How does timedilation apply to things other than lightclocks?

[eyxenia]

I'm studying special relativity and this does not make any sense to me:
I understand the lightclock example of how time dilation works.
But I don't understand how it applies to other things.

This is probably a stupid question, but I can't figure it out.

 

[A.T.]

The lightclock and "other things" at rest to the lightclock must have the same rate ratio in all frames:

If the mechanical clock would not be dilatated by the same amount as the co-moving light clock, you would run into paradoxes. Imagine the clocks trigger a bomb when they go out-of-synch. All observers must agree on whether the bomb exploded or not. But some observers would observe the clocks in-synch (those at rest to the clocks), some out-of-synch (those moving relative to the clocks).

 

[Dale]

I'm studying special relativity and this does not make any sense to me:
I understand the lightclock example of how time dilation works.
But I don't understand how it applies to other things.

This is probably a stupid question, but I can't figure it out.

Other people have had the same question, here is one answer that I gave which I liked:

So, from this comment it seems that you understand time dilation for light beam clocks. Remember that special relativity is founded on two postulates.

1) that all the laws of physics are the same in all inertial reference frames
2) that the speed of light is the same in all inertial reference frames

So the part that you understand, the time dilation of a light clock, is primarily based on the second postulate. But to understand how we make the jump from light clocks to time in general you need to consider the first postulate:

Imagine that we have a light clock, an atomic clock, a piezoelectric quartz clock, a windup spring clock, and a rat with a really steady heartbeat. All are clocks working on different physical principles. Because the laws of physics are the same in all inertial reference frames (first postulate) if they all beat at the same rate in one frame they must all beat at the same rate in any other frame. So, in an inertial frame where the clocks are moving at relativistic velocity, because the light clock slows down the other clocks must also slow down or the laws of physics would be different. Therefore, because any physics expression with a "t" in it must slow down, we say time slows down.

EDIT: scooped by A.T.!

 

[tom.stoer]

Suppose you have an arbitrary time-like path C for an observer O with speed v < c along C

Then you can calculate the proper time τ along the path using the integral

$$\tau[C] = \int_C d\tau = \int_0^T dt \sqrt{1-v^2(t)}$$

Here I have introduced a time coordinate t for an inertial reference frame S. In this frame S the time for traveling C is T, whereas the observer O measurement his proper time τ. Of course an inertial observer at rest in S, i.e. with v = 0, would measure T as his proper time.

The formula applies to arbitrary time-like paths C, including accelaration, changing directions, round trips etc. All what matters is the speed v(t) along C.

For constant speed v along C the formula reduces to

$$\tau[C] = \sqrt{1-v^2}\,T$$

Now you are able to compare different proper times τ, τ', τ', ... of different observers O, O', O'', ... along different paths C, C', C', ...

Note that the coordinate t and the duration T are just very special proper times, namely proper times for inertial observers at rest in S.

 

[Naty1]

I'm studying special relativity and this does not make any sense to me:

'Nature is absurd' says Richard Feynman...

In order for it to 'make sense' you need to adopt some new 'rules'...new perspectives, as Dalespam offered.

Wikipedia says it this way:

An accurate clock at rest with respect to one observer may be measured to tick at a different rate when compared to a second observer's own equally accurate clocks. This effect arises neither from technical aspects of the clocks nor from the fact that signals need time to propagate, but from the nature of spacetime itself...

and I think does a good job explaining more here:

http://en.wikipedia.org/wiki/Light_clock#Relative_velocity_time_dilation

Be prepared for some additional 'absurdity': not only does relative speed affect the passage of time [clocks], but so too does relative gravitational potential.

 

[eyxenia]

thank you guys, I have another question,
in the twin paradox, the brother who travels within the spaceship, as of what I've read his body slows down because it gets so heavy. Since e=mc2, the faster he goes the heavier his body gets. And the heavier he is, the more sluggish he gets, which is what happens with everything inside his spaceship. But I've also read that that has to do with time dilation, how?

 

[tom.stoer]

Just apply the formula for time dilation as described above.

Twin Alice is sitting at rest in her inertial frame, measuring T as arrival time = Alice' proper time
Twin Bob is making a round trip with speed v, measuring a different arrival time = Bob's proper time

 

[eyxenia]

Just apply the formula for time dilation as described above.

Twin Alice is sitting at rest in her inertial frame, measuring T as arrival time = Alice' proper time
Twin Bob is making a round trip with speed v, measuring a different arrival time = Bob's proper time

It's too complex for me because I'm not very good at equations.
Do you mind explaining it a little simpler?

 

[russ_watters]

in the twin paradox, the brother who travels within the spaceship, as of what I've read his body slows down because it gets so heavy. Since e=mc2, the faster he goes the heavier his body gets. And the heavier he is, the more sluggish he gets, which is what happens with everything inside his spaceship. But I've also read that that has to do with time dilation, how?

It has nothing to do with "getting heavy". In experiments performed in your own frame, you never notice any differences.

 

[Naty1]

... his body slows down because it gets so heavy. Since e=mc2, the faster he goes the heavier his body gets. And the heavier he is, the more sluggish he gets, which is what happens with everything inside his spaceship. But I've also read that that has to do with time dilation, how?

No that's just plain wrong; he gains no weight, nor energy, nor loses any time as HE sees things locally. If that were true, the twin could turn into a black hole by going fast enough...and that does NOT happen.

E = mc² is the energy mass equivalent in a frame at rest...no relative motion. For the fast moving twin, his clock...carried by him...always ticks at the same steady rate; it only is slowed when viewed by the stationary observer...it is a relative difference.

A basic rule to always remember in relativity is that a local clock always records proper [unaltered] time. Everything appears 'normal' locally to an observer. It is only when an observer views distant phenomena that relativity inserts its effects. Two observers who stay together always view the same phenomena...like the same passage of time.

 

[TheBC]

I'm studying special relativity and this does not make any sense to me:
I understand the lightclock example of how time dilation works.
But I don't understand how it applies to other things.

This is probably a stupid question, but I can't figure it out.

Are you familiar with 4Dspacetime diagrams?
Time dilation has a spacio-temporal origin.

 

[eyxenia]

No that's just plain wrong; he gains no weight, nor energy, nor loses any time as HE sees things locally. If that were true, the twin could turn into a black hole by going fast enough...and that does NOT happen.

E = mc² is the energy mass equivalent in a frame at rest...no relative motion. For the fast moving twin, his clock...carried by him...always ticks at the same steady rate; it only is slowed when viewed by the stationary observer...it is a relative difference.

A basic rule to always remember in relativity is that a local clock always records proper [unaltered] time. Everything appears 'normal' locally to an observer. It is only when an observer views distant phenomena that relativity inserts its effects. Two observers who stay together always view the same phenomena...like the same passage of time.

I must've confused it with something else that I've read.
Now, is this then a legit definition of timedilation?:

Time dilation: A time interval length is not absolute, it is not the same everywhere and always. Time can only be measured relatively.
Example: You have two clocks in the form of a rod with two mirrors at the ends that reflect a light beam back and forth, each time the beam reaches mirror a second has passed.
The two clocks A and B are exactly alike, the only difference is that A is still and B is moving sideways.
Since the B-clock is moving the light beam gets a longer distance to travel than the light beam gets in A. Thus a second in the A-clock is faster than in the B-clock. That means, time passes more slowly in the B-clock/the clock in motion.
If the light clock beat at the same rate as a mechanical watch in one frame they must also beat at the same rate in any other frame since ”The laws of physics are the same in all inertial frames of reference” which is the first postulate.
Hence, time moves slower if you move faster.

 

[Nugatory]

Example: You have two clocks in the form of a rod with two mirrors at the ends that reflect a light beam back and forth, each time the beam reaches mirror a second has passed.
The two clocks A and B are exactly alike, the only difference is that A is still and B is moving sideways.
Since the B-clock is moving the light beam gets a longer distance to travel than the light beam gets in A. Thus a second in the A-clock is faster than in the B-clock. That means, time passes more slowly in the B-clock/the clock in motion.
If the light clock beat at the same rate as a mechanical watch in one frame they must also beat at the same rate in any other frame since ”The laws of physics are the same in all inertial frames of reference” which is the first postulate.
Hence, time moves slower if you move faster.

That works as long as you also understand that as far as B is concerned, he is at rest and A is the one who is moving - so just as A says that B's clock is running slow, so does B say that A's clock is running slow.

One caution: It is a bad habit to say things like "A is still and B is moving" or "the faster you move the more your clock slows" without also saying what the motion is relative to and which clock you're comparing with. Any time you find yourself confused by anything in special relativity, the first step is to go back and put all the relative stuff back in.