Barium-144 Nucleus Is Surprisingly Pear Shaped
physics.aps.org
physics.aps.org
http://www.sciencealert.com/physicists-just-discovered-a-new...
Θ⁻¹HΘ = H means that when you reverse time, your physics looks the same as it did before. Such a thing (time-reversal invariance) is being called “time-even”. In the same way a function f(x) would be “even” with respect to its argument if f(x) = f(–x).
The author of that comment is pointing out that if we assume the Hamiltonian is time-even, then we can’t have a particle with an electric dipole moment. This is because the contribution to the Hamiltonian from the dipole interacting with an external electric field would be time-even. That interaction can be expressed as a kind of dot product of two terms, an electric dipole operator part and an electric field part, and the action of our time-reversal operator Θ can be applied separately to each part. Since the electric field is time-even, that means the dipole itself must also be time-even.
But this can’t really work, because a solitary particle has spin but no other symmetries which could generate the electric dipole moment. The spin gets reversed if we run time backwards, a “time-odd” symmetry. So if we find a particle with a static electric dipole moment in nature, then there must be some contradiction in our assumption that the Hamiltonian was time-even.
The rest of his comment is a somewhat analogous kind of argument related to a slightly more complicated situation and slightly more complicated kind of symmetry.
See https://en.wikipedia.org/wiki/Electric_dipole_moment#Dipole_...
> True time-reversal symmetry would prevent certain static multipole moments from existing in nuclei.
Not "Time travel ..."
Moreover, the notions of a "direction" are also inapplicable - there is no directions in a continuous process. They just continue, like radioactive decay. It is absurd to say that it goes to a direction of more decay.
https://en.wikipedia.org/wiki/Spontaneous_symmetry_breaking
Any direction is as good as any other, but one will be chosen.
In this case, the ones at the big end of the pear act differently than the ones at the small end because their neighbors are different then the ones at the small end. And the mid ones behave as they do because of who their neighbors are.
The reply of colanderman seems correct, though perhaps not terribly enlightening.
The Protons and Neurons that are properly paired up make a "sphere" that is nicely distributed, and the leftover neutrons are pushed to one side and make the tip of the pear.
Now you might think that mixing the extra neutrons evenly would makes things even more nicely distributed (which in an atom means: lower energy), but consider the Helium nucleus.
The nucleon binding energy of helium is very different from its neighbors: https://en.wikipedia.org/wiki/File:Binding_energy_curve_-_co...
That is because pairing up the way Helium does is just so favorable. It's the same with the Barium-144 - the nucleons that can pair up do so, at very low energy, and then you have some leftovers.
I suspect that lots and lots of unstable nuclei will be found to be asymmetrical this way.
By studying exactly how asymmetrical they are we can finally find out exactly how neucleons pair up, so we can actually model the energy levels.
Once we do that we'll be able to figure where the https://en.wikipedia.org/wiki/Island_of_stability is. Figuring that out might lead to some amazing new materials.
Even better, we'll actually start to understand neutron stars (understand what actually happens to those neutrons at those pressures), and maybe calculate the Quark degeneracy pressure - it could be that pressure is so high that black holes can not exist.
Black holes would exist, but not as point-like singularities, right? There'd still be an event horizon.
But it's not really known though, what the inside of a black hole looks like.
My less-dramatic summary: Barium-144 is a short-lived isotope that was predicted to have an unusual "pear" shape. A new study suggests that it does have the shape that was predicted.
A better example is http://www.sciencealert.com/physicists-just-discovered-a-new...
(This is the crowd that brought us 'quarks' - notorious lack of 'gravitas' there ...)
... that math processing error was really confusing until I understood its real meaning.
http://vixra.org/pdf/1107.0031v1.pdf
But yes I know, a crackpots physical model... how bad it fits so well.