> The increased nuclear mass causes orbiting electrons to speed up to a significant fraction of the speed of light, where the rules of Einstein’s theory of relativity are important.
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)
Relativistic effects are observed with many other 6th and 7th period elements. For example, the yellow colour of gold and caesium comes from altered electron energy levels due to relativistic orbital contraction, so are the special catalytic and bonding properties of platinum.
OP claimed relativistic effects explain why mercury is liquid at room temperature. That may be part of the story, but it isn't the whole thing, since other heavy elements are not liquid at room temperature.
It also has an effect, it is a small correction in the energies and bounding. Sometimes it's enough to change the color or state, sometimes it's a correction like making it 1% softer or harder and is not interesting unless you are a specialist.
It would be the element underneath it which is synthetic. But it is interesting that all the elements in that row are soft or brittle in pre form or in some compounds.
> The increased nuclear mass causes orbiting electrons to speed up to a significant fraction of the speed of light, where the rules of Einstein’s theory of relativity are important.
> 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.
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?
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
> 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).
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.
> 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.
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.
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
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.
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?
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.
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.
Cool details, thanks. To help me understand your life, what would be like a one year and a five year research goal for you? I never spent time in lab sciences so it’s kind of a black box for me.
Disclaimer: I'm only a freshman, so there's still a ton I don't know :)
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 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.
Thank you for the kind words! I've been wanting to do this research precisely because of firsthand experience with how hard chronic illness can be, and I'm hoping to attack it with a systems approach.
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.
do you think quantum computers would help simulating this? I've seen contradictory opinions from the experts - it can in theory but not really in practice (even assuming sufficiently large quantum computers will be built)
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.
If you want to get pedantic we can't simulate anything with complete accuracy in the absence of a theory that encompasses all the known forces. Which we don't have. (Damn you gravity. Can't you just get along with the others)
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).
Am I right with my assumption that by "fundamentally different problem", you mean we lack a good simulation model, but that the number of degrees of freedom would actually be manageable?
To simulate a proton you need to solve a strongly coupled highly relativistic SU(3) gauge theory (naturally non-abelian i.e. the force carrier field itself carries charge and is self-interacting at tree order) problem with constituents that have masses orders of magnitude below the relevant energy scales (i.e. you have many matter AND force particles that can pop in and out of existence and they all strongly interact with one another).
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.
Physical Chemistry (I think it was Chem 361 at UofI) took most of the semester to get to the point where we could derive the shape of the hydrogen orbitals. Probably the best lecture of that class.
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.
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.
“Physical chemistry” is the search term for what you’d be interested in.
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 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.
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.
Chemistry fundamentally is about producing a result. Physics, especially when you get into particles, is about explaining a result. Ultimately, chemistry, electronics,even civil engineering, is applied physics, but we are a long way from consolidating and closing the gaps. Empirical results stand in for complete understanding in the vast majority of engineering disciplines, both because complete understanding is not needed and also because we don’t have it yet. Fundamentally, chemistry is a variety of engineering discipline, being mostly an applied science.
The wild thing is that the understanding of electron arrangement made a _huge_ difference in chemistry texts where overnight they went from myriad descriptions of reactions being commented as "...and this is not well understood" to quite thorough and rigorous explanations of chemical interactions.
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).
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”.
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.
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.
Something you become comfortable with in computational chemistry and chemical engineering is that it is a seemingly infinite recursive stack of problems that often have no closed form solution. Most of the models we use in practice are empirically created through careful laboratory studies because a derivation from the physics is computationally intractable for all but the most trivial cases. This leads to phenomena like getting different numbers for the same thing depending on how you compute and derive them.
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.
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.
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.
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.
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.
I had the same issue! I absolutely destroyed AP Physics (first person in the history of the school to get a 5 on the AP and 100 on the NYS Regents) but got a D in AP Chem one semester, my lowest grade ever!!
I hated chemistry in school as well for the same reason. I studied physics afterwards... Oddly, once I was looking for information about some experimental physics problem with electron orbitals and found some very well-written theoretical chemistry lecture notes :P
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.
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.
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.
this was my experience as well. "here's a trend, it's not true in these cases for reasons we won't explain." I only had two semesters and the second was much better than the first.
Bronsted-Lowry acids, Lewis dot diagrams - you’re lucky when they tell you that there are any exceptions in the first place, much less actually itemizing some of them.
Chemistry is very empirical. While we today can explain nearly everything from physics, you still always have check how things will work in experiment, unlike in physic where you often can calculate the outcome of experiments very precisely from first principles.
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.
One of the disappointing realisations I got from my physics degree was that as you move into the real world with non-spherical cows you can no longer solve any of the equations.
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.
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."
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.
> If I would have stuck with it, would things have improved?
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 :-)
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 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.
Not in the sense that the electrons would be orbiting "outside" the star. Neutron stars are already a conglomeration of particles, including a sizeable fraction electrons that are effectively "squeezed out" of neutrons to have equivalent fermi energies. Any additional charge you add would immediately grab an "orbiting electron" into the existing system.
As written that sentence is wrong. The increased nuclear mass is not the cause of the effects. It's the increase in the nuclear charge and subsequent modification of the coulomb potential that is relevant.
Wait... wasn't it already understood that relativity influences electron orbits of heavy elements? I clearly remember being taught some of this in physics, in the mid-noughties.
For instance, we know that gold gets its color from relativistic effects.
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."
In general, yes. Spin-orbit coupling and relativistic effects in heavier elements is not new. A rather... significant elements where this was studied was uranium (and plutonium, of course). Even napkin maths show that for heavy elements, some of the electrons have relativistic velocities.
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".
Yes, I was taught that relativity is a significant part of quantum chemistry equations in gold atoms 25 years ago. The idea is quite old and the title is misleading.
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.
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.
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
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.
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??
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.]
(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?
"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.)
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].
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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}.
"Bismuth could be an alternative to toxic lead in next-generation solar cells."
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.
Relativity is also responsible for a lot of weird behaviors of heavy elements, such as the color of gold. Or that lead is a good material for batteries.
Can equivalent theoretical predictions be calculated in a Bohmian framework for the quantum aspects, or is this (potentially) an interesting case where there’s divergence and falsifiability?
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.
Very farsighted, after working as a patent clerk, to lay claim on such a foundational technology. Back in the day, they must've been like, oh, so Mercury blocks the sun at the wrong time, but where's the commercial value - and now every chemical company throughout the universe is about to get a bill every time they make something more complex than hydrogen gas.
Meanwhile, Galilean relativity has long gone out of patent, and people on board planes and other vehicles just move around like they were in a stationary reference frame paying no royalties.
I had a couple drinks so having one of those moments. I am always so fascinated by the science and experiments done to prove what we know. I consider myself at least of average intelligence probably slightly above but the things scientists research and solve always blows me away.
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.
In general, anything that is observed to be true at a smaller scale or context can't be extended to much larger scales. That involves assumptions on logic and mathematics to be homogenous across all scales. A pure theoretical extrapolation without bounds is quite common in mathematics, such as proof by induction etc.
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.
> 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.
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.
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.
> The increased nuclear mass causes orbiting electrons to speed up to a significant fraction of the speed of light, where the rules of Einstein’s theory of relativity are important.
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)
I guess the more interesting question is why this doesn't happen for neighbouring elements in the periodic table?
Relativistic effects are observed with many other 6th and 7th period elements. For example, the yellow colour of gold and caesium comes from altered electron energy levels due to relativistic orbital contraction, so are the special catalytic and bonding properties of platinum.
https://en.wikipedia.org/wiki/Relativistic_quantum_chemistry
OP claimed relativistic effects explain why mercury is liquid at room temperature. That may be part of the story, but it isn't the whole thing, since other heavy elements are not liquid at room temperature.
It also has an effect, it is a small correction in the energies and bounding. Sometimes it's enough to change the color or state, sometimes it's a correction like making it 1% softer or harder and is not interesting unless you are a specialist.
It would be the element underneath it which is synthetic. But it is interesting that all the elements in that row are soft or brittle in pre form or in some compounds.
Meanwhile there are quarks inside every regular atom moving at speeds like 0.99995c ...
Interesting -- does that have any macroscopic/real world impact?
well, 90%+ of the mass of a proton comes from moving stuff, rather than rest mass of the quarks.
so the real world impact is, having anything at all
And this mass is again an emergent property of Einstein's relativity ...
I think I recently learned that the Higgs is actually not that much part of imparting mass for atomic particles. I thought it imparted all mass.
just enough to keep electrons from staying at light speed like photons
This is the coolest fact I’ve learned in a long time. Thank you!
> The increased nuclear mass causes orbiting electrons to speed up to a significant fraction of the speed of light, where the rules of Einstein’s theory of relativity are important.
> 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
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?
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.
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.
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.
how does biology depend on "dogma and mysticism"? I am really curious - a Google search yielded nothing much relevant.
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.
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.
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
Where is physics chock full pf exceptions?
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.
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.
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.
> 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.
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.
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.
Freezing water is life?
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.
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.
> 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.
> 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).
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.
> 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.
doesn't that also apply for the maths-> physics layer? id say maths is the bottom layer
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/
> 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
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.
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?
yet there are problems there too we do not know the "true axioms of math", people disagree (math foundations)
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.
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.
its the same... physics hand-waves the 'why' all the same as chemistry or biology...the gap might be wider but its the same
Physics has a long history of throwing out laws with exceptions in favour of laws that cover larger and larger numbers of observations.
The subject in chemistry isn't theory. It's what actually happens in nature. Even immense levels of theory just don't close the gap.
All this computing power. Can we even simulate a water molecule yet from scratch with QM?
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.
Cool details, thanks. To help me understand your life, what would be like a one year and a five year research goal for you? I never spent time in lab sciences so it’s kind of a black box for me.
Disclaimer: I'm only a freshman, so there's still a ton I don't know :)
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.
Good luck!
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.
Thank you for the kind words! I've been wanting to do this research precisely because of firsthand experience with how hard chronic illness can be, and I'm hoping to attack it with a systems approach.
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!
do you think quantum computers would help simulating this? I've seen contradictory opinions from the experts - it can in theory but not really in practice (even assuming sufficiently large quantum computers will be built)
I'm only a freshman, so I don't feel very qualified to comment on that :) I hope so though!
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.
If you want to get pedantic we can't simulate anything with complete accuracy in the absence of a theory that encompasses all the known forces. Which we don't have. (Damn you gravity. Can't you just get along with the others)
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).
That's a fundamentally different problem and a terribly unfair comparison.
Am I right with my assumption that by "fundamentally different problem", you mean we lack a good simulation model, but that the number of degrees of freedom would actually be manageable?
To simulate a proton you need to solve a strongly coupled highly relativistic SU(3) gauge theory (naturally non-abelian i.e. the force carrier field itself carries charge and is self-interacting at tree order) problem with constituents that have masses orders of magnitude below the relevant energy scales (i.e. you have many matter AND force particles that can pop in and out of existence and they all strongly interact with one another).
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.
Physical Chemistry (I think it was Chem 361 at UofI) took most of the semester to get to the point where we could derive the shape of the hydrogen orbitals. Probably the best lecture of that class.
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.
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.
“Physical chemistry” is the search term for what you’d be interested in.
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 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.
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.
Chemistry fundamentally is about producing a result. Physics, especially when you get into particles, is about explaining a result. Ultimately, chemistry, electronics,even civil engineering, is applied physics, but we are a long way from consolidating and closing the gaps. Empirical results stand in for complete understanding in the vast majority of engineering disciplines, both because complete understanding is not needed and also because we don’t have it yet. Fundamentally, chemistry is a variety of engineering discipline, being mostly an applied science.
The wild thing is that the understanding of electron arrangement made a _huge_ difference in chemistry texts where overnight they went from myriad descriptions of reactions being commented as "...and this is not well understood" to quite thorough and rigorous explanations of chemical interactions.
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).
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”.
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
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.
Oh alright fair enough, measured vs. expected basically?
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.
Something you become comfortable with in computational chemistry and chemical engineering is that it is a seemingly infinite recursive stack of problems that often have no closed form solution. Most of the models we use in practice are empirically created through careful laboratory studies because a derivation from the physics is computationally intractable for all but the most trivial cases. This leads to phenomena like getting different numbers for the same thing depending on how you compute and derive them.
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.
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.
Assuming the model doesn't decide you are trying to build a bomb and refuses to answer.
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.
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.
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.
That sounds like Caltech. The ochem major is notorious for how hard it is.
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...
I had the same issue! I absolutely destroyed AP Physics (first person in the history of the school to get a 5 on the AP and 100 on the NYS Regents) but got a D in AP Chem one semester, my lowest grade ever!!
I hated chemistry in school as well for the same reason. I studied physics afterwards... Oddly, once I was looking for information about some experimental physics problem with electron orbitals and found some very well-written theoretical chemistry lecture notes :P
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.
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.
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.
this was my experience as well. "here's a trend, it's not true in these cases for reasons we won't explain." I only had two semesters and the second was much better than the first.
Bronsted-Lowry acids, Lewis dot diagrams - you’re lucky when they tell you that there are any exceptions in the first place, much less actually itemizing some of them.
Chemistry is very empirical. While we today can explain nearly everything from physics, you still always have check how things will work in experiment, unlike in physic where you often can calculate the outcome of experiments very precisely from first principles.
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.
One of the disappointing realisations I got from my physics degree was that as you move into the real world with non-spherical cows you can no longer solve any of the equations.
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.
> physics that predicts chemistry
Do we have this?
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?
Yes. We also simulate cosmology and quantum systems and play Sims.
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.
No.
We have answers. It’s called physical chemistry. The problem is that it takes a shit ton of math
> If I would have stuck with it, would things have improved?
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
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 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 not covered in AP chemistry this is just your typical "when I studied differential geometry in high school" HN comment
they are featured in collegeboard's course and exam description: https://apcentral.collegeboard.org/media/pdf/ap-chemistry-co...
Could electrons orbit a neutron star if we gave it a positive charge?
Not in the sense that the electrons would be orbiting "outside" the star. Neutron stars are already a conglomeration of particles, including a sizeable fraction electrons that are effectively "squeezed out" of neutrons to have equivalent fermi energies. Any additional charge you add would immediately grab an "orbiting electron" into the existing system.
As written that sentence is wrong. The increased nuclear mass is not the cause of the effects. It's the increase in the nuclear charge and subsequent modification of the coulomb potential that is relevant.
Wait... wasn't it already understood that relativity influences electron orbits of heavy elements? I clearly remember being taught some of this in physics, in the mid-noughties.
For instance, we know that gold gets its color from relativistic effects.
https://physics.aps.org/articles/v10/s3
Seems to be the first time this was confirmed via direct experimental observation of the orbitals:
I came to the comments exactly for this ("wait I thought we 'knew' this already").
I'm so happy we have HN with likeminded people and no noise.
In general, yes. Spin-orbit coupling and relativistic effects in heavier elements is not new. A rather... significant elements where this was studied was uranium (and plutonium, of course). Even napkin maths show that for heavy elements, some of the electrons have relativistic velocities.
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".
Yes, I was taught that relativity is a significant part of quantum chemistry equations in gold atoms 25 years ago. The idea is quite old and the title is misleading.
The article seems to be more specific, about relativistic effects in triple bonds
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
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.
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
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.
There's even a Wikipedia page for it https://en.wikipedia.org/wiki/Relativistic_quantum_chemistry
Yes: the article says "since the 70s"
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.
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??
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.]
(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?
"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.
I don’t get it, someone explain? Doesn’t everything get color from relativistic effects?
Most colors in synthetic pigments are from conjugated double bonds that don't need relativistic effects to explain: no heavy atoms here!
It's beautiful to see Einstein's work still being validated.
His brilliance transcends science, e.g:
<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}.
His name will still go way down in history, that is assured
"Bismuth could be an alternative to toxic lead in next-generation solar cells."
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.
Bismuth can also be used as a collector metal for smelting precious metals instead of lead. It even cupells the same way as lead.
For context: this is one more experimental confirmation of Dirac's equations (incorporating special relativity into quantum physics).
Very cool.
The paper PDF: https://bpb-us-w2.wpmucdn.com/sites.brown.edu/dist/0/196/fil...
Relativity is also responsible for a lot of weird behaviors of heavy elements, such as the color of gold. Or that lead is a good material for batteries.
But what about superfluids (BEC Bose-Einstein Condensates)?
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
Can equivalent theoretical predictions be calculated in a Bohmian framework for the quantum aspects, or is this (potentially) an interesting case where there’s divergence and falsifiability?
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.
Very farsighted, after working as a patent clerk, to lay claim on such a foundational technology. Back in the day, they must've been like, oh, so Mercury blocks the sun at the wrong time, but where's the commercial value - and now every chemical company throughout the universe is about to get a bill every time they make something more complex than hydrogen gas.
Meanwhile, Galilean relativity has long gone out of patent, and people on board planes and other vehicles just move around like they were in a stationary reference frame paying no royalties.
They’re already taxed to fund pure research, it would be unfair to charge royalties for non-rivalrous products they can’t monetise.
I had a couple drinks so having one of those moments. I am always so fascinated by the science and experiments done to prove what we know. I consider myself at least of average intelligence probably slightly above but the things scientists research and solve always blows me away.
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.
In general, anything that is observed to be true at a smaller scale or context can't be extended to much larger scales. That involves assumptions on logic and mathematics to be homogenous across all scales. A pure theoretical extrapolation without bounds is quite common in mathematics, such as proof by induction etc.
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.
> 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.
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.
Attempts to formalize dialectics do exist, but it mostly stays at a word-weaving level.
Isn't superposition a contradiction for classical physics? Being partly here and there.
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.
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.
Those axioms do not have a basis other than observations at human scale.