepts of Space. As the Aether theory strengthened the hope gradually increased that a unification of mechanics and electromagnetism might be achieved by designing a workable model of the Aether with characteristics that somehow eliminate the problems of duality.
     Nevertheless, a century of relentless search for that model has failed!
     Seemingly, there was no gas, no liquid, no solid, nor any combination of any known substance that would serve as a universal medium.
     Toward the end of the nineteenth century experimental facts began to accumulate, which made any further isolation of mechanics and electromagnetism impossible. The Michelson-Morley Null Result demonstrated an unresolvable clash between the Aether theory and Celestial Mechanics. Furthermore, electromagnetic experiments with particle accelerators showed that Newtonís First Law, the Principle of Inertia looses its validity when the speed of motion of the particles approaches the speed of light.
     From the point of view of the initial duality of Space the new experimental facts forced the conclusion that there could be no compromise between the featureless void and the all-pervading Aether.
     Modern physics is primarily a declaration of this fact and that this problem cannot be and will not be solved by classical logic or common sense. Thus, Modern Physics concluded that one of the two fundamental theories of classical physics, or both must be definitely wrong.
     The theories of Relativity and their postulates did not resolve this problem. They discard the Aether as the conveyer of light-waves, electromagnetism and other action at a distance forces, but at the same time endow the physically featureless empty Space with the exact same characteristics which were initially attributed to the Aether.
     As stated in Einsteinís book, ëThe Evolution of Physics, in 1966: îOur only way out seems to be to take for granted the fact that space has the physical property of transmitting electromagnetic waves, and not to bother too much about the meaning of this statement.î The General Theory goes even further, attributing an ability to Space to curve itself into orbits in the vicinity of a physical mass as a replacement for the force of gravity. This description is also suspiciously resembles Descartesí  Solar Vortex in the Aether.
     Hence, Aether has been replaced by this unique mathematical Space but it has preserved the whole initial duality conflict within itself. Neverthe-less, being already beyond the scope of classical logic and common-sense it  also automatically became unchallengeable by them.
     In the earlier paper I attempted to show that to find our way out from the present labyrinth, we must open up the trap door that modern mathematical philosophy slammed on classical physics. We gain nothing by knit-picking on the inconsistencies of modern theories because the germs of our present perplexities were not originated by them. They must have been created by some misconceptions buried in the closed files of classical physics.
     Accordingly, Iíve suggested that the failure of the nineteenth century to produce a workable model of the Aether was caused by the single stumbling block of the transverse wave nature of light, which was required and invented solely and exclusively for the classical wave theory of the  phenomenon of polarization.
     The misconception of the transverse wave hypothesis was uncovered in that previous paper and opened up the possibility of a re-interpretation of polarization without the paralyzing constrictions. With this, a mechanical gaseous model of the Aether became a theoretical potential.
     Now, consider a short familiarization of some of the fundamental characteristics of this hypothetical medium:
     Aether is an ultramundane version of the simple macroscopic ëideal gasí of the classical atomic, kinetic theory of gases. The constituents of this fluid, called íAethronsí are particles of infinitesimal extension, having no other characteristics but their equal unit masses, their impenetrability of one another, their unceasing random motion and the perfectly elastic collisions among them. There are no ëaction at a distanceí forces between Aethrons and therefore no need to assume  any internal structure. Statis- tically they have an average speed and an average collision free path, meaning that the gas has an average density, a given compressibility and elasticity. -- The Aether obeys the laws of Newtonís Fluid Mechanics and the statistical principles of the Kinetic Theory. -- The Aethrons possess all the characteristics of a Newtonian particle, but existing only in a system of equal, individual masses. Therefore, their statistical mechanical description does not invoke any of the mysterious Newtonian macroscopic concepts of inertial mass, momentum and force, but simply the basic concepts of motion and perfectly elastic collisions. The Aether, with its supermundane granularity, is a direct analogy to the hypothetical ëideal gasí of our macroscopic order of magnitude.
     The power of this analogy will be demonstrated on the most perplexing phenomenon of modern physics, the so-calledërelativistic mass increaseí.
     In the 1880-s, working with the earliest particle accelerators, scientist discovered some discrepancies in their calculations which were based on Newtonís equation of the first law of motion: F = ma.
     This formula tells us that the relation between force, mass and acceleration is totally independent from the initial and final speed of the object. To accelerate the same mass from 100 m/s to 110 m/s requires the same force as to accelerate it from 1000 m/s to 1010 m/s. The surprising experimental results were that the particles approaching the speed of light required increasingly greater force for the same unit of acceleration.
     Before the appearance of Einstein, Lorentz attempted to explain this phenomenon based on the electromagnetic structure of matter and its motion relative to the Aether.  He derived a mathematical formalism which, in a roundabout way explained the Michelson Null Result and the discrepencies found in particle accelerators. Nevertheless, his hypothesis bogged down like all others because of the lack of a workable model of the Aether.
     Einstein abolished the Aether and declaired the incapability of classical physics to resolve its own contradictions between mechanics and electromagnetism. The postulates of relativity were not based on logic or understanding but on the total surrender to the bare experimental facts.
     Since the electricmagnetic forces used for the acceleration was precisely known and the difference between the initial and final speed of the particle was easily measurable, the only remaining unknown factor in the experiments was the unmeasurable inertial mass of the particle. Thus, relativity interpreted the phenomenon as a result of the relative motion between the observer and the particle, which somehow produces the so-called ërelativistic mass increaseí. Thus, in relativity the speed of light became a constant and limiting velocity of the universe, while the Newtonian concept of originally constant inertial mass became a variable quantity depending on the relative motion of the measurer. The quantitative predictability of the phenomena was provided by the original formula derived by Lorentz:
 
                                                            1
                                     B  =  --------------------------       (1).
                                              sqrt (1 --  v^2 / c^2)

where b  is the factor that must be added to the Newtonian prediction of the required force, v is the initial speed of the particle and c is the speed of light.
     The mathematicalëformalism guarantees that the beta factor will be unmeasurable at macroscopic velocities and predicts infinite inertial mass when the particle reaches the limiting velocity of light.
     Applying this factor to the requirement of force for unit acceleration:

                                                            Fo
                                     Fr =  --------------------------       (2).
                                              sqrt (1 --  v^2 / c^2)

where FO  is the initial Newtonian requirement and FR is relativistic requirement of an increased force which is proportional to the initial speed.
     According to the relativistic hypothesis, in contradiction with Newtonís first law, the increasing force requirement results from the increase of the inertial rest mass  of the particle from/ mo to m. Thus:

                                                          mo
                                      m  =  ----------------------       (3).
                                                sqrt 1 --  v2 / c2

     This is the relativistic mass-increase side of the promised analogy. Now, we present the other side by a macroscopic, aerodynamic phenomena and its explanation based clearly on the laws and principles of classical physics:
     Newtonís Hydrodynamic Law of resistance states, that the retarding force of a medium against the motion of a solid object depends on the density of the fluid and proportional to the square of the velocity of the object.
     The same law is valid in Aerodynamics and is used to calculate the retarding forces involved in the flight of airplanes. For conventional mathematical simplification, in the derivation of the resistance force,  air is taken as a fluid of constant isotropic density and as an incompressible substance.
     This hypothetical incompressibility mainly means that in an isotropic fluid, like the air, all locally produced density fluctuations are continuously dissipated in the form of waves with the speed of sound. Therefore, as long as the speed of the object is much smaller than that of sound, no bulk density changes accumulate in front of the moving object.
     Nevertheless, the validity of these simplifications is limited, because at higher speeds of flight the air is unable to dissipate the accumulating density in front of the moving solid and therefore cannot preserve its isotropic density. Thus, at flight-speeds approaching the speed of sound, air must be taken as compressible for the consideration of the accumulation of a local density increase and therefore an increase in the local air-resistance.
     A few decades after the acceptance of the Special Theory, in the late 1920ís when airplanes began to approach sonic speeds Ernst Mach analyzed the phenomenon and arrived at a mathematical treatment for the relation between flight speed and air resistance. His formula became known as the Mach theory, or Mach-number, which expresses the increasing resistance based on a certain ratio between the square of the velocity of the plane and the square of the velocity of sound. This ratio is expressed as;

                                                        Ro
                              Rm  =  ---------------------------       (4).
                                          sqrt (1 --  V^2 / S2^)

where Ro is the original Newtonian resistance and Rm is the increased Machian resistance, reflecting the accumulated density of the air in front of the plane, due to its initial speed, V approaching the speed of  sound, S.

 

     As Figure 1. illustrates, the relativistic Lorentz Formula and the Aerodynamic Mach-number formula are mathematically identical.
     Could the identical formulas describe two entirely different conceptual contents ? -- If that is unlikely, then which conceptual theory is right ?
     Now the scientific choice is quite clear:
     Obviously, the two equations are totally interchangeable. We can use the Lorentz transformation for the airplane and the Mach-number for the accelerated electron by a simple switch of the symbols, c  and S.But are the two conceptual interpretations interchangeable ?
     Absolutely not!
     Should we be seeking for the cause for a relativistic increase in the inertial mass of the airplane instead of accepting the simple, common sense explanation of the physical retarding force of air-resistance ?
     Or should we rather accept the existence of an all-pervading Aether medium through which the electron flies and where the dissipation speed of local density fluctuations is equivalent with the speed of light. By the removal of the stumbling block of the transverse wave theory of light, this ideal gas model of the Aether is now rendering a humanly comprehensible alternative for the misconceived hypothesis of /relativistic mass increase.
     But we can draw one further conclusion from this analogy.
     Considering the different conceptual interpretations of the same phenomenon, the two contradictory theories must arrive at two contradictory quantitative predictions for a suitably designed experiment.
     On the one hand, relativity agrees with the Newtonian principle of inertia which states that uniform motion on a straight line in empty space is eternally constant. In the absence of external force there is no change in the state of motion. Now, since the space of relativity is totally empty, when a particle is accelerated up to a certain speed and the force is removed, the  theory must predict that the particle will perform an unchanging uniform motion on a straight line ad infinitum, at its latest, final uniform speed.
     On the other hand, the Aether theory states that all space is pervaded by the gas of Aether which exerts a retarding force of resistance against the motion of an object and the magnitude of that force is described by the Mach-Lorentz formula.
     Consequently, for a Synchrotron experiment in which a particle is accelerated to a high speed on a circular orbit and then released into a long straight vacuum chamber with a target at the end, the prediction of the two theories with regards to the arrival time of the particle must be measurably different:
     According to Relativity from the instant of release, the particle will move with constant velocity equal to its state of motion imposed on it by the last acceleration. It follows that, the relativistic arrival time, Tr  will be equal to the length of the channel, L  divided by the final uniform velocity, Vf  of the particle:

                                                     Tr =  L / Vr     (5).

     Aethro-Kinematics, the theory of the gaseous Aether, predicts that the particle in the straight channel will only start with the final velocity, Vf   but it will be continuously decelerated by the resistance force of the Aether, in agreement with the Mach-Lorentz formula. Thus, the time of flight  will be longer and the arrival time, Ta  will be later then predicted by relativity.
     Without getting involved in complex mathematics it can be seen that the velocity,/VA of the gradually decelerating particle in the Aether will be decreasingly smaller than Vr   by the factor of
                                                                    1
                                         B  =   -  --------------------------       (6).
                                                      sqrt (1 -  V^2 /c^2 )
     Therefore

                                                              Tr  <  Ta              (7)

and a measurable experimental discrimination only depends on the length of the chamber, since the longer the distance, the greater the difference will be between the two predictions. I believe that all equipments required for this experiment are readily available.
     It should be noted, that when this experiment verifies the present theory, it also resolves the fundamental duality of the Space of Classical Physics. It simply becomes evident that Space has never been empty and Galileoís Principle of Inertia was a mere approximation for strictly macroscopic phenomena. In his thought experiment Galileo discounted all frictional and retarding forces even that of the resistance of air. For four centuries Galileoís Principle was the unshakable foundation of Physics, now with the mechanical ideal gas of the Aether it is still preserved, except one more miniscule factor of resistance has to be dealt with; the resistance of the all-pervading Aether. -- This is precisely what the Mach-Lorentz Formula does and by that also making sense of the Principle of Correspondence.
     Note here that this example of the power of the ideal gas model of the Aether is not unique and special. My book, AETHRO-KINEMATICS suggests alternate explanations for most of the perplexing philosophical interpretations of modern physics. It seems to be only a matter of our ability to design the right kinematic model of a seemingly incomprehensible phenomenon to restore classical logic and common sense and thereby find the right experiment to verify their validity.
 
     The 500 page book with 150 illustrations is also published on CD-Rom  for all computers.
 

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