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Einstein proved wrong about blue sky

  1. May 31, 2003 #1


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    Einstein proved wrong about blue sky!!!!

    In 1911 Einstein published an explanation of why the sky is blue
    based on analysis of Rayleigh scattering by nitrogen and oxygen molecules.

    His analysis was sufficiently detailed and accurate that it was used to provide an independent measurement of the Avogadro number.

    See Usenet Physics FAQ



    However according to recent posts on PF, revisionists have overturned Einstein, dismissed the idea that the blue is caused by scattering from N2 and O2 molecules, and demonstrated
    that it is caused by an alternative mechanism---fluctuations in air density.

    This is certainly possible but no URLs have been offered to allow verification. Can anyone say if the standard explanation of blue sky has, in fact, been credibly supplanted?

    Here is a quote from a recent post stating that it has, but without online corroboration:

    "Molecule of N2 is too small (d~0.3 nm) to give any essential contribution into blue sky color. Recall that intensity of scattered light is proportional to (d/λ)4, so it drops dramatically with size. It would take about hundred times more air to get essential contribution into scattering from individual molecules. But the distribution of molecules in air is fluctuating, and it turns out that most contribution into intensity of scattered light comes from fluctuating pockets of air of order of 10-100 nm in size. These pockets can have dramatically different number of molecules per unit volume."

    This SOUNDS reasonable. But the analysis flies against Einstein's calculations and the standard picture from, for instance, Usenet FAQ! This is curious and provocative---hope someone has some links about this.
  2. jcsd
  3. May 31, 2003 #2
    Both are correct and Einstein with Smoluchowski solved the problem and developed the Einstein-Smoluchowski equation. Which in a dilute gas reduces to the Rayleigh scattering result. The Einstein-Smoluchowski result, which take into account density fluctuations, is a more general valid result than just considering a dilute gas.

    Science is about the details.

  4. May 31, 2003 #3


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    I would also like it to be about knowing some order of magnitudes and which effects are negligible in a given context.

    From what you say, if the bulk of the atmosphere can be
    considered a "dilute" gas, then the main contribution to the
    blue color I see out there is scattering from nitrogen and oxygen molecules. Do I understand you correctly?

    This would be good because all the explanations I noticed on the web said that----including the Usenet FAQ----and it would be a nuisance if they all turned out to be wrong.
  5. May 31, 2003 #4
    Markus, do you learn physics by web? Not good. There is alternative way - textbooks.

    Or thinking (analysing). Set of COHERENT dipols does not scatter.

    Recall wave equation, and diffusion equation - what is the difference? Q: Why in one case a media transmits without change of direction and in another scatters? A: first case arises when all secondary sources are in phase, second - when they are not. Call it constractive interference and random scattering.

    Say, crystals have thousand times more molecules than thin air, nevertheless they are sometimes much longer transparent than 5 miles (standard thickness of atmosphere), especially at low temperature when scattering on thermal motion diminishes. Fiber optics - glass being not a crystal but random (to some degree) distribution of atoms (and again thousand times more of them per unit volume than in air) is more transparent that atmosphere.

    Metals and alloys (both in crystallic and amorphous form) do not scatter electrons at low temperature (thus very little electric resistance) DESPITE that there is tons and tons of ions inside. Coherence, dude. As temperature rises, thermal motion makes ions "forget" their original position during interaction and scattering (resulting in electric resistance) is increasing with temperature.
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  6. May 31, 2003 #5


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    Your first proof that Einstein was wrong made better sense. I said (following Einstein) that Rayleigh scattering by nitrogen and oxygen molecules is the main reason for blue sky. You denied this and said:

    What you said there was wrong, but at least it was to the point. The nitrogen molecule is NOT too small to preferentially scatter shorter wavelengths and cause blue sky, but at least you were saying something about that, even if mistaken.
    Your next attempt to prove Einstein wrong is totally unrelated to what I said or to the point. The point is what is the main cause of the sky being blue. Try to make your second argument at least as cogent as your first, please. Try to prove, as you claimed, that preferential Rayleigh scattering by N2 and O2 is not responsible for the blue color. Of course the molecules are randomly oriented and positioned--air is not a crystal. That can be taken for granted. Draw some connections for your eagerly expectant audience Here is your second argument.

  7. May 31, 2003 #6
    Einstein was a human. Humans can make mistakes.

    Markus, why don't you just lift a finger and open optics textbook instead of you long "blah blah blah... empty posts? You save us a lot of disk space here.
  8. May 31, 2003 #7


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    What concerns me is this statement from Alexander:

    ...Molecule of N2 is too small (d~0.3 nm) to give any essential contribution into blue sky color. Recall that intensity of scattered light is proportional to (d/λ)4, so it drops dramatically with size.

    This is clearly wrong. The molecule is not to small to scatter light and do so preferentially (by a fourth-power dependence) at shorter, bluer, wavelengths. Indeed Feynmann explained the blue sky this way in his Physics Lectures. Alexander would have him wrong as well as Einstein.

    The critical dimension is not the size of the molecule, which is adequate, but the average distance between molecules. In the upper atmosphere where the distance is on the order of the wavelength, the scattered light adds. Rayleigh's original picture works!

    In the lower atmosphere the N2 molecules are still the same size and scatter just fine! The only trouble in dense air is the destructive interference of scattered light. So turbulence in the air creating temporary pockets of low density can play a significant role. The mechanism, however, is still Rayleigh scattering mostly by nitrogen molecules.

    Smoluchowski and Einstein both made similar calculations about the same time, according to this source:


    Smoluchowski's result in 1908 in fact preceded Einstein's in 1910, according to this. Both took account of variable density. Neither of them thought N2 molecules "too small" to scatter light but indeed both were attributing the blue color to Rayleigh scattering by molecules. Or so this source implies.

    Alexander often makes false claims and then is arrogant and adamant about them. This is a more or less permanent feature here and of no particular interest. But I think we should get clear that a nitrogen molecule can scatter light and tends to scatter around 10 times more blue than it does red---a simple fact explaining more than one of the colors one sees in the sky.
  9. May 31, 2003 #8
    Markus, I am sorry but you keep insisting on wrong things without even proving elementary facts on a calculator. You have just proven that you don't understand physics even on the level of arithmetics.

    Let's indeed check how far from each other are air molecules in upper atmosphere. Density of atmosphere drops with altitude as ~exp(-E/kT), where E = mgh = energy needed to lift a molecule of mass m at the altitude h).

    Assuming that the average air molecule has mass 80%N2+20%O2=29 a.m.u.=4.8x10-26kg, we get that air density drops as ~exp(-h/ho), where ho=kT/mg =7.5 km (average for altitudes 0-30 km, assuming average temperature to be about -15 C (more near Earth surface and less at higher altitude)). We don't have to go above 30 km, because contribution into scattering at above 20-25 km is negligible compared to lower altitudes. (Indeed, numerous tourists riding Mig planes and other high-altitude military aircrafts in Russia report black sky at ~25 km and above). So, the density of atmosphere at h~25 km is about 30 times less than near ground, or about 1.4 kg/30~33 g/m3. Anyone with a calculator can estimate that there is N~0.033kg/4.8x10-26kg~7x1023 molecules in 1 m3, and then find the average distance between molecules (equating sphere with one molecule times number of them to one cubic meter: (4[pi]r3/3)N=V) is about r~(V/4N)1/3~ 7 nm.

    Now recall from optics that the wavelength of blue light is about 450 nm, which is more than SIXTY times larger value.

    So, Markus, the conclusion is obvious: either Rayleigh, Einstein and Feynamnn are wrong in their assumptions that the scattering is uncoherent because molecules are father away than wavelength (in fact they are way less away than the shortest wavelength we discuss), or you are wrong in reading them in a great hurry. Or both. Take a calculator and check the arithmetics.

    Don't parrot internet information - it frequently is of LOW quality information. Think. Analyse. Check. Use a calculator, after all.
    Last edited by a moderator: May 31, 2003
  10. May 31, 2003 #9
    Again wrong. Scattering on fluctuations of density has nothing to do with turbulence of air.


    This is plain lie. I do make false claims - as everybody else here, including you - but NOT often.

    Please, stop lying (and cut pathetics), ok?
  11. Jun 1, 2003 #10


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    As before I am concerned with this
    This is what I am waiting for you to explain or retract.

    Meanwhile, as I like to calculate and you invite me to do so, I will.
    A rough back of envelope calculation gives me that at
    sealevel average dist betw. molecules is 3.4 nm and at 30 km
    it is 14 nm. these are just rough approximations. But the blue wavelength is 400 nm, so at no relevant point in the atmosphere is my statement about the average distance right.

    However I remember calculating long ago that the nitrogen molecule could scatter visible light, I worked out the cross section. I dont think I need to do that calculation again. As I recall I got the cross section from the electron's Compton. And
    I got that blue was 9 or 10 times more likely to scatter than red. The factor was essentially just (7/4)4.

    these are fun calculations and just confirm that Einstein and Feynmann and everybody else who says air molecules scatter light (and scatter blue preferentially over red) are correct.

    And that you are wrong to say the molecules are too small.

    So calculations don't help prove your point. If you have some nontrivial point, which wasnt obvious to these other people, you have to explain it.

    Personally I would be delighted for you to prove all these people---especially the consensus of websites that searching comes up with---wrong! I like surprises and would be happy to have another mechanism for the blue sky explained to me---if it really makes sense.

    But you cant just shout at me and tell me to use a calculator.

    Indeed at one time I remember calculating the brightness of the daytime sky based on the scattering crossection for N2 molecules--again just back of envelope--and it worked out.

    Anyway, explanation is needed on your part, or retraction of your statement that the nitrogen molecule is too small to "make any essential contribution to blue sky".
  12. Jun 1, 2003 #11


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    While your derivation of atmospheric pressuer at 25 km is shoddy, it gives roughly the right result (0.0342 kg/m3 at 26 km, so I can't complain too much.

    I'm more concerned about your calculation of the average distance between particles. In particular it seems heavily biased to yield a low result.

    For example, if instead we modeled the particle distribution as a cubic lattice, each particle is allotted a cube of side r, and neighboring particles will be a distance r apart. Running the same calculation yields:

    r3 N = V => r = (V / N)1/3 ~ 11 nm

    That simple modification of the hypothesis increased the average distance by over 50%. I wonder up to what a more random distribution could bump that.

    Also, if you have n uniformly distributed partices in volume V on average, then the probability of a particular volume v being empty is (for n large):

    P(v empty) = exp(-v n / V)

    Your spheres of radius 7 nm have a volume of 1.43*10^-24 m^3, so the probability that any particular 7 nm radius sphere is empty is 37%, so these 14 nm diameter empty spheres are pretty common.

    Other empty shapes are pretty common too. For instance, a 450 nm long cylinder of radius 1 nm has volume 1.41*10^-24 m^3. The probability it is empty is also 37%. On average, more than one out of every three such tubes we check will have no particle in them.

    There's definitely more to the picture than you're letting on.
  13. Jun 1, 2003 #12
    Re: Einstein proved wrong about blue sky!!!!

    Hi Marcus,
    Both modelings you have mentioned are proposed solutions to the same "thought experiment" and in their own way appear to be credible; however, consideration of a pair of real experimental phenomena makes possible another, and perhaps more credible, modeling. One of these phenoms is the known interaction between near-blue UV radiation and the excited elevation of an electron in a molecular bond of Oxygen. Another phenom is the existence of the Ionospheric filtering blanket at the outer limits of the stratosphere where the gases are in plasma state. Rather than "scattering" or simple "gas density" the proposed modeling here is that the excess energy above that of say, 400 nm, is used up in the process of repeated ionizations of the atmospheric gases. The following short essay hopefully predicates my alternate modeling.

    The sky is blue because the atmospheric layer is a filter rather than a diffuser. Quite simply, all photo energies greater than blue do not merely translate and rotate the elastic molecular gases, principally O2 and N2, but also attack the molecular bonds of those gases. That seems paradoxical considering that for greater photo energies, such as x-rays and ã-rays, matter that is so easily penetrated by these rays is also opaque (excepting diffracting and crystallographic phenomena) to visible light.
    Because only quantum orbitals comprise all the electrons in these two gases, the orbital strength of individual molecular bonds determines the sensitivity to the influence on bond excitement caused by the high-energy absorption. For example, the most sensitive electron in the O2 double bond is the one whose excitement causes the fleeting existence of O2* -> O3 -> O2. Whether or not the stronger triple bond of N2 undergoes a similar non-ionizing and analogous type excitement of a bonding electron aside, the proof of the ability of the stronger rays to ionize these gases by electron expulsion, is manifest by the highly evident “Ionosphere”. It follows that most of the energy exceeding blue results in positive ions whose repulsion drives them to the outer reaches of the stratosphere where they ultimately recombine with electrons and can again be ionized. Incidentally, the weakest quantum orbitals after the molecular bonding orbitals of these gases are the 1s orbitals of the nuclei.
    BTW: the belief that Ozone absorbs UV is a fallacy. Au contraire, it’s the O2 that absorbs the UV and the existence of Ozone merely proves the point. It is also true that even stronger radiation gets trapped in a blanket of ionized gases. Cheers, Jim

    "Logic is easy when done Nature's way"
  14. Jun 1, 2003 #13
    Nope. Once again, you misunderstand how SCATTERING works. A molecule itself does not SCATTER - all it does is oscillating in phase with incident electric field. It is up to dynamic distribution (due to thermal motion) of many molecules if the INTERFERENCE of multiple oscillators (molecules) results in scattering or is coherent.

    Take a liquid - it has THOUSAND times more molecules per same volume than a gas at a sea level (not to say at 25-30 km). So according to your back of the envelope estimations, a liquid shall scatter THOUSAND times more than air at sea level. Experiments with scattering in liquids (by Landsberg, Motulevich, Jakovlev, etc done in Russia ~60 years ago) shown, however, that liquids not only scatter LESS than gases, but turns out that threy scatter SIGNIFICANTLY LESS light (about 50 times) than air. This is 50x1000=5x104 discrepancy than what follows from your (and everyone else be it Rayley, Einstein, Feynmann, etc.) suggesion that scattering is molecular. Light scatters on microscopic statistical fluctuations of density (due to thermal motion of molecules), and in liquids those fluctuations are way way less than in gases. Thus much less scattering despite thousand times more molecules.

    Scattering in crystals is much less than in liquids despite the fact that crystals may contain several times MORE molecules per volume than liquids. Just because crystals have much less fluctuations due to much limited molecular motion than liquids. Ideal homogenious non-fluctuating media consisting of molecules does not scatter. Indeed, have dipole oscillators oscillate in phase with electric fielf of passing e/m wave - the result of interference will be CANCELLING radiation in ALL direction except of the direction forward. That is exactly what we have in well ordered solids - practically no scattering, only re-radiation forward resulting in straight propagating.

    Also experiments show drop of scattering with temperature. If scattering were not on statistical fluctuations of number of molecules per volume, then the intensity of scattering would be independent on temperature which contradicts observations.

    Another experimental evidence NOT in favor of molecular scattering is that quarts at phase transition (of second kind, or second order - not the transition from solid to liquid but the transition from one type of crystal lattice to another) abruptly increases scattering of light by many orders (104) - and only in very narrow temperature interval (~0.1 C) around the point of phase transition - just when molecules are in unsettled motion between two states. Past the point scattering again is dramatically less (molecules have settled in new order, no fluctuations). Notice that NUMBER of molecules per volume is about the SAME before, during and after transition - yet the scattering rises dramatically only during phase transition (quarts literally becoms hasy while being transparent at temperatures slightly below and slightly after transition point).

    I think, Mandelstam, Landsberg and a few other russian scientists pointed out on Rayley (and followers) wrong assumption long ago, and derived accurate light scattering theory long ago - it is in every russian textbook ever since then. That is why I know of it.

    So, Marcus, I should follow your advice:

    Can YOU please retract your wrong statements that scattering is molecular and not on microscopic FLUCTUATIONS of density? Just acknowledge (as you advised me to do) that you (and those who you cited) were wrong here. Sorry, I would not ask you for that if you did not mention it, ok?

    And, please don't cite what others say without checking first if they are wrong, ok? As I said, internet is choke full of low quality information. Referring to such information without thinking is pointless.
    Last edited by a moderator: Jun 1, 2003
  15. Jun 1, 2003 #14
    This cylinder is still quite small compared to blue wavelength volume v~450nm3~10-19m3 - about 4-5 orders of magnitude smaller.
  16. Jun 1, 2003 #15


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    I understand that scattering works by molecules (or more correctly their electrons) oscillating in phase with incident electric field. I take for granted that their spacing is irregular (from random walk, collisions, thermal motion) so
    that the sideways re-radiation from them does not all cancel out.

    Because they (or actually their outer electrons) DO oscillate in phase, and preferentially for shorter wavelengths, we get scattering.

    The blue of the sky is caused by scattering from nitrogen and oxygen molecules (irregularly spaced by random motion) because
    of a fourth power law that says they scatter blue 10 times more effectively than red.

    This is called Rayleigh scattering by air molecules.

    I happily retract anything I said that was inconsistent with this view, since this has been my view up til now. Anything I said that doesnt fit that picture must have been sheer carelessness!

    My impression of what you were saying was that Rayleigh scattering by N2 molecules was NOT responsible. Your long rambling discussions about solids and crystals gave me the impression that you had some other mechanism mind.

    Your mentioning thermal motion today seems to clear this up.
    You seem to use words differently to describe the same basic picture. So we are in essential agreement!!!

    I would call
    what the molecules do (by their electrons oscillating in phase with the wave) scattering.
    They behave like a bunch of irregularly spaced dipoles and dipoles scatter, in my lexicon. But you say they do not scatter
    but do something else. This is fine with me call it what you want.

    I still think Einstein and Smoluchowski (1910 and 1908) were probably right in how they described it and that the blue is caused by what I would call "Raleigh scattering by air molecules" and you would call something else-----since when that mechanism was proposed by nbo you said "No, they are too small." But I chalk that up to your speaking a different language, not to a different underlying picture.
  17. Jun 1, 2003 #16
    You're arguing the same point Einstein and Smoluchowski solved the problem taking into account density fluctuations. Density fluctuation of what? N and O.

  18. Jun 1, 2003 #17


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    BTW, I retract the use of the word "shoddy"; that's not what I meant in my previous post.
  19. Jun 1, 2003 #18
    Condense air into liquid. It will have about thousand times MORE molecules per same volume. According to Rayley, etc there shall be thousand times MORE scattered light.

    In reality it is way LESS.

    The reason that Rayley formula (derived on the assumption that each molecule radiates incoherently from others) was originally considered as a satisfactory explanation, is that for an ideal gas mean of SQUARES of deviations (fluctuations) of number of molecules from the average for any given volume by chance coincides with the number of molecules in that volume. In the absense of those deviations scattering is zero (like in solids and to some degree in liquids).

    I think first this was cleared by L.I. Mandelstamm in his paper "About optically homogenious and inhomogenious media" published in 1907.

    It is important to understand that a molecule does NOT radiate sideway (=scatters) if there are other non-moving and evenly distributed similar molecules around. It only radiates forward then.
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