Never mind whether the universe is "fine tuned" for anything in particular,just the idea that there is a nested hierarchy seems incredibly constraining on the outcome, and anything but accidental.
locked by Noldorin Jan 23 '11 at 0:21
closed as not a real question by mbq♦ Jan 23 '11 at 0:16
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You have to define exactly what you mean by 'nested hierarchy', but I suppose you deliberately pose your question in loose terms, and just wonder about systems that can be meaningfully described in markedly different ways at a hierarchy of levels.
Let's take a simple system as example: Conway's 'Game Of Life' (GoL). We all know this simple binary callular automaton and its local update rule. A hierarchy of structures is known to develop in GoL: gliders get produced in glider guns, these gliders move and interact, etc. Yet, the occurrence of such structures was not build into GoL. Someone just tried out some simple rules. It was only later when people started to simulate this system in more depth that a 'hierarchy of structures' was discovered.
You might argue whether 'fine tuning' was applied by John Conway when he constructed this model, but in any case it appears that cellular automata with similar complex behaviors result for a wide range of cellular automata rules. So my answer is 'no'. It is entirely possible that a 'hierarchical system' is emergent from 'accidental rules'.
your assumption is right at the naive level: the hierarchy seen in the objects' being composite at many levels implies that there have to be many different scales, and these many scales imply the natural existence of parameters of Nature that differ by many orders of magnitude. If all the parameters were random, you wouldn't expect a hierarchy - at least not one that has many layers - because most of the parameters would be of the same order.
In some sense, this is a more general statement than the hierarchy problem.
However, just because some parameters are different by several orders of magnitude - e.g. the size of the atom and the size of its nucleus - it doesn't mean that there exists no non-fine-tuned theory that actually explains these hierarchies. So we know many parameters in Nature that are vastly different than their friends - and able to create hierarchies - but they don't require any unnatural fine-tuning.
In particular, the emergence of molecules (and cells) as bound states of many atoms is inevitable. One can show that it is energetically favored for many atoms to create various larger molecules, so they will inevitably do so. The emergence of life is of course much more complex and miraculous but there exists no evidence that life requires anything else than the laws of physics we know to be valid for atoms.
You need to go inside atoms to see things that require new components of the physical explanation. You find nuclei and quarks inside them. And you may go to the very Planck scale - 19 orders of magnitude shorter than the size of the nuclei. That's where the "matryoshka setup" has to end because the geometry itself as we know it becomes inapplicable.
However, various big ratios are understood.
For example, the nucleus is much larger than the Planck scale, as I have just said. Although the difference is 19 orders of magnitude, one doesn't really need any excessive fine-tuning. It's because the strong interactions' "fine-structure constant" inevitably takes a value near the Planck scale which is of order one - something like $1/24$. However, it's running and getting stronger at longer distances - proportionally to the logarithm of the distance scale. Because the running is (naturally, calculably, and demonstrably) logarithmic, you need to go to exponentially longer distances than the Planck scale - namely the size of the proton - and that's where the force starts to confine the quarks. This is therefore the size of the protons that emerge out of these interacting quarks.
Other hierarchies - such as one between the Higgs mass and the Planck scale - are not understood in the same way at the present moment, or at least it hasn't quite been established which of the candidate explanations we possess is the right one (although all people "in the know" know that it's almost certainly supersymmetry haha). It's likely that a well-defined answer will be found in the future - for this hierarchy or any other hierarchy. However, even today, we already know enough to say that your general statement that "any hierarchical architecture of matter requires fine-tuning" is not correct, however attractive such an assertion could be for various emotional reasons.
Best wishes Luboš