Does Relativistic Speed Affect Mechanical Watch Oscillation?

[Jurgen M]

Does mechanical watch ticks slower when move fast, due to relativistic effects?

To make watch tick slower you must change oscillation of balance wheel inside watch, so if answer is yes, what myster "force" change balance wheel oscillation in mechanical watch to ticks slower?

 

[Orodruin]

Yes. No, there is no mystery force. Just mechanics working differently close to the speed of light.

Note that the clock ticks at its normal rate in its own rest frame.

 

[Ibix]

There is no force needed. If you do a full relativistic analysis of a watch moving very fast with respect to you, you will find that it is unsurprising that it ticks slowly. As Orodruin says, a concurrent analysis run by someone moving alongside the watch will find that it ticks normally.

I must admit I've never done a full analysis of a wheel-based clock, but a pendulum clock isn't enormously difficult to analyse. Light clocks are, of course, almost trivial, which is why they are routinely used in teaching relativity. It's easy to see, of course, that the principle of relativity demands that if a light clock ticks slow then so must any other kind of clock - otherwise you could get a measure of some absolute speed (and there is no such thing in a relativistic universe) by comparing tick rates of different clocks.

 

[Jurgen M]

Yes. No, there is no mystery force. Just mechanics working differently close to the speed of light.

Note that the clock ticks at its normal rate in its own rest frame.

In which frame ticks slower?
How math would explain change in oscillation of balance wheel, because this is only way to change time in watch?

 

[Ibix]

In which frame ticks slower?

Any frame in which it is not at rest measures the clock ticking slower than in its rest frame by a factor of $1/\sqrt{1-v^2/c^2}$, where $v$ is the speed of the clock in that frame.

How math would explain change in oscillation of balance wheel, because this only way to change time in watch?

In a frame where the clock is moving, the balance wheel is not round, nor is the material of it isotropic, and the accelerations it undergoes are not uniform around the wheel. Relativistic analysis of a wheel is rather non-trivial, but that's the kind of thing that is at the base of why a frame where the clock is moving does not see it tick at the same rate as one in which it is at rest.

 

[Orodruin]

Any frame in which it is not at rest measures the clock ticking slower than in its rest frame, y a factor of $1/\sqrt{1-v^2/c^2}$, where $v$ is the speed of the clock in that frame.

In a frame where the clock is moving, the balance wheel is not round, nor is the material of it isotropic, and the accelerations it undergoes are not uniform around the wheel. Relativistic analysis of a wheel is rather non-trivial, but that's the kind of thing that is at the base of why a frame where the clock is moving does not see it tick at the same rate as one in which it is at rest.

Now that appearing just as I started writing saved a lot of typing ...

 

[Ibix]

Now that appearing just as I started writing saved a lot of typing ...

<Cracks knuckles, blows smoke off keyboard>

 

[Jurgen M]

. Just mechanics working differently close to the speed of light.

So mechanics inside watch works slightly differently at 150km/h compare to 200km/h?

Why if constant speed is equal to no speed = zero net force?
I would somehow understand that oscillation of balance wheel works differently during accelration, but at constant speed nothing really happened..hmm

 

[Ibix]

So mechanics inside watch works slightly differently at 150km/h compare to 200km/h?

Whether it's "different" or not is arguable (a matter of taste in language, not physics), but it isn't Newtonian mechanics, which is probably what you're naively using.

Why if constant speed is equal to no speed = zero net force?

No forces are needed here, beyond the ones driving the wheel and keeping it together. Of course, as I've already commented, the way those work at relativistic speeds is messy and complicated.

I would somehow understand that oscillation of balance wheel works differently during accelration

Oh yeah, a mechanical watch will go badly wrong under any serious acceleration because it's calibrated on the assumption it's working under a proper acceleration of 9.81ms^-2, and if you accelerate at a different rate you'll probably get a malfunction. This is a completely separate phenomenon from what happens at constant speed.

at constant speed nothing really happened..hmm

That's not true, though. As I pointed out already, a moving wheel is not generally circular, nor is the material nor the internal forces isotropic. The transforms of all of these quantities are more complicated in relativistic mechanics than in Newtonian mechanics.

Do you understand how a light clock works?

 

[Dale]

Does mechanical watch ticks slower when move fast, due to relativistic effects?

To make watch tick slower you must change oscillation of balance wheel inside watch, so if answer is yes, what myster "force" change balance wheel oscillation in mechanical watch to ticks slower?

Mechanical watches are usually designed using Hooke’s law and Newton’s laws. Neither of those are relativistic in their usual form. If you generalize Hooke’s law and Newton’s laws to their relativistic forms then you naturally get that mechanical watches exhibit time dilation as normal. In other words, it is not any additional force, it is just how the usual forces actually work at high speeds.

 

[Jurgen M]

Do you understand how a light clock works?

Yes understand how light clock works.
When you look at moving watch, light must pass longer path to make one tik-tok = 1 second.
So longer path / C = more time

it take more time from tik to tok. 1 second last longer

 

[Orodruin]

Yes understand how light clock works.
When you look at moving watch, light must pass longer path to make one tik-tok = 1 second.
So longer path / C = smaller time

Do you also understand that if you have two light clocks, they will both tick slower in the ither’s rest frame?

 

[Jurgen M]

Do you also understand that if you have two light clocks, they will both tick slower in the ither’s rest frame?

If one clock is at rest and one clock moving, both clocks can say I am at rest and you are moving toward me..

So qestion is which clock is really moving?

 

[PeterDonis]

So qestion is which clock is really moving?

Neither one. There is no such thing as "really moving". All motion is relative.

 

[Jurgen M]

Neither one. There is no such thing as "really moving". All motion is relative.

Yes I know that..so clock1 see clock2 to ticks slower and clock2 see clock1 to ticks slower

 

[DaveC426913]

@Jurgen M : Just to see where you are in terms of understanding relativity: do you understand that everything moving at relativistic speeds wrt you will be observed to be occurring slower?

People will be observed to move slower, our hearts will be observed to beat slower, cellular metabolism will be observed to operate slower, atomic chemistry will be observed to react slower.

 

[PeterDonis]

Yes I know that..so clock1 see clock2 to ticks slower and clock2 see clock1 to ticks slower

Ok, so what's the problem?

 

[Jurgen M]

@Jurgen M : Just to see where you are in terms of understanding relativity: do you understand that everything moving at relativistic speeds wrt you will be observed to be occurring slower?

People will be observed to move slower, our hearts will be observed to beat slower, cellular metabolism will be observed to operate slower, atomic chemistry will be observed to react slower.

I just understand concept of light watch...visualization how balance wheel will tick slower don't understand at all

 

[Jurgen M]

Ok, so what's the problem?

visualization how/why balance wheel will ticks slower...

 

[Orodruin]

visualization how/why balance wheel will ticks slower...

Again, that is a rather complex problem that requires you to essentially do relativistic mechanics. It would involve taking relativistic momenta and force transformations into account and more. It is not something that can be seen easily.

 

[PeterDonis]

visualization how/why balance wheel will ticks slower...

If you know that the balance wheel clock will be synchronized with a light clock that is at rest relative to it, then you know that two balance wheel clocks in relative motion will each see the other running slow--just have a light clock moving along with each balance wheel clock. Any periodic motion of each balance wheel clock must be synchronized with the periodic motion of the light clock that is moving along with it.

 

[Dale]

visualization how/why balance wheel will ticks slower...

Did you miss my response? There is no additional force involved. It arises naturally from a relativistic generalization of Hooke’s law and Newton’s laws

 

[DaveC426913]

I just understand concept of light watch...visualization how balance wheel will tick slower don't understand at all

Look at it another way.

You are currently moving at relativistic velocity with respect to Andromeda galaxy. Andromedans will observe you as being time dilated. If the watch you're holding were not also time dilated from their perspective, that would mean you should see your own watch moving fast.

Relativistic time dilation is not "operating on" individual things like your your muscles and watch movements; it is an observed effect by a remote observer.

 

[FactChecker]

It's the relativity of simultaneity. To the observer, $O_1$, who is "moving" with the clock, nothing at all is happening to the clock. It is running at the exactly correct speed. The observer, $O_2$, in the other reference frame is only seeing the clock at greatly separated locations (in his reference frame) from one tick to the next. So the argument is about whether $O_2$'s clocks are all set correctly when they are that far apart. That is called the "relativity of simultaneity".

 

[Sagittarius A-Star]

Does mechanical watch ticks slower when move fast, due to relativistic effects?

To make watch tick slower you must change oscillation of balance wheel inside watch, so if answer is yes, what myster "force" change balance wheel oscillation in mechanical watch to ticks slower?

The period of oscillation of the balance wheel in it's rest-frame $S$ for non-relativistic angular velocity is:
$T = 2\pi\sqrt{I/\kappa}$

For simplicity assume, that the frame $S'$ moves with relativistic velocity in direction of the wheel axis.

The spring constant in transversal direction must transform in the same way as transversal forces do:
$\kappa' = \kappa/\gamma$

The moment of inertia in transversal direction must transform in the same way as $E/c^2$ does:
$I' = I \gamma$

$$T' = 2\pi\sqrt{I'/\kappa'} = 2\pi\sqrt{\gamma^2 * I/\kappa} = \gamma T$$

 

[Ibix]

The conversation has moved on a bit, I see, but you might find these illustrations of a rotating wheel moving relativistically to be of interest:

All three wheels are the same shape in their rest frame, but are deformed in various ways in frames where they are moving. This is the kind of thing that makes analysing relativistically moving mechanical systems quite difficult.

However, do remember that all matter is made of atoms held together by electromagnetic forces, and relativity was specifically created to make electromagnetic theory work. However odd things may look, that's a pretty strong argument that it's self consistent.

It occurs to me that analysing a mass oscillating transversely on the end of a spring shouldn't be too hard if you look up the transform rules for forces. I haven't actually tried that, so I accept no responsibility for loss of hair if you try it and it's trickier than I think.

 

[docnet]

The conversation has moved on a bit, I see, but you might find these illustrations of a rotating wheel moving relativistically to be of interest: View attachment 295217
All three wheels are the same shape in their rest frame, but are deformed in various ways in frames where they are moving. This is the kind of thing that makes analysing relativistically moving mechanical systems quite difficult.

Which ways are the wheels moving? (seriously, just wondering).

 

[Sagittarius A-Star]

It occurs to me that analysing a mass oscillating transversely on the end of a spring shouldn't be too hard if you look up the transform rules for forces. I haven't actually tried that, so I accept no responsibility for loss of hair if you try it and it's trickier than I think.

The "transversely" is the key to create an easy to calculate scenario. Then you avoid complications by length contraction and relativity of simultaneity. For the same reason, the standard "light clock" scenario is set up transversely.

Unfortunately, they use in the following calculation the "relativistic mass m' ", instead of using $m\gamma$ or $E/c^2$:
https://www.mathpages.com/home/kmath068/kmath068.htm

 

[Ibix]

Which ways are the wheels moving? (seriously, just wondering).

I can't track down the source for it at the moment. From memory, the red wheel is at rest, the green wheel is moving perpendicular to its rotation axis but has light travel time delay subtracted out, and the blue one is moving along the line you can see, perpendicular to its rotation axis, and including the variation in light arrival time due to its finite size so it is Terrel rotated. So the green wheel is what you have to cope with (irregular tooth spacing, not round) in an analysis and the blue is what you'd see.

 

[Sagittarius A-Star]

Which ways are the wheels moving? (seriously, just wondering).

It should be shown by the video in the middle:
https://www.spacetimetravel.org/rad/rad.html