Gravity adding energy in an isolated system?

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Discussion Overview

The discussion revolves around the concept of energy conservation in the context of gravity within an isolated system. Participants explore whether gravity can add energy through potential and kinetic energy transformations, particularly in hypothetical scenarios involving two masses. The conversation touches on both Newtonian and general relativistic perspectives.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants propose that while gravitational potential energy exists, the total energy remains constant as it merely transforms between potential and kinetic forms.
  • Others argue that in an expanding universe, the total energy is not conserved due to the dynamic nature of spacetime, suggesting that new vacuum energy is created over time.
  • A later reply questions the meaningfulness of total energy in non-asymptotically flat spacetimes, indicating complexities in defining energy in general relativity.
  • Participants discuss the Newtonian formula for gravitational potential energy and its implications for energy transformations as masses approach each other.
  • There is mention of a general relativistic analogue to Newtonian potential, though uncertainty remains about the calculation of gravitational potential energy in general relativity.

Areas of Agreement / Disagreement

Participants generally disagree on the conservation of total energy in the universe, with some asserting it is conserved in isolated systems while others contend that it is not due to the effects of spacetime dynamics. The discussion remains unresolved with multiple competing views present.

Contextual Notes

Limitations include the dependence on definitions of energy in different frameworks (Newtonian vs. general relativity) and the unresolved nature of energy conservation in non-asymptotically flat spacetimes.

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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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.
 
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.
 
Last edited:
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.
 
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.
 
In the Newtonian picture, the potential energy is
U=-GMm/R
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.
 
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.
 
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.
 

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