Tag Archives: thermodynamics

The Arrow of Time

I’ve been thinking about time recently; mostly about how I don’t seem to have enough of it. My PhD work seems to be expanding to take over my life, so all sorts of other persuits (cooking, cleaning, blogging, reading other people’s blogs) have taken a bit of a backseat. Hopefully the work-life balance will re-establish itself soon, but in the meantime, I’ve been thinking about the nature of time.

One of the really weird things about physics as we know it is that the very basic laws are all time-symmetric; they’re indifferent to time going forwards or time running backwards. For instance, the Earth’s motion around the Sun: if time switched direction, the Earth would just go around the other way. The equations would all work and be consistent.

As it happens this isn’t the whole story, as we actually seem to live in a universe in which the laws of physics stay the same if you do something called a CPT transformation: you reverse the direction of time, mirror-flip the entire universe, and then change all the particles for anti-particles. So an electron going right and forwards in time could equally be described as a positron going left and backwards in time, and the physics would all be the same — if you lived in such a universe you wouldn’t notice the difference, you’d think our universe is the crazy flipped one!

The weird and interesting thing is that from our point of view, time obviously has a direction! It marches ever onwards into the future. We remember yesterday, but not tomorrow. It’s blindingly obvious when a piece of film has been reversed, because ludicrous things happen like teacups forming from ceramic shards. That obviously isn’t reversible, so what gives?

Physicists call this problem the arrow of time; why does an arrow, a preferred direction, exist when all the most fundamental laws tell us that the two directions of time should be indistinguishable?

One possible answer is entropy. Broadly speaking, entropy is a measure of disorder in a system. It’s a way of counting how many microscopic ways there are to make a particular macroscopic system. Take for example our smashed teacup. Consider that there are two states that cup can exist in: smashed, and whole. There is only one way for the cup to be whole, so it has a low entropy. There are untold millions of ways that cup can exist as a pile of smashed fragments, so that state has high entropy.

The second law of thermodynamics tells us that, on average, the entropy of a closed system will always increase, based on simple probability – for the cup it is easier to be smashed than to be whole, because there are more ways to be smashed. The laws of physics remain reversible, but the fact that so many more high entropy states exist than low entropy ones mean that playing the odds, you’ll go from low to high entropy.

So cups will always tend to smash rather than spontaneously re-form, energy will tend to turn from ordered forms which we can use (like electricity) into unordered forms, spread through the environment that we cannot use (like heat). There are some pretty compelling thought experiments (see Maxwell’s Demon, for those interested) which suggest that remembering (or more precisely, forgetting) is a process which generates entropy. There’s only one way to remember something, but millions of ways you can forget it.

So maybe that’s why we can remember the past and not the future – our memory works by increasing entropy, and entropy increases into the future. But that doesn’t answer the question as to why entropy appears to have “chosen” a particular direction in which to operate.

Well, consider a universe that starts in an high-entropy state. If that universe is already near or at maximum entropy, then only reversible processes can ever happen, because irreversible processes are the ones which generate entropy. Nothing can live, or die (because death is irreversible). Cups cannot smash, and there is no free energy around with which to do work. Some people speculate that this fate awaits our universe, and it’s called “heat death”. It simply becomes impossible to extract useful energy from the environment because it’s all become useless heat. (The other possible fate is a deep freeze, where the universe spreads out so much that the average energy density of the universe goes to zero. It’s the same problem, a lack of available energy, but much, much colder).

So instead, imagine a universe which starts in a low-entropy state. This universe is then free to be full of entropy-generating events, like smashing cups, machines, and computers (and people!) with memories capable of remembering the past. So maybe the mystery of the arrow of time is solved by our universe beginning in an incredibly unlikely low-entropy state, and evolving towards a higher entropy one, just because higher entropy is more likely than low entropy. The laws of physics all remain fully reversible, it’s just bloody unlikely that our universe started so favourably.

Although, I did have an idea: what if what we think of as the beginning, this low-entropy state, is actually the middle of the existence of a universe? From that point, you could use the laws of physics to extrapolate that universe both forwards, and backwards, but the internally perceived arrow of time, pointing along the direction of entropy growth, would point in different directions in each half of the universe’s history. Furthermore, quantum indeterminancy would guarantee that each “sub-universe” would evolve differently, despite both having come from the same low-entropy seed. Maybe beyond the big bang lies another universe after all.