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**New Theories / In regards to the 1st Postulate of STR**

« **on:**16/02/2015 22:54:22 »

The following scenario utilizes events that are applicable to Einsteins Special Relativity Theory. What follows requires further analysis regarding application of the first postulate WRT SRT. For information with images, see http://gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/5916.

- Definitions; (Beta) β = v/c, (Gamma) γ = (1-v^2/c^2)^-1/2.

- Electromagnetic relations (second postulate); x = cΔτ, x = cΔτ.

- There are two parallel linear events (A and B) with uniform velocity along the positive x-axis.

- Event A is an electromagnetic event (velocity = c) following the path from point x = 0 to x.

- Event B is an inertial body event (velocity = u) following an identical and parallel path from point x = 0 to x.

EVENTS OCCURRING IN REST FRAME (v = 0)

- These events now occur within a reference frame considered to be at rest (rest frame).

- The event time for A is; Δτ = x/c.

- The event time for B is; Δt = x/u.

- The ratio of these event times gives us the relationship between their event times;

Δτ/Δt = (x/c)/(x/u) = u/c.

EVENTS OCCURRING IN INERTIAL FRAME (v)

- These events now occur within a reference frame considered to be in uniform motion (inertial frame).

- The SRT event time for A is; Δτ = (Δτ+vx/c^2)γ. Applying the second postulate;

Δτ = (Δτ+vx/c^2)γ, x = cΔτ

Δτ = (Δτ+v(cΔτ)/c^2)γ

Δτ = (Δτ+vΔτ/c)γ

Δτ = Δτ(1+ β)γ

- The SRT event time for B is; Δt = (Δt+vx/c^2)γ.

- The ratio of these event times gives us their the relationship between their event times;

Δτ/Δt = [Δτ(1+ β)γ]/[(Δt+vx/c^2)γ]

Δτ/Δt = [Δτ(1+ β)]/[(Δt+vx/c^2)]

Δτ/Δt = [Δτ(1+ β)]/[Δt(1+vx/(c^2)Δt)]

Δτ/Δt = [Δτ(1+ β)]/[Δt(1+ βx/cΔt)]

In order to satisfy the first postulate, the relationship between their event times must remain unchanged in order to prevent one from ascertaining the motion of the inertial frame utilizing this scenario. As we can clearly see, the relationship between their event times can only be regained by allowing an electromagnetic relation (x = cΔt) to be utilized to reduce the Δt relation to (1+ β) in order to regain equality for these events.

Δτ/Δt = [Δτ(1+ β)]/[Δt(1+ βx/cΔt)], x = cΔt

Δτ/Δt = [Δτ(1+ β)]/[Δt(1+ β)]

Δτ/Δt = Δτ/Δt

If we were to allow this substitution, then we would have to admit that in order for the first postulate to remain valid, then the Lorentz transformations (in their current format) could only apply to electromagnetic events. It appears that the only recourse would be to reformat the Lorentz temporal transformation to;

***Δτ = Δτ(1+ β)γ

- Definitions; (Beta) β = v/c, (Gamma) γ = (1-v^2/c^2)^-1/2.

- Electromagnetic relations (second postulate); x = cΔτ, x = cΔτ.

- There are two parallel linear events (A and B) with uniform velocity along the positive x-axis.

- Event A is an electromagnetic event (velocity = c) following the path from point x = 0 to x.

- Event B is an inertial body event (velocity = u) following an identical and parallel path from point x = 0 to x.

EVENTS OCCURRING IN REST FRAME (v = 0)

- These events now occur within a reference frame considered to be at rest (rest frame).

- The event time for A is; Δτ = x/c.

- The event time for B is; Δt = x/u.

- The ratio of these event times gives us the relationship between their event times;

Δτ/Δt = (x/c)/(x/u) = u/c.

EVENTS OCCURRING IN INERTIAL FRAME (v)

- These events now occur within a reference frame considered to be in uniform motion (inertial frame).

- The SRT event time for A is; Δτ = (Δτ+vx/c^2)γ. Applying the second postulate;

Δτ = (Δτ+vx/c^2)γ, x = cΔτ

Δτ = (Δτ+v(cΔτ)/c^2)γ

Δτ = (Δτ+vΔτ/c)γ

Δτ = Δτ(1+ β)γ

- The SRT event time for B is; Δt = (Δt+vx/c^2)γ.

- The ratio of these event times gives us their the relationship between their event times;

Δτ/Δt = [Δτ(1+ β)γ]/[(Δt+vx/c^2)γ]

Δτ/Δt = [Δτ(1+ β)]/[(Δt+vx/c^2)]

Δτ/Δt = [Δτ(1+ β)]/[Δt(1+vx/(c^2)Δt)]

Δτ/Δt = [Δτ(1+ β)]/[Δt(1+ βx/cΔt)]

In order to satisfy the first postulate, the relationship between their event times must remain unchanged in order to prevent one from ascertaining the motion of the inertial frame utilizing this scenario. As we can clearly see, the relationship between their event times can only be regained by allowing an electromagnetic relation (x = cΔt) to be utilized to reduce the Δt relation to (1+ β) in order to regain equality for these events.

Δτ/Δt = [Δτ(1+ β)]/[Δt(1+ βx/cΔt)], x = cΔt

Δτ/Δt = [Δτ(1+ β)]/[Δt(1+ β)]

Δτ/Δt = Δτ/Δt

If we were to allow this substitution, then we would have to admit that in order for the first postulate to remain valid, then the Lorentz transformations (in their current format) could only apply to electromagnetic events. It appears that the only recourse would be to reformat the Lorentz temporal transformation to;

***Δτ = Δτ(1+ β)γ