The Greek philosopher Plato is well known for his allegories and metaphors. Of particular interest is his Allegory of the Cave, which appeared in The Republic, written around 380BCE. In it, Plato describes a group of prisoners which are chained to a wall within a cave, and have been all of their lives. They have no direct interaction with the world outside of the cave. They only know of the world via shadows that are cast on the wall opposite of them. For the prisoners, the shadows are their reality. Though you and I know the shadows are only a very low-resolution representation of that reality.
Theoretical physicist Steven Weinberg, a Nobel Prize winner who works out of the University of Texas at Austin, once likened himself to a prisoner in Plato’s cave. We are forever chained to this cave by the limitations in measurements we can make and experiments we can perform. All that we can know are shadows of the reality that exists in the sub-atomic world. We can see the shadowy figures lurking in our math and as wisps of misty vapor trails in our cloud chambers. We attempt to pierce the veil with the power of our imagination and draw nifty looking charts and animations depicting what our mind’s eye thinks it can see. But in the end, we are all trapped in a cave… staring at shadows. Reflections of a reality we can never truly know.
In our last Quantum Mechanics article, we introduced you to the idea of quantum electrodynamics, or to put it more simply — quantum field theory. In this article, we’re going to explore how QED lead to the prediction and eventual confirmation of something known as the Higgs Boson, also known as the God Particle. As usual, we’ll aim to keep things as simple as possible, allowing anyone with a curious mind to know what this God particle talk is all about. Like so many things in the quantum world, it all started with an unexpected outcome…
The start of World War II threw quantum theory research into disarray. Many of the European physicists left Europe all together, and research moved across the ocean to the shores of the United States. The advent of the atomic bomb thrust American physicists into the spotlight, and physicists began to meet on Shelter Island to discuss the future of quantum theory. By this time one thing was certain: the Copenhagen interpretation of quantum theory had triumphed and challenges to it had mostly died off.
This allowed physicists to focus on a different kind of problem. At this point in time quantum theory was not able to deal with transitional states of particles when they are created and destroyed. It was well known that when an electron came into contact with a positron, the two particles were destroyed and formed at least two photons with a very high energy, known as gamma rays. On the flip side, gamma ray photons could spontaneously turn into positron-electron pairs.
No one could explain why this occurred. It had become obvious to the physicists of the day that a quantum version of Maxwell’s electromagnetic field theory was needed to explain the phenomenon. This would eventually give rise to QED, short for quantum electrodynamics. This is a severely condensed story of how that happened.
Symmetry is everywhere in our natural world. Just take a look at your hands, a butterfly, or a sunflower. It’s easy to pass off the idea of symmetry and symmetric structures as a simple quirk of existence, and to pay it little mind. If this is your view, I can assure you it will no longer be by the end of this series. If we force ourselves to look beyond the grade school applications of symmetry, we find a world rich in connections via many different types of symmetric identities. One of the most interesting is Gauge Symmetry, which lies at the heart of Quantum Electrodynamics, or QED (we’ll get into this a bit later in the series). Several branches of higher level mathematics study symmetry in detail, allowing a host of sciences, from physics to chemistry, to view difficult problems and theories from a different perspective.
The subject matter of the ideas explored in symmetry is complicated, and not well known outside of academia and the theoretical sciences. It is the goal of this series of articles to simplify some of the concepts that underpin the study of symmetry, so that the average hacker can gain a basic (and I mean basic) understanding of this fascinating body of knowledge, and put it to use in future projects. We’ll start things off by taking a look at a machine that has crossed the Hackaday server many times – those nifty Rubik’s Cube solvers. Just how do those things work anyway?