# 2 spinning or orbitting objects and their effect on time

If 2 balls or cylinders with watches inside were spun one at close to the speed of light, the other at half the speed of light, both with clocks or timers in them; would they show different times when stopped after having been spun for a certain length of time.

I'd presume if they were made to orbit at the same radius at different speeds this would be the case to?

Its a simple question and one I'm confident of the answer on, that being said I want to make sure before making a follow up question.

## Answers and Replies

HallsofIvy
Homework Helper
No, that is not a simple question. To a "stationary" observer, (the one with respect to whom there velocities are "close to the speed of light" and "half the speed of light"), the watch moving faster would appear to be ticking slower than the slower moving clock.

But whether one or the other would be showing a different time "when stopped" depends heavily upon how, exactly, they were stopped.

Sorry should have made my question clearer. Lets say both objects with clocks in them were spinning cylinders, both next to each other and both stopped at exactly the same time. Or in very small orbits say an inch in radius, as spheres.

The experiment taking place on earth, so the observer being any scientist part of the experiment say.

Satellites have to be readjusted for timing because of their high velocity and our relative need of their accuracy.

It would make sense to me the the two cylinders would show different times, as relative to each other they have been moving at vastly different speeds through time.

If you'd do me the favour of elaborating the holes that are in the above (don't mean that to sound arrogant, it's a genuine ask for help, so I can try and ask follow up questions) it would help immensely.

In the same area of questioning, if 2 objects were sent out in the same direction at c and 1/2c (or whatever speed with difference) these objects essentially being clocks they would show different times to an observer from earth.

The question i'm leading up to involves information which can roughly be transmitted at light speeds, at least some types of information.

It ultimately involves a question of reading time, information within it.

I'm not a physicist, the job would bore me though the ideas fascinate me. I was a high level maths student of sorts, all sciences interest me, but i'm an imaginer; punching numbers would take that away from me so I gave it up.

Humoring me would be greatly appreciated, as with all the best of imaginings it came upon awaking. Sure i'm wrong but want someone who knows i'm wrong to tell me so.

Understandable if you dont wish to humor me, but i've never met a physicist who doesn't enjoy imagining.

Ich
If 2 balls or cylinders with watches inside were spun one at close to the speed of light, the other at half the speed of light, both with clocks or timers in them; would they show different times when stopped after having been spun for a certain length of time.
Yes.
I'd presume if they were made to orbit at the same radius at different speeds this would be the case to?
That's not possible. Radius is a one-to-one function of speed for a circular orbit.
It would make sense to me the the two cylinders would show different times, as relative to each other they have been moving at vastly different speeds through time.
"speed through time" is a useful concept, but it works only if you pick (arbitrarily) one inertial frame - which defines the "time" direction we're talking about - and stick to it.
If your follow-up includes something like rotating frames or different inertial frames for the definition of "time": forget it.
I'm not a physicist, the job would bore me though the ideas fascinate me. I was a high level maths student of sorts, all sciences interest me, but i'm an imaginer; punching numbers would take that away from me so I gave it up.
Yeah, you're not a physicist.
It's not about punching numbers. It's whether you allow an ugly fact to slay a beautiful hypohesis or not.

atyy
It's not about punching numbers. It's whether you allow an ugly fact to slay a beautiful hypohesis or not.
Well, are you a physicist? Why didn't you say allow a beautiful fact to slay an ugly hypothesis? :tongue:

Ich
Well, are you a physicist? Why didn't you say allow a beautiful fact to slay an ugly hypothesis?
I'm a physicist, but not necessarily an experimental physicist. To the contrary, I'm convinced that reality (and experiments) are controlled by some kind of red and green gnomes, who will do what they want. At least, that's my experience.
I'd really like to have beautiful hypotheses prevail, but sadly, usually they don't.

atyy
I'm a physicist, but not necessarily an experimental physicist.
I should have guessed.

To the contrary, I'm convinced that reality (and experiments) are controlled by some kind of red and green gnomes, who will do what they want. At least, that's my experience.
I'd really like to have beautiful hypotheses prevail, but sadly, usually they don't.
I'm a biologist - things are really ugly here - but we haven't seen the gnomes yet (or maybe they are even uglier than I imagined )

Sorry should have made my question clearer. Lets say both objects with clocks in them were spinning cylinders, both next to each other and both stopped at exactly the same time. Or in very small orbits say an inch in radius, as spheres.

The experiment taking place on earth, so the observer being any scientist part of the experiment say.
O.K. in the lab frame, two cylinders both of radius r and spinning about their long axes of symmetry. Clocks on the surfaces of the cylinders are of negligible dimensions relative to the radius of the cylinders. In the lab frame the cylinders complete one rotation in time t. The tangential velocity of a clock on the surface of the cylinder is v= 2*pi*r/t. In lab time t, the proper time of a clock on the surface of one of the cylinders is t*sqrt(1-v^2/c^2). The clock on the surface of the fastest spinning cylinder shows the least elapsed proper time when the clocks are all brought to rest. The time dilation is a function of the tangential velocity of the cylinder and is numerically equal to the time dilation that would occur if the clock had the same relative velocity in a straight line. Centrifugal or centripetal acceleration has no affect on the time dilation. See the entry in the experimental evidence FAQ's about the clock hypothesis http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#Clock_Hypothesis

I'd presume if they were made to orbit at the same radius at different speeds this would be the case to?
I think orbit is defined as moving inertially (no proper acceleration) and that excludes orbiting at the same radius at different speeds. However if we had one satellite orbiting naturally at radius r and another satellite orbiting at twice the velocity in the opposite direction with its radius artificially maintained by a tether or rockets firing inwards to provide the additional centripetal force, then the relative proper times that elapse on the two satellite clocks would be a function of their orbital speeds as measured in the non rotating frame exactly as if they had been moving in a straight line (and remained at a constant gravitational potential). Again, acceleration makes no difference to the calculation of elapsed proper times.

If 2 balls or cylinders with watches inside were spun one at close to the speed of light, the other at half the speed of light, both with clocks or timers in them; would they show different times when stopped after having been spun for a certain length of time.
This is where the gnomes make an appearance. If the clocks were as large as the balls and the balls were large, then different parts of the clock are time dilated to different extents and things get gnarly (gnomey?). At the opposite extreme if the clock was infinitesimal in size and exactly at the centre of the ball then it would probably experience almost no time dilation however fast the ball spun.