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I've looked in and out the forum, and found no precise definition of the meaning of fine-tuning in physics.

QUESTION

Is it possible to give a precise definition of fine-tuning?

Of course, I guess most of us understand the empirical meaning of the phrase... but it seem so ethereal, that's the reason behind my question.

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  • $\begingroup$ In practice, everyone uses a definition of fine-tuning that puts their model in favourable light :P Then again, there since there is no precise definition, you must forgive all those attempts for one of them might turn out to be the right way to look at things. $\endgroup$
    – Siva
    Commented Nov 8, 2014 at 19:11

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All we can do precisely is give a probability for some physical quantity to have its observed value. For example (subject to various assumptions!) the probability of the cosmological constant having it's observed value is around 1 in $10^{120}$. Since this is absurdly low we say it's fine tuned.

But where you draw the line between fine tuned and not fined tuned is a matter of debate. Most of us wouldn't consider a 10% probability fine tuned, but what about 1% or 0.1%? Particle physics required a $5\sigma$ probability to be considered proof, and this is about 1 in 3.5 million and this is about 0.00003%, so that seems like a reasonable lower bound for not fine tuned. However I'd guess most people would consider considerably higher probabilities than this as evidence of fine tuning.

The point is that the probability of an observed value can be calculated precisely, but whether this corresponds to fine tuning is a matter of personal opinion.

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    $\begingroup$ Isn't it kind of funny to talk about dark energy (via the cosmological constant) when we don't have a physics theory that it fits into? In Einstein's field equations, I'm unsure how we ascribe a maximum value to $\Lambda$ to begin with, but I would assume that eventually we'll come up with a theory that relates it to other parameters, giving a probability distribution function (somewhat similar to some Higgs mechanism parameters). Within that PDF, it could then be more or less likely to be in the hospitable region than what we've assessed so far. $\endgroup$
    – Alan Rominger
    Commented Nov 7, 2012 at 16:03
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    $\begingroup$ Agreed, and any probability for the observed value of the CC should be taken with a large pinch of salt. It was just the first example I could think of that most people will have heard of. Whether you agree or disagree with any particular probability for the value of $\Lambda$ I think you'd have to concede it appears to be fine tuned. $\endgroup$
    – John Rennie
    Commented Nov 7, 2012 at 16:13
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John Rennie's answer describes the term "fine tuning" as used in high-energy physics, but the term is often used in a very different way in the study of critical phenomena. In that context, it often has a much sharper definition: a Hamiltonian is "fine-tuned" if it lies on a particular lower-dimensional submanifold of Hamiltonian parameter space (typically a critical hypersurface). In this case we can even say that multicritical points are more fine-tuned than singly critical points, because they lie on a submanifold of higher codimension (and are corresponding more difficult to achieve in an experiment).

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