The Difference between Left and Right
By: Manuel Brenner
Tags: Parity, Physics, Aliens, Philosophy, Science

In times of increasing political division between the Right and the Left, I want to spend a couple of minutes leaving all the tension and controversy aside, approaching the whole problem of Left and Right from a somewhat different angle.

In answering this question, I will touch upon phone calls with aliens, an angry exchange of letters between the 17th centuries greatest thinkers, and of course particle physics.

An Unusual Phone Call

Imagine you answer your phone one day and an alien is on the other side of the line. It has learned to speak English very well, and, once you overcome your intial shock, you start to speak with it quite casually. After a bit of polite smalltalk, you realize the alien wants something from you, and soon enough, it reveals to you that it mainly called you because a question has been nagging it for quite some time. It has learned to speak English by listening to lots and lots of signals of humans talking with each other that it intercepted in the wide expanses of space, but it can’t really seem to understand a very important distinction: where left is and where right is.

Photo by Pablo García Saldaña on Unsplash

You immediately tell the alien that it is stupid, because the answer must of course be obvious. But the more you think about it, the more you realize you have a problem. You start out with giving the alien simple instructions on how to construct a three dimensional cube that, quite naturally, has a left side and a right side. But once the cube is nearly finished, the alien asks you again how to assign the labels left and right. You start pointing at your left hand or the left side of the room, but the alien can’t see you, so it doesn’t understand what you mean. You have an idea: you point to the milky way (and say that it rotates in a certain direction), but unfortunately, the alien tells you it is floating somewhere in empty space, without seeing any of the things you are seeing, and without having any access to the objects you have around you. The alien asks you who is stupid now?…and you hang up the phone in frustration.

While the odds are small that you will really be faced with this situation, it serves as an introduction to a more general problem with some serious philosophical implications.

The Ozma Problem

The Ozma Problem was introduced by Martin Gardner in his book The Ambidexterous Universe in 1964. It is characterized by the problem of communicating the difference between left and right via a serial communication channel.

If we assume that we don’t have shared access to any chiral objects like hands or spiral galaxies, the problem becomes quite tricky to resolve.

Children learn the distinction by pointing to things like their hands. I remember my class in elementary school singing a song (that has a nicer ring to it in German) that went something like “whoever can’t distinguish between left (upon which we would shake our left hand) and right (upon which we would shake our right hand) is a poor man.” I only later realized it’s a bit insensitive considering there are many people with left-right orientation, f.e. as part of the Gerstmann Syndrome. But it’s such an ordinary skill in daily life that it is easy to overlook the deeper significance behind the distinction.

Hands are chiral objects connected to each other through a mirroring operation which is formally called a parity transformation. When you see your left hand in a mirror, it looks like a right hand. Accordingly, Cartesian coordinate systems, which are chiral counterparts of each other, are called left-handed and right-handed systems, as the orientation of the axis neatly maps onto our fingers.

We can instruct the alien to build chiral objects, but as long as there is no palpable difference between the two mirror versions of the object, we can’t teach it to assign the labels left and right.

Leibniz, Newton and the Reality of Space

Photo by NASA on Unsplash

The Ozman problem brings us to the debate about the reality of physical space. In our thought experiment, the alien is floating in empty space, so it can not see any specific configurations of matter that have distinguishable left and right sides.

Note that the notion of space can be expanded to a more general concept: what is the structure of the vacuum state of the universe, as we would call it in quantum field theory? Is nothingness, i.e. complete emptiness of matter, really nothing, or is there some structure to nothing?

The alien is therefore constrained to solving the Ozma problem by finding a difference between left and right in the fundamental makeup of the universe. As we assume the laws of physics to be homogeneous in the universe, it could probe them everywhere in the universe, independent of its location.

We can rephrase the Ozma problem and ask whether the laws of nature are invariant under parity transformations. Do we see a difference between physical processes that are mirror images of each other? Are there physical processes that would work one way, but not as their mirror image/chiral counterpart? If this were indeed possible, we could instruct the alien to build both “versions” of the physical process, and see in which they worked differently. This one would then allow us to clearly distinguish between left and right.

Do mirror images of natural phenomena lead to different physics? Photo by Javier Graterol on Unsplash

As I mentioned, Leibniz and Newton already argued about this in a heated exchange of letters in the 17th century. They never met in person and groomed a personal dislike for each other (in part owing to their battle over the creative claims to calculus, which is admittedly something one wants to be credited for), but their differences extended to a professional level.

When it came to positing the reality of space, Leibniz took the position of a relativist. He claimed that space does not in itself exist, but only the things in space exist. Leibniz’ argument is the following: if one were to carry out a symmetry transformation (e.g. a rotation or a parity transformation) on all contents of spacetime, this would not lead to any observable difference. Assuming the identity of things that have no observable difference, the reality of space itself were an unnecessary assumption within the theory, as it does not lead to any observable differences.

On the other hand, Newton was substantialist in positing a reality to space that goes merely beyond its content, and has ontological status. The notions of absolute space and time were introduced by Newton in his Philosophiæ Naturalis Principia Mathematica, and play an important foundation when defining Newtonian mechanics. They are necessary for a coherent definition of inertial systems, which in turn are the foundation for the definition of forces.

So who is right? Or do we even know today who was right?Answering the question brings us to modern particle physics.

Parity Violation

As it turns out, there is indeed a solution to the Ozman problem (within our universe): we can instruct the alien to rebuild the most upbeat experiment in the history of physics: the Wu experiment.

The basic premise behind the experiment is to build to physical processes which are mirror images of each other, and test if there is a difference.

The Wu experiment. Credit to nagualdesign [CC BY-SA 3.0]

The beta emissions observed in the Wu experiment are communicated through the weak interaction, which is one of the four fundamental forces of nature.

In 1956, Madame Wu built two mirror image versions of the experiment (the left side and the right side of the figure), as you can see in the orientation of the coils. The beta decays in the mirror version (the right one) were pointing in the wrong direction, showing that parity symmetry in the weak interaction was indeed not conserved.

This, and many other consecutive experiments, have lead to the conclusion that the weak interaction is what physicists call maximally parity-violating, and that the laws of physics really make a difference between left and right (in technical terms, only left-handed fermions and right-handed antifermions interact via the weak force).

One can see this is an indicator that relationialist accounts of the world are incorrect, and there is something substantial to space. Nevertheless it is not as clear cut if this pertains to the reality of physical space. Parity symmetry is intrinsically related to time reversal symmetry and charge conjugation through the CPT theorem, which states that every physical theory that is Lorentz invariant has to be invariant under simultaneous time reversal, charge conjugation and parity transformations. Parity violation therefore implies time reversal symmetry violation (because both have to be violated if the combination is not), which has indeed been found to be violated as well (more on this in another article).

As always the case with modern physics, the implications are hard to make sense of. I’m leaning towards Newton’s substantialist notion in thinking that the laws of physics really have their own structure and reality, along the lines of structural realist interpretations of the world. These make the claim that the structures that are the contents of our physical theories do exist in a meaningful way.

Problems of interpretation aside, at least we can now walk through our daily lifes a little more confident knowing that in case an alien floating in space calls us out of the blue to ask us about the difference between left and right, we have a good answer for it.