Symmetry is Your Future!

We all understand symmetry, most of us have been familiar with it since primary school (except with its spelling, maybe). You may have heard that a symmetrical face is a beautiful one (debatable, but generally held as true). In the same light, a hexagon is often a prettier sight than a random scribble. At the more extreme end of the reverence of symmetry, we have the advocates for the symmetry-underliying-reality principle. To these people, symmetry is not merely tasteful but can also be profoundly meaningful: its prevalence in the Chinese Yin and Yang is empirical to the fundamentalism of symmetry.

So, is symmetry just a neat consequence of the laws of nature, coincidental and fortunate to those that perceive it? Or, is there truly a symmetrical order at the heart of our reality?

Wouldn’t it be great if everything was symmetrical?

Following the example of the yin-yang, it can be seen as logical to believe in a symmetrical directive underpinning reality. For something to move, for example, directions must be established. An object cannot move unless it is moving away from one thing and towards another, even if the things it is moving away from and towards are backwardness and forwardness, respectively. The polarity of direction is necessary for movement, as is the polarity of energy (the gain or loss of energy). In this manner, we can attribute an opposite to everything, and pretty much discern that the whole universe could be contained within a symmetrical framework.

For just a quick note on this topic before we get to the real physics, I want to address a question that you may ask. The question that you may be wondering at present is, “What caused everything to move in the first place? Wasn’t this an asymmetry?” I don’t think that this was the case. For ‘everything’ to suddenly begin moving, there must have either been a chain of causation continuing infinitely, or some supernatural and sudden change somewhere in the universe. If there was a chain of causation, then the universe has always been in motion (at least some part of it), hence — no asymmetry.

On the other hand, if there was a sudden change that caused everything to be in motion, then our laws of physics would not be adequate to describe the universe. Since our laws of physics are accurate, that is, we can predictably describe what is happening and what will happen (at least probabilistically), we can pretty much rule out any contribution from supernatural randomness — that same primordial randomness would have left us in the predictably symmetrical state of being that we see today.

Because of this and other reasons (one of which we will cover in a moment), physicists tend to believe that there is a deeply symmetrical description of the universe waiting to be discovered. Einstein held the view that nature was inherently symmetrical and he actually looked for symmetries in the world as part of his pursuit of new theories. In looking at the way that physical phenomena remain the same in different circumstances, professor Einstein paved the way for symmetry to be used as a basis for physical explorations.

“I suppose that I tend to be optimistic about the future of physics. And nothing makes me more optimistic than the discovery of broken symmetries.” — Steven Weinberg, Nobel Lectures

Today, symmetries are at the cornerstone of modern physics. Both of the main branches of physics — the standard model of particle physics and general relativity — contain symmetries at the heart of their formulations. In quantum mechanics, we have the symmetries of gauge invariance which describe which transformations can occur within equations while maintaining the same result (like the global phase invariance of the Schrödinger equation). In addition, general relativity is presented with the continuous symmetries of spacetime; matter, curvature and many other vector fields are conserved within its specific applications.

You may have heard that general relativity and quantum mechanics are irreconcilable, but we’ve just mentioned that symmetry seems to be a feature that both have in common. Does this mean that any theory of everything would have to exhibit some level of symmetry as part of its bodywork? Some scientists think so! You see, Lie groups are a useful mathematical tool for describing continuous symmetries. They’re part of a subsection of mathematics called ‘abstract algebra’, which is really quite beautiful (R.I.P. Évariste Galois). The continuous symmetries that we have spoken about for general relativity, combined with the continuous symmetries in particle physics (like the special unitary and lorentz groups, for example), might form the base for a new, geometric theory of everything.

Introducing Quantum Gravity Research

I’ve written about Quantum Gravity Research before — the group’s self-simulation hypothesis is a marvel of philosophical ingenuity. Quantum Gravity Research (QGR), base their studies largely around a paper written by Garrett Lisi entitled, “An Exceptionally Simple Theory of Everything.” Aptly named because it’s centered around the link between particle physics and the largest simple, exceptional Lie group (nicknamed ‘E8’). Dr. Garrett Lisi managed to match part of the algebra of E8 with both particle physics and general relativity in 2007 — following a spur of celebration and publicization, Quantum Gravity Research were inspired by some of Lisi’s concepts and have now established a research program dedicated to developing the ideas.

While the ‘exceptionally simple’ theory has been matched with a critical reception, it is still a novel theory and should not be taken lightly. Furthermore, you may be interested to know that its proprietor asserts that string theory, a long heralded candidate for unification, is feeble by comparison. Amusingly, string theory is a theory that also relies on deep (and unproven) symmetries to come to fruition (supersymmetry is currently crucial to string theory, and no gripping evidence has been realized to date).

So, a deeply symmetrical proponent of unification is yet to be proven, but does anything else lend credence to the idea?

There is one last point that I would like to discuss — the gravity double-copy. The double-copy theory is relatively new, like Garrett Lisi’s theory of everything. To be honest, quantum gravity theories and related theories are generally quite new, as Quantum Mechanics only began to arise in the early 20th century. All the same, the double-copy theory is far from a theory of everything, but is an inventive way of solving the challenges posed by general relativity. The theory describes the process of altering the equations of quantum kinematics to serve as a shortcut to the solutions of gravitational equations — this massively cuts down the time needed to make calculations about gravity.

The surprising and intriguing element is in the success of using gauge theory calculations to assist with gravity (as we’ve mentioned, the two are normally mutually exclusive). What this modification reveals is that there is a deeper connection between the two that is so far unprobed. Since gauge theory is all about symmetries, this connectedness hints at a hardcore symmetrical theory of quantum gravity.

Thanks for reading! This was a guest post from my website (Unique Philosophy), so if you loved it, check out the other articles there!

Featured image copyright holder Jgmoxness, copyright usage under CC (link).