Why doesn't the entropy portion of thermodynamics have anything to say about time reversal symmetry? Or does it say that but we're not smart enough to see it yet?
Θ⁻¹HΘ is a way to write a new Hamiltonian which is the “reflection” with respect to time of the original Hamiltonian H, see https://en.wikipedia.org/wiki/Hamiltonian_mechanics for an explanation of what the Hamiltonian is.
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.
Because one cannot travel through a mere a conditioned by senses concept of the mind.
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.
Can someone explain how a nucleus can be anything other than a sphere? How do the protons and neutrons at one end of the nucleus "know" to be pointed, while the same collection of particles at the other end "know" to be rounded?
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.
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.
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.
It's probably just the lowest energy state. The same way marbles at the top of a pile "know" to form a peak, and those at the bottom "know" to form a wide flat base.
In that case the direction of gravity breaks the symmetry between the peak and the base. The grandparent's question is what breaks the symmetry between the big and small end of the pear.
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.
I suppose, if the interactions with particles external to the nucleus are weak enough, that the nucleus could be in a quantum superposition of all/most/many orientations anyway? (Not sure whether I'm off-base here.)
Symmetry can be broken spontaneously (see the first sentence in the paper, https://arxiv.org/abs/1602.01485), if the symmetric state is not a global energy minimum. (E.g. a needle standing on its tip on a table is in a state with rotational symmetry --- however, after it has fallen on its side on the table, the symmetry is broken.) The explanation in wikipedia seems be OK: https://en.wikipedia.org/wiki/Spontaneous_symmetry_breaking
The article seems incredibly over-dramatic of a genuinely interesting study. Saying that this is evidence of it being "more distorted than theorists expected" is irresponsible from a scientific point of view.
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.
http://www.sciencealert.com/physicists-just-discovered-a-new...