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Starts With A Bang

This Is The One Symmetry That The Universe Must Never Violate

The combination of charge conjugation, parity, and time-reversal symmetry is known as CPT. And it must never be broken. Ever.

The ultimate goal of physics is to accurately describe, as precisely as possible, exactly how every physical system that can exist in our Universe will behave. The laws of physics need to apply universally: the same rules must work for all particles and fields in all locations at all times. They must be good enough so that, no matter what conditions exist or what experiments we perform, our theoretical predictions match the measured outcomes.

The most successful physical theories of all are the quantum field theories that describe each of the fundamental interactions that occur between particles, along with General Relativity, which describes spacetime and gravitation. And yet, there’s one fundamental symmetry that applies to not just all of these physical laws, but for all physical phenomena: CPT symmetry. And for nearly 70 years, we’ve known of the theorem that forbids us from violating it.

There are many letters of the alphabet that exhibit particular symmetries. Note that the capital letters shown here have one and only one line of symmetry; letters like “I” or “O” have more than one. This ‘mirror’ symmetry, known as Parity (or P-symmetry), has been verified to hold for all strong, electromagnetic, and gravitational interactions wherever tested. However, the weak interactions offered a possibility of Parity violation. The discovery and confirmation of this was worth the 1957 Nobel Prize in Physics. (MATH-ONLY-MATH.COM)

For most of us, when we hear the word symmetry, we think about reflecting things in a mirror. Some of the letters of our alphabet exhibit this type of symmetry: “A” and “T” are vertically symmetric, while “B” and “E” are horizontally symmetric. “O” is symmetric about any line that you draw, as well as rotational symmetry: no matter how you rotate it, its appearance is unchanged.

But there are other kinds of symmetry, too. If you have a horizontal line and you shift horizontally, it remains the same horizontal line: that’s translational symmetry. If you’re inside a train car and the experiments you perform give the same outcome whether the train is at rest or moving quickly down the track, that’s a symmetry under boosts (or velocity transformations). Some symmetries always hold under our physical laws, while others are only valid so long as certain conditions are met.

Different frames of reference, including different positions and motions, would see different laws of physics (and would disagree on reality) if a theory is not relativistically invariant. The fact that we have a symmetry under ‘boosts,’ or velocity transformations, tells us we have a conserved quantity: linear momentum. The fact that a theory is invariant under any sort of coordinate or velocity transformation is known as Lorentz invariance, and any Lorentz invariant symmetry conserves CPT symmetry. However, C, P, and T (as well as the combinations CP, CT, and PT) may all be violated individually. (WIKIMEDIA COMMONS USER KREA)

If we want to go down to a fundamental level, and consider the smallest indivisible particles that make up everything we know of in our Universe, we’ll look at the particles of the Standard Model. Consisting of the fermions (quarks and leptons) and bosons (gluons, photon, W-and-Z bosons, and the Higgs), these comprise all of the particles we know of that make up the matter and radiation we’ve directly performed experiments on in the Universe.

We can calculate the forces between any particles in any configuration, and determine how they’ll move, interact, and evolve over time. We can observe how matter particles behave under the same conditions as antimatter particles, and determine where they’re identical and where they’re different. We can perform experiments that are the mirror-image counterparts of other experiments, and note the results. All three of these test the validity of various symmetries.

The particles and antiparticles of the Standard Model obey all sorts of conservation laws, but there are slight differences between the behavior of certain particle/antiparticle pairs that may be hints of the origin of baryogenesis. The quarks and leptons are examples of fermions, while the bosons (bottom row) mediate forces and arise as a consequence of the origin of mass. (E. SIEGEL / BEYOND THE GALAXY)

In physics, these three fundamental symmetries have names.

  1. Charge conjugation (C): this symmetry involves replacing every particle in your system with its antimatter counterpart. It’s called charge conjucation because every charged particle has an opposite charge (such as electric or color charge) for its corresponding antiparticle.
  2. Parity (P): this symmetry involves replacing every particle, interaction, and decay with its mirror-image counterpart.
  3. Time-reversal symmetry (T): this symmetry mandates that the laws of physics affecting the interactions of particles behave the exact same ways whether you run the clock forwards or backwards in time.

Most of the forces and interactions that we’re used to obey each of these three symmetries independently. If you threw a ball in the gravitational field of Earth and it made a parabola-like shape, it wouldn’t matter if you replaced the particles with antiparticles (C), it wouldn’t matter if you reflected your parabola in a mirror or not (P), and it wouldn’t matter if you ran the clock forwards or backwards (T), so long as you ignored things like air resistance and any (inelastic) collisions with the ground.

Nature is not symmetric between particles/antiparticles or between mirror images of particles, or both, combined. Prior to the detection of neutrinos, which clearly violate mirror-symmetries, weakly decaying particles offered the only potential path for identifying P-symmetry violations. (E. SIEGEL / BEYOND THE GALAXY)

But individual particles don’t obey all of these. Some particles are fundamentally different than their antiparticles, violating C-symmetry. Neutrinos are always observed in motion and close to the speed of light. If you point your left thumb in the direction that they move, they always “spin” in the direction that your fingers on your left hand curl in around the neutrino, while antineutrinos are always “right-handed” in the same way.

Some decays violate parity. If you have an unstable particle that spins in one direction and then decays, its decay products can be either aligned or anti-aligned with the spin. If the unstable particle exhibits a preferred directionality to its decay, then the mirror image decay will exhibit the opposite directionality, violating P-symmetry. If you replace the particles in the mirror with antiparticles, you’re testing the combination of these two symmetries: CP-symmetry.

A normal meson spins counterclockwise about its North Pole and then decays with an electron being emitted along the direction of the North Pole. Applying C-symmetry replaces the particles with antiparticles, which means we should have an antimeson spinning counterclockwise about its North Pole decay by emitting a positron in the North direction. Similarly, P-symmetry flips what we see in a mirror. If particles and antiparticles do not behave exactly the same under C, P, or CP symmetries, that symmetry is said to be violated. Thus far, only the weak interaction violates any of the three, but its possible that there are violations in other sectors below our current thresholds. (E. SIEGEL / BEYOND THE GALAXY)

In the 1950s and 1960s, a series of experiments were performed that tested each of these symmetries and how well they performed under the gravitational, electromagnetic, strong and weak nuclear forces. Perhaps surprisingly, the weak interactions violated C, P, and T symmetries individually, as well as combinations of any two of them (CP, PT, and CT).

But all of the fundamental interactions, every single one, always obeys the combination of all three of these symmetries: CPT symmetry. CPT symmetry says that any physical system made of particles that moves forwards in time will obey the same laws as the identical physical system made of antiparticles, reflected in a mirror, that moves backwards in time. It’s an observed, exact symmetry of nature at the fundamental level, and it should hold for all physical phenomena, even ones we have yet to discover.

The most stringest tests of CPT invariance have been performed on meson, lepton, and baryon-like particles. From these different channels, the CPT symmetry has been shown to be a good symmetry to precisions of better than 1-part-in-10-billion in all of them, with the meson channel reaching precisions of nearly 1 part in 1⁰¹⁸. (GERALD GABRIELSE / GABRIELSE RESEARCH GROUP)

On the experimental front, particle physics experiments have been operating for decades to search for violations of CPT symmetry. To significantly better precisions than 1-part-in-10-billion, CPT is observed to be a good symmetry in meson (quark-antiquark), baryon (proton-antiproton), and lepton (electron-positron) systems. Not a single experiment has ever observed an inconsistency with CPT symmetry, and that’s a good thing for the Standard Model.

It’s also an important consideration from a theoretical perspective, because there’s a CPT theorem that demands that this combination of symmetries, applied together, must not be violated. Although it was first proven in 1951 by Julian Schwinger, there are many fascinating consequences that arise because of the fact that CPT symmetry must be conserved in our Universe.

We can imagine that there’s a mirror Universe to ours where the same rules apply. If the big red particle pictured above is a particle with an orientation with its momentum in one direction, and it decays (white indicators) through either the strong, electromagnetic, or weak interactions, producing ‘daughter’ particles when they do, that is the same as the mirror process of its antiparticle with its momentum reversed (i.e., moving backwards in time). If the mirror reflection under all three (C, P, and T) symmetries behaves the same as the particle in our Universe, then CPT symmetry is conserved. (CERN)

The first is that our Universe as we know it would be indistinguishable from a specific incarnation of an anti-Universe. If you were to change:

  • the position of every particle to a position that corresponded to a reflection through a point (P reversal),
  • each and every particle replaced by their antimatter counterpart (C reversal),
  • and the momentum of each particle reversed, with the same magnitude and opposite direction, from its present value (T reversal),

then that anti-Universe would evolve according to exactly the same physical laws as our own Universe.

Another consequence is that if the combination of CPT holds, then every violation of one of them (C, P, or T) must correspond to an equivalent violation of the other two combined (PT, CT, or CP, respectively) in order to conserve the combination of CPT. It’s why we knew that T-violation needed to occur in certain systems decades before we were capable of measuring it directly, because CP violation demanded it be so.

In the Standard Model, the neutron’s electric dipole moment is predicted to be a factor of ten billion larger than our observational limits show. The only explanation is that somehow, something beyond the Standard Model is protecting this CP symmetry in the strong interactions. If C is violated, so is PT; if P is violated, so is CT; if T is violated, so is CP. (PUBLIC DOMAIN WORK FROM ANDREAS KNECHT)

But the most profound consequence of the CPT theorem is also a very deep connection between relativity and quantum physics: Lorentz invariance. If the CPT symmetry is a good symmetry, then the Lorentz symmetry — which states that the laws of physics stay the same for observers in all inertial (non-accelerating) reference frames — must also be a good symmetry. If you violate the CPT symmetry, then the Lorentz symmetry is also broken.

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Breaking Lorentz symmetry might be fashionable in certain areas of theoretical physics, particularly in certain quantum gravity approaches, but the experimental constraints on this are extraordinarily strong. There have been many experimental searches for violations of Lorentz invariance for over 100 years, and the results are overwhelmingly negative and robust. If the laws of physics are the same for all observers, then CPT must be a good symmetry.

Quantum gravity tries to combine Einstein’s General theory of Relativity with quantum mechanics. Quantum corrections to classical gravity are visualized as loop diagrams, as the one shown here in white. If you extend the Standard Model to include gravity, the symmetry that describes CPT (the Lorentz symmetry) may become only an approximate symmetry, allowing for violations. Thus far, however, no such experimental violations have been observed. (SLAC NATIONAL ACCELERATOR LAB)

In physics, we have to be willing to challenge our assumptions, and to probe all possibilities, no matter how unlikely they seem. But our default should be that the laws of physics that have stood up to every experimental test, that compose a self-consistent theoretical framework, and that accurately describe our reality, are indeed correct until proven otherwise. In this case, it means that the laws of physics are the same everywhere and for all observers until proven otherwise.

Sometimes, particles behave differently than antiparticles, and that’s okay. Sometimes, physical systems behave differently than their mirror-image reflections, and that’s also okay. And sometimes, physical systems behave differently depending on whether the clock runs forwards or backwards. But particles moving forwards in time must behave the same as antiparticles reflected in a mirror moving backwards in time; that’s a consequence of the CPT theorem. That’s the one symmetry, as long as the physical laws that we know of are correct, that must never be broken.

Ethan Siegel is the author of Beyond the Galaxy and Treknology. You can pre-order his third book, currently in development: the Encyclopaedia Cosmologica.


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