# Is there a universal minimum energy state?

I'm imagining this: if everything was separated (even on the nuclear level) and then the parts were recombined so that they were in the lowest possible energy state, do we have any way of knowing what that might be? Particularly, would it be something simple like a helium atom or could it be something very complex and unusual? And I mean that you might grab a few parts and make a helium atom or grab a whole bunch of parts and make whatever else.

I guess one problem is we need a way of totaling how much the energy is decreasing per some amount of something else. Similar to how nuclear binding energy is often expressed on a "per nucleon" basis.

I'm interested to see what people think.

• That's pretty much what happens in the stars, so yes, the end result is more or less well known. – Ivan Neretin Nov 19 '15 at 8:11

This is an interesting and actually surprisingly hard question, which reaches the edge of our understanding of physics, so really a physicist would be more equipped to answer this.

I'm not sure if there is rigorous mathematical/physical proof that energy must have a minimum. Energy is a continuous, real-valued, state function, which as far as I know makes it mathematically very well-behaved, so it's unlikely that it can display weird behaviour. The extreme value theorem suggests that taking any finite collection of states into account, at least one of them must be a global energy minimum. However, I'm not sure if the Universe has a finite amount of states it can assume (probably not, if it is infinite in size). All that said, even if strictly speaking there is no global minimum, it's likely there is some asymptotically low value. So what is it?

What you're trying to imagine, essentially, is a Universe where there is no kinetics, only thermodynamics. Equivalently, you're thinking about the state of the Universe at $\mathrm{t→+ \infty}$. All finite kinetic barriers are surpassed and all finite distances are traversed. With this much time, a lot of unintuitive events take place. Two very interesting sources to read are "Time without end: Physics and biology in an open universe", (1979) Rev. Mod. Phys., 51, 447, and "A dying universe: the long-term fate and evolution of astrophysical objects", (1997) Rev. Mod. Phys., 69, 337. There are many processes, varying from almost certain to extremely speculative, which can happen in overlapping time scales, so it is hard to determine exactly which route the Universe (or a toy model of a universe) might take. I'll present several events which may happen as the Universe marches on towards $\mathrm{t→+ \infty}$, and thus which reach closer to the minimum energy state of the Universe, but be aware that there are many uncertainties, especially near the deep end.

Starting with chemistry, allowing systems to evolve for very long periods would have some interesting consequences. Only the most stable compounds could survive, so for example, all nitrogen atoms would eventually recombine to form gaseous $\ce{N2}$. Other very stable molecules would be $\ce{H2O}$, $\ce{CO}$, and $\ce{H2}$. The Universe would turn into a mixture of small molecules. This would take at least something of the order of $10^{65}$ years. For comparison, the Universe is currently $1.38\times 10^{10}$ years old.

But why stop there? Chemical energy is only one of many factors to be taken into account in the total energy, and really it's one of the smallest. For example, nuclear energy scales completely dwarf chemical energy scales, so forget about optimising molecular abundances to minimise energy, because optimising atomic abundances will reach much lower energies. What would really happen is that, given tremendous amounts of time, light/heavy nuclei would overcome the barrier to fusion/fission, even at very low temperature and pressure. As you mention, the ultimate effect would be that all of the atoms in the Universe would fuse/fission into $\ce{^{62}Ni}$, the nucleus with the highest nuclear binding energy per nucleon. This would take on the order of $10^{1500}$ years.

This still isn't the end, though. Given a ridiculous amount of time, much of the nickel could still coalesce and compress into degenerate neutron matter (like neutron stars), releasing even more energy. The kinetic barrier for this is truly colossal, though, so it would take some $10^{10^{76}}$ years.

It's possible to keep going. Sufficiently large chunks of matter could compress further into black holes, releasing even more energy. Depending on the mass of the lightest possible black hole, this process may take "only" $10^{10^{26}}$ years, or up to a scale comparable to neutron matter formation. If the lightest possible black hole has a non-zero mass, then objects lighter than that threshold may be stable indefinitely. The black holes that did form would evaporate almost instantly relative to this time scale, producing an abundance of subatomic particles which would eventually decay into photons and neutrinos.

There's another speculative process which may severely undercut the previous possibilities, however. Currently many types of string theory posit the existence of proton decay. If it does happen, it could happen as quickly as $10^{40}$ years. This would be the end of Chemistry in the Universe; all atoms would eventually decay into photons, neutrinos, electrons and positrons. Black holes would survive this, but they would evaporate by $10^{100}$ years at the latest, quickly resulting in a Universe sparsely filled only with photons and neutrinos.

Last but definitely not least, it may be that even completely empty vacuum is not the minimum energy state of the Universe. It's conceivable that the vacuum we know is less stable than another type of vacuum, separated by an enormous kinetic barrier. If this is the case, then given enough time there could be a vacuum metastability event, a tremendously energetic process in which the Universe as we know it would cease to exist, being replaced by another with entirely different physics.

• Wow. Thank you for that incredibly detailed answer. I'll have to ponder some of that. I'll take a look at those papers too. Thanks. – jheindel Nov 19 '15 at 17:53

And I mean that you might grab a few parts and make a helium atom or grab a whole bunch of parts and make whatever else.

Why helium if hydrogen is simpler? The universe is indeed dominated by hydrogen: monatomic hydrogen is the most abundant chemical substance in the Universe, constituting roughly 75% of all baryonic mass.1

According to the widely accepted Big Bang theory, once the universe became cool enough (at about 379,000 years) the electrons and nuclei combined into atoms, and the atoms were mostly hydrogen atoms because previously despite the presence of neutrons most protons remained uncombined as hydrogen nuclei. The reason is that when the universe was hot protons and neutrons transformed back and forth into each other, and their ratio was determined solely by their relative masses: it was about 1 neutron to 7 protons.

A bit later, once it was cool enough, neutrons combined with protons to form deuterium and helium nuclei by a process called Big Bang nucleosynthesis. Eventually these nuclei gave rise to deuterium and helium atoms. The theoretical estimates of the end result of Big Bang nucleosynthesis are (in mass abundances): about 75% of hydrogen-1, about 25% helium-4, about 0.01% of deuterium and helium-3, trace amounts (on the order of 10−10) of lithium, and negligible heavier elements.

The bottleneck of to the absence of a stable nucleus with 8 or 5 nucleons was passed only much later in evolving and exploding stars by stellar nucleosynthesis, so that the elements heavier than lithium and beryllium were formed. The triple-alpha process should be mentioned specifically in that respect in which three helium-4 nuclei are transformed through the unstable beryllium-8 nuclei into a carbon-12 nuclei which is finally stable. Note that the triple-alpha process is very unlikely and requires very high temperatures (about $10^8$ K and higher) for nuclear fusion, and thus, it needs these special conditions and a lot of time to produce much carbon.

1) "Baryonic" is important here, because most of the mass-energy in the universe is not even in the form of baryons or chemical elements: the universe is dominated by the dark matter and dark energy which collectively amount for about 95% of the total mass–energy content of the universe.

On a per nucleon basis, Ni-62, Fe-58, and Fe-56 are all about 930 MeV.

However, as explained in Strange Quark Matter and Compact Stars

Theoretically the energy per baryon of strange quark matter may be below 930 MeV, which would render such matter more stable than nuclear matter.

• Thanks for that great reference. Whenever I get time to try to comprehend 62 pages of dense physics I'll take a look at that :) – jheindel Nov 19 '15 at 18:21
• @jheindel section 3.3 is the part most relevant to your quesiton – DavePhD Nov 19 '15 at 18:26