Hey ,if we need to calculate time dilation with an accelerating frame

[anantchowdhary]

Hey ,if we need to calculate time dilation with an accelerating frame of reference,cant we simply use the lorentz trasnformations and use instataneous velocity in place of relative velocity?

Alsousing einsteins derivation of the lorentz transformations we get 2ct=0

Now how do we explain this?

 

[bernhard.rothenstein]

time dilation+acceleration

Hey ,if we need to calculate time dilation with an accelerating frame of reference,cant we simply use the lorentz trasnformations and use instataneous velocity in place of relative velocity?

Alsousing einsteins derivation of the lorentz transformations we get 2ct=0

Now how do we explain this?

IMHO the time dilation can be derived without using the LT. It relates a proper time interval in one of the reference frames to a coordinate time interval measured in the moving reference frame. In the case when the moving clock performs an accelerated motion (usually the hyperbolic motion) we should take into account that during the reception of two successive light signals the velocity of the receiver and the angle under which he receives the light signals could change. The best way to solve the problem is to use a relativistic space time and to intersect the world line of the accelerating observer with the world lines of the light signals.
the best thing a physicist can offer to another one are information and constructive criticism.

 

[quantum123]

Hey ,if we need to calculate time dilation with an accelerating frame of reference,cant we simply use the lorentz trasnformations and use instataneous velocity in place of relative velocity?

Alsousing einsteins derivation of the lorentz transformations we get 2ct=0

Now how do we explain this?

Wouldn't that violate the principle of equivalence?

 

[anantchowdhary]

which situation the first or the 2ct=0 one?

 

[Chris Hillman]

Citation for standard treatment of uniformly accelerated observers

Hi, anant,

Hey ,if we need to calculate time dilation with an accelerating frame of reference,cant we simply use the lorentz transformations and use instantaneous velocity in place of relative velocity?

This doesn't quite make sense as stated ("time dilation" always refers to some specific pair of observers in a specific spacetime, in this case Minkowski spacetime).

I feel that I must caution you to make sure you study mainstream sources before investigating more idiosyncratic approaches. For the simplest mainstream treatment of accelerated observers (known as the Rindler chart for Minkowski spacetime), see the classic textbook Misner, Thorne, and Wheeler, Gravitation, Freeman, 1973.

It is easy to write down a generalized Rindler chart which will handle an arbitrarily accelerating congruence of observers. If, after reading MTW, you need some help finding that, ask a followup question.