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by NancyLebovitz
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20

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?

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Local truth
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[-]Shmi190

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?

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5Gunnar_Zarncke
'Local' is a suitable qualifier to make this distinction I'd say. Local basically means 'falsified outside its domain'.
3Jack
I read the title and immediately thought "that's a phrase that's going to bother people". The fact that people here tend to prefer wordy literalisms to a catchy bit of clear poetic license is really illustrative of Less Wrong's cognitive profile. I'm sure it goes hand-in-hand with everything I like about the place, but it is a custom that irks me.
[-]Luke_A_Somers150

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.

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[-]RolfAndreassen100

(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.

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4Luke_A_Somers
I meant actual fundamental physics, not the standard model, which is already known to be a (very good) approximation. There are some statements we can make which at least have the possibility of being exactly correct - the general form of the Schrodinger equation, General Relativity, conservation of momentum... that sort of thing. As for truncated series etc, that fits exactly into the sort of approximation I was talking about.
[-]Dentin80

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... (read more)

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6kalium
Indeed! The notion of the octet rule being a "foundation of chemistry" when boron compounds typically have an incomplete octet and phosphorus and sulphur compounds (like SF_6) often exceed the octet... I guess you could call this "classical chemistry" in the sense of "classical physics"---a lie that covers most of the bases and gets corrected a couple years later for those who are interested enough to keep studying.
3NancyLebovitz
A lot of things seem obvious after they've been thought out and demonstrated. Do you have any earlier sources for the idea?
[-]Dentin110

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.

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0NancyLebovitz
Thanks. I'm wondering now if there are no (more? diamonds are good for something) useful compounds to made under high pressure, or if it's just a matter more time being needed for research.
2Dentin
There's plenty of neat new stuff to be discovered in high pressure regimes, and I'm sure there will be reseach on it for quite some time. I wasn't objecting to the paper itself, I object to the vastly overblown hype. The research itself is probably valid if relatively uninteresting, but it certainly does not live up to the claims given.
[-]Gunnar_Zarncke50

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:

  • All chemical substances arise in a dynamical equilibrium.

Meteorology:

  • The weather cannot be predicted more than a few days in advance.

Biology:

  • DNA defines cell behavior.

  • D

... (read more)
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6maia
Oh man! Disagreement! I like disagreement! I'm not sure what you mean by this, but based on what I'm guessing you mean, I don't think this is actually accepted as truth by physicists. In particular, physics is supposed to work the same in reverse. This is more of a moral claim than a psychological one; it's normative, not descriptive. I don't think most people believe this. I think the economists I know would say that it's closer to something like, "Markets tend towards efficiency in the absence of outside influences." Not sure what you mean by this, but it sounds probably wrong to me intuitively. Why do you think this is true - or if you don't, why do you think other people think it is true?
0Gunnar_Zarncke
How do you mean this? * You enjoy disagreements. In this case that I proposed opportunities for that. * You are happy to get an apportunity to disagree with what I wrote. * You see my comment as a disagreement with established truth.
0Gunnar_Zarncke
That is mostly so because physicists know about falsifiability and are mostly ready to revise a theory for one that makes better predictions (provided it's not their own). That's not what I meant. I thought more about something like Segals chronometric cosmology which "presents a continuation of the nonanthropocentric tradition, in that it distinguishes between the observed time x_0, which takes the same form as in special relativity, and global time t, which is sychnonous with x_0 in the short run ...". The development of the universe is usually pictured to have started with the big bang. But in Segals theory that is only because it looks that way due to the curvature. Every point in that universe model would see a different point (at 90°) as 'big bang'. Note that Segals theory was found to make wrong predictions, but that doesn't mean that other alike theories might be found which don't. That is exactly the 'non-locality of truth' meant by Nancy. The question is: What (kind of) influences. I have heard this often. Ad hoc I can give only a German link: http://www.uni-protokolle.de/Lexikon/Wachstum_%28%D6konomie%29.html
3ChristianKl
Formulation is probably to strong. Cell behavior gets influenced through hormones and other external influences. Retroviruses also have no DNA and there might very well by other organisms that only have RNA. Might well be false. Gödel found a while ago cases where standard Einstainian fomula violated that principle and I think there are still cases near black holes where that doesn't hold in string theory. The many world hypothesis also replaces arrow with tree. That's not a consensus belief. It very possible that life first existed on some other planet and a few microbes moved to earth after an asteroid impact and afterwards doublicated. It's only safe as long as they are no quantum computers or substantial advances in the underlying math.
2JoshuaZ
This depends pretty heavily on what you mean by interesting, since it requires something like being able to model Peano Arithmetic or at least Robinson arithmetic. But first order reals or first order C are "interesting" systems (in the sense that we study them and there are open problems that can be phrased in terms of them) and are consistent and complete.
0Gunnar_Zarncke
I wasn't aware of that. Can you give some link?
3JoshuaZ
See here.
0Gunnar_Zarncke
Thanks. I know quantifier elimination from CS and it makes for some useful practical algorithms but it seems not to be very powerful.
2NancyLebovitz
I'm hoping for more specificity about where a generalization might break down. That being said, I might include some mere noodling. No one that I've asked seems to know much about how mathematicians choose axioms-- there's got to be some process of choosing axioms which are likely to generate interesting mathematics. There are important parts of mathematics which don't get explored because they're too boring for mathematicians to want to work on. There may be truths about the universe which are complex beyond the human ability to manipulate ideas. It might even follow that there are truths which are too complex even for any conceivable augmented intelligence. Reductionism has taken people a long way and will take us farther, but it might have limits. I'm fond of the idea that life on earth might be on the receiving end of some alien meddling. This doesn't undercut evolution in general, but it adds some history to what seemed like a relatively simple story of physics and chemistry. Vegetables are not healthy for everyone-- some people have digestive tracts which can't handle them. Exercise isn't necessarily good for people. Optimizing nutrition and exercise for basically healthy people might not do that much good. Politics/economics: People don't have much sense, whether they're in business or government. Organized crime is a significant part of economies and governments, and ignored by most theories. Most of the economy isn't measured or considered-- I'm not just talking about organized crime, I'm including what people do for themselves and each other that doesn't involve money.
0Gunnar_Zarncke
I'm not sure whether this is meant as a proposal for a 'local truth' or some reply/explanation to something else. You mean most economic theories I take it. I'd guess that from an econimicsts point of view (organized) crime is not different from other economic transactions only that it involves a penalty of (temporarily) exclusion from trade or other costs that could be translated into monetary amounts. The question is how much this aspect has actually been taken into account. There is also Rational choice theory. Yes. I also have always wondered why there seem to be no statistical approaches to modelling social population development. E.g. by measuring and predicting the moments of Bourdieus types of capital of a sample of the population. Such an approach should allow to much better predict (and thus address) effects like social inequality, aging society, precariat development. It shoud be simple (much less particles involved that in climate models) and I really hope that it is not already employed to actually do steer society (to the unjust).
0NancyLebovitz
My point about organized crime is that its transactions are much less likely to be recorded, so they don't go into economists' calculations. Now that I think about it, the same applies to non-organized crime, but I assume it's a smaller part of the economy, but really, who knows?
0Lumifer
In that case what you care about is grey economy which is much bigger than organized crime. The grey economy is also more important since it actually produces goods while crime activities tend to just redistribute wealth.
3NancyLebovitz
I thought most of organized crime was selling illegal products and services-- drugs (not about redistribution of wealth), prostitution (I've heard mixed things about the % of slavery), lotteries (I wonder how they're doing now that there are legal lotteries), and smuggling.
0Nornagest
Racketeering's also a traditional pursuit of organized crime, and one that's more obviously coercive. In the modern era there's also electronic theft and fraud to deal with -- botnets, trade in stolen identity information, that sort of thing. I'd agree that drugs, prostitution, and gambling are at least equally prominent no matter what era we're looking at, though.
0Lumifer
Crime is rather different from other economic transactions primarily in that the transaction is not voluntary and is driven by the power differential. It also often enough involves a penalty of death which is difficult to translate into monetary amounts.
0Gunnar_Zarncke
Difficult maybe. But it is done youte often not only in economics: http://en.wikipedia.org/wiki/Value_of_life
0Lumifer
Statistically and externally, sure. But will you find it easy to translate the value of your life into monetary amounts?
0Gunnar_Zarncke
I'm not clear what you are driving at? The question was a statistical economic one, or? So my or other persons individual problems with this question do not matter for a valid incorporation of crime. And easy could be meant morally or effortwise. As a rationalist I obviously have no inhibitions on placing a monetary value on my life. Not placing a value on human life is a taboo intended to prevent dam breaking. It is not a truth. It won't break a dam for me. It takes some effort to arrive at a suitable amount though because there are so many aspects to take into account: * Economic value: Depending on your utility function there are multiple different cases: ** If you are seflish you will place a high value on your life - but only to ensure that you live, not to compensate others for your demise. Thus rather no life ensurance but instead safety measures against hazards of your choosing. ** You might also consider life or disability insurance if your loss will place your relatives in existential risks. Thus you consider your value to very high for your more or less large environment. ** You might avoid the social insurance if you think that you can invest yourself better. Thus you value yourself less for the society and/or your family (which might need/want to catch you if you fall). * Symbolic value: By placing a value on my life e.g. in the form of life-insurance I signal how much I value my life. If it is in the form of life or annuity insurance this may signal to my significant other that I cater for future safety in case of my demise. This is related to the financial value above but different in so far as the other person(s) may not completely grasp the derivation of the other aspects and just look at the symbolic value. * Societal value: Should I die that will be a loss for the society I live in. The investments the society made will not pay out as much as expected. This is measured by the SVL mentioned previously. As I care for the future well bein
1Lumifer
Not quite. The question already morphed into what makes crime different from "normal" economic transactions and whether you can represent it as a only slightly different economic transaction. So which amount of money would you be willing to exchange your life for?
0Gunnar_Zarncke
As suicide has a high symbolic value (see my list above; in this case signalling to a large number of persons including to myself and my children) and that is not the kind of exchange I have thought about before (where I considered external causes for (my) life) I cannot easily say so.
0Gunnar_Zarncke
Interesting. As a limit on ideas this implies truth (structures) which show no observable effect (otherwise the effect would allow to at least name the truth even if it cannot be understood fully). As a limit on understanding of truth (structures) this implies irreducibility not only in the horizontal dimension (the number of parallel items cognitively manageable - those can be offloaded to computer) but at least also in the vertical dimension (the number of reduction steps required). Examples of the latter might be structures which * change so little with each reduction step as to make the reduction undetectable in itself and build an unmanageable number of these on each other. Or * Contain reductions which feed back on lower reductions thus creating cycles. Something like humans which on a high reduction level (social) but feed back on effects observed under the microscope (an effect that probably (note: 'probably' is a catch-word) cancels out on the social level). My intuition on these structures is that they are indistinguisable from noise. If they were there they couldn't have an effect at all (except being there). Theological note: Some beliefs in god imply exactly such irreducible undetectable truth.
0Gunnar_Zarncke
My comment was more about horizontal exploration (before it most comments were physics-related) than about elaborating any details. That is one aspect of my first item "Mathematics is explained by reduction of propositions to axioms". The axioms as "premise so evident as to be accepted as true without controversy" (Wikipedia) still possess or require some structure - albeit a non-mathematical implied and/or often 'soft' one. I once had a discussion with a mathematician about this and also a longer web dialog about how vague notions crystalize into concrete structures but couldn't convice anyone that this is a real problem instead of a wishy washy relativization of the truth of math. I will address your other items with separate comments.
[-]JQuinton40

Doesn't water freeze at different temperatures depending on the local pressure?

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9NancyLebovitz
Yes., though I don't think it's enough to affect ordinary experience. On the other hand, the boiling point changes enough with differences of air pressure to affect cooking. Another example: I talked with someone who just couldn't get basil (which I think of as a very easy plant) to grow. She was living in Wales at the time, and there wasn't enough sunlight.
5TrE
That effect is well-known in chemistry, phase diagrams are a common tool to describe this. Linked is a phase diagram of water - the phases "Liquid" and "Ih" are commonly known as liquid water and normal ice, but at high pressures other phases exist. Note that this diagram is by no means complete - further to the right there's water vapor, then at higher pressures supercritical water, then gradually water is not favoured anymore and Hydrogen/Oxygen are stable, and even further out there's a smooth transition to plasma - nonrelativistic and classical at "low" temperatures and pressures, relativistic at high temperatures, governed by the rules of quantum mechanics for high pressures. What do we learn from this? Our models of reality can always be valid only for certain assumptions and in certain ranges for the variables we consider. It doesn't surprise me at all that there's novel chemistry at high pressures as the electrons get squished closer together. Similarly, at very low pressures, unionized matter is in the minority, so that the chemistry is different yet again. The only question is where this transition occurs. Likewise, I'd guess that the psychology of animals or aliens might be radically different from ours, as will be the biology of these aliens, depending on the conditions of their homeworld.
[-]RolfAndreassen00

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!)

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1A1987dM
What would it even mean for the speed of light to not be constant, other than we're using the wrong system of coordinates?
3CronoDAS
It could mean that the dimensionless constant "alpha", also known as the "fine structure constant", varies, and the simplest way to express that change mathematically is as a change in C rather than in one of the other parameters (such as the charge of the electron). (I read a book about this.)
-1Shmi
Well, speed of light is not a fundamental constant, so they probably mean the fine structure constant or some other dimensionless quantity.
0RolfAndreassen
Taboo 'fundamental'; what distinction are you trying to get at? Change the speed of light holding other parameters constant, and the fine structure constant changes; and vice-versa. Whether you want to consider this a "change in the speed of light" or a "change in alpha" seems to me pretty strictly a matter of taste; and the speed of light (especially its constancy) is much more familiar to most people than is alpha. (Which anyway may not be so constant at high energies, in spite of having 'constant' in the name.)
4Shmi
We are pretty far off the original question, but, yeah, there is a distinction. The fine structure constant is indeed more fundamental than the speed of light. How do you change the speed of light and not much else? You have to change at least the fine structure constant (in the IR limit, as you point out) and probably the gravitational coupling strength, and possibly some other free parameters in the standard model, like masses of the electron and quarks (again, in some dimensionless units). Otherwise something will go wrong with the Universe, the common example being carbon not being synthesized by stars. But I agree, these "side effects" of changing the speed of light may not have been important long time ago, or maybe in the galaxy far far away.
2RolfAndreassen
But this is just as true if you change alpha! At a minimum, to restore the carbon synthesis rate, you'd have to mess with the proton charge.
0A1987dM
The numerical value of a dimensionful constant depends on the system of units you're measuring it in; that of a dimensionless constant doesn't.
0RolfAndreassen
Well yes, but who cares about the numerical value? Hold the system of units constant and look at the actual physics!
2A1987dM
How would you do that? (The metre is now defined in terms of the second and the speed of light.)
-1RolfAndreassen
I would define the unit of distance in terms of the size of the King's lower extremities, as God intended. :rolleyes:
0A1987dM
How would you distinguish an universe where the, ahem, King's lower extremities grow and everything else stays the same from one where the King's lower extremities stay the same and everything else shrinks? (This is essentially the same point as that of this post but for scaling rather than rototranslations.) (Well, the last time I had this discussion IIRC I initially had John Baez on my side then the person I was arguing against managed to convert him via private e-mail, but I couldn't understand what he said she said to him.)
0RolfAndreassen
Why would I want to? My point being, you are not under any obligation to define the meter in terms of the speed of light when you are discussing a possible change in the speed of light. You are attempting an argument by definition, and rather a silly one. Define the meter in a way that's convenient to what you're trying to do, and have done.
0A1987dM
Like what?
2RolfAndreassen
Like using the King's foot, or the curvature of the Earth, or a platinum bar, or indeed anything that isn't defined in terms of the thing whose changes you are trying to talk about.
2A1987dM
The fact is that platinum atoms are bound together by the electromagnetic force, so if c = 1/sqrt(mu_0 epsilon_0) changes their distance changes too. (Who the hell is downvoting the entire thread, anyway?)
2RolfAndreassen
Equally a problem with the fine structure constant, since it directly measures the strength of the electromagnetic force. However, while the length of a platinum bar would, as you say, change under a change in the speed of light, it would not change linearly; so you can measure ratios of lengths and presumably pinpoint the constant that changed. The curvature of the Earth, for example, presumably depends on the strength of gravity in addition to the electromagnetic repulsion of its constituent particles, so it should change more slowly than the platinum bar's length.
4A1987dM
But the fine structure constant is dimensionless, so you don't need to find a standard to measure it which doesn't change when it changes.
2RolfAndreassen
Ah, now I see what you're saying. Good point.
0Decius
One of the points is that different frames of reference have different ratios of the length of artifacts, when those artifacts are moving relative to each other.
0A1987dM
Usually when defining lengths in terms of an artefact you use the rest frame of the artefact (i.e. the one in which the artefact is longest).
0Decius
Doesn't the time required to traverse the rest length of an artifact vary between observers? Edit: Also, how does knowing the length some other observer sees useful at all?
0RolfAndreassen
So what? Stick to one frame of reference; thought it doesn't matter which one you use, that doesn't mean you're not allowed to use one. Every observer will see the same change in the speed of light using their own measure of distance; or at any rate can agree on the change by mathing out the frame-of-reference effects.
0Decius
So, measuring distance in 'the average length of these two sticks' and time in 'how long it takes half of a stationary sample of this radioactive element to decay', various observers get radically different values for the speed of light. That's without any changes to the current world, if the sticks are moving.
0RolfAndreassen
Then I suggest that your observers not go out of their way to be stupid. Put everything in the same frame of reference first. Just because you can play nitwit games with picking silly units of measurement doesn't mean you have to. To do particle physics, for example, you often have to calculate away the frame-of-reference effects; so what? Just put everything in a convenient frame and then be consistent about it. You seem to be assuming some kind of idiot-savant observer who is informed enough to deliberately pick a unit that's vulnerable to frame-of-reference effects, but not bright enough to calculate what the effect is.
0Decius
The speed of light is postulated to be the same in both frames of reference; If they 'correct' length to some arbitrary frame of reference, then the amount of time that elapses will be irreconcilable between them- more seconds will elapse for some observers during the average period in which 1/4 to 1/2 of a total mass of an isotope has decayed.
0RolfAndreassen
Now you're making the same mistake with the time. Transform your clock into the same frame of reference you're using for length. Duh. Really now, this is not difficult; why are you going out of your way to assume observers who can't manage to make all their observations in a consistent frame of reference?
0Decius
Are you assuming (or concluding) that distance and relative motion add the way they do in Newtonian physics? That is observed to not be the case, on the scales and precisions of the GPS system. In other words, the vector difference between the velocity of object B and C varies depending on the observer, and adding the same constant vector to the velocity of B and C changes the difference between their vectors.
0RolfAndreassen
No, I'm saying that you can do or transform all your observations to one frame of reference, and all observers will agree on the results within that frame of reference, no matter what they're transferring from.
-2Decius
Your assertion is not consistent with current observational evidence. Observers in different frames of reference will not agree on what percentage of a sample of an unstable isotope will decay in the time it takes light to travel the length of an artifact.
-2RolfAndreassen
Not until they have transformed their observations to a common frame, no. Please re-read what I said. Then let's see some math. Make an observation of length in one frame of reference, transform it to another, and show that it still disagrees with what observers in that frame of reference measure. Alternatively, make two observations in different frames, transform them to a third, and show that they disagree.
-2Decius
Observer C notices that at time 2, object C is stationary, object L is moving left at 9 Million Kilometers/minute, is 18 Million Kilometers long, and that stick L is 18 Million Kilometers long. C also notices that object R is moving right at 9 Million Kilometers/minute, is 18 Million Kilometers long, and that stick L is 18 Million Kilometers long. C notes a distance of 36 MKm between L and R when they pass the ends of their co-named sticks. Observers L and R observe that sticks L and R are moving right at 9 Million Kilometers/minute, and that their observed length is 13.5 MKm. They observe that they are 27 MKm apart when they pass the end of their sticks. Lights at the extreme ends of sticks L and R flashed simultaneously (at the same place and time) with lights located on objects L and R. 45 seconds later, the light from objects L and R has traveled the 13.5 MKm to C; 15 seconds after that, the light from the ends of the sticks arrives (having traveled 18 MKm). The speed of L to R (and distance between them) is left as an exercise to the reader.
0RolfAndreassen
You don't appear to understand what I mean by "transform". What does L say the speed (or length, or time) is in the reference frame of C?
0Decius
10.1 MKm (13.5MKm *(1-(1/2)^2) for the distance between L and C, but 18MKm for the length of the stick which extends between them. in the reference frame of C. (Distance only diminishes in transformation, while length increases when transformed towards a frame of reference closer to that of the object in question)
-2RolfAndreassen
Observer L is in the rest frame of object L; consequently he measures its proper length. Observer C is not in the rest frame of object L, and therefore measures a shorter length. Your claim that L measures a shorter length than C indicates that you're using something other than special relativity, that you're using special relativity wrong, or that I didn't understand your description. Please clarify which it is. A diagram may be helpful. Additionally, this: is plain wrong, since you can always do the transformation in the other direction! It doesn't diminish both ways! And this claim: appears to be meaningless; there's no such thing as a frame of reference "closer to an object". A frame of reference doesn't have a location, it has a speed relative to an observer.
-2Decius
Sticks L and R are stationary in the frame of C; objects L and R just happen to be close to the other ends of the sticks at some time, and are stationary in their own reference frames.
-2RolfAndreassen
At this point I have no idea what is supposed to be happening in your scenario. You've got sticks, objects, and observers, and it's not clear whether any of them are the same or what frames they are in. Please draw a diagram.
[-][anonymous]-40

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).

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