# Curl added to the spacetime metric.

1. Dec 13, 2008

### David S.W

Hello!

I was thinking the other day, of the earth's rotation around its axis.
If one spins a boiled egg, it maintains spin longer than does an unboiled. Eventually both stops because of the friction against the floor, but not at the same time.

The earth has different levels of viscosity and is exposed to alot of internal friction, just like the unboiled egg. Well the egg seems to violate the principle of conservation of angular momentum. So why don't the egg act like the earth?

I looked into it and found out that the conservation of angular momentum only applies to angular momentum of what's
referred to as an isolated system; this is what's said about an isolated system:

"An isolated system implies a collection of matter which does not interact with the rest of the universe at all - and as far as we know there are really no such systems. There is no shield against gravity, and the electromagnetic force is infinite in range. But in order to focus on basic principles, it is useful to postulate such a system to clarify the nature of physical laws. In particular, the conservation laws can be presumed to be exact when referring to an isolated system"

http://hyperphysics.phy-astr.gsu.edu/Hbase/conser.html#isosys

After reading this my question changed to: What keeps the earth spinning?

Seems like it depends on whether or not you attach the point of reference to the rotating metric, when doing calculations. If you attach the point of reference to the rotating metric, which we do(it's a flexible way to get rid of things like torque and coriolis force etc.) the friction becomes really nasty to deal with.

I then came across an interesting solution to this. What it did was basically that it addressed the nature of torque and the Coriolis forces as dynamic properties of the spacetime metric and the stress-energy tensor, detaching the frame of reference from the rotating metric. Making the spacetime not only curve, but curl.
Any thoughts or corrections to this idea? I found it quite interesting.
I'm not sure I posted this in the right place, bare with a fragile newcomer in case i didn't.

Last edited: Dec 13, 2008
2. Dec 14, 2008

### tiny-tim

Welcome to PF!

Hello David! Welcome to PF!
The Earth keeps spinning because of conservation of angular momentum and energy … it will keep the same motion unless there is something to alter it.

Internal "eggy" forces, such as friction, ought not to change the angular momentum.

However, gravitational interaction with the Moon (and other bodies) does have tidal effects which dissipate energy, and help to exchange angular momentum.

3. Dec 14, 2008

### David S.W

Well, the conservation of angular momentum only applies to the angular momentum of an isolated system, which as far as we know doesn't exist. As soon as you have two particles in the universe, it's not an isolated system anymore.

Thanks for your warm welcoming btw. :)

Last edited: Dec 14, 2008
4. Dec 14, 2008

Staff Emeritus
That's not true. Angular momentum is always conserved. It's a constant (note the difference) unless acted on by an external torque, and the change is proportional to the torque applied.

If we could always dismiss the conservation of angular momentum the way you suggest, why would we bother teaching it?

5. Dec 14, 2008

### Crazy Tosser

Angular momentum is an old concept from classical mechanics, back when people didn't know that mater was composed of atoms, and I don't even know why teachers bother to teach it.

There is only linear momentum. When an object spins, all it's molecules have linear momentum (tangent to the circle around the point of rotation), but because of chemical bonds, fluid pressure, or etc. they are always accelerated towards the center ( a more or less rigid object will tend to maintain it's shape). That creates rotation - it always changes linear momentum of all molecules, which makes the molecules travel in circles, but it doesn't mean that the momentum stops being linear...

6. Dec 14, 2008

### tiny-tim

Emmy Noether

I blame Emmy Noether

she proved that every geometrical symmetry has an associated physical current …

translation symmetry gives us linear momentum,

and rotational symmetry gives us angular momentum.

'nuff said?