Author: Sean Carroll

[Update: Prof. Anderson was kind enough to reply in the comments.]

Another somewhat problematic response to Brockman’s World Question Center is given by Philip Anderson, one of the world’s leading condensed-matter theorists. Like fellow Nobel Laureate Robert Laughlin, Anderson takes a certain pleasure in tweaking the noses of his friends on the high-energy/astrophysics side of the department. We can all use a little tweaking now and then, but must be expected to get tweaked back in return.

Anderson talks about dark matter and dark energy; his piece is short enough that we can go through the whole thing.

Dark Energy might not exist

I hope this idea isn’t too dangerous, by the way, since certain of your favorite bloggers have been quite active in this area. Overall, one gets the impression in the World Question Center that these folks somewhat overestimate how dangerous they are really being.

Let’s try one in cosmology. The universe contains at least 3 and perhaps 4 very different kinds of matter, whose origins probably are physically completely different. There is the Cosmic Background Radiation (CBR) which is photons from the later parts of the Big Bang but is actually the residue of all the kinds of radiation that were in the Bang, like flavored hadrons and mesons which have annihilated and become photons. You can count them and they tell you pretty well how many quanta of radiation there were in the beginning; and observation tells us that they were pretty uniformly distributed, in fact very, and still are.

All true, although the “you can count them” bit is a little confusing — I think the “them” he’s referring to is the photons. The basic idea is that the total number of photons hasn’t changed much since the extremely early universe, which is basically right; it may have increased by a factor of 100 or so during phase transitions when other stuff annihilates into photons, but by cosmological standards that’s not a big change.

Next is radiant matter — protons, mostly, and electrons.

I think by “radiant” he means “not the non-baryonic dark matter.” Neutrons would also count.

There are only a billionth as many of them as quanta of CBR, but as radiation in the Big Bang there were pretty much the same number, so all but one out of a billion combined with an antiparticle and annihilated. Nonetheless they are much heavier than the quanta of CBR, so they have, all told, much more mass, and have some cosmological effect on slowing down the Hubble expansion.

Not even “much” more mass — a factor of 10² or 10³, but okay, now we’re nit-picking.

There was an imbalance — but what caused that? That imbalance was generated by some totally independent process, possibly during the very turbulent inflationary era.

Yes; that’s baryogenesis. Maybe it happened during inflation; that’s not a leading candidate, but certainly a plausible one. So far, just a slightly idiosyncratic retelling of the conventional story.

In fact out to a tenth of the Hubble radius, which is as far as we can see, the protons are very non-uniformly distributed, in a fractal hierarchical clustering with things called “Great Walls” and giant near-voids. The conventional idea is that this is all caused by gravitational instability acting on tiny primeval fluctuations, and it barely could be, but in order to justify that you have to have another kind of matter.

Now we’re getting into a bit of trouble. This statement would have been perfectly reasonable, if somewhat alarmist, fifteen or so years ago. These days we know a lot more about the distribution of matter on very large scales, from the microwave background as well as large-scale structure surveys. It’s not a fractal in any interesting sense on very large scales; certainly the density fluctuations on those scales are quite tiny. And when he says “barely could be,” I think he means “fits the data remarkably well.” The Cold Dark Matter model has some issues with the structure of individual galaxies and clusters, but for the overall distribution it’s a fantastic fit.

So you need — and actually see, but indirectly — Dark Matter, which is 30 times as massive, overall, as protons but you can’t see anything but its gravitational effects. No one has much clue as to what it is but it seems to have to be assumed it is hadronic, otherwise why would it be anything as close as a factor 30 to the protons?

That’s just a mistake. “Hadronic” means “made of quarks”; almost nobody thinks the dark matter is hadronic, and in fact it would be extremely difficult to reconcile that idea with primordial nucleosynthesis. The fact that it’s close to the density of protons is certainly interesting, and we don’t know why.

But really, there is no reason at all to suppose its origin was related to the other two, you know only that if it’s massive quanta of any kind it is nowhere near as many as the CBR, and so most of them annihilated in the early stages. Again, we have no excuse for assuming that the imbalance in the Dark Matter was uniformly distributed primevally, even if the protons were, because we don’t know what it is.

I’m not sure what “no excuse” means. If he means “no data support the assumption,” that’s wrong; the idea that fluctuations are adiabatic (correlated fluctuations in dark matter, photons, and baryons) has been pretty well tested, and agrees with the CMB very well. There is some room for a bit of variation (known as “isocurvature perturbations”), but the limits are pretty constraining. Perhaps a real cosmologist could chime in. If he means “we have no idea why the distributions are correlated,” that’s also false; in the simplest models of inflation, it’s exactly what you would expect, as the energy density from the inflaton decays into everything with some fixed amplitudes. Again, there are ways around it, and we don’t know that inflation is correct, but it’s by no means inexplicable.

Finally, of course there is Dark Energy, that is if there is. On that we can’t even guess if it is quanta at all, but again we note that if it is it probably doesn’t add up in numbers to the CBR.

Well, we actually guess that it is not quanta (i.e., particles) — if it were, the number density of particles would presumably dilute away as the universe expands, decreasing the density of dark energy, which isn’t what we observe. The dark energy is nearly constant in density, which is why most people imagine that it’s vacuum energy or the potential of some very light field, not particle excitations.

The very strange coincidence is that when we add this in there isn’t any total gravitation at all, and the universe as a whole is flat, as it would be, incidentally, if all of the heavy parts were distributed everywhere according to some random, fractal distribution like that of the matter we can see — because on the largest scale, a fractal’s density extrapolates to zero.

This “very strange coincidence” is of course a prediction of inflation, that the universe is spatially flat. The bit about the random fractal distribution manages to somehow be simultaneously wrong and ill-defined. Again, we know what the distribution looks like on large scales, from CMB fluctuations, and it’s incredibly smooth. If it were wildly fluctuating, including on scales much larger than our Hubble radius, then most of the universe would have a large amount of spatial curvature — that’s certainly what we see in the local distribution. Not that it’s very clear what such a distribution would actually look like in general relativity.

That suggestion, implying that Dark Energy might not exist, is considered very dangerously radical.

Well, not so much “radical” as “incorrect.” Anderson doesn’t mention the fact that the universe is accelerating, which is curious, since that’s the best evidence for dark energy. His offhanded proposal that density fluctuations are somehow responsible is similar in spirit to the original proposal of Kolb, Matarrese, Notari, and Riotto, that ultra-large-scale inhomogeneities could mimic the effects of dark energy. Everyone now agrees that this idea doesn’t work, although the authors are trying again with small-scale fluctuations. While that hasn’t been cleanly ruled out, it’s a long shot at best; most folks agree that we either need dark energy, or somehow to modify gravity.

Anderson then goes on to argue against any particular conception of God, on the basis of Bayesian probability theory. I’m not a big God booster, but he probably didn’t run this idea by anyone in the Religious Studies department, any more than he ran his dark-energy ideas by any of the local cosmologists (I understand that Princeton has one or two). I think it’s great when smart people step outside their areas of expertise to make interesting suggestions about other fields (if I didn’t, the blogging thing would be kind of indefensible). But we shouldn’t forget that there are smart people in other parts of the university, and have some respect for their expertise. Or is that another one of those dangerous ideas?