The ratchet of time

25 February 1999

New results remind us how, in the strange world of the neutral kaon, a fast rewind does not necessarily take you back to where you started.


The neutral kaon is one of Nature’s trickiest particles and has to be handled with respect by experimenters. Measuring its detailed behaviour has kept many physicists busy for over 30 years, and the quest continues, with major experiments still to make definitive precision measurements.

The neutral kaon comes in two forms, which are particle and antiparticle of each other, distinguished only by their strangeness quantum number. The problem is that strangeness is only conserved in strong nuclear interactions, so that when the weak force is in action, the neutral kaon and its antiparticle get mixed up. This gives some unusual and interesting results which could have implications for our understanding of the universe.

The conventional theory of particle physics is completely time symmetric ­ a video of a simple particle interaction would be equally valid whether run forwards or backwards. The neutral kaon defies this rule and shows there can be a one-way valve in the passage of time.

This delicate asymmetry could help explain how a universe created in a Big Bang that was matter­antimatter symmetric has evolved into one that contains no antimatter at all. Perhaps time is the arch-enemy of antimatter.

How Nature is asymmetric

In 1956 the world of physics was startled to discover that the weak force looks very different when viewed in a mirror. Weakly interacting particles have a definite “handedness”. If nuclear beta decay is reflected in a mirror, a right-handed particle becomes left-handed, and the physics scenario is not the same. In the trade, such a mirror reflection is called a parity operation, P. Parity is violated in weak interactions.

The parity violation blow was quickly followed by another. Physicists also discovered that the weak force scenario also changes if particles are switched into antiparticles and vice versa. This “charge conjugation symmetry”, C, is also violated in weak interactions.

If P and C separately are not respected by the weak force, what is? Physicists suggested that perhaps the separate P and C violations compensate for each other, and that the compound CP symmetry would be good. In such a CP mirror, a left-handed particle (such as a neutrino) changes into a right-handed antiparticle (such as an antineutrino), etc.

The next shock came in 1964 when a fraction of a per cent of the decays of the neutral kaon were found to violate CP symmetry. What symmetry would be the next to fall? Powerful theorems said that the underlying formalism should be invariant under CPT ­ when the compound CP operation is supplemented by time reversal, T. If CPT went, then the underlying formalism would sink and physics would be in deep trouble, as nobody would understand very much any more.

If CPT is to hold good, and CP is violated by the neutral kaons, then the neutral kaons necessarily violate time reversal symmetry ­ rewinding a “videotape” of a neutral kaon interaction would not take you back to the point of departure.


The traditional description of CP violation by neutral kaons includes two alternatives: CPT good and T violation, and CPT violation and T good. The first evidence for the first alternative was found in 1970 in an experiment at CERN’s PS proton synchrotron which looked at the time dependence of neutral kaon decays. This result was of key importance for the understanding of neutral kaon decay. Ever since, physicists have been searching for other glimpses of time symmetry violation.


One of the major experiments continuing to probe neutral kaon physics to provide precision measurements of CP violation is Fermilab’s KTEV study, which began in 1996 and is currently churning through the data accumulated so far. Most of the time the long-lived neutral kaon decays into three particles, respecting CP. One rare neutral kaon decay is into two charged pions accompanied by an electron­positron pair, a decay channel only recently seen for the first time. It accounts for only 3 x 10-7 of the total decays, much smaller than CP violation in the mainstream decay channels.

This decay can happen via several mechanisms, some of them CP violating, some not, and these different mechanisms interfere. Several years ago, Lalit Sehgal at Aachen realized that because of this subtle quantum mechanical interference, the angle between the plane of the two pions and that of the electrons is sensitive to the arrow of time. If such a decay were run backwards, momenta would be reversed, but the “resultant” involvement of the neutral kaon would not always correspond to the original process.


From some 1800 such decays, the KTEV experiment reports an asymmetry of some 13%, in line with the prediction. This time asymmetry is much larger than the usual levels of CP violation, seen in the dominant neutral kaon channels, and shows how a rare decay channel, once found, can be a rich source of information.

Also studying this decay process is the big NA48 experiment at CERN, which began gathering precision data in 1997. Its major objective is to measure the elusive parameters of the more usual examples of CP violation.

Another example of T violation comes from the CPLEAR collaboration, which studied CP violation physics at CERN’s LEAR low energy antiproton ring from 1990 until LEAR was closed in 1996. CPLEAR looks at the many different particle combinations emerging from proton­antiproton annihilation.

Among them are two interesting quantum opposites: a positive kaon, a negative pion and a neutral kaon; or a negative kaon, a positive pion and a neutral kaon antiparticle. Whether the annihilation produced a neutral kaon or its antiparticle is “tagged” by the electric charge of the associated kaon.

This contrasts with the situation in experiments using secondary beams of neutral kaons, which are particle­antiparticle mixtures.

Once formed in the initial strong interaction annihilation, the CPLEAR kaons or antikaons are then free to decay under the weak force. Comparing these decays with the original strangeness tags from the annihilation process shows whether a kaon has subsequently transformed into an antiparticle, or vice versa. If time reversal is good, as many kaons will change into antikaons as antikaons into kaons.

CPLEAR finds a mismatch between the two rates. The time asymmetry is measured at 6.6 x 10-3 and is compatible with the observed levels of CP violation. The arrow of time is broken, but in such a way that the master CPT symmetry is good.

More work to do

The major experiments probing CP violation in with neutral kaons ­ NA48 at CERN, KTEV at Fermilab and KLOE at Frascati’s DAFNE electron­positron collider ­ still have a lot of work to do before these effects are measured definitively.

But the big mystery remains. Why is CP, and therefore time reversal symmetry, violated at all? To answer this question, physicists will probably have to use the longer CP violation (and therefore T violation) lever expected with B particles containing the fifth, beauty, or “b” quark.

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