Curl added to the spacetime metric.

In summary, the conversation discusses the concept of conservation of angular momentum and how it applies to the Earth's rotation. It is noted that the Earth is not an isolated system and thus other factors, such as gravitational interactions with the Moon, can affect its rotation. The conversation also touches on the history and relevance of the concept of angular momentum in classical mechanics.
  • #1
David S.W
2
0
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 a lot 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.
 
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  • #2
Welcome to PF!

Hello David! Welcome to PF! :smile:
David S.W said:
"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"
…
After reading this my question changed to: What keeps the Earth spinning?

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. :smile:
 
  • #3
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. :)
 
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  • #4
David S.W said:
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.

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
Vanadium 50 said:
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?

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
Emmy Noether

Crazy Tosser said:
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.

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? :smile:
 

1. What is curl added to the spacetime metric?

Curl added to the spacetime metric is a mathematical concept used in physics to describe the curvature of spacetime. It is a measure of how much the direction and magnitude of a vector field changes over a given region of space.

2. How does curl affect the properties of spacetime?

Curl plays a crucial role in Einstein's theory of general relativity, which describes how mass and energy affect the curvature of spacetime. The presence of curl in the spacetime metric indicates the presence of gravitational fields and how they can affect the motion of objects in space.

3. What are the implications of adding curl to the spacetime metric?

The inclusion of curl in the spacetime metric has significant implications for understanding the behavior of objects in the presence of gravity. It allows us to better describe and predict the motion of objects in space, as well as understand the effects of massive objects on the fabric of spacetime.

4. How is curl added to the spacetime metric calculated?

The calculation of curl added to the spacetime metric involves using mathematical equations known as tensor calculus. These equations take into account the components of the metric tensor, which describe the curvature of spacetime, and how they change over space.

5. What are some real-world applications of understanding curl added to the spacetime metric?

Understanding curl added to the spacetime metric has many practical applications in the field of astrophysics and cosmology. It allows us to accurately predict the motion of objects in space, such as planets, stars, and galaxies. It also helps us understand the behavior of black holes and the expansion of the universe.

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