B Effects on time by gravity or motion

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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.
 
This difference is the gravitational field itself. It's a main result of General Relativity. In the Newtonian limit you have $$\Delta t_{1}=\left(1-g\left(\phi_2-\phi_1\right)\right)\Delta t_{2}$$ where ##\phi_i## is the gravitational potential.
 
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OK. And our clock, if it was far from any source of gravity but was traveling the same path through space would also, because of this travel, experience an effect on the rate of time it experiences?
 

Ibix

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General relativity regards space and time as parts of a single thing, imaginatively named "spacetime". It turns out that, just as in space there is a notion of "distance" there is a notion of "distance" in spacetime, usually called interval. For massive objects, such as ourselves and clocks, the interval along our path through spacetime turns out to be equal to the amount of elapsed time we measure - called proper time (proper in the Latin sense of "your own", like property, not in the modern English sense of "correct").

As you say, it turns out that if I arrange to start two clocks simultaneously, one on the floor and one on a shelf, and stop them simultaneously (I'm glossing over a few subtleties in the meaning of simultaneous), they will show different times. This is because the elapsed time (the "distance") between the "clock start" and "clock stop" events was different along the paths followed by the two clocks. This is a consequence of spacetime being curved - one of the other consequences of which is what we call gravity.

So I wouldn't actually describe the effect as "the rate of time being different", although you certainly do see that written. I'd rather say that the curvature of spacetime is such that clocks at different altitudes follow different paths through spacetime, and if one compares the clock readings at two different times, the lengths of the paths between the first and second comparison are different.
 

Ibix

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OK. And our clock, if it was far from any source of gravity but was traveling the same path through space would also, because of this travel, experience an effect on the rate of time it experiences?
"Travelling through space" isn't something you can define without reference to something else. So I'm not sure what you are trying to ask here. What object are you thinking of as "not moving"?
 
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So, it is not the gravitational field that is causing the difference? 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. Which is it?
 

Ibix

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So, it is not the gravitational field that is causing the difference?
The curvature of spacetime is the gravitational field.

The point is that if you set up a way to compare the reading on two clocks now, and wait a little bit and compare them again, you will find that the higher clock has advanced slightly less. The reason for that is that spacetime is curved, and the path through spacetime followed by the higher clock is of a different "length", which turns out to be equivalent to elapsed time. It doesn't have anything to do with travelling through space (again, glossing over some subtleties here). This effect would happen if the Earth did not rotate or orbit anything.
 
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What "path" is the higher clock traveling, where does "length" of this pat come from? I can think that the higher clock is experiencing a different space-time because the gravity field for it is different but do not see any traveling involved. If this is just semantics are there different words that can be used?
 
What "path" is the higher clock traveling, where does "length" of this pat come from? I can think that the higher clock is experiencing a different space-time because the gravity field for it is different but do not see any traveling involved. If this is just semantics are there different words that can be used?
Is travelling in time, not in space.
 
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OK. Not to confuse things but if we have our spaceship going at a good percentage of C then it is experiencing a different rate of time because it is moving through space-time? Our clock in a different gravity field is experiencing a different rate of flow only because of the strength of the gravity field and not because it is moving through space. So we have different ways to change the rate at which time passes, adjust gravity or speed of motion through space. Does anyone know what causes the rate of time to change in either case?
 

Ibix

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What "path" is the higher clock traveling,
It's usually called a worldline. Imagine drawing a picture of a planet with two clocks sitting on it on a piece of paper. Then draw another picture of the planet and clocks a second later, then another a second after that, and another and another. Stack all your pictures up, then imagine dissolving the paper and leaving just the ink floating there. You'd have a cylindrical lump of ink, the planet, with two tubes on the side of it, the clocks. The length I'm talking about is essentially the height of the cylinder.

Now imagine that each sheet of paper was slightly thicker at one edge than the other, so my stack would curve slightly to one side. This time, when I dissolve the paper, one of the clock tubes will be slightly longer than the other because it was going through thicker paper. If the top of each sheet is "the universe at a given time", now I've got slightly more time for one clock than the other, due to curvature.

That's only an analogy - it's usually called the block universe (google with care - there's a lot of nonsense out there). It uses Euclidean geometry instead of the rather more complex pseudo-Riemannian geometry that underlies relativity, so there's quite a lot wrong with it. Nevertheless, it hopefully conveys a sense of what I'm getting at.
 

Ibix

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Not to confuse things but if we have our spaceship going at a good percentage of C then it is experiencing a different rate of time because it is moving through space-time?
As I asked before, what is it travelling at high speed with respect to?

Actually, the underlying mechanism is the same - two clocks in relative motion are following different paths through spacetime, and those paths have different "lengths". However, in the case of motion (far from a gravitational field, just to keep things simple) the reason is closely analogous to why the hypotenuse of a right angled triangle doesn't have the same length as the other sides of the triangle. Loosely speaking, the worldline of one clock is one side of the triangle, the worldline of the other clock is the hypotenuse, and the distance it travelled through space according to the first clock is the third side.
 
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"As I asked before, what is it travelling at high speed with respect to? "

Just to step aside for a second, if my two space ships traveling at nearly C relative to their homeworld decide to say that ship one is just a 1/4 mph faster than its partner so it should be able to accelerate away from its partner very fast because the speed between the two is nowhere near C. Now if you say, wait, it is relative to where it left together and I point out that homeworld was traveling through space relative to something else at nearly C and our two ships cannot be going anywhere C relative to homeworld which is already too speedy. Sorry for the detour but I do not understand your reference to speed respect to.
 

Ibix

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I do not understand your reference to speed respect to
There's no absolute speed. When you say you are travelling at 30mph, you mean 30mph with respect to the surface of the Earth (which is to say, as measured by someone for whom the Earth's surface is stationary). But you are also doing up to 1000mph relative to a point at the north pole as the Earth turns, and roughly 20km/s relative to the Sun as the Earth orbits it. All of these speeds are correct - but all are meaningless unless I tell you what I'm regarding as "at rest".

That's why you need to specify what you are considering to be "at rest" when you tell me how fast something is going.
if my two space ships traveling at nearly C relative to their homeworld decide to say that ship one is just a 1/4 mph faster than its partner so it should be able to accelerate away from its partner very fast because the speed between the two is nowhere near C. Now if you say, wait, it is relative to where it left together and I point out that homeworld was traveling through space relative to something else at nearly C and our two ships cannot be going anywhere C relative to homeworld which is already too speedy.
Speeds don't add. If I'm doing a speed ##u## in one direction and you are doing ##v## in the opposite direction, you will say that my speed is $$u'=\frac{u+v}{1+uv/c^2}$$If ##u## and ##v## are very small compared to lightspeed then ##uv/c^2## is very nearly zero and ##u'## is very nearly the sum of our speeds, which is why you can add every day speeds - the error from neglecting the ##uv/c^2## for car speeds (even supersonic jet speeds) is smaller than neglecting the effect of bugs splattering on the front of your car by several orders of magnitude. But as you go faster and approach the speed of light, you can no longer neglect that term. Its effect is such that ##u'## is always less than ##c##, regardless of ##u## and ##v##. For example, if your ship is doing 0.99c relative to your homeworld and your homeworld is doing 0.99c relative to me, then your ship is doing (0.99+0.99)/(1+0.99*0.99)=0.99995c relative to me.
 
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Does anyone know what causes the rate of time to change in either case?
I would say it is the metric. It “changes” for the same reason that the hypotenuse of a triangle is longer than one of the legs. That is a function of the metric.
 
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I just finished my nap, you do those at my age. Now, saying it changes because it does, well, not useful if you want to create a test of the "how." Yes, I know, a lot of things are not yet known, but there must be some speculation. It would seem the fabric, vacuum of space, how this could interact on the very small scale of the things that make "matter" might explain something. And I am interested in thinking about such speculation but I know I lack the science to even do that, but some people must have.
 

Ibix

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Now, saying it changes because it does, well, not useful
I don't think @Dale is saying that it changes because it does. I think he's saying that time is a consequence of the metric - so the "rate of time" measured by a clock changes in different circumstances because of the structure of the metric. The metric is the mathematical object that leads to the notions of distance and elapsed time - in a sense, it's the mathematical formalisation of the stack-of-paper model I was talking about earlier.

Actually, that's all GR says about this - Einstein's equations simply let you define a metric that is consistent with the mass and energy that's in play, and to work out their future dynamics. If you want a more fundamental understanding, you need to study our theories of quantum gravity. Unfortunately, we don't yet know which (if any) of them is correct. You're running up against the limits of what we know here.
 
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Yes, I know, a lot of things are not yet known, but there must be some speculation.
I don’t think this is in the unknown category. The metric is determined by the distribution of energy, momentum, pressure, and stress.
 

Janus

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I just finished my nap, you do those at my age. Now, saying it changes because it does, well, not useful if you want to create a test of the "how." Yes, I know, a lot of things are not yet known, but there must be some speculation. It would seem the fabric, vacuum of space, how this could interact on the very small scale of the things that make "matter" might explain something. And I am interested in thinking about such speculation but I know I lack the science to even do that, but some people must have.
Try thinking of it this way:
You and someone else are standing next to each other on a flat featureless plane. You start walking North at a fixed pace, and your companion starts walking Northeast at the same pace.
It is obvious that your companion is not traveling North at the same rate as you are. He is dividing up his motion between Northward and Eastward movement.

Now swap "moving North" with "moving through time" and "moving East" with "moving in space"

Now with this view, you are moving forward through time at a fixed rate, but not moving in space. You are "at rest". Your companion is also moving through time, but also is moving through space. But he still has to "divide up" his over all "motion" between these two. Thus he doesn't move through time as fast as you do.

This is basically the idea behind time dilation due to motion. Space and time have been combined into a single idea of Space-time that are no longer independent of each other.

However, there is an additional rub. With the above example, both parties involved agree as to who is progressing "North" or through "time" at the greater rate.

But there is no equivalent to North-South or East-West in space-time. Only the equivalents of forward-back and Left-Right.

So in our examples above, each of you judges that the direction you are walking in as being "forward", and that the other person is making slower progress in the "forward" direction than you are.

If forward movement is the space-time equivalent of moving through time, and left-right as space, then each of you judge yourself as moving through time, but not space and the other as moving through both time and space. Each considers himself as being at "rest". It also means that each of you judges the other as moving more slowly through time ( aging slower).

The gist of it is that the relationship between time and space is more complicated than it is assumed to be in Newtonian physics, and everyone measures their movement through it according to their own reference, as there is no fixed "direction" to time or space.
 
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Relative... OK, it is the end of time, everything has gone over the horizon and all matter has evaporated. It is just me and my spaceship. I start accelerating in any direction, but with nothing left in the universe, there is nothing to be relative to. I am accelerating so I know I am going faster, time slows for me, what happens, do I reach the ultimate speed limit, but that is relative to something and there is nothing in the universe to be relative to. Is it just time that is the limit, if I go so fast time stops incrementing and I can not go faster because the clock has stopped?
 

Ibix

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I am accelerating so I know I am going faster
Faster than what? You've nothing to judge it by. And there's no way to tell (without something to define as stationary) whether you're accelerating or decelerating.
time slows for me
No it doesn't - your clock continues to tick at one second per second.
do I reach the ultimate speed limit, but that is relative to something and there is nothing in the universe to be relative to
If there's nothing to measure your speed relative to, you can't really define your speed.
Is it just time that is the limit, if I go so fast time stops incrementing and I can not go faster because the clock has stopped?
No. Your clock always ticks at one second per second. Other people - who you've specifically excluded from this scenario - might regard your clock as ticking slowly, but you would also regard their clock as ticking slowly. That may seem paradoxical but it isn't - not any more than Janus' example where both people regard the other as advancing more slowly because they disagree about forwards. In this case, you disagree about which direction in spacetime is "time".

As you go faster relative to me, I regard your clock as ticking more slowly. But nothing happens to your clock from your perspective, because you can always regard yourself as stationary and that will always be the natural choice of perspective for you. There is no absolute speed.
 
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Try thinking of it this way:

I can do that, as I read I comprehend the words and their meaning and the image it causes in my mind. There is a "but", if I look at (stay with me) a very tasty cake and then I read through the recipe, all the necessary steps, a careful list of ingredients (with no background how they came into existence) of the proper measure, how to mix, the pans to use, temp and bake times. Perhaps a frosting and all the rules for that. Finish the cake, put it on the table. Look at it. None of the recipes is apparent, It just is.

What I want is the recipe for time, all the little things that must be just so for it to work as it works. I know I could put the bits of the cake in a mass spectrometer, I was a developer for one (2001 to 2015) but that would only tell me what was there, not how it got constructed. We are learning to make clocks that are much smaller and more accurate than ever so we should be able to design some tests to learn the secrets of time. I am getting old, science needs to do better.
 

Ibix

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What I want is the recipe for time
In GR, it falls out of the metric. Future theories may say other things, but as noted above, we don't know which, if any, of our current candidates is the correct one.
I am getting old, science needs to do better.
I'm afraid we can't make these things run to your personal timetable. Discoveries will happen when they happen.
 
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It is just me and my spaceship. I start accelerating in any direction, but with nothing left in the universe, there is nothing to be relative to.
You would be accelerating relative to your rocket’s exhaust and your rocket+exhaust center of mass.

time slows for me,
Time never slows for you in your own reference frame. It only slows for you in someone else’s frame.

What I want is the recipe for time
Again, that is the metric. Or maybe the Einstein field equations which tell you how to determine the metric from the energy, momentum, pressure, and stress distribution

Edit: Having thought about it a bit, in your analogy I think the cake is the metric and the recipe is the EFE
 
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Janus

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Relative... OK, it is the end of time, everything has gone over the horizon and all matter has evaporated. It is just me and my spaceship. I start accelerating in any direction, but with nothing left in the universe, there is nothing to be relative to. I am accelerating so I know I am going faster, time slows for me, what happens, do I reach the ultimate speed limit, but that is relative to something and there is nothing in the universe to be relative to. Is it just time that is the limit, if I go so fast time stops incrementing and I can not go faster because the clock has stopped?
Imagine you are carrying an endless supply of clocks. as you accelerate your drop clocks overboard (carefully so you don't give them any extra velocity. Yo want them to have the same velocity as the ship at the moment of release.
Since you are accelerating, each clock will fall "behind you" . Now remember that addition of velocities equation from post #14? You'll need to apply it here. So let's say that you drop off clock 1 and then continue to accelerate until you are moving at 0.1c relative to clock 1. You now drop of clock 2 and then continue accelerating until you are moving at 0.1c relative to clock 2. How fast are you moving relative to clock 1?
Not 0.2c, but just 0.198c. Even though you measure your speed relative to clock 1 as being 0.1c and Clocks 1 and 2 measure their speeds realtive to each other as being 0.1c, you measure your relative speed with respect to clock 1 as being less than 0.1c+0.1c.
If you now drop clock 3 and accelerate to 0.1c relative to it, you'll measure your speed as being 0.296 c relative to clock 1. Nothing will ever stop you from accelerating to 0.1c relative to the last clock you dropped, but no matter how many clocks you drop, you will never measure your speed relative to clock 1 as being other than less than c.

Nothing effects your time rate (as measured by you), but if you measure the rate of the clocks you leave behind, they will run slow compared to your own. The further behind, the slower they run. (It's a bit more complicated if you consider yourself under constant acceleration as you make the measurements. So for simplicity's sake we will assume that you cut your engine just before you drop off each clock and make your measurements, and then fire it up again)

On the other hand, an observer left with clock 1 would note that your rate of acceleration decreases with time as you drop off the clocks. So for example, while for you, upon dropping off clock three, you will have measured yourself as having accelerated to 0.1c relative to Clock 1, while the difference between clocks 1 and 2 has deceased to 0.096c, The observer with clock 1 would say that the relative velocity between himself and clock 2 is and always has been 0.1c, and you have only accelerated by 0.096c between dropping off clocks 2 and 3. he would also say that your clock runs slower and slower as you accelerate.

The point is that both viewpoints are equally valid and you can't choose one over the other as being the "correct" one.
 

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