# Mirror, Mirror on the Wall…

…which of the symmetries hold at all? The universe is a curious place and cosmologists endeavour to contain this curiosity into one theory. Or maybe two, if they’re unlucky.

At the current position we are far from proposing a theory of everything that encompasses the various branches of physics into one theory, in particular quantum field theory and general relativity. The issue here is that these two theories are mutually incompatible – ‘neither can live while the other survives’ to quote J.K. Rowling. A successful theory of everything would have the absolute power to explain and predict all physical phenomena in the universe.

Nevertheless we do know quite a bit about what the theory must contain, and one question that we must ask is: what would the universe be like if all matter was replaced with its corresponding antimatter? This leads to the concept of CPT symmetry.

‘Ah yes, symmetry, I recognise that word!’

You may be able to relate to using cheap, bendy mirrors with tattered edges when you were younger to study reflective symmetry, or small square pieces of tracing paper to study rotational symmetry. CPT symmetry has essentially the same underlying principles. Instead of transforming a two-dimensional shape and checking if the shape matches, we are transforming the entire universe and checking if the current laws of physics still apply. If they do, the symmetry holds.

In order to do this, we can look at if the four fundamental forces are invariant under the transformation. What transformations are we testing out? This is where the three special little letters come in.

The first transformation is charge conjugation (C). This is reversing all the electrical charges and internal quantum numbers (such as lepton number, baryon number and strangeness), and as a consequence all matter becomes antimatter and vice versa.

It turns out that the electromagnetic, gravitational and strong nuclear forces obey C-symmetry, but the weak nuclear force does not. Therefore C-symmetry does not hold, and this shows that the universe can indeed tell its positives from its negatives.

The second transformation is parity inversion (P). A universe that has had its parity inverted can be thought of as a mirror image only in space but not in time – left and right has swapped, up and down has swapped, etc.

The electromagnetic, gravitational and strong nuclear forces obey P-symmetry, but once again the weak nuclear force does not. It looks like the universe can also tell its left from its right!

It was originally thought that, even though C-symmetry and P-symmetry do not hold individually, when they were applied together they would cancel each other out, i.e. CP-symmetry would hold. However experiments in the 1950s involving radioactive beta decay (a weak interaction) confirmed this to be false. CP violations are thought to be one of the reasons why the universe has resulted in more matter than antimatter.

The third transformation is time reversal (T). You would expect T-symmetry to not hold either, because were you to view life in reverse, it would not look natural, and this is a consequence of the second law of thermodynamics. Otherwise you could see broken glass shards reforming themselves into a uniform sheet, or spilt drinks voluntarily flying up and containing themselves back into a mug. That for sure doesn’t happen in my household.

Or does it?

Interestingly, T-symmetry is found to be invariant over all the fundamental forces, showing that T-symmetry holds on a microscopic scale, even though we see a clear asymmetry on a macroscopic scale. If you take a simple physical system, such as a swinging pendulum, you can’t tell a difference in its reverse (ignoring accounts of air resistance and friction).

If you were to apply all the three transformations simultaneously, experimental evidence has shown that this master combination holds. This is the basis of the CPT theorem that was developed in the 1950s, and it forms one of the fundamental properties of nature. In other words, if there was another universe that was made of antimatter instead of matter, and was an exact mirror image, and moved backwards in time, you wouldn’t be able to tell the difference between that universe and ours.

Since CPT-symmetry holds but CP-symmetry does not, the implication is that T-symmetry does not hold also, which agrees with what we see in real life. Then what causes the contradiction in the ‘arrow of time’ between microscopic and macroscopic scales? This is a question to explore for another time.

CPT symmetry is an important concept to consider as it provides gateways into further understanding the arrow of time and why we only remember the past but not the future.

Yanhao