Any suggestions for other truths which could turn out to be local?
I don't think "truth" is a good term here. How about, "widely applicable models" falsified outside of their usual domain?
Just about every approximation, ever. The further you are from math, the more of these there are, and you don't need to go far (all physics other than fundamental physics) to be loaded with them.
Simple harmonic oscillators? In 99% of cases, that's locally true around the minimum.
PV = nRT? Ideal gases are an approximation that is often strong, but right around condensation points or if there are long-ranged forces in the gas, it isn't.
So on, so on.
(all physics other than fundamental physics)
You don't even have to leave fundamental physics. Firstly the existing equations are (presumably) approximations to the underlying unified theory; secondly, we can't solve them exactly anyway, and even in the relatively tractable electroweak case we use the approximation of a truncated sum. As for the strong force, where that technique doesn't converge, don't even ask.
I'm quite frankly disappointed in this one. The idea that you could get unusual compounds at pressures high enough to distort the outer electron orbitals should be more than trivially obvious to anyone with even a smidgen of P-chem, and further should be modelable with computers these days. This is what happens when you need to get papers published to advance your career, instead of doing research that's actually important.
[edit] And classical chemistry? This guy is talking about 'classical' chemistry in a 3 million PSI environment? There is nothing at...
At the most trivial level, look at wikipedia's article on diamond, the phase change diagram in particular. Diamond starts to be thermodynamically preferred over graphite at around 100k atmospheres, and has been known about for a century.
For a 2012 paper, there's this. Note that the first thing in the paper is the unquestioned statement "High pressure can fundamentally alter the bonding patterns of light elements and their compounds, leading to the unexpected formation of materials with unusual chemical and physical properties."
Here's a 2006 paper from Germany that directly looks at how high pressures affect the chemistry of alkalai metals, including sodium.
And a 1998 reference book containing five hundred pages of high pressure chemistry notes, including a handful of sodium compounds.
Seriously, nothing new here. Vastly overblown and irresponsible hype.
Some random 'truth' grouped by discipline:
Math:
Mathematics is explained by reduction of propositions to axioms.
There are no interesting consistent and complete axiom systems (recently discussed here by probabilistic approches).
Physics:
Dark matter exists.
The universe started with the big bang.
There is a universal arrow of time.
There is no cold fusion.
Chemistry:
Meteorology:
Biology:
DNA defines cell behavior.
D
There are hints in cosmological observations that the speed of light may not be constant over sufficiently long timescales, and that the gravitational constant may vary over sufficiently long distances. (NB, both are speculative!)
Sir Karl Popper suggested reality is objective, our description of reality (conjectures) only provisionally true and subject to further inquiry (refutations). I can see that as truth being local in time, true for now. Most or all conjectures will be refuted over time, at minimum by being added to and clarified.
I think some of what we know about nutrition will endure (humans prosper when we drink clean water in some amount and with some regularity) but much of it seems in great flux. What constitutes nutrition in different nations today differs, whatever the objective truth might be. And nutrition within a single nation isn't for all (what an infant needs versus an adult, for example).
New Salt Compounds Challenge the Foundation of Chemistry
The title is overblown (it depends on what you think the foundation is), but get a load of this:
"I think this work is the beginning of a revolution in chemistry," Oganov says. "We found, at low pressures achievable in the lab, perfectly stable compounds that contradict the classical rules of chemistry. If you apply the rather modest pressure of 200,000 atmospheres -- for comparison purposes, the pressure at the center of the Earth is 3.6 million atmospheres -- everything we know from chemistry textbooks falls apart."
Standard chemistry textbooks say that sodium and chlorine have very different electronegativities, and thus must form an ionic compound with a well-defined composition. Sodium's charge is +1, chlorine's charge is -1; sodium will give away an electron, chlorine wants to take an electron. According to chemistry texts and common sense, the only possible combination of these atoms in a compound is 1:1 -- rock salt, or NaCl. "We found crazy compounds that violate textbook rules -- NaCl3, NaCl7, Na3Cl2, Na2Cl, and Na3Cl," says Weiwei Zhang, the lead author and visiting scholar at the Oganov lab and Stony Brook's Center for Materials by Design, directed by Oganov.
"These compounds are thermodynamically stable and, once made, remain indefinitely; nothing will make them fall apart. Classical chemistry forbids their very existence. Classical chemistry also says atoms try to fulfill the octet rule -- elements gain or lose electrons to attain an electron configuration of the nearest noble gas, with complete outer electron shells that make them very stable. Well, here that rule is not satisfied."
And here's the philosophical bit:
"For a long time, this idea was haunting me -- when a chemistry textbook says that a certain compound is impossible, what does it really mean, impossible? Because I can, on the computer, place atoms in certain positions and in certain proportions. Then I can compute the energy. 'Impossible' really means that the energy is going to be high. So how high is it going to be? And is there any way to bring that energy down, and make these compounds stable?"
To Oganov, impossible didn't mean something absolute. "The rules of chemistry are not like mathematical theorems, which cannot be broken," he says. "The rules of chemistry can be broken, because impossible only means 'softly' impossible! You just need to find conditions where these rules no longer hold."
The obvious example of local truth is relativistic effects being pretty much invisible over the durations and distances that are normal for people, but there's also that the surface of the earth is near enough to flat for many human purposes.
Any suggestions for other truths which could turn out to be local?