Archive for August, 2013

It’s always a nervous moment when, as a scientist, you discover that a documentary has been made on one of your favourite topics. Science journalism is rather hit and miss. So it was when the Australian Broadcasting Corporation (ABC), our public TV network, aired a documentary about the fine-tuning of the universe for intelligent life as part of their Catalyst science series. (I’ve mentioned my fine-tuning review paper enough, haven’t I?).

The program can be watched on ABC iView. (International readers – does this work for you?). It was hosted by Dr Graham Phillips, who has a PhD in Astrophysics. The preview I saw last week was promising. All the right people’s heads were appearing – Sean Carroll, Brian Greene, Paul Davies, Leonard Susskind, Lawrence Krauss, Charley Lineweaver. John Wheeler even got a mention.

Overall – surprisingly OK. They got the basic science of fine-tuning correct. Phillips summarises fine-tuning as:

When scientists look far into the heavens or deeply down into the forces of nature, they see something deeply mysterious. If some of the laws that govern our cosmos were only slightly different, intelligent life simply couldn’t exist. It appears that the universe has been fine-tuned so that intelligent beings like you and me could be here.

Not bad, though I’m not sure why it needed to be accompanied by such ominous music. There is a possibility for misunderstanding, however. Fine-tuning is a technical term in physics that roughly means extreme sensitivity of some “output” to the “input”. For example, if some theory requires an unexplained coincidence between two free parameters, then the “fine-tuning” of the theory required to explain the data counts against that theory. “Fine-tuned” does not mean “chosen by an intelligent being” or “designed”. It’s a metaphor.

Ten minutes in, the only actual case of fine-tuning that had been mentioned was the existence of inhomogeneities in the early universe. Sean Carroll:

If the big bang had been completely smooth, it would just stay completely smooth and the history of the universe would be very, very boring. It would just get more and more dilute but you would never make stars, you would never make galaxies or clusters of galaxies. So the potential for interesting complex creatures like you and me would be there, but it would never actually come to pass. So we’re very glad that there was at least some fluctuation in the early universe.

Paul Davies then discussed the fact that there not only need to be such fluctuations, but they need to be not-too-big and not-too-small. Here’s the scientific paper, if you’re interested.

The documentary also has a cogent discussion of the cosmological constant problem – the “mother of all fine-tunings” – and the fine-tuning of the Higgs field, which is related to the hierarchy problem. Unfortunately, Phillips calls it “The God Particle” because “it gives substance to all nature’s other particles”. Groan.

Once we move beyond the science of fine-tuning, however, things get a bit more sketchy.

The Multiverse

Leonard Susskind opens the section on the multiverse by stating that the multiverse is, in his opinion, the only explanation available for the fine-tuning of the universe for intelligent life. At this point, both the defence and the prosecution could have done more.

Possibilities are cheap. Sean Carroll appears on screen to say “Aliens could have created our universe” and then is cut off. We are told that if we just suppose there is a multiverse, the problems of fine-tuning are solved. This isn’t the full story on two counts – the multiverse isn’t a mere possibility, and it doesn’t automatically solve the fine-tuning problem. (more…)

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The ABC’s opinion pages has posted my introduction to the debate between Lawrence Krauss and William Lane Craig, happening this evening at the Sydney Town Hall. The debate topic is “Why is there something rather than nothing?”. Can science answer the question? Can God? Can anyone? Read on.


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A commenter over at my post “Got a cosmology question?” asks:

Someone told me “there is not a single paper which finds fine tuning that has allowed multivariation”. Can you please refute this?

Incidentally, cosmology questions are still very welcome over there.

“Multivariation” is not a word, but in this context presumably means varying more than one variable at a time. There is an objection to fine-tuning that goes like this: all the fine-tuning cases involve varying one variable only, keeping all other variables fixed at their value in our universe, and then calculating the life-permitting range on that one variable. But, if you let more than one variable vary at a time, there turns out to be a range of life-permitting universes. So the universe is not fine-tuned for life.

This is a myth. The claim quoted by our questioner is totally wrong. The vast majority of fine-tuning/anthropic papers, from the very earliest papers in the 70’s until today, vary many parameters1. I’ve addressed these issues at length in my review paper. I’ll summarise some of that article here.

The very thing that started this whole field was physicists noting coincidences between the values of a number of different constants and the requirements for life. Carter’s classic 1974 paper “Large number coincidences and the anthropic principle in cosmology” notes that in order for the universe to have both radiative and convective stars we must have (in more modern notation to his equation 15, but it’s the same equation),

\alpha_G^{1/2} \approx \alpha^6 \beta^2

where, in Planck units, \alpha_G = m_{proton}^2\alpha = e^2\beta = m_{electron}/m_{proton}, and e is the charge on the electron. (Interestingly, Barrow and Tipler show that the same condition must hold for stars emit photons with the right energy to power chemical reactions e.g. photosynthesis.) Similarly for cosmological cases: for the universe to live long enough for stars to live and die, we must have,

|\kappa| \lesssim \left( \frac{\eta^2}{m_{proton}} \right)^{1/3} m_{proton}^3

where \kappa is related to the curvature of space and \eta is roughly the baryon to photon ratio.

This continues in the classic anthropic papers. Carr and Rees (1977) show that to have hydrogen to power stars left over from big bang nucleosynthesis, and to have supernovae distribute heavy elements, we must have (in Planck units, rearranging their equation 61),

m_{electron}^{-3/2} \sim g_w

where g_w is the weak coupling constant.

Barrow and Tipler’s “The Anthropic Cosmological Principle” shows that, for carbon and larger elements to be stable, we must have:

\alpha_s \lesssim 0.3 \alpha ^{1/2}

where \alpha_s is the strong force coupling constant (evaluated at m_Z, if you’re interested).

The whole point of these relations and more like them, which the early anthropic literature is entirely concerned with, is that they relate a number of different physical parameters. There are approximations in these calculations – they are order-of-magnitude – but this usually involves assuming that a dimensionless mathematical constant is approximately one. At most, a parameter may be assumed to be in a certain regime. For example, one may assume that \alpha and \beta are small (much less than one) in order to make an approximation (e.g. that the nucleus is much heavier than the electron, and the electron orbits non-relativistically). These approximations are entirely justified in an anthropic calculation, because we have other anthropic limits that are known to (not merely assumed to) involve one variable – e.g. if \beta is large, all solids are unstable to melting, and if \alpha is large then all atoms are unstable. See section 4.8 of my paper for more information and references.

More modern papers almost always vary many variables. Examples abound. Below is figure 2 from my paper, which shows Figures from Barr and Khan and Tegmark, Aguirre, Rees and Wilczek. (Seriously, people … Wilczek is a Nobel prize winning particle physicist and Martin Rees is the Astronomer Royal and former president of the Royal Society. These people know what they are doing.)

figure2 from my paperThe top two panels show the anthropic limits on the up-quark mass (x axis) and down-quark mass (y axis). 9 anthropic limits are shown. The life-permitting region is the green triangle in the top right plot. The lower two panels show cosmological limits on the cosmological constant (energy density) \rho_\Lambda, primordial inhomogeneity Q, and the matter density per CMB photon. Tegmark et al. derive from cosmology 8 anthropic constraints on the 7 dimensional parameter space (\alpha, \beta, m_{proton}, \rho_\Lambda, Q, \xi,\xi_{baryon}). Tegmark and Rees (1997) derive the following anthropic constraint on the primordial inhomogeneity Q:

equation for Q(1)

Needless to say, there is more than one variable being investigated here. For more examples, see Figures 6, 7 (from Hogan), 8 (from Jaffe et al.) and 9 (from Tegmark) of my paper. The reason that the plots above only show two parameters at a time is because your screen is two dimensional. The equations and calculations from which these plots are constructed take into account many more variables than can be plotted on two axes.

This myth may have started because, when fine-tuning is presented to lay audiences, it is often illustrated using one-parameter limits. Martin Rees, for example, does this in his excellent book “Just Six Numbers“. Rees knows that the limits involve more than one parameter – he derived many of those limits. But equation (1) above would be far too intimidating in a popular level book.

My paper lists about 200 publications relevant to the field. I can only think of a handful that only vary one parameter. The scientific literature does not simply vary one parameter at a time when investigating life-permitting universes. This is a myth, born of (at best) complete ignorance.


Postscript: The questioner’s discussion revolves around the article of Harnik, Kribs & Perez (2006) on a universe without weak interactions. It’s a very clever article. Their weakless universe requires “judicious parameter adjustment” and so is also fine-tuned. Remember that fine-tuning doesn’t claim that our universe is uniquely life-permitting, but rather that life-permitting universes are rare in the set of possible universe. Thus, the weakless universe is not a counterexample to fine-tuning. There are also concerns about galaxy formation and oxygen production. See the end of Section 4.8 of my paper for a discussion.


1. Even if fine-tuning calculations varied only one parameter, it wouldn’t follow that fine-tuning is false. Opening up more parameter space in which life can form will also open up more parameter space in which life cannot form. As Richard Dawkins (1986) rightly said: “however many ways there may be of being alive, it is certain that there are vastly more ways of being dead, or rather not alive.” For more, see section 4.2.2 of my paper.

More of my posts on fine-tuning are here.

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