Quantum Physics in a Mirror Universe (Script) (Patreon)

When you look in mirror, and see what you think is a perfect reflection. You might be looking at universe whose laws are fundamentally different.

When we think about symmetry, the first thing that comes to mind is mirror symmetry. Butterflies, Rorschach tests, and classically attractive faces all look the same when flipped left-to-right. In physics, a symmetry is when the laws of physics are unchanged due to some transformation of coordinates. We’ve seen examples where it is - the universe is symmetric to coordinate shifts in space, time, and even the rather abstract phase of the wave function. So it might be surprising to learn that with all the weird ways in which the universe IS symmetric, it’s NOT entirely symmetric under this most intuitive one. The laws of physics work differently in the universe of the mirror.

Let’s talk about the physics of entering the mirror universe. The technical name for such a reflection is a parity transformation, and something remains identical under such a transformation then we say the thing is parity-symmetric – P-symmetric. Parity is a weird type of symmetry. In the case of those other symmetries I mentioned, the shift in position, time, or phase can be by any amount, small or large. These are continuous symmetries. But there’s no such thing as a partial reflection – you either reflect or you don’t. Parity is a discrete symmetry. Other types of discrete symmetries include charge conjugation–flipping the sign of the electric charge, and time reversal–sending the clock ticking backwards. We’ll come back to both of these. They’re going to save us in the end.

Parity transformations involve the flipping of spatial axes. If we define the mirror to be in the x-y plane; reflection sends z to minus-z and vice versa. Objects are turned back to front and front to back. And it looks like your right hand becomes your left and vice versa – as though you’d actually flipped in the x direction, not the z. Actually a true x-axis reflection would look like this. Left still goes to right but forward-back facing stays the same. But this is exactly the same as a z-axis reflection plus a rotation. In fact a reflection on any single axis can be reproduced by a reflection on a different axis plus a rotation. A reflection on two axes then puts things back to normal, while reflection on all three axes gives the same left-right switch as a reflection on one axis. Formally, a full parity inversion means flipping all three axes.

Now when you reflect the universe obviously it IS different. All position vectors all point in the opposite direction. Same with velocity-slash-momentum. Throw a ball at the mirror, away from yourself and its reflection looks like its coming towards you. In the language of parity, we call properties that flip sign “odd” functions. Properties that don’t change under reflections are called “even” – things like energy of the ball, its mass, the time on its clock, and, as we’ll see, angular momentum don’t change in the mirror universe.

Even though some signs get flipped, the laws of physics should be unaltered in that mirror world. Newton’s laws will still give the ball’s trajectory. Those laws work the same no matter the direction of motion. In fact if we rotate the whole mirror-ball’s trajectory by 180 degrees, it’s identical to the original trajectory. But that’s only true if the ball itself is unchanged in the reflection. But what if we try something else. Let’s put some spin on the ball – say, clockwise spin. The reflected ball is still spinning clockwise. Its angular momentum is unchanged. But the relationship between angular momentum and regular momentum – its direction of motion – is flipped.

This is similar to the switching of left and right hands in a mirror reflection of a person. In fact we talk about the direction of spin as handedness. You can grab the ball with your fingers pointing in the direction of its spin and your thumb pointing in the direction of motion; if you need to use your right hand to do that then the spin is right-handed relative to the motion. That’s the case of the unreflected ball in our example. If you need to use your left hand, as in the case of the reflected ball, then the spin is left-handed relative to motion.

The “handedness” of a moving, spinning object is called its helicity. A spot on its surface draws a surface that spirals either one way or the other. But the general term for handedness is chirality. A chiral object is one that is fundamentally changed by reflection. Parity transformations flip from left-handed to right-handed chirality. Hands have left- or right-chirality, so do spinning, flying balls, so do many molecules. And some quantum particles. But chirality in quantum mechanics means something quite specific. Quantum chirality is connected to quantum spin, but for any particle with mass, motion doesn’t factor into it. It’s not the same as helicity. It’s best to think of quantum chirality as a fundamental internal right- or left-handed asymmetry. And most chiral particles have both right- and left-handed versions.

Do these version behave differently? Well you wouldn’t think so, would you? Why should the universe treat righties and lefties differently? In fact it was assumed for the longest time that the universe DID conserved parity. And it appeared to be the case in experiments – at least for tests involving gravity, electromagnetism and the strong nuclear forces. It was assumed that the weak nuclear force was the same deal. That’s until the tau-theta problem came along. Tau and theta were a pair of particles – 2-quark mesons to be precise - that looked the same in all respects – same spin, same mass, same electric charge. But different decay products – the tau decayed into 3 pions – also mesons – while the theta decayed into two pions. That was the only difference between them. So couldn’t a single particle have two decay outcomes? Well the problem is that those two decay outcomes have different parity. The combination of the 2 pions had even parity, while the combo of 3 pions had odd parity. A single particle should produce decay products with the same parity - the same response to reflections. That’s what we mean by conservation of parity. At least one of these decay products broke conservation of parity.

[This] was the solution pointed out by Yee and Lang in 1956 – and for which they later won the Nobel Prize. They proposed that tau and theta are the same particle – which turns out to be the kaon – and that the weak interaction, which governs this decay, does not conserve parity. But how to test this? Yee and Lang found a brilliant experimentalist to test their hypothesis, the “her” being Chien-Shiung Wu, who for some reason didn’t get in on that Nobel prize. In 1957 Wu conducted an experiment based on a simple argument. If parity is conserved, then there should be no experiment you can do to determine whether you live in the regular universe or a mirror universe. That means that left-handed and right-handed particles should decay in the same way. Wu tested this using the Cobalt-60 atom. The nucleus of this radioactive isotope of Cobalt decays via the weak interaction into Nickel by emitting an electron, some gamma ray photons and neutrinos. The Cobalt-60 also happens to have an unusually high nuclear spin, which means it’s possible to align the spin of the nucleus using a magnetic field. So Wu and team applied a magnetic field to a layer of Cobalt-60 and watched them decay. They found that almost all of the electrons produced in the decay emerged in the opposite direction to the nuclear spin axis. That right there was the smoking gun of parity violation. Let’s see why.

The important thing is that the momentum of the ejected electrons had any correlation with the spin of the nucleus at all. Why? Let’s look at how both momentum and spin are affected by parity transformations. To do this properly we need to reflect the cobalt nucleus in all three directions–left-right, forward-back, up-down. You can see that the spin of nucleus – which we represent with the angular momentum vector along the axis –  isn’t changed. It’s still spinning in the same direction, so the axis of that spin still points up. But the same transformation on the electron’s momentum vector leaves it pointing in the opposite direction. So if there’s ANY relationship between the direction that electrons are ejected and spin, then that relationship must flip in the mirror universe. But that gives us an easy test to see which handed universe we live in. Ergo, parity symmetry is violated.

In fact the only way for parity to be conserved is if there was absolutely no correlation between spin direction and the direction of the emitted electrons. That way nothing would change in the reflection. But that’s not what the experiment showed. So how does the spin of the cobalt nucleus relate to all of this chirality stuff? Well you can define a “handedness” by the relationship of electron emission to spin direction. That’s not the same handedness as the quantum chirality of all the quarks comprising that nucleus. But it’s probably connected. Parity transformation flips the handedness of those quarks, and apparently it should affect the direction of decay electrons also.

In fact we know that there is parity violation must be at the level of quantum chirality. It’s

the ultimate source of the different rules of the mirror universe. Why? Because the carriers of the weak interaction - the W- and Z-bosons - only interact with left-chiral particles. They completely ignore right-handed particles. The universe of the mirror really does behave in a fundamentally different way to our universe. This realization has vexed physicists ever since Wu’s experiment. The resolution to this broken symmetry could be in a greater symmetry. See, parity is intrinsically tied to electric charge and the direction of time. Just as a reflection in two directions will get you back where you started, a parity transformation, followed by a flipping of electric charge – positive to negative and vice versa, AND a reversal of the direction of time will also restore a system to its original state. This is CPT symmetry, and so far it appears to hold in all experiments. We’ll come back to this ongoing quest to discover whether CPT is the true underlying symmetry of the universe: deeper than the broken symmetry of parity in a mirror-reflected space time.