Sunday, November 22, 2015

Why Does Time Always Run Forwards And Never Backwards? (2/3)


Continued from Part 1

Once again, Boltzmann's colleagues argued that it wasn't possible to explain why entropy always went up. It just did. And again, Boltzmann was unsatisfied, and went searching for a deeper meaning. The result was a radical new understanding of entropy — a discovery so important that he had it engraved on his tombstone.

Ludwig Boltzmann's tombstone, complete with entropy equation (Credit: Daderot, CC by 3.0)
Boltzmann found that entropy measured the number of ways atoms, and the energy they carry, can be arranged. When entropy increases, it's because the atoms are getting more jumbled up.

According to Boltzmann, this is why ice melts in water. When water is liquid, there are far more ways for the water molecules to arrange themselves, and far more ways for the heat energy to be shared among those molecules, than when the water is solid. There are simply so many ways for the ice to melt, and relatively few ways for it to stay solid, that it's overwhelmingly likely the ice will eventually melt.
You cannot un-break an egg (Credit: Pierangelo Pirak)

Similarly, if you put a drop of cream into your coffee, the cream will spread throughout the entire cup, because that's a state of higher entropy. There are more ways to arrange the bits of cream throughout your coffee than there are for the cream to remain in one small region.

Entropy, according to Boltzmann, is about what's probable. Objects with low entropy are tidy, and therefore unlikely to exist. High-entropy objects are untidy, which makes them likely to exist. Entropy always increases, because it's much easier for things to be untidy.

That may sound a bit depressing, at least if you like your home to be well-organized. But Boltzmann's ideas about entropy do have an upside: they seem to explain the arrow of time.

Boltzmann's take on entropy explains why it always increases. That in turn suggests why we always experience time moving forwards. If the universe as a whole moves from low entropy to high entropy, then we should never see events go in reverse.

We won't see eggs un-break, because there are lots of ways to arrange the pieces of an egg, and nearly all of them lead to a broken egg rather than an intact one. Similarly, ice won't un-melt, matches won't un-burn, and ankles won't un-sprain.

Boltzmann's definition of entropy even explains why we can remember the past but not the future. Imagine the opposite: that you have a memory of an event, then the event happens, and then the memory disappears. The odds of that happening to your brain are very low.

According to Boltzmann, the future looks different from the past simply because entropy increases. But his pesky opponents pointed out a flaw in his reasoning.
Once done, this cannot be undone (Credit: Kevin Twomey/Alamy)

Boltzmann said that entropy increases as you go into the future, because of the probabilities that govern the behavior of small objects like atoms. But those small objects are themselves obeying the fundamental laws of physics, which don't draw a distinction between the past and the future.

So Boltzmann's argument can be turned on its head. If you can argue that entropy should increase as you go into the future, you can also argue that entropy should increase as you go into the past.

Boltzmann thought that, because broken eggs are more likely than intact ones, it was reasonable to expect intact eggs to turn into broken ones. But there's another interpretation. Intact eggs are unlikely and rare, so eggs must spend most of their time broken, very occasionally leaping together to become intact for a moment before breaking again.

In short, you can use Boltzmann's ideas about entropy to argue that the future and the past should look similar. That's not what we see, so we're back to square one. Why is there an arrow of time at all?
Messy universe (Credit: NASA/ESA/Hubble Heritage Team (STSclAURA)/A. Aloisi (STSclESA)

Boltzmann suggested several solutions to this problem. The one that worked best came to be known as the past hypothesis. It's very simple: at some point in the distant past, the universe was in a low-entropy state.

If that's true, then the flaw in Boltzmann's reasoning disappears. The future and the past look very different, because the past has much lower entropy than the future. So eggs break, but they don't un-break.

This is neat, but it raises a whole new question: why is the past hypothesis true? Low entropy is unlikely, so why was the entropy of the universe in such a remarkable state sometime in the distant past?

Boltzmann never managed to crack that one. A manic-depressive whose ideas had been rejected by much of the physics community, he felt sure that his life's work would be forgotten. On a family holiday near Trieste in 1906, Ludwig Boltzmann hanged himself.

His suicide was particularly tragic since, within a decade, physicists accepted his ideas about atoms. What's more, in the decades that followed, new discoveries suggested that there might be an explanation for the past hypothesis after all.
We now know the universe is about 14 billion years old (Credit: NASA/ESA)

In the twentieth century, our picture of the universe changed radically. We discovered that it had a beginning.

In Boltzmann's time, most physicists believed that the universe was eternal – it had always existed. But in the 1920s, astronomers discovered that galaxies are flying apart. The universe, they realized, is expanding. That means everything was once close together.

Over the next few decades, physicists came to agree that the universe began as an incredibly hot, dense speck. This quickly expanded and cooled, forming everything that now exists. This fast expansion from a tiny hot universe is called the Big Bang.

This seemed to support the past hypothesis. "People said 'okay, the trick is clearly that the early universe had low entropy,'" says Carroll. "But why [entropy] was ever low in the first place, 14 billion years ago near the Big Bang, is something we don't know the answer to."
Large clouds of gas condense into stars and planets (Credit: Mopic/Alamy)

It's fair to say that an enormous cosmic explosion doesn't sound like something with low entropy. After all, explosions are messy. There are plenty of ways of rearranging the matter and energy in the early universe so that it is still hot, tiny, and expanding. But as it turns out, entropy is a little different when there's so much matter around.


Imagine a vast empty region of space, in the middle of which is a cloud of gas with the mass of the Sun. Gravity pulls the gas together, so the gas will get clumpy and ultimately collapse into a star. There are more ways to arrange the gas when it's wispy and scattered. So how is this possible, if entropy always increases?

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