# B Effects on time by gravity or motion

#### pervect

Staff Emeritus
Summary: I have read that depending on your distance from a gravitational source your flow of time is different.

I read that just a few feet difference in height would show a different rate of time and that was measurable. However, If the clock that is at a more elevated position it will be traveling through more space, is that what is responsible for the difference in the rate of time for that clock? I understand that clocks at different heights from the earths gravity field do experience different rates of the flow of time. I wish to know what is the cause of this difference.
I assume your question is based on the rotating Earth?

On a non-rotating planet, a higher clock (at rest relative to the surface of the planet) would always tick faster than a lower clock, pre-supposing one has the usual synchronization scheme so that we can talk about comparing clock rates at all.

By "at rest", I basically mean having a constant latitude and lognitude relative to the surface of the planet.

On a rotating planet, if we assume that the clock is still at rest relative to the surface of the planet by keeping a constant lattitude and longitude, there may be an additional effect that counters this. This effect goes in the opposite direction if it is present, and may even become large enough to counter the first effect if the altitude is high enough.

The opposing effect will be largest for a clock on the equator, and totally absent for a clock at the poles.

It's possible to be more quantitative, but the original question wasn't phrased very precisely to I think this may be an adequate answer. Assuming I have guessed the question correctly, of course.

#### Suppaman

I do follow your thoughts and would like to ask/comment on the first point. When something takes off on a journey to C it appears that the starting point is a fixed reference point. Almost like it is entangled, the point and the ship. These starting points may not have any physical location that is specified by some map coordinate, it is just where the journey started. And you can never get too far from this point that you lose track of where you started. You might not ever find it again and I do not know when the link is broken, if ever. If you built a ship from matter that was sent flying from the big bang at near C then you might not be able to get this ship to go very fast as it would always be referenced to whence it started. If I have this wrong, please tell me what I misunderstand. I believe I followed the balance of your reply.

#### Dale

Mentor
When something takes off on a journey to C it appears that the starting point is a fixed reference point. Almost like it is entangled, the point and the ship.
Wow! That is a truly impressive intuitive leap in a completely wrong direction.

Points don’t get entangled, particles do. All of the rest of your post reads like one of those train wrecks where one small defect causes one car to skip the track and then the whole train follows. I don’t even know where to start. Best if you just go back and delete this whole line of reasoning and ask some clarifying questions about whatever point was said above that triggered this departure.

#### Ibix

When something takes off on a journey to C it appears that the starting point is a fixed reference point.
This is a matter of choice. If you are willing to pay the price in terms of increased mathematical complexity, you can regard yourself as stationary even if you accelerate.
These starting points may not have any physical location that is specified by some map coordinate, it is just where the journey started.
Of course the start points have a physical location. It might be specified in different ways (and may mean different things) for different frames, but it absolutely has a location.
If you built a ship from matter that was sent flying from the big bang at near C then you might not be able to get this ship to go very fast as it would always be referenced to whence it started.
I have no idea what you are trying to communicate here. You can always regard yourself as "at rest", so of course you can always accelerate.

#### Mister T

Gold Member
I am not arguing, I just do not see what is causing the time difference as both answers I get to my question say it is one thing or another thing.
Suppose you have two clocks. You place them next to each other and synchronize them. Then you do something, like move one of the clocks relative to the other. You might slowly move it to the top of a mountain, leave it there for awhile, and then slowly return it. Or, you could fly one of them around the world. Or send one away at a high speed relative to you and then have it return (twin paradox). At the end, the clocks are next to each other again. They won't still be synchronized. If they were still synchronized what would be the cause of that?

#### pervect

Staff Emeritus
I suspect the usual confusion here, though I can't follow the original poster's argument well enough to be positive I'm right. (There are other issues that cause confusion than the one I'll present, but the one I'll present is very common).

The "usual issue" is that people assume, both explicitly and/or implicitly, that the notion of synchronizing clocks is independent of the observer.

The notion of "synchronizing clocks" is needed, for instance, to determine the idea of "now". When we have a model of space-time, "now" is the set of points that occur "at the same time".

The notion of synchronizing clocks, the notion of "now" in special relativity, is observer dependent. Trying to understand special relativity without realizing this issue inevitably leads to confusion. The bad assumption that causes much confusion is to assume that the notion of "now" independent of the observer, that everyone agrees on what "now" is.

An implicit assumption of the existence of "now" is needed to talk about the rate at which clocks tick when they are at different locations. We compare the time on one clock "now" to the time on a clock at a different location "now".

This usually first shows up in the twin paradox, in flat space-time - a much easier topic to talk about than gravity.

Basically, the only way that in A's frame of reference that B's clock can run slow, and that in B's frame of reference, A's clock runs slow, is when A and B have different notions of "now".

There's a name for this issue, it's called the "relativity of simultaneity". However, just giving the name of the issue doesn't explain it enough so that people who are not already aware of the issue understand it. In general, it seems very hard to talk about this issue in a way that will be understood, but I keep trying.

Things get very complicated if someone tries to understand general relativity without understanding this feature of special relativity. Special relativity is much easier to talk about.

#### PAllen

Some of this will be beyond the OP, but I thought it would be useful to quantify 3 effects in question in this thread:

1) Time dilation between two clocks, each with constant proper acceleration, maintaining fixed distance from each other.

2) time dilation (in comparison to a system of stationary clocks as in (1)) due to change in tangential velocity with altitude of clocks comoving with the surface of the earth.

3) Tidal gravity corrections to (1), that is how much the time dilation from top to bottom of a building is diffferent from in a uniformly accelerating rocket of the same altidude.

The relevant quantity I compute is (d/dx)(dτ/dt) for physically appropriate coordinates. This gives a rate of time rate change per meter (in the units I use).

For (1), the exact value of this quantity is simply g/c2. This is about 10-16, thus time rate changes about 1 part in 1016 per meter. Note that this is the only one of these effects that has been observed on the surface of earth. Even the latest research clocks are not yet precise enough to measure either of the other effects. Let us call (1) the Rindler time dilation as distinct from (3).

For (2) the exact value of this quantity is -vϒω/c2, where omega is radians per second for earths rotation. If you compare this with (1), specifically (1)/(2), with the approximation that gamma near earth is close to 1, you get g/rω2, which is about 300. Thus this effect is 300 times smaller than the Rindler time dilation. This is currently undetectable, but another order of magnitude improvement research clocks should make this detectable.

For (3), assuming near earth, the time rates are near 1 compared to Schwarzschild t, and that changes in r are very close to physical distance, then the derivative quantity is given by:

(R/2r2) (1 - R/r)-.5

where R is the Schwarzschild radius and r is the SChwarzschild r coordinate. Noting that with Newtonian approximation, g=GM/r2; and R = 2GM/c2, we can write this as:

(g/c2) (1 + gr/c2), using one term taylor expansion of the square root.

This shows the tidal correction to Rindler dilation is about 6*10-10 times the Rindler dilation. This also means it is about 5 million times smaller than the tangential velocity dilation change with altitude. There is no likelihood of directly detecting this correction near the earth's surface, in the foreseeable future.

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"Effects on time by gravity or motion"

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