- #1
dianaj
- 15
- 0
Imagine two spaceships a distance z apart both moving with the same constant acceleration a. The trailing spaceship shoots a beem of light which will be redshifted by an amount
[tex]\frac{\Delta \lambda}{\lambda_0} = \frac{az}{c}[/tex]
(assuming that [tex]\frac{\Delta v}{c}[/tex] is very small). Due to the equivalence principle the same redshift will happen in a uniform gravitational field - this is the famous gravitational redshift. In a non-uniform gravitational field a is not constant, and
[tex]\frac{\Delta \lambda}{\lambda_0} = \Delta \Phi[/tex]
I have a pretty good understanding of the latter type of redshift, I think. Basically it expresses how time moves at different speeds in areas with different potentials. The deeper you are in a potential well, the slower time goes.
But what about the equation for the uniform field? Does it imply as well that time moves slower for the front spaceship? I hardly think that is 'fair' - I mean, the two spaceships are moving at the exact same speed. The same goes for the uniform gravitational field - why should time move faster for an observer in a uniform field, just because he is higher up?
[tex]\frac{\Delta \lambda}{\lambda_0} = \frac{az}{c}[/tex]
(assuming that [tex]\frac{\Delta v}{c}[/tex] is very small). Due to the equivalence principle the same redshift will happen in a uniform gravitational field - this is the famous gravitational redshift. In a non-uniform gravitational field a is not constant, and
[tex]\frac{\Delta \lambda}{\lambda_0} = \Delta \Phi[/tex]
I have a pretty good understanding of the latter type of redshift, I think. Basically it expresses how time moves at different speeds in areas with different potentials. The deeper you are in a potential well, the slower time goes.
But what about the equation for the uniform field? Does it imply as well that time moves slower for the front spaceship? I hardly think that is 'fair' - I mean, the two spaceships are moving at the exact same speed. The same goes for the uniform gravitational field - why should time move faster for an observer in a uniform field, just because he is higher up?