# Dark energy and the first law of thermodynamics

1. Dec 27, 2007

### stevebd1

This has probably been posted elsewhere within the forums but I'm unable to find a thread relating to it. Could some one explain how the existence (and the expected eventual increase) of dark energy doesn't violate the first law of thermodynamics?

regards
Steve

Last edited: Dec 27, 2007
2. Dec 28, 2007

### stevebd1

I did some research regarding the above-

The very nature of the first law of thermodynamics is what gives dark energy it's peculiar anti-gravity quality. Dark energy has negative pressure. In Einstein's law of gravity, the sign of the gravitational force is determined by the algebraic combination of the total energy density plus three times the pressure. If the pressure of the material is negative and big enough, it can cancel out the energy density, nullifying gravity.

If the pressure is negative and bigger still, then the 'sign' of the gravity-generating term in Einstein's equation actually reverses, and instead of gravity attracting, it repels. This negative gravitational energy exactly cancels out the positive energy represented by the matter introduced. The total energy of the universe remains zero.

Any feedback or indication that I'm on the right track is welcome.

regards
Steve

Last edited: Dec 28, 2007
3. Dec 28, 2007

### Garth

You are on the right track stevebd1.

The critical value for DE negative pressure to make gravitation repulsive is
$$p < - \frac13 \rho$$

where p and $\rho$ are the total pressure and density of the source of the gravitational field.

In cosmology, with an equation of state of DE $p = - \rho$, and where DE is thought to comprise 73% of the density of the universe in the present epoch, the universe accelerates in its expansion in this epoch, rather than decelerates.

However it is a little problematic to conclude that
For one thing there is not a clear definition of the total energy of the universe, however it makes more sense to interpret the data by saying the universe is flat, $\Omega$ = 1.

Garth

Last edited: Dec 29, 2007
4. Dec 28, 2007

### stevebd1

Thanks for your response Garth. I still have an issue with the fact that dark energy appears to be 'created' which seems to be in direct violation of the first law of thermodynamics (basically energy cannot be created or destoyed). The idea of the negative pressure of dark energy cancelling out the positive energy of the matter made sense to me.

On a side note, I would be interested to know how virtual particles fit into all of this. As space expands, it is believed that particle/antiparticle pairs are pulled into existence, annihilating each other and disappearing, contributing to the vacuum energy. Again, how is this possible without violating the first law? The other option is to consider the fact that the universe is not a closed system.

Any info or links to other threads relating to this subject would be welcome.

Steve

Last edited: Dec 28, 2007
5. Dec 29, 2007

### stevebd1

In reference to my second post, would it be less problematic to state 'The anti-gravity induced by the negative pressure of dark energy exactly cancels out the positive energy represented by the matter introduced, meaning DE complies with the principle of the first law' or is there just too little known about dark energy to make this sort of claim.

Steve

6. Dec 29, 2007

### Garth

I think too little is known about 'energy' to make this sort of claim, or rather about how the first law applies to the universe as a whole.

GR does not conserve energy, it conserves energy-momentum, which is different.

To measure energy, in order to say whether it is conserved or not, you have to specify in which frame it is to be measured. GR subsumes the SR principle of 'no preferred frames, so there is no one definite definition of energy even in the case of a spherically symmetric gravitating mass.

Having said that the presence of matter in the universe makes it possible to define a cosmological frame of reference that co-moves with the Hubble expansion and in which the CMB is globally isotropic.

Energy is a content of the RHS of the Einstein field equation:

$$R_{\mu \nu} - \frac{1}{2}g_{\mu \nu}R + \Lambda g_{\mu \nu} = \frac{8 \pi G}{c^4} T_{\mu \nu}$$

The LHS describes the curvature of space-time, the RHS describes the distribution of stress, mass and energy that cause that space-time curvature. ('Matter' tells space-time how to curve, curved space-time tells 'matter' how to move)

The gravitational field is described by the LHS; so what about gravitational potential energy, where is that to be accounted for? On the RHS or the LHS?

If there is a Killing vector then energy is conserved, such as when a falling stone is observed from a static gravitating spherically symmetric body - such as the Earth, but when it is the other way round and the Earth is observed from a freely falling laboratory acting as a test particle then energy is not conserved! Remember there are no gravitational forces in GR, because gravitation is the effect of space-time curvature, yet the Earth appears to increase in speed and therefore kinetic energy as observed from that freely falling laboratory.

Suffice it to say that the question of the total energy of the whole universe is a problematic concept so the First Law probably should not be assumed to apply.

As I said the equivalent cosmological statement would be to say the universe is spatially flat $\Omega_{total} = 1$, but of course it might not be.

Garth

Last edited: Dec 29, 2007
7. Dec 31, 2007

### Electrolight

Dear Sirs, Nice to read both of yours conversation, extremely interesting, well i am a mechanical engineer so well i am not that much understanding you both, but whatever i am understanding is very beautiful, but dear sirs, u brought here into the discussion the First law of thermodynamics. So well just talking at the very basic level of the science and physics that i know, the law of conseravation of energy states that the energy cannot be created nor destroyed, so i was just thinking that look when we say that the universe came into being from a size of proton and now expanding, well i would here like to know your comments here on my point that look THE BIG BANG is not just an explosion, IT WAS A BANG, and there were the things flying around and at the same time generation of energy (which later is appaering to us in the form of the dark energy as u say), also there was the generation of matter, cause if it would only be the expansion as we normally say the small photon would just vanish out into whole space it was contained into. so i am having multi-dimensional questions here randomly connected to each other, cause in my opinion for any event to take place there should be some space provided to it. so i think that space was already there, secondly the proton breaks up, crushed into pieces, and at the same time there was creation, NOT ONLY EXPANSION, referring BIG BANG and imagining it just an explosion is like INSULTING the WHOLE THING. IT WAS EXPLOSION AND CREATION AT THE SAME TIME. OUT OF NOTHING, everything JUST CAME INTO BEING. SO my point the the first law of thermodynamics even fails to explain the creation of the matter which is also a form of energy according to einstein. So, kindly help what the hell is going on......

Last edited: Dec 31, 2007
8. Dec 31, 2007

### stevebd1

Some time ago I put together a brief summary of what happened in the first second after the big bang. It doesn't answer your question directly but it may be of some interest to you.

Apparently, most cosmologists don't like the term 'the big bang' even though it's widely recognised as the term used to describe the beginning of the universe, most prefer the 'big stretch' or 'expansion' as apposed to the idea of an explosion.

The 4 fundamental forces-

Force, Relative Strength, Interaction

Gravity, 1 x G, Objects of mass

Weak, 10^25 x G, Types of nuclear decay

Electromagnetic, 10^36 x G, Atomic/chemical structures, electromagnetic phenomena

Strong, 10^38 x G, Nucleus structure

From between zero and 10^-43 seconds (the Planck epoch) a bubble of incredibly dense and hot energy appeared within a space approx. 10^20 smaller than the size of a proton (a planck length, 10^-33 cm). Within this bubble, the supersymmetry that maintained that the 4 fundamental forces (gravity, electromagnetic, weak & strong) all had the same strength and were unified into one single fundamental force (the superforce) collapsed. (What exists when supersymmetry is in place is unknown, future experiments with particle accelerators and the advancement of M-theory might shed some light on this state). Gravity began to separate from the other forces and at 10^-33 seconds, the strong force began to separate (the 2 remaining forces, electromagnetism and weak, were still bound as the electroweak force). The universe then began to inflate rapidly. One theory for the rapid cosmic inflation is that the separation of the fundamental forces created a sort of anti-gravity (or inflaton field) that filled empty space with 'vacuum energy', pushing the fabric of space to expand without diluting itself in the process. This is like a dam breaking and the false vacuum- the dammed river- releasing a tremendous amount of force as it returned to its true vacuum state- sea level. The primordial universe expanded at faster than the speed of light to the size a galaxy in less than a picosecond, and kept going. Quarks and antiquarks formed soon after. Electromagnetism and the weak force separated at the end of the electroweak epoch at 10^-12 seconds resulting in the 4 fundamental forces as they are today. At 1 microsecond, electrons and positrons formed, quarks combined to create protons and neutrons. 1 second after the big bang, protons and neutrons bind to create atomic nuclei.

Steve

Last edited: Dec 31, 2007
9. Dec 31, 2007

### Electrolight

Dear Sir, Thanks u very much... i would like to keep in touch with u and such a nice discussion. can u plz recommend me some book to read......... : )