Fun fact: this is why mercury is liquid at room temperature. Its inner electrons move at close to 60% the speed of light, pulling in its outer electrons more tightly, making it harder for it to bond and be solid. (I am not a physicist, don't rely on my statements for your space ship design)

https://en.wikipedia.org/wiki/Relativistic_quantum_chemistry

so the real world impact is, having anything at all

> In the relativistic regime, an electron’s spin — the magnetic moment that points either up or down — and the electron’s orbit are no longer independent of each other, a state known as spin-orbit coupling.

Interesting stuff. I've never heard of sigma or pi bonds.

https://www.science.org/doi/10.1126/science.aei1285

If I would have stuck with it, would things have improved?

Of course, they could still do a much better job useful providing pointers into this knowledge, instead of just handwaving over it and insisting on rote memorization.

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.

* Because God said so

* Find out yourself and get a nobel prize

Either way, even if you don't know what the answers are, you can still do serious work at a higher level of abstraction.

so there is no way to extrapolate/interpolate, anything which was not directly measured is basically unknown since it could be yet another exception

or in programming language, the worse spaghetti code you could imagine, full of feature flags randomly enabled inconsistently

Dark matter is a great example.

Our understanding of gravitation didn't cleanly apply at ultra-large scales so we had to add a massive fudge factor.

You can't "go faster" than the speed of light, but space in between things can expand faster than the speed of light.

It seems like things that are "settled" regularly get an "ope, but except for this special case..." treatment.

I’m not a physicist, so I’ll let them pipe up on how much is in and out of the descriptive line, and how much is in and out of the theoretical explanation line. But I don’t know many physicists who think we’re close to “done” with either endeavor.

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

Also, this is where Rutherford's "all science is either physics or stamp collecting" holds a lot of water. As you move up the science layers, the laws themselves become less mathematically rigid until by the time you get to the social sciences, explanations are all hand-waving, and all "laws" are statistical at best and empirical.

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.

Yes, this is key in my mind. It's not really that the laws and definitions become less strict of themselves, it's that the subjects under study become less uniform. It's fine to study a few atoms in isolation and describe their features, but if you put a lot of them together they'd better be in a uniform lattice or your calculations will take more than a lifetime to complete. If you want to describe the interaction in a drop of water, you don't use the Standard Model to integrate over 3e22 baryon fields.

Yes, physics underlies all other fields. But fundamental physics is also completely untractable to solve problems in those other fields, even if Heisenberg would allow it.

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).

In other words, physics can explain Shakespeare's plays when you hand-wave away the biggest reason it cannot.

> theoretically

... meaning not in reality, but in an abstraction of reality that conveniently leaves out the hard part.

> This is just a data problem though.

The word "just" makes it sound like that data problem is a minor inconvenience, and not a fundamental obstacle.

Becoming a billionaire is simple, after all it's just a money problem.

I mean, you're right in that (leaving out quantum randomness), you could predict macroscopic outcomes based on a physics simulation that includes all elementary particles explicitly, if you assume that such a simulation can be scaled from <10 particles to macroscopic numbers. But there is no evidence that this assumption is true, so it remains an interesting thought experiment that gets confused with reality because people like to slap the "in theory" label on it.

Math isn't attempting to describe a physical universe. It provides the substrate upon which such a description can be expressed and validated - found to be consistent with itself - but many valid descriptions do not describe our universe. Physics is the empirical search for the correct mathematical description of our universe.

[1] https://xkcd.com/435/

Are there any papers where this possibility is explored? What does it mean to have a complete understanding of mathematics?

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.

Right now the lab is having me get comfortable using software like Gaussian and ORCA by simulating a bifurcating reaction. This is a reaction that, depending on the catalyst's momentum, will change what site it bonds to (it makes either a 6-membered or 7-membered ring). I'm finding the intermediate states (where the molecule is most stable) and transition states (the tipping point), and then running trajectories to see which output is more likely.

Once I've finished simulating that, I should be comfortable enough with the process to jump on the bigger project, which is machine learning interatomic potential (MLIP) model distillation. There's a lot of exciting work around speeding up DFT methods by using machine learning (note this is not generative AI, it's merely predicting the molecule energy based on atomic positions). So my one year goal is to get on that project and start contributing.

My five year goal is to, well, graduate. But then I'll probably do a PhD in computational chemistry, since I'm really interested in ways to speed up and scale existing methods. My big dream is to simulate large biological systems while still having bond formation and breaking, to automatically elucidate biochemical pathways, but there's still a lot of steps in-between.

I assume you are familiar with:

https://matt.might.net/articles/phd-school-in-pictures/

I hope and pray that your research helps to make the world a better place and that the rest of us can use your knowledge to help to make the world a place which merits your research.

I haven't seen that website before, but it sounds pretty accurate from what I've heard. It's insane how high of a mountain needs to be climbed just to catch up to the state-of-the-art, and how much work is needed to push through to figure out something truly new.

Here's to making the world a better place!

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 a useful level of accuracy we can certainly simulate water. And we can do the same for a single proton for some definitions of useful (but not other definitions).

To simulate a water molecule you do so with a weakly coupled SU(1) gauge theory (light does not interact with itself at tree order) problem where the masses of all constituents are orders of magnitude above the relevant energy scales (you can think of it as the electrons and nuclei and particles coming in and out of existence are contained in a renormalization scheme).

We have "good simulation models" of both, but the former is extraordinarily complicated compared to the latter for the reasons stated above.

General physics and chemistry take different approaches forced by the subject matter. Physics abstracts to problems over concepts with details abstracted away, but at higher levels of education you learn to apply these corrections.

Chemistry starts with practical reality and a lot of rote memorization. Only at the higher levels do you get the unifying theory. Since the unifying theory is quantum electrodynamics (in this case, relativistic QED), that makes sense.

I also had an amazing physics professor who was able to tie literally everything we learned back to real practical and observable events. There is an art to teaching these subjects. This is all undergrad level though, and it wasn’t my major.

The curious always wanted to know why some magic coefficient was there. Where did it come from? How is it measured / calculated? How to derive the magic coefficient?

Eventually you learn that it’s turtles all the down. You can pick apart the magic coefficient and dive into the nuanced physics that its derived from…but then you still end up with a new magic coefficient.

So eventually, the curious students learn that the mysteries are out there for when you want to go out and explore them. But otherwise, we pick our level of abstraction for the problem we’re currently working on and accept the magic coefficients that apply to that level of abstraction.

The real trick is knowing the conditional boundaries when those magic coefficients no longed apply and you either need different ones or “here be dragons”.

A general theory of everything might describe all of it from first principles, without magic coefficients. But likely computing it would take a decade with current methods.

“A” is described as being derived from the collision frequency of molecules in that specific reaction but really it’s just an arbitrary magic number you look up in a book for the specific reaction that you’re working with. It’s often relatively temperature invariant across some range of temperatures but go outside that range and it becomes a function of temperature too.

Pulling up the wikipedia for “Collision theory” will show you that there has been some work to derive values of A rather than just find them all experimentally for every reaction. But it’s still very unsatisfying to the curious mind.

“k” is the thermal conductivity of a particular material. Curious minds might wonder what’s hidden behind this constant. How would someone predict “k” for a novel theoretical material? Like, say, tetrahedrane?

It’s been awhile, otherwise I’d walk you through a graph containing a couple hierarchical nodes where one constant leads to another equation. But it’s a bit too late to pour through Perry’s Handbook right now to jog my memory.

There are multiple approximate models for the same thing. Part of the skill is choosing a model likely to produce results that map closely to the real-world in a particular context with the least amount of effort. Chemical engineering as a discipline is effective at navigating and constraining the internal inconsistencies of these myriad models in a tractable way.

The sausage factory is real. There isn’t a tidy bit of theory or math under this that is useful in real settings. This partly explains the handwaving nature of the explanations if working in that sausage factory isn’t going to be your profession. Even if you wanted to understand the theoretical basis, that becomes extremely non-trivial very quickly, so it isn’t the kind of thing worth spending much time on if you aren’t going to go deep in it.

Not a satisfying answer, I know.

I hated these sorts off classes, where if you had your notes with you, you'd ace the exam and be able to explain everything. Passing or failing depended not on understanding, but simply whether you cram all the specifics and covered edge cases all into your head at once, given the rest of your present courseload preventing you from actually digging in to the best you could. Wrong answers didn't come from not knowing how to solve something, but not remembering exactly how to solve something.

To not have to resort to rote memorization you first have to have the interest. That way you accumulate the knowledge over time, then the patterns feel logical at some point. The logic isn't very precise, maybe that's where you have problems? Some molecules are similar in some molecules in this regard and other molecules in another regard. You will get a feel how stuff behaves. You certainly have a lot of chemistry knowledge you are not aware of.

For example, I'm sure you have a good intuition how things burn and you probably know the basics of why it burns. The invisible oxygen in the air is the main chemical insight to explain why stuff burns. You can explain the whole process to whatever detail you like with physics, but many chemists lack the math and physics knowledge to do much of that.

Do we have this?

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.

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

Those other simulators aren't there to tell you the result. Instead people put the result in to find how the simulation behaves in cosmology, and don't care about them in Sims.

Yes.

I have a B.Sc in Chemistry (Honours) from late 1980s and it was not until the final year that things finally began to click. The main catalysts were the books "Concise Inorganic Chemistry by J.D.Lee" and "Mechanism in Organic Chemistry by Peter Sykes". Both beautifully written and try to give a framework within which to think viz. the former based on the periodic table and the latter on carbon valence bond properties. I think i need to revisit these (and other books) to justify my degree in Chemistry :-)

For background and inspiration, consult Linus Pauling's classics; The Nature of the Chemical Bond and General Chemistry - https://archive.org/search?query=creator%3A%22Pauling+Linus%...

Linus Pauling (the only scientist in history to be awarded two undivided, unshared Nobel Prizes) - https://en.wikipedia.org/wiki/Linus_Pauling

For instance, we know that gold gets its color from relativistic effects.

https://physics.aps.org/articles/v10/s3

  “This idea that relativity is important in heavy elements has been around since the 1970s,” said Lai-Sheng Wang, a professor of chemistry at Brown and the study’s corresponding author. “But we show direct spectroscopic evidence that what we learned in high school about chemical bonding isn’t true in heavy elements."

I'm so happy we have HN with likeminded people and no noise.

This discovery is about a (seemingly, I haven't been keeping up too much) new case of one specific bond in one specific ion. Do not read the university's breathless press release, go straight to the article. The third sentence of the editor's summary is "It’s long been clear that this model starts to fray when the atoms get heavy enough for relativity to come into play".

You start with the Schrödinger equation, add relativity to get the Klein-Gordon equation which is a mess because it's second order in time involving negative probabilities, if you in ways "take the square root" of it you get the Dirac equation.

Relativity has been part of the understanding of electrons since 1928.

https://en.wikipedia.org/wiki/Dirac_equation

So yes very much so relativistic effects are a foundational part of QM.

The idea is that it has not a clearly definite position, but it has a distribution of probability to find it that looks like a "cloud" https://en.wikipedia.org/wiki/Atomic_orbital

In a more abstract sense, has not a clearly definite speed, but it has a distribution of probability to find it in a speed graphic.

The distribution of position and speed are defined by an equation and you must add a relativistic correction to the classic version. For lighter atoms you can just ignore the correction. For heavy atom (like Bismuth in this case) the correction is important.

Informally, the correction is important only when the "average" speed is fast enough to be somewhat close to the speed of light, like 50%c.

The correction changes the energy of the expected distribution of position and speed, and the energy. When an electron jumps from an orbital to another orbital, the difference of energies is related to the color.

> Are all atoms on a piece of gold being “observed” in the quantum sense??

[Ignoring that "observer" is a very misleading word and causes a lot of confusion, but it's the standard one and we are stick with it...]

The observation is only of the energy level of the orbital electron. We know the energy, but we don't know the position or the speed. When you observe some quantum object you don't get magically all the properties, only one of them, in this case the energy. In other experiments you can get only the position, in others only the speed. [And there are a lot of weird cases and technical details.]

Re "observed all the time": when gold interacts with light, the light's normally of a strength that's a small perturbation on the fields internal to the atom, which is basically why you can treat the atom/light-field system as two weakly coupled quantum systems. It's an "observation" when the light leaves a classical trace such as a current in a CCD.

(I don't expect this to leave you unmystified about QM, but hopefully a bit clearer about it.)

<https://assets.press.princeton.edu/chapters/s6681.pdf>

He was a very proud Jew, who questioned whether he would have been had he not been born into such life. I disagree immensely with him on his pure-fatalism POV, but obviously everybody reading this knows his last name more than anyelse's [& definitely not mine].

----

I have a degree in medicinal chemistry, back from the ancient mid-00s (pre Youtube) and just cannot imagine how incredible science education is/could_be with all the modern visual aids [†]. That models for every single element are just a click away and highly interactive, within any online web_browser (and without additional softwares).

Old is new again. Thanks Einstein. I cannot even begin to imagine just how far ahead his own brain was processing this complexity.

[†] Back then I was still doing organic chemistry rotations entirely within my own spatial cortex, because the only visuals were 2D prints in the library. Somehow earned 'A's {thanks brain}.

Is lead still used in common, mass-produced solar panels currently on the market? Wikipedia:

"Lead-based semiconductors such as lead telluride and lead selenide are used in photovoltaic cells and infrared detectors."

Wiki page for lead telluride mentions thermo-electric materials, page for lead selenide mentions IR imaging & detectors. Neither page even mentions solar panels.

Searching turns up mentions of use in flexible solar panels, which have a tiny market share. And iirc some/most of those use cadmium rather than lead compounds? (ok cadmium is equally nasty)

There's mention of lead solders used in solar panel construction. Leaded solders have been banned in EU due to its RoHS directive for a looong time, spare a few niche applications. Solar panels among those? If ever: still the case in 2026?

True: bismuth is used in some solders for similar reasons as lead.

And ofcourse there's recycling. One source mentioned ~0.1% of recycled panels by weight. Another source says overall lead content lower-level than safety limits for material on children's playgrounds.

All in all, that "toxic lead" statement reads more like outdated info. If not FUD.

Very cool.

The paper PDF: https://bpb-us-w2.wpmucdn.com/sites.brown.edu/dist/0/196/fil...

Is it a different set of rules for superfluids like 3He, or should the laws of superfluids cover heavy elements, too?

Here, again, a need for a model of superfluid quantum gravity

My guess to the Fermi paradox is that there actually are intelligent life across the universe but just like in Star Trek they stay quiet until we reach a certain level of knowledge.

Also, the foundational axioms of logic themselves could be valid only at a scale that is familiar to humans. For example, the strict bounday between true and false might get blurred and things could be true and false at the same time at other scale.

Being true and false at the same time is a contradiction. But yeah, there is such a thing as mathematical intuitionism that rejects the law of excluded middle (which is not "being true and false at the same time"). It's just one philosophical stance among others though.

Similar to how Earth's tectonic plates are floating on liquid magma, while appearing to be fully solid and fixed at the surface.

The axioms of a logic that are consistent will definitely not let a statement be true and false at the same time.