Expansion and Conservation of Energy

[mrspeedybob]

Suppose two massive bodies are far enough apart that the expansion of space precisely counteracts their gravitational attraction. While in this configuration a tether is strung between them, tied off to body A and wound around a pulley on body B. One of the bodies is then nudged so that the distance between them increases. At this point the expansion of space is greater then the force of gravity and so the two bodies move apart. As they do so the tether unwinds from the pulley on body B and turns a generator. This action would obviously slow the rate at which the bodies diverge but the point is that energy is being extracted from the expansion of space. Where does this energy come from? Is it possible that the energy source which gave rise to the big bang is still adding energy to our universe?

 

[mysearch]

Hi,
I am not qualified to answer your questions, but have added a couple of comments below for what they are worth. However, I would also be interested in any additional comments as to current thinking in mainstream cosmology

Where does this energy come from?
Is it possible that the energy source which gave rise to the big bang is still adding energy to our universe?

I guess this might depend on whether the universe is considered to be a closed or open energy system. If it is a closed system, then I assume you need to consider whether the universe started off with some a fixed amount of energy or whether it had a net zero amount energy, i.e. positive + negative = zero. Alternatively, quantum theory may point to the possibility of a reservoir of vacuum energy that is not normally taken into account, but can be tapped. However, if the universe were part of some larger system, i.e. open, then it would seem possible that our ‘local’ universe might acquire or lose energy to this larger system.

The assumed inflation process is said to have expanded the universe from the Planck scale to ~10-20cm in a fraction of the first second of existence and, as far as I understand it, what drove this process then went through some sort of phase transition. Based on the subsequent LCDM energy-density model, dark energy is assumed to remain constant throughout the subsequent expansion of the universe, but was initially negligible, i.e. ~0%, in comparison to radiation and matter (both normal and dark). However, the constancy of the energy density of dark energy means that it is now assumed to account for ~73% of the total critical energy density. Again, as far as I understand the details, the LCDM model would then imply a 2.7 fold increase in the total energy density of the universe over the last 13.7 billion years.

Apologises if these comments are tangential to the questions you were trying to raise.

 

[Ich]

Is it possible that the energy source which gave rise to the big bang is still adding energy to our universe?

Maybe. The energy you're using is Dark Energy, and it may be a similar thing to what drove inflation, which gave the initial "kick" for all matter in the universe.
Defining the energy content of the whole universe is quite difficult and to some extent arbitrary. What matters is that, in the presence of Dark Energy, there is a "force" trying to push things apart, and that one could use that force like any other force to create usable energy.

 

[Tanelorn]

Perhaps dark energy and the expansion of space is simply warped space time correcting itself like a coiled spring, caused by the total mass and energy of the universe from the moment of the big bang and high density right up until the distant future when space time has reached its normal flat state again? Also wouldn't galaxies tend to continue moving away from each other due to conservation of momentum?

 

[Amanheis]

Energy in GR is simply not conserved in the sense that we are used to. You might have found an example for how to gain energy.

On the other hand, you could use a battery to shoot a laser beam on a mirror that is a couple mega parsecs away, then use the returning light and the photoelectric effect to recharge the battery. Because of redshifting, even with a perfect laser, mirror, battery and solar cell, the energy stored in the battery will be less after the whole procedure.

Hence, you just destroyed energy. Or did I miss something besides the absurd experimental requirements that are necessary for this?

 

[zonde]

Hence, you just destroyed energy. Or did I miss something besides the absurd experimental requirements that are necessary for this?

It seems so. Only you should say you lost energy not destroyed.

Extending it a bit further if this lost energy somehow affects expansion (either contributes to it or opposes it) then it might change things a bit in places where there is high density of radiation (near hot radiating matter) i.e. it might change expansion rate.
That would change gravitation gradient as additional gravity or as "anti-gravity".

 

[Ich]

Hence, you just destroyed energy.

It depends. If you choose a static coordinate system - which is always possible nowadays in a region of megaparsecs -, the "lost" energy is added to the kinetic energy of the reflector.
If you choose comoving, (i.e. expanding, non-stationary) coordinates instead, where you claim that the reflector is "at rest" somehow, the energy is lost. Non-conservation of energy is a general feature of non-stationary coordinate systems, they come hand in hand due to the Noether theorems.

 

[Deuterium2H]

As Ich explained in his previous post, energy is not conserved in an expanding Universe. Using comoving coordinate methodolgy, one can think of the Universe being partitioned into cells, or the "cosmic box". As each comoving box expands, particles contined within any partitioned cosmic box lose momentum, and radiation loses energy (becomes red-shifted).

The progressive loss of energy in any given cell (box) is not gained by any adjacent cell (box) because they are also expanding. The pressure inside the cells (caused by the collision of particles on the cells walls as well as radiation pressure) work against one another, and energy is lost everywhere in all cells, and does not reapper to do work.

Conservation of energy and momentum only holds in bound (local) regions which do not expand with the Universe (e.g. planets, solar systems, galaxies, gravitationally bound galaxy clusters).

So if energy is not conserved in an expanding Universe, then where does it go? At the risk of sounding like a tautology, the simple answer is that the energy goes nowhere, because in an expanding Universe energy is not conserved.

 

[mysearch]

Using comoving coordinate methodolgy, one can think of the Universe being partitioned into cells, or the "cosmic box”.
.
.
So if energy is not conserved in an expanding Universe, then where does it go?

If we sized the ‘cosmic box’ to be 1 cubic metre, then the energy-density within this box would fall as a function of the expansion of the universe with time. As such, we might well ask: where the energy went?

However, if we count the number of cosmic boxes in an expanding universe, I would assume that the number (N) would increase. If we now multiply the current energy-density in the cosmic box by (N), would the ‘total’ energy have increased over time? If so, might we actually have to ask: where is the energy is coming from?

 

[zonde]

It depends. If you choose a static coordinate system - which is always possible nowadays in a region of megaparsecs -, the "lost" energy is added to the kinetic energy of the reflector.

I wanted to ask if I understood this right.
If we can approximate the case so that it fits SR then it seems quite simple to me. Redshift is due to Doppler effect and returning beam is redshifted twice because it reflected from moving reflector. And if we observe spherical (in it's own restframe) light source there will be drop in expected luminosity because of effect that Lorentz transformation will create when transforming from source's restframe to observer's restframe.
Is this along the lines with what you said?

If that is so then "lost" energy is due to difference in radiation pressure as viewed from different reference frames.

 

[Ich]

Is this along the lines with what you said?

Yes. You don't even need SR in many cases, Newton is enough.

If that is so then "lost" energy is due to difference in radiation pressure as viewed from different reference frames.

Yes (not radiation pressure, but photon energy).
There's a http://www.scientificamerican.com/article.cfm?id=is-the-universe-leaking-energy", where T. Davis for once gave an accurate description, IIRC.