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CPT Symmetry

October 29, 2015

In my childhood, I enjoyed cutting out paper dolls. Lest you wonder about such an early transcendence of gender stereotyping, these were not the dress-up type of paper dolls beloved by girls. Rather, these were fold-and-cut paper dolls in which a piece of paper with multiple folds, when cut in a certain way, would yield a daisy chain of figures, as shown below.

fold-and-cut paper dolls
An example of a daisy chain of fold-and-cut paper dolls. (Created with Inkscape.)

This process was applicable, also, to other shapes, such as angels, snowflakes, hearts, and Christmas trees, the later rendered vertically to allow for a linkage between items. Cutting out paper dolls is one of the arts-and-crafts activities stereotypically given to mental patients to keep them busy, so this might have been good practice for a career as a "mad scientist," In actuality, it was good training in the mathematical concept of symmetry.

Humans are exposed to symmetry from birth though observation of nature. Plants and animals exhibit approximate symmetries, such as radial symmetry and bilateral symmetry. An example of human bilateral symmetry can be seen in the following figure.

Figure caption
A photograph of American suffragette, Alice Paul (1885-1977), center, has been processed into two images in which each half of her face has been replaced with a mirror image of the the other side. This illustrates the approximate bilateral symmetry of the human body. (Source image, via Wikimedia Commons.)

Aside from these visual aspects of symmetry, there are deeper mathematical definitions of symmetry. Some of these, such as the concepts of even and odd functions and symmetric polynomials, are even accessible to secondary school students. Where there's math, there's usually some associated physics, and physics has its own symmetries.

When looking at isolated objects where thermodynamics and the concept of entropy is not an issue, we can make a video of a particle being acted upon by forces, play the video backwards, and the laws of physics as inferred from this backwards playback are no different than those in the actual case. This is known as time-reversal symmetry. likewise, we can view what's happening in a mirror, and nothing would seem amiss. This is parity-inversion symmetry.

There is also a charge-conjugation in which every particle is replaced by its antiparticle. The antiparticles have a charge of opposite sign to normal particles. Just like the approximate symmetry of the human face, these symmetries are almost true, just not always true. A 1956 experiment involving the beta decay of cobalt-60 showed that parity was not always conserved. This meant that it was possible to have an experiment distinguish left from right.

Chien-Shiung Wu (1912-1997)Life among the beamlines.

Physicist, Chien-Shiung Wu (1912-1997), in a 1963 photograph. Wu proved parity violation in a 1956 experiment.

(Portion of a Smithsonian Institution Archives image, Accession No. 90-105, via Wikimedia Commons.)

While parity was not conserved, it was thought that a combined charge-parity (CP) symmetry was still true in all cases. It was not long before CP violation was found. James Cronin and Val Fitch found CP violation in neutral kaon decay in 1964, a discovery that resulted in their winning the 1980 Nobel Prize in Physics. CP violation may explain why our universe is made of matter and not an equal mixture of matter and antimatter.

Theoretical physicists, now with their backs against the wall, decided that everything is explained when you simultaneously invoke all three symmetries; that is, CPT symmetry. According to CPT symmetry, an antimatter universe (C) that's a mirror image of our own (P) in which particle momentum is reversed (T) would have the same laws of physics that we observe. The experimentalists have taken up the challenge to see whether CPT symmetry is violated in some cases. At this point, no violation has been discovered.

Figure captionA CPT of another sort.

Some of my early scientific papers were rendered on a CPT 8100, as shown. This word processor, manufactured by the CPT Corporation in the early 1980s, used an 8080 microprocessor.

(Via Wikimedia Commons.)

In their continued checks for CPT violation, experimentalists have brought out the heavy guns in the form of the Large Hadron Collider (LHC). Scientists on the ALICE (A Large Ion Collider Experiment) team at the LHC have just published results on their study of the mass-to-charge ratio of helium-3 nuclei and deuterium nuclei, along with that of their respective antiparticles.[1-3] This follows an experiment at CERN's Antiproton Decelerator that looked at the charge-to-mass ratio of protons and antiprotons.[4-5]

While the ALICE experiment was not specifically dedicated to test CPT invariance, physicists take their opportunities where they can. In the experiment, the ALICE team measured the difference between the ratios of the mass and charge of deuterons and anti-deuterons generated by Pb–Pb collisions at 2.76 TeV. The collision of lead ions provides an abundant source of particles and antiparticles at nearly equal rates.[3] ALICE is a high precision time-of-flight detector with a resolution of 80 picoseconds that provided a clear indication that CPT violation is unlikely.[3]

The earlier, CERN experiment captured antiproton and hydrogen ion pairs in a Penning trap and measured their cyclotron frequency. This measurement allowed a close determination of the charge-to-mass ratio. The research team was able to measure about 6,500 pairs over a 35-day period.[5] They found that the charge-to-mass ratio is identical to within just 69 parts per trillion, which is evidence that CPT is not violated.[4-5] The CERN team has plans to increase the precision of their measurements by one or two orders of magnitude.[5]


  1. ALICE Collaboration, "Precision measurement of the mass difference between light nuclei and anti-nuclei," Nature Physics (August 17, 2015), doi:10.1038/nphys3432. This is an open access article with a PDF file here.
  2. CERN: Most precise measurement of mass and charge of light nuclei and anti-nuclei, Technical University of Munich Press Release, September 2, 2015.
  3. Diego Freire, "Experiment confirms fundamental symmetry in nature," São Paulo Research Foundation, September 16, 2015.
  4. S. Ulmer, C. Smorra, A. Mooser, K. Franke, H. Nagahama, G. Schneider,T. Higuchi, S. Van Gorp, K. Blaum, Y. Matsuda, W. Quint, J. Walz, and Y. Yamazaki, "High-Precision Comparison of the Antiproton-to-Proton Charge-to-Mass Ratio", Nature, vol. 524, no. 7564 (August 13, 2015), pp. 196-199, doi: 10.1038/nature14861. This is an open access article with a PDF file here.
  5. Protons and antiprotons appear to be true mirror images, RIKEN Press Release, August 13, 2015.

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