
#145
Dec1409, 02:42 AM

P: 622

Are there any fundamental allembracing theories in physics? Or are there only "effective" theories, like electromagnetism (which is important far from an electron, where the charge doesn't "run') or superconductivity (which is important when electrons and phonons coexist only in cold solids). The importance of gravity as we know it seems to stretch over the lifetime of the observed universe, but if it didn't always rule in its present form, with a small cosmological constant, could it be classed as an "effective" theory that has running constants? Incidentally, has anyone yet devised a dimensionless version of c that could run? 



#146
Dec1509, 12:39 AM

Astronomy
Sci Advisor
PF Gold
P: 22,809

Interesting questions!
About c: what occurs to me is that the scale parameter k is a momentum and there is no way you can combine c with a power of k to get something dimensionless. So apparently, according to renormalization conventions, c cannot run. (Yet people construct frameworks in which they can talk about variable speed of light. I think there's a radical difference though.) According to what I think is normal usage, we set c = hbar = 1 and then, since k is a momentum, Gk^{2} is dimensionless. And Lambda is a reciprocal area, so it is the square of a momentum, and Lambda/k^{2} is dimensionless. In electromagnetism the operative running constant is alpha (approx. = 1/137) that relates charge to attraction and distance. Charge does not have to run, because alpha runs. As I recall it increases to more than 1/137 at very high energy and close proximity. Seem to recall alpha can get as big as 1/128 ================ What I think is an intriguing question is what is meant by "fundamental". It's not as simple an issue as some people may imagine. Percacci has a bit about this in his chapter in Oriti's book. And the new paper by Shaposhnikov and Wetterich has some bearing on the issue. For very high k, say with k being the momentum transfer in a collision, the Planck energy itself increases as k. The Planck mass and the Planck energy go to infinity as k increases. So Shaposhnikov and Wetterich deal with this, and set out formulas for it, and build it into their equations. Not everybody is so astute or careful. Others may for example assume that the Planck mass and energy are always equal to their lowenergy values. So the question arises what do you mean by saying a theory purports to be predictive out to arbitrarily high energy. Do we know enough about how nature behaves at Planck scale to distinguish between a "fundamental" theory and one which merely aspires to be applicable out to Planck scale? And what is the appropriate "k" to use? People use various different handles on the scale, all supposed to give the same physical results. But why? what makes something a good handle? Energy density, collision energy, momentum transfer etc etc. And why do coupling constants run? Can you always explain it by screening and antiscreeningby vacuum myths in other wordsjust so stories about the vacuum. And what is the vacuum. What is it when we throw out Minkowski space and declare that geometry is a dynamical something included in what we wish to explain? Why then do coupling constants run with scale? And what is scale? My basic feeling is that humans are wonderful animals but still rank beginners in this game. So I can't answer your question about are there any really fundamental, not merely effective, physical theories. But glad you asked. Maybe someone else will put it into perspective for both of us. 



#147
Dec1509, 01:04 AM

Sci Advisor
P: 8,009

A fundamental theory is one that does not predict its own breakdown. So QCD is a fundamental theory, as is Newtonian gravity, but both do breakdown.




#148
Dec1509, 01:09 AM

P: 2,828





#149
Dec1509, 05:42 AM

Sci Advisor
P: 299

I thought that the renormalized theory (i.e. one which has a continuum limit), is the renormalization group flow which emerges (roughly perpendicularly) from the critical surface at the fixed point. Provided the fixed point has only a finite number of rupulsive directions, then you have a theory. As long as the workers in this field can show that there is a critical point with a finite number of repulsive directions, then there will be finitely paramterised flows emerging from the fixed point. Which means a continuum theory with a finite number of parameters. I don't see why tuning would be necessary. 



#150
Dec1509, 05:50 AM

Sci Advisor
P: 299

However the problem of renormalization has been replaced by the problem of taking a continuum limit, with no [tex]a[/tex] where is the continuum limit [tex]a \rightarrow 0[/tex]. This problem is solved by the lattice correlation length, which roughly tells you how big correlations are in lattice units. If you fix the correlation length in physical units, then the lattice correlation length has to diverge as you approach the continuum, as lattice units are smaller and smaller compared to physical units. So the continuum limit is associated with points with infinite lattice correlation length, which are fixed/critical points. 



#151
Dec1509, 07:04 AM

P: 622





#152
Dec1509, 11:28 AM

Astronomy
Sci Advisor
PF Gold
P: 22,809

General Relativity has its Penrose et al singularity theorems. The particle Standard Model has (correct me if I am wrong) Landau polesblowup pointswhich can be shifted around but not entirely avoided. Both theories illuminate their own limitations. 



#153
Dec1609, 04:09 AM

Sci Advisor
P: 299

Sorry, in message #150 reply to atyy, I should clear up what I meant by "Yes" in the first line. I meant yes Asymptotic freedom needs a critical point and no it cannot do with a limit cycle.




#154
Dec1609, 08:47 PM

Sci Advisor
P: 8,009





#155
Dec2109, 06:56 AM

Sci Advisor
P: 299





#156
Dec2109, 07:51 AM

Sci Advisor
P: 8,009

http://arxiv.org/abs/nuclth/0303038
An Infrared Renormalization Group Limit Cycle in QCD Eric Braaten (Ohio State U.), H.W. Hammer http://arxiv.org/abs/0803.2911 The impact of bound states on similarity renormalization group transformations Stanislaw D. Glazek, Robert J. Perry 



#157
Dec2109, 09:18 AM

Sci Advisor
P: 299

The paper is concerned with the infrared behaviour of the theory, in that specific case I'm not familiar with the meaning of limit cycles. However asymptotic safety is related to the ultraviolet behaviour of a field theory and obtaining a continuum limit. For this you need a critical point, a limit cycle would not do, as it wouldn't provide a diverging lattice correlation. So for the ultraviolet the theory cannot make do with a limit cycle. However maybe I haven't understood what you are asking, providing the links on their own without commentary doesn't indicate what you are trying to say. 



#158
Dec2109, 09:48 AM

Sci Advisor
P: 8,009

But don't we just need all the couplings to be finite for arbitrary energies?



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