Steven Weinberg offers a way to explain inflation


by marcus
Tags: explain, inflation, offers, steven, weinberg
oldman
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#145
Dec14-09, 02:42 AM
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Quote Quote by marcus View Post
.....(the) idea of doing barebones unification and barebones early-U cosmology based on renormalization group flow is a new initiative and just getting under way ........We live with running constants all the time........the answer is that with the asymsafe early-U picture
*you cant avoid inflation
*and inflation is still useful in explaining flatness and scale invariance
*and asymsafe early-U will be shown to predict observable effects and be falsifiable.
Your perspective is illuminating, especially when taken together with your thread on "QMG" and Reuter's no-frills QG, which clarified what is meant by asymptotic safety for me. The kinds of questions that seem to be floating around these days are fascinating. One that interests me is:

Are there any fundamental all-embracing 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 co-exist 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?
marcus
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#146
Dec15-09, 12:39 AM
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Interesting questions!

Quote Quote by oldman View Post
...
Are there any fundamental all-embracing 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 co-exist 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?
Some people might say it's all cut and dried---they might have a "correct" answer for each of your questions. On the contrary, I am not even sure that humans know what a "fundamental" theory is, or would recognize one if it stared them in the face.

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, Gk2 is dimensionless. And Lambda is a reciprocal area, so it is the square of a momentum, and Lambda/k2 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 low-energy 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 antiscreening---by vacuum myths in other words---just 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.
atyy
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#147
Dec15-09, 01:04 AM
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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.
humanino
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#148
Dec15-09, 01:09 AM
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Quote Quote by atyy View Post
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.
It is an interesting point of view. Then I would say fundamental theories are in some sense inferior to effective theories, because we usually do not expect Nature to "breakdown", the prediction of new physics is the best we can get of any theory.
DarMM
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Dec15-09, 05:42 AM
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Quote Quote by hamster143 View Post
It's not just that. It's the question whether we live in a universe that lies on the critical surface. Since the critical surface is most likely finite-dimensional and the space of all couplings is infinite-dimensional, the a priori probability that we actually live in such universe is zero. It would require either some not-as-of-yet-understood mechanism that puts the gravity in the UV fixed point, or the incredible amount of fine-tuning, to justify this scenario.
I don't fully understand this comment, maybe I'm missing something about the renormalization group.

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.
DarMM
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#150
Dec15-09, 05:50 AM
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Quote Quote by atyy View Post
Does AS really need a fixed point? Could it live with, say, a limit cycle?
Yes, the Wilson-Kandoff renormalization group takes place on a block lattice with everything in units of the lattice spacing [tex]a = 1[/tex]. In lattice units the regularized integrals of perturbation theory have no divergences as [tex]a \rightarrow 0[/tex], because [tex]a[/tex] has disappeared.

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.
oldman
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#151
Dec15-09, 07:04 AM
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Quote Quote by marcus View Post
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.
Thanks for this correction.


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. ......
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.
I hope so. But I suspect that it depends on "times that are a-changing", as Bob Dylan once sang, so that any answer may not be final. Perhaps Newton's gravity was once viewed as quite fundamental. It still is in atyy's sense:
A fundamental theory is one that does not predict its own breakdown
Maybe a lifetime ago General Relativity was formulated as a fundamental theory of gravity. There seem to be doubts nowadays.
marcus
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#152
Dec15-09, 11:28 AM
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... any answer may not be final. Perhaps Newton's gravity was once viewed as quite fundamental. It still is in atyy's sense:
A fundamental theory is one that does not predict its own breakdown
Maybe a lifetime ago General Relativity was formulated as a fundamental theory of gravity. There seem to be doubts nowadays.
It begins to seem as if accurately predicting its own limitations ("effective" in Atyy's sense) is a VIRTUE to be appreciated in a theory.

General Relativity has its Penrose et al singularity theorems. The particle Standard Model has (correct me if I am wrong) Landau poles---blow-up points---which can be shifted around but not entirely avoided. Both theories illuminate their own limitations.
DarMM
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#153
Dec16-09, 04:09 AM
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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.
atyy
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Dec16-09, 08:47 PM
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Quote Quote by DarMM View Post
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.
Do theories with a limit cycle have a physical interpretation?
DarMM
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#155
Dec21-09, 06:56 AM
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Quote Quote by atyy View Post
Do theories with a limit cycle have a physical interpretation?
No, one needs a critical point to have a continuum limit. So a renormalization group flow which exhibits a limit cycle is simply another theory without a continuum limit. No different from a theory without a limit cycle which doesn't approach the critical point.
atyy
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#156
Dec21-09, 07:51 AM
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http://arxiv.org/abs/nucl-th/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
DarMM
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#157
Dec21-09, 09:18 AM
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Quote Quote by atyy View Post
http://arxiv.org/abs/nucl-th/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
The second paper is not related to field theory, so I'll only talk about the first.
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.
atyy
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#158
Dec21-09, 09:48 AM
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But don't we just need all the couplings to be finite for arbitrary energies?


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