1. The point with the missing epsilon is not so much that it changes the results – two orders of magnitude isn’t too bad – but that it ignores the role of the strong force, and in so doing leaves out an important case of fine tuning.

2. I didn’t see the point about gravity in the articles I read, but I’ve since found the relevant argument and I think you’re right. I’ll amend the original post.

3. Which probability argument are you referring to? In this post or my previous one: https://letterstonature.wordpress.com/2010/04/11/what-chances-me-a-fine-tuned-critique-of-victor-stenger-part-1/

I’ll summarise both briefly:

Part 1: I took your argument to be: “Sperm + egg = William Lane Craig is a low probability event, and yet here he is. So low probability is not sufficient to discount a chance hypothesis”. That’s true, but now the question is: what are the sufficient conditions to discount chance? I’d say that it’s low probability plus an independently specified rejection region (Fisher) or an alternative hypothesis that explains the data better and has a non-vanishing prior (Bayes). I’d say that the fine-tuning of the universe satisfies these, where the alternative hypothesis need not be a designer – a multiverse will do.

Part 2: Your probabilistic conclusion (“half the stars … “) relies crucially on your prior. Yet (in the material I have read), you don’t even mention this fact, let alone attempt to justify it.

I look forward to your book! In this blog post, I was just trying to take a bite-sized piece and it still ended up rather long-winded.

]]>Gravity is taken into account through the mass of the proton, as i explained.

My Philo article gives all the references used.

I don’t understand the long critique of my probability argument. All I am saying is the obvious. Low probability happens and you have to compare numbers for alternatives.

In any case, there is so much more to my case against fine-tuning that these one or two objections are no consequence to the final conclusion. I have a book coming out next year called “The Fallacy of Fine-Tuning.” If anyone wants to assist me by commenting on the drafts, please email me and I will send you the location of the drafts and the password.

]]>I’m 99.9% sure that that’s not what Stenger has done. Once again – epsilon is what it is, and it must remain in the formula. It is defined as the ratio of the energy in the star which is radiated away to the total rest-mass energy of the star. It is not a fitting parameter.

The obvious question that remains is – how do we turn a minimum stellar lifetime into a typical stellar lifetime? I think Barrow and Tipler (pg 333) do it a different way. Instead of the Eddinton luminosity, they estimate the luminosity by estimating the radiation energy contained in a star, and then estimate the amount of time it takes for all that energy to leave the star via a random walk. They arrive at the formula:

t_star = 10^10 yrs * (M/M_min)^2

where M is the mass of the star, and M_min is the minimum stellar mass (i.e. capable of sustaining nuclear fusion). That’s probably closer to a “typical” stellar lifetime, although perhaps we’re closer to the “maximum” end of the spectrum …

]]>(Remark: surely 0.2Gy couldn’t possibly be the shortest-possible main-sequence lifespan; a main-sequence star with that lifespan would only be about 3 solar masses, and you can get stars a lot bigger and hence shorter-lived than that.)

I wasn’t claiming that there’s any kind of fundamental reason why ignoring epsilon would have to give the typical (as opposed to the minimal) lifetime. I was saying: it seems to turn out, in our universe at least, that epsilon happens to be close to the ratio of minimal to typical lifetime. In lieu of a difficult analysis (does anyone even know how to do it?) of how the ratio between epsilon and (min/typ) varies in hypothetical different universes, Stenger may simply have chosen to suppose that it remains close to 1. I repeat: if that’s what he was doing then he absolutely should have said so; it’s possible that he did, in fact, simply screw up; but it’s not clear that that’s what actually happened.

Leaving aside the question of how Stenger happened to arrive at his version of the formula, I think the issue is the merits of the following two hypotheses:

1. If you take a random sample of hypothetical universes, we should expect (min/typ) to remain roughly what it is.

2. If you take a random sample of hypothetical universes, we should expect epsilon/(min/typ) to remain roughly what it is.

If #1 is better, then to do Stenger’s calculations right (assuming for the sake of argument that there’s any point in doing so) we should restore the factor of epsilon, then add another fudge factor that happens to be ~1/epsilon, and look at how epsilon varies across the possible worlds we’re interested in.

If #2 is better, then we should instead take out the factor of epsilon, as Stenger (by luck or judgement or whatever) did.

If #1 and #2 are both no good, then of course we should do something else again.

Note well: it is simply not true that omitting epsilon could only be appropriate if stars always converted their whole rest mass into other forms of energy. It could also be appropriate if there were some reason to expect the efficiency of stellar hydrogen-burning to be close to that (min/typ) ratio. And, on the other hand, simply using the formula *with* the epsilon is only appropriate if there’s some reason to expect the (min/typ) ratio to be close to 1. And simply using the formula with the epsilon and an extra correction factor is only appropriate if there’s some reason to expect the (min/typ) ratio to be close to its value in our universe.

(Strictly, for “expect X to be close to Y” above means “hold X=Y while allowing other parameters to vary, when doing a thought-experiment about other possible universes”.)

I have no inkling what actually controls the (min/typ) ratio. I would be very happy to be enlightened on that point.

]]>Second: I understand, but you can’t make the formula for the “minimum lifetime” into the “typical lifetime” by ignoring epsilon. Epsilon is not a free parameter to be fit by the data from our universe. It can be calculated (in principle) from the strength of the strong force and various other constants. Setting it to 1 can *only* be valid if stars convert their entire rest mass into other forms of energy. But this simply isn’t true.

Regarding the minimum vs typical – in a sense, Stenger and Hogan are both right. The derivation proceeds as follows: estimate the total available energy to be radiated away, estimate the rate at which it is radiated away (the luminosity – energy per unit time). Then the energy divided by the luminosity gives a rough estimate of how long it will take for a star to radiate away the available energy.

The estimate for the luminosity uses an upper limit – called the Eddington luminosity. Stars can’t be brighter than that or they’d blow off their outer layers (photons have momentum!). Since we have used a large luminosity, we get a “minimum” stellar lifetime.

It turns out that this minimum timescale is pretty close to the typical timescale … within an order of magnitude or two. In other words, stars have a luminosity that is pretty close to the Eddington limit. Thus Stenger is not wrong to use this timescale as a typical timescale. He just get’s the formula wrong. (I assume it was just an accident on Stenger’s part – I’ve made plenty of mistakes dumber than that one!)

Finally, let’s do the calculation in google: copy and paste –

0.007*((1/137^2)/(G*(mass of proton)^2/h/c))*(mass of proton/mass of electron)^2*h/(mass of proton * c^2)

(alpha = fine structure constant = 1/137)

I get 0.189 billion years …

]]>First: I am not attempting any sort of comprehensive defence of Stenger’s argument; I’m just commenting on your first objection to it. (So any possible fine-tuning of epsilon is irrelevant *to what I’m saying*, even if it demolishes Stenger’s argument as a whole.)

Second: I appreciate that the numerical values aren’t all that important in themselves. I mentioned the one I did just as evidence that if Stenger wanted to describe *typical* main-sequence lifetimes, the formula with the epsilon does that worse than the formula without. (In our universe.)

According to Hogan, his formula (with the epsilon factor) describes the *minimum possible* lifetime of a main-sequence star. (Or did I misunderstand his article?) I just re-did the calculations again using different tools and different sources of information, and I got the same answer: 4.7Myr. That does indeed seem reasonable (I think — I’m no astrophysicist) as a minimum main-sequence lifetime.

So, if Stenger said “this formula gives the minimum lifetime of a main-sequence star” then, no question, he’d be wrong and I’d agree with your point 1. But what he actually says is “minimum lifetime of a typical star”, which is kinda silly (how can it be minimum *and* typical?) but seems quite likely to mean “typical main-sequence lifetime”. (After all, that’s surely much more relevant to the point at issue than the minimum possible lifetime.)

So I’m wondering whether there’s some implicit (and hence shoddy; let me remind you that I’m commenting *only* on you first criticism of Stenger and not defending him generally) thinking along the following lines: we’ve got this formula, with a factor of epsilon in it, for the minimum possible lifetime of a main-sequence star; we’re interested in the typical lifetime of a main-sequence star; it happens that in our universe you get a pretty decent approximation to that just by dropping the factor of epsilon; since for this calculation we’re not interested in the strong force, let’s just suppose it does whatever it needs to so that the ratio (typical lifetime / minimum lifetime / epsilon), which happens to be 1 in our universe, remains 1 in the others; now proceed.

There’s no question that leaving all this stuff implicit would be a poor way to proceed. There’s not much question that assuming that that ratio stays constant is a bit artificial. (But I’m not quite sure; perhaps you can see it as a dimensionless representation of the strength of the strong force, given all the others, in which case holding it constant would be reasonable.) So (to repeatedly repeat myself again) this is not a general defence of Stenger. But I do think that “Stenger just got it wrong” is only justifiable if he really, truly claimed that his formula gave the minimum possible lifetime for a main-sequence star, and I don’t think he did.

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