A Dark, Misleading Force

Certain subsectors of the scientifically-oriented blogosphere are abuzz — abuzz, I say! — about this new presentation on Dark Energy at the Hubblesite. It’s slickly done, and worth checking out, although be warned that a deep voice redolent with mystery will commence speaking as soon as you open the page.

But Ryan Michney at Topography of Ignorance puts his finger on the important thing here, the opening teaser text:

Scientists have found an unexplained force that is changing our universe,
forcing galazies farther and farther apart,
stretching the very fabric of space faster and faster.
If unchecked, this mystery force could be the death of the universe,
tearing even its atoms apart.

We call this force dark energy.

Scary! Also, wrong. Not the part about “tearing even its atoms apart,” an allusion to the Big Rip. That’s annoying, because a Big Rip is an extremely unlikely future for a universe even if it is dominated by dark energy, yet people can’t stop putting the idea front and center because it’s provocative. Annoying, but not wrong.

The wrong part is referring to dark energy as a “force,” which it’s not. At least since Isaac Newton, we’ve had a pretty clear idea about the distinction between “stuff” and the forces that act on that stuff. The usual story in physics is that our ideas become increasingly general and sophisticated, and distinctions that were once clear-cut might end up being altered or completely irrelevant. However, the stuff/force distinction has continued to be useful, even as relativity has broadened our definition of “stuff” to include all forms of matter and energy. Indeed, quantum field theory implies that the ingredients of a four-dimensional universe are divided neatly into two types: fermions, which cannot pile on top of each other due to the exclusion principle, and bosons, which can. That’s extremely close to the stuff/force distinction, and indeed we tend to associate the known bosonic fields — gravity, electromagnetism, gluons, and weak vector bosons — with the “forces of nature.” Personally I like to count the Higgs boson as a fifth force rather than a new matter particle, but that’s just because I’m especially fastidious. The well-defined fermion/boson distinction is not precisely equivalent to the more casual stuff/force distinction, because relativity teaches us that the bosonic “force fields” are also sources for the forces themselves. But we think we know the difference between a force and the stuff that is acting as its source.

Anyway, that last paragraph got a bit out of control, but the point remains: you have stuff, and you have forces. And dark energy is definitely “stuff.” It’s not a new force. (There might be a force associated with it, if the dark energy is a light scalar field, but that force is so weak that it’s not been detected, and certainly isn’t responsible for the acceleration of the universe.) In fact, the relevant force is a pretty old one — gravity! Cosmologists consider all kinds of crazy ideas in their efforts to account for dark energy, but in all the sensible theories I’ve heard of, it’s gravity that is the operative force. The dark energy is causing a gravitational field, and an interesting kind of field that causes distant objects to appear to accelerate away from us rather than toward us, but it’s definitely gravity that is doing the forcing here.

Is this a distinction worth making, or just something to kvetch about while we pat ourselves on the back for being smart scientists, misunderstood once again by those hacks in the PR department? I think it is worth making. One of the big obstacles to successfully explaining modern physics to a broad audience is that the English language wasn’t made with physics in mind. How could it have been, when many of the physical concepts weren’t yet invented? Sometimes we invent brand new words to describe new ideas in science, but often we re-purpose existing words to describe concepts for which they originally weren’t intended. It’s understandably confusing, and it’s the least we can do to be careful about how we use the words. One person says “there are four forces of nature…” and another says “we’ve discovered a new force, dark energy…”, and you could hardly blame someone who is paying attention for turning around and asking “Does that mean we have five forces now?” And you’d have to explain “No, we didn’t mean that…” Why not just get it right the first time?

Sometimes the re-purposed meanings are so deeply embedded that we forget they could mean anything different. Anyone who has spoken about “energy” or “dimensions” to a non-specialist audience has come across this language barrier. Just recently it was finally beaten into me how bad “dark” is for describing “dark matter” and “dark energy.” What we mean by “dark” in these cases is “completely transparent to light.” To your average non-physicist, it turns out, “dark” might mean “completely absorbs light.” Which is the opposite! Who knew? That’s why I prefer calling it “smooth tension,” which sounds more Barry White than Public Enemy.

What I would really like to get rid of is any discussion of “negative pressure.” The important thing about dark energy is that it’s persistent — the density (energy per cubic centimeter) remains roughly constant, even as the universe expands. Therefore, according to general relativity, it imparts a perpetual impulse to the expansion of the universe, not one that gradually dilutes away. A constant density leads to a constant expansion rate, which means that the time it takes the universe to double in size is a constant. But if the universe doubles in size every ten billion years or so, what we see is distant galaxies acceleratating away — first they are X parsecs away, then they are 2X parsecs away, then 4X parsecs away, then 8X, etc. The distance grows faster and faster, which we observe as acceleration.

That all makes a sort of sense, and never once did we mention “negative pressure.” But it’s nevertheless true that, in general relativity, there is a relationship between the pressure of a substance and the rate at which its density dilutes away as the universe expands: the more (positive) pressure, the faster it dilutes away. To indulge in a bit of equationry, imagine that the energy density dilutes away as a function of the scale factor as R-n. So for matter, whose density just goes down as the volume goes up, n=3. For a cosmological constant, which doesn’t dilute away at all, n=0. Now let’s call the ratio of the pressure to the density w, so that matter (which has no pressure) has w=0 and the cosmological constant (with pressure equal and opposite to its density) has w=-1. In fact, there is a perfectly lockstep relation between the two quantities:

n = 3(w + 1).

Measuring, or putting limits on, one quantity is precisely equivalent to the other; it’s just a matter of your own preferences how you might want to cast your results.

To me, the parameter n describing how the density evolves is easy to understand and has a straightforward relationship to how the universe expands, which is what we are actually measuring. The parameter w describing the relationship of pressure to energy density is a bit abstract. Certainly, if you haven’t studied general relativity, it’s not at all clear why the pressure should have anything to do with how the universe expands. (Although it does, of course; we’re not debating right and wrong, just how to most clearly translate the physics into English.) But talking about negative pressure is a quick and dirty way to convey the illusion of understanding. The usual legerdemain goes like this: “Gravity feels both energy density and pressure. So negative pressure is kind of like anti-gravity, pushing things apart rather than pulling them together.” Which is completely true, as far as it goes. But if you think about it just a little bit, you start asking what the effect of a “negative pressure” should really be. Doesn’t ordinary positive pressure, after all, tend to push things apart? So shouldn’t negative pressure pull them together? Then you have to apologize and explain that the actual force of this negative pressure can’t be felt at all, since it’s equal in magnitude in every direction, and it’s only the indirect gravitational effect of the negative pressure that is being measured. All true, but not nearly as enlightening as leaving the concept behind altogether.

But I fear we are stuck with it. Cosmologists talk about negative pressure and w all the time, even though it’s confusing and ultimately not what we are measuring anyway. Once I put into motion my nefarious scheme to overthrow the scientific establishment and have myself crowned Emperor of Cosmology, rest assured that instituting a sensible system of nomenclature will be one of my very first acts as sovereign.

A Dark, Misleading Force Read More »

326 Comments

Presidential Science Debate

Chris Mooney and Sheril Kirshenbaum of The Intersection have joined forces with Matthew Chapman have put together a call to have a 2008 Presidential debate devoted to science.

sciencedebate2008.jpg

Here is their statement:

Given the many urgent scientific and technological challenges facing America and the rest of the world, the increasing need for accurate scientific information in political decision making, and the vital role scientific innovation plays in spurring economic growth and competitiveness, we call for a public debate in which the U.S. presidential candidates share their views on the issues of The Environment, Health and Medicine, and Science and Technology Policy.

Just click here to get involved. The only downside I can see is that the Republican candidate will express skepticism about evolution, global warming, and heliocentrism, and the world’s image of the U.S. will plummet even further.

Presidential Science Debate Read More »

5 Comments

Dating Your Food Before You Marry It

05entr1901.jpg The New York Times (via Marginal Revolution) reports on what I hope does become a trend: the diminution of the role of the entree in American restaurant cuisine. That is, what Americans call an entree, which is really the main course. The French, who apparently invented the concept of the main course (plat principal) (and who would think that something like that needed to be “invented”?), use the word “entree” to mean what you might guess, namely a starter. But Americans like to be different.

Anyway, apparently the concept of the main course dominated by a single large item is, in advanced food circles, losing ground to the increasing popularity of smaller plates. From the consumer’s point of view, it just makes perfect sense — isn’t it more fun to design your own dinner from a variety of options, than to have the kitchen make all those choices for you? And isn’t it more interesting to sample several different options, than to focus on a single oversized dish? Takami, my favorite new local restaurant, features not only small plates, but dishes from three different kitchens with different specialties (sushi, robata, and everything else). If you savor the meal as a multi-level sensory experience rather than a obligatory intake of calories, it’s definitely the way to go.

Small plates mean extra work for the restaurant, of course — customization on the consumer side works against standardization and economy of scale on the producer side. So I doubt that the trend will soon be penetrating to the Bennigans and Applebees of the world. I suspect the true food snobs wouldn’t have it any other way.

Dating Your Food Before You Marry It Read More »

25 Comments

Arrow of Time FAQ

The arrow of time is hot, baby. I talk about it incessantly, of course, but the buzz is growing. There was a conference in New York, and subtle pulses are chasing around the lower levels of the science-media establishment, preparatory to a full-blown explosion into popular consciousness. I’ve been ahead of my time, as usual.

So, notwithstanding the fact that I’ve disquisitioned about this a great length and considerable frequency, I thought it would be useful to collect the salient points into a single FAQ. My interest is less in pushing my own favorite answers to these questions, so much as setting out the problem that physicists and cosmologists are going to have to somehow address if they want to say they understand how the universe works. (I will stick to more or less conventional physics throughout, even if not everything I say is accepted by everyone. That’s just because they haven’t thought things through.)

Without further ado:

What is the arrow of time?

The past is different from the future. One of the most obvious features of the macroscopic world is irreversibility: heat doesn’t flow spontaneously from cold objects to hot ones, we can turn eggs into omelets but not omelets into eggs, ice cubes melt in warm water but glasses of water don’t spontaneously give rise to ice cubes. These irreversibilities are summarized by the Second Law of Thermodynamics: the entropy of a closed system will (practically) never decrease into the future.

But entropy decreases all the time; we can freeze water to make ice cubes, after all.

Not all systems are closed. The Second Law doesn’t forbid decreases in entropy in open systems, nor is it in any way incompatible with evolution or complexity or any such thing.

So what’s the big deal?

In contrast to the macroscopic universe, the microscopic laws of physics that purportedly underlie its behavior are perfectly reversible. (More rigorously, for every allowed process there exists a time-reversed process that is also allowed, obtained by switching parity and exchanging particles for antiparticles — the CPT Theorem.) The puzzle is to reconcile microscopic reversibility with macroscopic irreversibility.

And how do we reconcile them?

The observed macroscopic irreversibility is not a consequence of the fundamental laws of physics, it’s a consequence of the particular configuration in which the universe finds itself. In particular, the unusual low-entropy conditions in the very early universe, near the Big Bang. Understanding the arrow of time is a matter of understanding the origin of the universe.

Wasn’t this all figured out over a century ago?

Not exactly. In the late 19th century, Boltzmann and Gibbs figured out what entropy really is: it’s a measure of the number of individual microscopic states that are macroscopically indistinguishable. An omelet is higher entropy than an egg because there are more ways to re-arrange its atoms while keeping it indisputably an omelet, than there are for the egg. That provides half of the explanation for the Second Law: entropy tends to increase because there are more ways to be high entropy than low entropy. The other half of the question still remains: why was the entropy ever low in the first place?

Is the origin of the Second Law really cosmological? We never talked about the early universe back when I took thermodynamics.

Trust me, it is. Of course you don’t need to appeal to cosmology to use the Second Law, or even to “derive” it under some reasonable-sounding assumptions. However, those reasonable-sounding assumptions are typically not true of the real world. Using only time-symmetric laws of physics, you can’t derive time-asymmetric macroscopic behavior (as pointed out in the “reversibility objections” of Lohschmidt and Zermelo back in the time of Boltzmann and Gibbs); every trajectory is precisely as likely as its time-reverse, so there can’t be any overall preference for one direction of time over the other. The usual “derivations” of the second law, if taken at face value, could equally well be used to predict that the entropy must be higher in the past — an inevitable answer, if one has recourse only to reversible dynamics. But the entropy was lower in the past, and to understand that empirical feature of the universe we have to think about cosmology.

Does inflation explain the low entropy of the early universe?

Not by itself, no. To get inflation to start requires even lower-entropy initial conditions than those implied by the conventional Big Bang model. Inflation just makes the problem harder.

Does that mean that inflation is wrong?

Not necessarily. Inflation is an attractive mechanism for generating primordial cosmological perturbations, and provides a way to dynamically create a huge number of particles from a small region of space. The question is simply, why did inflation ever start? Rather than removing the need for a sensible theory of initial conditions, inflation makes the need even more urgent.

Arrow of Time FAQ Read More »

161 Comments

Mike Huckabee is a Funny Guy

Former Arkansas governor Mike Huckabee is enjoying a late surge in the polls for the Republican nomination, especially in the crucial early caucus state of Iowa. Part of his appeal is a sense of humor, as evidenced by this clever appropriation of the Chuck Norris Facts meme:

Chuck Norris, in addition to his considerable thespian credentials, is a proud creationist who wants the Bible taught in public schools. So it is not surprising to find Mike Huckabee denying the reality of evolution during a televised debate.

But this video, while also quite funny, is pretty scary. Via Cynical-C, it’s a 2004 speech to the Republican Governors’ Association.

A phone call from God! Quite the thigh-slapper. Huckabee artfully includes an assurance that God doesn’t take side during elections — although we all know his preferences, apparently.

I understand that it’s a joke. But there are moments of solemnity during the “phone call,” when Huckabee is being perfectly serious. One of those is at the 2:00 mark, where we are reminded that the President talks to God. And then we receive a list of instructions, including “protecting marriage.” (It needs to be protected from The Gays, for those who don’t have your decoder rings.) George W. Bush himself has occasionally mentioned talking to God, although usually in private meetings where it’s difficult to get objective verification, and admittedly his theology is somewhat unsystematic.

A lot of people who don’t really believe in the old-fashioned supernatural nevertheless think it’s a good idea to appropriate spiritual terminology for their own uses — re-defining “faith” as “any hypothesis that has not yet been proven,” or “God” as “the warm feeling I get when contemplating the universe,” or “religion” as “a nice kind of social club that brings people together to reinforce each other’s goodness.” It’s not a good idea. These are words, and they have meanings when you say them — people think they know what you have in mind. When you say “God,” most people think of the dictionary definition — “the one Supreme Being, the creator and ruler of the universe.” They’re not thinking of “the laws of nature.” And they honestly believe in this dictionary-definition God. And they let that belief affect, or at least justify, how they govern the country. Shouldn’t every non-religious person be deeply alarmed about this state of affairs?

At the Beyond Belief II conference, Stuart Kauffman gave an interesting (although flawed, I thought) talk about complexity and reductionism, and then ruined the whole thing by suggesting at the end that we should re-define “the sacred” as something arising from the radical contingency of the empirical path of biological evolution. Or something like that, it was a bit vague. What an abysmally bad idea. If you want to choose a word that refers to something other than the traditional religious conception of supreme beings and all that, then don’t use religious language. Because there are other people out there — far vaster in number than you — that are using those same words to mean exactly what they straightforwardly denote: a supernatural power with a vested interest in smiting the wicked, especially boys and girls who fall in love with boys and girls, respectively. And they’re running this country at the moment, and their beliefs are enacted into policy.

Of course, arguing with Mike Huckabee and his friends runs the risk that Chuck Norris will come along and kick your ass. That’s just the chance we have to take.

Mike Huckabee is a Funny Guy Read More »

96 Comments

The Rain Stick

By Seamus Heaney.

Up-end the rain stick and what happens next
Is a music that you never would have known
To listen for. In a cactus stalk

Downpour, sluice-rash, spillage and backwash
Come flowing through. You stand there like a pipe
Being played by water, you shake it again lightly

And diminuendo runs through all its scales
Like a gutter stopping trickling. And now here comes
a sprinkle of drops out of the freshened leaves,

Then subtle little wets off grass and daisies;
Then glitter-drizzle, almost-breaths of air.
Up-end the stick again. What happens next

Is undiminished for having happened once,
Twice, ten, a thousand time before.
Who care if all the music that transpires

Is the fall of grit or dry seeds through a cactus?
You are like a rich man entering heaven
Through the ear of a raindrop. Listen now again.

For those wishing a more literal interpretation, here is what YouTube can teach you about the rain stick.

The Rain Stick Read More »

9 Comments

Things Happen, Not Always for a Reason

Two stories, superficially unrelated, neatly tied together by a deep lesson at the end.

The first is the case of Lucia de Berk, a Dutch nurse sentenced to life imprisonment in 2003 for multiple murders of patients under her care. However, there was very little direct evidence tying her specifically to the deaths of the individual cases. Much of the prosecution’s case against her was statistical: it was simply extremely unlikely, they argued, that so many patients would die under the care of a single nurse. Numbers like “one in 342 million chance” were bandied about.

But statistics can be tricky. Dutch mathematician Richard Gill has gone over the reasoning presented in the case, and found it utterly wrong-headed; he has organized a petition asking Dutch courts to re-open the case. Gill estimates that 1 in 9 nurses would experience a similar concentration of incidents during their shifts. And he notes that there were a total of six deaths in the ward where de Berk worked during the three years she was there, and seven deaths in the same ward during the three years before she arrived. Usually, the arrival of serial killers does not cause the mortality rate to decrease.

But patients had died, some of them young children, and someone had to be responsible. Incidents that had originally been classified as completely natural were re-examined and judged to be suspicious, after the investigation into de Berk’s activities started. The worst kinds of confirmation bias were in evidence. Here is a picture of what de Berk actually looks like, along with a courtroom caricature published in the newspapers.

          445254a-i30.jpg                     1045d-1-thumb.gif

Also, she read Tarot cards. Clearly, this is a woman who is witch-like and evil, and deserved to be punished.

The other story involves a brilliant piece of psychological insight from Peter Sagal’s The Book of Vice, previously lauded in these pages. It involves the reason why people play slot machines, or gamble more generally. There are many complicated factors that go into such a phenomenon, of course, but it nevertheless remains a deep puzzle why people would find it so compelling to roll the dice when everyone knows the odds are against you.

Peter asks us to consider the following joke:

An old man goes to the synagogue and prays, every day, thusly: “God, let me win the lottery. Please, just one big win. I’ll give money to the poor, and live a righteous life. . . . Please, let me win the lottery!”

For years, he comes to the synagogue, and the same prayer goes up: “Let me win the lottery! Please, Lord, won’t you show your grace, and let me win the lottery!”

Finally, one day, after fifteen years of this, as the man mutters, “The lottery, Lord, let me win the lottery. . . ,” a golden light suffuses the sanctuary, and a chorus of angels singing a major C chord is heard. The man looks up, tears in his blinded eyes, and says, “Lord . . . ?”

And a deep resonant voice rings out, “Please . . . would you please BUY A TICKET already?”

And that’s why we gamble: so God can answer our prayers. Fortune’s wheel, in other words, might occasionally want to favor us, but how can it if we don’t give it a chance? By playing the slots, we make it so much easier for Providence to bestow its bounty upon our deserving heads.

The common thread, of course, is the deep-seated aversion that human beings have to accepting randomness in the universe. We are great pattern-recognizers, even when patterns aren’t really there. Conversely, we are really bad at accepting that unlikely things will occasionally happen, if we wait long enough. When people are asked to write down a “random” sequence of coin flips, the mistake they inevitably make is not to include enough long sequences of the same result.

Human beings don’t want to accept radical contingency. They want things to have explanations, even the laws of physics. They want life to have a purpose, chance events to have meaning, and children’s deaths to have a person to blame. They want life to make sense, and they want to hit the triple jackpot because they’ve been through a lot of suffering and they damn well deserve it.

Of course, sometimes things do happen for a reason. And sometimes they don’t. That’s life here at the edge of chaos, and I for one enjoy the ride.

Things Happen, Not Always for a Reason Read More »

55 Comments

Turtles Much of the Way Down

Paul Davies has published an Op-Ed in the New York Times, about science and faith. Edge has put together a set of responses — by Jerry Coyne, Nathan Myhrvold, Lawrence Krauss, Scott Atran, Jeremy Bernstein, and me, so that’s some pretty lofty company I’m hob-nobbing with. Astonishingly, bloggers have also weighed in: among my regular reads, we find responses from Dr. Free-Ride, PZ, and The Quantum Pontiff. (Bloggers have much more colorful monikers than respectable folk.) Peter Woit blames string theory.

I post about this only with some reluctance, as I fear the resulting conversation is very likely to lower the average wisdom of the human race. Davies manages to hit a number of hot buttons right up front — claiming that both science and religion rely on faith (I don’t think there is any useful definition of the word “faith” in which that is true), and mentioning in passing something vague about the multiverse. All of which obscures what I think is his real point, which only pokes through clearly at the end — a claim to the effect that the laws of nature themselves require an explanation, and that explanation can’t come from the outside.

Personally I find this claim either vacuous or incorrect. Does it mean that the laws of physics are somehow inevitable? I don’t think that they are, and if they were I don’t think it would count as much of an “explanation,” but your mileage may vary. More importantly, we just don’t have the right to make deep proclamations about the laws of nature ahead of time — it’s our job to figure out what they are, and then deal with it. Maybe they come along with some self-justifying “explanation,” maybe they don’t. Maybe they’re totally random. We will hopefully discover the answer by doing science, but we won’t make progress by setting down demands ahead of time.

So I don’t know what it could possibly mean, and that’s what I argued in my response. Paul very kindly emailed me after reading my piece, and — not to be too ungenerous about it, I hope — suggested that I would have to read his book.

My piece is below the fold. The Edge discussion is interesting, too. But if you feel your IQ being lowered by long paragraphs on the nature of “faith” that don’t ever quite bother to give precise definitions and stick to them, don’t blame me.

Turtles Much of the Way Down Read More »

110 Comments

Update: Lemaitre vs. Hubble

We’ve previously celebrated Father Georges-Henri Lemaitre on this very blog, for taking seriously the idea of the Big Bang. His name has come up again in the post expressing thanks for Hubble’s Law — several commenters, including John Farrell, who wrote the book and should know — mentioned that it was actually Lemaitre, not Hubble, who first derived the law. That offered me a chance to haughtily dismiss these folks as being unable to distinguish between a theoretical prediction (Lemaitre was one of the first to understand the equations governing relativistic cosmology) and an observational discovery. But it turns out that Lemaitre did actually look at the data! Shows you how much you should listen to me.

I received an email from Albert Bosma that cleared up the issue a bit. Indeed, it was not just a theoretical prediction (as I had wrongly presumed) — Lemaitre definitely used data to estimate Hubble’s constant in a 1927 paper. He obtained a value of about 625 km/sec/Mpc, not too different from Hubble’s ultimate value. Of course, Lemaitre’s paper was in French, so it might as well be in Martian. Arthur Eddington translated the paper for the Monthly Notices of the Royal Astronomical Society, in 1931, but left out the (one-sentence) discussion of the data!

Here is a slide from Albert containing the original paragraphs. Click for a larger version, and you can compare the French to the English. Thanks to Albert for sending it along.

lemaitre-hubble.jpg

However — Lemaitre didn’t have very good data (and what he did was partly from Hubble, I gather). And for whatever reason, he did not plot velocity vs. distance. Instead, he seems to have taken the average velocity (which was known since the work of Vesto Slipher to be nonzero) and divided by some estimated average distance! If Hubble’s Law — the linear relation between velocity and distance — is true, that will correctly get you Hubble’s constant, but it’s definitely not enough to establish Hubble’s Law. If you have derived the law theoretically from the principles of general relativity applied to an expanding universe, and are convinced you are correct, maybe all you care about is fixing the value of the one free parameter in your model. But I think it’s still correct to say that credit for Hubble’s Law goes to Hubble — although it’s equally correct to remind people of the crucial role that Lemaitre played in the development of modern cosmology.

Further update: Albert has now sent me more snippets from Lemaitre’s original paper (one, two, three), and the English translation. (All jpg images.)

Update: Lemaitre vs. Hubble Read More »

11 Comments

Thanksgiving

Last year we gave thanks for the Lagrangian of the Standard Model of Particle Physics. This year, we give thanks for Hubble’s Law, the linear relationship between velocity and distance of faraway galaxies:

v = H0 d.

(We could be sticklers and call it the “effective velocity as inferred from the cosmological redshift,” but it’s a holiday and we’re in an expansive mood.) Here is the original plot, from Hubble 1929:

Hubble’s Law

And here is a modern version, from Riess, Press and Kirshner 1996 (figure from Ned Wright’s cosmology tutorial):

Hubble’s Law (recent supernovae)

Note that Hubble’s distance scale goes out to about two million parsecs, whereas the modern one goes out to 500 million parsecs. Note also that Hubble mis-labeled the vertical axis, expressing velocity in units of kilometers, but he discovered the expansion of the universe so we can forgive him. And yes, the link above is to Hubble’s original paper in the Proceedings of the National Academy of Sciences. Only 146 citations! He’d never get tenure these days. (Over 1000 citations for Freedman et al., the final paper from the Hubble Key Project to measure H0.)

Hubble was helped along in his investigations by Milton Humason; together they wrote a longer follow-up paper. (Some habits don’t change.) Here is a sobering sentence from an article about Humason: “During the period from 1930 until his retirement in 1957, he measured the velocities of 620 galaxies.” These days projects measure millions of velocities. So let’s give thanks for better telescopes, CCD cameras, and software, while we’re at it.

Hubble’s Law is an empirical fact about photons we receive in our telescopes, but it’s implications are profound: the universe is expanding. This discovery marks a seismic shift in how we think about the cosmos, as profound as the Copernican displacement away from the center. It was so important, Einstein felt the need to visit Hubble on Mt. Wilson and check that he wasn’t making any mistakes.

Einstein and Hubble

Thanksgiving Read More »

40 Comments
Scroll to Top