At what we might call the most “fundamental” level, the laws of nature do not much care in which direction time flows. Yet from our point of view, as participants in the physical universe, the arrow time is an inescapable and supremely important fact. Put briefly, some things cause other things, and we get old.

A snooker, or pool, game provides a good image to help understand the problem¹. Film the moment of impact of any shot, or any collision between two balls, and run the video forwards and backwards. Assuming the cue and the player are out of frame, the video looks just as realistic backwards as forwards. With one exception. The break, the opening shot, will look ridiculous when played backwards. In the correct time direction, an orderly triangular array of balls is shattered. In the other direction, it spontaneously assembles out of nowhere. This never happens, and so the correct time direction is determined. Even though the fundamental physical laws that cover the collisions run the same backwards as forwards.

the Big Bang as the most impressive pool break of all time

This is also why particles made in colliders, such as the Higgs bosons made in collisions between protons at CERN, decay. They are like the triangle in pool, a specially ordered configuration of energy that will fall apart rapidly under the general buffeting of quantum fluctuations. The LHC has to go to enormous lengths - not just lots of energy, but many, many attempts - to “rack them up””.

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The incongruity between the lack of microscopic time direction and the omnipresence of macroscopic time has been the subject of discussion and enquiry for a long ... er ... time. A recent and particularly enjoyable entry into that discussion is Carlo Rovelli’s book, “The Order of Time”.

Rovelli also points out that there is no universal agreement possible on “now”. We have known since Einstein gave us relativity that the question “What is happening right now at some other place in the universe?” has no unique answer. It depends on the relative speed and position of the person asking the question and the place they are asking about. Over distances which can be covered quickly at the speed of light, the practical effect is not so noticeable (though it is measurable). But for astrophysicists trying to build an understanding of the cosmos and how it changes, it is inescapable.

The usual approach to the physics of cosmology and the arrow of time is to assume that somehow time began at a very organised moment – the Big Bang as the most impressive pool break of all time – and the dissipation of that initial order, measured as the increase of total entropy in the universe, is what gives us the arrow of time. Indeed, the second law of thermodynamics states that total entropy either stays the same (at best) or (more often) increases over time.

There is something suspiciously circular here though. To be able to say something increases over time, we must already have defined time. Yet the increase of entropy, in this thinking, is what defines time.

Rovelli explores this idea. What is real is how things change with respect to each other, and time does not really exist as anything independent of that. Our perception of an inexorable flow of time comes from the observed increase in entropy, and the traces of more ordered arrangements of the universe that we observe in our own particular “now”. The direction of time arises because we see these traces of a more ordered universe in the current disorder, while the Big Bang contains no trace of astronomers, telescopes or the planet Earth.

Cross Section: Carlo Rovelli – Science Weekly podcast Read more

The younger me contained no trace of this disordered and ageing physicist, but my brain still houses connections, memories of that lower entropy me. The fact that my bedroom was so much more chaotic then than now just shows that you have to consider the entropy of the whole system, of course.

In fact, as Rovelli points out, the apparent entropy of a system depends upon how closely you look at. A solar system, with planets orbiting a star, looks very orderly, notwithstanding the fact that if you were to look closely into the politics on one of the planets you would see total chaos. Put another way, if you have eight planets, there are a few different ways they can be arranged around a star; but if you look closely, and count all the possible ways life might be arranged on the planets, as well as the arrangement of the planets themselves, the possibilities for disorder are endless.

So time is (a) not universal, (b) may just be defined by the direction of increasing entropy anyway, and (c) the entropy of something depends how closely you look. Given all this, it is possible to imagine time flowing not just at different rates in different parts of the universe, but also in different directions. At least it seems possible for Rovelli to imagine this. I’m struggling a bit, but I think I get a glimmering.

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Something Rovelli is surely aware of but doesn’t really deal with is the fact that the microscopic laws of the universe do, in fact contain a way of defining time. These effects are currently being measured at the Large Hadron Collider (especially by the LHCb experiment) and the Belle II experiment in Japan is just now getting underway to study them further .

What this means is that in some very rare collisions of our snooker balls (or in reality, decays of particles made of quarks and antiquarks) it is possible to distinguish between forward time and backward time without invoking entropy. However, this distinction vanishes if (at the same time as swapping forward time for backward) you swap matter for antimatter and left for right. So, does entropy have something to say about space as well as time? Does it tell us left from right, matter from antimatter, as well as future from past?



I don’t know, right now, to be honest. Whatever now means. I recommend Rovelli’s book, though I am not sure it is right and I’m not sure I have got it all right even if he has. It is a great read.

I think I will finish (or possibly start) with a joke. So:

Q: What composer always sets up the balls for the break in pool, but then fouls immediately?

A: Rachmaninoff.

Tish, badum. Sorry. And congratulations to Mark Williams.

¹ I know I didn’t invent this analogy but I can’t remember where I heard it first. If it was from you, well done it is great and sorry for forgetting².

² Note added 10/5/18: Got it. It was in this documentary!

Jon Butterworth’s latest book A Map of the Invisible: Journeys into Particle Physics is published by Penguin.