Gravity adding energy in an isolated system?

In summary: The potential energy is U=-GMm/R where G is the gravitational constant and m is the mass of the object. The potential energy is always positive, but the actual gravitational force is negative.
  • #1
04qWIGk3
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Disclaimer: I am not a physicist and this was just some random question that popped into my head.

According to the law of conservation of energy, energy cannot be destroyed or created. So the energy in our current universe is the same as it was right after the big bang right?

But can't gravity add more energy in a universe thru potential/kinetic energy?

Another way of looking at this: imaging an isolated universe with two grains of sand. Each grain of sand has 100% same amount of atoms, neither of them has any movement speed in any way. Yet each is separated by a distance that it would take gravity a millennium to move them to the point where they eventually orbit each other. If you were to then examine this universe a millennium after its creation, it would appear that it would now have more energy than when it was created.
 
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  • #2
04qWIGk3 said:
But can't gravity add more energy in a universe thru potential/kinetic energy?
No. The total energy would be the same, you'd just be exchanging potential energy for kinetic.

Another way of looking at this: imaging an isolated universe with two grains of sand. Each grain of sand has 100% same amount of atoms, neither of them has any movement speed in any way.
But they have gravitational potential energy.

Yet each is separated by a distance that it would take gravity a millennium to move them to the point where they eventually orbit each other. If you were to then examine this universe a millennium after its creation, it would appear that it would now have more energy than when it was created.
The gravitational PE they had initially would have been changed to kinetic energy.
 
  • #3
Doc Al said:
No. The total energy would be the same, you'd just be exchanging potential energy for kinetic.

The total energy of the universe is not conserved because the metric isn't static (and the dynamic effects due to the geometry of the metric are what we collectively call 'gravity'). With space expanding, there is new vacuum energy (or whatever the cosmological constant is) being created, and the total energy of the universe is increasing with (comoving) time.
 
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  • #4
LastOneStanding said:
The total energy of the universe is not conserved because the metric isn't static (and the dynamic effects due to the geometry of the metric are what we collectively call 'gravity'). With space expanding, there is new vacuum energy (or whatever the cosmological constant is) being created, and the total energy of the universe is increasing with time.
Good point, but I suspect that's a bit too much for this thread. (But good to be accurate, nonetheless.) I was just responding to his toy "universe" and the idea that two particles approaching one another somehow create energy.
 
  • #5
Doc Al said:
Good point, but I suspect that's a bit too much for this thread. (But good to be accurate, nonetheless.) I was just responding to his toy "universe" and the idea that two particles approaching one another somehow create energy.

Fair enough, though part of the question was, "So the energy in our current universe is the same as it was right after the big bang right?" The answer for the hypothetical toy universe would be 'yes', as you described, but it's 'no' for our universe. Just not for the reasons he/she suggested.
 
  • #6
In the Newtonian picture, the potential energy is
[itex]U=-GMm/R[/itex]
M and m are two masses. When the masses get closer together, the potential energy decreases and the kinetic energy increases by exactly the same amount. The center of mass and momentum also stay the same; you can use that fact to figure how the kinetic energy is portioned out.

In general relativity, I don't think people know how to calculate gravitational potential energy, but I may be wrong.
 
  • #7
LastOneStanding said:
The total energy of the universe is not conserved because the metric isn't static (and the dynamic effects due to the geometry of the metric are what we collectively call 'gravity'). With space expanding, there is new vacuum energy (or whatever the cosmological constant is) being created, and the total energy of the universe is increasing with (comoving) time.
Actually, if we're going to be pedantic, there is no meaningful notion of total energy for a non-asymptotically flat space-time. Komar energy exists for any stationary asymptotically flat space-time (not necessarily static) and Bondi energy / ADM energy-momentum exist for non-stationary asymptotically flat space-times but you still need to have asymptotic flatness. The FRW metric is not asymptotically flat in general so the very notion of total energy is an ill-fated one.
 
  • #8
Khashishi said:
In general relativity, I don't think people know how to calculate gravitational potential energy, but I may be wrong.
There is a general relativistic analogue of the Newtonian potential for stationary space-times.
 

Related to Gravity adding energy in an isolated system?

1. How does gravity add energy in an isolated system?

In an isolated system, the total energy is conserved, which means it cannot be created or destroyed. However, gravity can transfer energy within the system by converting potential energy into kinetic energy.

2. Why is gravity considered a conservative force in an isolated system?

A conservative force is one that does not dissipate energy, and gravity fits this description in an isolated system. The work done by gravity is independent of the path taken, and the total energy of the system remains constant.

3. Can gravity add energy to a system without any external force?

Yes, in an isolated system, gravity can add energy without any external force acting on it. This is because the potential energy of an object in a gravitational field can be converted into kinetic energy without any external work being done on the object.

4. How does the strength of gravity affect the amount of energy added to the system?

The strength of gravity directly affects the amount of energy added to a system. The stronger the gravitational force, the more potential energy an object has, and thus, more energy can be converted into kinetic energy.

5. What happens to the energy added by gravity in an isolated system?

The energy added by gravity in an isolated system remains within the system. It can be transferred between objects or converted into different forms, but the total energy of the system will remain constant due to the conservation of energy principle.

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