[deleted]
Dear Sergey,
We must remember that we are concerned in this discussion about the foundational problems of physics.
When considering the motion of a particle in relation to reference frames, if the INTERACTION BETWEEN THE ENERGY OF THE PARTICLE AND THE ENERGY OF MOTION OF THE OBJECT THAT THE LOCAL REFERENCE FRAME IS ATTACHED to is disregarded, then that itself is a foundational error.
I will explain it:
Newton's theory was hailed as the ultimate triumph of the Copernican Revolution. Why, it hit the final nail in the coffin of kinematics in physics. Newton in his Principia says that it is to distinguish between apparent motions (kinematics) from true motions (dynamics) that he wrote Principia. "But how we are to obtain the true motions from their causes, effects, and apparent differences, and the converse shall be explained more at large in the following treatise (Principia). FOR TO THIS END I COMPOSED IT.
(Note in Newton's terminology 'motion' = momentum, so the above concerns how to distinguish whether a particle has true momentum or no momentum - false apparent momentum)
An essential foundational concept in Newtonian theory is: "a body, which is moved from a place in motion, also partakes in the motion of its place" (Principia p.9).
For Newton 'place' is not an arbitrary reference frame but the local frame, attached to the location where the particle is at rest.
This means when the particle is at rest in K' (local reference frame of the particle) Even when at rest in K' it is has a real component of momentum already in it and co-moves with K' relative to K (local ref frame of K'). When it moves relative to K' it is has two real components of momentum.
If you read my essay http://fqxi.org/community/forum/topic/1549
You will find that Einstein was desperately in search of a dynamic explanation for the relativistic phenomena, since the way Newtonian mechanics has developed had come to the end of the road. He indicated that it had come to the point of writing the obituary of Newtonian Mechanics.
Unfortunately, Einstein resurrected kinematics. In this sense he has negated the progressive aspect of Newtonian dynamics, and brought about a counter revolution in intellectual thinking. Einstein has made a grave foundational error to turn the wheel of history of physics back into thinking in terms of kinematic paradigms
When you ask me the questions about velocities relative K and K' you are asking me those questions from a kinematic basis.
In my essay I have explained how Einstein was trying to find the "Right Way" in terms of generalizing the laws of thermodynamics.
I will follow this up with another article giving the solution without the use of kinematic reference frames.
Best regards,
Viraj