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For example say the gravitation constant instead of equaling G, was actually a range bounded between 0 and infinity.

Our Universe would be at a point on this range (equal to our G value) where things could physically exist and produce stars, galaxies and life. Yet in the gravitation constant's dimension it is able to be lower and higher then our G value.

All other physical constants being equal, this would allow the sort of full universe we recognise to exist on only a very tiny part of the full range of the gravitation constant's dimension. The rest of the dimension would be full of non-universes that would not be able to support anything.

The other non-dependent physical constants perhaps also represent dimensions. And there might even be a set of useful life supporting universe's on a continuous 'line' inside this n-dimensional structure.

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  • $\begingroup$ This is more-or-less the raison d'être for multiverse theory (specifically the so-called Level II multiverse) $\endgroup$ – Kyle Kanos Jan 25 '14 at 21:26
  • $\begingroup$ Yep, our universe is assumed to be a point in the parameter space of the theory that describes it. But this does NOT mean that there have to exist tons of other universes that correspond to other values of the parameters... A more reasonable point of view is think of the parameter space as the allowed solutions of the equations, and that's it . $\endgroup$ – Dilaton Jan 25 '14 at 22:24
  • $\begingroup$ And indeed there are serious physicists investigating what would work no longer or different in our Universe, which parts of the parameter space could potentially support some kind of life, etc ... From thinking out of the box like this, many things about our universe (such as how the parameters must interply to allow the formation of stars, atoms, planets) $\endgroup$ – Dilaton Jan 25 '14 at 22:34
  • $\begingroup$ Why is this question being downvoted? $\endgroup$ – mcFreid Jan 25 '14 at 22:53
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That is an open question in physics: why are there so many non dependant constants? Approx twenty in the standard model.

Some proponents of string theory would agree with your way of describing non-dependant constants, and say they could be any value but have to be the value they are due to the Anthropic Principle.

Einstein is quoted as having said:

... is whether God had any choice in the creation of the world.

What he meant by that is that the more we discover about physics the more dependencies we find between these constants the less truly non-dependant constants there are. Each non-dependant constant is a "choice" but if there are enough dependancies then there in no "choice for god" at all.

For example consider the three constants, the speed of light:

$$ c $$

The Permittivity of free space

$$ \epsilon_0 $$

The permiability of free space

$$ \mu_0 $$

There are three constants there but since we have one equation relating them:

$$ c= \frac{1}{\epsilon_0 \mu_0 } $$

This leads us to there being two (three constants minus one equation) non-dependant constants with the third beind depentand on the other two.

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