# Correct definition of time dilation

1. Nov 9, 2013

### suryanarayan

Can someone give me the correct definition of time dilation(or explain it in such a way that it can be used to tackle any problem)??

What i believe now is

"a moving clock ticks more slowly than a clock at rest"..but according to me this is inadequate because there can be two situations from this definition..
1) two observers look at the same clock ,one observer is at rest with respect to clock while the other is in relative motion..here the time as measured by the moving observer will be dilated.

2)a single observer looks at two clocks ,one with him and other moving relative to him...here time shown by the moving clock is dilated according to the observer or is it??

thanks

2. Nov 9, 2013

### Mentz114

Time dilation is not a directly observable physical effect. It comes about when the change of coordinates is made between inertially moving frames. What is actually observed is that an approaching clock appears to run faster and a receding clock appears to run more slowly, like the relativistic Doppler effect.

I forgot to answer your question. You have got it right. A clock that is moving inertially wrt another observer will be dilated.

Last edited: Nov 9, 2013
3. Nov 9, 2013

### ghwellsjr

The reason why you are getting so confused, I believe, is that you are defining Time Dilation in terms of two clocks. The easiest definition I know is to take the ratio of a Coordinate Time interval to the Proper Time interval on each single clock that is inertial over the interval. And you need to use coordinates according to an Inertial Reference Frame (IRF). This always works for any IRF in Special Relativity.

Thus, when you have multiple clocks, they all have a definition that is independent of all the other clocks. The Time Dilation ratio is identical to gamma which is a function of the speed of each clock according to the IRF. You can use the Lorentz Transformation process to convert all the coordinates in one IRF to the coordinates in another IRF moving inertially with respect to the first one, and all the clocks can have a different speed and thus a different Time Dilation.

I have made many spacetime diagrams to illustrate Time Dilation. Do a search on "dilation" with my name and you'll find some.

And as Mentz114 said, it's not a directly observable physical effect. How could it be? Just transforming to another IRF changes all the Time Dilation factors. Of course, it is an indirectly calculable effect, and you can see in some of my other posts how that is done.

So if you want to see what an observer would calculate the Time Dilation of a moving clock to be, just transform to the IRF in which the second clock is at rest, and the Lorentz Transformation will show you the correct Time Dilation.

4. Nov 9, 2013

### dauto

The question isn't clear to me. I don't see what's the difference between the two setups. In both situations you have two observers each one with its own clock (otherwise how would they measure time?), and each one sees the other clock tick more slowly than their own. What's the question again?

5. Nov 9, 2013

### Bararontok

Time is relative because of gravitational time dilation and relative velocity time dilation. Gravitational time dilation is caused by gravitational force slowing down physical phenomena because of its interaction with all matter and forces, with the speed of the passage of time inversely proportional to the strength of the gravitational field. Relative velocity time dilation is caused by the amount of time it takes for information to travel from one point to another because all forms of information must be carried by various types of signals which have to be mediated by physical entities such as space-time and photons which are limited by the invariant (assuming a vacuum) speed of light.

Sources:

http://en.wikipedia.org/wiki/Gravitational_time_dilation
http://en.wikipedia.org/wiki/Time_Dilation#Time_dilation_due_to_relative_velocity

http://imageshack.us/a/img707/4162/rbfd.png [Broken]

http://imageshack.us/a/img822/4218/4gu6.png [Broken]

Last edited by a moderator: May 6, 2017
6. Nov 9, 2013

### Staff: Mentor

This is simply not true. You can send information by light signals, but you can also send information by sound or even by FedEx. Using a different method of information does not cause a change in the time dilation.

Time dilation is not because c is finite, it is due to the invariance of c. The speed of a sound wave is not invariant, nor is the speed of FedEx. So even if your information is limited to those speeds, it does not cause time dilation.

7. Nov 10, 2013

### Bararontok

Yes, the statement I have made may be too general. Would it be more appropriate to say that the time dilation due to relative velocity occurs because the speed of the information sent by the fastest methods: the mass-less gauge bosons and space-time are limited by their invariant speeds (assuming a vacuum).

But I think the proper term for the delay in receiving information because of the finite variant or invariant speeds of signals is called 'Propagation Delay'.

Source:

http://en.wikipedia.org/wiki/Propagation_delay#Physics

Another appropriate term for this limit in the speed of propagation of information is called 'Latency'.

Source:

http://en.wikipedia.org/wiki/Latency_(engineering)

****

The relative velocity time dilation occurs because an object traveling faster in reference to another object will have a slower passage of time than the slower or stationary object. Could this be because when an object is accelerated to a high speed, especially relativistic speeds, it exerts increased gravitational force and this dilates time?

Last edited: Nov 10, 2013
8. Nov 10, 2013

### Staff: Mentor

No, because an object that is traveling at relativistic speeds relative to one observer may be traveling very slowly or even be completely at rest relative to another observer. Consider that right now you are moving at 99.99999% of the speed of light relative to some observer in some distant galaxy - but you can't expect that that causes you to "exert increased gravitational force", or that if that distant observer changed his speed relative to you something would somehow change for you.

9. Nov 10, 2013

### Bararontok

So does this mean that the relative velocity time dilation is caused by the invariant speed of c causing the information traveling between two objects whether in motion with respect to a reference frame or not to be distorted and cause the effects of motion or a running clock to appear to be faster or slower than its actual rate?

10. Nov 10, 2013

### Staff: Mentor

Nothing "causes" time dilation, just as nothing causes gravity to be an inverse-square force instead of (for example) an inverse-cube force - it's just the way the universe is.

In the case of time dilation, we start with the observed fact ("that's the way the universe is") that the speed of light is the same for all observers regardless of their relative motion. A page or so of algebra shows that the Lorentz transforms are a consequence of that fact; and time dilation follows from that.
(This is pretty much what DaleSpam said above when he said that "Time dilation...is due to the invariance of c")

11. Nov 10, 2013

### Bararontok

Alright, the speed of light is the same for all objects regardless of their relative motion, because c is an invariant fundamental constant (assuming a vacuum) of the universe just like the fine structure constant and the gravitational constant and this invariant speed limit in the transmission of signals from objects in relative motion or stationary objects is what causes relative velocity time dilation.

Additionally, I think what can sometimes cause confusion is the difference between finite and invariant. To clear up the confusion, finite means that there is an upper and lower bound giving a specific range of values while invariant means that there is only a single constant value.

Last edited: Nov 10, 2013
12. Nov 10, 2013

### Staff: Mentor

No. If you had a relativistic tachyon communication device you would violate causality, but you would still have time dilation.

It is not a matter of terminology. The concept is incorrect. Time dilation is not a result of the fact that it takes time for information to travel. It is simply a result of the fact that c is invariant.

13. Nov 10, 2013

### dauto

Yes, time dilation has nothing to do with signal transmission. It is a geometric effect due to the shape of spacetime. And your explanation for gravitational time dilation is also wrong. There as well time dilation is an effect due to the geometry of space time.

14. Nov 10, 2013

### Staff: Mentor

I think that the most general definition of time dilation is that it is the ratio of coordinate time dt to proper time dτ. If you think of it that way then you can easily derive the two most famous time dilation formulas:

Starting from the Minkowski metric
$d\tau^2 = dt^2 - dx^2/c^2 -dy^2/c^2 - dz^2/c^2$
$d\tau^2/dt^2 = 1 - v^2/c^2$
$dt/d\tau=1/\sqrt{1-v^2/c^2}$

Starting from the Schwarzschild metric
$d\tau^2 = (1-R/r)dt^2 - (1-R/r)^{-1} dr^2/c^2 - r^2 d\Omega^2/c^2$
for a clock at rest $dr=0$ and $d\Omega=0$ so
$d\tau^2/dt^2 = 1-R/r$
$dt/d\tau = 1/\sqrt{1-R/r}$

15. Nov 10, 2013

### Bararontok

Well, this is true because space-time is a physical entity in itself so, as I mentioned in the passage of gravitational time dilation, it interacts with all matter and forces. Does this mean that, assuming there is only one object in motion, its time would still slow down as it accelerates to relativistic speeds because its interaction with space-time would grow stronger and stronger with space-time forcing the time in the object to run slower and slower?

16. Nov 10, 2013

### Staff: Mentor

No, and you're still stuck on a basic misconception. Time dilation (and length contraction, and other interesting relativistic effects) are not things that happen to a moving object and that would stop happening if the object stopped moving. That is, they have nothing to do with the motion or non-motion of the object.

It has to be that way when you consider that right now you're moving at .9c relative to some observer somewhere in the universe, .5c relative to some other observer, and you're at rest relative to me. The three of us will each find your time dilated differently, so whatever is happening, it's not caused by your motion through space-time but is a property of how our relative motions are related.

A more stark example: I am rest while you're moving past me. I find that your clocks are running slow relative to mine, so we say that your time is dilated. But as far you are concerned, you are at rest while I am moving past you in the other direction - and you will find that my clocks are running slow relative to yours and we will say that my time is dilated. And we're both right. There's no way you can explain that by saying that the moving one is interacting with space-time differently than the non-moving one because we get the same result no matter which one we consider to be the moving one.

17. Nov 10, 2013

### Bararontok

So this means that the mere existence of space-time and the invariance of c is enough to cause these phenomena because all objects are interacting with space-time at all times and because of the limit of c which is (in a vacuum) always invariant and always applies to all situations. And it is because these physical laws are always in effect that time dilation occurs rather than happening because of specific conditions, it is just that the effects of time dilation are negligible in weak gravitational fields and non-relativistic speeds.

18. Nov 10, 2013

### dauto

Yes, time dilation is a very general effect. I just don't like when you say "because all objects are interacting with space-time at all times". The word interact seems misleading to me. Suppose there were two different routes from your home to your work and that one route is longer than the other. Would it make sense to you if I said that one path is longer than the other because of the way it interacts with space? It seems that saying that the geometry of the paths is different causing one to be larger (dilated) than the other would make more sense. Time dilation is analogous to that.

19. Nov 10, 2013

### Staff: Mentor

That's better, but you still have to let go of this notion of objects interacting with space-time... It will tempt you into thinking that objects can be at rest or moving more or less quickly against the background of space-time. They aren't; all notions of speed, time dilation, clocks running faster or slower, are relative to other bodies, not space-time.

If you really want to understand this stuff, there's no substitute for starting with Einstein's two postulates, working from them to the Lorentz transforms (no sophisticated math required, just high school algebra and a willingness to let go of preconceptions from a lifetime of non-relativistic speeds and weak gravitational fields), and practicing how to correctly apply the transforms.

Last edited: Nov 10, 2013
20. Nov 10, 2013

### Bararontok

Of course because there will always have to be a frame of reference to do a comparison. So the correct statement would be: the passage of time relative between moving objects is dilated because of space-time and the invariance of c but this time dilation occurs relative to other objects and not to space-time itself. It can then be said that relativistic time dilation is caused by the time taking place in the movement of objects relative to each other to be dilated by the geometry of spacetime and the invariance of c. Because these laws cannot be violated, these 2 physical phenomena forcibly dilate time.

Last edited: Nov 11, 2013
21. Nov 11, 2013

### TheBC

???
This is wrong.
In SR any clock moving (leaving of approaching) relative to an observer ticks slower.
You probably errouneously think SR is about an optical illusion...? That's why you probably write the clock appears to run etc.
Clocks do not 'appear' to run slow. They do run slow in your 3D frame/world of simultaneous events.
Any spacetime diagram shows this at first sight.

 Mea culpa. you were correct. You stated what is actually, litterally, observed, seen.... In that case you are correct.

22. Nov 11, 2013

### Naty1

There are some excellent hints already posted. But if you have not carefully considered time dilation before, it is easy to miss them:

Mentz:
ghwells:
Dalespam:
Nugatory: