# What is the cause of time dilation in Special Relativity?

Tags:
1. Jul 9, 2015

### giulio_hep

One of the basic foundation of special relativity is that the speed of light is a constant, hence time is relative to the inertial framework reference. Usually GPS is also mentioned as a modern experimental evidence. My questions: if Maxwell's equations describe EM fields, how can we derive a more general notion of time (*)? It is said that lenght's contraction is measured by Einstein's convention between different points according to the reference framework and is not seen as "real" difference, how is time dilation interpreted in a more "paradoxical" (**) sense? Finally, in the experimental evidence (for instance the ticking of clocks on satellites) what is the mathematical tool used to separate the effect of acceleration/deceleration (***) from the mere inertial one?

[notes]
(*) with the term "more general" I mean the fact that (starting from an EM law, the constant light speed limit) we apply the spacetime diffeomorphism also to clocks not based on electromagnetic fields;
(**) I don't want to discuss the so called paradoxes, I'm simply focused on the fact, under Lorentzian signature, the spatial coordinates maintain a strict ordering while for the time coordinates only time-like events can be ordered, even though the invariant equations appear quite symmetric in space and time...
(***) my final question is the least important to me: maybe the clock postulate is already an answer, but I'm just wondering whether the effect of time dilation could be ascribed more to the past acceleration than to the current speed.

[meta-note]
Please, forgive me if my question seems too unclear or metaphysical... I would be happy to better clarify my doubts after your replies and I hope that can be considered enough to start a question or a dialog here.

EDIT

I have to better clarify an important point that was unclear in my question but is maybe the main point I'd like to ask. If you look at the first lecture of Susskind about Special Relativity at 1:16:30 he says: "notice that we are really talking about two really different things" and he is speaking about the end of a meter stick in a moving reference frame compared to a rest one... What I'm asking is: if you can explain the length contraction as due to different points in different reference frames, couldn't you do the same with time, saying that the time dilation is due to different instants in different reference frames?

Last edited: Jul 9, 2015
2. Jul 9, 2015

### harrylin

Hi giulio welcome to physicsforums!

So many questions in one...
Time is what always was used to describe the progress of physical processes. That notion has not changed; we compare physical processes with a process that we use as a reference, such as the day (which has been divided in hours, minutes, seconds). Only nowadays atomic clocks are used as they are more stable.
That is not correct: length contraction can in principle (in practice it's nearly impossible) be measured indirectly with a single clock, just by bouncing light from a mirror at the end. The synchronization convention makes the different measurement methods consistent.
Usually it is assumed that the effect of acceleration forces can be neglected. If that is not the case then this is corrected for separately. In experiments you can distinguish between the two.

Last edited: Jul 9, 2015
3. Jul 9, 2015

### Staff: Mentor

You will be best off if you go with Einstein's definition: "Time is what a clock measures". In this context a "clock" is any time-dependent process: Sand flowing through an hourglass, the progressive graying of my hair, the motion of the hands of an analog clock, the length of a burning candle, the amount of decay that has taken place in a sample of radioactive material or a chunk of meat, .....
That definition directly parallels our intuitive notion of distance: "Distance is a what a meter stick measures", and says that a clock is to time measurement as a meter stick is to distance measurement.

The asymmetry is not as great as you may be thinking. Two timelike-separated events must happen at different times although they may happen at the same place, while two spacelike-separated events must happen at different places although they may happen at the same time. That's looking pretty symmetrical to me. Could you be more precise about what you mean by the spatial coordinates "maintaining a strict ordering"

That's not answerable without a much more precise statement of what you mean by "the effects of time dilation".

4. Jul 9, 2015

### Staff: Mentor

There is nothing special about electromagnetism in special relativity. There is a universal speed scale, which is called "speed of light" for historical reasons only. Things without mass travel at this universal speed limit. Light is massless and easy to observe, so it is a well-known example, and historically it had a large impact on the development of relativity. It is not the only example - gravity shares that propagation speed (but that is hard to measure), so does the strong interaction (but we cannot observe its effect over larger distances).

5. Jul 9, 2015

### harrylin

PS: Looking at the title of this thread, it may be useful to clarify that time dilation is a function of of speed and not of acceleration. There is of course a connection: in order to achieve a different speed, a change of speed (and thus acceleration) is necessary. But a high acceleration can be achieved at not so high speed in an ultra centrifuge.

6. Jul 9, 2015

### giulio_hep

Thanks to you all! I have to better clarify an important point that was unclear in my question but is maybe the main point I'd like to ask. If you look at the first lecture of Susskind about Special Relativity at 1:16:30 he says: "notice that we are really talking about two really different things" and he is speaking about the ends of a meter stick in a moving reference frame compared to a rest one... What I'm asking is: if you can explain the length contraction as due to different points in different reference frames, couldn't you do the same with time, saying that the time dilation is due to different instants in different reference frames?

Last edited: Jul 9, 2015
7. Jul 9, 2015

### giulio_hep

Thanks! Sorry, isn't the constance of light said to be derived (because it is an invariant) from Maxwell E.M. equations? If I correctly understand, you are saying that this is only an historical reason. Very interesting! I would like to better understand: why the strong interaction or the gravity should share the same propagation limit? Is it a postulate? Thank you very much!

Last edited: Jul 9, 2015
8. Jul 9, 2015

### Staff: Mentor

We know, from the example of light, that there is at least one "same for all observers" speed in the universe.

We have mathematical proof that there can be only zero or one such speed. The easiest way to see this is to try assuming that there are more than one and then deriving coordinate transforms under that assumption - you will very quickly come up with a contradiction, so we know the assumption is false.

Therefore, we know that there is exactly one such speed. The speed of gravitational waves and the strong interaction, like light, are calculated from physical laws that don't change with speed so must be "same for all observers", so must move at the one and only such speed.

9. Jul 9, 2015

### giulio_hep

Ok, very clear, I mean that, whenever you take two different places in a reference frame, they will be different places also in any other reference frame: is there a mathematical property why this is not happening for two different instants of time even though proper time and proper distance appear to be pretty symmetrical concepts? If we take two different instants in a reference frame, they can be simultaneous (= the same instant, not different ones) in another reference frame when they are space like.

Last edited: Jul 9, 2015
10. Jul 9, 2015

### ZapperZ

Staff Emeritus
Please note also that there is a relativistically covariant form of Maxwell Equations. From reading your posts, I am unsure if you are even aware of that.

Zz.

11. Jul 9, 2015

### giulio_hep

Thank you! I think I am (to some extent). My questions are:
1) starting from the relativistic covariance of Maxwell's eqs, why we derive a time dilation also for atomic clocks not based on such equations (not on E.M. fields)? And I think Nugatory has already answered to this (at least I'm not able to reply, I could only be curious to know a reference of the mathematical proof)
2) my question above about the apparent asymmetric effect of Lorentz transformation on different places and instants... if it makes sense

12. Jul 9, 2015

### giulio_hep

I think I see the symmetry of time and space coordinates in Special Relativity now:
• two different time-events occurring in the same space-location are always different time-events for any reference frame just like two different space-locations at the same time are always two different space-locations in any reference frame.
• two different time-events in different locations can be the same time-event for a particular reference frame if they are space-like and - symmetrically - two locations that are different in one reference frame can be represented by the same location in another reference frame at different times.
Please correct me if my conclusion is wrong, otherwise thanks to you all for your support!

13. Jul 9, 2015

### pervect

Staff Emeritus
What makes you think atomic clocks are not basically governed by electromagnetic fields, and hence Maxwell's equations? If you want an example of a "clock' that involves the concept of time but doesn't involve electromagnetism, you've picked a poor example.

To anticipate a bit, after (or if) the issues are clarified enough so one knows what sort of clocks rely on electromagnetism and what sort of clocks do not, one can start examining the experimental evidence to see if there's any evidence that the idea of "clocks" keeping "time" makes sense as a universal notion that applies to all sorts of clocks.

I'm not sure what your question is, really. I'm guessing that you may not realize that there is no asymmetry in time dilation in special relativity. If I'm guessing correctly, then the thread "symmetrical time dilation implies the relativity of simultaneity" https://www.physicsforums.com/threa...on-implies-relativity-of-simultaneity.805210/ might help you understand that how time dilation IS symmetrical in special relativity.

14. Jul 9, 2015

### giulio_hep

Thank you!
Yes, in my first question, I was trying to find an example of clock that doesn't rely on electromagnetism (sorry if I chose a poor example) and I wanted to ask why (or if) we think that a universal notion of time applies to all sorts of clocks. Thanks for better redefining my question! Is the answer still yes (the notion of time is universal)?

And my second question (hopefully I answered it myself here) is: can I apply a similar concept of space-like/time-like to the spatial coordinates? In other words, the second question can be reduced to ask a confirmation of what I've written here.

Last edited: Jul 9, 2015
15. Jul 9, 2015

### Mentz114

What is a 'time-event' ? Your questions don't make sense.

An event is a spacetime point located by four values (t,x,y,z).

16. Jul 9, 2015

### PAllen

Yes, this is completely correct (if not the most elegant wording).

17. Jul 9, 2015

### Staff: Mentor

Here is how what I think you are trying to say here would be phrased in standard relativity terminology:

(first part of first bullet) Two events that are timelike separated will occur at different times in any inertial frame.

(second part of first bullet) Two events that are spacelike separated will occur at different spatial locations in any inertial frame.

(first part of second bullet) Two events can happen at the same time (at different spatial locations) in some inertial frame if and only if they are spacelike separated.

(second part of second bullet) Two events can happen at the same spatial location (at different times) in some inertial frame if and only if they are timelike separated.

18. Jul 9, 2015

### Mentz114

@giulio_hep I think this is what you mean -
Two different-time events $P(t_1,x), Q(t_2,x)$ will always have different times. Yes, because if the events are transformed then $t'_2-t'_1=\gamma (t_2-t_1)$ with the $x$ terms cancelling

The second case $P(t,x_1), Q(t,x_2)$ is the same with $x$ and $t$ interchanged.

The third case $P(t_1,x_1), Q(t_2,x_2)$ the transformed values are

$t'_2-t'_1 = \gamma (t_2-t_1) + \gamma \beta (x_2-x_1)$
$x'_2-x'_1 = \gamma (x_2-x_1) + \gamma \beta (t_2-t_1)$

If the events have the same time in the unprimed coordinates then $t'_2-t'_1 = \gamma \beta (x_2-x_1)$ which means they cannot have the same time coordinates in another frame unless $x_1=x_2$.

Your final proposition "two locations that are different in one reference frame can be represented by the same location in another reference frame at different times" requires

$0= \gamma (x_2-x_1) + \gamma \beta (t_2-t_1)\ \rightarrow (x_2-x_1) + \beta (t_2-t_1)=0\ \rightarrow \beta = -(x_2-x_1) /(t_2-t_1)$ which is fine if $(x_2-x_1)^2 \lt (t_2-t_1)^2$ and $t_1 \ne t_2$.

Last edited: Jul 9, 2015
19. Jul 9, 2015

### giulio_hep

So....
Proposition A
in Reference 1 I have space-time point P1 ([t1,x0,y0,z0) (in my terms at place (x0,y0,z0) and instant t1) and spacetime point P2 (t2,x0,y0,z0) (in my words same location but different instant)
=> it doesn't exist a Reference 2 (inertial, etc...) where the two space-time points (the two instants t1 and t2 in my terms) happen at the same time.
Symmetric of A
in Reference 1 I have space-time point P1 (t0,x1,y1,z1) (in my words at place (x1,y1,z1) and instant t0) and spacetime point P2 (t0,x2,y2,z2)
=> it doesn't exist a Reference 2 where the two space-time points (the two places (x1,y1,z1) and (x2,y2,z2) in my terms) are identified by the same spatial coordinates.

Proposition B
two space-time points that are space-like separated can have the same time coordinate in Reference 1 and a different time coordinate in Reference 2.
Symmetric of proposition B
I can find two references where two spacetime points P1(t1,x1,y1,z1) and P2 (t2,x2,y2,z2) (with all different coordinates in the first Reference 1) transform in two spacetime points with the same space coordinates in Reference 2 (under some constraints... as per the answer of PeterDonis the constraint here is that the two spacetime points are time-like separated)