Re: The Dark Matter Problem has been Solved
Posted by Pasti on May 12, 2004 at 10:46
(67.69.237.203)Re: The Dark Matter Problem has been Solved (MirrorMan)
"Shouldn't any well defined 'variable c theory' be equivalent to a 'variable x' theory, where x is a dimensionless quantity? Otherwise, as Mike has said, it becomes similar to saying that the ratio of the gallon to the liter has changed."
If I understand well what you are saying,it should, in a certain sense, if you rescale c to some comfy constant having the same units.But that would not make much of a difference, when it comes to actually using the theory quantitatively.
The problem is not that the ratio of the gallon to the liter changes at a point in spacetime; I would say that a liter at a point in the spacetime might be different from a liter at another point in the spacetime (and mind you not because of special relativistic effects).
"So, assuming that the theory is well defined, the criticism Mike has against 'variable c theory' is its name, a bit similar to your and Dan's criticism agains the choice of the title of this thread."Not quite.You see, in theoretical physics it is quite often that people do "tricks" to get rid of cumbersome constants, like setting h=c=1, or G=16pi in some units, and so on and so forth.And these constants, of course, will have magnitudes depending also on the unit used.
But as I said earlier, to see them just as conversion factors is a restricted view, in my oppinion.The Hubble constant is one example.The speed of light is another example, and a better one for that matter, since it has an intrinsic dynamical significance.You can consider that the gravitational constant is just a conversion factor, with no dynamical value, so to speak, but you cannot claim the same for the speed of light."Mike's point of view is that dimensional constants arise because we choose to use incompatible units. As a result of that you get additional 'constants', that are nothing more than conversion factors."
I am aware of his viwpoint, but I do not agree with it in totality.In certain cases, he is right.But let me give you a counterexample:in vacuum elmg interactions propagate at c, the speed of light.In glass, with n=1.5, the elmg interaction propagates (we consider continuum theories, which are smilar to GR) at c/n.Both are limiting speeds, and both are conversion factors from say, length to time, but they are different.Rescaling one to the other introduces a dimensionless variable, in practice, this is of quite little significance.
If say the lagrangean density is homogeneous of degree c/n in c, rescaling pulls a c^p in front of the lagrangean density.Which would agree with Mike's statement, IF you can find a universal/global constant c that does the trick.And in the context of traditional GR,you can find it, since it is postulated by Einstein, which is fine.And on paer, it works great.
But what if there isn't such a constant?This is in fact Moffat's idea,that such a constant might not exist (as we know it, it might have changed or it might be changing, generally speaking).
And one other (more important) problem:suppose that such a global constant exists,and you write your theory in terms of this constant and the dimensionless variable.Fine.But then you want to go to practice, you want to measure things.How do you measure the dimensionless variable?You cannot, your measurements will involve the "absolute" local value of the constant at the spacetime points you make the measurements.This is the main reason why I do not agree with Mike's viewpoint.On paper,he might be right within certain bounds,but in practice, that's another story.
Follow Ups:
- Re: The Dark Matter Problem has been Solved MirrorMan 13/5 20:19 (0)