- #1

- 82

- 2

*inertial*frames.

However, if we differentiate velocity with respect to time, we obtain acceleration.

The Lorentz factor says:

t(0 reference frame observer at rest) / t(moving) = 1 / Sqrt[1–(v/c)^2]

t

_{0}/ t

_{m}= 1/[(1-(v/c)

^{2}]

^{1/2}

If we want t(moving) to be changing then we need to differentiate the lorentz factor with respect to t(moving)

v is a function of t so

t

_{0}/ t

_{accelerating}= ∂ (1/ [(1-(v(t) / c)

^{2}]

^{1/2}) ∂t

t

_{0}/ t

_{accelerating}= (v[t] ∂v[t]/∂t) / (c

^{2}(1 - v[t]

^{2}/c

^{2}])

^{3/2}]

It looks better here:

https://www.wolframalpha.com/input/?i=differentiate+1/(1-(v(t)/c)^2)^1/2

so the calculation would require we know the acceleration AND velocity at the moment we want to know what the time dilation is doing.

Although we can do the mathematical gymnastics, I do not know if there are any assumptions in the derivation of the Lorentz transformation that REQUIRE an inertial frame.

Or is the equation above really valid?