Dear Gene Barbee/ Gurchan,
You wrote to Gurchan Sandhu: "I was sympathetic to your argument that we need a foundation that does not depend on an inertial frame".
My paper not only shows the way to work motions of particles without reference frames, it explains all relativistic phenomena under this new foundation.
Please see: http://fqxi.org/community/forum/topic/1549
(Note my essay in the competition is handicapped because the diagrams have not come out proper and FQXi rules do not permit any changes. Therefore I am attaching the essay separately as well.
I am copying what I wrote to Sergey Fedosin yesterday:
HERE IS HOW TO SEE THE PROBLEM OF MOTION OF A PARTICLE WITHOUT THE USE OF THE ERRONEOUS FOUNDATIONAL PROBLEM OF REFERENCE FRAMES AND FALLING INTO KINEMATICS.
It is done by developing an anlogy between thermodynamics and particle mechanics.
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0. The zeroth law of motion is that,
a) In the motion of a particle it occurs by way the fusing on its intrinsic energy Mc2 and the applied energy of motion (pc). The fusion takes place by both quantities of energy losing fractions of energy in equal proportion - thus each quantity of energy gets scaled down by the factor (gamma).
After this fusion has occurred, the scaled down quantities of energy are: net intrinsic energy Mc2/gamma and net energy of motion pc/gamma = Mvc, where gamma = 1/(1- v2/c2)1/2
b) The converse of the fusion theorem is that when a quantity of energy X is to break up into two parts aX and (1-a) X, the original energy X gets scaled up by a factor ' (gamma)' so that the parts become equal to (gamma)'aX and (gamma)'(1-a) X,
(Note: In my essay I have explained the physics of fusion and fission interactions)
1. In a system of particles moving relative to their common centre of mass, the energy of motion of the centre of mass cannot be made use of to make discrete changes in the particles relative to each other.
(Applied to earth, we earthlings cannot tap energy from the orbital motion of the earth for terrestrial use. 'Impossibility of the perpetuum mobile of the first kind)
This is analogous to the first law of thermodynamics.
2. In applying energy of motion (pc/gamma = Mvc) on a particle within a co-moving the system of particles (about their centre of mass), it is impossible to for the particle to acquire a motion of velocity v, relative to the other co-moving particles to the full extent of the net energy (Mvc) applied.
This is analogous to the second law of thermodynamics. (Carnot's cycle - see my essay p. 4 last para)
2a. The conversion of the applied net energy Mvc must occur with respect to the energy level of relative to which the motion of the common centre of mass occurs.
Recognizing that energy Mvc also possesses inertia Mv/c2, this energy too must move in common motion with the centre of mass (at velocity u). For this common motion it requires Mvc to break up and dedicate the fraction (Mvc).u/c. Hence the balance energy would be Mvc( 1-u/c). From zeroth law (b) this fission causes the energy of motion to scale-up by the factor gamma'= 1/(1- u2/c2)1/2 at the moment of fission.
Hence the energy that remains for motion relative to the centre of mass is Mvc(1-u/c)/(1-u2/c2)1/2.
Consequently the displacement of the particle relative to another particle (co-moving with the centre of mass) is: x' = vt(1- u/c)/(1-u2/c2)1/2 --------------(1).
At Newtonian velocities v/c tends to 0, hence x' tends to(gamma)'vt. Since for a particle moving relative to a lab frame on earth(gamma)' = 1.000000005, for terrestrial displacements at Newtonian velocities (v/c tends to 0), the scaling up of the displacement due to ' has gone unnoticed and in practice we have formed the convention
x = vt.-------------(2)
When very accurate measurements are made for particles moving at near light velocities v/c tends to1, the effect of the scaling up also has come to the notice. Then the equation (1) takes the appearance of
x' = (x -ut)/(1- u2/c2)1/2 -----------------------(3) (Lorentz transformation).
Equation (3) is valid only for very fast moving particles. When the velocity of a particle reaches the range 0.5c the results start to significantly deviate from the equation. When it reaches the value of earth's orbital velocity, the equation (3) breaks down totally.\
Unlike (3) Equation (1) provides accurate results for all velocities between low (Newtonian) velocities to near light velocities. This can be tested by analyzing the results of all the particle accelerator experiments carried out in the last 100 years.
Best regards/ Viraj
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Please see my essay: Have you seen any explanations for the following anywhere a) the mechanism through which gamma-factors arise. b) are you aware that there are two gamma-factors involved in the motion of a particle and why? c) from where the energy for the centrifugal force comes? d) The process which causes internal processes of particles to slow down? e) Why matter particles cannot reach the velocity c? f) why it requires momentum gammaMv for a particle to move with momentum Mv? f) Physical basis of Lorentz transformation? g) Have you come across a single equation with is applicable for the motion of a particle at any velocity (very slow or near light)? The story does not end there, there is many more things explained under the new foundation but I could not squeeze in everything within 25,000 characters that FQXi permitted.Attachment #1: 2_A_TREATISE_ON_FOUNDATIONAL_PROBLEMS_OF_PHYSICS2.doc