Tag Archives: Galaxy

Of God and Hubble

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Edwin Hubble and Andromeda Photograph

Edwin Hubble and Andromeda Photograph

Perhaps my favorite proof of God is that, as best we can tell using the best science we have, everything we see today, popped into existence some 14 billion years ago. The event is called “the big bang,” and before that, it appears, there was nothing. After that, there was everything, and as best we can tell, not an atom has popped into existence since. I see this as the miracle of creation: Ex nihilo, Genesis, Something from nothing.

The fellow who saw this miracle first was an American, Edwin P. Hubble, born 1889. Hubble got a law degree and then a PhD (physics) studying photographs of faint nebula. That is, he studied the small, glowing, fuzzy areas of the night sky, producing a PhD thesis titled: “Photographic Investigations of Faint Nebulae.” Hubble served in the army (WWI) and continued his photographic work at the Mount Wilson Observatory, home to the world’s largest telescope at the time. He concluded that many of these fuzzy nebula were complete galaxies outside of our own. Most of the stars we see unaided are located relatively near us, in our own, local area, or our own, “Milky Way” galaxy, that is within a swirling star blob that appears to be some 250,000 light years across. Through study of photographs of the Andromeda “nebula”, Hubble concluded it was another swirling galaxy quite like ours, but some 900,000 light years away. (A light year is 5,900,000,000 miles, the distance light would travel in a year). Finding another galaxy was a wonderful find; better yet, there were more swirling galaxies besides Andromeda, about 100 billion of them, we now think. Each galaxy contains about 100 billion stars; there is plenty of room for intelligent life. 

Emission from Galaxy NGC 5181. The bright, hydrogen ß line should be at but it's at

Emission spectrum from Galaxy NGC 5181. The bright, hydrogen ß line should be at 4861.3 Å, but it’s at about 4900 Å. This difference tells you the speed of the galaxy.

But the discovery of galaxies beyond our own is not what Hubble is most famous for. Hubble was able to measure the distance to some of these galaxies, mostly by their apparent brightness, and was able to measure the speed of the galaxies relative to us by use of the Doppler shift, the same phenomenon that causes a train whistle to sound differently when the train is coming towards you or going away from you. In this case, he used the frequency spectrum of light for example, at right, for NGC 5181. The color of the spectral lines of light from the galaxy is shifted to the red, long wavelengths. Hubble picked some recognizable spectral line, like the hydrogen emission line, and determined the galactic velocity by the formula,

V= c (λ – λ*)/λ*.

In this equation, V is the velocity of the galaxy relative to us, c is the speed of light, 300,000,000 m/s, λ is the observed wavelength of the particular spectral line, and λ*is the wavelength observed for non-moving sources. Hubble found that all the distant galaxies were moving away from us, and some were moving quite fast. What’s more, the speed of a galaxy away from us was roughly proportional to the distance. How odd. There were only two explanations for this: (1) All other galaxies were propelled away from us by some, earth-based anti-gravity that became more powerful with distance (2) The whole universe was expanding at a constant rate, and thus every galaxy sees itself moving away from every other galaxy at a speed proportional to the distance between them.

This second explanation seems a lot more likely than the first, but it suggests something very interesting. If the speed is proportional to the distance, and you carry the motion backwards in time, it seems there must have been a time, some 14 billion years ago, when all matter was in one small bit of space. It seems there was one origin spot for everything, and one origin time when everything popped into existence. This is evidence for creation, even for God. The term “Big Bang” comes from a rival astronomer, Fred Hoyle, who found the whole creation idea silly. With each new observation of a galaxy moving away from us, the idea became that much less silly. Besides, it’s long been known that the universe can’t be uniform and endless.

Whatever we call the creation event, we can’t say it was an accident: a lot of stuff popped out at one time, and nothing at all similar has happened since. Nor can we call it a random fluctuation since there are just too many stars and too many galaxies in close proximity to us for it to be the result of random atoms moving. If it were all random, we’d expect to see only one star and our one planet. That so much stuff popped out in so little time suggests a God of creation. We’d have to go to other areas of science to suggest it’s a personal God, one nearby who might listen to prayer, but this is a start. 

If you want to go through the Hubble calculations yourself, you can find pictures and spectra of galaxies here for the 24 or so original galaxies studied by Hubble: http://astro.wku.edu/astr106/Hubble_intro.html. Based on your analysis, you’ll likely calculate a slightly different time for creation from the standard 14 billion, but you’ll find you calculate something close to what Hubble did. To do better, you’ll need to look deeper into space, and that would take a better telescope, e.g.  the “Hubble space telescope”

Robert E. Buxbaum, October 28, 2018.

A simple, classical view of and into black holes

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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 E is the photon energy, h is Plank’s constant and ν is frequency. The photon mass is related to its energy by way of the formula m=E/c2, a formula that is surprisingly easy to derive, and often shown as E= mc2. The version that’s relevant to photons and black holes is:

m =  hν/c2.

Now consider that gravity affects ν by affecting the energy of the photon. As a photon goes up, the energy and frequency goes down as energy is lost. The gravitational force between a star, mass M, and this photon, mass m, is 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 and M is the mass of the star. The amount of photon energy lost to gravity as it rises from the surface is the integral of the force.

∆E = – ∫Fdr = ∫GMm/r2 dr = -GMm/r

Lets consider a photon of original energy E° and original mass m°= E°/c2. If ∆E = m°c2, all the energy of the original photon is lost and the photon disappears. Now, lets figure out the height, r° such that all of the original energy, E° is lost in rising away from the center of a star, mass M. That is let calculate the r for which ∆E = -E°. We’ll 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).

schwarzschild

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 a small asteroid. 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 an asteroid and is not a black hole: we can see light from the sun’s surface with minimal space-time deformation (there is some seen in the orbit of Mercury). Still, if the mass were a lot bigger, the radius would be a lot bigger and the density would be less. Consider a black hole the same mass as our galaxy, about 1 x1012 solar masses, or 2 x 1042  kg. This number is ten times what you might expect since our galaxy is 90% dark matter. The Schwarzschild radius with the mass of our galaxy would be 3 x 1012 km, or 0.3 light years. That’s far bigger than our solar system, and about 1/20 the distance to the nearest star, Alpha Centauri. This is a very big black hole, though it is far smaller than our galaxy, 5 x 1017 km, or 50,000 light years. The density, though is not all that high.

Now let’s consider a black hole comprising 15 billion galaxies, the mass of the known universe. The folks at Cornell estimate the sum of dark and luminous matter in the universe to be 3 x 1052 kg, about 15 billion times the mass of our galaxy. This does not include the mass hidden in the form of dark energy, but no one’s sure what dark energy is, or even if it really exists. A black hole encompassing this, known mass would have a Schwarzschild radius about 4.5 billion light years, or about 1/3 the actual size of the universe when size is calculated based on its Hubble-constant age, 14 billion years. The universe may be 2-3 times bigger than this on the inside because space is curved and, 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 actual size of the known universe is remarkably similar to its Schwarzschild radius, and this is without considering the mass its dark energy must have if it exists.

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 source of the energy might be some zero-point effect, but wherever it comes from, 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 and aesthetically pleasing. Einstein originally didn’t consider the possibility that the hole could be expanding, but a reviewer of one of his articles convinced him it was possible.

Based on the above, we now know how to calculate the size of a black hole of any mass, and we now know what a black hole the size of the universe would look 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 the tidal forces around black holes, they are horrific only for the small black holes that most people write about. If the black hole is big, the tidal forces are small.

 Dr. µß Buxbaum Nov 17, 2014. The idea for this post came from an essay by Isaac Asimov that I read in a collection called “Buy Jupiter.” You can drink to the Schwarzchild radius with my new R° cocktail.

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.