Over the last one-hundred years or so we as humans have been vouchsafed through science an overarching view of the universe we inhabit. At the beginning of that last century, around 1920, we knew that the stars were incredibly far away, but figured that the entire universe was embodied in what we now call our galaxy. Only eighty-two years before that in 1838 had the first accurate distance to a star been calculated using the phenomenon of parallax, a shift in the apparent position of nearer objects relative to those further away when observed from different viewpoints. A simple way to observe and understand parallax, is to hold up a finger at arm’s length in front of one’s nose, close one eye and then the other. The apparent position of one’s finger jumps back and forth relative to a background further away. One half the angle of the shift defines the parallax. One uses half of the shift because the direction straight out from one’s nose towards the outstretched finger defines a base direction for where one is looking. A line to the finger from either eye meets the straight out line at the parallax angel. Knowing this angle and the distance between one’s eyes, one can calculate the distance to one’s finger using simple trigonometry. That calculation seems rather academic until one realizes that instead of the distance between one’s eyes, one can take instead the distance between opposite sides of the earth’s orbit around the sun and by measuring the apparent shift in position of nearby stars relative to those further away, one can calculate the distance to those nearby stars.
The fact that there should be parallax in the heavens was understood in ancient times, was known to many in the sixteenth century and could be used to calculate the distance to the moon. The seminal transitional figure, Tycho Brahe, 1546 – 1601, thinking that the stars could not be all that much further away than the planets, expected that if the earth really circled the sun in a Copernican manner, he could over six months easily measure parallax of some stars, simultaneously confirming Copernicus and finding a rough idea of the distance to those nearby stars. The telescope had not yet been invented, but Tycho Brahe, was using various instruments, such as quadrants and sextants, each like a piece of a giant protractor, with which he could measure angles to a minute of arc. Recall that a “minute” is a sixtieth of a degree.
Over a year’s time Tycho could detect not the slightest parallax in any candidate star. This meant one of two things. Either the earth and the stars were fixed in the cosmos, OR the stars were unbelievably far away. Tycho guessed the former possibility and made up a model in which all the planets besides earth and her moon circled the sun, while the whole shebang of sun and planets, circled the central, spinning earth inside the sphere of the fixed stars. Tycho’s guess was reasonable but wrong, as so many scientific guesses are. With the invention of the telescope, Kepler’s laws of planetary motion (based on Tycho’s data), and with the contributions of Galileo and Newton, the Copernican model made more sense, although it took over another 100 years for stellar parallax to be detected and yet another 100 years before it was actually measured by Friedrich Bessel in 1838. Before its detection in the early 1700’s there were still die-hard anti-Copernicans who could use the lack of stellar parallax as the primary evidence for their views. As it turns out, the parallax of the nearest star is less than an arc second, more than 60 times smaller than Tycho Brahe could detect. An arc second is the angle subtended by a quarter 3.3 miles away. (See Wikipedia’s article, “Stellar Parallax”.)
It’s worth doing some simple math in a short paragraph to show how the distance to nearby stars is calculated and find its value. (Feel free to skim.) It turns out that one doesn’t even need to use trig, because if the parallax angle is small, one can use the formula r = s/ø relating the arc length s on a circle to its radius r and the angle ø which s subtends. In the astronomical situation r is the distance to the star, s is the radius of the earth’s orbit around the sun, 93,000,000 miles or so, and ø is the parallax angle. The angle ø needs to be in radians, an angular unit = π/180 times the angle in degrees. These days with a smart phone one can easily grind out the calculation. Let’s take ø to be half a second of arc. We need that half second to be in degrees so we can multiply by π/180 and have it in radians. So, .5 times 1 /60 x 60 = .5/3600 = 0.000138888 degrees. Multiply that by π and divide by 180 and we have our half second as 0.00000242407 radians. Divide 93,000,000 miles by this last amount and lo, we have 38,400,000,000,000 miles to a nearby star. Astronomers like to cut these big numbers down to size. If we used an entire second rather than a half as our parallax, the distance would be half as much. Astronomers name this latter distance a parallax second, abbreviated as a parsec, pc. Our hypothetical star is 2 parsecs away and there are, in fact, stars that are that close to us. There are none as close as a parsec. Another distance unit in popular usage is the light year, the distance light goes in a year’s time, traveling 186,000 miles or so each second throughout the year. You can whip out your phone and show that a parsec is about 3.26 lightyears.
The satellite Hipparcos, aloft 1989 – 1993, could detect a parallax of 0.001 arcseconds (like measuring the diameter of a quarter in New York from San Francisco), so could measure the distance to stars one-thousand parsecs away. Meanwhile, since the late nineteenth century the “cosmic distance ladder” has developed. The crucial discovery, which enabled astronomers to go beyond parallax to the ladder’s second rung, was made by Henrietta Swan Leavitt, 1868 – 1921, working at the Harvard Observatory, as an assistant measuring the brightness of stars on photographic plates. According to the Wikipedia article about her, Henrietta Leavitt, while measuring the brightness of 1777 so-called Cepheid variable stars noticed a relation between the oscillation time and the relative intensity of their overall brightness. The brightness was only relative rather than absolute because the stars in question were in the Magellanic Clouds, located at an unknown distance from earth. In 1912 her work was published (not under her name). She noted that if one could measure the parallax of nearby Cepheids, an absolute measure of brightness could be established and distances could then be found to stars lying beyond what parallax could deal with. By 1924, using parallax, the distance to several nearby Cepheids had been measured and the time was ripe for momentous discoveries. The first of these was made by Edwin Hubble using the newly built 100-inch Wilson observatory telescope above Pasadena, California. (When I lived in Pasadena in 1953-4, I would hike up to the observatory on weekends and occasionally be amused by the spectacle of California drivers skidding around in a rare snowfall.) By the end of 1924 Hubble had been able to detect and measure the brightness of several Cepheids in the Andromeda and several other nearby “nebulae”. Clearly, the distance to these stars was much greater than to any star in our milky way galaxy and the “nebulae” were, in fact, “island universes”, each consisting of a several hundred billion or so stars. Hubble thus settled a controversy since some influential astronomers at the time thought that the nebulae were simply large star clusters inside our milky way. As a distance measure, astronomers still cling to the parsec, an established convention, but now mostly in the form of a kilo or mega pc, a thousand or million times the distance mentioned in the last paragraph. For example, our nearest neighbor galaxy, according to the Wikipedia article “Andromeda Galaxy”, lies at a distance from us of 778 kpc or 2.54 million light years.
As the 1920’s wore on (remember: this is the time of the quantum revolution, the German hyperinflation and the inexorable growing foundation for Hitler’s rise) Edwin Hubble made another earthshaking discovery, measuring a Doppler shift in the spectra of various galaxies. One experiences a Doppler shift here on earth when an emergency vehicle with “lights and sirens”, passes by. The pitch of the siren suddenly lowers as the vehicle passes. Hubble found that the frequency of light from galaxies lowered (were Doppler shifted towards the red), the amount of shift being directly proportional to the estimated distance of the galaxies. What this meant was that the farther a galaxy was from us, the component of its velocity in our direction was always away and greater. Imagine in your mind being in the middle of all these galaxies. Anywhere you imagine being, you are always in an apparent center (so says general relativity) and all the galaxies are moving away. The number of threads in the fabric of the entire universe is increasing so distance measures are growing. The speculation this situation suggests is that at one time there was a beginning of this spread and that the entire universe exploded out of nothingness. This idea is called “the big bang” theory, “big bang” being an expression coined by Sir Fred Hoyle, a brilliant, creative, quirky British physicist and astronomer, who proposed a rival, steady-state theory of an eternal, expanding universe, kept homogeneous by the rare, occasional creation of a stable elementary particle. Hoyle claimed he was not being pejorative in his term, but with it he was implying that the very idea of a “big bang” was ridiculous.
Hubble published the paper about his red-shift observations and some of their consequences in 1929. His ideas had been anticipated in greater detail and published in a somewhat obscure journal, two years earlier by Georges Lemaître, a priest, mathematician and physicist, then a part-time lecturer at the Catholic University of Louvain in Belgium, see Wikipedia. Lemaître, rediscovered a metric, predicting the expansion, in the equations of General Relativity. Also, he realized that Einstein’s solution for a static universe was untenable. Then, using red-shift observations in the literature, Lemaître made the first estimate of the Hubble constant (now renamed the Hubble-Lemaître constant). Lemaître was also the first to imagine the “big bang” arising from a densely packed “primeval atom” containing the entire (footnote link here) mass-energy of our then infant universe. When Lemaître translated his paper to English in 1931 he left out his section about the Hubble constant because by then Hubble’s 1929 paper had come out and Lemaître figured that his own value was obsolete. Ironically, Hubble’s value was off by a factor of 10 or so. Nowadays we know that the constant(?) is about 70 although at the moment (7/14/2020) there are at least two different values which disagree, with a gap beyond their error estimates. The units of the “70” which I left out of the previous sentence are worth explaining briefly. (70, without units, has the same status as 48, mentioned in Douglas Adams Hitchhikers Guide to the Galaxy as the answer to “life, the universe and all that.”) To understand the Hubble expansion unit, imagine that we “look” out from our earthly center of the universe a megaparsec. We will find that out there, all the galaxies are moving away from us at an average speed of 70 kilometers per second. Go out another mpc and they’re going at 140, etc. The unit is thus a kilometer per second per megaparsec. Incidentally, the variation of galaxy velocities making up this average is small. The universe is incredibly homogeneous, a fact Hoyle could have used, had he known, in his long battle with the big bang.
Until fairly recently Hubble received the credit (for whatever it’s worth) of discovering the red shift and the big bang because of his well-publicized 1929 paper. Hubble did nothing dishonest in accepting his honors and fame, but also did nothing in the way of discouraging such. Why should he? Lemaître remained an obscure figure partly because he was not at all interested in self-promotion and possibly because he was a Catholic priest, with the baggage of being considered anti-science because of his religion.
As the 20th century wore on, the picture suggested in the first third of the century fleshed out. People researched the different kinds of galaxies, realizing in the process that there are 100 billion or so in our universe to say nothing of quasars and “black holes”. Between 1963 and 1965 perhaps the most exciting astronomical discovery of the century occurred. I can remember my excitement in 1965, as a newly installed Associate Professor at Auburn University, when the news came out that a cosmic microwave radiation had been accidentally observed by Penzias and Wilson at a Bell Labs site, using a large so-called horn antenna. The signal was to them, when first detected, unwanted noise, and they tried in vain to get rid of it. Finally, they called Professor Dicke at Princeton, whose design was incorporated in their antenna. According to Wikipedia when Dicke got the call, he said to his team, “Boys, we’ve been scooped”. The radiation had been theoretically predicted and Dicke’s team was about to search for it. As the shape of the radiation spectrum was filled in, it fitted exactly, the formula that Planck had found in 1900, for black body radiation. Link to Black Body discovery. The temperature of the radiation was 2.7 degrees above absolute zero, having cooled from an incredible high temperature through the expansion of space from the time when the universe became transparent to electromagnetic radiation some 200,000 years after the big bang. This observation of cosmic black-body radiation was a striking confirmation of the big bang theory, and, in no way, could be twisted to be compatible with Hoyle’s rival theory. The decline of the Hoyle theory is a good example of Karl Popper’s idea of how science advances as I discussed in an earlier post. However, in science, nothing is ever really settled and continuous creation could easily again rear its [ugly?] head.
Towards the end of the 20th century, as more and better measurements of the cosmic radiation were made, it became clear how remarkably homogeneous it was. How could this be? As the fabric of the universe expands, regions become separated in a way special relativity calls “spacelike”. No signal could pass back and forth to soothe out fluctuations. Thus, unlike a cooling liquid, there is no mechanism to bring about homogeneity. Between 1979 and 1981, a young physicist, Alan Guth, developed a theory of inflation. This was not an economic theory, but, instead, the idea, that in the early instants of the big bang, “negative vacuum pressure” caused a wild, exponential expansion of the infant universe. After the inflationary expansion stopped, the universe was much larger and the ordinary Hubble type of expansion took over. Recent satellite measurements of the remaining non homogeneity agree well with Guth’s theory. I must confess that an intuitive understanding of the math behind this theory is totally beyond me.
In more recent times, deep mysteries concerning dark matter, dark energy and the idea of a multiverse have arisen. At this point I will not talk about them, leaving a possible discussion for later. Instead I will ask, “what is the significance for a thinking, aware human being of what we have found out about the place in which we live?” Many have noted that the history of cosmic discovery is one which displaced the human race further and further from the central significance we thought we had in the scheme of things back in ancient and medieval times, a displacement towards utter insignificance and humiliation. I want to take an almost opposite point of view. I wish to disregard the finer points of the science and look at the universe in the largely non-quantitative way as I have described in the previous paragraphs. I want to consider our picture of the universe as an aesthetic object, an unbelievably magnificent work of art. I want to suggest that this picture of the universe is, as well, a gigantic Zen Mondo, making clear an ultimate religious view beyond any language in which it could be couched.
If I am able to proceed in this direction, I must switch to an entirely different language game. So, in the next post I need to go further into the meta-language concept as suggested and developed by Wittgenstein, Kuhn and Meagher.