Can Time Dilation Affect the Mechanical Functioning of a Clock in Orbit?

[ISamson]

Hello.
I want to clear a doubt on Special Relativity, time dilation and clocks.
If we get an accurate clock and make it orbit the, for example, Earth very, very fast, will the actual mechanical clock lag behind from the accurate clocks on Earth? The thing in this question is about the actual mechanical lag or what? I don't understand...
Thank you for your patience...

 

[Ibix]

You need to be careful orbiting the Earth because gravitational time dilation can make matters more complicated. Stripped of that bit, what youare asking about is basically the twin paradox. Yes, the stay-at-home clock willshow less elapsed time than the traveling clock when it returns.

Note that this is not something you can interpret purely in terms of time dilation. If you want to think in terms of time dilation, you need to look up the relativity of simultaneity as well.

I prefer the geometric explanation. It turns out that your wristwatch measures the "interval" along your path through spacetime. Interval is the four-dimensional equivalent of distance in space. Since the two clocks followed different paths, it should not be entirely surprising that the interval along those paths is different, and therefore that the clocks show different times.

 

[Dale]

I prefer the geometric explanation. It turns out that your wristwatch measures the "interval" along your path through spacetime. Interval is the four-dimensional equivalent of distance in space. Since the two clocks followed different paths, it should not be entirely surprising that the interval along those paths is different, and therefore that the clocks show different times.

I also like the geometric explanation. You don’t have to think in terms of clocks slowing or speeding. They both correctly measure the length of their path. Just one took a shortcut and the other went the long way around.

 

[ISamson]

You need to be careful orbiting the Earth because gravitational time dilation can make matters more complicated. Stripped of that bit, what youare asking about is basically the twin paradox. Yes, the stay-at-home clock willshow less elapsed time than the traveling clock when it returns.

Note that this is not something you can interpret purely in terms of time dilation. If you want to think in terms of time dilation, you need to look up the relativity of simultaneity as well.

I prefer the geometric explanation. It turns out that your wristwatch measures the "interval" along your path through spacetime. Interval is the four-dimensional equivalent of distance in space. Since the two clocks followed different paths, it should not be entirely surprising that the interval along those paths is different, and therefore that the clocks show different times.

Sorry, but could you please rephrase that.
I don't get it...
Thanks!

 

[Ibix]

I said that you don't want to involve gravity in your experiment, that the clocks show different elapsed times, and that there are different ways to explain that, but time dilation is not enough on its own. Which bit don't you get?

 

[ISamson]

I said that you don't want to involve gravity in your experiment, that the clocks show different elapsed times, and that there are different ways to explain that, but time dilation is not enough on its own. Which bit don't you get?

Ok.
But if we actually now conducted this experiment, would the clocks really, physically show different times?
I don't understand how the time dilation affects the inner timer, clock, processor of the watch.
Thank you very much for your patience, Ibix.

 

[Ibix]

As I said, your watch turns out to measure the 4d equivalent of distance along the route it has traveled through spacetime (you may wish to look up the term "interval"). If two clocks travel by different routes the routes can have different "lengths" so the clocks show different elapsed times when they meet up.

If two cars start in the same factory and meet up later, their odometers may not read the same. The key difference between Newton and Einstein is that in Einsteinian physics clocks behave like odometers. They measure their own personal time and there is no notion of "the" time. Nor is there an unambiguous distinction between time and space. They are part of one combined thing called spacetime.

So why do clocks show different elapsed times? The answer is whatever answer you would accept for why the cars' odometers have different readings.

 

[ISamson]

Thank you. I understand now. Thank you for your patience.

 

[asca]

If it can be oy any help, here is a short (20min) video that shows you the role of relativity of simultaneity in an unusual way. It is in Italian but with english subtitles.
Enjoy.

 

[Grinkle]

@ISamson For me, trying to understand time dilation through thinking about clocks was not a very useful exercise. Instead, I had to get my head around the fact that if the speed of light, or conceptually the speed of information, is going to be constant for all observers, then something that can't be constant for all observers is the passage of time. If you can successfully reason through that logic, then you stop worrying about clocks and what slows them down - for me thinking of clocks was an enormous red herring.

That all reference frames agreeing on the speed of light (and this being a maximum speed of anything) implies that all reference frames cannot agree on the rate of time is not a matter of opinion, and it has nothing to do with any human constructed clock.

 

[laymanB]

Hello.
I want to clear a doubt on Special Relativity, time dilation and clocks.
If we get an accurate clock and make it orbit the, for example, Earth very, very fast, will the actual mechanical clock lag behind from the accurate clocks on Earth? The thing in this question is about the actual mechanical lag or what? I don't understand...
Thank you for your patience...

This is how I understand it and someone can correct me if this is incorrect.

First of all, I think it is helpful to banish the idea of clocks running "slow" or "fast" from your mind. This implies that there is a universally correct clock in which to compare if your clock is running slow or fast, this is incorrect. These ideas lead you to the questions of what is changing in the mechanism of the clock to produce such a change. Like was said above, forget about Earth's gravity to simplify the thought experiment. It is important to remember that if you are on the surface of the Earth or orbiting around the planet "very, very fast", that your clock will work fine. It doesn't depend on what kind of clock it is or the internal mechanisms. When you look at your clock, nothing will look suspect to you and it will operate the same, no matter where you find yourself with the clock.

It all depends on how you define "very, very fast" and also the precision of your timepiece. If you are orbiting the planet at the speed of a jetliner and your clock is not very precise (you can measure nothing more precise than one second), when you return to Earth both imprecise clocks will read the same and you will notice no difference. If your clocks are accurate to 100 decimals places, you will see a difference. If by "very, very fast" you mean close to the speed of light, then when you return to the surface of the Earth, you will notice a sizable difference proportional to the time of your orbital trip as measured by you. And you will notice that your clock shows much less time has elapsed since you left compared to the clock on the surface of the Earth.

The part about clocks running "slow" or "fast" is how your clock would "appear" to tick by to someone from a different reference frame. It has to do with the light from the face of the clock reaching you at different times as the spaceship (reference frame) speeds by you. If someone on the surface of the Earth could see your clock as you were orbiting the Earth close to the speed of light, it would appear to them to that your clock was extremely slow, and their clock would look equally slow to you, but to you in the spaceship your clock would look fine.

 

[pixel]

The part about clocks running "slow" or "fast" is how your clock would "appear" to tick by to someone from a different reference frame. It has to do with the light from the face of the clock reaching you at different times as the spaceship (reference frame) speeds by you. If someone on the surface of the Earth could see your clock as you were orbiting the Earth close to the speed of light, it would appear to them to that your clock was extremely slow, and their clock would look equally slow to you, but to you in the spaceship your clock would look fine.

In relativity, a frame of reference is considered to have observers with synchronized clocks in fixed locations throughout the frame. Saying that time dilation has to do with how someone would "see" the clock is adding an extra complication involving what is referred to as "look back," which takes into account the travel time of light to reach a single observer. The time of an event in a given frame of reference is the same for all fixed observers in that frame.

I think the OP may be asking whether time dilation is the result of the motion causing a mechanical change in the workings of a clock. That's not the case. Clocks of all kind are equally affected.

 

[laymanB]

I think the OP may be asking whether time dilation is the result of the motion causing a mechanical change in the workings of a clock. That's not the case. Clocks of all kind are equally affected.

I think that’s where some of the confusion comes in. To say that clocks are affected and run slowly seems to imply that you should be able to tell that your clock is affected in your inertial reference frame where the clock is at rest. If that were true, special relativity would be false.

 

[ISamson]

I think the OP may be asking whether time dilation is the result of the motion causing a mechanical change in the workings of a clock.

I am asking if time dilation will affect the mechanical functioning of the clock, which results in it showing different time - time dilation.

I think that’s where some of the confusion comes in. To say that clocks are affected and run slowly seems to imply that you should be able to tell that your clock is affected in your inertial reference frame where the clock is at rest. If that were true, special relativity would be false.

 

[jartsa]

I am asking if time dilation will affect the mechanical functioning of the clock, which results in it showing different time - time dilation.

This is what happened during the experiment:

The clock hand of the mechanical clock on the surface of the Earth moved mechanically around the clock face 5 times.

The clock hand of the mechanical clock on the mechanical vehicle that moved around very fast, moved mechanically around the clock face 4.5 times.

We say that "differential aging" occurred, to those two clocks.

When we say "that clock is time dilated", we mean "that clock is ticking slowly".

 

[ISamson]

Yes, thank you. This is what I was looking for!
Thank you.

 

[Grinkle]

I am asking if time dilation will affect the mechanical functioning of the clock, which results in it showing different time - time dilation.

No, the mechanical functioning of a clock is not affected by relative velocity between two inertial frames.

Imagine a toy car that moves at 5 mph when its electric motor is turned on. Put the car on a train moving towards you at 80mph. Now ask -

Does the car move towards me at 85mph because its electric motor has been affected and that makes it move faster?

The answer is obviously no (of course this has nothing to do with SR, I am just picking something where our human intuition leads us to the right answer). Its the same level of obviousness for the time dilation question if you have reasoned through the implications of the speed of light being invariant.

 

[Mister T]

I am asking if time dilation will affect the mechanical functioning of the clock, which results in it showing different time - time dilation.

Think about a mechanical clock ticking away on your mantle. Does the passage of time affect the clock? Of course not, the clock is just a device used to measure the passage of time. Put another clock next to it and notice that they stay in sync. It makes no difference if this other clock is mechanical or some other type. As long as the two clocks stay in sync, and you know one of them is properly measuring the passage of time, then you know the other one is as well. The clock you place in orbit will behave the same if you rest it on your mantle, but if you place it in orbit you notice that when it returns it shows that less time has elapsed than do the clocks on your mantle. Again, it makes no difference if the orbiting clock is mechanical or some other type.

So how is it that two clocks on the mantle stay in sync, but two clocks that move relative to each other don't?

I do not believe that you can learn this by looking at the geometry of spacetime and paying no mind to time dilation and the relativity of simultaneity, but this is just my pedagogical opinion. You must understand how the geometry is used to provide an explanation that is equivalent to the explanation using time dilation and the relativity if simultaneity. Fortunately, this very issue has been discussed thoroughly and you will have no problem finding material to study. It's called the twin paradox. You can find it on the web as well as at your local bookstore or library. Of course, you will need some help as you will have questions along the way that you won't be able to answer on your own. That's where a forum like this can provide a lot of help.