# Time dilation - effect on clock or 'time' itself?

1. Nov 27, 2014

### henry555

I understand that this topic have been discussed many times, but I just haven't found the answer, at least one I could understand. I'm not a physicist, just curious.

I've been reading all around the internet about time dilation and SR. I understand that time dilation is real, at least when it comes to our ways to measure time. What I don't understand about all the 'proofs' of time dilation is that why there's not a huge possibility that only the clocks have been affected by gravity/velocity, not actual 'time'? Would love to hear explanation that I could understand.

2. Nov 27, 2014

### A.T.

If the "actual time" cannot be measured by clocks, then it is irrelevant to physics.

3. Nov 27, 2014

### Staff: Mentor

There is more than one type of clock, so it would be quite a coincidence if all showed exactly the same error -- and an error that matched a theory on time dilation.

4. Nov 27, 2014

### PeroK

One of Einstein's great insights was to realise that time is what a clock measures. It's as simple as that!

5. Nov 27, 2014

### Jonathan Scott

To see how a clock is affected, one only need consider a hypothetical simple clock which bounces a light beam in vacuum between two mirrors a fixed distance apart and counts the number of times the light has bounced, effectively counting the distance that the light has travelled. It is very clear that the value indicated by such a device matches what we call "time" and transforms with Lorentz transformations in the same way as time.

6. Nov 27, 2014

### VantagePoint72

I can see two possible ways of interpreting this question. You may be asking, as I think the others have taken it, something like, "How do we know we know time (whatever it is) isn't chugging along as usual and every possible way of measuring it just ends up being wrong in exactly the same way?" In this case, the other answers have you covered—time is what a clock measures, there's no other sensible definition. If every conceivable dynamical process in one frame happens slower according to some other frame, how else could you possibly describe this but to say that the former's time is running slowly according to the latter?

However, there's a second reading of your question with a more direct answer so I want to cover all the bases. Are you asking, "How do we know all dynamical processes run slow by the same amount?" In other words, suppose we follow Einstein's thought experiment of the light clock in a moving frame (relative to yourself) and conclude that the "ticks" of the light clock are farther apart. Might this not just mean that light clocks are a poor time keeping device and that something less exotic like a Swiss quartz watch would still keep the usual pace of time? The answer to this is a very simple no: unless all dynamical processes—light clocks, mechanical clocks, radioactive decay, chemical reactions, biological aging, etc.—all slowed by exactly the same factor that the light clock slows in the thought experiment, then the principle of relativity is violated. Recall that this says that the laws of physics are invariant between inertial reference frames or, more informally, that there is no experiment you could do that would ever tell you you're moving relative to some absolute standard of rest. If only light clocks ran slow, you would be able to tell you were in motion because you could build a light clock and see that it disagrees with every other time keeping device you have.

Last edited: Nov 27, 2014
7. Nov 27, 2014

### Staff: Mentor

I like russ waters' answer above. Let me expand on it a little.

Suppose that we had a situation where there was some "true and absolute space and time" and there was some law of physics that caused EM processes to slow down compared to "true time" as they passed through this "absolute space". Now, it would already be a HUGE coincidence that the amount of slow-down of EM processes was exactly the right amount to act as though there were no "true and absolute space and time" but simply space and time relative to each inertial frame. That a the mechanism of slowdown would have exactly the right form to make itself completely undetectable is already so preposterous that it is too hard for most scientists to swallow.

However, we have also found that the weak nuclear force undergoes the same amount of slowdown as the EM force. If EM forces were being slowed down by some mechanism, then you would need a separate mechanism to account for the slowdown of the weak force. This undetectability of this mechanism would also be as preposterous as that of the EM mechanism. So each mechanism by itself is preposterous, but together they are preposterous on top of preposterous with the additional huge coincidence that they just happen to slow down by exactly the same amount.

Similarly with the strong nuclear force and gravity. In the end you wind up with something like preposterous to the fourth by coincidental to the third. It just rapidly becomes an untenable scientific position.

8. Nov 28, 2014

### henry555

Thanks for all the replies. I'm still trying to fully understand most so I'll leave my follow up questions for later. This whole concept is fascinating but really hard to grasp.

9. Nov 28, 2014

### CKH

Elaborating on the above post:

For "light clocks", the reason for time-dilation has a simple physical explanation. In a moving light clock, the light pulse takes a longer (slanted) path to go from the bottom mirror to the top mirror (and vice versa) than in a similar stationary light clock. So, fewer ticks occur in the moving clock than in the stationary clock over any given period of time.

The times that a light pulse requires to traverse the path from mirror to mirror can be calculated in the stationary frame for the stationary clock and in the same frame for the moving clock.

Assume identical light clocks one stationary and one moving at velocity $v$ in the x direction. Let the mirrors in both clocks be vertically aligned and spaced apart by the distance $h$. A light pulse travels from bottom mirror to the top mirror of either clock at the velocity of light $c$. Designate the time a pulse of light takes to travel from the bottom to the top mirror by $t_s$ for the stationary clock and $t_m$ for the moving clock.

Now we can calculate a relationships between these times noting that the following points on the path of the moving clock define a right triangle:

1) The original position of the bottom mirror,
2) the final position the bottom mirror and
3) the final position of the top mirror

(the final position is the position of the moving clock when the pulse reaches the top mirror of the moving clock).

Side 1-2 is the base of the right triangle with length $vt$.
Side 2-3 is the vertical side of the right triangle with stated distance between mirrors $h$.
Side 1-3 is the hypotenuse of the right triangle (the light path in the moving clock) with length $ct_m$.

Now the Lorentz transformation for a light clock follows directly from the pythagorean theorem. That theorem says:

$(vt_m)^2 + h^2 = (ct_m)^2 ⇒$
$(v/c)^2t_m^2 + (h/c)^2 = t_m^2 ⇒$
$(h/c)^2 =t_m^2 (1-(v/c)^2) ⇒$

$h/c = t_m\sqrt{1 - v^2/c^2}$

The time it takes light to travel from the bottom mirror to the top in the stationary clock is
$t_s = h/c$
so we now have a relationship between the periods of the stationary and moving light clocks which is the same as the Lorentz transformation for time:

$t_s = t_m \sqrt{1 - v^2/c^2}$

This physically explains why a light clock runs slower and by how much when moving. The only assumption is constant $c$ in the stationary frame. From this alone we know exactly how and why a light clock runs slower when moving.

This analysis of a light clock does not demonstrate that all other types of clocks also run slower when moving. But, by applying the Principle of Relativity (PoR, the postulate that physical laws are the same in all inertial frames) all types of clocks must tick in same relationship to one another regardless of the inertial rest frame of the clocks. So in SR, by the PoR postulate we can extend the above time dilation equation to all clocks.

Note that we used the postulate "the speed of light is independent of the motion of the source" to derive time dilation for the moving light clock, since we assumed that although the bottom mirror was moving when it the emitted the light pulse, the pulse still moved at velocity $c$.

Also note that we did not use the PoR Postulate to find time dilation for the light clock.

Thus, we have a physical explanation of time dilation for the light clock. For this clock we are not forced to say "time itself" runs a different rates, we could simply say that motion causes a light clock to tick more slowly. With a physical explanation in hand for the light clock, can we not ask: "What is the physical explanation that other types of moving clocks also run slower?"

10. Nov 28, 2014

### pervect

Staff Emeritus
Because all clocks seem to measure the same thing, we need a name for that. We call what clocks measure "time", since clocks based on different principles all seem to be agreeing with each other and measuring the same thing.

There is actually a useful elaboration here. It turns out that what clocks measure is actually proper time. There's an additional notion that's so simple we don't usually think about it, that is the notion of simultaneity, two events having "the same time". We need the notion of simultaneity to turn the reading of a master clock into a way to give time coordinates to distant events that don't happen to happen at the same location as the master clock, for instance.

However, it turns out that, non-intuitively, this notion of siultaneity isn't universal. So we wind up with proper time, which clocks measure, which is independent of the observer, and coordinate time, which requires the additional notion of simultaneity, which is observer dependent.

11. Dec 11, 2014