Seems to be the first time this was confirmed via direct experimental observation of the orbitals:

  “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."

There's even a Wikipedia page for it https://en.wikipedia.org/wiki/Relativistic_quantum_chemistry

Sigma and Pi bonds are typically covered in AP Chemistry, even if the “why/how” is hand waved pretty heavily. The valence cloud shapes get wild for heavier atoms and bonds between two or more atoms add even more to the mix.

I had incredible difficulties with Chemistry, more than any other subject, because most everything was hand waved away, requiring mostly rote memorization. I could never get an intuitive understanding, partly because my profs seemingly refusing to think about things from a physics perspective. My physics prof was able to help with some of it. It was very odd.

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

Granted I took AP Chem 20 years ago, but I don't remember those names (sigma and pi bonds) being covered at all. (I got a 5 on the test, for what it's worth.)

I don't know, I'm not very chemical, but fwiw: a friend and I were favorably impressed with Linus Pauling's general chemistry textbook. It tries to supply enough of the physics for the chemistry to make sense. We only studied for a few weeks before moving on, though, and it's a big fat book.

that's because chemistry is heavily involved in describing the nature of how elements and molecules interact with each other. There has to be some element of understanding that nothing is quite as clear because we use experiments and their conclusions to slowly but surely eliminate some theories while keeping others until disproven.

Part of the problem is that the difficulty curve becomes, like, superexponential if you try to do the actual math. Fairly elementary atoms require the full theory of quantum mechanics to justify rigorously, and anything more complicated than that requires huge bodies of specialist knowledge on approximation schemes (I assume; I haven't studied them, but given that helium already requires approximations I'm assuming the trend continues..)

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.

Yes and no. It depends which branch of chemistry you world have chosen to go down. Physical Chemistry certainly improves a fair amount of the hand waving, but even there the underlying physics is simplified fairly often (as I understand it — I went straight Physics and dabbled in Chemistry from the other side).

The physics that predicts chemistry is about 100 years old. Almost nothing people study up to high-school is that recent, and that modern physics tends to be really hard.

I don’t get it, someone explain? Doesn’t everything get color from relativistic effects?

Pi and sigma bonds fall out of thinking of it from a physical/symmetrical/statistical perspective. There's not too much hand waving in the modeling of atomic and molecular orbitals.

As a chemical engineer, one of the signs of maturity was myself and each of my classmates individually coming to accept and embrace the inevitable “magic coefficient”.

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”.

Gold electrons at inner orbits travel at a large fraction of the speed of light, which is why gold isn't a silver color. That is really neat.

Yes: the article says "since the 70s"

They are not covered in AP chemistry this is just your typical "when I studied differential geometry in high school" HN comment

The Dirac equation which is the equation for describing the wavelike behavior of electrons. It predicted the existence of antimatter and particle spin.

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

I think this lines up with my experience. The way chemistry is often taught its very abstract, borderline magical.

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.

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

At upper undergrad and grad levels, it probably would have improved a lot. The issue is that a lot of the why requires quantum mechanics to really explain and even that becomes intractable extremely quickly. Like you can probably do the analytic solutions for hydrogen atoms and electrons but once you get to helium or past that, you basically need to use a computer to do numeric calculations and even there, you are very quickly using approximations instead of solving the quantum equations directly.

Not in undergraduate chemistry at least. Maybe chem majors had it different. Organic chemistry 1 was basically rote memorization of various reactions and catalysts and their required conditions. Exam questions would be some organic molecule start and some organic molecule end result and you'd have to draw out each and every intermediary step to get to that end result. Organic chemistry 2 was exactly the same just more reactions to memorize. Biochem was a little easier since the exams didn't ask for full pathways but still pretty much pure memorization.

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.

I also took it 20 years ago but I feel like they were (of course I also did undergrad chem 16 years ago so I may be conflating things). It's difficult to explain isomers without explaining why multiple bonds don't rotate.

they are featured in collegeboard's course and exam description: https://apcentral.collegeboard.org/media/pdf/ap-chemistry-co...

To add to this, this "square root" operation done to derive the Dirac equation is where spinors i.e. electron spin i.e. the Pauli exclusion principle i.e. the reason atoms exist at all comes from. Likewise antimatter. The "second order in time" of the Klein-Gordon equation comes from adding relativity and the "fix" reducing that to first order time is the source of antimatter and spin.

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

They’re already taxed to fund pure research, it would be unfair to charge royalties for non-rivalrous products they can’t monetise.

Yes its like cooking or music. You start just by learning whats in the kitchen and on repeating steps. This creates latent or tacit knowledge that helps with the Why questions down the road.

Bohmian mechanics is nonrelativistic, so it has been "falsified" since its inception. It generally makes identical predictions to nonrelativistic quantum mechanics (i.e. the Schrödinger equation), but finding a relativistic version, equivalent to the Dirac equation in QM, has been difficult due to the nonlocality of the pilot wave.

Most colors in synthetic pigments are from conjugated double bonds that don't need relativistic effects to explain: no heavy atoms here!

> 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.

I don’t understand how something that has no clearly defined position like an electron can have a well defined speed. I thought I had understood that at that level, particles are more like clouds, or vibrations in the quantum field, and they had no well defined position until you tried to measure it, causing its cloud to collapse to a smaller region. But if non observed electrons can have a speed that defines the color of a material, that whole understanding seems to be wrong! Where is the error? Are all atoms on a piece of gold being “observed” in the quantum sense?? Even if we just capture the spectrum? Or it’s something else??

P ^ not P => _|_

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

Thanks for the insights. I am interested in learning all this stuff. Am currently going through just Schrodinger's Equation. Do you have book recommendation(s) that include insights everywhere just like what you shared? Thanks.

But oftentimes theoretical chemistry is not as important as what we get out of experiments because unlike physics, which attempts to derive general laws of nature, chemistry has to deal with the nitty gritty of the diversity of actual miscroscopic interactions of things. Any theory that is not entirely rigorous or even has slight room for an exception will be ignored by necessity, and physics is chock full of such examples. Biology is in a certain sense better (since it deals with larger things) and in a certain sense worse (as it relies on dogma and mysticism, at its essence, to explain the systems of life), and still nobody has gone beyond Aristotle and Kant in giving anything close to a rigorous definition of life as such.

> physics that predicts chemistry

Do we have this?

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

As you move up levels starting from physics (eg. physics-> chemistry-> biochemistry-> biology), each layer has several "laws" which are generally pretty established, but a causal connection between the layers is hard to provide satisfactorily. And that is how I think it'll always be, else we'll be expecting to explain Shakespeare's plays using physics.

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.

And also emergent behavior means that at each level, we need different abstractions to deal with the problem. Even with chemistry, there's ideas like benzene rings that are aromatic, that you couldn't predict that from particle-particle interactions. So it's not just that it's hard to understand quantum mechanics, it's that understanding QM doesn't mean you'll understand the problems that chemistry deals with.

I was lucky enough to have Morrison and Boyd as my undergrad ochem textbook. they built the material up really well from first principles.

And people clutch their pearls at ai not really understanding anything when people describe university experiences and lessons like this...

You had a poor organic course. Even orgo 1 should have you thinking about resonance + electron-rich or -deficient areas of molecules and how those lead to reactions.

It's a different kind. Say, some reaction should run 1.23x faster theoretically. But the theory is approximate (in order to be tractable at all), and so are its predictions. This particular element is special in its own way, diverging from the theory a bit, even though its neighbors fit well. That particular bond requires a bit less energy to break than the theory predicts, due to a complex interplay of bonds nearby, understood only qualitatively. Etc, etc.

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.

These are books to train physicists, accessable-ish to a math heavy engineering undergraduate degree holder. The insights above are my own and extractable from this material but not necessarily stated out loud (unless I'm unconsciously plagiarizing which is entirely possible)

* David Griffiths - Introduction to Elementary Particles

* Chris Quigg - Gauge Theories of the Strong, Weak, and Electromagnetic Interactions

And the wonderful Richard Behiel's videos on YouTube https://www.youtube.com/watch?v=8Iu74b5iCuQ

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.

"High speed" here can be taken in terms like this: the phase of the wave function changes rapidly with position and time. (Changing with position -> a superposition that's heavy on short wavelengths, high momentum; with time -> high frequency, high energy.)

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.)

The uncertainty principle says that the less well-defined the position, the more well-defined the velocity, and vice versa.

Those axioms do not have a basis other than observations at human scale.

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.

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

You are mostly correct.

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.]

> 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).

It is a contradiction only because you chose to call it so, or you built a framework that interprets something as a contradiction. Logic and mathematics are built on shaky grounds on larger scale.

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

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

> 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.

Isn't superposition a contradiction for classical physics? Being partly here and there.

Where is physics chock full pf exceptions?

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.

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.

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?

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.

Oh alright fair enough, measured vs. expected basically?

I would think just because everything is so cumulatively complicated and interconnected that if you tried to trace a line through a complex biological processes and explain it all you will end up with 1,000 PhD thesis topics to figure out and thousands more you just hadn't noticed yet. And at the end of the day none of that might be all that useful for describing the larger process at work. So at some point when someone ask "Why does X do Y" you gotta just settle on "because that's the way it is" and move on.

I think he's being a little facetious - what he probably means is that if you attempt to get any true scientific rigor of that is going on in biological or chemical systems you end up facing the limits of physics in being able to explain what is going on. So rather and try to have scientific rigor, you just accept things the way they are and memorize the outputs and if anyone asks "why is it like that", your answers are either:

* 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.

> and less universal

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.

biology is full of exceptions to exceptions to exceptions. like immunology

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

(Newbie here). And then going further, shouldn't there also be acceleration and its distribution? It says classical models could not explain why accelerating electrons were not radiating. If acceleration also shows up in QM, then ... a distribution of radiation?

Attempts to formalize dialectics do exist, but it mostly stays at a word-weaving level.

> From the perspective of a deterministic universe, creative works theoretically can be explained as a physics outcome

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.

Yeah, but that’s like saying predicting next week’s lottery numbers, or the precise weather exactly one year from now, is a data problem. There’s no simulation that could answer those questions even in principle even if the universe were fully classical.

Look into Aristotle and Kant on ‘the organized /and self-organizing/ being’; apply a couple thermodynamic abstractions known to adolescents ; be named Erwin Schrödinger ; hackernews will respond accordingly.

yet there are problems there too we do not know the "true axioms of math", people disagree (math foundations)

I guess that is true, but it isn't much. But my basic point was that before you can have "life" you have to have a theory of life which ultimately requires metaphysics, and there hasn't been much of an update to our understanding of what would ground a definition of life beyond Aristotle and Kant, and even their work is not determinative by any means.

Freezing water is life?

I'm not a physicist but I've always seen physics as a bit hand-wavy myself.

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.

That sounds like Caltech. The ochem major is notorious for how hard it is.

I think they meant the opposite; physics throws things out as soon as there's a need for exceptions, and there are examples of that.

Maybe we’d say “physics” is really just the delineation between things we have an accurate model for and everything else (the exceptions?). Theoretical physics would be the search for the “why” of everything, inside and out of that line in that case.

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.

More like, “the unmeasurable” or “unmodelable”. Examples could be the “A” in the Arrhenius equation or the “k” in Fourier’s law of conduction.

“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.

Classical physics doesn't have particles that are simultaneously here and not here. It's a discrepancy between theory and experiment. And there's no point of accepting contradictory statements that are both true to deal with that. You can't fix a wrong description of reality by using some fancy logic that allows (apparent) contradictions.

Yes, we've all seen the xkcd[1] but you've misunderstood it. Physics applies mathematics but mathematics cannot derive physics in the way that a complete physics (and a lot of compute) could derive chemistry and biochemistry.

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/

Maths lacks the physical grounding, so in that sense, it's less "real", and more "made up", even though of course it's so pure.

Yes. We also simulate cosmology and quantum systems and play Sims.

Downvoters are probably misunderstanding this. Mathematical theory is based on axioms and inference. The axioms do not have to be true in any cosmic sense for the math to be correct or even useful.

> mathematics cannot derive physics

thats just at the current state of the art...doesnt mean a complete maths cannot...its arguably debatable why physics follow some maths and why the specific constrains

The difference being that the chemical simulations get the correct answers on most conditions. And probably the few they miss are because of the simulation limitations, not of the underlying model.

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.

its the same... physics hand-waves the 'why' all the same as chemistry or biology...the gap might be wider but its the same

I don't think that's true. Mathematics can model every conceivable universe; you cannot derive the values of c or G in our universe from a purely mathematical model. Even if there were a proof that the current values for cosmological constants are the only possible values, that proof would necessarily have to rely on lemmas from physics.

Physics has a long history of throwing out laws with exceptions in favour of laws that cover larger and larger numbers of observations.

It could be that once we truly understand math in a complete way it would lead inexorably to the definition of one and only one possible universe with only one possible set of rules and c and G would simply fall out naturally. I'd agree it seems unlikely given our current understanding of math and physics (and their relationship to each other). But given both are incomplete it remains a possibility. The one theme that seems to hold true as we dig deeper and deeper into how the world works is that the fundamental rules seem to get more and more unified.

Please tell us more about this. I’m not familiar with any definition of mathematics that would support the idea that it can prove statements about our universe without access to observed facts.

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