Entropy in the Universe

If you click on this picture, you’ll see a zoomable image of the Milky Way with 84 million stars:

But stars contribute only a tiny fraction of the total entropy in the observable Universe. If it’s random information you want, look elsewhere!

First: what’s the ‘observable Universe’, exactly?

The further you look out into the Universe, the further you look back in time. You can’t see through the hot gas from 380,000 years after the Big Bang. That ‘wall of fire’ marks the limits of the observable Universe.

But as the Universe expands, the distant ancient stars and gas we see have moved even farther away, so they’re no longer observable. Thus, the so-called ‘observable Universe’ is really the ‘formerly observable Universe’. Its edge is 46.5 billion light years away now!

This is true even though the Universe is only 13.8 billion years old. A standard challenge in understanding general relativity is to figure out how this is possible, given that nothing can move faster than light.

What’s the total number of stars in the observable Universe? Estimates go up as telescopes improve. Right now people think there are between 100 and 400 billion stars in the Milky Way. They think there are between 170 billion and 2 trillion galaxies in the Universe.

In 2009, Chas Egan and Charles Lineweaver estimated the total entropy of all the stars in the observable Universe at 10⁸¹ bits. You should think of these as qubits: it’s the amount of information to describe the quantum state of everything in all these stars.

But the entropy of interstellar and intergalactic gas and dust is about ten times more the entropy of stars! It’s about 10⁸² bits.

The entropy in all the photons in the Universe is even more! The Universe is full of radiation left over from the Big Bang. The photons in the observable Universe left over from the Big Bang have a total entropy of about 10⁹⁰ bits. It’s called the ‘cosmic microwave background radiation’.

The neutrinos from the Big Bang also carry about 10⁹⁰ bits—a bit less than the photons. The gravitons carry much less, about 10⁸⁸ bits. That’s because they decoupled from other matter and radiation very early, and have been cooling ever since. On the other hand, photons in the cosmic microwave background radiation were formed by annihilating electron-positron pairs until about 10 seconds after the Big Bang. Thus the graviton radiation is expected to be cooler than the microwave background radiation: about 0.6 kelvin as compared to 2.7 kelvin.

Black holes have immensely more entropy than anything listed so far. Egan and Lineweaver estimate the entropy of stellar-mass black holes in the observable Universe at 10⁹⁸ bits. This is connected to why black holes are so stable: the Second Law says entropy likes to increase.

But the entropy of black holes grows quadratically with mass! So black holes tend to merge and form bigger black holes — ultimately forming the ‘supermassive’ black holes at the centers of most galaxies. These dominate the entropy of the observable Universe: about 10¹⁰⁴ bits.

Hawking predicted that black holes slowly radiate away their mass when they’re in a cold enough environment. But the Universe is much too hot for supermassive black holes to be losing mass now. Instead, they very slowly grow by eating the cosmic microwave background, even when they’re not eating stars, gas and dust.

So, only in the far future will the Universe cool down enough for large black holes to start slowly decaying via Hawking radiation. Entropy will continue to increase… going mainly into photons and gravitons! This process will take a very long time. Assuming nothing is falling into it and no unknown effects intervene, a solar-mass black hole takes about 10⁶⁷ years to evaporate due to Hawking radiation — while a really big one, comparable to the mass of a galaxy, should take about 10⁹⁹ years.

If our current most popular ideas on dark energy are correct, the Universe will continue to expand exponentially. Thanks to this, there will be a cosmological event horizon surrounding each observer, which will radiate Hawking radiation at a temperature of roughly 10^-30 kelvin.

In this scenario the Universe in the very far future will mainly consist of massless particles produced as Hawking radiation at this temperature: photons and gravitons. The entropy within the exponentially expanding ball of space that is today our ‘observable Universe’ will continue to increase exponentially… but more to the point, the entropy density will approach that of a gas of photons and gravitons in thermal equilibrium at 10^-30 kelvin.

Of course, it’s quite likely that some new physics will turn up, between now and then, that changes the story! I hope so: this would be a rather dull ending to the Universe.

For more details, go here:

• Chas A. Egan and Charles H. Lineweaver, A larger estimate of the entropy of the universe, The Astrophysical Journal 710 (2010), 1825.

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