arcadi7

Rutherford, planck , bohr jumpstarted the 20th century physics .

and they _always_ have few percent of protons and electrons — every single neutron star .

and they _always_ have few percent of protons and electrons — every single one of them .

protons can generate neutrons and neutrons can generate protons . why are there no nuclea with only neutrons ? — these could be as big as you want because there is no electric repulsion . the answer is that only neutron nucleus would have — by pauli exclusion principle — very large kinetic energy . so nucleus turns couple of its neutrons into protons to lower the kinetic energy of neutrons . same reason for small fraction of protons in neutron stars

nucleus is extremely fluffy by general relativity standards . for black holes the mass and size are linearly proportional . the solar mass black hole has few mile size and has density few times smaller than that of the nucleus . solar mass is about 10^57 protons or about 10^55 heavy nuclea like uranium . so in order for general relativity to be important for uranium nucleus, it has to have a size of 5 miles/10^55 or about 10^-49 cm . instead heavy nuclea have a size of about 10^-15 cm . so nuclea are 34 orders of magnitude fluffier than they should be for any general relativity to be of any relevance . they are as good as grain of salt

nonsense . heavy nuclea are bound states of many constituents . no different from grain of salt . grain of salt can be much heavier than planck mass (which is about few micrograms

Short answer: talk about quantum wells in this context is meaningless .

Not metaphors . We know these are out there — we just don’t know a lot about them. The situation is similar to atoms in second half of 19th century : we knew they are there , we knew some of their properties but only it the first quarter of 20th century we learned how much more there is to learn about atoms

the funny thing is that the calculation in this article misses the point, especially in the Feynman context. First, beyond all trickery, the log(alpha) answer might suggest that something bad happens at alpha=0 . What makes this integral interesting is that it is equal to zero identically for alpha<1 .

The reason, of course, is that this integral is not randomly chosen -- it represents the two-dimensional coulomb potential (log(r)) of the sphere (circle) of radius 1 at distance alpha from the center. By when point alpha is inside the circle , the potential is constant (or zero -- no force) . When alpha is outside, the potential is log(r) as if all the mass of a circle is at its center. The expression under the log in the integral is just (square of ) the distance between the point alpha and point on a unit circle.

beyond tricks -- the physical reason for the singular behavior of this integral is gauss theorem for coulomb potential . so no magic.

find a small group of people that are excited about what they are doing -- then go from there