The Color of Infinite Temperature
johncarlosbaez.wordpress.com
johncarlosbaez.wordpress.com
https://en.wikipedia.org/wiki/Planckian_locus
That's the image of the temperature range (0,∞), mapped to the corresponding blackbody color in chromaticity space. The limit T -> ∞ is a point discontinuity near the center of CIE space.
Wikipedia's coverage of this topic has regrettably been unstable over the years. Broken chromaticity diagrams are so common, each time the graphic is swapped, it's a toss up whether it's a correct one. And then edits reflect that, and common misconceptions. Perhaps if WP had not just Article and conversational Talk pages, but also something like a writer's notebook, it might serve as memory, as immune system, as a place to caution "make sure when editing that you don't ...". Perhaps it will stabilize some day - the Sun[4] page seems to have at long last settled on a white-not-yellow Sun. Yay. That's more than several of the most used intro astronomy college textbooks have managed. Science education content is... something we struggle to do well.
[1] https://en.wikipedia.org/wiki/File:PlanckianLocus.png https://commons.wikimedia.org/wiki/File:PlanckianLocus.png (13:38, 3 January 2012) [2] Obvious errors: the blackbody curve shown doesn't go through white, and does go through yellow. Incorrect white-point math is a recurring cause. [3] "It goes from deep red at low temperatures through orange, yellowish white, white, and finally bluish white at very high temperatures." (emphasis added) [4] https://en.wikipedia.org/wiki/Sun
https://www.livescience.com/17948-red-green-blue-yellow-stun...
1) Constant vigilance, to monitor the article and revert drive-by edits putting up random nonsense.
2) Solid political backup from other long-time wikipedia editors, to fight off constant AFDs and DRN attempts to destroy whatever you've done.
If at any point you slack off, the article will be gutted and replaced with garbage. This resembles any other human endeavor, in that you're valiantly resisting entropy while everyone in the world calls you a moron for even bothering.
As a disclaimer, I suppose I don't see any way this could be technically "fixed", short of replacing humanity with something else.
Most of those edits are minor. Most vandalism has already been reverted before I see it. A substantial wrong edit needs my attention maybe once a week.
When you speak of "valiantly resisting entropy", it sounds like a battle against the forces of Mordor. For me it's more like weeding the garden; a fairly pleasant activity, that's easiest if you do a little every day. You're still working against entropy, of course, but as you note that is like every other human endeavour.
There are articles I care about that I don't edit. These are mostly articles that some person or group reckons they "own". I don't edit anything to do with the Middle East, for example, nor any article about nationalist politics. Life's too short. I agreee there's no technical fix for that problem. There doesn't seem to be a social fix either; such articles are presumably just going to remain unreliable. Perhaps Wikipedia just isn't suitable as a repository for certain kinds of information.
Incidentally, articles on food seem to get nationalists going. The article on Biryani, for example is the subject of constant drive-bys, constantly flipping back and forth between India, Persia and Pakistan.
what does this mean?
I think the edit history is quite harmless on this article at least.
Strangely, I'm struggling to write this comment in a way that doesn't sound trolling...sorry, I don't mean trolling at all. If you could see my facial expression it would be easier...
A good set of people to practice this on is doctors, teachers and Twitter users you admire.
I work on displays within an OS team. Having some basic understanding of colour theory is critical for a significant number of modern display projects, particularly for the high end. For example, enabling colour accurate rendering (games, photos, etc), shipping wide-gamut displays (how do you render existing content on a WCG display?), etc. More specifically to the planckian locus, it generally comes up when deciding which white point to calibrate a given display to at the factory (e.g. iPhone is 6470K, S20 is 7020K in Vivid)[1][2] and if you're doing any sort of chromatic white point adaptation, like Apple's True Tone[1][2].
My background before joining the team was a degree in math, but I really enjoyed doing low level projects in my spare time, so ended up on an OS team. We also have colour scientists who study this full time and have a _significantly_ better understanding of it all than I do :)
[1]: https://www.displaymate.com/iPhone_13Pro_ShootOut_1M.htm#Whi... [2]: https://www.displaymate.com/Galaxy_S20_ShootOut_1U.htm#White... [3]: https://support.apple.com/en-gb/HT208909 [4]: http://yuhaozhu.com/blog/chromatic-adaptation.html
https://colab.research.google.com/drive/1Oyn913zkXYB8Uf8k1hi...
Have you checked if the values change if you increase the temperature even further? Looks like their color is bluer than yours at least..
Yes, and as discussed on Twitter, sRGB is defined for the CIE 1931 2 Degree Standard Observer, not other observers. It is not defined spectrally but as a set of chromaticity coordinates (in the CIE 1931 Chromaticity Diagram). Thus, strictly speaking, sRGB values can only be computed for the CIE 1931 2 Degree Standard Observer. I tried four different observers, using strict integration:
- CIE 1931 2 Degree Standard Observer: [ 153.9026317 , 180.75617631, 255. ]
- CIE 1964 10 Degree Standard Observer: [ 150.32288938, 184.67113624, 255. ]
- CIE 2012 2 Degree Standard Observer: [ 145.14899585, 180.69807338, 255. ]
- CIE 2012 10 Degree Standard Observer: [ 148.44893332, 185.66849549, 255. ]
- Article: (148,177,255)Perhaps think of it as two steps? One of physics and biology, using minimally-flawed spectra, CMFs, and math, to get a plausible chromaticity. And a separate step of communication, using standards of sRGB and image ICC tags (rendering intent), to get browsers to convey that chromaticity to the user as a minimally-misleading (for the use case) color.
Thus the 10 vs 2 deg CMF choice might depend on the physical angular size of the emitting area. And before browsers supported rendering intent, for use cases where users were eyeball comparing the color with screen white, one might calculate using a very non-standard D58 white-point, as the blue-ish D65 would make white chromaticity render as a pink color, with users misled to think the chromaticity was pink.
That's a little hard to imagine, because a rainbow contains a full spectrum of colours, whereas an emerald usually has a single colour, so some translations interpret the rainbow as being like the shine/gleam/glow of an emerald. But the idea that at infinite energy a spectrum might be perceived to human eyes as a single bluish hue is a nice thought, like the coincidence(?) that this colour happens to look like a clear summer's sky.
Anyway, for comparison, here's an image from Wikipedia of a synthetic emerald:
For example if I was John and I saw the color of infinite temperature around God's throne, I would probably say something more like:
> and there emanated from the throne an incredibly bright blue halo, as if a clear summer sky was shooting forth from God's throne.
https://en.wikipedia.org/wiki/Blue%E2%80%93green_distinction...
And regardless, my point was more that "emerald" is clearly a worse analogue than "sky" for this particular color.
https://www.bbc.com/future/article/20180419-the-words-that-c...
A western civilisation member might do something like Red, Brown, Orange, Yellow, Green, Blue, Pink, Violet, Grey and perhaps do something special with White/Black. (11 basic colours)
A Russian will most likely split blue into light blue and dark blue. (12 basic colours)
Himba people have 5 basic colours:
Serandu – used to describe reds, browns, oranges and some yellows
Dambu – includes a variety of greens, reds, beige and yellows
Zuzu – used to described most dark colours, black, dark red, dark purple, dark blue, etc.
Vapa – used for some yellows and white
Buru – used to describe a collection of greens and blues
σμαραγδίνῳ smaragdinō - https://biblehub.com/greek/4664.htm smaragdinos: made of emerald, emerald-green from σμάραγδος smaragdos: an emerald.
[1] https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext...
[2] https://www.perseus.tufts.edu/hopper/morph?l=i%29%3Dris&la=g...
(History of God is an interesting book, even/especially for atheists)
- neutronium
- catastrophic violet
- Rayleigh-Blue-Jeans
I get super irritated by kids books that teach seven colors. We have an impoverished color vocabulary, as a result. Can't even describe the color of infinite temperature, sheesh.
E.g. look at a periwinkle flower and look at the periwinkle in the list. They call periwinkle "Aero" but what is that?!
https://images.app.goo.gl/8Qs5FARoBhEwYG2N8
I think color names should only be included if they match objects, have historical precedent or are composed of these plus basic descriptors. Or approved by the trans galactic color authority.
https://www.atozflowers.com/wp-content/uploads/2017/12/Vinca...
Aero originates from the Royal Air Force, don't presume the name doesn't match historical precedent when you don't know of one. Of course there are tons of competing names for various colours (and also many competing views on what set of colour coordinates belongs under a particular named colour) across cultures.
The list above cannot hope to be objective or complete.
Not sure if this is a gold dress blue dress situation.
What a delightfully, understatedly terrifying phrase.
Unexpectedly salty coming from a pure mathematician! But maybe it's just professional jealousy of a field that comes up with new terms regularly? ;)
Is the low-pressure low-speed definition of temperature a special case of the relativistic definition, or a completely different concept?
What is the precise definition of temperature?
How do these definitions relate to our everyday understanding of temperature, i.e. feeling hot/cold?
Or which textbook should I read to find out?
Sorry for asking so much...
There are many mathematically equivalent versions of the "complete" definition. My favorite is the zeroth law of thermodynamics: If body A and B have the same temperature (meaning there is no heat flow between them when they touch) and body B and C have the same temperature, then body A and C also have the same temperature. Basically, you define the words "thermal equilibrium" to mean "there is no heat flow when they touch" and you also define temperature to be the quantity that is equal in that case. This together with the "conservation of energy" and "growth of entropy" (basically the axioms of thermodynamics) is sufficient to derive most properties of temperature you know.
If you have already defined entropy in some other way, you can say "the temperature of an object tells you how much the entropy of the object rises for a unit rise in the internal heat energy of the object":
ΔEntropy = ΔEnergy / Temperature
If you have not yet defined entropy, but have defined temperature (which I personally see as easier to understand), then the above equation can be your definition of entropy.
Notice that "definition" just needs to be mathematically sound (i.e., self consistent). But for a physicist to want to use such definitions, they *also* need to be practical. Any of the (equivalent) definitions above are a fair choice, as they happen to be the self-consistent principles which do lead to behavior like the one we experimentally observe.
I do imagine that a rigorous mathematician might have a reason to prefer one of the aforementioned definitions more than the other. I do not have such concerns.
Lastly, concerning the gases: If you happen to know that gases are made out of moving atoms then you can do a bit more. Mind you, you can build most of thermodynamics without that knowledge. But if you know that fact, then you can derive that temperature is related to some measure of average energy per atom. If the atoms are relativistic, then energy per atom will need to be written in the relativistic form (which does not grow to infinity as velocity approaches the speed of light). At lower speeds, the formula for the energy becomes numerically indistinguishable from the one from classical mechanics.
See https://en.wikipedia.org/wiki/Zeroth_law_of_thermodynamics#F...
Then I would suggest reading:
- https://en.wikipedia.org/wiki/Zeroth_law_of_thermodynamics in its entirety
But on its description, there are probably plenty of movement (depends on what your particles are).
My gripe with this is that if our understanding of quantum mechanics and general relativity is correct there is a limit of temperature. When a photon has a wavelength equal or smaller than the Planck length said photon contains enough energy to create a black hole. So, the upper limit of temperature should be the point at which the generation of black holes dominates the spectrum.
I mean, replacing v_rms by c in equation 3 in https://chem.libretexts.org/Bookshelves/Physical_and_Theoret... gives us an upper limit for the temperature of a gas, right?
[0] https://news.ycombinator.com/item?id=29963147
[1] https://en.wikipedia.org/wiki/Planck_units#Planck_temperatur...
- Specific RGB values always depend on a selected white balance temperature. If the WB temp is the same as the object's temp it would be white, not blue. If the WB temp were higher than the object's temp it would appear red.
EDIT: the article does say sRGB which implies a 6500K wb.
- "infinitely hot" is not physically possible. The Neutron star example is fine, that temp would be around 10^12 K
At that temperature virtually all of the emission would be in gamma rays, but emission in the visible spectrum would not be zero. Blue wavelengths would be stronger than green, which would be stronger than red so the color would appear Blue for any "normal" white balance temp (like 5500 K).
Infinity is a well understood mathematical construct. I don't know what is the issue with evaluating limit value of some function, in this case color, "at infinity"? Nowhere it says it's physically possible.
I was writing a black hole simulator, and needed to figure out the color shift of the stars as one approaches the black hole. The calculation gave me this blue at the one end of the spectrum which was very underwhelming tbh. For some reason I always though this color would be either 0xffffff, or some deep blue. Glad that my calculation is finally confirmed to be right!
This is in the context of trying to produce the closest sRGB colors to a set of LEDs, for use in documentation. No published method could actually do it. I did have to assume the LED was a single-wavelength source, gaussian with specified FWHM, or Lorentzian, rather than measuring the spectrum (I was too lazy to mess with the spectrophotometer), but I don't think that would have made the difference for an LED.
https://johncarlosbaez.wordpress.com/2012/01/19/classical-me...
https://johncarlosbaez.wordpress.com/2012/01/23/classical-me...
https://johncarlosbaez.wordpress.com/2021/09/23/classical-me...
https://johncarlosbaez.wordpress.com/2021/09/26/classical-me...
An excerpt from the first article:
> The big picture
> Now let’s step back and think about what’s going on.
> Lately I’ve been trying to unify a bunch of ‘extremal principles’, including:
> 1) the principle of least action
> 2) the principle of least energy
> 3) the principle of maximum entropy
> 4) the principle of maximum simplicity, or Occam’s razor
> In my post on quantropy I explained how the first three principles fit into a single framework if we treat Planck’s constant as an imaginary temperature. The guiding principle of this framework is
> maximize entropy
> subject to the constraints imposed by what you believe
> And that’s nice, because E. T. Jaynes has made a powerful case for this principle.
> However, when the temperature is imaginary, entropy is so different that it may deserves a new name: say, ‘quantropy’. In particular, it’s complex-valued, so instead of maximizing it we have to look for stationary points: places where its first derivative is zero. But this isn’t so bad. Indeed, a lot of minimum and maximum principles are really ‘stationary principles’ if you examine them carefully.
> What about the fourth principle: Occam’s razor? We can formalize this using algorithmic probability theory. Occam’s razor then becomes yet another special case of
> maximize entropy
> subject the constraints imposed by what you believe
> once we realize that algorithmic entropy is a special case of ordinary entropy.
Infinity is very much in extrapolation territory.
But then the Rayleigh-Jeans Law has been shown to be incorrect, see Ultraviolet Catastrophe.
https://en.wikipedia.org/wiki/Rayleigh%E2%80%93Jeans_law#Com...
Combined it's: Anywhere the temperature is high relative to the frequencies being analyzed.
Hot bodies emit various wavelengths, but the distribution of intensities is roughly a bell curve. If you sum up all these intensities, but weight them by the aforementioned weights in the previous paragraph, you would calculate what color would be perceived when looking at that object.
Barely glowing hot objects emit a ton of infra-red (with perceptual weight zero) and a bit in the visual spectrum, on the red end of it (with a non-zero weight). So we perceive a red glow.
Extremely ludicrously hot objects emit a ton of ultra-violet, X-ray and gamma rays (all with zero weight for visual perception), but also a bit on the blue end of the visible spectrum (with a non-zero weight for perception). So they look blue. Well, they would have looked blue, if the invisible bombardment of gamma rays did not immediately evaporate you.
At the low end of those frequencies, the intensity at each fequency is roughly proportional to the object's temperature multiplied by the frequency squared.
Once an object is hot enough, all of visible light is in the low end of the frequency range. Which means the ratios between all visible frequencies are based on frequency squared and nothing else.
That gives us a specific spectrum, where blue is about twice as intense as red. That spectrum has a specific color, the same color as #94B1FF.
(Note that other RGB values also represent the same color at different brightnesses. That's fine, because we're not worried about brightness in this math. Brightness scales linearly with the temperature of the object.)
This doesn't make sense to me. If we're talking about what color our eyes would see, all our cones would be 100% saturated. Correct me if I'm wrong, but we would still perceive that as white regardless of where the spectrum peak is.
I had no idea that periwinkles were touchy about such matters. I thought they were considered an invasive weed that can grow on waste ground.
That said Planck's law derives from Gibb's distribution and applying that rule to it suggests it immediately radiates all energy, until it stops having a negative temperature so I'm not sure if negative temperature is compatible with thermal radiation.
Right-clicking and opening the image in its own tab works.
Inspecting both, the server is setting Content-Type to "image/webp" on the page (and sending 58 bytes), but setting it to "image/png" when displayed in its own tab (and sending 139 bytes).
On the request Safari says it can accept "image/webp,image/png,image/svg+xml,image/*;q=0.8,video/*;q=0.8,*/*;q=0.5" so the server choosing to send a webp is fine. For some reason apparently Safari cannot display this particular webp.
The graph below that on the page, the one of intensity vs. frequency, is also a webp and Safari has no trouble with it.