B Expanding Universe: How Does It Conserve Energy?

[sqljunkey]

I read somewhere that expanding universes create more energy as they expand, and I was thinking over time there would be a considerable amount of energy created due to this expansion. Even with a very small cosmological constant the energies created over time would probably dwarf anything that existed before in orders of magnitude. I was wondering how does the universe deal with all this additional new energy, is there a way it dissipates? How can this model have an equilibrium?

 

[PeroK]

Try:
https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

 

[sqljunkey]

I have not tried it yet but I am assuming if I even take a simple two body Newtonian problem, and expand the space between the bodies ever so slightly over time the two orbiting bodies would just fly off in different directions. So I don't see how saying that "the density of vacuum energy in empty space is absolute constant" somehow brings back the equilibrium in the system.

 

[PeroK]

I have not tried it yet but I am assuming if I even take a simple two body Newtonian problem, and expand the space between the bodies ever so slightly over time the two orbiting bodies would just fly off in different directions. So I don't see how saying that "the density of vacuum energy in empty space is absolute constant" somehow brings back the equilibrium in the system.

You assume a solution that is not supported by the theory or the mathematics. That puts you in the difficult position of having assumed a conclusion with no theoretical, mathematical or empiral support.

What's the question?

 

[sqljunkey]

Well I thought about this, and rather than coming up with complicated math to explain my assumption I'll just quote wikipedia. "This can be seen when observing distant galaxies more than the Hubble radius away from us (approximately 4.5 gigaparsecs or 14.7 billion light-years); these galaxies have a recession speed that is faster than the speed of light. " Which essentially is saying that two bodies that should be attracting each other are moving away at very fast speeds.

My question was how can an expanding universe be in equilibrium. But I am starting to see that it is not. I don't know how all of this works microscopically.

 

[Orodruin]

My question was how can an expanding universe be in equilibrium.

What makes you think the Universe is in some sort of equilibrium state?

 

[sqljunkey]

@Orodruin well at the scale of galaxies and solar systems, it does seem that it is in equilibrium. This led me to believe that the rest of the universe, even when in expansion, is in equilibrium. I thought that somehow even though the universe is expanding, the forces are canceling each other out by the additional volume created somehow.

But when I try this, over time everything goes out of wack, and it doesn't matter how small I make the cosmological constant. I heard Leonard Suskind say many times that this constant doesn't take effect at small scales only at big scales. But then what if I let a small system evolve over time, wouldn't it become a big system since it's expanding?

 

[Orodruin]

Gravitationally bound systems do not expand.

In general, you should not try to do physics based on words. Physics needs to be done using the actual underlying theories and the math that describe them.

 

[PeterDonis]

I'll just quote wikipedia.

You should not be trying to learn cosmology from Wikipedia. A better source would be a textbook. Sean Carroll, who wrote the blog post linked to earlier (which you should definitely read), has online lecture notes that are a good place to start:

https://arxiv.org/abs/gr-qc/9712019

at the scale of galaxies and solar systems, it does seem that it is in equilibrium

The universe as a whole is not in equilibrium. Gravitationally bound systems like galaxies and solar systems (and stars and planets) are (at least to a good approximation), but they are not the same as the universe as a whole.

expanding universes create more energy as they expand

No, they don't. More precisely, no stress-energy (matter, radiation, anything) is created or destroyed anywhere in spacetime.

Read the Carroll article. It goes into all of this.

if I even take a simple two body Newtonian problem, and expand the space between the bodies ever so slightly over time

You can't. There is no Newtonian model corresponding to the GR model of an expanding universe. Newtonian thinking will only confuse you; it will not help you to understand what the GR model of an expanding universe says.

 

[pervect]

You might also try "Is Energy conserved in General Relativity", http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html.

That's not as good a source as Caroll's textbooks, but it is probably about as good a source as the "preposterous universe" link. Both are written by persons knowledgeable in the field, but both are popularizations with the associated pitfalls.

The basic issue, though, is that an "expanding universe" is not a Newtonian concept, but a concept in General Relativity. So Newtonian theory is not enough to tackle this issue, if all you have is Newtonian theory, you'll wind up somewhere between slightly confused and very confsued. And General Realtivity is basically a graduate level topic - there are some undergraduate level introductiory treatments, but typically a discusssion of energy is not included in introductory treatments.

At the lay level, the most accurate statements tend to be very vague. For instance, from the FAQ I cited:

Is energy conserved in General Realtivity?

In special cases, yes. In general, it depends on what you mean by "energy", and what you mean by "conserved".

The more detailed exposition explains this a bit further, but it may be hard to follow without the right background, and is still rather general.

In flat spacetime (the backdrop for special relativity), you can phrase energy conservation in two ways: as a differential equation, or as an equation involving integrals (gory details below). The two formulations are mathematically equivalent. But when you try to generalize this to curved spacetimes (the arena for general relativity), this equivalence breaks down. The differential form extends with nary a hiccup; not so the integral form.

The preposterous universe article takes a different course:

Energy is not conserved

At first glance this seems to disagree with Baez's article, but they're both simplificaitons/popularizations of the same, complex, theory. The point behind Caroll's statement is that in the most general case, we do not have a conserved notion of energy in General relativity. Historically, this was noticed early on by Hilbert. In another tidbit, rather than tackling the issue himself, Hilbert gave the problem to his assoicaite, Emily Noether, and this resulted in Noether's theorem, which relates symmetries to conservation laws.

 

[sqljunkey]

Ok thanks all, I will read the suggested papers and articles. I just had a problem understanding how this all works in the global universe but not in the micro universe.

I will append this paper, I know it is not a well reputed paper, but in an effort to be complete I append it anyway.

 

[PeterDonis]

I will append this paper,

This paper has nothing to do with the thread topic, so I don't see why you are referencing it.

 

[sqljunkey]

Well that paper talks about dark energy and how there might not be such a thing based on their measurements. We were talking about expanding universes, and cosmological constant. I did not mention dark energy but it was heavily implied.

 

[PAllen]

Well that paper talks about dark energy and how there might not be such a thing based on their measurements. We were talking about expanding universes, and cosmological constant. I did not mention dark energy but it was heavily implied.

But it turns out that presence or absence of dark energy has nothing whatsoever to do with the feature of GR that there is no way to define a large scale total energy, in general, and specifically this is true for all cosmological solutions. If you can’t even define a total energy of a large volume in a consistent way, you can’t even ask about conservation.

 

[PeterDonis]

that paper talks about dark energy and how there might not be such a thing based on their measurements

Which has nothing to do with the topic of this thread.

We were talking about expanding universes, and cosmological constant

Everything we are saying in this thread is true regardless of whether there is a nonzero cosmological constant or not, or what underlies the cosmological constant physically. You keep mentioning the cosmological constant, but that doesn't mean it actually makes any difference to what we're discussing here.

 

[sqljunkey]

ok i will admit that I don't know much about the subject as you probably do. I was just running some simulations on my computer and the universes i kept building kept collapsing. so i tried to expand these universes and instead of getting a smooth well balanced expansion i found that the energies went way high and the thing collapsed anyways, but faster. so i thought i was doing something wrong and i asked here. This is a very difficult subject even einstein had troubles with it. I will read further the articles seem promising.

 

[Orodruin]

I was just running some simulations on my computer

Based on what theory?

 

[sqljunkey]

GR, well my interpretation of it anyways, I asked someone if I could create Rd charts of an Rd manifold instead of Rd-1` charts and whether these charts were a good approximation for the Rd manifold and they said yes, with reservations.And I went ahead and did it. Prolly not very accurate at all since it gave me the wrong results so far

 

[Orodruin]

GR, well my interpretation of it anyways

This begs the question, what is your formal training in GR?

 

[PeterDonis]

I was just running some simulations on my computer

The topic of doing numerical simulations in GR is (1) way beyond the scope of this thread, (2) way beyond the scope of a "B" level discussion, and (3) I strongly suspect way beyond the scope of your knowledge of GR.

If you want to ask about numerical simulations of GR, please start a separate thread, and be advised that it probably needs to be an "A" level thread, since any feedback you would get would probably not be understandable unless you have that level of background knowledge.

Please keep this thread focused on discussion of the specific question you posed in the OP.

 

[haushofer]

After years of high school physics training, you tend to think of energy as something possesed by objects in a fixed spacetime background.

But GR is about dynamical backgrounds by using geometry. Spacetime takes part in the dynamics, hence in the exchange of energy. This creates an ambiguity about what to call "energy" and what to call "geometry".

 

[pervect]

Historically, the problems with energy conservation in General Relativity were noticed early on, in particular by Hilbert and Klein. Hilbert recruited help from Emily Noether, a female mathematician of the time, to help resolve the issue. As an aside, she faced a lot of sexism - the history is not relevant to the point at hand, but quite interesting, though I've only read popularized histories. The fact that Hilbert felt the need to seek some help with the problem should illustrate that it wasn't an easy problem to solve. I would say that Noether's theorem isn't a complete solutoin to the issue of energy in General Relativity, but it's certinainly helpful and relevant.

Let me mention something on a different topic you've raised. Detailed followups and questions would best belong in another, separate thread. Even in Newtonian physics, where the notion of conserved energy is well established, numerical algorithms will in general not conserve it due to round of errors. Symplectic integrators are a well-known workaround for this issue. I won't go into any of the theoretical details here, especially since I might make a hash of it as well as it being off-topic. But you might look at the popularization "Newton's Clock", https://www.amazon.com/dp/0716727242/?tag=pfamazon01-20 for a popularization. Reading up a bit on symplectic integrators would also be useful. If you want to start a PF thread, I'd suggest a separate theread, and it'd probabl fit better in another sub-forum, as it's not a GR issue.

My recollections of what I've read about sympectic integration are that it's often presented in terms of the Hamiltonian formulation of physics, a form that you may or may not be familiar with. Possibly there are other ways to introduce it. It can be used as a tool even if you don't fully understand the Hamiltonian formalism, though.

Symplectic integrators won't cure any issues you may have with false expectations of what GR says and how it works, but it might help you with simulation issues such as having your Newtonian planetary simulators running code to simulate Newtonian gravity "fly apart".