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:
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 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.
According to an article in this week’s New Scientist, the cosmological horizon is currently at a distance of 43 billion light years which, as it predates the Big Bang, is presumably fictitious or virtual in some sense.
But if cosmic expansion keeps accelerating, so that the cosmological horizon shrinks, is there likely to be any change in the character of cosmic expansion if/when the cosmological horizon falls below 13 billion years so that the Big Bang is no longer “visible”?
Observational astronomy has a rich history that must be respected. These astronomers documented reality and today, we are trying to learn how to understand what they actually observed.
Today’s cosmology, is often a form of mental masturbation.
Relative to us, parts of the universe with a huge doppler redshift far back in time near the BB are not only receding at velocities near the speed of light; their mass is, by relativity, much greater.
I’m not at all convinced, especially since we now know that the universal expansion is accelerating, that this Hubble relationship really is linear, considering our limits of accuracy in measurement. Time dilation function is a pretty straight line until we are pretty close to the speed of light.
We are dealing with relativistic relationships when are talking this distant aspect of astronomy. The simple linear relationship which Hubble proposed may not be quite so simple- or linear 13BLY out.
Yes that paper was a hoot! Notice the date and the co-author Ali Frolop = April Fool!
Garth
Sean mentioned the coincidence of the almost exact apparent size of the sun and moon in the sky, as viewed from the surface of the Earth. The shadow of the moon on the Earth at totality is no more than about 200 miles wide. Sometimes no umbra strikes the Earth.
I did a few quick calculations using the measured angular diameter of the Moon and Sun in the sky at the apogee and perogee of appropriate orbits, and a guestimate of a rate of withdrawl of the moon from the Earth of 4 CM per year, and came up with numbers indicating it would take a full billion years for total solar eclipses to be eliminated. It seemed to me like an unbelievably long period of time for this trivial cosmic coincidence to be eliminated.
I checked with NASA and they told me that taking the increase in the size of the Suns disc into consideration and using a correct 3 CM annual withdrawl rate for the Moon, it would take a bit less than 600,000.000 years for total solar eclipses to be eliminated….a pretty stable coincidence indeed.
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Neil B: the “hard” spheres would lead to a large positive pressure
which would cause the contraction to go faster. This seems
paradoxical but recall that objects are accelerated by
pressure gradients, not by a uniform pressure, and that both
pressure and density contribute with negative signs to the
second derivative of the scale factor. So to slow down a contraction,
which would be a positive second derivative for the scale factor,
one needs a large negative pressure.
Garth: H_o*t_o is not equal to 1 with an accuracy of 0.6%.
t_o is known (but model dependent) to 1% and H_o (also
model dependent) to 4%. So while the product is very close to 1, the propagated uncertainy is 4%.
Sean: I read Luminet’s review (pointed out by Daniel Fischer)
and it makes the point that Le Maitre’s little cited 1927 paper
in French to the Belgian Academy actually did the data analysis
and derived the Hubble constant two years before Hubble. Then
Luminet didn’t list this paper in his reference list! I wish
this 1927 paper were in the ADS, but last time I checked only
the translation in the 1931 MNRAS was there.
Hi Sean —
The discovery of the Hubble expansion was indeed a profound advance. But there’s even more to it than that, as you well know, so let me point out for your readers:
1. The pattern of Hubble’s law, that the recessional velocity of distant galaxies is proportional to their distance away, directly implies that contemporary observers on any galaxy will see the same pattern, and with the same proportionality. Thus the Hubble law contains the idea that the expansion has no preferred center.
2. If we extrapolate the Hubble-law motions of the galaxies backward, assuming no acceleration (a not entirely unreasonable thing to do), we discover that there was a singular moment at a finite time into the past when they were all on top of each other. So Hubble’s law also raises directly the idea of a Universe with finite age.
Hubble could/would have declared an expanding Universe based on any observation of velocity going up monotonically with distance. It is the special linear result v=Hd that also leads to the also profound picture of a uniform expansion with a finite history. It all came in the same package! as long ago as 1930, for which we can indeed be thankful.
Cheers,
Paul
Yes Ned, although my post #22 was submitted before it was properly prepared (I have you Preview button on this Forum), I was simply using your Cosmology Calculator http://www.astro.ucla.edu/~wright/CosmoCalc.html,.
The present best accepted values of cosmological parameters
(using the table in WMAP Cosmological Parameters http://lambda.gsfc.nasa.gov/product/map/dr2/params/lcdm_all.cfm)
Ho = 70.4 km/sec/Mpsc
Omega_Lambda = 0.732
Omega_matter = 0.268
Feeding these values into your calculator I obtain:
The age of the universe is = 13.81 Gyrs.
But with h_100 = 0.704,
Hubble Time = 13.89 Gyrs. i.e. 0.6% difference!
In other words the calculated age turns out to be equal to Hubble Time to within the limits of the observational error of 4%.
Is this just a coincidence or is the universe trying to tell us something?
Garth
Hey folks, what about that “axis of evil” stuff etc? You can google for it … It looks like something preferred, but too early to tell what’s up.
As for hard spheres in the contracting universe: the point is, not how they affect the forces, but they are an obstruction – I don’t think they could be just pulverized as if nothing there. There are contradiction problems if you try to imagine what happens to all the bodies in expanding/contracting universes if some things are impeded by material barriers/obstructions and other things just move like dust in free fall.
I first saw that famous picture of Einstein at the telescope with Hubble looking on in high school, more years ago than I would care to discuss. Suffice it to say I saw that picture for the first time while Albert Einstein was still very much alive!
If anybody is into non-verbals, look at the expressions on Albert and Edwins faces!
A picture is truly worth 1,000 words!
I realize the picture was posed…for all we know it was taken in the daytime.
ABSTRACT: Don N. Page; December 13, 2007…last sentence…
“SQM also suggests the possibility that past steps along our evolutionary ancestry may be so rare, that they have occurred no where else in the past history of the universe that we can observe”.
It is almost certain that life in the universe is a common phenomenon. It is also almost impossible that beings identical to ourselves exist anywhere else. One does not have to be a quantum theorist to fathom that! However it is interesting that certain quantum theories point to such an obvious conclusion about our uniqueness in the universe.
For similar reasons, related to genetic inheritance and environmental upbringing, each human individual who has ever lived is also unique. Cloning people doesn’t produce robots, just individuals with identical genetic inheritance- as identical twins. However, no pair of identical twins live exactly identical lives.
This comment in Don’s abstract has profound implications…
Errata: See: “A Dark, Misleading Force” thread….
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