Another Fine Mess You Have Got Yourself Into, Luke Barnes

In his New Atlantic article, The Fine Tuning of Nature's Laws, Luke Barnes provided this image:

Below it was explanatory text:

“What if we tweaked just two of the fundamental constants? This figure shows what the universe would look like if the strength of the strong nuclear force (which holds atoms together) and the value of the fine-structure constant (which represents the strength of the electromagnetic force between elementary particles) were higher or lower than they are in this universe. The small, white sliver represents where life can use all the complexity of chemistry and the energy of stars. Within that region, the small “x” marks the spot where those constants are set in our own universe.”

While he doesn’t specify clearly, I think he is making an error here.  Unfortunately he doesn’t talk much about charge (both mentions are in reference to what electromagnetic force is not about charge per se), but it seems like he might be suggesting that it could be possible to change the fine-structure constant without changing the elementary charge.  I have a vague recollection of having even read it, make it less of a suggestion and more of an explicit statement, but for the life of me I can no longer find it.

Even if he is not making such a claim, he is still putting the cart before the horse.  Electromagnetic force between elementary charges is going to be proportional to the magnitude of the elementary charge, full stop.  It has nothing to do with the value of the fine structure constant which is merely a representation of the ratio between the elementary charge and the Planck charge (α_(e)=e²/q_Pl², where the (e) subscript highlights that the calculation of the electromagnetic coupling constant [also known as the fine structure constant] is calculated on the basis of the elementary charge).  He should be talking about the value of the elementary charge perhaps, and not the fine structure constant.

Sure, if a hypothetical elementary charge were z times that of the elementary charge (e_hyp=ze), then (at the same separation, r) the repulsive electromagnetic force between two protons would be z² times as strong – and the attractive force between an electron and a proton would also be z² times as strong.

For two protons, it seems that the maximum value of e_hyp may well be the Planck charge, noting that it was calculated in SI World and Planck World that the strong force is more than sufficient to hold two Planck charges together at a distance of femtometre.  This means that there is another way to look at the fine structure constant – that is as a representation of how finely tuned the strong force is not.  It is quite bit stronger than it needs to be (perhaps in the order of a thousand times).  Alternatively, if there is a natural limit to the possible charge on subatomic particles to the Planck charge, then it is possible that the elementary charge could have any non-zero magnitude below that of the Planck charge, giving the fine structure constant any non-zero value below unity.

Consider then an electron and a proton bound in a hydrogen atom.  The electron can be thought of as being prevented from spiralling into the nucleus by the balance of forces (there is also an argument from the basis of the kinetic/potential energy balance but note that this argument, as presented, uses a leap that is not explained and is thus not accounted for adequately – see also the Bohr model which co-incidentally points towards the nature of the leap). 

For hydrogen, (note the subscript used here is to emphasise that we are talking about an electron):

m_ev_e²/r_e=e²/4πε₀r_e²

m_ev_e²=e²/4πε₀r_e

Note that 2πr_e=λ_e so

m_ev_e²=2π.e²/4πε₀λ_e

e²/4πε₀= m_eλ_ev_e²/2π

but note that p_e=m_ev_e and λ_e=h/p_e, so m_eλ_e=h/v_e and so

e²/4πε₀=(hv_e/2π)=ħv_e

Thus

v_e= e²/4πε₀ħ

Note that this lines up with the value calculated here for a hydrogen atom where the principal quantum number n=1.

Now consider that α_(e)=e²/4πε₀ħc and q_Pl=√(4πε₀ħc), we have

v_e=(e²/q_Pl²).c=α_(e).c

It follows, therefore that

v_hyp=α_hyp.c

This clearly places a natural limit on the charge of an electron such that 0<α_hyp<1, meaning that 0<e_hyp<q_Pl (assuming non-zero mass, otherwise “≤” might apply at the upper end).  This is a form of mathematical confirmation of the intuition obtained from consideration of the case of two protons.

Note the immutability of this equation.  If you change the magnitude of the elementary charge, you change the magnitude of the electromagnetic coupling constant and therefore you change the speed of the electron.

Looking back at an earlier equation and multiplying through by ħc/ħc

m_ev_e²= ħc.e²/4πε₀ħcr_e

Recalling that α_(e)=e²/4πε₀ħc and that v_e=α_(e).c

m_e(α_(e).c)²= ħc.α_(e)/r_e

m_e.α_(e).c = ħ/r_e

Rearranging for r_e

r_e=ħ/(m_e.α_(e).c)

Compare this with the Bohr radius which is given by

a₀=4πε₀ħ²/m_ee²

Multiplied through by c/c and noting that α_(e)=e²/4πε₀ħc

a₀= ħ.4πε₀ħc/e²/(m_e.c)

a₀=ħ.1/α_(e)/(m_e.c)= ħ/(α_(e).m_e.c)=r_e

By extension, we see that

r_hyp=ħ/(m_hyp.α_hyp.c)

---

The implication here is that there is some flexibility in the related values for our hypothetical electron, α_hyp, m_hyp and r_hyp.  We have already established that 0<α_hyp<1.  Looking at the extremes:

If α_hyp→0, and m_hyp has any value, then

r_hyp→∞

If α_hyp→1, and m_hyp=m_Pl=√(ħc/G), then

r_hyp→ħ/(√(ħc/G).c)=√(ħG/c³)=l_Pl

If α_hyp→1, and m_hyp>m_Pl=√(ħc/G), then

r_hyp<l_Pl

If α_hyp→1, and m_hyp→0, then

r_hyp→∞

In other words, the orbital radius of the electron could (depending on the choices for the other two values) be anything greater than the Planck length.  The mass of the electron has a soft limit at the Planck mass, but could have higher values if the fine structure constant were sufficiently low.  Note that we would eventually run into problems with low values of the fine structure due constant gravitational attraction swamping the electromagnetic repulsion meaning that there is another soft limit hidden in there.  Also, there is a limit due to the size of the nucleus, meaning that r_hyp would have to be significantly above the femtometre scale. The magnitude of the fine structure constant is limited to between 0 and 1, as explained above.

In reality, the only possible driver of any fine tuning here, if anything, is the value of the strong coupling constant, but this only affects particles in the nucleus, and it is more than sufficient to bind two particles with a unit of Planck charge each as close as a femtometre to each other.  The tuning, such that it is, is with respect to the separation at which the force is maximised – but even then, this is about 10⁴ tighter than the electron orbit.

It appears, therefore, that the much vaunted “fine tuning” is, in fact, pretty damn coarse.

---

I don’t know enough about the (residual) strong force to work out if there are any natural limitations to its strength.  But the valid magnitude for the fine structure constant is certainly limited to between zero and unity, so Barnes’ image should at least look like this:

Since nothing happens in the region above where the strong constant has a strength of 1, we could safely ignore that space – which Barnes sort of does with his squeezing 10-∞ in a region that is about half that of 1-10.  Just keep in mind that this is arguably a hypercorrection:

Barnes’ scale is strangely pseudo-logarithmic, centred on unity with more than one half of it taken up by values, on both axes, between 0.1 and 10.  At first glance (especially prior to correction) it seems that the line above the “carbon-impossible” region might have a shape that is merely an artifact of his selection of scale.  But with the cut-down version, we can see clearly that this isn’t the case, the point [0.1,01] sits on the line, but neither [0.01,0.01] nor [1,1] do.

While there is very limited data, I suspect that what Barnes did was use a combination of logarithms and square roots of the offset from unity to construct his scale.  I don’t know why he did that.  If he’d not used such a scale, he could still have made his point, perhaps even more strongly.  If he didn’t use his strange logarithm scale, he could have had something more like this:

Note that I’ve just used his scale and plotted the intersections, I’ve not tried to reproduce the curves.  I am not commenting on his claims in the coloured sections per se, but I have added my caveat to try to prevent the image being misused.  Remember, you cannot change the fine-structure constant without affecting the elementary charge – by definition.

Why didn’t Barnes present his case more like this?

I suspect that the problem is that it would appear to make his case too strongly and that would have attracted closer, unwanted sceptical scrutiny.  There is good reason to label apologists as “liars for Jesus”, Barnes among them.

---

Interestingly, in a later paper, Barnes does not mention the fine-structure constant at all (although he does use the symbol α without saying what it means, it is used in a claim about the mass of a proton).

Fine-Structured but not Fine-Tuned

There has been a lot of fuss about the fine-structure constant (α), perhaps because it’s a specifically odd value, at very very close to 1/137.  And 137 is an odd number, both in that it’s not even and also in that it’s a prime.  And it’s a special prime, being a Pythagorean prime because 88*88+105*105 = 137*137, and the square root of 137 is the hypotenuse of a triangle with integer legs (4*4+11*11=137).  1/137 has a palindromic period number.

The value of the fine-structure constant is not, however, precisely 1/137.  It’s closer to 137.036, which is not as sexy.

This doesn’t stop some people from getting excited about, including our fine-tuning friends – for example Luke Barnes.  The reason for this (they argue) is that if the fine-structure constant were even slightly different then stars would either fail to produce oxygen (which I think we can all agree is important) or fusion could not occur at all – with a margin of about 4% either way.

The thing that’s a bit odd is that the discussion is all about this fine-structure constant, and yet the value of the elementary charge seems never to be mentioned.

What, you may ask, does the elementary charge have to do with the fine-structure constant?  If so, that means you didn’t follow the Wikipedia link regarding what the fine-structure constant is, because the very first two sentences are:

In physics, the fine-structure constant, also known as Sommerfeld's constant, commonly denoted α (the Greek letter alpha), is a dimensionless physical constant characterizing the strength of the electromagnetic interaction between elementary charged particles. It is related to the elementary charge e, which characterizes the strength of the coupling of an elementary charged particle with the electromagnetic field, by the formula (4πε₀).ħcα = e².

So the fine-structure constant is proportional to the square of the elementary charge, because ε₀, ħ and c are all constants (and 4 and π are also constant – note that I added the brackets above, they aren’t there on the Wikipedia site).  What I find interesting is that 4πε₀, ħ and c are not only constant but, in Planck units, they all resolve to 1.  Note also that ħ is the reduced Planck constant, the Planck constant divided by 2π.  We could call 4πε₀ “raised permittivity of free space” or the “raised electric constant”.

This might seem to be a little bit of a cheat, but it should be noted that µ₀ has as similar but inverse relationship to Planck units, in that µ₀/4π (“reduced permeability of free space” or the “reduced magnetic constant”) resolves to 1 in Planck units, so that not only does c²=1/ µ₀ε₀ but that relationship remains the same when µ₀ and ε₀ are replaced with their increased and reduced versions respectively.  Note also that the fine-structure constant can be expressed in terms of permeability, by the formula (ε₀/4π).ħcα = e².  And these two constants frequently appear with a 4π in the appropriate place, almost they are begging someone to normalise them in a similar way to how the Planck constant is normalised.

Normalisation removes the mystery of why, when all the other fundamental constants seem to resolve to 1 at the Planck scale, these two (µ₀ and ε₀) don’t.  They do when normalised.  What remains outstanding however is the fine structure constant.  It’s a dimensionless value, so how could we possibly resolve it down to 1?

The answer is hiding in those equations - (4πε₀).ħcα = (4π/µ₀).ħα/c = e².  Or, once reorganised - α = e²/(4πε₀).ħc = (e/√((4πε₀).ħc))².  So does √((4πε₀).ħc) have any meaning that we should be aware of?  You bet it does – it’s the Planck charge, or the charge on the surface of a sphere that is one Planck length in diameter and has a potential energy of one Planck energy.

So, put another way: α = e²/q_pl², the fine-structure constant is effectively an expression of the ratio of the elementary charge (e) to the Planck charge (q_pl), in much the same way as the gravitational coupling constant is effectively an expression of the ratio of the rest mass of an electron (m_e) to the Planck mass (m_pl), or α_Ge = m_e ²/m_pl².  (If you look up “electromagnetic coupling constant”, you’ll be redirected to the fine-structure constant.)

If you read about the gravitational coupling constant, you will note that there “is some arbitrariness in the choice of which particle’s mass to use”.  It appears less arbitrary to select the elementary charge when considering the electromagnetic coupling constant (ie the fine-structure constant), but it is still a little arbitrary.  There is a smaller charge that could be selected, that associated with quarks, which could be as low as e/3 (positive or negative depending on the type of quark).

Before I take the next step, I have to point out that while the gravitational and electromagnetic coupling constants (as commonly understood) are effectively an expression of the ratio between the relevant characteristic of an electron to the relevant Planck unit, this isn’t the meaning of these coupling constants.  They are both defined as “a constant characterizing the attraction between a given pair of elementary particles”, electromagnetic attraction in the case of the fine-structure/electromagnetic coupling constant and gravitational attraction in the case of the gravitational coupling constant.  There is also a definition based on the interaction of these elementary particles with the related field.

We could naturalise both of these constants by considering instead “the attraction between a pair of Planck particles” or the interaction of Planck particles with the relevant field, considering them to have both Planck charge and Planck mass.  When we do, the values both resolve to 1.

Another way of saying this is the fact that the coupling constants don’t have a value of 1 is merely because the electron mass and charge are both smaller than the Planck equivalents (the mass is much smaller, but the gravitational coupling constant is also much smaller than the fine-structure constant).  When people are talking about the range in which the fine-structure constant could be varied without affecting life in this universe (by preventing stars from doing what they need to do to create the basic building blocks of life as we know it), they are really talking about how much higher or lower the charge on the electrons and protons can be.  It’s actually a bit odd that fine-tuners don’t do this because when they say that the fine-structure constant can only vary by as much as 4% before we run into trouble, this is equivalent to saying that the charge on an electron or proton can only vary by as much as 2%.  If there is fine-tuning here, then there’s actually twice as much fine-tuning (on this single measure) as the fine-tuners are claiming.

Either way, it’s a bit unreasonable to point at the fine-structure constant as an example of fine-tuning in and of itself.  If the fine-tuners want to claim any fine-tuning here, they need to point to the elementary charge.  However, if they can explain why elementary charge is odd in some way or could be something else than it is, they are welcome to try.  There doesn’t seem to be anyone else looking into that and when people ask awkward questions there’s a lot of “we just don’t know”.  And, so far, the fine tuners appear to have steered clear of the elementary charge.

The Dark Energy of Luke Barnes

Maybe I’m being a bit unfair with the title since the articles in question are attributed to more than just Luke, there are eight other authors:  Jaime Salcido, Richard Bower, Geraint Lewis, Pascal Elahi, Tom Theuns, Matthieu Schaller, Robert Crain and Joop Schaye.  However, as far as I know, the others aren’t Templeton Research Fellows – one of the articles has LAB (Luke A Barnes) but only LAB tainted with an association with Templeton.  And I note that there is a statement distancing that paper from Templeton (“The opinions expressed in this publication are those of the author and do not necessarily reflect the views of the John Templeton Foundation”.)  Oddly enough, the other article “The impact of dark energy on galaxy formation. What does the future of our Universe hold?”, despite having the same authors (admittedly in a different order), does not acknowledge that Luke is supported by Templeton.  Perhaps because Luke was not lead and Jaime Salcido didn’t want to have anything to do with Templeton if he could help it?

Anyways, I’m pondering not so much the paper as the raft of articles that are based on the papers, helpfully listed by Luke at Letters to Nature.  The spin of these articles varies somewhat, at least going by their headlines, from “Life in the multiverse could be commonplace” to “Bad information for the multiverse: it is nonetheless not going (sic)”.  Either life is teeming in the multiverse, or there’s no multiverse.

Interestingly, if you look at an example of the former – for example A multiverse may be hospitable to life:study – you will see that the scientist quoted is Jaime Salcido.  But if you take a look at an example of the former – for example Bad news for the multiverse: it's still not likely – the featured scientist is Luke Barnes.  There’s also a third spin, namely that there needs to be a “new law” for dark energy, which means that the article headline writer chose to focus on the words of Richard Bower – for example New Research Questions The Multiverse Theory, Calls For A New Law Of Dark Energy.

It looks very much like Barnes and Salcido have looked at the same data and Barnes has opted to interpret it as negating the multiverse (more on that in a moment) and Salcido has interpreted it as saying that life is probable no matter which universe in the multiverse you are in.  This would mean that we’re not that special and not even our universe is that special, as even one of the more Barnes-centric articles put it “That’s bad news for the multiverse, because it means there’s nothing particularly special about our universe - and no need for a multiverse to explain our existence.”  I’m pretty sure that Barnes wouldn’t be happy with that comment.

Barnes, you see, wants fine tuning, because that supports his god and as I have argued elsewhere, he’s a closeted apologist.  If we don’t need a multiverse to explain our existence, because our universe isn’t particularly special, then we don’t need Barnes’ god either.  If there’s evidence against a multiverse, that’s not going to bother real scientists because real scientists aren’t pushing an agenda.  Not that Barnes et al have come up with evidence against a multiverse, all they have is an argument that you don’t need to call on a multiverse to explain the amount of dark energy we have – as far as the star formation rate goes.  That’s alright, we don’t even know for certain that there is dark energy (see sceptical interpretations of dark energy related measurements – such as this).

Some of the articles present an argument that, if it comes from Barnes and/or Bower and isn’t merely a misinterpretation on the journalist’s part, is worryingly deceptive.  There is a suggestion, for example at Inquisitr, that the multiverse theory is there to explain (in part) the value of dark energy.  This is a ludicrous suggestion given that the multiverse has been suggested since as far back as 1952 and the term “dark energy” was only coined in 1998.  Additionally, it is argued that the multiverse simply falls out of string theory to the extent that if string theory is true then, necessarily, there is a multiverse.  String theory dates back to the 1940s, so again predating dark energy.

Basically, multiverse theory needs a fine-tuned value of dark energy to about the same extent as the value of dark energy needs a multiverse theory – namely, not at all.

Could the Universe have Created Itself?

Skydive Phil has a new Before the Big Bang episode out, “Can the Universe Create Itself?”  In The Boundary Proposal and i-Time, before having seen the video, I suggested that the answer would be no.  Now, after having seen it, my answer remains a steadfast no.  Note that I have changed the tense in the title of this article, effectively making it a different question, but the answer to both questions is no.

I think that the star of the video, Gott (amusingly the German word for “god”, noting that all nouns in German are capitalised), was addressing a different question: could the universe have emerged from a closed timelike curve? or, could a universe which is temporally unbounded have a beginning in the finite past?  The answer to both of these, according to Gott, is yes.

My issue, however, is that all the clever folding of space (and balancing of different types of vacuums to result in zero energy and zero pressure) doesn’t provide you with an escape from the problem of (infinite) regress in which you keep going back to an initial state and ask how that “initial” state got there – at which point you admit to a new “initial” state.  Even if there was a primordial closed timelike loop out which our universe sprung (somehow resulting in the hot dense, pre-Big Bang state), you can ask how that closed timelike loop got there.  And was (is?) the medium in which that closed timelike loop existed (exists?)?  Clearly it’s not “in space”, but it would be a loop of something, presumably, “in” something.

I agree that, given the assumption of an initial closed timelike loop, we could have a universe that just happens due to a quantum fluctuation but I don’t think we really have an argument here against a theist (the believer in a different kind of Gott) who might argue for a quantum engineering version of the Creator, one that carefully sculpts a very specific closed timelike loop – from nothing and in nothing – out of which the pre-determined universe springs entirely in accordance with some divinely inscrutable plan.

---

I have a somewhat different view on cosmogony, the origins of the universe.  As I described in The Boundary Proposal and i-Time, I see this universe as being inside a black hole.  I also see the universe that is “outside” (and in a sense “outwhen”) our black hole as also being inside a black hole, although I don’t have the same level of evidence to support that notion – I am just assuming the consistency of relativity (some of the initial conditions would be not need to be consistent across universes).  And so on, each universe is encapsulated in a black hole nestled in the next universe up.  (I say “up” because a black hole is a gravity well and you go down into wells.)

Although this universe (and all universes in this chain) may be future eternal, we can nevertheless consider them as being a sequence of expansion-contraction phases (ECPs) – because the part that matters, the mass-energy will inevitably contract even if the empty space around it expands forever.

My concept is that it is possible, if unlikely, under quantum physics for things to wobble into existence.  Not things like Boltzmann brains, which are far too complex to actually eventuate, but tiny amounts of mass-energy.  Even if only miniscule amounts of mass-energy eventuate in each link of the universal chain, the chain is not limited as far as the number of links (the ECPs) so eventually, you will end up with a universe as large as ours.

I have no idea how much mass-energy could come into existence via quantum mechanical processes in each universe, but if we limit it to, for example, one joule per ECP, then to arrive at a universe our size would take 10⁷⁰ ECPs.  This is a lot of iterations and it becomes less surprising that, eventually, a species such as ours should eventuate.  It could be that less mass-energy is added each time, perhaps the least amount of energy possible at the time it comes into existence - which today would be c.h/(width of the universe) and that is a pretty small amount of energy.

Now this idea can be applied to another problem – if only very small amounts of energy are added each time, how could it be that the first black hole formed?  If there was only a tiny bit of energy at first it would not be enough to form a black hole, because you need at least a Planck mass in a Planck volume (which is notionally the smallest volume).  However, if the lowest amount of mass-energy that can be added by quantum mechanics to a universe is defined by c.h/(width of the universe) then, when the universe is as small as it can be, at Planck volume, the width is one unit of Planck length and in that case the lowest possible amount of energy is precisely one unit of Planck energy, precisely what you need for your first black hole.  This first black hole would commence the ECP process, which is initially instantaneous (actually one unit of Planck time), until there is another quantum mechanical event that adds another minimum amount of energy.  So the number of ECPs between us and that first quantum mechanical event could be, well … astronomical.  Beyond astronomical.

In my model, the universe does not create itself, but its beginnings are extremely humble, it is equivalent to a multiverse – but at least partially sequential (I have no issue with each individual black hole spawning their own chain of future eternal universes, prior to be being subsumed in the final universal black hole) – and it gives support to the idea that a universe as suitable for life as ours could indeed arise merely by chance, even if “fine tuning” for it were necessary.

---

I did mention above that the universe, or at least the part of it that matters, will inevitably contract.  This sounds like it might be a big claim, so I will try to address that another day.

The Problem with the FTA

Well, it's a problem.  There are other problems, and the problem I am about to describe might not even be the biggest problem that the fine-tuning argument has.  But it's snappy title for a post.  (Oh, and I mean the Fine Tuning Argument not the Free Trade Agreement ...)

When people like Luke Barnes go on and on about all the limitations on physics and cosmology that you'd be faced with if you were building a universe from scratch in order to ensure that (intelligent) life existed in it, they eventually reach a point in which their expertise is no longer relevant to the argument.  Basically, if we were wondering about the magnitude of the design problem, trying to come up with a figure that describes how unlikely it would be that a life permitting universe would be the result if we just threw the "randomise" switch, then Barnes has something to bring to the table.  But once we've arrived at a figure, say that there's only one chance in 10^240 that a universe like ours would result, then Barnes' training in astrophysics is no longer relevant, he's still a smart guy, but he can't wave his doctorate around anymore and pretend that it means anything.

In brief, what Barnes can do is help us focus in on whether the universe as it is unlikely, very unlikely or very very freaking unlikely.  He argues for something in the region of very very freaking unlikely.

Now, here's the problem.

To try to explain it, I am going to use an analogy.  It's not a perfect analogy and certain elements of it aren't strictly relevant, they are just there as part of the narrative to help explain the key point.

---

Say you are given an urn.  In the urn you see there is a little pork sausage.  This means that you have in your hands an LSU or an LPU, Little pork Sausage Urn or Little Pork sausage Urn, depending on your point of view.  These acronyms might seem completely arbitrary to some readers, but they’re not.  LSU and LPU are common acronyms in the discussion of fine-tuning and mean “life supporting (or sustaining) universe” and “life-permitting universe”.  The latter seems more common, perhaps because LSU is also used by Louisiana State University.  Let’s avoid confusion and talk about the Little Pork sausage Urn.

What is the probability that you have, in your hands, an LPU?  You could think about all the things that could possibly be in the urn: a balls, a sock, a small beaver, a cat, an alarm clock, a stone, the list of potential items is literally endless (using "literally" in sense of "not literally").  Thinking of it that way, you could say it's one in a bazillion, or one in 2 gazillion, or something like that.

However, you have already looked in the urn, you know there was a little pork sausage in there, so you've got very good reason to believe that there's a one in one chance that you are holding an LPU.

Alternatively, you could be led into a warehouse containing bazillions or gazillions of urns.  At random (problems with the term "random"aside), you select an urn.  What are the chances that the urn you selected contains a little pork sausage?  We don't know, do we?  The warehouse might specialise in producing urns with sausages in them, urns with pork sausages in them, urns with pork products in them, urns with nothing in them, urns with something random in them, or who the hell knows what.  To match the FTA, we have to specify that some relatively small number of urns must contain little pork sausages (so that LPUs are possible).

Ok, so we have two scenarios.  One in which we are holding an urn with a pork sausage in it and the other in which we are in a warehouse and know that there are pork sausages in one or more of a very large number of urns, but we don't know which.

Which is the scenario in which we find ourselves, with regard to the FTA?

It must be that we are holding the urn, because we cannot be in a scenario in which an LPU (now talking about a life-permitting universe) is not available to us because we are alive).

Here is the problem:  The FTA is always argued as if we are in the warehouse and there is a possibility that we don't have an LPU available to us.  It doesn't matter if the urn we are holding with a little pork sausage in it is the only such urn in the whole history of the universe (past and future) or how unlikely it is that we happen to have it in our hands.  Without it, we are in a completely different scenario, in which we have no LPU and, switching seamlessly from analogy to the thesis of the FTA, if there were no LPU, we would not exist.

No amount of jiggering with the numbers will affect that brute fact.  So the involvement of people like Luke Barnes in the promotion of the FTA is, at the end of the day, without any real value.

---

That's not to say that the involvement of Barnes is without rhetorical value, or value for anyone wanting to make a fallacious appeal to authority.  But that's about tricking you into believing that the argument has merit, not about showing that you that argument has merit.

Turning Fine-Tuning on its Head

The existence of you and me is, in a sense, fine-tuned.  This statement might come as a surprise to anyone who has noticed that I am vehemently against the fine-tuning argument, but I can explain.  The fine-tuning argument goes a little like this:

Fine-tuning,

Therefore, god.

I've stripped it down a bit, but those are the basics of the argument.  I don't have much against the first line, given the inherent (often ignored) caveats, but I do have problems with the second as I would have problems with the first premise of an expanded fine-tuning argument, namely the assertion "If fine-tuning then god".  The stripped-down but deluxe version of the argument, which I also have problems with, is:

If there is fine-tuning, then either god or something else,

Fine-tuning,

Not something else,

Therefore, god.

My problem is with the third line of this version.  When argued by such luminaries as WLC the main thrust is that the idea that we should be here purely by chance, when the odds against are so staggeringly high, beggars belief.  The problem is that there remains a gap between unlikely and impossible.  The answer "something else" remains possible, and to some it is believable despite being unlikely, while the god solution is simply not believable. 

What I don't argue against is the line "Fine-tuning", so long as that line is short-hand for "if things were slightly different in this universe, then intelligent life would almost certainly not exist".  If "fine-tuning" is short-hand for "this universe was designed by a divine being of some sort", then of course I have a problem but then the whole fine-tuning argument resolves down to begging the question, "god, therefore god".

Now, about you and me being fine-tuned - let's get all excited about it!  Think about how amazing it is that we exist on one little planet in such a massive universe.  What are the chances of that?  If we go by volume, we can see that the Earth is only about 10^-56 of the observable universe's volume.  If we were just about anywhere else, we'd be dead. 

But of course it'd be silly to compare our location with a random spot in intergalactic or even interstellar space.  It's pretty cold out there, and we need to be a bit warmer than that, without being too warm.  So we could consider how remarkable it is that we are in orbit around just this star, one that is so suitable for intelligent life to develop.  While our sun is one of about 10²¹ stars, it's a pretty common type of star - roughly one in five is a G-class star.  And about one in five of those is estimated to have an "Earth-like" planet in orbit around it - in the habitable zone.  So about one in twenty-five stars are of the right type with the right type of planet in orbit around it.  (ed. - these numbers have changed with more observation, but not in a direction that helps the apologists)

Not that amazing after all.  Although, to get the one in twenty-five figure we are assuming that once we've got the right type of star, and it's got the right sort of planet in the right sort of zone, then we get that one automatically.  That's a little unreasonable.  Our solar system is jam-packed with planets, moons, asteroids and comets (by which I mean generally "very sparsely packed, but with more than half a million objects").   The chances of ending up on the one habitable object out of all of those is about, well, one in half a million (after we've select the right star, with the right planet in orbit around it). 

If we did limit ourselves to a suitable planet in orbit around a suitable star though, the fact is that we are on a very privileged part of that planet - standing somewhere close to the surface (ISS residents aside, plus anyone currently on a high-altitude international flight).  We're sitting or standing rather comfortably on the surface instead of floating high in the atmosphere, floundering at the bottom of an ocean or being crushed and then burnt to a cinder in the core.  And we live in a community that is relatively well placed on that surface: not in a volcano crater, not in Death Valley, not in Antarctica, not just below the summit of Everest.  What great fortune!  However, only about one sixth of the Earth's surface is habitable (half of the land mass).

Then there is timing.  This is a rather good time for intelligent life.  The planet that we are on has sufficient oxygen, not too much carbon dioxide, it still retains enough of the ozone layer that we don't die too quickly of cancer and the temperature is about right - not too cold that we freeze to death and not too warm that we are constantly flayed by killer storms or reduced to desiccated husks.  We have flowering plants, most importantly variations of grass that permit large populations to feed themselves, and they have only been around for about 55 million years, so 1.4% of the time that the Earth has been a planet.  Humans (as Homo sapiens) have only been around for about 200,000 years, or one thousandth of one per cent of the age of the Earth.  Genetic research indicates that humanity has gone through a few bottlenecks, the most recent may have been about 70,000 years ago - meaning that we were lucky, as a species, to not go extinct at that time.

It's remarkable that we're alive at all.  It's in the order of one in a billion, even aside from all the unlikeliness of one particular human meeting another particular human and producing a specific human at a specific time (with none of them being killed by any of the lethal flora and fauna that is abundant on this planet).  So … sure, we're fine-tuned, in a sense.

---

The thing is that what I have just provided is a continuous stream of indicators that our universe is not finely tuned for human life.  Our planet is not finely tuned for human life – there’s a very narrow band geologically and temporally.  We are finely tuned to exist in that very narrow band and the fine-tuned-ness of a biological organism to its environment is far more elegantly explained by evolution than it is by the introduction of a creator being.

The bottom line is that fine-tuning is not a challenge to naturalism or evolution or atheism, the real challenge is to the creationist or intelligent design theorist to explain why the universe is so unrelentingly hostile to humanity.

A Weak Argument

Perhaps, like me, you have become tired of me attacking Max Andrews' thesis.  If so, good news!  Now I want to attack something Max Andrews wrote in a blogpost.  It's quite a minor element of the post, but it blossoms out quite rapidly:

Let’s look at the weak force coupling constant, g_w = 1.43 x 10^-62.

He hasn't even got into the argument with this statement and it's taken out of context (the specific context isn't actually important) but even so there is so much to talk about.

If you take the time to look up the value of the "weak force coupling constant" you may find that α_w ≈ 10^-7.  The sharp eyed among you might see that we are talking about what appears to be apples and oranges, or g_w and α_w.  Admittedly, at first I thought that Andrews couldn't work out how to display an α and was using g instead (which would be strange).  However, if you dig deeply enough around the net you will find that

α_w = g_w² / 4π

which means that g_w ≈ 1.1 x 10^-3.  That's a big error margin when one is talking about how weak the weak force coupling constant is (10⁵⁹ times bigger than claimed).

(There is a real difference between α_w and g_w.  The former, α_w, is the "weak interaction coupling constant" or " weak nuclear force coupling constant" or "weak force coupling constant" or even "weak fine structure constant" and it represents the strength of the weak force in an interaction.  The latter, g_w, is a less frequently mentioned value.  It is known as the "effective charge of weak interaction" or "weak gauge coupling constant" and is a measure of the strength of the interaction with the weak gauge field (in gauge field theories).)

But wait … there's more.  Andrews might not be entirely wrong about this value (he is though, as we shall discover below).

Like quite a few other constants, the weak force coupling constant is not actually a constant.  It varies with distance, so it can (and should) be expressed as a function of range.  There is undoubtedly a specific range at which g_w = 1.43 x 10^-62 (one not terribly far off the radius of a proton at about 10^-15m).  The question, however, is whether Andrews - who talks about a number of constants in the article - uses the same point of reference.  Note that he refers to the strong coupling constant this way:

g_s = 15

This shares the same relationship with α_s as above, so this corresponds with α_s ≈ 13.7.  Note however, that an actual theoretical physicist, Matt Strassler, has this to say:

But at longer distances, the strong nuclear force gradually becomes (relatively!) stronger. [Again, remember what we mean by “weak” and “strong” here; the force is actually becoming weaker in absolute terms as r increases, but relative to, say, electromagnetic forces at the same distance r, it’s becoming stronger.]

§  α_strong = 0.3 (at r ~ 10^-16 meters)

That’s quite strong indeed! And by the time r reaches 10^-15 meters, the radius of a proton, α_strong is bigger than 1, and becomes impossible to define uniquely.

It's still going to fall with distance, but distance isn't the only measure against which to measure the value of the strong coupling constant.  You also need to consider the energy range, for example on the chart in this article, it can be seen that α_strong peaks at about 0.7 GeV (billions of electron volts) with a value of about 1.2 which equates to a g_s ≈ 3.9.

Andrews' suggested g_s of 15 seems quite unreasonable.  But at least this time he is only out by a factor of about four, rather than a factor of 10⁵⁹.

Which brings us back to Andrews' claim for the value of the weak force coupling constant at 1.43x10^-62.  This is, fortunately enough, a rather specific number so that when I stumbled across it again, at WikiUniversity, it leapt out at me.  But note that this value, while associated with the weak force coupling constant isn't the weak force coupling constant.  It's the Fermi coupling constant, G_F, as expressed in J.m³.  To get the weak force coupling constant, you need to go a step further ("at sufficiently small distances"):

α_w = G_F.M_p².c / ħ³ = 10^-5

This corresponds with a g_w of about 8x10^-12.

Admittedly, the value of α_w is directly proportional to the value of G_F, so Andrews could structure his argument in terms of how the extremely low value of G_F appears to be fine-tuned.  But this isn't the problem usually talked about in physics circles.  They talk about how the measured (effective or renormalised) value of G_F is so much larger than might otherwise be expected (the hierarchy problem).

Interestingly, they suggest that, once normalised, G_F lies very close to G (the gravitational constant).  Personally, this is what I'd expect at least in terms of natural units - furthermore, I'd expect both of them to have a value of precisely 1 (like the gravitational constant, the speed of light, the reduced Planck constant, all the Planck units - mass, length, time, charge, temperature - the Boltzmann constant and the Coulomb constant (which is related to the permittivity constant)).  If this is the case, then their values are not an instance of fine tuning at all, they would be just yet another expected reflection of the nature of the universe.

Even if this isn't the case, Andrews should be a lot more mindful when making bold claims about the values of fundamental constants and try to avoid being out by such huge factors.