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Starts With A Bang

No, The Laws Of Physics Are Not The Same Forwards And Backwards In Time

The laws of physics are not time-reversal invariant. Here’s how we know.

No matter when, where, or what you are in the Universe, you experience time in only one direction: forwards. In our everyday experiences, clocks never run backwards; scrambled eggs never uncook and unscramble themselves; shattered glass never spontaneously reassembles itself. But if you were to look at the laws of physics that govern the way the Universe works ⁠ — from Newton’s laws of motion down to the quantum physics of subatomic particles ⁠ — you’d find something peculiar and unexpected: the rules are exactly the same whether time runs forwards or backwards.

This corresponds to a certain symmetry of nature: T-symmetry, or time-reversal invariance. Our everyday experience indicates to us, quite strongly, that the laws of physics must violate this symmetry, but for decades, we couldn’t demonstrate it. But a few years ago, we experimentally proved the laws of physics are different depending on which direction time runs. Here’s how we know.

According to legend, the first experiment to show that all objects fell at the same rate, irrespective of mass, was performed by Galileo Galilei atop the Leaning Tower of Pisa. Any two objects dropped in a gravitational field, in the absence of (or neglecting) air resistance, will accelerate down to the ground at the same rate. This was later codified as part of Newton’s investigations into the matter. A ball dropped off of the tower and a ball thrown up from the bottom of the tower could have the same trajectory, as the laws of motion are the same regardless of the direction in which time flows. (GETTY IMAGES)

Imagine you and a friend decide to go to Pisa, with one of you standing atop the famous leaning tower and the other located down at the bottom. From the top, whoever throws a ball off the edge can easily predict where it will land down on the bottom. Yet if the person at the bottom were to throw the ball upwards with an equal-and-opposite velocity to the ball that just landed, it would arrive exactly at the location where the person at the top threw their ball from.

This is a situation where time-reversal invariance holds: where the T-symmetry is unbroken. Time reversal can be thought of the same way as motion reversal: if the rules are the same whether you run the clock forwards or backwards, there’s true T-symmetry. But if the rules are different when the clock runs backwards from when the clock runs forwards, the T-symmetry must be broken.

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)

There are two very, very good (but indirect) reasons to believe that T-symmetry must be broken at some deep, fundamental level. The first is a proven theorem known as the CPT theorem. If you have a quantum field theory that obeys the rules of relativity ⁠ — i.e., is Lorentz invariant ⁠ — that theory must exhibit CPT-symmetry.

There are three symmetries that are both discrete and fundamental in the context of the Standard Model of particle physics:

  • C-symmetry, which demands that you replace all particles with their antiparticles,
  • P-symmetry, which demands that you replace all particles with their mirror-image reflections, and
  • T-symmetry, which demands that you run the laws of physics backwards in time instead of forwards.
Changing particles for antiparticles and reflecting them in a mirror simultaneously represents CP symmetry. If the anti-mirror decays are different from the normal decays, CP is violated. Time reversal symmetry, known as T, must beviolated if CP is violated. The combined symmetries of C, P, and T, all together, must be conserved under our present laws of physics, with implications for the types of interactions that are and aren’t allowed. (E. SIEGEL / BEYOND THE GALAXY)

The CPT theorem tells us that the combination of all three symmetries must always be preserved. In other words, a spinning particle moving forwards in time must obey the same rules as its antiparticle spinning in the opposite direction moving backwards in time. If C-symmetry is violated, then PT-symmetry must also be violated by an equal amount to keep the combination conserved. As CP-symmetry violation has already been observed (dating back to 1964), we know that T-symmetry must be violated as well.

The second reason is that we live in a Universe where there’s more matter than antimatter, but the laws of physics we know are completely symmetric between matter and antimatter.

If you create new particles (such as the X and Y here) with antiparticle counterparts, they must conserve CPT, but not necessarily C, P, T, or CP by themselves. If CP is violated, the decay pathways — or the percentage of particles decaying one way versus another — can be different for particles compared to antiparticles, resulting in a net production of matter over antimatter if the conditions are right. (E. SIEGEL / BEYOND THE GALAXY)

It’s true that there must necessarily be additional physics to what we’ve observed to explain this asymmetry, but there are significant restrictions on the types of new physics that can cause it. They were elucidated by Andrei Sakharov in 1967, who noted:

  1. The Universe must be in an out-of-equilibrium state.
  2. Both C-symmetry and CP-symmetry must be violated.
  3. And baryon number-violating interactions must occur.

Even if we hadn’t observed CP-violating interactions directly, we’d have known that they must occur in order to create a Universe that’s consistent with what we observe. And therefore, since again T-violation is necessarily implied by CP-violation, T-symmetry cannot always hold true.

The rate of orbital decay of a binary pulsar is highly dependent on the speed of gravity and the orbital parameters of the binary system. We have used binary pulsar data to constrain the speed of gravity to be equal to the speed of light to a precision of 99.8%, and to infer the existence of gravitational waves decades before LIGO and Virgo detected them. However, the direct detection of gravitational waves was a vital part of the scientific process, and the existence of gravitational waves would still be in doubt without it. (NASA (L), MAX PLANCK INSTITUTE FOR RADIO ASTRONOMY / MICHAEL KRAMER (R))

But there’s an enormous difference, in any science, between either theoretical or indirect evidence for a phenomenon and a direct observation or measurement of the desired effect. Even in instances where you know what the outcome must be, experimental verification must be demanded, or we run the risk of fooling ourselves.

This is true in any area of physics. Sure, we knew by watching the timing of binary pulsars that their orbits were decaying, but only with the direct detection of gravitational waves could we be certain that’s how the energy was being carried away. We knew that event horizons must exist around black holes, but only by directly imaging them did we confirm this prediction of theoretical physics. And we knew that the Higgs boson must exist to make the Standard Model consistent, but only by discovering its unambiguous signatures at the LHC did we confirm it.

The first robust, 5-sigma detection of the Higgs boson was announced a few years ago by both the CMS and ATLAS collaborations. But the Higgs boson doesn’t make a single ‘spike’ in the data, but rather a spread-out bump, due to its inherent uncertainty in mass. Its mass of 125 GeV/c² is a puzzle for theoretical physics, but experimentalists need not worry: it exists, we can create it, and now we can measure and study its properties as well. (THE CMS COLLABORATION, “OBSERVATION OF THE DIPHOTON DECAY OF THE HIGGS BOSON AND MEASUREMENT OF ITS PROPERTIES”, (2014))

In order to directly, experimentally confirm the existence of T-violation, scientists had to be incredibly clever. What one must do is design an experiment where the laws of physics could be directly tested for differences between an experiment that runs forwards in time versus one that runs backwards. And since — in the real world — time only runs forwards, this required some truly creative thinking.

The way to think about this is to remember how entangled quantum states work. If you have two quantum particles that are entangled with one another, you know something about their combined properties, but their individual properties are indeterminate until you make a measurement. Measuring the quantum state of one particle will give you some information about the other one, and will give it to you instantaneously, but you cannot know anything about either individual particle until that critical measurement occurs.

If two particles are entangled, they have complementary wavefunction properties, and measuring one determines properties of the other. If you create two entangled particles or systems, however, and measure how one decays before the other decays, you should be able to measure the time-reversed reaction to test for T-symmetry conservation or violation. (WIKIMEDIA COMMONS USER DAVID KORYAGIN)

Typically, when we think about quantum entanglement of two particles, we perform experiments involving stable particles, like photons or electrons. But there’s only one type of physics process where CP-violation is known to occur: through decays that proceed through the weak nuclear interaction. In fact, this direct type of CP-violation was observed in 1999, and by the CPT theorem, T-violation must occur. Therefore, if we want to test for direct violation of time reversal symmetry, we’d have to create particles where T-violation occurs, which means creating either baryons or mesons (unstable composite particles) that decay via the weak interactions.

These two properties, of quantum indeterminism and of a decay through the weak interactions, can be leveraged to design the exact type of experiment required to test for the direct violation of T-symmetry.

B mesons can decay directly into a J/Ψ (psi) particle and a Φ (phi) particle. The CDF scientists found evidence that some B mesons unexpectedly decay into an intermediate tetraquark structure identified as a Y particle, where the tetraquark consists of two quarks and two antiquarks. When a composite system, such as the Y particle, decays into two states that have different values for their CP properties, they must have different properties for their T properties as well, allowing scientists to create an experiment that can test for T-violation directly. (SYMMETRY MAGAZINE)

The way to go about testing time reversal violation directly first proposed only recently, as the technology to produce large numbers of particles that contain bottom (b) quarks has only come about in the past few years. The ϒ particle (the Greek letter Upsilon) is the classic example of a particle containing bottom quarks, as it’s actually a meson made of a bottom quark and a bottom antiquark pair.

Like most composite particles, there are many different energy states and configurations it can exist in, similar to how the hydrogen atom exhibits a variety of possible energy states for the electron to be in. In particular, it was suggested that the 4s energy state holds some special properties, and might be the best candidate for observing T-symmetry violation directly.

In an atomic system, each s orbital (red), each of the p orbitals (yellow), the d orbitals (blue) and the f orbitals (green) can contain only two electrons apiece: one spin up and one spin down in each one. In a nuclear system, even in a meson which has just a quark and antiquark, similar orbitals (and energy states) exist. In particular, the 4s state of the Upsilon (ϒ) particle has particularly interesting properties, and was created hundreds of millions of times for the BaBar collaboration at SLAC. (LIBRETEXTS LIBRARY / NSF / UC DAVIS)

The reason? The ϒ(4s) particle, when you create one, decays into into both a neutral B-meson (with a down quark and an anti-bottom quark) and a neutral anti-B-meson (with a bottom quark and an anti-down quark) about 48% of the time. At an electron-positron collider, you have the freedom to tune your collisions to occur at the exact energy needed to create a ϒ(4s) particle, meaning that you can create enormous numbers of B-mesons and anti-B-mesons for all your particle physics needs.

Each meson, either a B or an anti-B, can decay in a few possible ways. Either you can produce:

  • a J/ψ (charm-anticharm) particle and a long-lived Kaon,
  • a J/ψ particle and a short-lived Kaon,
  • or a charged lepton and other particles.

This is interesting, because the first decay has a known value of CP, the second has a known value for CP that’s opposite to the first, and the third decay identifies whether it’s a B or anti-B by virtue of the sign of the charge on the lepton. (A positively-charged anti-lepton indicates a B decay; a negatively-charged lepton indicates an anti-B decay.)

A setup of the system used by the BaBar collaboration to probe time-reversal symmetry violation directly. The ϒ(4s) particle was created, it decays into two mesons (which can be a B/anti-B combination), and then both of those B and anti-B mesons will decay. If the laws of physics are not time-reversal invariant, the different decays in a specific order will exhibit different properties. This was confirmed in 2012. (APS / ALAN STONEBREAKER)

When one member of the B/anti-B pair decays into a J/ψ and a Kaon and the other member decays into a lepton, this gives us the opportunity to test for time-reversal violation. Because these two particles, the B and the anti-B, are both unstable, their decay times are only known in terms of their half-lives: decays don’t occur all at once, but at random times with a known probability.

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Then, you’ll want to make the following measurements:

  1. If the first meson to decay does so into a positively charged lepton, you know that the second must be an anti-B particle.
  2. You then measure the decay of the anti-B particle, and see how many of them give you a decay into a short-lived Kaon.
  3. Then, you look for events where the order of decays is reversed and the initial and final states are exchanged, i.e., where the first meson decays into a long-lived Kaon and is followed by the second one decaying into a negatively-charged lepton.

This is a direct test of time-reversal violation. If the two event rates are unequal, the T-symmetry is broken.

There are four independent time-reversal-violating asymmetries in the decaying ϒ(4s) system, corresponding to decays into charged leptons and charm quark-antiquark combinations. The dashed blue curve represents the best fit to the BaBar data without T-violation; you can see how absurdly bad it is. The red curve represents the best-fit data with T-violation. Based on this experiment, direct T-violation is supported at the 14-sigma level. (J. P. LEES ET AL. (THE BABAR COLLABORATION), PHYS. REV. LETT. 109, 211801 (2012))

It took the creation of over 400 million ϒ(4s) particles to detect time-reversal violation directly, and this was accomplished by the BaBar collaboration back in 2012. The test for the reversal of initial and final entangled states is, to date, the only direct test ever performed to see if T-symmetry is conserved or violated in a direct fashion. Just as anticipated, the weak interactions violate this T-symmetry, proving that the laws of physics are not identical whether time runs forwards or backwards.

In particle physics, the gold standard for experimental significance is a threshold of 5-sigma. Yet BaBar physicists achieved a significance of 14-sigma: a remarkable accomplishment. The reason you’ve likely never heard about it? It was overshadowed by slightly bigger particle physics news occurring in the same year: the discovery of the Higgs boson. But this result maybe Nobel-worthy, too. The laws of nature are not the same forwards and backwards in time. After seven years, it’s time the world felt the impact of this discovery.

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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