Collins vs. Stenger

Robin Collins has written a paper responding to some criticisms Victor Stenger made of the Fine Tuning Argument.

Collins starts out by conceding to Stenger that many of the claimed fine tunings do not qualify  as such. He focuses on a few examples where he thinks Stenger's arguments fail, basing his argument on a close consideration of the physics involved. Collins is a philosopher but, according to his CV, did some grad work in physics.  Stenger is himself a physicist. Collins accuses Stenger of getting the physics wrong. So who's right?

For this post, I'm only going to consider their remarks about the relative strengths of the various physical forces. I haven't read Stenger's book, The Fallacy of Fine Tuning (FOFT), so I'm basing my comments on this paper and Collins's claims about FOFT. I also should make clear that I think the Fine Tuning Argument is a bad argument overall. But I think it might be worthwhile for me as another physicist to try to evaluate the physics part of these arguments.

On the strength of gravity, Stenger writes,

The reason gravity is so weak in atoms is the small masses of elementary particles. This can be understood to be a consequence of the standard model of elementary particles in which the bare particles all have zero masses and pick up small corrections by their interactions with other particles.

Collins responds,

Although correct, Stenger’s claim does not explain the fine-tuning but merely transfers it elsewhere. The new issue is why the corrections are so small compared to the Planck scale. Such small corrections seem to require an enormous degree of fine-tuning, which is a general and much discussed problem within the Standard Model.

Collins is correct: the only natural energy scale in terms of fundamental physical constants is the Planck scale, and we have as yet no understanding of why the proton and neutron masses should be so small compared to the Planck scale. (I should point out, though, that when physicists talk of a parameter being "fine-tuned" it has nothing to do with being fine tuned for the existence of life. Rather, it is a matter of fine tuning for the observed physics of the universe.)

With regard to the relative strength of gravity compared to other forces, Stenger writes,

The gravitational strength parameter α_G is based on arbitrary choice of units of mass, so it is arbitrary. Thus α_G cannot be fine-tuned. There is nothing to tune.

Now, I have to say I find this statement very unclear.  α_G is a dimensionless parameter: it doesn't depend on any choice of units. It is defined as

α_G ≡ G(m_p)²/ℏc,

where G is the gravitational constant, m_p is the proton mass,  ℏ is Planck's constant, and c is the speed of light. No matter what system of units you use to measure those quantities,α_G will have the same value.

Collins, who has read FOFT, says that Stenger means the we can replace the proton's mass in α_G by the mass of some other fundamental particle. Collins, correctly, points out that this is irrelevant to the question of whether α_G as defined is fine tuned. In the absence of any reasonable alternative interpretation I have to agree with Collins again: changing from one parameter to a different parameter can't save you from fine tuning of the original parameter.

Collins goes on to give a rather involved discussion of how various physical properties scale as we allow α_G to change. This is a sophisticated bit of argument; Collins pulls in arguments based on biology, plate tectonics, and planetary science. I tried hard to find some flaws in this analysis, but only came up with a few minor quibbles.

Stenger does make an important point that Collins simply ignores. He points out that if we just change one parameter, that parameter might appear to be fine-tuned. But if we allow for two (or more) parameters to vary at the same time, there might be a much wider range of values that allow for life. For instance,

The relative values of α and the strong force parameter α_S also are important in several cases. When the two are allowed to vary, no fine-tuning is necessary to allow for both nuclear stability and the existence of free protons.

As I said, Collins makes no comment about this claim. There is an obvious counter to it, though: if we increase the number of parameters that vary, we also increase the available parameter space. Even if the life-permitting range of some value is increased in this way, the relative volume of parameter space might still be small.

What's worse, Stenger goes on in the very next paragraph to step on his own toes:

There are two other facts that most proponents of fine-tuning ignore: (1) the force parameters α, α_S, and α_W are not constant but vary with energy; (2) they are not independent. The force parameters are expected to be equal at some unification energy. Furthermore, the three are connected in the current standard model and are likely to remain connected in any model that succeeds it.

If Stenger is right here, then the values of α and α_S cannot be varied independently. So which is it?

First off, I don't know what Stenger means by, "the three are connected in the current standard model." In the current standard model, the three are independent parameters and can be varied independently.

Second, it is true that these couplings change with the energy scale at which they are measured: physicists call this "running coupling constants." But it's not clear to me why Stenger thinks this is relevant. Is he suggesting that at some vastly different energy scale, they might again have the correct ratios to allow for life? I'm not sure what the point of this remark is.

Thirdly, "The force parameters are expected to be equal at some unification energy." This is true in grand unified models (GUTs) and in some supersymmetric models, but these have not been verified experimentally and so remain highly speculative. Anyway, this causes problems for Stenger, because if these parameters are related by physical theory then they can't be varied separately and so his argument about varying two parameters at the same time is no longer available. 

Finally, let's return to Collins. He writes,

Next, I define a constant as being fine-tuned for ECAs [embodied conscious agents] if and only if the range of its values that allow for ECAs is small compared to the range of values for which we can determine whether the value is ECA-permitting, a range I call the “comparison range.” For the purposes of this essay, I will take the comparison range to be the range of values for which a parameter is defined within the current models of physics. For most physical constants, such as the two presented here, this range is given by the Planck scale, which is determined by the corresponding Planck units for mass, length, and time.

Taking the Planck scale as defining the comparison range is badly wrong, for two reasons.

First, the Planck scale sets a limit on current physics in the sense that we expect it to break down around that scale. But in fact we have good reason to think current physics breaks down very much before that scale. Physicists have high hopes that the LHC will reveal "new physics," at an energy that is a factor of 10¹² below the Planck energy. This has not yet happened, unfortunately. But to suppose that we can understand physics at energies all the way up to the Planck energy is just way off.

Secondly, even apart from the issue of new physics, it's absurd to suggest that we can determine whether ECAs are possible for values of parameters that differ greatly from the values we know as the actual ones. Think about it like this: if someone handed you the equations of the Standard Model and of general relativity, together with the values of the constants therein, would you be able to predict the existence of complex life forms? Certainly there are some ranges of some parameters that let us rule out complex life. For instance, if the cosmological constant is to big, then the universe will expand so fast that matter will never be able to clump together into stars and planets. But changing the ratio of (say) electromagnetic to gravitational force is a very delicate matter, and all sorts of unforeseen possibilities might arise, especially for values very far from the true values. Sure, you could say that life like ours would be impossible under those parameters. But the argument is supposed to be about embodied conscious agents in general, not just life like ours.

What's strange is that Collins himself took a much more modest view of the comparison range in a previous paper. There he showed a sophisticated appreciation of both of the points I just made. For example, he writes,

One limitation in the above calculation is that no detailed calculations have been performed on the effect of
further increases or decreases in the strong and electromagnetic force that go far beyond the 0.5 and 4 per
cent, respectively, presented by Oberhummer et al. For instance, if the strong nuclear force were decreased
sufficiently, new carbon resonances might come into play, thereby possibly allowing for new pathways to
become available for carbon or oxygen formation.

He introduces the "epistemically illuminated range" for a parameter: that range for which we can calculate with reasonable assurance of success whether a given value allows the formation of complex life. He applies this procedure to the fine tuning of the strong force for carbon and oxygen production in stars, and comes up with a not-very-fine-tuned value of 0.1. Here, too, he treats only of the possibility of there being life like ours, and makes no attempt to address whether some very different sort of complex life might arise.

To sum up, I think Collins has done a pretty good job of pointing out problems with Stenger's analysis. His treatment of the physics here is a big improvement over some of his earlier work. But his arguments aren't enough to establish his claim. Collins's chosen "comparison range" is certainly too large to be reasonable. And his arguments only address the possibility of life that is substantially similar to ours. Yet vastly different forms of life might be possible in other parameter regions: we simply don't have the sophistication to predict their existence from bare physical laws. (It's possible that life-permitting regions might be scattered, fractal-like, through the parameter space, so that at any life-permitting point small changes don't allow life, while overall the probability of life is quite large.)