The discussion revolves around the concept of energy conservation in the context of an expanding universe. Participants explore how gravitational potential energy behaves as space expands and the implications of dark energy on this conservation principle. The conversation touches on theoretical aspects, conceptual clarifications, and challenges related to energy definitions in general relativity.
Participants express differing views on the nature of energy conservation in an expanding universe, with no consensus reached on how these principles apply universally or locally. The discussion remains unresolved regarding the implications of dark energy and the definitions of potential energy in general relativity.
Limitations include the dependence on definitions of energy in curved space-time and the unresolved nature of energy conservation on cosmological scales versus local scales.
Well, energy conservation isn't terribly simple in curved space-time. If you want a good, fairly in-depth description of what's going on here, take a look at this:kasperm said:How is energy conserved in an expanding universe? As space expands between, say, stars in a galaxy, don't they gain potential energy in the gravitational field of the galaxy? Which mechanism lessens the total kinetic energy?
Not quite. Normal matter does this because it is largely pressureless. But any matter that experiences pressure (such as photons) loses energy per comoving volume.Chronos said:I'm with you edpell. IMO, the energy content of the universe is essentially fixed [save for dark energy]. Expansion merely dilutes it.
Well, there are a couple of different issues here. First, if the two are in orbit around one another, they won't be affected at all by the expansion. If the two are far away, and there is no dark energy, then they will simply coast along away from one another, slowing down the entire way. It's only with the existence of dark energy that things start to get a little weird.kasperm said:Im sorry, my question might have been a bit unclear.
Consider this: Two stars a unit distance apart has a well defined potential energy in their gravitational field, or equivalently, a well defined amount of work needs to be done against the field to move each of them from the center of mass out to their respective positions. If we wait a given amount of time and measure their distance once again, it will have increased due to the expansion of the universe so the amount of work need to move them from CoM to their new positions has increased proportionally.
Well, bear in mind that this statement is only true for a closed universe.yogi said:Ed Tryon was probably the first to advance the idea that the total energy of the universe is always zero - specifically the potential gravitational energy at all times is balanced by the expansion energy. Within the Hubble sphere, equating the 1/2 mv^2 energy of each shell of the expansion using Hubble's law to the potential results in a required matter content equal the critical density of an Einstein - de Sitter universe
Chalnoth said:the fundamental flaw with your analysis is that the potential energy is not well-defined in General Relativity.
Well, locally, any space-time is flat. In flat space-time, energy is conserved.kasperm said:This makes sense. So this is why people say energy is conserved on a local scale but not on large scales?