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 = H_{0}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:

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

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 *H*_{0}.)

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.

I call a caption contest on the Einstein picture.

Let me amend that, I call for a contest for the intertitle following this scene.

“Why indeed professor, it is true, Tesla has established a base on the moon!”

“He must have found Jules Vernes lost diaries, I shall telegraph immediately to call a gathering of the League!”

The way the universe expansion and deceleration (at least, before negative energy/cosmological constant) was very elegant when thinking of little particles on the surface of an expanding balloon, etc. However, I have always wondered about consistency problems if the universe is filled with hard balls and in a state of deceleration. What happens when the balls touch each other? They should crunch up a bit and just sit there, but then we have strange problems trying to apply the pseudoNewtonian approximation. For example, any point in the center of a ball can imagine that light propagating from itself loses energy traveling up through successive spheres of matter (the radii of which are always just wherever the photon is, since the stuff beyond that cancels out. So, the receiver should get a red shift, but the receiver could imagine himself at the bottom of the same self-defined spherical region etc. and expect a blue shift.

Then there’s the issue of what happens to little bodies inside bigger spheres: By simple extrapolation of the incoming motion of the little bodies as seen by any given observer, they should continue moving toward that central observer until the smack into the sides of whatever sphere they’re in. But again, this does not provide a consistent picture because it produces contradictory preferred central observers in every place.

Sure, GR is not Newtonian gravity, but then what would happen if our universe was filled with hard spheres with contents, sending light signals to each other, when the spheres scrunched together? I hope this is thought-provoking. “Problems” may deserve more thanks than anything else, since they stimulate science to grow.

“You’re right, Ed. That’s one hot babe on the 87th floor.”

OK, OK, You’re right, too crass. How ‘bout

“Dang! I can’t see the back of my head. I guess it’s not closed after all.”

Well, regarding problems with body surfaces stopping continued contraction: I already suspect that Doppler shift is going to continue to be based on relative scale factor, and presumably motion of contained particles would be correlated with that, etc. However, it starts getting sticky so to speak if a region of space has bodies clump together before the rest of space over a wide area does: then, to what extent and under what rules does such a local region act like an isolated Newtonian or small GR system (where the test bodies in the centers of larger spheres keep moving towards the extrapolated contraction point, grav Doppler shifts depend on local distributions of mass, etc. ) versus acting consistently with concepts properly applying in GR to “space as a whole”?

Oh, I meant to write: “… if the universe is filled with hard balls and in a state of contraction.” (Our universe is not going to reverse expansion and contract, due to current combination of factors such as Hubble “constant” and dark energy, but it is logically possible and “could have” turned out that way if this or that was different. In any case, this serves as a proper “what if” problem for general relativity as a theoretical construct.)

interesting post Sean. Is it also true that the rate of expansion is accelerating, and if so what can we draw from this?

Really enjoy the science stuff on this site, more of the same please whenever you have time! (i like the other stuff too)

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To borrow from the Simpsons:

“Wow… the universe is soooo… boring!”

Thank you Hubble for all. Expecially for your extremly linear law!

Humason’s story is itself quite interesting as his career path on Mt Wilson was mule driver, janitor, night assistant, observer, member of the scientific staff. It would be very difficult to do that today. If only because few observatories have entry-level mule-driving positions. Humason and Hubble measured most of those velocities with the 100-inch Hooker telescope on Mt. Wilson, which actually (by reputation) is/was a pretty good telescope. It is the same aperture as the SDSS 2.5-m telescope, in fact. The improvement comes mostly from vast increases in detector technology, sensitivity, and size. And a little bit from improvements in our abiliity to build spectrographs. Of course, we also need software to deal with the flood of data. And we’re also grateful for the invention of the off-axis TV guider.

Sean wrote, “we could be sticklers….”

That is *not* being a stickler. That is making an honest effort to avoid propagating one of the most basic misunderstandings in cosmology! And worse by far: it is missing an opportunity to enjoy something which is a lot of fun, namely the fact that [peculiar velocities apart] the distant galaxies are *not* moving away from us — they are just becoming more distant. Pythagoras’s theorem has a function of time in it! Surely that is much more fun than a boring old Newtonian expansion!

We could be even more ‘stickler’ and mention that Lemaitre actually derived Hubble’s Law two years before Hubble did.

But I’m no less thankful!

As usual it is forgotten that Lemaitre wrote down the “Hubble” law – in the same mathematical form – two years before Edwin did. A major

review recently explained this well – and highlighted the fact that “his papers remain desperately unquoted” …

Surely things have not gotten so bad that we’ve lost the ability to distinguish between a theoretical prediction and an observational discovery.

That’s because of all that ‘discovered’ DE and DM!

Garth

BTW: Just a reminder, that even without dark energy etc. the Hubble “constant” isn’t really a constant over cosmic time scales. For example, in a traditional just barely open universe (asymptotic deceleration to “v” = 0), the scale factor varies as t^(2/3), v(relative distance expansion) varies as t^(-1/3), and so Hubble factor varies as t^(-1).

Well, I was hoping to find at least some interest in the question about what happens if obstructive surfaces impede contraction of the universe (and the issue of things being tied together with elastic tethers is good too, in a case of expansion: what about the work done pulling on them, since outward forces pull in all directions?

The fact that the relationship is so obviously linear is profound…

What is interesting is the age of the universe, having allowed for the current best values of the density of matter (0.04), DM (0.23) and DE (0.73) is 13.81 Gyrs, and Hubble Time (the inverse of the H, with h = 0.704) is 13.89 Gyrs.

Is this too great a coincidence?

Garth

Always worth noting that Einstein initially predicted an expanding universe based on his GR thoery, but he felt this was so ridiculous that he introduced a “cosmological constant” into his equations. That issue is apparently still in play, however.

Here’s a nice picture of the Hubble redshift from calcium lines.

Garth, et al: isn’t the near equality of universe age and Hubble time a mark of the universe being so widely “open”? If it was instead an asymptopic just-open expansion, I think t(H) is 2/3 of the actual age, or is it the other way around, I keep forgetting. The really interesting thing, what is the time we get from taking the value of lambda, which has units a/r = 1/T^2, and thus taking lambda^(-1/2): IIRC and rough estimate it’s about the same as the age of the universe, right? But if lambda is really a constant, then a certain time after the BB is equal to that and therefore “special” – are we in it? See the discussion on dark energy etc. at Backreaction.

Neil, s grea

If the universe is flat with a total density parameter Omega = 1 then:

if there is no DE then the Age = 2/3 Hubble Time

if there is DE that reduces the rate of

thenthe Age > 2/3 Hubble Time, from that value up to infinity, depending on the amount and the exact equation of state of the DE.

As Omega = 1 it seems a suspicious coincidence that Age = Hubble Time to within +/- 0.6%, which is equal to within observational error.

GarthThe Moon and the Sun, as seen from the Earth, subtend the same angle in the sky. You are welcome to discern deep cosmic conspiracies underlying this fact if you like.

Agreed it could be just pure coincidence, but the Universe Age/Hubble Time coincidence is linked with the near equality to an OOM of the densities of baryonic matter (4%), non-baryonic Dark Matter (23%) and Dark Energy (73%).

Why should these be approximately equal?

The two coincidences are linked because it is the mix of DE/Matter that determines the age of the universe in terms of Hubble’s constant.

Garth

This has been discussed elsewhere:

http://arxiv.org/abs/astro-ph/0604011

One might want to do to read the stuff before the abstract though, … the paper did not quite manage to achieve what they had set out to do.