Einstein's relativity rules chemical bonds in heavy elements, new research shows
Comments
gcanyon
sigmoid10
I guess the more interesting question is why this doesn't happen for neighbouring elements in the periodic table?
Laforet
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
gweinberg
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.
nyrikki
Explaining relativistic effects in plain text forums to a general audience is a big ask, but here is a link to the first study[0] that gave evidence but it has long expected.
[0] https://onlinelibrary.wiley.com/doi/epdf/10.1002/anie.201302...
gus_massa
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
You can start your car.
Without relativistic effects a lead acid battery would put out about .2V rather than 2V.
lr1970
Thanks for the link to the paper published in 2010 (16 years) ago. The OP article from Brown reads as if they were the first to establish importance of Special Relativity for heavy atoms which is not true.
beacon294
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.
sehugg
And relativity describes the orbit of the quick-moving planet Mercury which shares its name with the quick-flowing element. What a world.
amelius
Meanwhile there are quarks inside every regular atom moving at speeds like 0.99995c ...
Jblx2
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.
CamperBob2
Quarks don't have quantum energy states to transition between, hence they aren't subject to radiating photons due to acceleration.
Similar to why the electron in a hydrogen atom doesn't keep emitting radiation and crash into the nucleus once it reaches its ground state... there's no lower state for it to jump to.
IAmBroom
"The laws that bind an ox do not bind Jupiter" applies to quantum particles.
dustingetz
because conservation of energy dominates
gcanyon
Interesting -- does that have any macroscopic/real world impact?
moelf
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
gigatexal
This is the coolest fact I’ve learned in a long time. Thank you!
kristianp
> 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.
aaaronic
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
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?
ajkjk
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.
scheme271
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.
SlightlyLeftPad
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.
abecedarius
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.
adastra22
“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.
jona-f
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.
asdff
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.
aaaronic
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).
nsz65
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.
ahartmetz
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
K0balt
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.
pmarreck
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!!
timcobb
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.
WillAdams
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.
ahahs
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.
lacunary
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.
dboreham
The waving, and the resulting need to memorize a zillion special cases, put me off Chemistry for life.
rramadass
> 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
marcosdumay
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.
nickcw
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.
aduty
No.
whatever1
We have answers. It’s called physical chemistry. The problem is that it takes a shit ton of math
loeg
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.)
compass_copium
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.
timcobb
They are not covered in AP chemistry this is just your typical "when I studied differential geometry in high school" HN comment
abcarey
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.
bilsbie
Could electrons orbit a neutron star if we gave it a positive charge?
terminalbraid
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.
nanolith
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.
Diogenesian
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
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.
colechristensen
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.
colechristensen
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-g
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.
colechristensen
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
ThrowawayTestr
There's even a Wikipedia page for it https://en.wikipedia.org/wiki/Relativistic_quantum_chemistry
kergonath
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
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.
762236
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
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??
gus_massa
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.]
abecedarius
"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.)
Sharlin
The uncertainty principle says that the less well-defined the position, the more well-defined the velocity, and vice versa.
wasabi991011
The article seems to be more specific, about relativistic effects in triple bonds
turtlesdown11
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.
ferfumarma
Yes: the article says "since the 70s"
deadbabe
I don’t get it, someone explain? Doesn’t everything get color from relativistic effects?
wbl
Most colors in synthetic pigments are from conjugated double bonds that don't need relativistic effects to explain: no heavy atoms here!
Svoka
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
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.
de6u99er
It's beautiful to see Einstein's work still being validated.
ProllyInfamous
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}.
blaqq2
His name will still go way down in history, that is assured
michaelsbradley
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
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.
seanhunter
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
westurner
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
westurner
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
westurner
Is the dilatant quantum superfluid of spacetime itself also fracturable?
Like Oobleck? (2 parts cornstarch to 1 part water)
Joska929
[flagged]
IAmBroom
> 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.
RetroTechie
"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
Bismuth can also be used as a collector metal for smelting precious metals instead of lead. It even cupells the same way as lead.
14
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
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
They’re already taxed to fund pure research, it would be unfair to charge royalties for non-rivalrous products they can’t monetise.
devmaster2
[flagged]
zkmon
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.
red75prime
> 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.
zkmon
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.
red75prime
Attempts to formalize dialectics do exist, but it mostly stays at a word-weaving level.
worldthruword
Isn't superposition a contradiction for classical physics? Being partly here and there.
red75prime
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.
vatsachak
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.
zkmon
Those axioms do not have a basis other than observations at human scale.
vatsachak
They have a basis in the formal scale. The cool thing about formal logic is that it's all about physical changes.
Now, the meaning of the statements is definitely human, but the proofs go beyond
> 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)