I apologize for my prolonged absence.

Butch

This explanation by example should make the concept easier to understand. The math is basic.

The contention uses only the principles as set forth in The Theory of Special Relativity (SR) and the speed formula, v=d/t. It proves mathematically that length contraction and time dilation as set forth by SR contradict the fundamental assumption of SR that the speed of light is constant and the same for all observers. Judged from within the frame of the observer the speed of light is 300,000 km/s. The same observer judges the speed of light perpendicular to the direction of motion to be 150,000 km/s and the speed of light in the direction of motion to be 75,000 km/s in an inertial frame in relative motion at the at the speed .866c.

FOR THESE PURPOSES:

A light clock is an imaginary construction that consists of two reflectors with a light pulse continuously reflected from one reflector to the other.

Judged from within the inertial frame it occupies the length of a light clock is its proper length.

For a light clock judged as its proper length, the round trip distance for the light pulse in that light clock is 300,000 km.

For a light clock judged as its proper length contracted by the length contraction factor, the round trip distance for the light pulse in that light clock is judged as 300,000 km contracted by that same factor.

There are 2 identical circular clocks and 3 identical light clocks.

The light pulse in each light clock completes 1 round trip in the time it takes for the pointer in the circular clock in that same frame to complete 1 revolution.

Judged from within the inertial frame it occupies the pointer in a circular clock completes 1 revolution in 1 second.

1 circular clock and 1 light clock are in frame K with the observer.

1 circular clock and 2 light clocks are in frame K’.

Inertial frame K’ is in motion relative to inertial frame K at the speed .866c.

THE LIGHT CLOCK IN FRAME K:

Judged by the observer in frame K the length of the light clock is its proper length. Then judged by the observer in frame K the round trip distance for the light pulse in that light clock is 300,000 km. Judged by the observer in frame K the amount of time for that light pulse to complete 1 round trip and the time for the pointer in the circular clock to complete 1 revolution is identical, 1 second.

The speed formula

v=d/t

Judged by the observer in frame K

d= 300,000 km - the round trip distance for the light pulse

t= s - 1 second

v= c the speed of the light pulse

Substitute 300,000 km for d, s for t, c for v

c=300,000 km/s

Judged by the observer in frame K the speed of light in the light clock in frame K is 300,000 km/s.

Inertial frame K is at relative rest, inertial frame K’ is in relative motion at .866c.

Per SR relative to time in frame K time in frame K’ is dilated/slower.

Per SR for the relative speed .866c the time dilation factor is 2.

Per SR judged by the observer in frame K length perpendicular to the direction of motion in frame K’ is the proper length.

Per SR judged by the observer in frame K length in the direction of motion in frame K’ is the proper length factored by the length contraction factor.

Per SR for the relative speed .866c the length contraction factor is .5.

FOR BOTH LIGHT CLOCKS IN K’:

The light pulse in each of the light clocks in K’ complete 1 round trip and the pointer in the circular clock in K’ completes 1 revolution in the same amount of time. As the time dilation factor is 2, judged by the observer in frame K the pointer in the circular clock in K’ completes 1 revolution and the pointer in the circular clock in frame K completes 2 revolutions in the same amount of time. Then judged by the observer in frame K the light pulse in each of the light clocks in K’ complete 1 round trip and the pointer in the circular clock in frame K completes 2 revolutions in the same amount of time. Judged by the observer in frame K the pointer in the circular clock in frame K completes 1 revolution in 1 second. Then judged by the observer in frame K the pointer in the circular clock in frame K completes 2 revolutions in 2 seconds. Then judged by the observer in frame K the light pulse in each of the light clocks in K’ complete 1 round trip in 2 seconds.

THE LIGHT CLOCK PERPENDICULAR TO THE DIRECTION OF MOTION IN FRAME K’:

Judged by the observer in frame K the length of the light clock that is perpendicular to the direction of motion in frame K’ is the proper length. Then judged by the observer in frame K the round trip distance for the light pulse in that light clock is 300,000 km. Stated in “FOR BOTH LIGHT CLOCKS IN K’ ”, judged by the observer in frame K the light pulse in each of the light clocks in K’ complete 1 round trip in 2 seconds.

The speed formula

v=d/t

Judged by the observer in frame K

d= 300,000 km - the round trip distance for the light pulse

t= 2s - two seconds

v= c the speed of the light pulse

Substitute 300,000 km for d, 2s for t, c for v

c=300,000 km/2s

Simplify

c=150,000 km/s

Judged by the observer in frame K the speed of light in the light clock perpendicular to the direction of motion in frame K’ is 150,000 km/s.

THE LIGHT CLOCK IN THE DIRECTION OF MOTION IN FRAME K’:

Judged by the observer in frame K the length of the light clock that is in the direction of motion in frame K’ is the proper length factored by the length contraction factor .5. Then judged by the observer in frame K the round trip distance for the light pulse in that light clock is 300,000 km factored by .5. Stated in “FOR BOTH LIGHT CLOCKS IN K’ ”, judged by the observer in frame K the light pulse in each of the light clocks in K’ complete 1 round trip in 2 seconds.

The speed formula

v=d/t

Judged by the observer in frame K

d= .5*300,000 km the round trip distance for the light pulse factored by .5

t= 2s - two seconds

v= c the speed of the light pulse

Substitute .5*300,000 km for d, 2s for t, c for v

c=.5*300,000 km/2s

Simplify

c=150,000 km/2s

Simplify further

c=75,000 km/s

Judged by the observer in frame K the speed of light in the light clock in the direction of motion in frame K’ is 75,000 km/s.

Butch