An atom is comprised of dense nucleus of protons and neutrons surrounded by a diffuse cloud of electrons. Since an atomic nucleus is held together by the strong force, similar to the way gravity holds stars and planets together, you would think nuclei would be basically spherical. This isn’t always the case, and a few such as barium-144 are even pear shaped. This has to do with a subtle way the Universe works, which could explain one of its biggest mysteries. 

As Emmy Noether demonstrated in the early 1900s, symmetry is connected to the basic laws of physics. The presence of certain symmetries in the world is a property of certain unchanging quantity in the Universe. Noether’s theorem is an elegant demonstration of this connection, and is central to most modern physical theories. Noether showed us how some of the most powerful symmetries are those connected to space and time.

Take, for example, mirror symmetry, also known as parity. When you look in a mirror, the image you see is reversed. If you hold up your right hand, your mirror image would seem to hold up its left. Mirror image clocks would appear to move counter clockwise. So imagine a mirror universe. Not the evil Spock kind of mirror universe, but simply one in which the parity of everything is reversed. Americans would drive on the left side of the road, the Sun would rise in the west and set in the East, but fundamentally nothing would change. It would be no different than if we simply decided to switch the meanings of right and left.

The basic idea of the Wu experiment. Credit: Wikipedia user nagualdesign.

At least that would be the case if parity symmetry were true. While usually things are symmetrical under a switch of parity, there are some cases were parity is violated. This was first demonstrated by the Wu experiment in 1956. Chien-Shiung Wu looked at the radioactive decay of cobalt-60 atoms. If parity was conserved, then mirror image decay experiments should behave in exactly the same way. What she found was that mirrored experiments of cobalt-60 decayed in opposite directions. Since radioactive decay is driven by the weak nuclear force, this meant the weak force violates parity.

Another symmetry is related to electromagnetic charge. In our Universe protons have a positive charge while electrons have a negative charge. Charge symmetry considers what would happen if these charges were reversed. Since antimatter particles have the opposite charge of their regular matter partners, this would be like replacing all matter with antimatter. Since positive charges interact with each other the same way as negative charges, you would think that charge symmetry would hold. After all, it’s why charge is conserved.

The helicity of neutrinos and anti-neutrinos. Credit: Universe Review

But it turns out charge symmetry can be violated in a subtle way, again connected to the weak interaction, specifically neutrinos. While neutrinos don’t have any charge, they do have a kind of rotation known as helicity. If charge symmetry were true, then matter and antimatter should produce neutrinos with the same helicity. But it turns out matter produces neutrinos of one helicity, while antimatter produces antineutrinos of the opposite helicity. So charge symmetry is violated as well.  For a time it was thought that the symmetries of charge and parity could be combined into a more general CP symmetry that would be conserved, but there are radioactive particles that violate it as well.

So what does any of this have to do with pear-shaped atomic nuclei? The shape of a nucleus is determined by the various interactions that occur between the protons and neutrons (and quarks) within the nucleus. If those interactions were CP symmetric, there shouldn’t be a pear-shaped nucleus like barium-144. By studying odd nuclei like barium-144, we can gain clues about the ways CP-symmetry can be violated.

What does this have to do with astrophysics? Remember that charge symmetry is connected to matter and antimatter. Because charge is conserved, when any particle of matter is produced through some physical process, a corresponding particle of antimatter must also be produced. In the early moments after the big bang, when matter was being produced for the first time, there should have been an equal amount of matter and antimatter. But what we see today is a Universe dominated by matter. The origin of this matter-antimatter asymmetry is one of the great unanswered questions of cosmology. It’s been proposed that a violation of CP symmetry could have produced more matter than antimatter, but the currently known violations are not sufficient to produce the amount of matter we see. If there are other avenues of CP violation hidden within pear-shaped nuclei, they could explain this mystery after all.

Paper: C. S. Wu, et al. Experimental Test of Parity Conservation in Beta Decay. Physical Review 105 (4): 1413–1415. (1957)

Paper: B. Bucher et al. Direct Evidence of Octupole Deformation in Neutron-Rich ¹⁴⁴Ba. Phys. Rev. Lett. 116, 112503 (2016)  arXiv:1602.01485 [nucl-ex]

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Suppose you want to balance a ruler horizontally on your finger.  To to this you’ll likely place your finger in the middle of the ruler, so that half is on one side and half on the other.  Intuitively, you recognize that the middle makes both sides symmetrical, which is why you put your finger there.  In other words there is a connection between the symmetry of the ruler and the physics of balance.

Emmy Noether, 1930.

Symmetry is something we all tend to recognize, but probably find hard to quantify.  Things like mirror symmetry are easy to describe, but what about the image above.  It gives a feeling of symmetry, but exactly how would you describe it?  In the same way, we generally have an intuitive feel for the way symmetry is related to the physical world, such as balancing a ruler on our finger, but quantifying that connection is difficult.

This is why Emmy Noether should probably be put in the same group as Isaac Newton and Albert Einstein as one of the greatest physicists who ever lived, because in 1918 she published an elegant and mathematically precise connection between symmetry and physics.  It is now known as Noether’s Theorem, and it is so subtle and powerful it is hard to describe without mathematical formalism.

But I’ll give it a try.

In physics, symmetry is the ability to change a part of a system while the whole remains the same.  As an example, imagine if you were standing on a perfectly flat surface that extends as far as you can see.  If you were to close your eyes, take one step forward, then open your eyes, it would appear that nothing has changed.  You have moved forward (a change), but the surface appears unchanged (symmetry).

Through Noether’s theorem, such a symmetry of linear motion is connected to the fact that an object in motion will continue that motion unless something acts on it, what we call conservation of linear momentum.  In the same way, if you were to close your eyes, turn to the left or right a bit, then open your eyes again, the surface would appear unchanged.  This symmetry in rotation is connected to fact that a rotating object like the Earth will continue to rotate, which we call conservation of angular momentum.

But Noether didn’t just show these simple connections, she showed in general how every conservation law in physics is connected to a physical symmetry. Conservation in energy connects to a symmetry in time, conservation of charge to a symmetry in gauge, and on and on.  It is a connection that lies at the heart of every modern physical theory, and has deepened our understanding of earlier theories such as Newton’s mechanics and Einstein’s relativity.  Emmy Noether single-handedly revolutionized the way we understand physical theories.

Despite this fact, Noether is not widely known outside the physics and mathematics community.  Part of this is due to the fact that her work revolutionized existing physical theories rather than being a physical theory in its own right, but another reason is that she was a woman at a time when the work of women was often marginalized. Despite her world-class work, she struggled against discrimination in her field, and received a fraction of the recognition she deserved.  Although things have gotten better for women in the sciences, it isn’t quite what you would consider fully balanced.

So the next time you read about the discovery of cosmic inflation, or the search for supersymmetric particles, or the development of a theory of everything, think of Emmy Noether, and her theorem that lies at the heart of all of these ideas.  And remember that the sciences could always use a little more symmetry.

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