Energy & Gravity: Newton & Relativity Explained

[Leonardo Muzzi]

I'm an physics fan and while reading about gravity in general relativity I came to this:

It seems to me that both Newtonian gravity and general relativity gravity have an "energy" problem. Using Earth as an example for simplicity: In Newtonian gravity, the Earth applies a force on objects on its surroundings, accelerating them down. On general relativity, the Earth applies a force upward on the objects in its surface, accelerating them up and preventing them to follow their geodesic paths.

In both cases, where does the energy for the forces comes from? In my classical way of thinking, any force would require a source of energy. If Earth is accelerating everything (up or down), it seems to me that it should be using some kind of energy as a source to create a force on the objects.

 

[Matterwave]

An energy is not necessarily associated with a force, but it is associated with a force if the force is applied over a distance (that would be the work done). In Newtonian gravity, the "energy" imparted to an object which is accelerating downwards towards the ground comes from the gravitational potential energy the object had due to its relation to the Earth. If you ask "where does the gravitational potential energy come from?" then one can only say that the energy came from whatever process arose which gave this object its original configuration with regards to the Earth. So if I raise a ball up from the ground and drop it, then I am responsible for putting the gravitational potential energy into the ball when I raised it up from the ground. In Newtonian gravity, this is very simple and should not be a source of confusion. It is exactly analogous to the Coulomb interaction except there's only one charge and all charges attract each other.

In General Relativity, the question of "gravitational potential energy" is much more subtle. It is not a very well defined concept in GR. That's about all I have to say about this matter here...as I don't really want to write a wall of text talking about "gravitational potential energy" in GR. I would probably not be able to give a very clear and concise explanation. Perhaps someone more erudite than me can provide it. :)

 

[Leonardo Muzzi]

You're right, for Newtonian gravity is very clear, actually even obvious! Thanks! :)

So for GR I'm still confused. Thinking more about it, if the Earth is actually accelerating everything out of their paths, then there is a force applied over a distance and energy involved. So it would seem to be that Earth is actually spending energy all the time, and them this energy spending process would eventually consume the planet. As it obviously doesn't seem the reality, where is the "magic"?

 

[andresB]

On general relativity, the Earth applies a force upward on the objects in its surface, accelerating them up and preventing them to follow their geodesic paths.

Not a GR expert, but a body moving in a gravitational field does follow the geodesic path, in this case the Earth is saying what paths are the geodesic ones and the bodies (ignoring any other forces) follow it.

 

[wabbit]

Not a GR expert, but a body moving in a gravitational field does follow the geodesic path, in this case the Earth is saying what paths are the geodesic ones and the bodies (ignoring any other forces) follow it.

Not quite, here - maybe a geodesic of an effective metric incorporating other effects, but not a spacetime geodesic, which would be (for instance) free fall towards the center of the earth. I would say this is prevented by the repulsion between atoms which prevents a body from passing through another one.

 

[Finny]

Light, which is massless, IS affected by gravity or 'gravitational lensing'. In fact, nothing escapes the touch of gravity, not even time, which varies with gravitational potential yet has no imbalance of atomic structure.

The "amount of gravity produced" by an object is a function of its stress-energy tensor, of which energy is only one component. Pressure and temperature are also sources.

Massless light gains energy when moving to a higher [less negative] gravitational potential and loses energy the other way. It gives up potential energy to gain kinetic energy. This is referred to as 'redshift' and blue shift respectively...but the speed of light, locally, remains 'c'...it is it's color [frequency] that changes.

Ultimately, all the masses [particles] and forces [strong, weak, electromagnetic] and gravity, the curvature of space time, originated from the big bang. Likewise 'energy' forms although that gets complicated in general relativity. So an initially high energy, unstable state without structure led to the structure of matter, forces, energies, gravity and cosmological evolution we observe.

 

[Dale]

So for GR I'm still confused. Thinking more about it, if the Earth is actually accelerating everything out of their paths, then there is a force applied over a distance and energy involved. So it would seem to be that Earth is actually spending energy all the time, and them this energy spending process would eventually consume the planet. As it obviously doesn't seem the reality, where is the "magic"?

Energy in GR is more complicated than in Newtonian mechanics. Here is my favorite introduction to the topic.
http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html