Sunday, September 30, 2012

2.2. How to derive the special relativity equations of energy and momentum, ( in particular the E=mc^2), without assuming any principle of space-time relativity, no-constancy of the speed of light, neither that nothing goes faster than light!



Every physicist is familiar probably with the definitions of mass as number of particles (material mass) mass defined by the relation of          momentum giving in a body and acquired speed by it (inertial mass) and mass defined as a source of gravitational attraction (gravitational mass).
 Most of the physicists are also familiar with the claim of Einstein that always inertial mass is equal to gravitational mass.
In this paragraph we shall try to discuss the subject as the new experiments seem to be incompatible with classical concepts of special and general relativity.

SPECIAL AND GENERAL RELATIVITY ARE NOTHING MORE THAN MODELS OF AETHER FOR INERTIAL MASS, AND FOR THE UNIVERSAL ATTRACTION. ANY MODEL OF AETHER  AS "FIELD" (GRAVITATIONAL OR ELECTROMAGNETIC) THAT DOES NOT GET DEEPLY TO THE INDIVISIBLE FREE AND PERMANENT PARTICLES MATERIAL STRUCTURE OF THE FIELD ITSELF, IS INADEQUATE FOR A FULL MODEL OF AETHER AS WE SHALL SEE.  THE INDIVISIBLEs OR PARTICLES OF A FIELD ARE OBVIOUSLY NONE OF THE KNOWN PARTICLES, BUT STILL THEY CAN BE AS SIMPLE AS THE KNOWN TRIADS OF PROTON, NEUTRON ELECTRON ONLY AT RADICALLY SMALLER SIZE.
OTHER CLASSICAL MODELS OF AETHER ARE 1) THE MAXWELL'S ELECTROMAGMETIC FIELD (OR ELECTROMAGNETIZED AETHER AS MAXWELL WAS CALLING IT) 2) THE QUANTUM VACUUM THAT AS SUBSTRATUM GIVES RANDOMNESS TO MOTIONS OF PROTONS, NEUTRONS, ELECTRONS THROUGH THE SCHRODINGER WAVE EQUATION (DIRAC'S AETHER)
   
There is a historical irony in which at the end of the last century there were  people claiming that if particles were a kind of spin motion of condensed field-gas, then their inertia should change as they move in field-gas. They were rejected  with the argument that “as we know very well, bodies do not change their inertia as they move”! Some years later came  Einstein claiming the same thing with the formulas of special relativity,   but avoiding field-gas.
The misunderstanding in the history of physics followed three phases. At first it started as light  was falsely identified with the compression wave of the Field-gas (at that time called aether) which is a purely mechanical wave. This does not have nevertheless so much grave consequences as the two types of waves, the purely mechanical compression waves and the light waves, although of different nature, have the same speed. Second and mainly  it was falsely thought that   the  aberration of light that we observe (which is in the same direction of motion of the receiver) cannot occur if the receiver applies drag forces to the field-gas medium of propagation of light and makes it follow it at some area around it .This is not so!. The aberration  does occur, has  curvilinear light paths and is not annihilated by   the fact that the receiver may apply drag forces to the surrounding medium field-gas and take it with it, as far as it holds that at sufficient larger distance of the receiver, the medium  field-gas is not influenced my the motion of the receiver. Of course a whole range of velocities occur,  from a point of the field-gas that that has zero relative speed to the receiver, ( at the receiver) ,to a point of the field-gas that is sufficient away not to be influenced by the motion of the receiver. All that it takes for the aberration to occur  is a)  that there is an external area of the medium of propagation field-gas that it is not influenced by the motion of the receiver where we assume the source of the light placed and b) that the receiver is moving relative to the source. Of course the aberration path of the light is curvilinear! (not because of gravitation! Neither in the sense of Newton neither in the sense of Einstein's general relativity!) and the aberration direction is given by  the tangent of the relative to the receiver motion -path, at the point of the receiver!
    Both facts
 a) that`, at the round table of the Michelson-Morley experiment, the field-gas follows the motion of the source of the light,( and in fact it could be for many thousands of kilometers above the surface of the planet as the atmosphere puts also a drag force to the field-gas)
 b)  that the aberration could still hold,  if outside the planet's atmosphere the field-gas does not follow the motion of the planet ,

both these facts had been suggested by Lorenz himself (for b) Lorenz rightly remarked that it is little more difficult to analyze because of the curvilinear line of the light path) and silently supported by Poincare and others. But Einstein hushed to publish his conceptions before Lorenz and Poincare could explain also the increase on the inertia of particles, due to their motion. (And this is how the third misunderstanding occurred, after the publications of Einstein).

    Thus the results of the Michelson-Morley experiments and the experiments on aberration of light of distant starts are perfectly consistent between them without the need of Einstein's conceptions.  This by no means requires any abandoning of the Galileo's relativity transformations neither proves the necessity of introducing Einstein's special relativity and replacement of Galileo's transformations with Lorenz transformations. 
    What Lorenz and Poincare did not explained, (the third misunderstanding) in other words, the increase of inertia because of the motion, is still explainable and derivable within Galilean relativity in the following way, as I suggest. All that is required is:
a) To make the assumption that apparent increase of  the inertia of the bodies due to motion, comes from the  total resistance in their flow inside  the material layer of the field-gas (aether) . We assume that the interaction of the (neutral particle ) mass and the (neutral ) aether, is governed by the next equation, which is identical with the Maxwell equation of the scalar potential for charged particles, but here we assume it for neutral partices too (like neutrons). This equation simple states that any particle (e.g. a neutron) because of its spin, it creates a scalar compression wave ("sound" ) in the neutral aether (here a0 is the density of the neutral aether) which propagates at the speed of light c. Notice that in acoustics the above equation is nothing else that a forced sound wave, if it was to be interpreted in air rather than aether. 
(2.0.0)




b) That the motion of the particles is constrained by the field-gas (aether) so that at every state of the motion the next  equation of the interaction of the moving particle and the aether,  is the next
(2.0.1) 


where A is the vector of the momentum  of the (neutral) aether, and j is the momentum of the moving particle. Notice again that this equation is identical with the Maxwell equation of the vector electromagnetic potential , except that in the Maxwell equations the momentum J is of charges. This equations holds for speeds not very close to the speed of light, and when the motions is sufficient smooth. If the motion is not smooth, or it is close to the speed of light the turbulent flow occurs in aether (field-gas) , and more complicated non-linear equations are required. There is no axiom that nothing goes faster than light! Neither that in frames of reference the speed of light is the same, neither that the speed of light in the same reference of frames is always in all conditions constant! (To understand it better you may think that such assumptions were made for a sound-source in air, and c is the speed of sound. You could have all the above equations and assumptions without assuming that the speed of sound is the same in all frames of reference, or is  constant always in the same frame of reference, or that nothing goes faster than the sound!) 
c) Furthermore, we  notice that  a mathematical property of the coupling of a particle with the ambient field-gas (aether)  as described by the above two equations (formally equivalent to the Maxwell equations but of different interpretation) is that the equation of the relation of the energy and momentum of the moving particle system , is invariant to the Lorentz transformations interpreted here in the active not passive way, that is as symmetries of the system particle+wave (that it is coupled) .   This would  then be independent result , but not in contradiction with Galilean relativity!
The previous equation describes also the interaction of neutral particles (like neutrons) with neutral "aether" at laboratory mid-scale. At macroscopic celestial body scale it should be described with a new Universal Attraction (Gravitation) while at the micro-scale it should be describe in such a way that i would be possible to derive the Shroendingers equation of wave-mechanics of particles. 


The three conditions obviously define a special type of coupling of the particle and the field fluid. It is undergraduate university physics exercise to prove that the group of transformations in a fluid that leaves invariant the rectilinear compression waves propagation (in other words the group of automorphisms of the D' Alambert’s hyperbolic 2nd order wave equation) is exactly the group of Lorenz transformations.

Contrary to the Einstein's approach, we do not need to assume that nothing goes faster than light neither that the speed of light is the same inall references frames.

Instead we assume that both are wrong! 

1) There are particles and matter than goes faster than light
2) The transformations of one reference frame to another moving to account for moving refrences frames, is that of classical physics, namely the Galilean transformations that will not give the same speed of th light on all moving refrences frames

But in order to derive the formulae of special relativity with different interpretations and different meaning we assumethe next

AXIOM 1=THE PARTICLES OF MOLECULAR MATTER MOVING OR NOT ARE COUPLED INERTIALLY WITH THE FIELD MATTER IN VELOCITIES WITH DALAMBERT LINEAR ACOUSTIC WAVE EQUATION WHICH IS LORENTZ INVARIANT.

AXIOM 2=THE AUTOMORPHISMS OF THE HOMOGENEOUS INERTIAL WAVE EQUATIONS ARE THE SAME WITH THE AUTOMORPHIMS OF THE INHOMOGENEOUS WHEN COUPLED WITH MOLECULAR MATTER

Compare them with the wrong axioms of  Einstein

Axiom 1=All inertial systems of reference are equivalent for the description of motion of molecular particles

Axiom 2=In all inertial systems of reference the speed of light is the same. 


We should discriminate between a time varying pressure or density of standing molecular particle due its spin which would create a pressure sound wave in the field matter after the D’ Alambert hyperbolic wave equation  and the velocities D’Alambert non-homogeneous wave equation , which is created by a moving molecular matter particle. In the latter the non-homogeneous term may be constant in time, and the whole equation is the Lorenz invariant linear inertia. So the scalar  Dalambert equation with time varying non-homogeneous terms is an acoustic wave (neutral light) in the field matter, while the vector D’ Alambert equation is the Lorenz invariant wave  inertia equation that leads to the same formulae as with special relativity.


a) Let a small part of the space (assumed wirth Euclidean straight lines structure) that the temperature of aether (field or 2nd resolution material reality) is approximately constant (as we shall see in the next chapters this means also that the scalar gravitational potential is relatively constant) so that the speed of light is approximately conastant inall directions

b) The D Alambertian hyperbolic forced wave equations of velocities and pressures of aether as above holds for any particle, as waves created by the  spin of the particles (either neutron , electrons  or proton. The difference is that neutron does not create waves of charged aether, but only of neutral aether  while the  protons and electron create waves of charged or electromagnetized aether as described by the Maxwells equations). This holds either ofthe particle is at rest or moving at s conastnt speed u.

Based,on a) and b) and because the group of automorphisms or symmetries of the Dalambertian hyperbolic wave equation is the group of Lorentz tarnsformations, there is a Lorentz trasformation of the cartesian procuct of 3-space and time (actively interpreted not passively as refrence frames transformations) between the particle at rest and its aethe around it and the particle at speed u and its aether around it. These  hypotheses force a relation ofthe momentum and energy between the particle at rest and the particle at speed u, with arguments and calculations symbolically identical with that the Einstein presented in his paper which instruduced the special relativity, which in particular derive the relation E=mc^2 etc Neverthless although the formulae are identical the interpretation and axioms or postulates are completly different!  




Starting from the well known (non-relativistic) formulas of the kinetic energy and momentum of a moving particle and the sound wave, and by subjecting them to the Lorentz transformations as symmetries of the above coupling equations wave+particle it becomes a direct consequence of the above a), b) (and c) )  that the relation of the energy, and momentum of the system particle+wave is the

(2.0.3)

E2  =(m0)2 c4  +pc2




From which it is also easily deduced the 
(2.0.4) 
E  =m c2


The mathematical calculations for the derivation of the energy-momentum relation (2.0.3) is pretty the same as Einstein did it, but the physical interpretations is vastly different!.
It is said sometimes that Einstein's approach is equivalent with the aether explanation. It is not true. It is far from equivalent (e.g. with aether explanations as above , the speed of light is not a universal constant ,and it does not have an upper bound of 300.000 km/sec) 

Notice that here it is postulated a wave-and-particle coupling and not a wave-particle duality. Notice that this coupling, of a particle and a coupled linear scalar wave is neither exactly a) The DeBroglie a wave of a material partcle (no constant h in the above formulation) b) neither the Shroendiger (probability) wave of a material particle (that initially in quantum mechanics it is not Lorentz invariant). Inspite the fact that the above three mathematical formulations are different, the general underlying physical reality concept is one and only one: Behind and parallel to each material particle, there is a material aether coupled wave. We may formulate various different physical aspects  of this wave, in different mathematical terms, and we may also formulate the "probability wave" that it creates to the motion of the material particle. 


The above postulated concept is clear, any material particle, at rest or moving creates a "sound" and in general a wave in the surrounding aether, due its is inner motion like the spin. We also do not claim the naive causality, that the particle, creates the wave, and not vice-versa. It may be that a particle could be created also my such a wave, if it exists also in deeper material realities than just the (1st) aether. We simply make the statement of a the coupling of particle and wave , which is strong enough to constraint the motion of the particle at not very high speeds, and it is Lorenz invariant
It is direct from these, that the extra energy and momentum absorbed by the particle to bring it to some speed compared to its rest mass, is given to the field-gas close to the particle that follows it. A phenomenon similar to the well-known phenomenon of added-mass in fluid dynamics , which has the equivalent phenomenological effect as if of an increase of the mass of the particle.
 We get also as a consequence that if we represent the effective volume of a particle as a ball at the state of rest, at the state of motion  it becomes an ellipsoid contracted in the direction of motion! And that any  standing waves, in the effective volume, acquire a slower period. 
     These contraction results had already suggested and published by Lorenz himself (in his paper "Electromagnetic phenomena in a system moving with any velocity less than that of light" Proceedings of the Academy of sciences if Amsterdam, 6, 1904 )It is obvious that although these results have the same mathematical  formulas as  the Einstein's concepts of space contraction and time expansion, they are conceptually totally different, as the former are derived within classical Galilean relativity and may lead to different predictions.
We should also notice that it would not be surprising at all, that new experiments on the inertial motion of laboratory size bodies, would give totally new types of coupling of particles and the field-gas when the motion is not simple rectilinear but rotational or under other specific conditions. Thus it could turn out that the dependence of inertial on various parameters, including the speed and type of motion, is something on which we may very well know very little! There are celebrated experiments, at least since the decade of 1980 that prove such phenomena (e.g. The Aspden gyroscope effect [University of Southampton], Hayasaka-Takeuchi experiment, British Aerospace experiments, etc)
   If only Lorenz or Poincare had fallen upon the right hypotheses of coupling of the particles with the field-gas (Electromagnetised field-gas or electromagnetic field, if they are electrons or protons) and derive its increase of inertia, the whole landscape of 20th century physics would be different as far as the conceptions of space-time and Einstein's relativity is concerned!
   Fundamental Physics still can be as simple as Galilean relativity and there is no need to obscure it! And also we can still  make use of flat space and an independent time, even though the light ray paths may follow a curvilinear motion (due to aberration or Newtonian or other gravitation) . Not only because one day we may discover other means to measure space, than light rays, but also because Physics  had decided that whenever we discover a cause that influence the measuring devices, we should not assign it as a space curving but as an influence to the measuring device, that has to be abstracted to find the right strait distance. This is how the temperature expansion of material rulers was treated, when it was discovered. They did not claim a space expansion or contraction, but only such of the measuring device. And by correcting the measurement we get the result. And so is the case with the influence of the aberration or gravitation to the light rays. The argument that any measurement of distance with light rays cannot avoid curvilinear light paths is not different to an argument that would say that any distance measurement would eventually refer to a material instrument (even that reading the light) and in any such instrument we cannot avoid temperature expansion or contraction, too! But it was long ago the choice of physics that, (and  there are significant advantages of this choice), that this is not a reason not to define the space as flat Euclidean, independent from temperature , aberration , gravitation or other parameter.
  In the light of the above correct accounting of the Michelson-Morley experiment (which is not that given by Einstein and his special and general relativity) and  the aberration of light, and the, above mentioned, new experiments on the inertia of bodies, it should be considered that there are already sufficient many  laboratory experiments (neither astronomical, neither microphysical or of quantum physics) that reject both special and general relativity! On the other hand, almost all of the experimentally established formulas of special relativity are also derived in the above Galilean approach. 
    We may notice here how a little wrong turn in the history of theories, may have such severe limitations in our understanding of the world in our spirit and shape our beliefs for a whole century. It is not of course the first time in the history of the civilization. During the time of Galileo, all of the well-established physics believed that the earth is not moving and is square, and till the end of the 19 century all the theories of the atomic structure of matter, were rejected and discredited. At least we improve. At each new century the new misconceptions become  subtler and subtler!
In this paragraph we shall discuss how the basic formulas of special relativity like the  :

(2.1)

E2  =m2 c4  +pc2
 can be derived and interpreted as a special phenomenon of  “added mass” of moving bodies in a the field- fluid (=aether) .

     According to the phenomenon of added inertial mass,  a body moving in a fluid, experiences resistance, even in non-viscous fluids, making the fluid following the motion of the body around and at close distance of it.  In modern terminology we are speaking of coupling of the particle and the fluid . Here the reason the the particle and any (free, permanent particle like electrons, protons, neutrons) will create a wave in the field-gas (or 1st aether) is the spin of the particle. The self-rotation of the particle will result when moving in to a wave (not De Broglies wave neither probability wave of quantum mechanics. But true material wave of the field-gas or 1st aether, as e.g. describe by the Maxwell equation on the potentials, when the particle is charged.). 

After calculating the momentum of the fluid created by the motion of the body, the equations are such that we may de-couple the system particle-fluid asserting that the fluid does not exist and that instead the particle has an additional inertial mass depending on the velocity!
     The mathematical derivation of the formula (2.1) or of
(2.2) 
M = m/\sqrt{1 - v^2/c^2}
in special relativity from the Lorentz invariance of the expressions of the energy and momentum is exactly what we need  in our situation also ,so we shall not repeat it, only that we shall interpreted in a completely different way and in Galilean  inertial systems!
     The necessary assumptions are the next:

a) There is a phenomenon of added mass  for a moving particle in Field-gas as is the normal and usual in fluid dynamics, even for non-viscous Field-gas .
The phenomenon of added mass occurs also, for example, in airplanes when the move with speed close to the speed of sound, in which case the find a resistance on the a pressure-cone of air, and it is as if they have added inertia or mass. 

This in modern terminology, we call the coupling of field-gas and any particle .

b) The formula that connects the energy and momentum of the total system field-gas+particle has the same symmetries with the D’Alambertian wave (hyperbolic ) operator :
(2.3)

{\displaystyle {\begin{aligned}\Box &=\partial ^{\mu }\partial _{\mu }=g^{\mu \nu }\partial _{\nu }\partial _{\mu }={\frac {1}{c^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}-{\frac {\partial ^{2}}{\partial x^{2}}}-{\frac {\partial ^{2}}{\partial y^{2}}}-{\frac {\partial ^{2}}{\partial z^{2}}}\\&={\frac {1}{c^{2}}}{\partial ^{2} \over \partial t^{2}}-\nabla ^{2}={\frac {1}{c^{2}}}{\partial ^{2} \over \partial t^{2}}-\Delta ~~.\end{aligned}}}

At his point we need a lemma which can be proved without much difficulty. (We shall not state its proof but it can be solved as an undergraduate exercise in physics or mathematics department) :
Lemma 2.1 :The symmetries, (or group of automorphisms ,or transformations)  that leave invariant the D’Alambertian hyperbolic wave operator is exactly the Lorentz group .

So we notice that we can have, even in acoustics, the Lorentz group only that the speed c would  the speed of sound. In the case of field-gas we make use of the Lorentz group, only with its active interpretation (not in its passive interpretation as co-ordinate transformations of reference systems). We leave the Galilean group with the passive interpretation as reference systems transformations. The whole phenomenon that we study, takes place in the gravitational field and in a system which is at rest with the sources of  the dominating local gravitational field. 
An inertial system is one that is at rest on the field-gas and at rest relative to the dominating gravitational source. The “dominating” contains a quantitative assessment which is translated to a choice of space and time scale..
This solves the old question which systems are the inertial systems.
So on earth this system is earth ,on Mars its Mars and close to the sun it is the sun . A more detailed definition of it would resort to the time an space scale of interest for the phenomenon. Thus we should introduce scalability in our description of the physical systems.

We may mention here the work by Dr Ing Konstantine Meyl
The experimental kit of scalar waves free-energy , which is an easily reproducible experiment to measure free-energy, by professor  Dr-lng. Konstantin Meyl.
It is a miniature setting of the Tesla towers.
In the link and pdf below, professor Konstantin Meyl describes in detail simple experimental setting of miniature Tesla towers in University laboratory, so as to measure beyond doubt the free-energy. He also proves the existence of scalar (non-vector or non-Herz) ) waves of the electromagnetised aether (probably of displacement current too) . In neutral aether, such waves would be the aether sound compression waves (travelling of course at the speed of light). 




The scalar waves, that Dr Konstantine Meyl measures withe miniature Tesla towers in his experimental kit, are most probably , the scalar waves of the pressure of electromagnetised aether , or equivalently, the scalar waves of the scalar electromagnetic potential α. 

Notice also that the Maxwell equations (5.1) and (5.2) in post 2.5,  of the scalar electromagnetic potential α and vector potential A (e.g. around an electron) are a forced linear DAlambertian scalar wave of (electromanetised) aether presure and momentum  respectively, (as we shall see again in the next post 2.5) 





In other words that even a non-moving electron, through its spin, creates linear compression waves of scalar electromagnetic potential  (such waves are different from the De Broglie waves), and are Lorentz-transformations invariant. We may assume similar equations for neutrons , because again of their spin, in the neutral non-electromanetised (Dirac's) aether.  These scalar waves have obviously a frequency relevant to the spin of the particle.

We should discriminate between a time varying pressure or density of standing molecular particle due its spin which would create a pressure sound wave in the field matter after the D’ Alambert hyperbolic wave equation  and the velocities D’Alambert non-homogeneous wave equation , which is created by a moving molecular matter particle. In the latter the non-homogeneous term may be constant in time, and the whole equation is the Lorenz invariant linear inertia. So the scalar  Dalambert equation with time varying non-homogeneous terms is an acoustic wave (neutral light) in the field matter, while the vector D’ Alambert equation is the Lorenz invariant wave  inertia equation that leads to the same formulae as with special relativity.


After this parenthesis we go back to the arguments.
The conclusions to the previous assumptions is:

Conclusion:
c) We can consider the usual de-coupling of the particle and the field-gas (field-gas)  in which we can ignore the fluid (field-gas) but instead we have an increase of the inertial mass of the particle  depending on the velocity . The total coupled system here is 

Total Energy=kinetic energy of the particle+energy of the linear  wave it creates  


The exact formula is :
(2.2)
or (2.4)

E2  =m2 c4  +pc2

where E and p are the energy and momentum of the system.

THEREFORE WE CONCLUDE THE WELL KNOWN FORMULAS LIKE E=MC^2
OR E2  =m2 c4  +pc2      ARE THE RESULT OF THE APPLICATION OF THE AUTOMORPHISMS OR SYMMETRIES OF THE D' ALAMBERT WAVE EQUATION, WHICH ARE THE   LORENTZ TRANSFORMATIONS, TO THE CLASSICAL KINETIC ENERGY AND MOMENTUM OF THE PARTICLE THAT ARE TRANSFORMED TO THE ABOVE FORMULAS. THIS HAS NOTHING TO DO WITH 

A) ANY PRINCIPLE OF RELATIVITY OF TIME FRAMES (WHICH WOULD BE WRONG) 
B) ANY AXIOM OF CONSTANCY OF SPEED OF LIGHT (WHICH WOULD AGAIN BE WRONG).

BUT IT HAS ALL TO DO WITH AN ASSUMPTION OF THE MOVING PARTICLE CREATING A LINEAR WAVE. 

(To see it, we may notice that we may derive similar relativistic equations, for imaginary particles and sound-source , in air that create a sound wave of air when moving , so that the wave is described by the Dalambert wave equation, and c here would be the speed of sound. The Lorents transformations would be the anthropomorphism of the sound wave, and all the relativistic fomulae, for the imaginary particle, would not need any assumption a) either about the constancy of the speed of sound in reference time frames b) that nothing can go faster than sound.) 

IN OTHER WORDS WE MAY REMARK THAT EINSTEIN DERIVED MORE OR LESS CORRECT FORMULAS, ABOUT THE PARTICLE ENERGY AND MOMENTUM, WHEN SPEED CHANGES, BASED ON FALSE HYPOTHESES. BUT THIS IN LOGIC IS QUITE OFTEN, A FALSE ASSUMPTION DERIVING A CORRECT CONCLUSION MAYBE A TRUE FORMULA.  

IN OTHER WORDS EVEN IF (AND THEY ARE!) HYPOTHESES A) AND B) THAT EINSTEIN POSTULATED AS AXIOMS ARE WRONG, THE FORMULAS OF EINSTEIN MAY BE QUITE RIGHT, BECAUSE THERE ARE OTHER CORRECT ASSUMPTIONS LIKE THE WAVE CREATED BY THE MOVING PARTICLE , THAT CAN DERIVE THEM TOO!.

 

Table x1

THEORY

Absolute bound  of light velocity

Material existence of the fieldmatter

Ability to understand the mechanism of bending of light by gravitation

Ability to discover solar energy stored in he field matter as heat

Einstein’s special relativity

YES

NO

NO

NO

Linear Lorentz invariant inertia

NO

YES

YES

YES

Table x2

 

THEORY

Fieldmatter waves and molecular matter  particle coupling

Experimentally verified formulae

Relativity of inertial systems

Lorentz group invariance

Einstein’s special relativity

NO

YES

YES Lorentz transformations

YES

Linear Lorentz invariant inertia

YES

YES (same formulae)

YES Galilean transformations

YES

 

 


We are accustomed to derive classical non-relativistic formulas as an approximate limit of relativistic formulas. But what we observe here is that conversely the relativistic formulas are derived from a non-relativistic fluid of field-gas! So a non-relativistic layer -1 (or in the positive counting 4) , physical reality gives a relativistic behavior to the layer 0 (or in the positive counting 3), physical reality composed by protons ,neutrons ,electrons etc .This means that when the speed is not very close to the speed of light the formula (2.2) is not a very bad approximation ! Formulas such the (2.2) are of a very familiar form to aerodynamics .The term u/c is called the Mach number . Different assumptions for the coupling would , very well, lead us to the existence of speeds for protons electrons and neutrons much higher than the speed of light !
In addition we should remark that if the theory of the Newtonian gravitation, as an field-gas heat effect, is correct, then the gravitational mass and the inertial mass need not coincide! .The gravitational effect depends, strictly speaking, on the field-gas temperature as we shall discuss in the paragraph 7, while the inertial effect on the number of field-gas particles, accumulated, and the resistance in field-gas. 
So  we should keep that maybe the analysis of new experiments shall give that inertial mass ¹gravitational mass. And even if   inertial mass =gravitational mass, the new gravitation that we shall discuss below, may give that the inertial mass of a body at low (non-relativistic) speed can be decreased (without changing the amount of matter) by appropriate decrease of the gravitational mass (decrease of the universal attraction).
In most  situations, and under normal conditions, we may have that the inertial mass and the gravitational mass, coincide.

During the end of the 19th century and the beginning of the 20th century, there were many experiments trying to figure out if the "aether" (as the conceived it) was following the motion of matter or not. The experiments are the ones listed below. The experiments seemingly have contradictory results , some of them concluding that aether followed the motion of matter and some that that it does not. There was considerable confusion in the scientific community, because they did not understood and conceived aether in a simple and consistent material way. At that time A. Einstein found the opportunity to formulate his special and general relativity, which are essentially models of aether for inertial mass and gravitation But Einstein's model of aether  obscures the physical material reality of aether with  the buzzard concept of "vacuum space-time" and "gravitional field as curvature of this space-time", which (gravitational field) nevertheless has .energy density, momentum and even inertia, but still it was "vacuum" and "field" with no material nature with free permanent particle structure!

Much of  the confusion of the results of experiments about if the motion of matter induces motion of aether too, is resolved , by noticing that when the matter is electrified or magnetized , this means that it has electomagnetic field around it, or "electromagmetised aether" as  Maxwell was stating. And as the electromagnetic interactions are very strong, the "electromagnetised aether" strongly follows the motion of electrified or magnetized matter. While for neutral matter and neutral aether the situations is completely different , where the neutral aether follows very weakly only the motion of neutral matter.
For example as the earth has a significant magnetic field, its daily rotation around its axis, also makes the (electromagnetized) aether follow it. This is confirmed by the Michelson-Morley experiments which contrary to what Lorentz was believing it does not contradict the light aberration. 
We will discus in the next the experiments below, and explain their results.

The historic experiments are of
1) Michelson-Morley. This classical and celebrated experiments simply conforms that a static aether which is an absolute inertial reference frame not affected bythe motion of earth is not the reality. Indeed it confirms that the magnetized aether follows the motion of earth as is synonimous with the magnetic field of earth and it follows the motion of earth. (Of course there is neutral aether too but this is not the case here) 
2) Sagnac effect. This effect shows how rotation which is not an inetrial motion affects the speed of light.
3) Aberration of light. In the next article the correct explanation and calculation of the light aberration is that of the classical physics in the inertial frame of reference of sun, BUT with a correction on the speed of light  due to aether-drag by the motion of earth, which starts at about the boundaries of the magnetic field of earth. The light has always constant velocity within the electromagnetised or not aether, as long as the gravitational acceleration is constant (more precisely as long as the scalar Newtonian gravitational potential φ , which is proportional to aether temperature is constant. If this , or aether temperature , changes considerable the speed of light changes slightly. See post 2.7 ) . As the gravitation  from the sun and then due to earth,  changes, the velocity of light needs also a slight correction. The fact the the magnetic field also moves with earth is synonymous to that the magnetized aether also moves with the motion of earth. 
4) Trouton-Noble experiment. This experiment confirms with its null effect that a static aether which is an absolute inertial reference frame is not the reality. Indeed it confirms that the (magnetized) aether follows the motion of earth as the magnetic field of earth follows the motion of earth, and as the Michelson-Morley experiment confirms too. 
5) Experiments of Rayleih and  Brace. These experiments conform also that there is no static aether which is an absolute inertial reference frame. On the contrary there is no detection in these experiments of any relative motion of aether and aerth, which the reality as we metioned befor. But we need to say here that thsi is not absolute, it is close to the surface of aerth, and in fact as far away, from the surface of aerth as earth's magnetic field goes. At distances far away from the magetic field of earth, the aether does no follows the motion of the planet earth, but more that of the sun and of the solar system inside the galaxy.
6) Hammar experiment. This experiment attempted to detect aether-drag force from the motion of neutral bulk bodies on the surface of earth. Nevertheless these bodies were not electrified or magetised, but neutral therefore the very week "neutral aether wind" which indeed is created is not at  all at the order of the ''electomagnetized aether-wind" that the magetized earth creates by its motion. Therefore by the settings of the experiments and the way to measure the "neutral aether-wind" through the speed of light it was obligated to measure practically null "aether-wind". Because "weak neutral aether wind" at the speeds of the involved bodies will create so small change in the speed of light which is not measurable.   Measurements of very week neutral aether-wind and with completely different method , not involving the speed of light and sensitive enough to detect it was carried out much later at the end of the 20th century , by the experiments of Aspden gyrospcope (where a quantitative formula is given also the calculates it from the kind and motion of bodies), experiment of gyro-drom by Depalma ,  of which was mentioned in post 2. and  a Japanese experimental researcher mentioned in the article of Aspden [Aspden,H] Anti-gravity electronics Electronic &Wireless World January 1989 ,  [Hayasaka,HTackeuchi S.]   Phys. Rev. Lett 63, 2701 (1989)  , 
7) Michelson-Gale-Pearson experiment. This is similar to the Michelson-Morley experiment and Sagnac effect and conforms what these experiments conform too.  
8) Gravitational eather-drag experiments

etc






are all mutually compatible, and compatible to a sufficient sophisticated theory of existence of aether, and do not force necessarily to any aether-non-existence conclusion, neither to a special relativity axiom conclusion! 
Reality (as A. Einstein was suspecting in his book "Subtle is the Lord") is much more subtle than what special relativity postulates as far as aether-non-existence, and speed of light as being a universal constant is concerned. All the three cases :1) Aether-drag (especially for electromagnetised matter, 2) Aether non-drag (seemingly for neutral bodies slowly moving) 3) Aether partial drag (even for neutral bodies fast moving) , can occur and can be appropriated as interactions of aether (4th gaseous material density) and matter (3rd material density).


(By frequency of the matter here we do not mean
the Compton-De Broglie frequency of the electrons of the matter see but we may mean the actual average frequency of the spin of electrons , protons and neutrons.) For example if we utilize the data of the classical electron , the frequency fr of the spin of the electron is
fr=s*5/(2*m*R^2) where s is the spin s=+,- ½ ĥ , (ĥ=h/2π) , R is the radius, and m its mass.
While the Compton-de Broglie frequency fc is fc= (m*c^2)/h.
To make an estimate of the frequency of the visible matter reality we enter the data
ĥ=h/2π=6.58 *10^(-25) GeV *sec , electron mass me=0.10938356*10^(-31)kgr, and the classical radius of the electron R=re=(1/4πε0)*(e^2)/me*c^2 , where c is the speed of light.
So that re=2.817940326727*10^(-13) cm, and s=5.264*10^(-44)joules*sec.
Putting these data in the formula of the frequency of the spin and making the calculations it gives the result of about fr=1.81 Terra Hertz. As the range of the infrared is between 430 Terra Hz -300 Giga Hz, this frequency is in the range of the infrared. While the Compton-de Broglie frequency is 1.97 Giga Hertz. An increase of the frequency of the visible matter   reality will have the result of decrease of the radius of electrons, protons and neutrons.
Therefore with sufficient high frequency , the lattice of the atoms will become coarse enough for the photons to pass through it without hitting the atoms, which means that the matter will become invisible. 

We mentioned that the relativistic formulas are more-or-less correct, inspite the fact the the speed of light is not really constant or the same in all frame of reference.
You may ask of course how is this possible? Has it not been experimentally proved? In fact not! The E=mc^2 that it has been widely tested, as we mentioned, it can be derived in a different way, even if the speed of light changes. And the Michelson-Morley experiment as we mentioned means something else than what Einsteined assumed it means. 

The week point here of all the above relativistic formulas (even if we assume a changing speed of light) are the Lorentz transformations themselves. As we mentioned the D'Alambert linear wave equation, is invariant in the Lorentz transformations. And it is well known too that the Maxwell's equations of electromagnetism are also invariant in the Lorents tranformations, as well as the linear wave equation of electromagnetic waves. But we do know that due to the quantization of light waves (E=hν) , the energy (amplitude) does depend on the frequency, therefore the real wave equation of light is non-linear. And we discuss in subsequent paragraphs, that the weak point of the Maxwell equations is that they are linear, while many experiments and "free energy" devices indicate, that the true equations of the electromagnetic field (electromagntised aether) should be non-linear. Therefore the true non-linear equations will not be invariant to the Lorents transformations. And most probably the true equation of aether-sound (compression wave) is not the linear D' Alambert equation but a non-linear wave equations.  Rarely in flow dynamics the equations are linear. Therefore the above relativistic equations, might be almost exactly correct for relatively uniform motions of matter, inside the aether, that creates a smooth flow of aether. This is the limit of the above equations. 


The aether drag , in other words how much the aether (=electromagnetic and gravitational field) is influenced by the motion of molecular matter, also depends on the frequency of the matter. High frequency matter will drag stronger the fields with it as it moves. Lower frequency matter will drag the fields less as it moves. This is because from the E=hν , we realize that higher frequency spins in the electrons, protons and neutrons will result also to higher amplitude waves (in the details the waves are non-linear) that these particles create in the fields (=aether), and therefore the aether drag will be higher. Therefore if a material object can travel faster than the speed of light or not will depend also on the frequency of its particles. To be sure there is sufficient high frequency of matter that can allow traveling faster than the speed of light (which in its turn depends on the average temperature of aether (=electromagnetic and gravitational field) see post 2.7).
It is not a surprise if further experiments will indeed prove that THE AETHER-DRAG OR AETHER NON-DRAG FORCE  or types and measures of partial aether-drag (according to sufficient sophisticated theories of interaction of aether and matter, that include not only the planet but the sun too) DEPENDS ALSO ON THE FREQUENCY OF THE PRESENT MATTER close to the experimental devices, as well as the frequency of the permanent particles of aether itself.  (And by frequency  of the matter as we mentioned above we do not mean the Compton-De Broglie frequency of the electrons of the matter see but we may mean the actual average frequency of the spin of electrons , protons and neutrons, something considered constant for particles at rest  in quantum mechanics). And matter present close to the experimental device may include the frequency of the body of the human experimenter too. (Not all human beings of all civilization and all times, that perform such experiments have the same body (3rd density and 4th density matter as termed in post 1 ) frequency or frequency of surrounding used material objects.) And I would not be surprised either if experiments would prove that some human beings have the ability just with their minds and conscious decision, to change the frequency of their bodies and even to move directly the aether close to them.

The frequency of matter, is the true base of the dependence of the speed of the flow of time. It has nothing in reality to do with any principle of relativity, or any constraint that nothing goes faster than light. But it has all to do with the FREQUENCY OF THE MATERIAL BODY. Now the frequency e.g. of the human material body, DOES DEPEND ON THE HUMAN CONSCIOUSNESS, quality of habitual thinking, and emotions like love etc.   


Better quality thoughts, and emotions (like love) increase the aether temperature, and thus the speed of light, locally in the human body, therefore, from the last formulas of Compton-De Broglie, also increase the frequency of the matter in the body, and therefore make slower the flow of time, and WE LIVE LONGER! (exactly like the twin paradox of special relativity, except it can be at rest, and no need to move close to the speed of light). 

(for a very interesting talk by D. Wilcock with an abundance of experimental facts and scientific articles supporting partly the above see  http://www.youtube.com/watch?v=gOA6XFrGMW8 )

In post 2.7 , we will discuss in more details, what is the nature of Newtonian universal attraction

that gives the inverse square law of planetary attractions. There we will discover, that the aether temperature is proportional to the scalar Newtonian gravitational potential.

(2.7.3)  φ=λT


And therefore exactly as with the speed c of sound in air, where its speed is proportional (almost equal) to the average speed of the particles of air, therefore depending on the temperature in air (see   http://en.wikipedia.org/wiki/Speed_of_sound   ) , so is with aether too .

(2.4.3) c_{\mathrm{ideal}} = \sqrt{\gamma \cdot {p \over \rho}} = \sqrt{\gamma \cdot R \cdot T \over M}= \sqrt{\gamma \cdot k \cdot T \over m}\,

And thus we may state (after post 2.7)  an equation of dependence of the square of the speed of light, on the scalar gravitational potential φ

(2.4.4)  c^2=α*φ

where α is an appropriate constant with appropriate units.

And here is where the Einstein gravitation is wrong, in spite its alleged assertions that the speed of light is always in all systems constant.
Of course the changes of the speed of light are slight, as the curving of the path of the light, is 
slight. Einsteins predicts the curving of the speed of light, but not the change of the value of the speed of light. A photon traveling towards the sun, is slightly accelerating (and if not vertically, then also its ray-path is curved) and a photon traveling away from the sun is slightly, decelerating. So there are tangential and centripetal acceleration on the photon.

On the other hand neither Newtonian gravitation is entirely correct. Newtonian gravitation is  only the static gravitation, while there is no difference of any dynamic gravitation a with Einsteins gravitation. In Newtonian gravitation , all the (static) gravitation is created due to the presence of matter. But the correct is that the static gravitation, is created by the ether (field-gas) heat, and ether heat is certainly created by the presence of matter. But aether heat can also be created, by the absorption of aether (field-gas) of infrared solar radiation e.g. at the frequency of 1 Terra Herz.  Therefore large material spherical shells of diameter of more than 50 Km, floating in space , say between earth and the sun, would absorb solar radiation at infrared, and the aether inside them would too, creating a "green house" effect, thus raising the aether temperature inside them, which by the formula 2.7.3 above would be creating higher scalar gravitational potential φ, which results in to increased (static) gravitation as if the ball was compact and full of matter. This of course is n no way predictable, by the Newtonian gravitation. But I believe it is not predictable either by  the Einstein's gravitation,because it does not seem to be a way to incorporate the energy of the aether heat, in the energy-momentum tensor of the Einsteins gravitation. Besides, even if there was a way, Einstein's gravitation seem to be based on the cosntany of the speed of light which is wrong concept and physical fact.



Let us now go back to the experiments about if the motion of matter creates a motion in aether (aether-drag) or not.




It is reported by alien civilizations, (many reports that can be found in the web) that when a humanoid body is from an Oxygen-breathing biosphere, then because they have high frequency of  mind and body, they can stand traveling with vehicles up to 4 times the speed of light, as their practice prove. While if they are from Hydrogen-breathing biospheres they can stand to speeds only lower than the speed of light. These are hard  facts for them, and 


IT IS RIDICULOUS TO BELIEVE IN THEORIES LIKE SPECIAL THEORY OF RELATIVITY, ABOUT THE ABSOLUTE UPPER BOUND OF TRAVELLING SPEEDS BY THE SPEED OF LIGHT, WHEN THERE ARE SUCH ABUNDANT REPORTED FACTS FOR THE OPPOSITE. 



Here is also a relevant interesting video 

https://www.youtube.com/watch?v=yD8grqXhSqY