Category Archives: Astronomy

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?

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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.

Why isn’t the sky green and the sun orange?

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Part of the reason the sky isn’t green has to do with the color of the sun. The sun’s color, and to a lesser extent, the sky color both are determined by the sun’s surface color, yellow. This surface color results from black body radiation: if you heat up a black object it will first glow red, then orange, yellow, green etc. Red is a relatively cool color because it’s a low frequency (long wavelength) and low frequencies are the lowest energy photons, and thus are the easiest for a black body to produce. As one increases the temperature of a black object, the total number of photons increases for all wavelengths, but the short wavelength (high frequency) colors increase faster than the of long wavelength colors. As a result, the object is seen to change color to orange, then yellow, or to any other color representative of objects at that particular temperature.

Our star is called a yellow sun because the center color of its radiation is yellow. The sun provides radiation in all colors and wavelengths, even colors invisible to the eye, infra red and ultra violet, but because of its temperature, most of the radiated energy appears as yellow. This being said, you may wonder why the sky isn’t yellow (the sky of Mars mostly is).

The reason the sky is blue, is that some small fraction of the light of the sun (about 10%) scatters off of the molecules of the air. This is called Rayleigh scatter — the scatter of large wavelegth waves off of small objects.  The math for this will be discussed in another post, but the most relevant aspect here is that the fraction that is scattered is proportional to the 4th power of the frequency. This is to say, that the high frequencies (blue, indigo, and violet) scatter a lot, about 20%, while the red hardly scatters at all. As a result the sky has a higher frequency color than the sun does. In our case, the sky looks blue, while the sun looks slightly redder from earth than it does from space — at least that’s the case for most of the day.

The sun looks orange-red at sundown because the sunlight has to go through more air. Because of this, a lot more of the yellow, green, and blue scatter away before we see it. Much more of the scatter goes off into space, with the result that the sky to looks dark, and somewhat more greenish at sundown. If the molecules were somewhat bigger, we’d still see a blue sky, maybe somewhat greener, with a lot more intensity. That’s the effect that carbon dioxide has — it causes more sunlight to scatter, making the sky brighter. If the sun were cooler (orange say), the sky would appear green. That’s because there would be less violet and blue in the sunlight, and the sky color would be shifted to the longer wavelengths. On planets where the sun is cooler than ours, the sky is likely green, but could be yellow or red.

Rayleigh scatter requires objects that are much smaller than the light wavelength. A typical molecule of air is about 1 nm in size (1E-9 of a meter), while the wavelength of yellow light is 580 nm. That’s much larger than the size of air molecules. Snow appears white because the size of the crystals are the size of the sun wavelengths, tor bigger, 500-2000 nm. Thus, the snow looks like all the colors of the sun together, and that’s white. White = the sum of all the colors: red + orange + blue + green + yellow + violet + indigo.

Robert Buxbaum  Jan. 27, 2013 (revised)

True (magnetic) north

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Much of my wife’s family is Canadian, so I keep an uncommon interest in Canada — for an American. This is to say, I think about it once a month or so, more often during hockey season. So here is a semi-interesting factoid:

The magnetic north pole, the “true north” has been moving northwest for some time, but the rate has increased over the last few decades as the picture shows. It has now left the northern Canadian islands, so Canada is no longer “The true north, strong and free.” (It seems to be strong and free). True north  is now moving northwest, toward Siberia. true magnetic north heading to Russia

Why is the galaxy stable?

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We are located about 30,000 light years out from the galactic center (1.8E17 miles), and the galaxy goes round every 200,000,000 years. From the rotational rate and diameter I calculate that we’re moving at roughly 1,000,000,000 miles/year or 100,000 mph — not a bad speed to expect to come from random variation of the gas molecule speeds. Maxwell averaging should reduce the speed to 2000 mph at most, I’d think.

Even more interesting, the rotation speed suggests the galaxy’s gone around about 50 times since it condensed. That’s an awful lot of turns for our galactic arms to retain stable; you’d expect that the outer parts of the arms would have rotated far fewer times, perhaps only once, while the inner parts would rotate perhaps 1000 times. After a billion years, you’d expect the arms to be gone. The going explanation is dark matter, matter we can’t see.

After bugging astrophysicists for a few years, I’ve come to believe that many of their models (MACHOs, WIMPs) don’t make much sense. I’ve come to model the distribution of dark matter on my own, as a particular distribution gas cloud of light particles. There is only one distribution that will result in the galaxy rotating as a unit — can you figure out what that is? Not that I now know what dark matter is, but at least I think I know where it is. Now all we need to do is find the missing matter. As a challenge, see if you can calculate the distribution of dark matter that would result in the galaxy rotating as a unit.

— Robert Buxbaum

The universe is not endless

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You may have heard that the universe is not endless, ending at a brick wall, perhaps, some 15 billion light years out. But what you may not know is that there is a classic proof, going back to the middle ages to show that the universe is not an endless expanse of stars.

Consider an endless universe with a uniform distribution of stars. We would expect that, in any large-enough space of this universe there would have to be many stars, e.g. between 100 and 101 trillion miles from earth. At this distance, each of these stars is close enough to see, and the combination of them (the sum in this volumetric shell) will shed a small amount of heat on the earth. Now consider another shell, the same thickness but twice as far from us; if the universe is uniform, there will be 4 times as many stars, but since these stars will be at twice the distance; that is between 200 and 201 trillion miles from earth, each star will present us with ¼ as much heat as the stars in the first shell. Now, since there are 4 times more stars, the total effect is to radiate as much heat to us as from the first shell.

The same argument goes for each shell of 1 trillion miles thick: each one presents us with the same amount of heat. If the universe is infinite and uniform, we find there will be an infinite number of shells radiating this amount of heat, and therefore an infinite amount of heat bathing us. We should expect to roast from all of it. Since we have not roasted, we conclude that the universe is not an endless, uniform expanse.

The universe could still be uniform and not endless (ending with a brick wall, as in the Hitch-hikers guide), or it could be expanding from a big bang 15 Billion years ago. This latter is suggested by the red shift, but not a favored solution of creationists for some reason. Or it could be a closed, oscillating (or not) 4 dimensional hypersphere (Einstein). That is, it could be a non Euclidean, black hole. Or it could be fractal (Mandelbrot). Or it could be a combination of all of the above.

For a thought about galactic arms see here. October 22, 2012.