Final Temperature of the Universe: Effects of Dark Energy and Spatial Curvature

[wolram]

I know there are a few ways the universe can end, if it ever does, but at what temperature would the universe be in after heat death?

 

[wolram]

I have been googling and one paper i read said 0 degrees kelvin but that is hard to believe.

 

[newjerseyrunner]

It shouldn't ever get to zero, it should approach zero asymptotically.

 

[Chalnoth]

I know there are a few ways the universe can end, if it ever does, but at what temperature would the universe be in after heat death?

If the dark energy is a cosmological constant (or otherwise remains constant into the future), then the eventual temperature will be determined by the Hawking radiation coming from the horizon produced by the cosmological constant.

I'm not precisely sure what this temperature is, but it's really, really teeny. It should follow the same temperature law as black holes, given by the area of the horizon. But since the area of the cosmological horizon is so much larger than that of any black hole, its temperature will be correspondingly tinier.

 

[Khashishi]

In the heat death, the universe continues to expand exponentially, and the temperature continues to drop closer and closer to 0.

 

[rootone]

It would be very very close to absolute zero.
However at that stage, particles in the universe are so distant from any other particle that the concept of temperature doesn't have much meaning.
(since there can no longer be any thermodynamic interaction)

 

[Kevin McHugh]

As long as something is vibrating somewhere, it can't be zero.

 

[secur]

Any fermion has an irreducible "Zitterbewegung", i.e. jitter, (as it was once called) from the 1/2 hbar spin angular momentum. Also photons aren't going to just disappear, although their wavelengths get arbitrarily long. So Nernst is still right: absolute 0 is unattainable.

Anyway, the chance that the current-science concept of "heat death" is still considered correct in 10^2 years, much less 10^whatever years, also approaches zero.

As far as I know.

 

[Chalnoth]

As long as something is vibrating somewhere, it can't be zero.

The temperature of a single particle is meaningless: temperature is only a meaningful quantity for a large number of particles.

In this case, however, there will be more than one particle as long as there is a cosmological constant, due to Hawking radiation from the horizon.

 

[Chalnoth]

Anyway, the chance that the current-science concept of "heat death" is still considered correct in 10^2 years, much less 10^whatever years, also approaches zero.

There's no reason to believe this assertion of yours. Heat death is an inevitability given that the universe continues to expand.

 

[secur]

Chainoth, my assertion is based on history of science, more than science per se.

Just a couple of decades ago we all knew that the universe's expansion was slowing down. My old GR textbook devotes one sentence to the cosmological constant: assumes it's 0, admits it might not be. It then examines the 3 possibilities, k=-1, 0 or 1, for many pages: closed, asymptotically flat or open universe. The last, leading to heat death; the first, to the big crunch.

Then in 1998 studies of Type 1 Supernovae led to the current view that expansion is accelerating, as we all know. Don't get me wrong: I accept this finding; but feel it's provisional. It depends on hard-to-know assumptions: that the supernovae have the same light curve in early universe and that distance / age estimates are correct, within something like 5%; and others. I know that the astronomers involved give it 5 sigma confidence (or so) - and they're right, given their assumptions. But such results can easily change in the light of new information.

Some examples:

Just 3 days ago astronomers decided that a class of spiral galaxies (the "outrageously" luminous spirals) are at only 4 billion LY, not twice that! What are the chances that the supernovae estimated distances / ages are off by a few percent?

Recently LUX failed to find DM. The best physicist I ever knew - at the top of the field - told me in 2011, "If there's Dark Matter to find, LUX will find it!" (He was in charge of the North American effort). Admittedly if he were alive today he wouldn't actually give up on DM, just admit he was wrong about LUX. Still, I remember when we thought DM was probably brown dwarfs (undetectable by the technology of that era). 40 years of watching absolute certainty in physics turn into admission of defeat prompts me to take a wait-and-see attitude. If DM doesn't exist (remember aether!) all these expansion-of-the-universe calculations are thrown off.

Then there's galactic formation: everyone knew it must have taken 4 billion years, not long ago. Every time a new telescope sees deeper, they see more galaxies: now we're down to 400 million. What will the James Webb find? I'm certain of only one thing: it will find surprises.

Going back farther, Lord Kelvin - remembered today as a fool, for not seeing radioactivity, relavitity, and QM when it was right under his nose - was, in fact, one of the most brilliant physicists ever. If a man like that can miss things, so can we.

On the other hand, there have been great triumphs recently like the Higgs boson and gravitational waves. Higgs was very much against my expectations (I bet against it one year before it was found.) I remember when it was respectable to doubt Black Holes; that's no longer the case. The accuracy of physicists' theoretical predictions has often amazed me; it's incredibly gratifying to watch the steady accumulation of knowledge, much of it science-fiction just 4 decades ago, beyond doubt today. But I don't, yet, put accelerated expansion in that category.

But - let's assume it's perfectly correct. Alright, for 7 billion years expansion decelerated, then accelerated. What will happen 7 billion years from now? Might it decelerate again? Who knows? I can't believe that in that distant future, whatever strange intergalactic beings the human race has become will say to each other: "Darn it, those guys in the 21st century knew everything! Nothing left for us to discover!"

We don't even have a complete quantum gravity, and yet we're certain we know what happens 7 billion years, even 100 billion, from now - When not 20 years ago our ideas were upended.

We've gotten a very obscure look at MWBR from one point in space-time (here, today). Those future beings will have viewed it with resolution 10^whatever, from different galaxies over billions of years. Any possibility they come to different conclusions, when their database is something like 10^30 greater than ours? We're comparable to cavemen striking flint to make fire, and "knowing" how the sun works.

NOTE - I wrote the above, put it aside. Then, found talk in another post about MWBR strangely aligning with our solar system! May mean nothing at all; may mean we misunderstand MWBR. Unwarranted faith in tenuous theories can cause more problems than it solves. Have theories; but don't have faith.

"It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.” - A. Conan Doyle

As I say: this is not about science per se, but science history, and common sense. It's not about denying new discoveries, but rejecting hubris and keeping an open mind.

Thanks for the opportunity to clarify my statement!

 

[Chalnoth]

This is a common but fundamentally misguided understanding of the history of science. While we've learned many new things in the last hundred years, there's quite a lot that has remained the same.

In this particular case, heat death is a result of thermodynamics, the fundamentals of which have changed remarkably little since the mid-1800's. Since that time, the main advances in thermodynamics have had to do with understanding the statistical underpinnings of thermodynamics, extending thermodynamics to describe more complex systems, and the (mostly) minor changes to thermodynamics that occur as a result of quantum mechanics (the differences are mostly only relevant at very low temperatures).

The statement that heat death will happen is contingent upon the universe continuing to expand, but little else. There are some models where the universe doesn't continue to expand in the future, but these tend to be pretty speculative and substantially more complicated than models where it does continue to expand.

 

[secur]

People may disagree on interpretations of history without being misguided. Some focus on the leaps forward, others on the times the leaper falls flat on her face. It would be a useful exercise to catalog successful scientific theories vs. unsuccessful and see who's ahead.

We don't know the universe will be expanding in 7 billion years. The only way to find out is wait; it can't be proven now, by models however elegant. And then, what about the next 7 billion? Don't trust faith, it's tripped up many great minds over the years.

Thermodynamics was a resounding triumph of Lord Kelvin and others. The "surprising" fact is that at a uniform temperature, no work is available. But being right for 150 years is not too impressive, compared to the time to reach heat death.

There's another assumption here: no new energy will be created to keep things moving. Neither the first nor second law has been shown valid on galactic / universe scales; we have just a few decade's data on this tiny speck of earth. The Cosmological Principle is not an edict. By the way note that this thread, arguing whether absolute zero will be attained, ignores the third law!

Let's make a bet, for bragging rights. I bet, in that distant era, today's science will look laughably primitive; you bet it will still be accepted completely, and the names of Newton, Einstein and Hawking revered throughout the universe for all time. We'll get together in 7 billion years and let the winner brag.

 

[newjerseyrunner]

Isn't talking about temperature in extreme situations like this meaningless anyway due to quantum uncertainty. Technically, couldn't the universe, or at least parts of it, actually dip below absolute zero?

 

[DrClaude]

Isn't talking about temperature in extreme situations like this meaningless anyway due to quantum uncertainty. Technically, couldn't the universe, or at least parts of it, actually dip below absolute zero?

Negative temperatures are not "below absolute zero." They actually correspond to systems hotter than an infinite temperature. And it only applies to system that have a finite maximum energy, which is not relevant here.

 

[wolram]

Does is make a difference if the universe is open or closed?

 

[Chalnoth]

Does is make a difference if the universe is open or closed?

Only if dark energy goes away eventually.

If we have a cosmological constant, then the spatial curvature of our universe, if any, will only get more flat (as a fraction of the critical density).

If the dark energy turns out to decay due to some mechanism or other, so that the expected future energy density of our universe is zero, then the impact of the spatial curvature will grow until it becomes the dominant feature of the expansion. Then, if that happens, it will continue to expand forever if the universe is flat or open, but collapse back on itself if it's closed.