The Modern-day Olbers’ Paradox
Olbers’ Paradox of old was used to argue against the hypothesis that the universe had infinitely many stars, was infinitely old, and was spatially static. If there were infinitely many stars and the distance between them and the earth had remained the same for an infinite length of time, then every line of sight from earth would terminate on a star, and the night sky should be completely lit up. Now we know that the universe is not infinitely old and is expanding, so it is not a paradox.
A modern paradox was suggested by Murray Gell-Mann and James Hartle against Thomas Gold’s idea that, in keeping with the temporal symmetry of physical laws, entropy would decrease and electromagnetic processes will reverse themselves as the universe contracted to a Big Crunch. For some reason, all the explanations I’ve seen of this paradox have been unclear and sometimes outright misleading, so I will attempt to explain this to myself as clearly as possible to forestall further confusion.
In the diagram below (lifted from Huw Price’s book), the variable x represents the direction of time, where from our point of view +x is the future and -x is the past (damn notation, I keep typing t for time instead). Let the origin, O, be the “turning point” at which the universe stops expanding and starts contracting. Our present epoch is somewhere at a point on the negative side of the axis, say x=-a.
At -a, stars are emitting radiation towards the future (from our point of view). Given the reasonable assumption that the universe is mostly transparent to radiation, a good proportion of this radiation will reach the final singularity without being absorbed. Since, in a Gold universe, such large-scale entropic trends are time-symmetric, if a large amount of radiation is absorbed at the Big Crunch, there must be a matching amount of radiation that is emitted from the Big Bang. Generalising to all radiation that is emitted at all times x≤0 that is not absorbed by any matter by the time of the Big Crunch, there must be an enormous amount of matching radiation emitted by the Big Bang, so the night sky should appear bright. Since it doesn’t, Gold is wrong.
Now on to Price’s response (which he repeats in this paper). He questions if the light that, by a symmetric argument, supposedly reaches our eyes from the Big Bang, actually can reach our eyes. He imagines an observer (the eye) at O. Light from the “reverse galaxy” at x, which is the temporal inverse of a normal galaxy at -x, falls upon the blind “back” of the eye, that is, the side facing the future (human eyes, of course, can only see the past). The temporal inverse of this phenomenon would be the normal galaxy at -x emitting radiation that hits the “front” of the eye. Price, however, thinks this cannot happen, since if the light from the reverse galaxy hits the back of the eye, then it never reaches -x. Since its final destination is only the back of the eye, the temporal inverse of that is radiation being emitted from the back of the eye, which naturally cannot be seen by the eye, so although there is a lot of extra radiation bouncing about the universe, we never see it.
I must confess I have no idea how the light from the reverse galaxy hitting the back of the eye shows anything like that. Surely, all that suffices for Gell-Mann and Hartle’s argument to work is that there is radiation emitted from the Big Crunch (in the reverse time sense), and that this radiation does not run into any matter before it hits the point a. Then the temporal inverse of that will be an emission of radiation from the Big Bang, in the normal time sense, which does not run into any matter before it reaches -a, where the front of our eye is, and we can observe it. In short, I don’t see at all how Price comes to the conclusion that
When we look toward -x, looking for the radiation converging on the reverse galaxy at +x, then the relevant part of the radiation doesn’t come from the sky in the direction -x at all; it comes from the surface at the origin which faces +x — that is, from the back of our own head!
Granted, given that we are in the first half of the universe, and radiation from the Big Crunch hits the back of our eye, there will, I suppose, be a corresponding reverse process of radiation being emitted from the back of our eye and travelling towards the Big Crunch. But that’s in addition to there being a reverse process of radiation emitted from the Big Bang to match the radiation emitted from the Big Crunch, and this process is all that is needed for us to be able to see the extra radiation. Interestingly, the reverse process that Price seems to refer to, ignoring the other more obvious reverse process that I think is what Gell-Mann and Hartle are arguing for, will itself lead to further absorption of radiation at the Big Crunch and hence further emission from the Big Bang, and so on in a possibly infinite multiplier effect. Paul Davies mentions this runaway amplification briefly in this paper.
I find it hard to believe Price could have overlooked that obvious point, so I wouldn’t be surprised if I’ve horribly misinterpreted his argument.
March 30, 2007 at 3:17 pm
[...] There’s more out there, too: see, for example, this post discussing the much-storied Bayesian theorem and connections to Bell’s inequalities, or this post on ‘biophysical economics’, an economic theory rooted in biological and physical realities first put forth in the 20’s. Something that struck me as being particularly interesting was this post on the use of evolutionary algorithms in lattice QCD simulations. Meanwhile, Ponder Stibbons has been plowing through Huw Price’s book (Time’s Arrow and Archimedes’ Point) on some of the more philosophical questions of physics, with posts on Price’s objection to dynamical explanations of entropy increase (”they can never account for the asymmetry in our observations unless they themselves have asymmetric assumptions”
and a modern-day version of Olbers’ paradox. [...]
March 31, 2007 at 2:22 pm
I claim that Olber’s Paradox never was a paradox. It is based on a misunderstanding. At the time it was promulgated very little was known about cosmology. Nobody had any idea about galaxies external to the Milky Way. The distribution of stars that we observe from the earth is skewed by the fact that we are immersed in our own galaxy. Olber’s Paradox assumes that this distrubution is endemic to the entire Universe. Palpably false as we now know. Look at Hubble’s photographs of the most distant galaxies; plenty of empty space between galaxies - that has nothing to do with the expansion of the Universe.
Good example of how hard it is to eradicate a false idea once it gets traction.
April 9, 2007 at 10:48 pm
I don’t think it need assume the distribution of stars in our galaxy is endemic to the entire universe. Olbers’ Paradox was formulated as a response to those who thought the universe contained infinitely many stars. Unless all these stars lined themselves up along discrete rays emanating from the earth, if there were infinitely many stars, then every line of sight from earth would terminate on a star.
April 10, 2007 at 12:48 am
[...] Confusion in Gell-Mann and Hartle’s Olbers’ Paradox I finally found out where I misunderstood Huw Price’s argument against Gell-Mann and Hartle’s argument against the Gold universe. [...]