[Eternal Student]

Hi,

So if we have two rotating objects with mass (obviously in a vacuum)  does the rotation of  the one affect the rotation of the other?

   A brief answer:    Not usually.

   Our universe is big and contains many things:   uncounted galaxies,  dark energy spread over the place   etc.         This is what will determine the background, the curvature of spacetime.   The contribution from the two objects that you're focusing will be utterly insignificant by comparison.   We can approximate the situation as if space is just a static background:  Your two objects are simply in the space but do not really change the nature of space in any significant way.

     If your two objects were the only material in the universe, then that's different,  each one will now strongly influence the background geometry of spacetime.   Similarly, if your two objects were unusually dense, say two rotating neutron stars in close proximity, then they can be the dominant sources / causes of spacetime curvature in a small region of space around them.

     We have this phrase which is usually credited to  John Wheeler:
Spacetime tells matter how to move; matter tells spacetime how to curve.
   So, if one of your objects is the significant cause of spacetime curvature in a region, then it will influence how everything in the region can possibly move.

Best Wishes.

[alancalverd]

Given that angular momentum is conserved, I wonder whether the net angular momentum of the observable universe is zero, some entirely arbitrary number (i.e. the observable universe has an axis and two unique points) , or nonzero and precisely balanced by that of  dark matter?

[geordief]

Given that angular momentum is conserved, I wonder whether the net angular momentum of the observable universe is zero, some entirely arbitrary number (i.e. the observable universe has an axis and two unique points) , or nonzero and precisely balanced by that of  dark matter?

Well,since the earliest known  period in the universe is said to  have  been t+ 10^-43 seconds is there any indication whether any rotation  might have  occured then
?
If so ,perhaps that  rotation (angular momentum) might have been conserved  into later periods.

Would there be a connection between any primordial rotation and the initial degree of assymmetry  that I have heard talk of?

[Eternal Student]

Hi,

   You  ( @alancalverd ) are doing this deliberately, aren't you?

Given that angular momentum is conserved,.....

       Why would we assume angular momentum is conserved?   I mean to say, it's not as if we're sure that every spacetime and every solution of the EFE will have the sort of rotational symmetry that Noether's theoreom requires.

       We've had discussions about whether "Energy" is conserved in general relativity   (.... final conclusion:  it doesn't have to be).  "Angular Momentum" is much the same.   At best, it's a grey area.

Best Wishes.

[Eternal Student]

Hi again,

   I've just re-read your post and noticed something else:      Did you mean to say "observable universe" ?

New particles enter the observable universe as time progresses, so they bring angular momentum in with them.   The system doesn't seem suitably closed.

Best Wishes.

[alancalverd]

This surely allows us to explore the "unobservable" parts of the universe - a powerful insight - or predict the future of the observable universe.

If angular momentum is conserved then the net change in am of the observable universe with time tells us something about the source of said new particles - at least how its am is changing.

If am is not conserved, then the observable universe will either explode as the increase in am drives orbiting bodies further apart, or collapse as gravity overpowers a reducing am.

[Eternal Student]

Hi,

   What are you talking about @alancalverd ?   

....If am (angular momentum) is not conserved, then the observable universe will either explode as the increase in am drives orbiting bodies further apart, or collapse as gravity overpowers a reducing am...

    The notion of the observable universe coming apart doesn't actually seem all that unlikely.  We do think the universe is expanding, distances between galaxies are generally increasing and this rate of expansion seems to be accelerating.

Best Wishes.

[alancalverd]

Newtonian mechanics. If you increase the angular momentum ∑mr²ω of an assembly, it either gets heavier, spins faster, or gets wider.

[Bored chemist]

It's a pretty basic form of gravimeter, but an even simpler one just* uses a helical spring and a weight.

http://www.cleonis.nl/physics/phys256/eotvos.php  discusses some interesting experiments where a gravimeter in an airship flying east to west measured a different value from one flying west-east, the difference being due to the difference in centrifugal force.


*physicist's shorthand for hundreds of hours in an instrumentmaker's workshop.

This seems to have somewhat distracted people from answering my question.
Am I right in thinking that I can tell if the planet I'm on, alone in the universe is rotating?

[paul cotter]

The simple answer seems to be that if it is a single axis rotation then it should be possible. Generally rotation is specified in relation to some other object- does rotation have a valid meaning if there is nothing else in our imagined infinite empty universe to reference this rotation against?

[geordief]

The simple answer seems to be that if it is a single axis rotation then it should be possible. Generally rotation is specified in relation to some other object- does rotation have a valid meaning if there is nothing else in our imagined infinite empty universe to reference this rotation against?

If  it was the only object then wouldn't  it comprise  all there was ?
In the same way that  we cannot view our "present universe" from an outsider's viewpoint then perhaps the observer of this object would have to also be an integral part of it

If the object had a structure the observer would be somewhere in that structure and (I think)  be able to judge  whether the object was rotating by making observations of different regions of the object.

[alancalverd]

Am I right in thinking that I can tell if the planet I'm on, alone in the universe is rotating?

Certainly, if you know it is a homogeneous sphere, by using gravimetry.

[Bored chemist]

Did I misunderstand this?

Hi.

....in the total absence of external reference points would it be possible to tell if one was rotating or not?...

     Basically, no, it shouldn't be possible to know.   

[Eternal Student]

Hi  @Bored chemist ,

    Your earlier post  (post #16)  implied that you weren't considering any effects from relativity.

Not some strange relativistic thing, ......

    I think everyone then assumed that you wished only Newtonian mechanics and a corresponding notion of spacetime as Newton's spacetime to apply.
    In that situation,  the usual  mechanics holds and the equation describing the time period of pendulum,  T = 2π √(L/g) , will apply.    So an appropriate answer to your question would be "yes",  you could determine a planet was spinning by taking your pendulum clock to different places on the planet.   As @alancalverd suggested,  an even simpler "gravity meter" could be used.   

      Post #8 which you recently quoted describes the situation that is, in my opinion, actually more likely.   Specifically, the universe is under no obligation to comply with Newtonian mechanics and Newton's notion of spacetime.    Newton is a good approximation quite often but when your planet is the only thing in the universe,  then it ceases to be a good model of the situation.    Relativity, especially the theory of General Relativity, suggests that spacetime would be very different.   In particular, "frame dragging" effects should occur so that it would no longer be possible to determine if the planet was rotating.    To use your specific method of identifying planetary rotation:   A pendulum clock could be put anywhere on the surface of the planet and it would still have the same time period  (e.g.  T = 1 second).  It won't have a longer period somewhere (like at a place you would describe as the pole of the planet) and a shorter time period at the equator.   It would be as if the planet wasn't rotating.    This would happen even if we started from a standard universe in which we knew the planet was rotating and tried not to touch or adjust the motion of that planet at all but instead just deleted everything else around it.  Under GR, spacetime is NOT a static background.   Spacetime changes and reacts to any material in it and it isn't just the property of "mass" and its location that is important.   The motion (or momentum) of things is also important,  spacetime reacts to momentum within it and more generally to what could be called "stress-energy-momentum" to imply all the assorted things that are important and spacetime will react to.   Also the motion of matter must change and react to the nature of the spacetime.   Spacetime is poetically described as being an actor on the stage in its own right rather than just merely being the static background of the stage with lumps of matter being the actors that move around on it.

     Under Newtonian notions, spacetime is just a static background and the planet would still have been rotating in that standard static background even if we did delete everything else around it.  In particular a pendulum clock would still have had different time periods when you took it to different places on the surface of that planet.

    I hope that makes some sense.

Best Wishes.

[alancalverd]

This argument implies that the existence of centrifugal force depends on the proximity of other objects, since it disappears in an otherwise vacant universe. It would be interesting to calculate the magnitude of the effect and compare it with a simple experiment in which we send a Watt governor https://extrudesign.com/wp-content/uploads/2019/09/Governor-in-Engine-extrudesign.com-002.jpg or similar mechanism into deep space and measure the centrifugal force as a function of rotational speed as departs from the solar system.

Frame dragging surely applies to any moving object, so a further implication is that if we start an object spinning and gradually remove all other objects from its vicinity, it will gradually lose its unique poles. It seems counterintuitive that uniqueness (a mathematical concept) is dependent on the proximity (physics) of anything, and is in fact a continuous function rather than a discrete property.

But surely the whole business of relativity depends on there being at least two objects in the universe, else what is anything relative to?