I’m gradually revising my Albedo to Zodiac, and just now I came to a spot under H that needed attention and have had to work up a paragraph:
Hubble’s Law, or the Hubble-Lemaître Law: galaxies are receding from us at speeds proportional to their distances. The motion is called the Hubble flow. Hubble’s equation says that a galaxy’s recession speed (n), in kilometers per second per megaparsec, is the distance (D) in megaparsecs times the Hubble constant (H0). From the measured redshift of an object, which gives its speed of recession, can be found its distance. A cluster of galaxies has a common speed of recession, but superimposed on this are the motions of galaxies within the cluster, so the law does not apply to those in our local group. Alexander Friedmann in 1922 derived the idea of universal expansion from Albert Einstein’s 1915 general relativity; Georges Lemaître in 1927, and more definitely Edwin Hubble (1889-1953) in 1929, based the expansion on measurements of redshift made by Vesto Slipher in 1917. Estimates of the constant use many techniques, giving different results and a significant uncertainty, called the Hubble tension. Estimates have generally decreased, from Hubble’s 550 km/s/Mpc to around 100 in the 1970s, to current answers ranging from 73 to 67. Thus for each megaparsec of distance from us, a galaxy is receding about 70 km per sec faster. The smaller the constant, the greater the resulting Hubble distance, at which galaxies are receding at the speed of light – the radius of the observable universe. The “constant” is more neutrally called a “parameter”, because it changes over time. Its value also determines the Hubble time, which is, approximately, the age of the universe.
That may be the shortest possible statement of the vastest possible subject, and I may have to revise it, perhaps in light of your comments. Here’s the climax illustration of the Astronomical Companion that tries to suggest the eerie limit of the expanding universe.
Home Planet Extremes
Political labels! I’ve noticed some merry use of them in recent comments to this blog. So I’ll share with you a transcript of yesterday’s debate between the candidates of the two mainstream parties for the key position of sheriff of Oconee County: Mr. Molotov Hussain Cocktailovich of the Loony Lefty Liberals, and the Hon. Adolf Nero Shekelgrubber of the Far-Right Fascist Fanatics. (A third candidate, Mrs. Jane Smith of the Willing to Compromise Party, failed to get a word in, because of her incorrigible habit of waiting for a pause instead of interrupting.)
Herr Shekelgrubber: “Mr. Vladimir, or whatever your pinko name is, I charge you with wanting to raise taxes until the Net Worth of everyone is equal – ”
Bro Molotov: “Yes, everyone, over the age of six, that is. Whereas you would throw all taxes into Boston harbor and crowdung your battleship-sized yacht and your rooftop heliport from your billionaire cronies. Furthermore – ”
“Furthermore, further morons! You would use our tax money for the expansion of hospitals until they are as large as prisons. Moreover -”
“Moreover, more over the top! You would send Bad Hombres back to Guatemala – ”
“Of course. On foot. Whereas you would give them Equal Opportunity jobs in the Treasury, with keys. You would require every committee to have equal proprtions of male, female, and transgender members, with the casting vote for the latter if – ”
“Whereas you would restrict the vote to white Anglo-Saxon Protestant males – ”
“Only middle-aged ones, with suitable attitude, they would have to qualify by having beer bellies. Whereas you would extend Social Security to household pets – ”
“Don’t forget household plants. I believe your compassion is restricted not just to your race, clan, sect, and shareholders, but to your extedned family – ”
“My extended family? Let them eat crust. My immediate family. They are quite enough of a handful to govern. Or, come to think of it: If thy son offend thee – ”
“Yes, you would be emperor, wouldn’t you? Sole pinnacle – ”
“Who better? I am entitled to to tweet executive orders while playing golf – ”
“And order, no doubt, the execution of any dissenter – ”
“Not just executed, but something lengthier – ”
“So I’ll need to watch out for myself, if you get into power- ”
“And so will the other suckers who vote for me. You believe that policies should be based not on hardheaded calculation but on, forsooth, compassion – ”
“Yes, and not just for sentient beings but – after all, who knows whether a tree is sentient, or a brick? – think of the weight of all those other bricks on top of that poor brick – ”
“And bacteria, I bet you’re going to say bacteria need something to eat – ”
“They do, and even viruses have a right to life. ”
Momentary metaphysical silence.
Mrs. Smith: “Gentlemen – ”
Moderator: “Time’s up, I’m afraid.”
Mr. Cocktailovich and Mr. Shekelgrubber, in unison:
“I claim – ” “I demand – ”
” – the right – ” ” – my right – ”
” – to make one more comment.” ” – to rebut that last comment.”
Moderator: “Sorry. The clock has made the last comment.”
__________
ILLUSTRATIONS in these posts are made with precision but have to be inserted in another format. You may be able to enlarge them on your monitor. One way: right-click, and choose “View image”, then enlarge. Or choose “Copy image”, then put it on your desktop, then open it. On an iPad or phone, use the finger gesture that enlarges (spreading with two fingers, or tapping and dragging with three fingers). Other methods have been suggested, such as dragging the image to the desktop and opening it in other ways.
Sometimes I make improvements or corrections to a post after publishing it. If you click on the title, rather than on ‘Read more’, I think you are sure to see the latest version.
This weblog maintains its right to be about astronomy or anything under the sun.
HI Guy- Nice Hubble law capsule. One correction: units in 3rd sentence slightly garbled: recession speed is in km/s, not km/s/Mpc. The latter is the units of Ho itself, such that multiplying Ho by distance (Mpc) gives nominal recession speed…
Thanks – but, oh, my sentences was
Estimates have generally decreased, from Hubble’s 550 km/s/Mpc to …
That does refer to Hubble’s constant, H0, not to the speed of any one galaxy? I think I should just clarify by saying “Estimates of H0 have generally decreased…” Tellme if I’m still wrong.
I wondered whether I ought to have used “velocity” throughout, technically not the same thing as “speed”. Decided it reads more plainly with the plain word.
The correction I note is required in the 3rd sentence: “Hubble’s equation says that a galaxy’s recession speed (n), in kilometers per second per megaparsec, is the distance (D) in megaparsecs times the Hubble constant (H0).” Strike “per megaparsec” here to get the correct units of speed. I think the rest is fine as regards units, including the bit about the value of H0 coming down as we’ve gotten better at measuring it**. I think “speed” is sufficient, since all velocities considered here are recessional along our lines of sight out into the universe. Strictly, these are in different directions for different galaxies, of course, but for each galaxy, the speed and distance vectors are in the same direction. Effectively then, the Hubble law is a statement relating just the _magnitudes_ of the distance and velocity vectors. It is a scalar equation, and nominally applies consistently in all directions out into the universe (after our local peculiar velocities within the Milky Way and on smaller scales are accounted for).
**In fact, the current “value” of H0 is currently a matter of great debate. Different ways of measuring it are yielding different results, at a (now) statistically significant level: 68 (early universe measurements involving properties of the cosmic background radiation) or 73 (late universe measurements relating distance and velocity measurements to discrete objects). This so-called “Hubble tension” is an indication that one or both techniques have some as-yet unappreciated systematic flaw. Both cannot be strictly correct, and maybe neither are, at the claimed uncertainty levels…..
Speed in just km/sec. of course, thanks.
In light of your other remarks I’ve made a few other re-wordings, and will send the paragraph to you off-blog.
I hope you’ll post the revision here, too.
Okay; ignore the formatting codes; much yet to cover…
Hubble’s Law<$>, or the Hubble-Lemaître Law: galaxies are receding from us at speeds proportional to their distances. The motion is called the Hubble flow<$>. A galaxy’s recession speed (n), in kilometers per second, is the distance (D) in megaparsecs<$> times the Hubble constant<$> (H0). From the measured redshift<$> of an object, which gives its speed of recession, can be found its distance. A cluster of galaxies has a common speed of recession, but superimposed on this are the peculiar motions of galaxies within the cluster, so the law does not apply to those in our local group. Alexander Friedmann in 1922 derived the idea of universal expansion from Albert Einstein’s 1915 general relativity; Georges Lemaître in 1927. and more definitely Edwin Hubble (1889-1953) in 1929, based the expansion on measurements of redshift made by Vesto Slipher in 1917. Estimates of the constant use many techniques, giving different results Estimates have generally decreased, from Hubble’s 550 km/sec/Mpc to around 100 in the 1970s, to present answers ranging from about 73 (“late universe” measurements of actual galaxies) to 68 (“early universe” measurements of the cosmic background radiation<$>). One or both must be wrong, and the uncertainty, called the Hubble tension<$>, has become large enough to be statistically significant. For each megaparsec of distance from us, a galaxy is receding about 70 km per sec faster. The smaller the constant, the greater the resulting Hubble distance<$>, at which galaxies are receding at the speed of light – the radius of the observable universe. The “constant” is more neutrally called a “parameter”, because it changes over time. Its value also determines the Hubble time<$>, which is, approximately, the age of the universe.
Thank you!
Hi Guy- The revision you posted below looks good. My only quibble is with the word “uncertainty” (at “One or both most be wrong, and the…”). The Hubble tension arises from the *difference* between late and early universe measurements of H0 being distinctly larger than the small but finite error bars (the _uncertainties_) quoted for either. So “difference” would be a better word there, I think. Cheers, George
Thanks for the further correction. Off-blog I am sending to George another question about wording, too minor to need repeating here.
I VERY MUCH enjoy the satire! I trust these characters (with the possible exception of Ms. Smith) are not actually residents of Oconee County, South Carolina. Yes, there IS an Oconoee County, although my first thought before reading the dialogue was that it MIGHT be an English county! (BTW, I am loving these next editions of Last Tango in Halifax!)
Are some galaxies traveling away from us faster or is the difference in speed some kind of illusion?as I understand it, and it’s pretty difficult to get one’s head around,is the Big Bang occured everywhere at the same time and had no centre like say a bomb would.often the image of an inflating balloon is given with the galaxies being dots drawn on the balloon surface except for the fact that the universe appears to be flat with no curve suggesting it’s infinite.at the macro level of the universe itself wouldn’t all speeds be the same I wonder?
The farther away a galaxy is from us, the faster it is moving away from us. This is what allows us to use redshift to measure distance. The expansion of the universe means that, at cosmological distances, everything is moving away from everything else. Raisins in a baking cake have been a helpful analogy for me. As the dough rises during baking all the raisins are moving away from one another. The farther any two raisins are from one another the faster they’re moving in relation to one another. Now imagine that the cake is infinitely large, the raisins are galaxies, and dark energy is the heat that’s making the cake expand.
And, as Ludwig Wittgenstein said, “Raisins might be the best thing about a cake; but a bag full of raisins is no better than a cake, and a bag full of raisins does not make a cake.”
You left out one digit in Edwin Hubble’s birth year, 1889.
It’s much harder to write a definition than a book on the word or phrase being defined. You need to know everything that would be in the book, and figure out which few words are essential. Defining the Hubble Lemaitre law is a mind bending undertaking! Good work.
I hope Oconee County uses ranked-choice voting.
Thanks, corrected.
Approval voting, I hope you mean.
I’m an incrementalist. ;-)
Does that mean you support Approval Voting? Changing from Plurality to Approval Voting is about as “incremental” as you can get. Just change the “Vote for one” instruction to “Vote for one or more” and count all the votes. Any voting machine that works with Plurality elections can work with Approval elections.
Ranked Choice Voting (RCV, a.k.a. Instant Runoff Voting, IRV) is more complicated, generally requires upgrading voting equipment, and can sometimes make poor choices of winners, particularly when there are three or more candidates of roughly equal strength in a race. See rangevoting.org/Burlington.html for an example.
Approval Voting has been adopted in Fargo, ND (reformfargo.org/approval-voting), and St. Louis, MO (stlapproves.org), with one election completed in Fargo and early voting in progress in St. Louis. The Center for Election Science is working with local groups to bring Approval Voting to Denver, Seattle, and other places. If you’d like to bring Approval Voting to your area, check out electionscience.org/take-action/approval-voting-chapter-program/ .
Thanks for providing very thorough and persuasive information in response to my flippant comment.