- #1

Leepappas

- 32

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Consider two rulers that have the same rest length. Denote it by L0.

Now let the two rulers be in relative motion. First consider things from the rest frame of the unprimed ruler illustrated below.

A'_____B'

............A_______________B. State 1

............A'_____B'

............A'_______________B. State 2

....................…..…..A'_____B'

............A_______________B. State 3

The primed ruler length contracts in the rest frame of the unprimed ruler. Let ∆t1 represent the amount of time from State one to state two as measured by a clock at rest in the unprimed frame. Let ∆t2 represent the amount of time between states two and three as measured by the same clock. The relative speed v of the rulers satisfies

v = L0/(∆t1+∆t2), because the point B" travels a distance L0 an amount of time ∆t1+∆t2. But using the same definition of speed the point B' travel a distance L in time ∆t1, so

v = L/∆t1, where L=L0√1-v^2/c^2.

And in going from state two to state three B' travels a distance L0 - L in amount of time ∆t2, so

v = (L0 - L)/∆t2.

Now let ∆t = ∆t1 + ∆t2, so that

∆t' = ∆t/√1 - v^2/c^2.

Now delta t prime is the time between states one and three as measured by a clock at rest in the primed frame. In that frame the unprimed ruler's length contracts as it moves from right to left.

A'_______________B'

.............................A_____B. State 1

A'_______________B'

..................A_____B state 3

Therefore v = L/∆t', since A travels a distance L in the primed frame in amount of time ∆t' as measured by a clock at rest in the primed frame.

Now since v ∆t2 = L0 - L it follows that

L/∆t' (∆t2) = L0 - L, so

L0-L=L0√1-v^2/c^2 (∆t2/∆t') which equals

L0√1-v^2/c^2 (∆t2√1-v^2/c^2 /∆t), which equals

L0(1-v^2/c^2)∆t2/∆t, which equals

L0(1-v^2/c^2)∆t2/(∆t1+∆t2).

But v = L0/(∆t1+∆t2), so

L0 - L = v (1-v^2/c^2) ∆t2, but v∆t2=L0-L, so

L0-L = (L0-L)(1-v2/c^2).

Since v isn't equal to 0, L0-L isn't zero so we can divide both sides by it to obtain:

1 = 1 - v^2/c^2. The only way the preceding equation can be true is if v= 0, but the rulers are in relative motion by hypothesis so v is not equal to 0. Therefore

v =0 and not( v = 0).

Thus the theory of special relativity self-contradicts.

What say you?

Now let the two rulers be in relative motion. First consider things from the rest frame of the unprimed ruler illustrated below.

A'_____B'

............A_______________B. State 1

............A'_____B'

............A'_______________B. State 2

....................…..…..A'_____B'

............A_______________B. State 3

The primed ruler length contracts in the rest frame of the unprimed ruler. Let ∆t1 represent the amount of time from State one to state two as measured by a clock at rest in the unprimed frame. Let ∆t2 represent the amount of time between states two and three as measured by the same clock. The relative speed v of the rulers satisfies

v = L0/(∆t1+∆t2), because the point B" travels a distance L0 an amount of time ∆t1+∆t2. But using the same definition of speed the point B' travel a distance L in time ∆t1, so

v = L/∆t1, where L=L0√1-v^2/c^2.

And in going from state two to state three B' travels a distance L0 - L in amount of time ∆t2, so

v = (L0 - L)/∆t2.

Now let ∆t = ∆t1 + ∆t2, so that

∆t' = ∆t/√1 - v^2/c^2.

Now delta t prime is the time between states one and three as measured by a clock at rest in the primed frame. In that frame the unprimed ruler's length contracts as it moves from right to left.

A'_______________B'

.............................A_____B. State 1

A'_______________B'

..................A_____B state 3

Therefore v = L/∆t', since A travels a distance L in the primed frame in amount of time ∆t' as measured by a clock at rest in the primed frame.

Now since v ∆t2 = L0 - L it follows that

L/∆t' (∆t2) = L0 - L, so

L0-L=L0√1-v^2/c^2 (∆t2/∆t') which equals

L0√1-v^2/c^2 (∆t2√1-v^2/c^2 /∆t), which equals

L0(1-v^2/c^2)∆t2/∆t, which equals

L0(1-v^2/c^2)∆t2/(∆t1+∆t2).

But v = L0/(∆t1+∆t2), so

L0 - L = v (1-v^2/c^2) ∆t2, but v∆t2=L0-L, so

L0-L = (L0-L)(1-v2/c^2).

Since v isn't equal to 0, L0-L isn't zero so we can divide both sides by it to obtain:

1 = 1 - v^2/c^2. The only way the preceding equation can be true is if v= 0, but the rulers are in relative motion by hypothesis so v is not equal to 0. Therefore

v =0 and not( v = 0).

Thus the theory of special relativity self-contradicts.

What say you?

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