Einstein's relativity rules chemical bonds in heavy elements, new research shows

https://www.brown.edu/news/2026-07-09/chemical-bonds-relativity

by hhs • 12 days ago

414 196 12 days ago

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

kristianp• 12 days ago

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

aaaronic2• 12 days ago

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.

nomel• 12 days ago

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?

loeg• 12 days ago

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.)

bilsbie• 11 days ago

Could electrons orbit a neutron star if we gave it a positive charge?

terminalbraid3• 11 days ago

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.

abcarey• 11 days ago

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.

Svoka• 12 days ago

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...

cyberax• 12 days ago

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.

nanolith• 12 days ago

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

Diogenesian• 12 days ago

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."

fsloth• 12 days ago

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.

ThrowawayTestr• 12 days ago

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

762236• 12 days ago

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.

brabel• 12 days ago

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??

ferfumarma• 12 days ago

Yes: the article says "since the 70s"

deadbabe• 12 days ago

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

wbl• 12 days ago

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

colechristensen3• 12 days ago

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

colechristensen3• 11 days ago

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.

alok-g4• 11 days ago

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.

wasabi991011• 12 days ago

The article seems to be more specific, about relativistic effects in triple bonds

kergonath• 12 days ago

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".

alkyon• 12 days ago

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.

turtlesdown11• 10 days ago

subheader explains the article in case you were wondering

Researchers have shown the first direct experimental evidence that the textbook triple bond structure breaks down in heavy elements, where relativity makes the rules.

14• 12 days ago

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.

waldrews• 12 days ago

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.

eucryphia• 12 days ago

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

zkmon3• 12 days ago

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.

red75prime3• 12 days ago

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.

zkmon3• 12 days ago

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.

worldthruword• 12 days ago

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

vatsachak2• 12 days ago

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.

zkmon3• 12 days ago

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

michaelsbradley• 12 days ago

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?

fsh• 12 days ago

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.

de6u99er• 12 days ago

It's beautiful to see Einstein's work still being validated.

blaqq2• 12 days ago

His name will still go way down in history, that is assured

ProllyInfamous• 11 days ago

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}.

RetroTechie2• 11 days ago

"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.

tastyfreeze• 11 days ago

Bismuth can also be used as a collector metal for smelting precious metals instead of lead. It even cupells the same way as lead.

gcanyon2• 11 days ago

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)

sigmoid103• 11 days ago

I guess the more interesting question is why this doesn't happen for neighbouring elements in the periodic table?

Laforet• 11 days ago

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

beacon294• 11 days ago

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.

gus_massa4• 11 days ago

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.

LorenPechtel• 11 days ago

You can start your car.

Without relativistic effects a lead acid battery would put out about .2V rather than 2V.

amelius2• 11 days ago

Meanwhile there are quarks inside every regular atom moving at speeds like 0.99995c ...

gcanyon2• 11 days ago

Interesting -- does that have any macroscopic/real world impact?

Jblx22• 11 days ago

If the spatial extent of the proton is not infinite, this would imply that the charged quarks making up the proton are accelerating. Why aren't these quarks then emitting electromagnetic radiation, thus slowing down? I thought electrons were essentially standing waves around the nucleus, and thus not accelerating. Maybe there is a good youtube video explainer? Seems like there would also be an associated temperature and blackbody radiation of these quarks.

gigatexal• 11 days ago

This is the coolest fact I’ve learned in a long time. Thank you!

sehugg• 11 days ago

And relativity describes the orbit of the quick-moving planet Mercury which shares its name with the quick-flowing element. What a world.

westurner4• 11 days ago

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

westurner4• 11 days ago

Today I ran into this problem again.

What is the difference between sound and radio?

A traditional explanation with Relativity says: Sound is compression waves through a medium, and radio is electromagnetic waves through no medium, and light is photon waves through no medium but gravity due to mass attraction changes the paths of the massless photon particles transiting through spacetime in a vacuum at c the max speed of light and photonic causation.

(But is there spooky action at a distance faster than c that's more than chance correlation?)

Superfluid Quantum Gravity (SQG) and Superfluid Vacuum Theory (SVT) say that the vacuum of space is not nothing; at Bose-Einstein Condensate (BEC) phases of matter, there is a new description of the particles in space. And there should be, because really what is between atoms and electrons in the nothingness of the vacuum of space at what altitude and temperature?

And so to describe the path of massive photons and standard massless photons through the superfluid of space, additional or alternate or sufficient superset mechanics to describe dilatant fluid model of spacetime at macro and micro and particle scales.

Is it Proca fields for massive photons with Airy-beam-like curvature?

/?hnlog Ctrl-F dilatant; dilatant quantum fluid model of gravity :

- > How to test whether MHD or SQR [or SQG or SVT] best explain the given phenomena?

- "Persistent shock wave around dead star puzzles astronomers" https://news.ycombinator.com/item?id=46679704

- "A universal speed limit for spreading of coherence" https://news.ycombinator.com/item?id=45928486 :

"Physical vacuum as a dilatant fluid yields exact solutions to Pioneer anomaly and Mercury’s perihelion precession" (2019) https://cdnsciencepub.com/doi/10.1139/cjp-2018-0744 .. https://news.ycombinator.com/item?id=45220585

westurner4• 11 days ago

Is the dilatant quantum superfluid of spacetime itself also fracturable?

Like Oobleck? (2 parts cornstarch to 1 part water)

IAmBroom3• 9 days ago

and radio is electromagnetic waves through no medium, and light is photon waves through no medium but gravity due to mass attraction changes the paths of the massless photon particles transiting through spacetime in a vacuum at c the max speed of light and photonic causation.

Radio waves are light waves.

seanhunter• 11 days ago

My most recent fun fact about chemistry is that the shape of the periodic table is as a result of the symmetry group of a sphere. This was part of this great talk https://www.youtube.com/live/btlQl93qOhc?is=7v7GQ92ozW_kpQtk

Einstein's relativity rules chemical bonds in heavy elements, new research shows

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