Gravity time dialation and acceleration?

[Artlav]

Good evening.

After reading about the recently created record-breaking precision quantum clocks i got thinking about how gravity affect time.

Suppose we have two clocks that are precise enough to register the gravity-induced difference of time rates at distances of a few meters up/down near Earth surface.

Would such a pair of clocks be a gravity detector?
I remember a quote, probably by Einstein, that no experiment could tell apart gravity field acceleration and regular acceleration from inside the system.

I'm particularly interested in the expected outcomes of these three experiments:
1. Two clocks one above other standing still on the surface. I expect them to show the corresponding difference.

2. The pair in free-fall around the same altitude. Would they register the difference?

3. The same pair standing as in 1, but inside a constantly accelerating spaceship in outer space. Would the clocks register anything?

 

[Antiphon]

1 and 3 read the same gravity-induced shift. In 2, the clocks read the same.

 

[jerrywickey]

I understand the intent of your post is to clarify the notion that acceleration induced by gravity and that induced by some other means are indistinguishable.

2) is ambiguous. I understand it to mean the two clocks are in orbit of a gravitational body. or are held stationary at the same distance from a body expressing a gravitational field while both clocks and the body are all in free fall together. In either case, both clocks show the same rate for the passage of time. This would be the same as 3) The clocks show no difference, because in both cases, both clocks are accelerating at the same rate.

In 1) The clocks show different rates. The time they show diverges over time

Since the two clocks are not moving relative to one another, but they are accelerating relative to one another. The force required to maintain their relative positions is different. The lower one requires lightly more force. The divergence in force or time could be used to infer the respective strengths of the gravitational fields in which they reside. The conditions of case 1) show that the strength of the gravitational body. The fact that some force is maintaining the clock's respective positions against the force of gravity proves that the acceleration imparted to the clocks by those different forces acts on the clocks identically. The clocks can not differentiate between the force of gravity and the electromagnetic force of the solid structure holding them in place. The two forces are indistinguishable to the clocks, though we can infer their sources.

Acceleration from gravity is indistinguishable from acceleration caused by any other force. Inferring the source of acceleration by other means doesn't change that. If that is known is some acceleration, its source can not be differentiated from gravity.

Jerry

 

[Artlav]

So, am i right to understand, that the dilation is caused by any difference in accelerations, not only by gravity?

2 meant the same rig as 1 - two clocks one above each other, but dropped from an altitude at an airless body. Thus, they are still in gravity field, but with no extra acceleration.

If so, why there are no effects of it in a centrifuge spinning at a million G's (is it?), but there is near the surface of a neutron star?

 

[jerrywickey]

Either one or both relative speed or relative gravitational strength, not acceleration, is all that is required to experience time dilation or the difference in the rate of time passage between those same objects having the speed difference.

As for the two clocks dropped one above the other into free fall but mechanically supported so that they remain the same distance from each other: Your new explanation clears the description up. Both clocks will always be traveling at the same speed, so they will not experience a relative time dilation from speed. However, the lower clock will feel gravity slightly stronger than the upper clock and will therefore experience a slightly slower rate of time passage.

The force exerted on an object in a centrifuge does not cause any relativistic effect, but the speed which the centrifuge is spinning the object would.

I have not done the calculation, but at first glance I suspect that:

For an object spinning in a centrifuge: It experiences relativistic time dilation due to the speed not the force of acceleration. But I suspect, I have not done the calculations and could be wrong, an object which is held in a gravitational field with exactly the same force of accretion on it that the object in the centrifuge feels will experience the same relativistic time dilation. Not from the accretion, but from the speed for the first and the gravity for the second object.

Do the calculations. That will probably teach you more about relativity than you wanted to know.

the relationship between relative speed difference (s) and time dilation between two objects (t) is t = sqr( 1- (s/c)^2 ) Where c is the speed of light in the same units as s and a t =1 means the two objects are experiencing time at the same rate. t=0.5 means that the objects are experiencing time at half the rate of the other.

Now find the relationships between time dilation and a given force of gravity where the strength of the gravity is expressed in terms of force of acceleration (f) ( t = somegravfunction(f) ) and find the relationship between the force of acceleration felt by an object in a centrifuge and the speed at which the centrifuge is moving the object ( f = somecentfunction(s))

Then find if somegravfunction(f) = sqr( 1- (s/c)) where f = somecentfunction(s)
to simplify: Does somegravfunction( somecentfunction(s)) always = sqr( 1- (s/c)) for all values of (s)?

Please, Let me know the results if you do it.

Jerry

 

[Janus]

So, am i right to understand, that the dilation is caused by any difference in accelerations, not only by gravity?

2 meant the same rig as 1 - two clocks one above each other, but dropped from an altitude at an airless body. Thus, they are still in gravity field, but with no extra acceleration.

Then in this case, the higher clock will run faster.

If so, why there are no effects of it in a centrifuge spinning at a million G's (is it?), but there is near the surface of a neutron star?

Time dilation is related to the difference in gravitational potential, not gravitational strength. In the example of a centrifuge, for someone standing next to it watching it spin, there is no potential difference.

If you in the a frame rotating with the centrifuge, you could consider yourself at rest. In this case, there would be an apparent force acting outward from the center. The clock at the end of the arm would run slower than one at the center, and this would be related to how much work it would take to move something from the end of the arm to the center in that frame.

 

[Dale]

Would such a pair of clocks be a gravity detector?

Such a pair of clocks would be an accelerometer. They would measure the proper acceleration.