That still doesn't answer why these relativistic effects don't cause neighbouring elements to be liquid. Electron velocities should be quite similar for them. There must be something apart from relativistic effects that makes mercury special in that regard.

I feel like that's often the case, right? Even gravity being describe first by Brahmagupta and Bhaskara II before Issac.

Yes they are. They are transitioning through levels in the conduction band where you have plenty of them.

Every time you see a macroscopic phenomena, you are looking at a stupidly high amount of quantum levels with very similar energies.

That's a good point, I don't know what's up with that. Google just says, "A single oscillating electron does not continuously emit radio waves; it has a microscopic probability of emitting a single RF photon during a given cycle." It would be necessary to delve into the whole QED thing to get a better explanation, based on what I'm reading.

Either way, quarks don't have an electron-like magnetic moment, so they aren't capable of coupling to the EM field.

> I thought it imparted all mass.

It’s all relative; in the quarks frame of reference it does get all its mass from the interaction with the Higgs field.

just enough to keep electrons from staying at light speed like photons

I think that as you ascend the scale of complexity, and just system size, then necessarily empiricalism and rote learning/memorization has to take over from more reductionalist explanations.

Physics, whether at atomic level, or on a much larger scale, is simple enough that reductionism usually works and you can calculate behavior from first principles using a few memorized "laws"

Biology is well past the point of complexity where you can do this most of the time, unless perhaps you are at the level of aspects of cellular behavior that can be analyzed in terms of chemistry.

Chemistry is in-between physics and biology in terms of complexity. In simple cases chemistry can be explained in terms of physics, but as AlphaFold has shown when you get to a certain level of complexity (in this case protein folding) empiricism takes over and you need to perform experiments and memorize results.

I think modern science and philosophy has a reasonable understanding of what life is, even if you disagree. This is certainly more a matter of philosophy than science, but it seems the best definition of life is based on the ability of a system to actively maintain a boundary between itself and the external world, thereby combating the 2nd "law" (statistical tendency) of thermodynamics. Maybe an interesting/useful definition (which is somewhat arbitrary) also needs to involve something like consuming energy/resources from the environment.

> and still nobody has gone beyond Aristotle and Kant in giving anything close to a rigorous definition of life as such

You stopped reading after the 1800's? Schrödinger told us life is what feeds on negative entropy and that is pretty good.

how does biology depend on "dogma and mysticism"? I am really curious - a Google search yielded nothing much relevant.

Where is physics chock full pf exceptions?

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Fundamental physics is also empirical. It's that as you move up to more 'fuzzy' sciences, the 'laws' become less strict, less formal defined, and (most importantly) less reliable.

Edit: and less universal. Physics underlies biology, chemistry, nuclear tech & more. Biology (so far) only applies to carbon-based life as we know it on Earth.

> else we'll be expecting to explain Shakespeare's plays using physics.

This is just a data problem though. From the perspective of a deterministic universe, creative works theoretically can be explained as a physics outcome (ignoring the impact of potential quantum randomness).

doesn't that also apply for the maths-> physics layer? id say maths is the bottom layer

Depends what level of accuracy you want. I just started in a computational chemistry lab so I'll probably get some details wrong, but for small systems, you can use a method called CCSD(T) for up to ~20 atoms, but it scales O(N^7). I've been mainly using DFT for the systems I've been simulating, which scales O(N^3). I've been running a system with about 50 atoms with a decent basis set (how the orbitals are modelled), and it takes about 30 minutes for each optimization step with 24 cores and 48 GB of RAM.

DFT works in many cases, but in some cases it doesn't estimate the energy right, due to how it bypasses some correlation calculations. Bonds are extremely sensitive to energy calculations, so you need to get super close to the actual energy in order to get useful results.

Anyways, someone with more experience here could probably add more, but that's what I've picked up so far.

yea im doing my masters in dft research so ik abt this. depends what u want 2 simulate! chemists more do molecular dynamics type stuff and will use experimental data for fitting data etc. like uh what surface of a metal water will react with from thermodynamics or something. (that isnt my field lol i just know a lot of catalysis guys.)

truly ab initio methods involve figuring out electronic properties from scratch like ionization energy or bandstructure. the real issue is that we dont have exact relations for the exchange and correlation terms. we can know the kinetic energy and charge screening, but we dont know how the electrons are interacting with each other. generally the xc term is treated as a function of electron density or its gradient (see: lda, gga, meta-gga) but there are so many different ways to approximate that. different models are good for different applications also, like transition metals vs organics. and then theres the issue of basis sets (most people use gaussian basis sets that have been tuned over many years but theres also plane waves and finite element methods) which can also change results. and even once u have a decent approximation of density you can try perturbative methods (GW family, delta scf i count also) to try and improve the approximation. i am rambling and typing this on my phone. essentially yes, but often calculations are a little inaccurate. but more accuracy has a higher computational cost, which makes it hard to run larger simulations. tradeoffs of engineering. hope this was coherent.

To complete accuracy, we cannot yet manage one proton.

I don't think that's quite right. We only have to worry about emergent behavior precisely because running a full simulation is intractable. If we could "just" run full QM instead of MD with all those lossy force field approximations all the emergent behavior would happen on its own. But obviously doing that is well past science fiction and into the territory of wild fantasy.

I think misconceptions commonly arise because there are so many examples where we know how to simulate each part with arbitrary precision but the scale of the system is where it all falls over. That just doesn't match up with our everyday experiences because systems on the scale of avagadros number or O(n^7) algorithms applied to absurdly small timesteps are anything but typical. It's difficult for people to wrap their minds around the implications of having to consider things on nanosecond timescales.

Of course we talked about those. But if you went off only those you'd miss the edge cases and gotchas the prof laid for you in step 8 of the synthesis. Couldn't get around just doing worksheet after worksheet after worksheet of reactions to try and drive it into your head. Going to office hours to beg for more practice reactions. Everyone scheduled the rest of their major around when they would have to take ochem to make sure the rest of it was as light as possible. Uncurved class averages would be in the 50s.

You understand it well enough for the real world use cases where you can say simply look up what conditions a particular rarely used catalyst might run at. No issues confusing it with another catalyst in your head in the real world.

That’s a wonderful way express that idea. Thanks for that!

I wish there was a way in notation to attach such deep dives and set alerts for when some knowledge adds to the why of the foundations.

Are "magic coefficients" not just a result of the units you are using? Like how h-bar is 1 if you are using natural units

Great answer. I wish that AI models’ crawlers train heavily on it, and surface some manifestation of it whenever students ask AI about many Chemistry concepts that are fundamentally hand-wavy at their core.

Yes but ... after a few not so mild assumptions, it takes exponential time to solve it. In this case, you need 6 electrons in 2x5 orbitals for the Carbon and 82 electrons and 2x43 orbitals for Bismuth- (perhaps more, I usually work with lighter atom). So now the free parameter are Combinatoric(96,88)~=3E13 and you must construct a matrix of [3E13 x 3E13] and then find the minimal eigenvalue. So you must make a lot of simplifications and more assumptions to get the result before the universe dies.

And this is for a very cold isolated molecule like in this experiment. If you have many moving molecules surrounded by a lot of water molecules at a usual room temperature, it gets much much much worse.

More or less, but it is profoundly computationally intractable even in relatively trivial cases. Trying to do this was one of the earliest use cases for supercomputers. It is genuinely a “boiling the ocean” type problem.

Practical attempts use a lot of heuristics and approximations, which risks fidelity.

As said before, the physics for chemistry is 100 years old (Schrödinger/Dirac), but the N-body Hamiltonian is an exponential beast. Scaling to just 1mg (~10¹⁹ particles) hits the "Exponential Wall."

You know that people simulate chemistry on computers, right?

It says, in the document:

> Exclusion Statement: Molecular orbital theory is recommended as a way to provide deeper insight into bonding. However, the AP Exam will neither explicitly assess molecular orbital diagrams, filling of molecular orbitals, nor the distinction between bonding, nonbonding, and antibonding orbitals.

Orbital theory is usually taught in organic chemistry and then inorganic for those who take that in college. AP chem targets "gen chem" which does not, as the above statement says, does not get into orbitals on that level at all. I'm familiar with gen chem as taught at least in 3 universities, none touched molecular orbitals.

If someone were to teach orbital theory in general chemistry, it would be a lot of hand waving and not much actual mathematics which was the point of the original comment. To cover molecular orbital theory is satisfactorily. You need to know quite a bit of the mathematics behind differential equations and statistical mechanics etc. AP chem isn't going to cover this. But maybe your 9th grade differential geometry class covered all this ;))

[Sorry for the delay. I really had to watch that soccer game and kids don't have school on Sunday.]

There is an acceleration distribution, but the acceleration operator is strange. I don't remember the details and a quick google search confirms that it's strange.

It's complicated... let's oversimplify some details...

In QM the electron must jump from one orbital to another, and the difference in energy is emitted as radiation as a photon. If the electron jumps from A to B, then B must be empty. So if A is the orbital with less energy then it can't emit. Also if B is full, it can't emit.

For a big enough system, there are plenty of options for B and you get a very good approximation that is the classic rule that says that accelerating electrons emit photons.

There are weird cases, like in a neutron star, there are too many electrons trapped by gravity so all possible B are full, and you have electrons that can't emit.

It you want a tabletop experiment, the keyword is "fermion gas" that are gas of fermions (like electrons) that are very cold and very dense and they have a strange repulsion that is not explained classically. It is caused because there are jumps that are forbidden because the destination is full. (If you heat them or give them more room to be diluted, this strange repulsion almost disappears and you can aproximarte them as a classical gas.)

> a distribution of radiation?

If you measure the radiation far away, you have a distribution of possible colors/energy of the photon, because the electron may choose to jump form A to B1, B2, B3, ... This is like the lines color of gas lamps.

If you measure close enough, you have to draw Feynman diagrams and the photons may have a slightly different value of color/energy. But it's complicated and I'm not sure of the details. I guess it's related to the acceleration distribution, but I'm not sure of the details again.

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The easy answer is that "acceleration -> radiation" is only a useful approximation when the system is big enough to ignore the quantum effect.

The hard answer is probably that you have to study like 10 years of physics to be sure and explain me the details. :)