Acceleration or gravitational time dilation the same?

[pmb_phy]

My main question was if the equivalence principle of gravity and acceleration applies to time dilation as well.

The answer is yes. If it were otherwise then the equivalence principle wouldn't be valid.

The main difference between gravity and acceleration is that gravity changes with distance from the source, while acceleration remains constant.

It seems to me that you're speaking only of a particular gravitational field, i.e. that of a spherically symmetric body. The equivalence principle does not say that all gravitational fields are equivalent to all accelerating frames of reference. The (weak) equivalence principle states that a uniform gravitational field is equivalent to a uniformly accelerating frame of reference. The (strong) equivalence principle is about the form of equations and is known as the comma-goes-to-colon rule

So in an enclosed environment, putting two clocks at the top and bottom of a chamber, if the clocks don't run at the same speed, it's gravity (from a point source), and if they're the same, it's acceleration.

In order to observe a time dilation there must be two clocks at different gravitational potentials. Regarding an accelerating frame of reference something similar must hold. Two clocks at the same height in an accelerating frame is like being at the same gravitational potential and thus no difference in the clock rates is expected.

Pete

 

[yuiop]

My main question was if the equivalence principle of gravity and acceleration applies to time dilation as well.

The main difference between gravity and acceleration is that gravity changes with distance from the source, while acceleration remains constant. So in an enclosed environment, putting two clocks at the top and bottom of a chamber, if the clocks don't run at the same speed, it's gravity (from a point source), and if they're the same, it's acceleration.

It can get complicated because there are various ways to artificially accelerate a rocket but generally speaking the clocks at the top and bottom of an accelerating rocket will not run at the same rate and the onboard observers will not measure them to be running at the same rate. Redshift and blueshift are observed in an artificially accelerated rocket. So the answer to the main question you ask here is yes, but your summary is not correct.

 

[Ich]

My main question was if the equivalence principle of gravity and acceleration applies to time dilation as well.

Recently, I made a plot that shows gravitational time dilation in the equvalent case of two accelerated clocks. One can see immediately that the time between two light pulses is longer for the "upper" clock, according to the approximation (1+gh/c²). I don't deal with subtleties like different proper accelerations there, but this derivation of gravitational time dilation should be ok nevertheless.

 

[Dale]

My main question was if the equivalence principle of gravity and acceleration applies to time dilation as well.

Yes.

Please do not misunderstand my above responses. I was not stating that the equivalence principle did not hold, I was responding to the specific experimental set up you proposed in your OP which does not test the equivalence principle since it is not limited to a small (approximately flat) region of spacetime. The curvature would be detectable in the Swartzschild metric between the sea level clock and the space clock.

The main difference between gravity and acceleration is that gravity changes with distance from the source, while acceleration remains constant. So in an enclosed environment, putting two clocks at the top and bottom of a chamber, if the clocks don't run at the same speed, it's gravity (from a point source), and if they're the same, it's acceleration.

My understanding is that the equivalence principle holds only for small regions of spacetime where the curvature is undetectable. This type of experiment would rely on your room being big enough that you could detect the tidal gradient.

 

[kahoomann]

My main question was if the equivalence principle of gravity and acceleration applies to time dilation as well.

The main difference between gravity and acceleration is that gravity changes with distance from the source, while acceleration remains constant.

That's Not true. Einstein field equation does Not imply that gravity changes with distance from the source,
It depends on the source itself. So it's possible for gravity to change very little with distance from the source or no change at all, uniform gravitational field

 

[pmb_phy]

That's Not true. Einstein field equation does Not imply that gravity changes with distance from the source,
It depends on the source itself. So it's possible for gravity to change very little with distance from the source or no change at all, uniform gravitational field

That is quite correct. However one has to be careful in this respect because its tempting to use Newtonian intuition and as such you may arrive at the wrong answer. Consider the example of a uniform gravitational field. In Newtonian gravity the strength of the gravitational field, as measured by the gravitational acceleration ( the gravitational potential varies with height so it is not constant) is the same throughout space. In general realtivity the gravitational field is measured by the Christoffel symbols. The Christoffel symbols for a uniform gravitational field is, unlike the Newtonian case, a function of height.

Pete