And then 1.4 Solar masses is the upper limit. [1]
[0] https://physics.stackexchange.com/a/143174/43351 [1] https://en.wikipedia.org/wiki/Chandrasekhar_limit
[0] https://en.wikipedia.org/wiki/Tolman%E2%80%93Oppenheimer%E2%...
I was thinking of neutron stars all along - which, correct me if I’m wrong, look like they have similar density to an atomic nucleus and for which the upper limit is apparently 3 Sols. [0]
[0] https://en.m.wikipedia.org/wiki/Neutron_star#:~:text=Neutron....
The GR vs Standard Model breakdown occurs at the extreme limits of GR, for example Planck scale regions of space and black hole singularities. A heavy nucleus is way too big to probe these limits and is well within the domain of physics where we don't see a conflict between the two theories.
String theory may well be wrong/currently untestable, however failure to invalidate the null hypothesis is not proof that somehow we don't have a meaningful understanding of other, proven theories/laws.
Put a different way, if an apple falls from a tree on earth, I don't panic because I don't understand quarks or electron orbitals. I calculate the point/speed/force of impact to acceptable margins of error.
(Edit because we got a little confused in the replies: If it were all protons, they would repel and overcome gravity. But real matter isn't that, it's always protons and neutrons and electrons with close to no net repulsion so gravity wins.)
Similarly, radioactive nuclei (alpha emitters and spontaneous fission) happen because the electromagnetic repulsion exceeds the strong force, which has a very short range and doesn't reach across those large nuclei.
Is that true? All of the protons repel all other protons with the electric force and attract with the gravitational force, and it seems like gravity is just much weaker at all distances...
I haven't thought about this very hard though.
Now think of 10^50 protons in a line. They're all experiencing net gravity towards the middle.
With gravity, A is attracted inward, B is not attracted, C is attracted inward.
Of course, in practice, we don't know what the inside of a black hole is like, as quantum gravity is very much unsolved.
So the conclusion is any proton star would just explode? That's what I already thought.
Even if you make the argument that the energy complicit in the strong/weak forces is cumutavily much greater than the energy due to gravity, I'm still not sure "weak" is the right word for the job...
Gravity onstensibly runs at infinite speed over infinite area (the effect of gravity waves non-withstanding).
Protons can generate neutrons through beta decay. I suspect something like this happens in neutron stars, which don't spontaneously fly apart into a proton cloud, so far as we've observed.
This SE comment explains why neutron stars don't contain (many) protons:
<https://physics.stackexchange.com/a/149656>
(The ratio seems to be ~100:1 neutron:proton.)
They're ... both big (by atomic scales) and massive (atomic and astronomical).
The conceptualisation of elements is useful to us because physical characteristics of atoms are (mostly) stable over time, with atoms having distinctive masses, atomic numbers, and most importantly, electron shells. The latter account for most of what we consider to be "chemistry", along with some other effects, most notably the van der Waals force.
Neutron stars ... lack most of this. They're in constant flux, they (probably) don't have stable masses (if only due to constant accretion) or atomic numbers, they probably don't have anything resembling an electron shell, and in interactions with other objects any electromagnetic forces would probably be overwhelmed by gravity or, say, spin-induced magnetism. If a measure of a concept or model's usefulness is how much it explains behaviours, "neutron-star-as-element" doesn't buy you much.
Though there's possibly some truth or conceptual validity to it.
I subscribe strongly to a pragmatic approach to knowledge and understanding. That is, knowledge isn't so much true as it is useful, in that it provides a useful mental model of the world. There are cases where multiple truths are possible, as with wave-particle duality, or mass-energy. Either classification may be useful, that is, provide predictive, understanding, or manipulative power, depending on contexts and circumstances. Some of the classic philosophical paradoxes (Sorites, Ship of Thesus, falling tree in a forest) resolve at least somewhat under this view. What is often called "truth" I think of as "useful mental models". The distinction is that whilst both are grounded in observation and empiricism, "truth" is an absolute, whilst "usefulness" is a bit like evolutionary fitness: changing over time, dependent on circumstance, not entirely arbitrary, but also not perpetually fixed.
So, is a neutron star a gigantic nucleus? Yes, in a sense, in that it's primarily made of what we'd otherwise consider nuclear material. Does this give us useful insights on neutron star behavior above and beyond those given by gravitational, thermodynamic, and electromagnetic descriptions? No, not really, because the attendant characteristics and properties of much smaller nuclei (from atomic number 1 to the low 100s or so) simply don't apply. There's not much behaviour that is explained, predicted, or controlled by applying that knowledge.
I'm struggling to find a strong source, but this page, by M. Coleman Miller at the University of Maryland, describes properties suggesting modelling over observation. Specifically it describes "the guts of a neutron star":
Even further down, you mainly have free neutrons, with a 5%-10% sprinkling of protons and electrons.
With an subsequent 'graph:
Yes, you may say, that's all very well for keeping nuclear theorists employed, but how can we possibly tell if it works out in reality? Well, believe it or not, these things may actually have an effect on the cooling history of the star and their spin behavior!
What follows is more description of theory with a few points based in what is directly observable, largely spin (via radio astronomy) and some temperature observations largely in X-ray observations, and the occasional gamma-ray burst.
<https://www.astro.umd.edu/~miller/nstar.html>
Miller's bio at UMD emphasizes his theoretical work:
Cole Miller's research in the last few years has focused on theory and modeling of high-energy radiation from neutron stars and black holes.
More importantly, I think that the Coulomb's Law repulsion effect would more than cancel out the gravitational attraction effect - both laws work as Force = (constant x particle1 x particle2) / distance^2, and the electromagnetic force is much, much stronger than gravity at all distances.
P.S. Quote from the link:
> Would this black hole cause the universe to collapse? Hard to say.
There's also the whole menagerie of nuclear pasta [1] where gnocchi and spaghetti you could maybe consider "nuclei" unto themselves. There's also waffles & lasagna, but when you get into the anti-spaghetti and anti-gnocchi realms, then you're into the "one nucleus" region.