V.7 No 1

1

Non-unique-valued transforms between inertial frames in SRT

Non-unique-valued nature of transforms between inertial reference frames in the relativistic formalism 

S.B. Karavashkin and O.N. Karavashkina

Special Laboratory for Fundamental Elaboration SELF

187 apt., 38 bldg., Prospect Gagarina, Kharkov, 61140, Ukraine

phone +38 (057) 7370624

e-mail: selftrans@yandex.ru , selflab@mail.ru

On the specific example of passing from one inertial frame to another, also inertial frame moving under some angle to that initial, we will show the solution to be non-single-valued, because the relativistic conception violates the rule of parallelogram in the summation of velocities

Keywords: special theory of relativity, inertial reference frames, Lorentz transforms, Galilee transforms, commutativity of matrixes multiplication, theorem of single-valued resolution of vector into orthogonal vectors of affine basis

Classification by MSC 2000: 83C05, 83C57, 83C75

Classification by PASC 2001: 04.20.Cv, 04.20.Dw, 04.20.Ex, 04.40.Dg, 04.70.-s, 04.70.Bw, 97.60.-s, 97.60.Lf

1. Introduction

In a number of our works we multiply showed that the main discrepancy of relativistic conception is the illegal postulation of the lightspeed constancy in all reference frames. The expressions for the coordinate transform from one inertial reference frame (IRF) to another derived with this postulate have inclined the plane of events, and the theorem of relativistic addition of speeds derived with these formulas violated the basic law of parallelogram of the speeds addition. Of course, such gross violation of phenomenology of physics and mathematical formalism has resulted on the solutions yielded in the relativistic conception.

In this paper we use the problem – to find the transform from one frame to another that moves, keeping the axes parallel under an angle to the axis x of initial frame – that was suggested to one of the authors in a discussion. It helped us to show on this particular model, what results from the relativistic violation of the law of parallelogram of speeds summation which relativists think insignificant.

2.The problem of coordinate transform between the inertial reference frames arbitrarily moving on the plane from the view of relativistic formalism

2.1. Statement of problem

Consider the problem in which some inertial frame S₂ that remains the axes reciprocally in parallel moves inertially with respect to the resting frame S₁ with some velocity whose projections onto the axes x₁ and y₁ are relatively equal to v_x1 and v_y1, as it is shown in Fig. 1. Find the formulas of transform of coordinates and time from S₁ to S₂ within the relativistic formalism.

Fig. 1. Motion of the IRF S₂ with respect to the resting IRF S₁

In this problem we will strongly follow the formalism of theory of relativity, irrespectively of, how much substantiated and true this theory is. At the same time we will compare the yielded results with the related results of classical formalism. We also will not confine ourselves to a simple solving of this problem but will consider the variants of solution dependently on possible ways to pass from S₁ to S₂.