Gravitational time dilation, redshift and doppler

[Zman]

If as a result of the equivalence principle we can derive the gravitational red shift entirely from the perspective of an accelerating body with no reference to gravity and no reference to gravitational time dilation then one is essentially just working out the Doppler shift of a signal associated with an accelerating body. This of course is the essence of the equivalence principle, the fact that you can work out the equation for gravitational red shift from a situation without gravity.

As gravitational time dilation is associated with gravitational redshift, it is also assumed to be associated with an inertially accelerated body. This is a consequence of the equivalence principle.

I assume that the equivalence principle implies that an inertially accelerated body will experience time dilation. Time flow will be greater towards the front and less to the rear.

But if the Doppler shift can account entirely for the frequency of light that is measured in an inertial situation, it is as if the time dilation is having no effect at all.

If there is time dilation in an inertial situation (accelerating) then surely it has to have an effect on the wavelength measured beyond the calculated Doppler shift.

In a gravitational context, time dilation causes the red shift.

 

[yuiop]

A couple of things to consider.

Imagine we have a long rocket that starts from rest and then undegoes Born rigid acceleration for an extended period before switching its engines off and settling down to inertial (non accelerating) motion again. Imagine one twin is at the nose and one at the tail. After the acceleration is over, the twin at the tail and the twin at the nose move slowly towards each other and meet at the centre of the rocket. They find that the twin that was at the back has aged the least. In this sense the difference in time dilation between the front and back of he rocket is real and not just a Doppler effect.

The other point is that you seem (although I am not sure) to be using inertial acceleration to mean acceleration that is not due to gravity, whereas in relativity inertial acceleration usually is due to gravity (when free falling and no proper acceleration is felt) and acceleration due to rocket thrust is usually called non-inertial. Just thought I would try and clear that up.

 

[Zman]

Thanks so much for that Kev

I was a bit concerned with my use of the term inertial but never took the time to check it out. No wonder my question has had so few responses. Although the question itself isn’t very succinct.

But I am still interested to know why the time dilation effect (for an accelerating rocket outside of a gravitational field - non-inertial) seems to be superfluous when working out the equation for the Doppler shift? It is this equation that is the equation for gravitational redshift.

In a gravitational context it is the time dilation that causes the redshift. In a non gravitational situation, time dilation seems to be simply a superfluous side effect.

 

[starthaus]

If as a result of the equivalence principle we can derive the gravitational red shift entirely from the perspective of an accelerating body with no reference to gravity and no reference to gravitational time dilation then one is essentially just working out the Doppler shift of a signal associated with an accelerating body. This of course is the essence of the equivalence principle, the fact that you can work out the equation for gravitational red shift from a situation without gravity.

As gravitational time dilation is associated with gravitational redshift, it is also assumed to be associated with an inertially accelerated body. This is a consequence of the equivalence principle.

I assume that the equivalence principle implies that an inertially accelerated body will experience time dilation. Time flow will be greater towards the front and less to the rear.

But if the Doppler shift can account entirely for the frequency of light that is measured in an inertial situation, it is as if the time dilation is having no effect at all.

If there is time dilation in an inertial situation (accelerating) then surely it has to have an effect on the wavelength measured beyond the calculated Doppler shift.

What do you mean "beyond the calculated Doppler shift"? The gravitational shift can be explained by the Doppler effect in accelerated frames and vice-versa cf. the equivalence principle. You can see an exact explanation in the latest file I uploaded in my blog ("Equivalence Principle")