# Time dilation question

## Main Question or Discussion Point

Ok, I'm uneducated in physics and all I know is what I've learned from the internet and a single book "universe in a nutshell" by hawking.
I am hoping someone here can shed some light on my apparent misunderstanding of time dilation.

As far as I know time dilation is an effect of light frequencies, and works in two ways, one due to gravity differences, and one due to speed differences. Relatively, time goes slower when closer to a strong gravitational field, and faster when further from a strong gravitational field.
Also, time goes slower at faster (relative) speeds.

As an object accelerates, time for it will slow down, when compared to a relatively slower moving observer.
As an object approaches a strong gravitational field, its time will slow in comparison to an observer who is further from the gravitational field.

Is this correct so far?

Related Special and General Relativity News on Phys.org
More or less, but beware that it's not an effect for light frequencies. It's really the time on your (any) watch, real time related to aging you're talking about. Actually light is one of the few things that does not experience time, as it is moving with the speed of...light.

You are partly right, mikesvenson

To define time dilation, the phenomenon where the observer finds that the other clock among the two identical clocks, physically identical that is, is running relatively slower.

This is most of the time taken to mean that time has slowed down , but this is true, only from the point of view of the observer,that is, the observer's frame of reference.

But, you have taken time dilation with reference to the potentials of gravitational fields. You are in no way wrong. But you have explained time dilation with reference to the general theory of relativity. Your answer would be complete, only if you explain time dilation in accordance with the special theory of relativity as their difference is not small.

According to the special theory of relativity, clocks that are moving with uniform velocity with reference to the stars, that is which are not accelerating without the application of a physical force are observed to be running slower .

This is time dilation.

The difference which I mentioned is that:-

In the special theory of relativity , time dilation is observed only by the other person, that is , it will not be observed by the person who is in the same frame of reference as the clock.Of course, one of the clocks must be in motion with respect to the other.

But, in the time dilation, according to the general theory of relativity, gravitational time dilation, that is, time dilation will be accepted to be uniform by all observers.

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tiny-tim
Homework Helper
… Is this correct so far?
Hi mikesvenson!

Yes, that's a rather good summary of the effect of time dilation on clocks.

The only thing that's wrong is "time dilation is an effect of light frequencies" … no, it affects lots of things, including light frequencies, but it isn't a light effect.

It's Doppler shift (red-shift and blue-shift) that is an effect of light frequencies.

Light going away from us will be red-shifted by the Doppler shift, and also by "special relativity" (velocity-dependent) time dilation.

Light coming towards us will be blue-shifted by the Doppler shift, and red-shifted by "special relativity" time dilation; and if it is coming out of a gravitational field, it will also be be red-shifted by "general relativity" (velocity-independent) time dilation.

Regarding....

light is one of the few things that does not experience time, as it is moving with the speed of...light.

The way I've understood it is that light, if you imagine it in the form of waves, compresses and expands to accommodate the structure of space-time as gravitational fields shape it. Looking down at Earth from space, an observer would witness activities on Earth taking longer than usual. This would be the effect of the light waves decompressing as they travel towards you, as they travel into a gravitationally less dense region of space. The waves, although passing you at the same velocity as usual, are more spread out and therefore so is the information contained in it.
These waves are consequentially traveling at the speed of light; thus accelerating towards that speed while following a particular path of light, your time will slow down as the waves pass you slower and slower.
Is this a big misunderstanding?

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Looking down at Earth from space, an observer would witness activities on Earth taking longer than usual. This would be the effect of the light waves decompressing as they travel towards you, as they travel into a gravitationally less dense region of space.
I have the impression you mix up tow concepts: 1- time dilation and 2- red/blue-shift of light

Your space observation takes place independent of the fact you're observing it with light waves and as such it is not an effect due to the 'decompression'of the waves as you call it. What does happen at the same time is that the frequency of the light waves travelling toward you is shifted. You can better think of this as an energy phenomena, where energy is needed to leave the gravitational field of the earth so the waves become less energetic, i.e. redshifted (lower frequency).

So "redshifted (lower frequency)" means the light shifted to a lower frequency as a result of moving away from the Earth and towards the observer? And if it was moving towards the Earth from the observer, it would be recieved on Earth as a blue-shifted light frequency? Is this due to Earth's gravity alone?

Is this due to Earth's gravity alone?
Yes, although you can have the same effect when you move wrt the source of the light. This is the light-analogue of the normal Doppler effect.

Does any of this have an effect on the aging process of tall objects like the tops of traffic lights or the tops of buildings? I mean, if time is going faster near the edge of the atmosphere than at ground level, does that mean objects far up are aging faster than objects on the surface?

tiny-tim
Homework Helper
Great experiment!

ok now lets say that there is a very tall pole, mountain, or skyscraper. A clock at the bottom and a clock at the top. Lets say that after so many years the clock at the bottom has run slower than the clock at the top.

Ok, now due to the constant movement/rotation/ of the Earth, does this mean that after said amount of time the top of the object has reached a relative future when compared to the bottom? Has the top actually reached 4:00pm sooner than the bottom? Due to the rotation of the Earth, wouldnt an observer at the bottom while reading 3:00 on his watch, and seeing 4:00 at the top watch, wouldnt the bottom observer notice that the the top has reached the future before the bottom? Wouldnt this be percieved as a gradual lean of the object towards the direction of the rotation of the Earth? If not, then why?

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tiny-tim
Homework Helper
Ok, now due to the constant movement/rotation/ of the Earth …

Wouldnt this be percieved as a gradual lean …
This effect would happen even if the Earth wasn't rotating.

There's the gravitational (velocity-independent) effect, and the special-relativity (velocity-dependent) effect.

The first one makes the lower clock slower than the upper clock, and the second one makes it faster.

I can't remember which effect is bigger.

They only affects the rate at which things happen (like the ticks of a clock) … they has no effect on space, so nothing will either lean or even appear to lean.

lets take the tall object and put it upright in the back of a pickup truck and drive it in one direction for a long time----are you saying the when the truck reaches the end of the road, more time will have gone by for the top of the object than the bottom, even though the top and the bottom both reached the end of the road at the same time?

I was at first under the impression that in such a case, the top of the object would reach the end of the road before the bottom, since time at the top would be going faster than at the bottom, the top's trajectory would lead it from point A to point B before the bottom, and then the bottom would simply catch up to the top. This is what I have always thought, and conclusively there would have to be another mechanism that causes the object to always appear to be straight up and down in any frame of reference, or at any point in which the observer is located.

How does this sound? Could this make sense?

tiny-tim
Homework Helper
Hi mikesvenson!
lets take the tall object and put it upright in the back of a pickup truck and drive it in one direction for a long time----are you saying the when the truck reaches the end of the road, more time will have gone by for the top of the object than the bottom, even though the top and the bottom both reached the end of the road at the same time?
Yes
… I was at first under the impression that in such a case, the top of the object would reach the end of the road before the bottom, since time at the top would be going faster than at the bottom, the top's trajectory would lead it from point A to point B before the bottom, and then the bottom would simply catch up to the top. …
No … from everyone's point of view, the top and bottom reach the end of the road at the same time.

An observer on the ground will say that special relativity time dilation is making both the bottom clock and the top clock go slower than his own clock, and additionally that general relativity (gravitational) time dilation is making the top clock go faster.

But this only affects the rate of the clocks, not where the clocks are.

btw, even if the truck was stationary, time dilation would still affect the top clock, but it still would't lean over!

Does any of this have an effect on the aging process of tall objects like the tops of traffic lights or the tops of buildings? I mean, if time is going faster near the edge of the atmosphere than at ground level, does that mean objects far up are aging faster than objects on the surface?
Yes. If you had a twin and he remained on the surface of the Earth while you hovered far out in space he would be ageing less rapidly than you and you could see the difference if he eventually came up and joined you. The gravitational time dilation is a real effect and not just a change in the frequency of light.

This effect would happen even if the Earth wasn't rotating.

There's the gravitational (velocity-independent) effect, and the special-relativity (velocity-dependent) effect.

The first one makes the lower clock slower than the upper clock, and the second one makes it faster.

I can't remember which effect is bigger.....
This hyperphysics link on the Hafele-Keating experiment makes the magnitudes of the effects clearer: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html#c3

The gravitational effect due to the altitude of the flying clocks compared to the ground clock made the high clocks tick faster adding between 144 to 179 nano seconds to the total elapsed time of the flying clocks. The kinematical effect due to the velocity of the aircraft made the East bound clock tick slower than the ground clock (reducing the elapsed time for that clock by 184 ns giving a net reduction to the total time recorded by that clock) because it effectively had the velocity of the Earth's rotation plus the aircraft speed. The kinematic effect on the West bound clock made it tick faster than the ground clock adding a further 96 ns to its elapsed time because its effective velocity was less than the rotation speed of the Earth due to the aircraft flying in the opposite direction so that the West bound clock gained a total 275 ns compared to the ground clock. In other words the West bound clock was ticking faster both because of the higher altitude and slower velocity of that clock compared to the ground clock. (The velocity of the ground clock is the rotation speed of the Earth.)

tiny-tim
Homework Helper
Hi kev!

But if the aeroplane was hovering, so that it stayed above the same place on the ground, it would still be moving relative to the ground by πh.sin(latitude)/12 per hour, where h is the height … so how much would that Lorentz dilation be compared with the gravitational one?

Hi kev!

But if the aeroplane was hovering, so that it stayed above the same place on the ground, it would still be moving relative to the ground by πh.sin(latitude)/12 per hour, where h is the height … so how much would that Lorentz dilation be compared with the gravitational one?
Hi Tim :)

By a rough calculation assuming a radius of 6378 km at the equator, and a velocity of 1,600 kph at the surface (due to the rotation of the Earth) and a height of 10 km above the surface, the velocity of the hovering aircraft would be about 1602 kph due the increased radius. That additional 2 kph would make an almost negligable difference when you consider that an aircraft moving at 560 kph in the Westward direction adds only 96 ns to the total time. On a pro rata basis the kinematic time dilation would add less than a nanosecond to the elapsed time of the high hovering clock while the gravitational time dilation due to its altitude would add about 170 ns to the high clock when 48 hours has passed on the ground clock. The hyperphysics link shows some interesting ways to get aproximate results for low velocities and altitudes using binomial expansion that would probably be beyond the accuracy of a typical PC using the exact equations.

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They only affects the rate at which things happen (like the ticks of a clock) … they has no effect on space, so nothing will either lean or even appear to lean.
Why not? I think they do lean. But I know that they never appear to lean. The future of the object should be towards the projected path of motion. Motion in the atoms causing aging, motion in the clock ticking, and last but not least, the motion of its projected path. Therefore it should definitely be leaning. Although it appears not to lean,(can you explain this paradox for me?) Are you saying the time is something more than motion?

-sorry, forgive me if I sound like I'm on crack....but..."They only affects the rate at which things happen"--it just so happens to be moving at a rate in the direction of the rotation of the Earth, just like it also happens to have arms that move in a circular motion. Surely we should be seeing all of these time related motions being effected, unless we simply can't see it.

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tiny-tim
Homework Helper
Why not? I think they do lean. But I know that they never appear to lean. …
Surely we should be seeing …
Hi mikesvenson!

Imagine that we can see the electrons moving in tiny circles.

Then what do we see?

We see the electrons at the top go round the tiny circles more often than the electrons at the bottom.

But we see the centres of the circles go at the same speed. So there is no leaning.

That makes sense, but I'm still not so sure how that explains the absence of leaning. The dilation is effecting the rate of the electrons motion as you described, but what about the motion of the clock in general in regards to its projected path? Am I correct with assuming the solution lies in the idea that the dilation affects motion within a position, but not the position of the motion?

I'm sorry for being so confused, but it just seems to me that if the clock hands take a shorter time to get from A to B while the clock is moving through space, then it should consequentially take a shorter time for the clock itself to move from A to B. This would cause an observer in stronger gravity to witness the clock moving faster in ALL respects.

If the clock is floating up in space, and takes 1 min to get from A to B in respect to the clocks reference frame, then in the bottom observers reference frame, the clock should (by his watch) take shorter than a min to get from A to B. Right?

In the case the clock is very tall and resting on the ground and reaching far into the sky: The top of the clock would reach B before the bottom observers watch reads 1 min. How does this not cause a percieved lean?

tiny-tim
Homework Helper
… it just seems to me that if the clock hands take a shorter time to get from A to B while the clock is moving through space, then it should consequentially take a shorter time for the clock itself to move from A to B.
Hi mikesvenson!

No … the hand moves from A to A (in a circle round the centre, O)!

O isn't rotating … it's just a point … it goes at the same speed as the bottom of the tall object.

So the hand moves from A to A faster, but it does it round O, which isn't moving faster.

That's all!

So does that mean that the time dilation isn't affecting time, but is just affecting the oscillation of the matter's particles? Thus causing quicker decay but not defining "time" as a pliable medium?

tiny-tim
Homework Helper
So does that mean that the time dilation isn't affecting time …
No … time dilation does affect time

… it doesn't affect position!

The particles at the top stay level with those at the bottom … they just oscillate differently.

mikesvenson, you are trying to dissect time into all the possible "motions" by which we mark it
in order to find where the dilation breaks down since, as you say, both clocks reach the end of
the road at the same "time".
The effect that justifies the difference in time you are looking for is not a "lean"
due to a faster clock but a measure of speed (distance/time).
The observer at the top of the truck will say the speed of the truck is less (more seconds per mile)
according to their clock than the observer at the bottom of the truck.
This does not mean the top of the truck is moving slower than the bottom, it means that by
any and all means we have of marking time, we will mark more at the top of the truck than the bottom.
If at the halfway point of their trip the two observers exchange clocks, the clocks will
change to mark time according to their new position, the top clock running faster.
The truck does not lean, the top does not move slower, both clocks arrive with the truck at the
end of their trip at the same time, but .... which time is right? Both.
If an observer at the end of their trip was standing waiting for them with a stop watch running
since they began, they could agree with either clock on the truck depending on how high they
held their stopwatch during the whole trip.