*Certain symmetries are obeyed by the rules of physics, whereas others are defied. It’s tempting to add additional ones in theory, but reality disagrees.*

**TAKEAWAYS IMPORTANT**

**Many theoretical and practical discoveries in fundamental physics occurred throughout the twentieth century as a result of the identification of certain symmetries in nature.****While theoretically exciting, the attempt to impose new symmetries resulted in a huge number of predictions that were not supported by experiment or observation.****Many people now believe that theoretical physics has reached a stalemate because it has adhered to unproven notions. We must accept the fact that the Universe is not symmetrical.**

When you wave in the mirror at yourself, your reflection waves back. However, physiologically, there are several ways in which your mirror is essentially different from you. Your reflection lifts its left hand as you raise your right. If you looked at your body using X-rays, you’d see that your heart is in the center-left of your chest, but it’s in the center-right for your reflection. Your reflection closes its second eye when you close one. While most of us are left-right symmetric, any apparent difference will show in our mirror-image counterpart in the exact opposite way.

You could suppose that symmetry is merely a feature of macroscopic things composed of composites of basic particles, yet it turns out that the Universe is not symmetric at all. Allowing an unstable particle to decay reveals several basic discrepancies between the Universe’s permissible decays and the decays you’d see in the mirror. Certain particles, like as **neutrinos**, only arrive in left-handed variants, whereas **antineutrinos**, their antimatter counterparts, only appear in right-handed ones. There are electric charges that generate currents and magnetic fields, but there are no magnetic charges that generate magnetic currents and electric fields.

Nature is not symmetric, despite the mathematical temptation of more symmetries and the stunning physical repercussions they would have for our Universe. Here’s how physicists have been chasing after a magnificent possibility that isn’t borne up by reality after some initial triumphs conjuring it.

If a theory is not relativistically invariant, various frames of reference, including different locations and movements, will experience distinct laws of physics (and will disagree on reality). We have a conserved quantity: linear momentum, because we have symmetry under ‘boosts,’ or velocity changes. When momentum isn’t just a number linked with a particle, but a quantum mechanical operator, this is considerably more difficult to grasp (but still true!). (Image courtesy of Krea/Wikimedia Commons)

At a fundamental level, symmetries in nature and conserved quantities in the Universe are inextricably linked. Emmy Noether, whose namesake theory — Noether’s theorem — remains one of the core concepts of theoretical physics to this day, mathematically proved this discovery over a century ago. The theory, which was originally limited to continuous and smooth symmetries across physical space, has recently been expanded to reveal fundamental linkages between Universe symmetries and conservation principles.

- If your system is time-translation invariant, meaning it is the same today as it was in the past or will be in the future, the rule of conservation of energy applies.
- If your system is space-translation invariant, meaning it is identical here to how it was over there or will be in the future, the law of conservation of momentum applies.
- The rule of conservation of angular momentum applies if your system is rotationally invariant, which means you may spin it about its axis and its attributes remain the same.

The accompanying conservation rules do not exist where these symmetries do not exist. Time-translation invariance vanishes in the expanding Universe, for example, and energy is not conserved in those situations.

In the expanding Universe, this simplified animation depicts how light redshifts and distances between unbound things alter over time. Note that each photon loses energy as it travels through the expanding Universe, and that energy does not “move” anyplace; in a Universe that changes from instant to moment, energy is simply not conserved. (Photo courtesy of Rob Knop)

Although there are two types of symmetry: continuous symmetries like rotational or translational invariance, and discrete symmetries like mirror (reflection) symmetries or charge conjugation (replacing particles with their antiparticle counterparts) symmetries, the Universe does not obey every symmetry we can imagine.

If you watch an unstable particle like a meson, for example, you’ll see that it has a spin: an inherent angular momentum. The direction in which that meson “spits” a certain particle out will be associated with its spin when it decays. The particle that is spit out will point in the direction of your thumb if you imagine it rotating clockwise, like curling the fingers of your left hand as your left thumb points towards your face. The mirror-reflection variant, on the other hand, will appear right-handed rather than left-handed.

It’s a wash for some decays in some mesons: the quantity of right-handed and left-handed decays is equal. Others, on the other hand, believe that the Universe “prefers” one form of handedness over the other. The “mirror image” representation of reality differs significantly from the reality we see.

Along with time-reversal and charge-conjugation symmetry, parity, or mirror-symmetry, is one of the three fundamental symmetries in the Universe. If particles spin in one way and decay along a specific axis, flipping them in the mirror should result in them spinning in the opposite direction and decaying along the same axis. Madame Chien-Shiung Wu showed that this was not the case for weak decays, which was the first evidence that particles may have an inherent ‘handedness.’ (Beyond the Galaxy/E. Siegel/Credit: E. Siegel)

There are several additional natural instances of these basic asymmetries.

- When we witness
**neutrinos**, we notice that they are always left-handed; if the neutrino goes in the direction that your thumb points, your neutrino’s spin will only be described by the direction that your left hand’s fingers curl.**Antineutrinos**, meanwhile, are always right-handed; it’s as though the matter and antimatter versions of these particles are fundamentally different. - When we look at the stars, galaxies, and even intergalactic components of the Universe, we see that they are mostly constituted of matter rather than antimatter. A fundamental imbalance between matter and antimatter was generated at some point in the Universe’s distant history.
- When we examine the rules of physics, we can see that writing down the laws for magnetic charges and currents, as well as the electric fields they produce, is just as simple as writing down the laws for electric charges and currents that generate magnetic fields. However, it appears that our Universe only has electric charges and currents, not magnetic ones. The Universe might be symmetric, but it isn’t for whatever reason.

It’s possible to put down a variety of equations that explain the Universe, such as Maxwell’s equations. We can write them down in a number of ways, but the only way to determine their validity is to compare their predictions to physical observations. It is for this reason that the version of Maxwell’s equations with magnetic monopoles (right) does not correlate to reality, but the ones without (left) do. (Photo courtesy of Ed Murdock)

Despite this, the strong link between symmetries and conserved quantities resulted in a sequence of astonishing advances in physics over the twentieth century. There was an understanding that symmetries might be reestablished at high temperatures, and that as the Universe cools and those symmetries are disrupted, certain exciting physical consequences will occur. Furthermore, certain quantities seemed to be preserved without explanation, and linking those conserved values to a putative underlying symmetry yielded some intriguing and groundbreaking results in terms of what was going on in the Universe.

The Ward identity is a quantum identity that leads to electric charge conservation.

A massless particle called a Goldstone boson can emerge when certain symmetries break.

The application of group theory, Lie algebras, and other mathematical sciences to the fundamental physics that underpins the Universe resulted in a slew of incredible concepts. The idea that two seemingly unrelated forces — the electromagnetic force and the weak nuclear force — may combine at a high energy level was perhaps the most innovative. If this symmetry were to be broken, a slew of new particles would emerge, while previously massless particles would become huge. The superheavy weak gauge bosons, the W-and Z bosons, as well as the massive Higgs boson, were discovered, demonstrating the astonishing results attainable with imposing new symmetries and force unification.

The particles of the Standard Model and their (hypothetical) supersymmetric counterparts This spectrum of particles is an unavoidable result of String Theory’s unification of the four basic forces, but if String Theory and supersymmetry aren’t important to our Universe, this picture is only a mathematical curiosity. (Photo courtesy of Claire David)

Given the Standard Model’s unrivaled success in describing the Universe we live in, it’s only natural that physicists began to investigate the idea of imposing additional symmetries and working out the consequences of what would happen if reality had an even more symmetric structure at even higher energies.

The following were two of the most common suggestions:

- enforcing a left-right symmetry in which right-handed neutrinos/left-handed antineutrinos and magnetic charges (monopoles) are as common as left-handed neutrinos/right-handed antineutrinos and electric charges are today
- and a unification symmetry, in which the electromagnetic and strong nuclear forces unite at even higher temperatures than the electromagnetic and weak nuclear forces do: at the grand unification scale rather than the electroweak scale.

The more symmetric the Universe is, the easier it is to mathematically describe it. The notion behind this high-energy simplicity is that our Universe seems “messy” and “inelegant” because we dwell at low energies, and the underlying symmetries are (badly) broken today. However, in the early Universe’s hot, dense, energetic condition, the Universe may have been more symmetrical and simpler, and these extra symmetries would have intriguing physical repercussions.

The concept of unification states that the three Standard Model forces, as well as perhaps gravity at higher energies, are combined in a single framework. Although this notion is still popular and mathematically convincing, there is no concrete evidence to support its reality relevance. (Photo courtesy of ABCC Australia, 2015)

As soon as these concepts were addressed, it seemed conceptually appealing to construct a representation of nature that was as symmetrical, simple, and elegant as possible. Why should we stop at enforcing left-right symmetry or uniting the electroweak and strong nuclear forces?

- You might impose an extra symmetry between Fermions (half-integer spin fundamental particles, i.e., 1/2, 3/2, 5/2, etc.) and Bosons (integer spin fundamental particles, i.e., 0, 1, 2, etc.) that would put them on an equal footing. This leads to supersymmetry, which is one of the most important concepts in current basic physics.
- To expand the Standard Model, one might use bigger mathematical groups, resulting in models that were both left-right symmetric and united the three quantum forces.
- You might even take it a step further and try to weave gravity into the equation, combining all of nature’s forces into one massive mathematical structure: this is the core premise of string theory.

The mathematical structure of the Universe looks to be simpler and more elegant the more symmetries you’re ready to impose.

The difference between a Lie algebra based on the E(8) group (left) and the Standard Model (right). The Lie algebra that defines the Standard Model is mathematically a 12-dimensional entity; the E(8) group is fundamentally a 248-dimensional entity. There is a lot that has to go away to get back the Standard Model from String Theories as we know them. (Credit: Cjean42/Wikimedia Commons)

However, there are substantial issues with introducing more symmetries that are frequently overlooked. For one thing, each of the novel symmetries presented here leads to predictions of new particles and events, none of which have been confirmed by experimentation.

- Making the Universe left-right symmetric predicts the existence of magnetic monopoles, however no magnetic monopoles have been seen.
- Right-handed neutrinos and left-handed antineutrinos should both exist if the Universe is left-right symmetric, however all neutrinos seem left-handed and all antineutrinos appear right-handed.
- In the context of grand unification, combining the electroweak and strong nuclear forces predicts the existence of new, super-heavy bosons that link to both quarks and leptons, allowing the proton to disintegrate. Despite this, the proton is stable, having a lifespan bottom limit of more than a mind-boggling 1034 years.
- While the same grand unification paradigm suggests a means to create matter-antimatter asymmetry where none previously existed, particle physics tests have ruled out the process that leads to it.

Regardless of how appealing the possibilities for these new symmetries seem, reality just does not support them.

If we let X and Y particles decay into the quarks and leptons depicted, their antiparticle counterparts will decay into the antiparticle combinations as well. However, if CP is broken, the decay paths — or the fraction of particles decaying one way over another — for the X and Y particles might differ from the anti-X and anti-Y particles, resulting in a net creation of baryons and leptons over antileptons. Unfortunately, this interesting idea is irreconcilable with the Universe as we know it. (Beyond the Galaxy/E. Siegel/Credit: E. Siegel)

In fact, if you want to produce as huge a matter-antimatter asymmetry as we see today in our Universe, you’ll need a Universe that’s more asymmetric than the one we know. Even with the Standard Model’s asymmetries, we can only get a matter-antimatter asymmetry millions of times less than what we require to accord with observations. Additional symmetries will only assist if they are more severely broken than any existing symmetries we already have.

Indeed, it’s simple to argue that the “hints” of extra symmetries we observe are the result of our own aspirations, imaginations, and prejudices, rather than a physical requirement. Some physicists have noticed that the three coupling constants representing the three quantum forces, electromagnetism, weak force, and strong force, all change strength with energy and almost (but not quite) meet at the same high energy scale: approximately 1016 GeV. They could actually meet if you introduce some new particles or symmetries, like as supersymmetry or extra dimensions.

However, there is no certainty that this is how nature works in practice; this is only one mathematical option. (If you create three non-parallel lines on a log-log scale and zoom out, you’ll notice that they all have this attribute.) And, contrary what Max Tegmark claims, mathematics is not the same as physics. Mathematics provides possibilities for what physics may produce, but only observation of the Universe can reveal which mathematical possibilities are actually physical.

In the Standard Model (left) and with a new set of supersymmetric particles (right), the three fundamental coupling constants (electromagnetic, weak, and strong) are plotted against energy. The fact that the three lines are almost touching is appealing to some people, but not to everyone. (Credit: J. Phys. (2006), W.-M. Yao et al. (Particle Data Group))

In any undertaking, but especially in the sciences, there is always a strong desire to repeat what has previously worked. If you don’t have instant success, you can be tempted to believe that the desired discoveries are just barely, just slightly out of reach, and that with a little more data, just a little bit beyond the present frontiers, you’ll find what you’re looking for. However, after more than 40 years of adding symmetries beyond those seen in the Standard Model, the lesson we should take away is that there is no evidence to support these theories. There are no magnetic monopoles, “other-chirality” neutrinos, proton decay, or other phenomena.

The Universe is not symmetric, and we’ll all be better off if we let our measured Universe lead us rather than our theoretical biases. There are many other ways to imagine a more symmetric Universe, and if progress is to be achieved, it may be time for that mainstream but unsubstantiated view to make way to others. In a 2021 interview, physicist Lee Smolin said:

“When people talk about diversity, I don’t simply mean women, blacks, aboriginals, or anyone else; they are all extremely essential, but individuals who think differently are also very important… Yes yes yes yes … I hope that the next generation and the generation after that live in a scientific environment that is far more enjoyable. Because it’s not enjoyable if everyone is like you.”