I recently posted on Arxiv a paper titled “The Fine-Tuning of the Universe for Intelligent Life”. A slightly shortened version has been accepted for publication in Publications of the Astronomical Society of Australia. The paper is primarily a review of the scientific literature, but uses as a foil Victor Stenger’s recent book “The Fallacy of Fine-Tuning: Why the Universe Is Not Designed for Us” (FoFT). Stenger has since replied to my criticisms. The following is my reply to his reply to my article criticising his book which criticises fine-tuning. Everybody got that?

A few points before I get into details:

There isn’t much in this post that wasn’t in my original article. I write this to summarise the important bits.

“Barnes does not challenge my basic conclusions.” Not even close. Re-read.

“Barnes seems to want me to reduce this to maybe 1-5 percent.” Nope. I didn’t say or imply such a figure anywhere in my article. On the contrary, the cosmological constant alone gives . The Higgs vev is fine-tuned to . The triple alpha process plausibly puts constraints of order on the fine-structure constant. The “famous fine-tuning problem” of inflation is (Turok, 2002). The fine-tuning implied by entropy is 1 in according to Penrose. For more examples, see my article. Or just pull a number out of nowhere and attribute it to me.

. The Higgs vev is fine-tuned to . The triple alpha process plausibly puts constraints of order on the fine-structure constant. The “famous fine-tuning problem” of inflation is (Turok, 2002). The fine-tuning implied by entropy is 1 in according to Penrose. For more examples, see my article. Or just pull a number out of nowhere and attribute it to me. “He fails to explain why my simplifications are inadequate for my purposes.” Red herring. My issue is not oversimplification. I do not criticise the level of sophistication of Stenger’s arguments (with one exception – see my discussion of entropy in cosmology below). Stenger’s arguments do not fail for a lack of technical precision. Neither does the technical level of my arguments render them “irrelevant”.

Point of View Invariance (PoVI)

A major claim of my response (Section 4.1) to FoFT is that Stenger equivocates on the terms symmetry and PoVI. They are not synonymous. For example, in Lagrangian dynamics, PoVI is a feature of the entire Lagrangian formalism and holds for any Lagrangian and any (sufficiently smooth) coordinate transformation. A symmetry is a property of a particular Lagrangian, and is associated with a particular (family of) coordinate transformation. All Lagrangians are POVI, but only certain, special Lagrangians – and thus only certain, special physical systems – are symmetric. Stenger replies:

“PoVI is a necessary principle, but it does not by itself determine all the laws of physics. There are choices of what transformations are considered and any models developed must be tested against the data. However, it is well established, and certainly not my creation, that conservation principles and much more follow from symmetry principles.”

Note how a discussion of PoVI segues into a discussion of symmetry with no attempt to justify treating the two as synonymous, or giving an argument for why one follows from the other.

Of course conservation principles follow from symmetry principles – that’s Noether’s theorem. It’s perfectly true that “if [physicists] are to maintain the notion that there is no special point in space, then they can’t suggest a model that violates momentum conservation”. The issue is not the truth of the conditional, but the necessary truth of the antecedent. Physicists are not free to propose a model which is time-translation invariant and fails to conserve energy1. But we are free to propose a model that isn’t time-translation invariant without fear of subjectivity.

And we have! Stenger says: “But no physicist is going to propose a model that depends on his location and his point of view.” This is precisely what cosmologists have been doing since 1922. The Lagrangian that best describes the observable universe as a whole is not time-translation invariant. It’s right there in the Robertson-Walker metric: a(t). The predictions of the model depend on the time at which the universe is observed, and thus the universe does not conserve energy. Neither does it wallow in subjectivity.

Watch closely as Stenger gives the whole game away:

“… much of existing, empirically verified physics follows from a principle in which physicists force themselves to construct their models to be independent of the observer’s point of view. If, someday, experiment shows a violation of this principle, then we will have to discard it.”

Fine-tuning compares the set of life-permitting laws with the set of possible laws. Stenger’s argument can only be successful if it shows that symmetries restrict the set of possible laws. He must convince us that symmetry violations are not possible. It is to admit failure, then, to acknowledge that symmetry principles can be overturned by experiment. They are contingent. There are possible universes in which they do not hold, and that is all fine-tuning needs.

Stenger makes the same admission with respect to gauge invariance. “Barnes objects to my association of gauge invariance with PoVI, but gives no reason. Instead, he quotes various authors to the effect that gauge invariance could be wrong. Of course, it could be wrong.” It could be wrong! Gauge invariance is a contingent fact.

(Incidentally, the reasons I don’t give are on pages 14-15. Also, don’t confuse two different senses of “could be wrong”. I am not arguing that gauge invariance does not hold in this universe. There are possible universes that are not gauge invariant. Our universe is probably not one of them. It’s like the difference between “Bob could be a sailor, I just don’t know” and “Bob could have been a sailor, but instead became a plumber”.)

Gravitational Fictions

Our respective philosophies of science are irrelevant. I argue in Section 4.9 that fine-tuning claims can be understood and affirmed by realist, instrumentalist and every philosophy in between. Fine-tuning starts by asking: “what if the universe were different?” If the universe were different, we would (ex hypothesi) make different observations and propose different laws to account for them. Changing the laws and constants of nature on paper can be thought of as a convenient way of specifying which other universe (or set of observations) we are talking about. No commitment on the ontological status of the mathematical form of the laws of nature is required. I don’t have firm views on the philosophy of science. There is nothing in my article that defends Platonic realism.

FoFT claims that if there were no gravity then there would be no universe, that physicists must to put gravity into any model of the universe that contains separate masses. This isn’t a question of interpretation. It’s false. Take general relativity and set G = 0. All its PoVI properties remain, spacetime is Minkowskian, and you can fill your universe with matter to your heart’s content and yet there will be no gravity. It’s not our universe, but it is a possible universe. Further, physicists have proposed many different models for gravity which are observationally distinguishable (in principle) and yet are all PoVI: Newtonian gravity, general relativity, Brans-Dicke gravity, Einstein–Cartan gravity, Lovelock gravity, … (Wikipedia lists over 30). There is nothing to stop us asking the question: “what properties must gravity have in order for a universe to be life-permitting?”

Entropy and Cosmology

Stenger says: “Assume our universe starts out at the Planck time as a sphere of Planck dimensions”. That’s precisely the assumption I disputed – see the second last paragraph on page 25. The observable universe wasn’t Planck sized at the Planck time.

Secondly, as I mentioned above, this is the only place where I criticised the sophistication of Stenger’s arguments in FoFT. I gave my reasons in Section 4.3. For example, Bousso (2002) says that “a naive generalisation of the spherical entropy bound is unsuccessful. . . . [T]he idea that the area of surfaces generally bounds the entropy in enclosed spatial volumes has proven wrong. . . . [A] general entropy bound, if found, is no triviality”. Simplifications are fine, so long as we have good reason to believe that they capture the essentials of a more precise calculation. We can have no such confidence in Stenger’s argument. No one knows how to do the precise calculation, as there is no consensus on how to correctly apply the Bekenstein limit to cosmology. Even simple self-gravitating systems present major unsolved problems for statistical physics, problems that become immeasurably more difficult when the system in question is the entire universe in the quantum-gravity regime. These are not issues that can be ignored. Even Stenger’s simplified calculation is flawed, as it uses the Hubble sphere instead of a horizon, the particle horizon cannot be defined at the Planck time, and it assumes without justification homogeneity and isotropy. It’s a failed solution, abandoned by cosmologists decades ago.

Carbon and Oxygen Synthesis In Stars

Read page 41 again. Weinberg’s argument is inconclusive.

Expansion rate of the universe

“Barnes … goes into detail on the problems of inflation, showing that it could be wrong.” That is exactly what I didn’t say. In fact, I went to great lengths to make it clear that I wasn’t saying that. Section 4.4.1 spent three paragraphs asking “did inflation happen?”, concluding that the case is impressive but circumstantial. Section 4.4.2 then spent four pages asking a different question: “Is inflation itself fine-tuned?” The difference between these two questions is very important.

Suppose that I were defending this claim: in the space of all possible arrangements of metal and plastic, the subset of drivable cars is extremely small. Cars are fine-tuned. Ah yes, you reply, but Alan has hypothesised that cars are produced by a mechanism known as a car factory. Is there good evidence that my car was made by a car factory? Yes. Does that fact account for the fine-tuning of my car? No, because the car factory is at least as fine-tuned as my car. In the space of all possible arrangements of metal and plastic, the subset of working car factories is also extremely small.

Explaining one fine-tuned fact using another fine-tuned fact, even if true, doesn’t solve the fine-tuning problem. Stenger seems unable or unwilling to ask whether inflation is fine-tuned. In fact, at no point in his book does he ask whether any of his “solutions” are as fine-tuned as the problems they are supposed to solve. I’ll return to this point later.

Gravity and the Masses of Particles

Stenger: “I then propose a plausible explanation for this low mass, namely, in the standard model the masses are intrinsically zero and their observed masses are the result of small corrections, such as the Higgs mechanism.”

A perfect example of attacking a fine-tuned fact with a fine-tuned explanation. Here is what I said in my article: “It is precisely the smallness of the quantum corrections wherein the fine-tuning lies. If the Planck mass is the “natural” [Foft 175] mass scale in physics, then it sets the scale for all mass terms, corrections or otherwise. Just calling them “small” doesn’t explain anything.” The Higgs quantum corrections must be fine-tuned for the universe to be life-permitting. Once again, Stenger does not ask whether his solution is fine-tuned. It is not enough that the explanation is plausibly true in our universe. It must make a life-permitting outcome more probable to make a difference to fine-tuning2.

Charge Neutrality

Stenger has already admitted that gauge invariance doesn’t hold in all possible universes, and so we are free to consider universes in which it does not hold without fear of contradiction or subjectivity. Further, even if gauge invariance (and thus charge conservation) holds, it doesn’t imply that the net charge of the universe is zero, only that it is constant.

MonkeyGod

“Barnes makes his usual objections to my admitted oversimplifications. Does he really expect me to simulate entire universes?”

No … that’s best left to real cosmologists. I do, however, expect that when a model contains 8 equations, it will not botch 6 of them. I expect it to at least acknowledge the assumptions that it makes, and perhaps even attempt to justify them, especially when in the absence of such justification the model is worthless. I expect it to identify and attempt to correct any biases in its assumptions, such as the obvious selection effect that results from taking a region of parameter space around a known example of the phenomenon in question as being representative of the entire space. I expect it to understand the difference between the range of possible values and the range of values consistent with experiments in our universe.

Further, I expect simplifications to be just that. Einstein (supposedly) said that we must endeavour to make things as simple as possible but no simpler. The whole idea of a simplification is to neglect those features of the scenario that are least significant. Neglecting the mass of the Earth in a model of the solar system is a simplification. Neglecting the mass of the Sun is not.

Of all the constraints that a life-permitting universe must satisfy, Stenger has chosen to neglect many of the most significant. As I said in my article, “There are no cosmological limits, from big bang nucleosynthesis or from galaxy and star formation. The stability of hydrogen to electron capture, the stability of the proton against decay into a neutron, the limit on for stable structures, electron-positron pair instability for large , stellar stability, the triple-alpha process, and the binding and unbinding of the diproton and deuteron are not included … these are amongst the tightest limits in parameter space.” To ignore the most significant factors in a calculation is not simplification. It doesn’t even have the dignity to be an oversimplification. It’s not a toy model. It’s just incorrect.

Derived, Fundamental and Fine-tuned

“Barnes says, “to show (or conjecture) that a parameter is derived rather than fundamental does not mean that it is not fine-tuned.” Right. And the fact that we can’t prove that Bertrand Russell’s teapot is not orbiting the sun between Mars and Jupiter does not mean it is.”

Drivel. Stenger apparently believes that I am defending the principle: “Absence of evidence is evidence of existence”. Needless to say, I am not. The statement of mine quoted above is a mathematical fact. Suppose we have a probability space with probability measure , and outcomes parameterised by . Within this space, we specify a subset of interest . This subset is small if . Now suppose that we discover that the parameters are not fundamental, but derived from a set of parameters . We can form a new space in terms of the , and ask whether the subset of interest is still small. My claim is that it is not necessarily true that is large. In fact, the change of parameterisation will have to dramatically inflate or severely curtail $X$ for the smallness of not to imply the smallness of .

If that was too mathematical, let me rephrase the example I gave in Section 4.8.3. Suppose Bob sees Alice throw a dart and hit the bullseye. “Pretty impressive, don’t you think?”, says Alice. “Not at all”, says Bob, “the point-of-impact of the dart is a derived parameter. The more fundamental parameter is the velocity with which the dart left your hand (i.e. throwing speed and direction). Thus no fine-tuning is needed.” This conclusion obviously does not follow. All Bob has done is exchange the fine-tuning of the impact point for the fine-tuning of the initial velocity. This is true even though the initial velocity of the dart (plus Newtonian mechanics) explains the point of impact. Bob cannot claim that “as long as no one can disprove this explanation, I win the argument.”

We see this point again and again in the fine-tuning of the universe for intelligent life. The fine-tuning of the proton and neutron masses imply fine-tuning constraints on the quark masses, which in turn imply constraints on the Higgs vev and Yukawa parameters. If (broken) supersymmetry holds, then the constraints on the Higgs vev imply constraints on the supersymmetry breaking scale. The fine-tuning of the standard model coupling constants (e.g. and ) plausibly imply constraints on the parameters of GUTs (Section 4.8.2). The constraints on the initial expansion rate, density and perturbations of the universe imply constraints on the inflaton potential, coupling and initial conditions. The constraints on the cosmological constant still apply to quintessence models. The fact that a parameter may be derived does not mean that its fine-tuning will automatically go away3. Fundamental (Edit: 4/7/2012) Derived parameters can be fine-tuned.

Conclusion

Stenger’s two basic conclusions fail. Showing that “plausible explanations, consistent with existing knowledge, can be made for the observed values of [fine-tuned] parameters”, like showing that the impact point of a dart is explained by its initial velocity, doesn’t even address fine-tuning. Stenger has given us no reason to think that the life-permitting region is larger, or possibility space smaller, than has been calculated in the fine-tuning literature.

Stenger’s second conclusion, that “plausible ranges for the other parameters exist that are far from infinitesimal, contrary to what is claimed in the theistic literature” is meaningless. Any non-zero range is larger than an infinitesimal range. No reference to the theistic literature is given, here or in FoFT. At least some of the theist literature accurately represents the scientific literature4, something that Stenger has failed to do.

Postscript

Large red letters on Stenger’s homepage inform us that “No reputable physicist or cosmologist has disputed this book”. I guess that makes me a disreputable cosmologist. In the meantime, a shortened version of my paper has been accepted for publication by Publications of the Astronomical Society of Australia. The fate of Stenger’s paper ‘A Case Against the Fine-Tuning of the Cosmos’, submitted to the “Journal of Cosmology”, is unknown.

In any case, if you’d rather decide this issue by a show of hands rather than good arguments, then let’s play pick the odd one out of these non-theist scientists.

Wilczek: life appears to depend upon delicate coincidences that we have not been able to explain. The broad outlines of that situation have been apparent for many decades. When less was known, it seemed reasonable to hope that better understanding of symmetry and dynamics would clear things up. Now that hope seems much less reasonable. The happy coincidences between life’s requirements and nature’s choices of parameter values might be just a series of flukes, but one could be forgiven for beginning to suspect that something deeper is at work. Hawking: “Most of the fundamental constants in our theories appear fine-tuned in the sense that if they were altered by only modest amounts, the universe would be qualitatively different, and in many cases unsuitable for the development of life. … The emergence of the complex structures capable of supporting intelligent observers seems to be very fragile. The laws of nature form a system that is extremely fine-tuned, and very little in physical law can be altered without destroying the possibility of the development of life as we know it.” Rees: Any universe hospitable to life – what we might call a biophilic universe – has to be ‘adjusted’ in a particular way. The prerequisites for any life of the kind we know about — long-lived stable stars, stable atoms such as carbon, oxygen and silicon, able to combine into complex molecules, etc — are sensitive to the physical laws and to the size, expansion rate and contents of the universe. Indeed, even for the most open-minded science ﬁction writer, ‘life’ or ‘intelligence’ requires the emergence of some generic complex structures: it can’t exist in a homogeneous universe, not in a universe containing only a few dozen particles. Many recipes would lead to stillborn universes with no atoms, no chemistry, and no planets; or to universes too short-lived or too empty to allow anything to evolve beyond sterile uniformity. Linde: the existence of an amazingly strong correlation between our own properties and the values of many parameters of our world, such as the masses and charges of electron and proton, the value of the gravitational constant, the amplitude of spontaneous symmetry breaking in the electroweak theory, the value of the vacuum energy, and the dimensionality of our world, is an experimental fact requiring an explanation. Susskind: The Laws of Physics … are almost always deadly. In a sense the laws of nature are like East Coast weather: tremendously variable, almost always awful, but on rare occasions, perfectly lovely. … [O]ur own universe is an extraordinary place that appears to be fantastically well designed for our own existence. This specialness is not something that we can attribute to lucky accidents, which is far too unlikely. The apparent coincidences cry out for an explanation. Guth: in the multiverse, life will evolve only in very rare regions where the local laws of physics just happen to have the properties needed for life, giving a simple explanation for why the observed universe appears to have just the right properties for the evolution of life. The incredibly small value of the cosmological constant is a telling example of a feature that seems to be needed for life, but for which an explanation from fundamental physics is painfully lacking. Smolin: Our universe is much more complex than most universes with the same laws but different values of the parameters of those laws. In particular, it has a complex astrophysics, including galaxies and long lived stars, and a complex chemistry, including carbon chemistry. These necessary conditions for life are present in our universe as a consequence of the complexity which is made possible by the special values of the parameters. Guess who?: The most commonly cited examples of apparent fine-tuning can be readily explained by the application of a little well-established physics and cosmology. . . . [S]ome form of life would have occurred in most universes that could be described by the same physical models as ours, with parameters whose ranges varied over ranges consistent with those models. … . My case against fine-tuning will not rely on speculations beyond well-established physics nor on the existence of multiple universes.

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Footnotes

1. … and obeys the action principle.

2. Stenger says: “I explicitly attribute the mass differences of the d and u quarks to the electromagnetic force (Fallacy p. 178).” Still not correct, I’m afraid. Walker-Loud et al. explain: “There are two sources of [the proton-neutron mass difference] in the standard model, the masses of the up and down quarks as well as the electromagnetic interactions between quarks.” Gasser and Leutwyler say, “If the electromagnetic interaction is turned on, the quarks start emitting and absorbing photons. … A cloud of virtual photons surrounding a bound state of quarks contributes to the mass of the state.” Miller et al. says “If charge symmetry were exact, the proton and the neutron would have the same mass. … The electrostatic repulsion between quarks should make the proton heavier. But the mass difference between the quarks wins over their electrostatic repulsion”. The EM mass-energy of a proton is attributed to the virtual photon cloud, not the quarks, just as the QCD contribution is attributed to the gluons. The bare quark masses and the EM self-energy are separate contributions to the proton mass. (See also footnote 39 of my paper.) Note that nothing of relevance to fine-tuning hangs on this point.

3. As I noted at the end of Section 4.2.2, these aren’t independent constraints. We must not, for example, simply multiply the probability of a life-permitting proton mass and the probability of a life-permitting up-quark mass. The fine-tuning of a derived parameter is not further fine-tuning, beyond the fine-tuning of the fundamental parameters.

4. Of course, there are exceptions. I’m looking at you, Hugh Ross.

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More of my posts on fine-tuning are here.