The scope of this discussion was always limited to the violation of the constancy of the speed of light vis a vis length contraction and time dilation as hypothesized in the Theory of Special Relativity applied instantaneously to the properties of light in light paths delimited by a rigid body of fixed position within a relatively moving inertial frame as judged by an observer in a frame which is at relative rest rather than the comparison of the coordinates on a space time diagram of active events within both frames and simultaneity calculations which, though a more cumbersome process, when properly carried out yield the same result.

As such, all formulations, examples etc. in this discussion are pursuant to:

1. An inertial frame, which in relative motion

2. An inertial frame, which is at relative rest

3. Light paths delimited by a rigid body of fixed position only within the relatively moving inertial frame

4. An observer of a fixed position within relatively moving inertial frame

5. An observer of a fixed position within the frame, which is at relative rest

6. It is understood that the arms of the Michelson Morley experiment are one half the length of each associated light path

7. All judgments, observations etc. are those of one of the two observers for phenomenon in the moving frame only

8. The distance between the observer at relative rest and the contents of the relatively moving frame is of no consequence and is not a consideration

9. All values, magnitudes etc. within the relatively moving frame are, and judged by the observer within the moving frame as, the “proper” values, which are constant within the frame and independent of the relative velocity of the moving frame.

The MM apparatus is moving at 0.866c and we are moving with it...

The velocity of the apparatus compared to the velocity of the observer is zero. The velocity of one relative to the other is zero. At the relative velocity of zero there is no relativistic effect and all else is moot.

The MM apparatus is moving at 0.866c and we are stationary,...

Here it appears that phenomena from one frame crossed into the other frame. Only that which is entirely within the relatively moving frame is a consideration.

You're making exactly the same mistake as you did last time...arm is halved in length,... the length of the perpendicular arm...

No mistake was made. There was no mention of arm length in my last reply.

However, the lengths of the arms are one half the length of the corresponding light path in all circumstances without exception. The calculation for light path lengths at the relative velocity .866c is at the end of this reply.

Please share the mathematical calculations you used for your comment.

If the apparatus is contracted in its direction of travel, you're automatically working with a case where the behaviour of light has to conform to the rules of a frame in which there is no contraction.

Please share the mathematical calculations for this as well.

You're attacking a position I have never held.

I never attack a person or an idea. An attack does not promote constructive discourse, is generally counter productive and can easily result in avoidable useless acrimony.

It affects the frequency instead, so if the source is moving towards you it will result in blue shift, whereas if it is moving away it will result in red shift. The point I've been making concerns how you should handle the speed of light when you're working things out from within any particular frame of reference....

This is a discussion of simultaneity.

This illustrates why an understanding of Lorentz's theory should be considered as essential before people try moving on into exploring SR. All of this should be worked out under a theory which has a preferred frame. Once you've understood all the details of how that works, then you'll understand straight away how the rules have to be applied in SR to make SR work properly.

Thank you for your input.

The operative formula is the speed formula, d/t=v.

In which:

t= unit of time (proper time)

d= distance or length of the light path (proper length)

c= the speed of light

v= speed

v= c

Judged from within the relatively moving frame: The length of the light path in the direction of motion and the length of the light path perpendicular to the direction of motion are equal at one unit of proper distance (d). It takes one unit of proper time (t) for light to traverse each. Then, light traverses the proper length of each light path, d, in one unit of proper time, t, at velocity c.

d/t=v v=c then;

d/t=c

Judged from relative the relative velocity of the moving frame is .866c, so, the length contraction factor is .5 and the time dilation factor is 2. The length of the light path is .5 times the proper length (.5d) and time is 2 times proper time (2t) judged from relative rest. Then:

.5d/2t=v

.5d/2t * 2/.5= v * 2/.5 simplify

d/t=4v v=c then;

d/t=4c

Judged from within the relatively moving frame light traversed the proper length of the light path, d, in one unit of proper time, t, at velocity c. However, judged from relative rest light traversed the proper length of the light path, d, in one unit of proper time, t, at velocity 4c.

Judged from relative rest for light perpendicular to the direction of motion length is not contracted and time is slower in the moving frame by the factor of 2. Time is 2 times proper time (2t) judged from relative rest. Then:

d/2t=v

d/2t * 2= v * 2 simplify

d/t=2v v=c then;

d/t=2c

Again, judged from within the relatively moving frame light traversed the proper length of the light path perpendicular to the direction of motion, d, in one unit of proper time, t, at velocity c. However, judged from relative rest light traversed the proper length of the light path perpendicular to the direction of motion, d, in one unit of proper time, t, at velocity 2c.

This is more mathematical proof that length contraction and time dilation as hypothesized in the Theory of Special Relativity results in 3 distinctive values for the constant speed of light. Further, the length of the light path in the direction of motion is contracted judged from relative rest. Therefore, the light in the light path in the direction of motion is contracted judged from relative rest. The problem is light does not contract nor can light be judged as contracted by any observer.

Thank you,

Butch