[Edit, 4/2/2012: I’ve written a more complete critique of Stenger’s book The Fallacy of Fine-Tuning: Why the Universe Is Not Designed for Us. It’s posted on Arxiv. In particular, the program MonkeyGod is critiqued in Appendix B; most of the points raised below remain valid.]
This post is the second critiquing Victor Stenger’s take on the fine-tuning of the universe for intelligent life. Here are some more of Stenger’s claims. (The quotes below are an amalgam of the articles on this page.)
I think it is safe to conclude that the conditions for the appearance of a universe with life are not so improbable as the those authors, enamored by the anthropic principle, would have you think … [T]here could be many ways to produce a universe old enough to have some form of life.
How does Stenger reach this conclusion?
I have written a program, MonkeyGod … I have studied how the minimum lifetime of a typical star depends on three parameters: the masses of the proton and electron and the strength of the electromagnetic force. (The strong interaction strength does not enter into this calculation.) Varying these parameters by ten orders of magnitude around their present values, I find that over half of the stars will have lifetimes exceeding a billion years, allowing sufficient time for some kind of life to evolve. Long stellar lifetime is not the only requirement for life, but it certainly is not an unusual property of universes.
Warning: long post. Here’s the abstract: Stenger attempts to show that our universe isn’t really fine-tuned by showing that long-lived stars are not unusual. He fails for five reasons. 1.) He gets his formula wrong, and in so doing ignores an important case of fine-tuning. 2.) He fails to consider the effect of altering the strength of gravity. 3.) He “cherry-picks” a very favourable fine-tuning example to suit his purposes. 4.) His probability claims are vacuous, following trivially from his unjustified hidden assumptions. 5.) He rightly exhorts us to consider varying multiple parameters at once, but commits the opposite mistake: he fails to consider multiple life-permitting criteria. Even if he were right about long-lived stars, it doesn’t follow that life-permitting universes do not need to be fine-tuned. I conclude that Stenger’s claims are worse than mistaken; they are misleading.
Let’s have a closer look at Stenger’s claims. He uses the following order-of-magnitude estimate for the lifetime of a main sequence star ():
where is the fine structure constant, is the dimensionless gravitational strength, () is the proton (electron) mass, (h_bar) and c as usual.
He then varies , and by up to 5 orders of magnitude above and below their value in our universe. After sampling 100 “universes”, he arrives at the following distribution for :
Stenger then notes that about half of the universes have years. He concludes that long-lived stars don’t require much fine-tuning.
I have a number of points to make in response to Stenger’s work.
1. Equation (1) is wrong. Significantly wrong. The correct expression can be found in “Why the universe is just so” by Craig Hogan, along with a brief derivation. The right hand side of (1) needs to be multiplied by , which is the fraction of the total mass-energy () of the star that is released through nuclear reactions. In our universe, .
The inclusion of has a number of effects. Firstly, it reduces the lifetime of a given universe by more than two orders of magnitude. Secondly, depends on the strong force. It should be intuitively obvious that the strong force, which governs nuclear reactions, should be relevant to the lifetime of stars, which are essentially nuclear bombs held together by gravity. Yet Stenger somehow misses this, incorrectly asserting: “the strong interaction strength does not enter into this calculation”. Thus, Stenger fails to account for the effects of altering the strong force.
Most importantly, is a very good example of a fine-tuned constant. When Martin Rees chooses “Just Six Numbers” as the best examples of fine-tuned physical parameters, is one of them. In particular, is the parameter that Rees uses to illustrate the fine-tuning needed to produce life-permitting stars. If were 0.006, deuterium would be unstable, meaning that stars would be unable to produce larger elements. Only hydrogen, no chemistry, no planets, no complex structures. If were 0.008, no hydrogen would have survived the big bang. Stars that aren’t fuelled by hydrogen have their lifetimes reduced by a factor of at least 30. Stenger simply leaves this out.
2. Stenger doesn’t consider the effects of altering gravity. When the lifetime of stars is discussed in the context of the fine-tuning of the universe, the strength of gravity usually makes an appearance. If gravity were stronger by a factor of 3000 or more, stellar lifetimes would be significantly reduced. Is this fine-tuned? If we consider the possible range of the strength of gravity to be equal to the range of known force strengths in our universe, then gravity is fine-tuned to a factor of , or approximately 1 in . ( is the strength of the strong force). You may disagree with this line of reasoning, but then it would be up to you to justify a different range of possibilities or a different probability distribution. More on that topic to come.
[Edit (Jul 12, 2010): Victor has replied in the comments saying that the effect of gravity is taken into account in altering the proton mass. And he’s correct: we can write , so if we hold the Planck mass constant (which is reasonable – we simply regard it as setting the scale of the laws of nature), then altering gravity is equivalent to altering the proton mass. I had wrongly assumed that he did what Barrow and Tipler did, and merely altered . The weakness of gravity is then equivalent to the smallness of the proton mass compared to the Planck mass. In terms of the masses, the proton mass is fine tuned to a factor of , which is the square root of what it was before, and thus significantly larger. Still a small number, though, but now there is an important caveat: to speak of the range of the proton mass is to discuss the Higgs mechanism. I’ll wait to see what Prof. Stenger says about that in his new book before responding.]
3. Stenger chooses a life-permitting criterion (“long-lived-stars”) that is one-sided and continuous. By one-sided, I mean that there is no upper bound on – arbitrarily long-lived stars are permitted. (The need for supernovae to distribute heavy elements across the universe is ignored.) By continuous, I mean that is a smoothly varying (power law) function of the fundamental constants. Contrast this with the mass of the neutron (), which is 0.1% more than (proton). The decay of neutrons into protons in the early universe depends on their mass difference. Thus, as decreases (even by 0.1%), the mass difference changes dramatically from positive to negative, meaning that protons decay into neutrons. This leaves none left over for long-lived stars. This is an example of the sudden, discontinuous change that characterises many of the relationships between physical constants and life-permitting criteria.
By considering a one-sided, continuous life-permitting criterion, Stenger has chosen the most favourable case. He has fine-tuned his example in his favour.
4. The probability distribution for depends on the Probability Density Function (PDF) chosen for each of the parameters that are allowed to vary. For a parameter , with value in our universe, Stenger chooses the following PDF:
and zero otherwise, where A is a constant of normalisation. This PDF is uniform in , and the range of is 5 orders of magnitude above and below .
A few comments. This PDF is an extremely important assumption on Stenger’s part, yet he doesn’t even draw attention to it, let alone attempt to justify it. Considering a range of values is fine if you’re only interested in exploring what these other universes are like. But Stenger wants to make probability claims (“half the stars …”). Such claims are completely unjustified while ever is unjustified.
More importantly, Stenger has once again fine-tuned his assumptions. Let’s take a closer look at the resultant PDF for . Stenger only considers 100 universes, which is a rather small number for a Monte Carlo investigation. I’ve repeated Stenger’s calculations with my own code, this time using one million universes.
The red vertical line is the value of in our universe (). What can we see from this plot, which is not clear in Stenger’s? The distribution is symmetric around . Of course it is: we are considering PDF’s for the parameters that are symmetric in log-space around their value in our universe, and is related to these parameters as a nice, smooth power-law. The symmetry of the PDF for follows from the symmetry of the PDF’s for the parameters. And since any value for the stellar lifetime larger than is deemed life-permitting (one-sided criterion), Stenger’s claim that about half of these universes support life is trivial. It follows unavoidably from his (unjustified) choice of PDF. Stenger’s claims that “half of the stars will have lifetimes allowing for some kind of life to evolve … [L]ong stellar lifetimes are certainly not an unusual property of universes” are completely vacuous.
5. Stenger takes others to task for failing to consider the consequences of altering several parameters simultaneously. He says: “changes in other parameters may compensate for the change in a selected parameter, allowing more room for a viable, liveable universe than might otherwise be suspected. We and others have concluded that the so-called fine-tuning is not as fine as has been advertised.”
Stenger is right to exhort us to consider the full parameter space. (I’m looking at you, Hugh Ross.) But recognising “other possibilities” for life is not enough to overturn claims of fine-tuning. Expanding parameter space into other dimensions opens up new possibilities for life-permitting universes, but also increases the amount of “dead-space”. A quote from Richard Dawkins springs to mind: “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.” Finding other possibilities for life is not the same as showing that life-permitting universes dominate the space of possible universes. Remember: the claim is not that ours is the only universe that could support life, or that we are the only possible form of life. The claim is that if a universe were chosen at random from the range of possible universes, the probability of that universe being able to support intelligent life is very small. This claim is entirely consistent with the existence of other possibilities for life.
Secondly, and most importantly, Stenger makes the opposite mistake. He considers a range of values for the constants, but does not consider a range of life-permitting criteria. Again, he is choosing the most favourable test case: he considers a one-sided, continuous life-permitting criterion and then looks at all the possible ways to fulfil it, giving him the best chance of claiming “look at all these life-permitting universes!”
The list of life-permitting criteria is immense. Stenger, in his MonkeyGod code, ignores the following constraints on his model universes:
- The stability of atoms:
- The requirement that atoms larger than carbon are stable against nuclear fission places a lower limit: . Non-compliance is punished with the disintegration of all atoms used by living organisms.
- Electrons orbiting atoms with have enough kinetic energy to be unstable to electron-positron pair production. This places an upper limit on .
- Complex structures
- The relative fluctuation of the positions of ions and electrons in solids is governed by . The heaviness of ions ( small) means that they are essentially fixed, allowing the electrons to flow around them and bind the solid. If were of order unity, the electrons that are supposed to bind the solid would be able to dislodge ions from the lattice, melting the solid. As a result, solids would melt and molecules fall apart. The only structures possible would be like those built using only the strong force – roughly spherically symmetric.
- The weakness of EM compared to the strong force, and the smallness of , are required to create a clear energy gap between the regime of chemical and nuclear reactions. The reliable properties of the chemicals in your body would be for nought if the energy released in a chemical reaction could transmute elements into each other.
- To overcome the second law of thermodynamics, life needs a stable energy source, and stars are the most likely candidate. To power chemical reactions, the energy of photons from the sun needs to be close to typical molecular binding energies – too high, and molecules are simply disintegrated; too low and chemical systems would be unable to harness the sun’s energy. This coincidence holds because .
- Suitable stars: we have already noted the simple dependence of lifetime on the constants, including and its effect on element production and big bang nucleosynthesis.
- There are other ways to destroy hydrogen in the early universe. We have already noted the effect of the mass difference of neutrons and protons. The weak force also plays an important role – if it is too weak then there is too little hydrogen left over to power stars.
- Oberhummer et al. (1999) showed that a change in the strength of the strong force of 0.4% in either direction renders stars incapable of making both carbon and oxygen. They instead make one at the expense of the other. This would have a dramatic effect on the probability of life developing in such a universe.
- Stars also need to be stable. There is an optimum mass range – too small and degeneracy pressure prevents nuclear ignition; too large and radiation pressure can break up the star. If , then this “window of stability” closes and no stars are stable.
- Large planets: if gravity were a billion times stronger, then planets would need to be the size of a house in order that large-brained organisms are not crushed. This is not large enough to sustain an ecosystem.
- Craig Hogan also places constraints on the masses of elementary particles. See his paper “Why the universe is just so” for more details.
This is not an exhaustive list. Remember: one fine-tuned parameter is enough. One failed life-permitting criterion is too many. Even if Stenger were right about the lifetime of stars, it doesn’t follow that all proposed fine-tunings could be as easily dismissed. Stenger cannot make sweeping generalisations about whether the universe is fine-tuned for life by considering only one life-permitting criteria. He is aware of these other cases of fine-tuning – he describes them in his articles. Yet he does not incorporate these into MonkeyGod, under the pretence that this is just a “toy model.” The aim of a toy model is to teach the basics of more complex models, while not worrying about minor details. MonkeyGod does nothing of the sort. It teaches us precisely nothing.
Allow me to state my conclusions with the kind of candour only allowed in the blogosphere: MonkeyGod is bollocks. It is worse than irrelevant – it is misleading. It is a distraction, encouraging us to simply look the other way, to condescending dismiss the evidence for the fine-tuning of the universe for life. It is utter garbage, thinly concealed behind a veil of mathematics.
The worst part is that others are taking Stenger’s work as the definitive debunking of fine-tuning. Here are some quotes from internet articles and forums about MonkeyGod:
Monkey God is a serious research product, defended at length in a technical article. [LB: the article was published in a philosophical journal of a humanist society. Fail again, Richard Carrier.].
Particle physicist Victor Stenger has shown that our universe isn’t finely tuned at all.
Victor Stenger pretty much thoroughly debunked the premise that the formation of stars in the universe is “a house of cards”. To the contrary: as it turns out, you can alter the fundamental constraints of the universe pretty wildly and still come up with a universe capable of supporting stars.
[MonkeyGod gives us] good evidence that the average universe would live long enough to produce life.
MonkeyGod demonstrates that long-lived stars “occur in a wide range of parameters” … there is no reason to assume a priori that any change would result in the impossibility of life.
I’ve previously indicted Hugh Ross for often assuming the appearance of a “true-believer”: desperately searching for and uncritically accepting any “evidence” for fine tuning. Stenger’s feeble, evasive response to the fine-tuning of the universe evokes the opposite stereotype: the condescending “true-unbeliever” who refuses to engage the evidence, who is not searching for truth at all costs, but is instead rummaging for any excuse to explain it away. And it seems that others have followed him into condescension.
I’m being harsh because I expected more from Stenger. He has produced some excellent, original, thoughtful work on the laws of nature in a naturalistic worldview. One can only hope for better things in his forthcoming book.
(I can also endorse the following reply to Stenger from George Ellis.)
More of my posts on fine-tuning are here.