A synopsis of:

SPECIAL RELATIVITY CONTENTION 2.1

Thorntone E. Murray Feb. 19, 2012

The primary equation:

(ct’)

^{2}+(vt)

^{2}=(ct)

^{2} (a

^{2}+b

^{2}=c

^{2} the Pythagorean theorem)

The equation (ct’)

^{2}+(vt)

^{2}=(ct)

^{2} was formulated by Lorentz and is based on the Pythagorean theorem. Solved for t’ it is t’=t(sqrt(1-v

^{2}/c

^{2})) the time dilation equation, the mathematical foundation of the Theory of Special Relativity. In that primary equation the speed of light, c and time in the rest frame, t are constants. Time in the moving frame relative to time in the rest frame, t’ and relative velocity, v are variables. Given those parameters and given a change of the value of v it is obvious that the value of t’ must change appropriately to maintain the equality. For that right triangle the length of the hypotenuse, ct is constant. Therefore, change of the magnitude of the length of side vt necessarily results in change of the magnitude of the length of side ct’.

In the right triangle side vt represents the velocity of the moving frame relative to the rest frame and is in/parallel to the direction of motion. Then, by definition, side ct’ is length perpendicular to the direction of motion. It is in the moving frame and the magnitude of its length is judged from the rest frame.

The magnitude of the length of side vt is determined by the value of v, the relative velocity of the moving frame. The magnitude of the length of side ct’ which is perpendicular to the direction of motion is dependent on the magnitude of the length of side vt which is dependent on the relative velocity.

A crucial tenet of the Theory of Special Relativity is that the magnitude of a length perpendicular to the direction of motion in a moving frame as judged from the rest frame remains the same independent of relative velocity.

According to a crucial tenet of Special Relativity: Judged from rest the magnitude of a length perpendicular to the direction of motion is independent of the relative velocity.

According to the mathematical foundation of Special Relativity: Judged from rest the magnitude of a length perpendicular to the direction of motion is dependent on the relative velocity.

A serious incongruity within the Theory of Special Relativity is now confirmed. A crucial tenet and the mathematical foundation are proved mutually exclusive. The viability of Special Relativity as currently written and understood is questionable.

Thorntone E. Murray

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