Category Archives: Astronomy

Can you spot the man-made climate change?

As best I can tell, the only constant in climate is change, As an example, the record of northern temperatures for the last 10,000 years, below, shows nothing but major ups and downs following the end of the last ice age 9500 years ago. The only pattern, if you call it a pattern, is fractal chaos. Anti-change politicos like to concentrate on the near-recent 110 years from 1890 to 2000. This is the small up line at the right, but they ignore the previous 10000 or more, ignore the fact that the last 17 years show no change, and ignore the variation within the 100 years (they call it weather). I find I can not spot the part of the change that’s man-made.

10,000 years of climate change based on greenland ice cores. Ole Humlum – Professor, University of Oslo Department of Geosciences.

10,000 years of northern climate temperatures based on Greenland ice cores. Dr. Ole Humlum, Dept. of Geosciences, University of Oslo. Can you spot the part of the climate change that’s man-made?

Jon Stewart makes the case for man-made climate change.

Steven Colbert makes his case for belief: If you don’t believe it you’re stupid.

Steven Colbert makes the claim that man-made climate change is so absolutely apparent that all the experts agree, and that anyone who doubts is crazy, stupid, or politically motivated (he, of course is not). Freeman Dyson, one of the doubters, is normally not considered crazy or stupid. The approach reminds me of “the emperor’s new clothes.” Only the good, smart people see it. The same people used to call it “Global Warming” based on a model prediction of man-made warming. The name was changed to “climate change” since the planet isn’t warming. The model predicted strong warming in the upper atmosphere, but that isn’t happening either; ski areas are about as cold as ever (we’ve got good data from ski areas).

I note that the climate on Jupiter has changed too in the last 100 years. A visible sign of this is that the great red spot has nearly disappeared. But it’s hard to claim that’s man-made. There’s a joke here, somewhere.

Jupiter's red spot has shrunk significantly. Here it is now. NASA

Jupiter’s red spot has shrunk significantly. Here it is now. NASA

As a side issue, it seems to me that some global warming could be a good thing. The periods that were warm had peace and relative plenty, while periods of cold, like the little ice age, 500 years ago were times of mass starvation and plague. Similarly, things were a lot better during the medieval warm period (1000 AD) than during the dark ages 500-900 AD. The Roman warm period (100 BC-50 AD) was again warm and (relatively) civilized. Perhaps we owe some of the good food production of today to the warming shown on the chart above. Civilization is good. Robert E. Buxbaum January 14, 2015. (Corrected January 19; I’d originally labeled Steven Colbert as Jon Stewart)


Our expanding, black hole universe

In a previous post I showed a classical derivation of the mass-to-size relationship for black -holes and gave evidence to suggest that our universe (all the galaxies together) constitute a single, large black hole. Everything is inside the black hole and nothing outside but empty space — We can tell this because you can see outside from inside a black hole — it’s only others, outside who can not see in (Finkelstein, Phys Rev. 1958). Not that there appear to be others outside the universe, but if they were, they would not be able to see us.

In several ways having a private, black hole universe is a gratifying thought. It provides privacy and a nice answer to an easily proved conundrum: that the universe is not infinitely big. The black hole universe that ends as the math requires, but not with a brick wall, as i the Hitchhiker’s guide (one of badly-laid brick). There are one or two problems with this nice tidy solution. One is that the universe appears to be expanding, and black holes are not supposed to expand. Further, the universe appears to be bigger than it should be, suggesting that it expanded faster than the speed of light at some point. its radius now appears to be 40-46 billion light years despite the universe appearing to have started as a point some 14 billion years ago. That these are deeply disturbing questions does not stop NASA and Nova from publishing the picture below for use by teachers. This picture makes little sense, but it’s found in Wikipedia and most, newer books.

Standard picture of the big bang theory. Expansions, but no contractions.

Standard picture of the big bang theory: A period of faster than light expansion (inflation) then light-speed, accelerating expansion. NASA, and Wikipedia.

We think the creation event occurred some 14 billion years ago because we observe that the majority of galaxies are expanding from us at a rate proportional to their distance from us. From this proportionality between the rate of motion and the distance from us, we conclude that we were all in one spot some 14 billion years ago. Unfortunately, some of the most distant galaxies are really dim — dimmer than they would be if they were only 14 billion light years away. The model “explains this” by a period of inflation, where the universe expanded faster than the speed of light. The current expansion then slowed, but is accelerating again; not slowing as would be expected if it were held back by gravity of the galaxies. Why hasn’t the speed of the galaxies slowed, and how does the faster-than-light part work? No one knows. Like Dr. Who’s Tardis, our universe is bigger on the inside than seems possible.

Einstein's preferred view of the black-hole universe is one that expands and contracts at some (large) frequency. It could explain why the universe is near-uniform.

Einstein’s oscillating universe: it expands and contracts at some (large) frequency. Oscillations would explain why the universe is near-uniform, but not why it’s so big or moving outward so fast.

Einstein’s preferred view was of an infinite space universe where the mass within expands and contracts. He joked that two things were infinite, the universe and stupidity… see my explanation... In theory, gravity could drive the regular contractions to an extent that would turn entropy backward. Einstein’s oscillating model would explain how the universe is reasonably stable and near-uniform in temperature, but it’s not clear how his universe could be bigger than 14 billion light years across, or how it could continue to expand as fast as it does. A new view, published this month suggests that there are two universes, one going forward in time the other backward. The backward in time part of the universe could be antimatter, or regular matter going anti entropy (that’s how I understand it — If it’s antimatter, we’d run into the it all the time). Random other ideas float through the physics literature: that we’re connected to other space through a black hole/worm hole, perhaps to many other universes by many worm holes in fractal chaos, see for example, Physics Reports, 1992.

The forward-in-time expansion part of the two universes model.

The forward-in-time expansion part of the two universes model. This drawing, like the first, is from NASA.

For all I know, there are these many black hole  tunnels to parallel universes. Perhaps the universal constant and all these black-hole tunnels are windows on quantum mechanics. At some point the logic of the universe seems as perverse as in the Hitchhiker guide.

Something I didn’t mention yet is the Higgs boson, the so-called God particle. As in the joke, it’s supposed to be responsible for mass. The idea is that all particles have mass only by interaction with these near-invisible Higgs particles. Strong interactions with the Higgs are what make these particles heavier, while weaker – interacting particles are perceived to have less gravity and inertia. But this seems to me to be the theory that Einstein’s relativity and the 1919 eclipse put to rest. There is no easy way for a particle model like this to explain relativistic warping of space-time. Without mass being able to warp space-time you’d see various degrees of light bending around the sun, and preferential gravity in the direction of our planet’s motion: things we do not see. We’re back in 1900, looking for some plausible explanation for the uniform speed of light and Lawrence contraction of space.As likely an explanation as any the_hitchhikers_guide_to_the_galaxy

Dr. r µ ßuxbaum. December 20, 2014. The  meaning of the universe could be 42 for all I know, or just pickles down the worm hole. No religion seems to accept the 14 billion year old universe, and for all I know the God of creation has a wicked sense of humor. Carry a towel and don’t think too much.

A simple, classical view of and into black holes

Black holes are regions of the universe where gravity is so strong that light can not emerge. And, since the motion of light is related to the fundamental structure of space and time, they must also be regions where space curves on itself, and where time appears to stop — at least as seen by us, from outside the black hole. But what does space-time look like inside the black hole.

NASA's semi-useless depiction of a black hole -- one they created for educators. I'm not sure what you're supposed to understand from this.

NASA’s semi-useless depiction of a black hole — one they created for educators. Though it’s sort of true, I’m not sure what you’re supposed to understand from this. I hope to present a better version.

From our outside perspective, an object tossed into a black hole will appear to move slower as it approaches the hole, and at the hole horizon it will appear to have stopped. From the inside of the hole, the object appears to just fall right in. Some claim that tidal force will rip it apart, but I think that’s a mistake. Here’s a simple, classical way to calculate the size of a black hole, and to understand why things look like they do and do what they do.

Lets begin with light, and accept, for now, that light travels in particle form. We call these particles photons; they have both an energy and a mass, and mostly move in straight lines. The energy of a photon is related to its frequency by way of Plank’s constant. E= hν, where h is Plank’s constant and ν is frequency. Their mass is related to their energy by way of the formula m=E/c2. This formulate is surprisingly easy to derive, and is often shown as E= mc2. In classical form, the gravitational force between a star, mass M, and this photon or any other object of mass m described as follows:

F = GMm/r2

where F is force, G is the gravitational constant, and r is the distance of the photon from the center of the star. The potential energy of a photon of the mass increases as it rises from the star surface, but the internal energy (proportional to frequency) decreases — the photon gets redder. The amount of internal energy lost to gravity as it rises from the surface is the integral of the force, and is thus related to the mass of the object and of the star.

∆E =  ∫Fdr = ∫GMm/r2 dr = -GMm/r

Lets consider a photon of original energy E° and original mass m°. Lets figure out the radius of the star r° such that all of the original energy, E° is lost in rising away from the star. That is let calculate the r for which ∆E = -E° as the photon rises to freedom. Lets assume, for now, that the photon mass remains constant at m°.

E° = GMm°/r° = GME°/c2r°.

We now eliminate E° from the equation and solve for this special radius, r°:

r° =  GM/c2.

This would be the radius of a black hole if space didn’t curve and if the mass of the photon didn’t decrease as it rose. While neither of these assumptions is true, the errors nearly cancel, and the true value for r° is double the size calculated this way.

r° = 2GM/c2

r° = 2.95 km (M/Msun).


Karl Schwarzschild 1873-1916.

The first person to do this calculation was Karl Schwarzschild and r° is called the Schwarzschild radius. This is the minimal radius for a star of mass M to produce closed space-time; a black hole. Msun is the mass of our sun, sol, 2 × 1030 kg.  To make a black hole one would have to compress the mass of our sun into a ball of 2.95 km radius, about the size of an SUV. Space-time would close around it, and light starting from the surface would not be able to escape.

As it happens, our sun is far bigger than a SUV and is not a black hole: we can see light from the sun’s surface with minimal space-time deformation. Still, if the mass were a lot bigger, the radius would be a lot bigger and the needed density less. Consider a black hole the same mass as our galaxy, about 1 x1012 solar masses (mostly dark matter), or 2 x 1042  kg. The Schwarzschild radius of a star with the mass of our galaxy would be 3 x 1012 km, or 0.3 light years, about 1/20 the distance to Alpha Centauri. This is far bigger than the six of our solar system, but far smaller than the actual size of the galaxy, 5 x 1017 km, or 50,000 light years. Still, the difference between 0.3 light years and 50,000 light years isn’t that great on the cosmic scale, and it’s worthwhile to consider a black hole comprising something 10 to 100 Billion times more massive than our galaxy — the universe as a whole.

The folks at Cornell estimate the sum of dark and luminous matter in the universe to be about 15 billion times the mass of our galaxy, or 3 x 1052 kg. This does not include the mass of the dark energy, but no one’s quite sure what dark energy is. Considering only this physical mass, the Schwarzschild radius for the universe would be about 4.5 billion light years, or about 1/3 the size of our universe based on its age. The universe appears to be 14 billion years old, so if it’s expanding at the speed of light, the radius should be 14 billion light years. The universe may be 2-3 times bigger than this on the inside (rather like Dr. Who’s Tardis it’s bigger on the inside) but in astronomical terms a factor of 3 or 10 is nothing: the size of the universe is remarkably similar to its Schwarzschild radius, and this is without considering the mass its dark energy must have.

Standard picture of the big bang theory. Dark energy causes the latter-stage expansion.

Standard picture of the big bang theory. Dark energy causes the latter-stage expansion.

The evidence for dark energy is that the universe is expanding faster and faster instead of slowing. See figure. There is no visible reason for the acceleration, but it’s there. The significant amount of energy must have significant mass, E = mc2. If the mass of this energy is 3 to 10 times the physical mass, as seems possible, we are living inside a large black hole, something many physicists, including Einstein considered extremely likely. Einstein originally didn’t consider the possibility that the hole could be expanding. But now we know how to calculate the size of a black hole, and we know what a large black hole looks like from the inside. It looks just like home.

Wait for further posts on curved space-time. For some reason, no religion seems to embrace science’s 14 billion year old, black-hole universe (expanding or not). As for tidal forces, they are horrific only for the small black holes that most people write about. If the black hole is big enough, the tidal forces are small.

 Dr. µß Buxbaum Nov 17, 2014. You can drink to the Schwarzchild radius with my new R° cocktail.

Ozone hole shrinks to near minimum recorded size

The hole in the ozone layer, prominently displayed in Al Gore’s 2006 movie, an inconvenient truth has been oscillating in size and generally shrinking since 1996. It’s currently reached its second lowest size on record.

South pole ozone hole shrinks to 2nd smallest size on record. Credit: BIRA/IASB

South pole ozone hole (blue circle in photo), shrinks to its 2nd smallest size on record. Note outline of antarctica plus end of south america and africa. Photo Credit: BIRA/IASB

The reason for the oscillation is unknown. The ozone hole is small this year, was large for the last few years, and was slightly smaller in 2002. My guess is that it will be big again in 2013. Ozone is an alternate form of oxygen containing three oxygen atoms instead of the usual two. It is an unstable compound formed by ions in the upper atmosphere acting on regular oxygen. Though the ozone concentration in the atmosphere is low, ozone is important because it helps shield people from UV radiation — radiation that could otherwise cause cancer (it also has some positive effects on bones, etc.).

An atmospheric model of ozone chemistry implicated chlorofluorocarbons (freons) as a cause of observed ozone depletion. In the 1980s, this led to countries restricting the use of freon refrigerants. Perhaps these laws are related to the shrinkage of the ozone hole, perhaps not. There has been no net decrease in the amount of chlorofluorocarbons in the atmosphere, and the models that led to banning them did not predicted the ozone oscillations we now see are common — a fault also found with models of global warming and of stock market behavior. Our best computer models do not do well with oscillatory behaviors. As Alan Greenspan quipped, our best models successfully predicted eight of the last five recessions. Whatever the cause, the good news is that the ozone hole has closed, at least temporarily. Here’s why the sky is blue, and some thoughts on sunlight, radiation and health.

by Dr. Robert E. Buxbaum, dedicated to bringing good news to the perpetually glum.

Chaos, Stocks, and Global Warming

Two weeks ago, I discussed black-body radiation and showed how you calculate the rate of radiative heat transfer from any object. Based on this, I claimed that basal metabolism (the rate of calorie burning for people at rest) was really proportional to surface area, not weight as in most charts. I also claimed that it should be near-impossible to lose weight through exercise, and went on to explain why we cover the hot parts of our hydrogen purifiers and hydrogen generators in aluminum foil.

I’d previously discussed chaos and posted a chart of the earth’s temperature over the last 600,000 years. I’d now like to combine these discussions to give some personal (R. E. Buxbaum) thoughts on global warming.

Black-body radiation differs from normal heat transfer in that the rate is proportional to emissivity and is very sensitive to temperature. We can expect the rate of heat transfer from the sun to earth will follow these rules, and that the rate from the earth will behave similarly.

That the earth is getting warmer is seen as proof that the carbon dioxide we produce is considered proof that we are changing the earth’s emissivity so that we absorb more of the sun’s radiation while emitting less (relatively), but things are not so simple. Carbon dioxide should, indeed promote terrestrial heating, but a hotter earth should have more clouds and these clouds should reflect solar radiation, while allowing the earth’s heat to radiate into space. Also, this model would suggest slow, gradual heating beginning, perhaps in 1850, but the earth’s climate is chaotic with a fractal temperature rise that has been going on for the last 15,000 years (see figure).

Recent temperature variation as measured from the Greenland Ice. A previous post had the temperature variation over the past 600,000 years.

Recent temperature variation as measured from the Greenland Ice. Like the stock market, it shows aspects of chaos.

Over a larger time scale, the earth’s temperature looks, chaotic and cyclical (see the graph of global temperature in this post) with ice ages every 120,000 years, and chaotic, fractal variation at times spans of 100 -1000 years. The earth’s temperature is self-similar too; that is, its variation looks the same if one scales time and temperature. This is something that is seen whenever a system possess feedback and complexity. It’s seen also in the economy (below), a system with complexity and feedback.

Manufacturing Profit is typically chaotic -- something that makes it exciting.

Manufacturing Profit is typically chaotic — and seems to have cold spells very similar to the ice ages seen above.

The economy of any city is complex, and the world economy even more so. No one part changes independent of the others, and as a result we can expect to see chaotic, self-similar stock and commodity prices for the foreseeable future. As with global temperature, the economic data over a 10 year scale looks like economic data over a 100 year scale. Surprisingly,  the economic data looks similar to the earth temperature data over a 100 year or 1000 year scale. It takes a strange person to guess either consistently as both are chaotic and fractal.


It takes a rather chaotic person to really enjoy stock trading (Seen here, Gomez Addams of the Addams Family TV show).

Clouds and ice play roles in the earth’s feedback mechanisms. Clouds tend to increase when more of the sun’s light heats the oceans, but the more clouds, the less heat gets through to the oceans. Thus clouds tend to stabilize our temperature. The effect of ice is to destabilize: the more heat that gets to the ice, the more melts and the less of the suns heat is reflected to space. There is time-delay too, caused by the melting flow of ice and ocean currents as driven by temperature differences among the ocean layers, and (it seems) by salinity. The net result, instability and chaos.

The sun has chaotic weather too. The rate of the solar reactions that heat the earth increases with temperature and density in the sun’s interior: when a volume of the sun gets hotter, the reaction rates pick up making the volume yet-hotter. The temperature keeps rising, and the heat radiated to the earth keeps increasing, until a density current develops in the sun. The hot area is then cooled by moving to the surface and the rate of solar output decreases. It is quite likely that some part of our global temperature rise derives from this chaotic variation in solar output. The ice caps of Mars are receding.

The change in martian ice could be from the sun, or it might be from Martian dust in the air. If so, it suggests yet another feedback system for the earth. When economic times age good we have more money to spend on agriculture and air pollution control. For all we know, the main feedback loops involve dust and smog in the air. Perhaps, the earth is getting warmer because we’ve got no reflective cloud of dust as in the dust-bowl days, and our cities are no longer covered by a layer of thick, black (reflective) smog. If so, we should be happy to have the extra warmth.

Two things are infinite

Einstein is supposed to have commented that there are only two things that are infinite: the size of the universe and human stupidity, and he wasn’t sure about the former.

While Einstein still appears to be correct about the latter infinite, there is now more disagreement about the size of the universe. In Einstein’s day, it was known that the universe appeared to have originated in a big bang with all mass radiating outward at a ferocious rate. If the mass of the universe were high enough, and the speed were slow enough the universe would be finite and closed in on itself. That is, it would be a large black hole. But in Einstein’s day, the universe didn’t look to have enough mass. It thus looked like the universe was endless, but non-uniform. It appeared to be mostly filled with empty space — something that kept us from frying from the heat of distant stars.

Since Einstein’s day we’ve discovered more mass in the universe, but not quite enough to make us a black hole given the universe’s size. We’ve discovered neutron stars and black holes, dark concentrated masses, but not enough of them. We’ve discovered neutrinos, tiny neutral particles that fill space, and we’ve shown that they have rest-mass enough that neutrinos are now thought to make up most of the mass of the universe. But even with these dark-ish matter, we still have not found enough for the universe to be non-infinite, a black hole. Worse yet, we’ve discovered dark energy, something that keeps the universe expanding at nearly the speed of light when you’d think it should have slowed by now; this fast expansion makes it ever harder to find enough mass to close the universe (why we’d want to close it is an aesthetic issue discussed below).

Still, there is evidence for another, smaller mass item floating in space, the axion. This particle, and it’s yet-smaller companion, the axiono, may be the source of both the missing dark matter and the dark energy, see figure below. Axions should have masses about 10-7 eV, and should interact enough with matter to explain why there is more matter than antimatter while leaving the properties of matter otherwise unchanged. From normal physics, you’d expect an equal amount of matter and antimatter as antimatter is just matter moving backwards in time. Further, the light mass and weak interactions could allow axions to provide a halo around galaxies (helpful for galactic stability).

Mass of the Universe with Axions, no axions. Here is a plot from a recent SUSY talk (2010)

Mass of the Universe with Axions, no axions. Here is a plot from a recent SUSY talk (2010)

The reason you’d want the universe to be closed is aesthetic. The universe is nearly closed, if you think in terms of scientific numbers, and it’s hard to see why the universe should not then be closed. We appear to have an awful lot of mass, in terms of grams or kg, but appear to have only 20% of the required mass for a black hole. In terms of orders of magnitudes we are so close that you’d think we’d have 100% of the required mass. If axions are found to exist, and the evidence now is about 50-50, they will interact with strong magnetic fields so that they change into photons and photons change into axions. It is possible that the mass this represents will be the missing dark matter allowing our universe to be closed, and will be the missing dark energy.

As a final thought I’ve always wondered why religious leaders have been so against mention of “the big bang.” You’d think that the biggest boost to religion would be knowledge that everything appeared from nothing one bright and sunny morning, but they don’t seem to like the idea at all. If anyone who can explain that to me, I’d appreciate it. Thanks, Robert E. B.

The martian sky: why is it yellow?

In a previous post, I detailed my calculations concerning the color of the sky and sun. Basically the sun gives off light mostly in the yellow to green range, with fairly little red or purple. A lot of the blue and green wavelengths scatter leaving the sun  looking yellow because yellow looks yellow and the red plus blue also looks yellow because of additive color.

If you look at the sky through a spectroscope, it’s pretty blue with some green. Sky blue involves a bit of an eye trick of additive color so that we see the scattered blue + green as sky blue and not aqua. At sundown, the sun becomes reddish and the majority of the sky becomes greenish-grey as more green and yellow light gets scattered. The sky near the sun is orange as the atmosphere is thick enough to scatter orange, while the blue and green scatters out.

Now, to talk about the color of the sky on Mars, both at noon and at sunset. Except for the effect of the red color of the dust on Mars I would expect the sky to be blue on Mars, just like on earth but a lighter shade of blue as the atmosphere is thinner. When you add some red from the dust, one would expect the sky to be grey. That is, I would expect to find a simple combination of a base of sky blue (blue plus green), plus some extra red-orange light scattered from the Martian dust. In additive colors, the combination of blue-green and red-orange is grey, so that’s the color I’d expect the Martian sky to be normally. Some photos of the Martian sky match this expectation; see below. My guess is this is on a day when there was not much dust in the air, though NASA provides no details here.

martian sky; looks grey

On some days (high dust days, I assume), the Martian sky is turns a shade of yellow-green. I’d guess that’s because the red-dust absorbs the blue and some of the green spectrum, but does not actually add red. We are thus involved with subtractive color and, in subtractive color orange plus blue-green = butterscotch, not grey or pink.

Martian sky color

I now present a photo of the Martian sky at sunset. This is something really peculiar that I would not have expected ahead of time, but think I can explain now that I see it. The sky looks yellow in general, like in the photo above, but blue around the sun. I could explain this picture by saying that the blue and green of the Martian sky is being scattered by the Martian air (CO2, mostly), just like our atmosphere scatters these colors on earth; the sky near the sun looks blue, not red-orange because the Martian atmosphere is thinner (at noon there is less air to scatter light, but at sun-down the atmosphere is the same thickness as ours, more or less). The red of the dust does not show up in the sky color near the sun since the red-color is back scattered near the sun, and not front scattered. The Martian sky is yellow elsewhere where there is some front scatter of the reddish light reflecting off of the dust. This sounds plausible to me; tell me what you think.

Martian sky at sunset

Martian sky at sunset

As an aside, while I have long understood there was an experimental difference between subtractive and additive color, I have never quite understood why this should be so. Why is it that subtractive color combinations are different, and uniformly different from additive color combinations. I’d have thought you’d get more-or-less the same color if you remove red from one part of a piece of paper and remove blue from another as if you add red, purple, and yellow. A mental model I have (perhaps wrong) is that subtractive color looks like it does because of the details of the spectral absorption of the particular pigment chemicals that are typically used. Based on this model, I expect to find someday some new red and green pigments where the combination looks yellow when mixed on a page. I’ve not found it yet, but that’s my expectation — perhaps you know of a really good explanation for why additive color is so different from subtractive color.

Joke about antimatter and time travel

I’m sorry we don’t serve antimatter men here.

Antimatter man walks into a bar.

Is funny because … in quantum-physics there is no directionality in time. Thus an electron can change directions in time and then appears to the observer as a positron, an anti electron that has the same mass as a normal electron but the opposite charge and an opposite spin, etc. In physics, the reason electrons and positrons appear to annihilate is that it’s there was only one electron to begin with. That electron started going backwards in time so it disappeared in our forward-in-time time-frame.

The thing is, time is quite apparent on a macroscopic scales. It’s one of the most apparent aspects of macroscopic existence. Perhaps the clearest proof that time is flowing in one direction only is entropy. In normal life, you can drop a glass and watch it break whenever you like, but you can not drop shards and expect to get a complete glass. Similarly, you know you are moving forward in time if you can drop an ice cube into a hot cup of coffee and make it luke-warm. If you can reach into a cup of luke-warm coffee and extract an ice cube to make it hot, you’re moving backwards in time.

It’s also possible that gravity proves that time is moving forward. If an anti apple is just a normal apple that is moving backwards in time, then I should expect that, when I drop an anti-apple, I will find it floats upward. On the other hand, if mass is inherently a warpage of space-time, it should fall down. Perhaps when we understand gravity we will also understand how quantum physics meets the real world of entropy.

Why isn’t the sky green?

Yesterday I blogged with a simple version of why the sky was blue and not green. Now I’d like to add mathematics to the treatment. The simple version said that the sky was blue because the sun color was a spectrum centered on yellow. I said that molecules of air scattered mostly the short wavelength, high frequency light colors, indigo and blue. This made the sky blue. I said that, the rest of the sunlight was not scattered, so that the sun looked yellow. I then said that the only way for the sky to be green would be if the sun were cooler, orange say, then the sky would be green. The answer is sort-of true, but only in a hand-waving way; so here’s the better treatment.

Light scatters off of dispersed small particles in proportion to wavelength to the inverse 4th power of the wavelength. That is to say, we expect air molecules will scatter more short wavelength, cool colors (purple and indigo) than warm colors (red and orange) but a real analysis must use the actual spectrum of sunlight, the light power (mW/m2.nm) at each wavelength.

intensity of sunlight as a function of wavelength (frequency)

intensity of sunlight as a function of wavelength

The first thing you’ll notice is that the light from our sun isn’t quite yellow, but is mostly green. Clearly plants understand this, otherwise chlorophyl would be yellow. There are fairly large components of blue and red too, but my first correction to the previous treatment is that the yellow color we see as the sun is a trick of the eye called additive color. Our eyes combine the green and red of the sun’s light, and sees it as yellow. There are some nice classroom experiment you can do to show this, the simplest being to make a Maxwell top with green and red sections, spin the top, and notice that you see the color as yellow.

In order to add some math to the analysis of sky color, I show a table below where I divided the solar spectrum into the 7 representative colors with their effective power. There is some subjectivity to this, but I took red as the wavelengths from 620 to 750nm so I claim on the table was 680 nm. The average power of the red was 500 mW/m2nm, so I calculate the power as .5 W/m2nm x 130 nm = 65W/m2. Similarly, I took orange to be the 30W/m2 centered on 640nm, etc. This division is presented in the first 3 columns of the following table. The first line of the table is an approximate of the Rayleigh-scatter factor for our atmosphere, with scatter presented as the percent of the incident light. That is % scattered = 9E11/wavelength^4.skyblue scatter

To use the Rayleigh factor, I calculate the 1/wavelength of each color to the 4th power; this is shown in the 4th column. The scatter % is now calculated and I apply this percent to the light intensities to calculate the amount of each color that I’d expect in the scattered and un-scattered light (the last two columns). Based on this, I find that the predominant wavelength in the color of the sky should be blue-cyan with significant components of green, indigo, and violet. When viewed through a spectroscope, I find that these are the colors I see (I have a pocket spectroscope and used it an hour ago to check). Viewed through the same spectroscope (with eye protection), I expect the sun should look like a combination of green and red, something our eyes see as yellow (I have not done this personally). At any rate, it appears that the sky looks blue because our eyes see the green+ cyan+ indigo + purple in the scattered light as sky blue.220px-RGB_illumination

At sunrise and sunset when the sun is on the horizon the scatter percents will be higher, so that all of the sun’s colors will be scattered except red and orange. The sun looks orange then, as expected, but the sky should look blue-green, as that’s the combination of all the other colors of sunlight when orange and red are removed. I’ve not checked this last yet. I’ll have to take my spectroscope to a fine sunset and see what I see when I look at the sky.