sage
发表文章数: 1125
武功等级: 天山六阳掌
(第六重)
内力值: 535/535
Mass Problem I: Intro
From a modern point of view, mass is a parameter in the Lagrangian. It
is a little bit special in the sense that we could not shut this
interaction off asymptotically. It is part of the definition of free
particle states. For example, it labels irreducible representations of
Lorentz group.
On the other hand, there is nothing really that special about mass
comparing with other parameters in the Lagrangian, it is just one of
them.
The first thing we could probably say about mass is that it is a
dimensionful parameter, i.e., a parameter with a unit. Therefore, its
absolute size does not mean that much. The meaningful thing to ask
about mass is the ratios of masses of various stuff we see.
Let's think about what we could hope for a ultimate explanation of
mass. Suppose we have a theory of everything. Such a theory will have
some fundamental scale in it. Then, with this theory, we should be
able to predict the ratios between every mass parameter in the
Lagrangian and the fundamental scale. This is the best we can do and
is a satisfactory explanation of mass.
Somehow, we worry mostly about the fermion masses. The reason is
mainly that the 'stuff' of which we are made are mainly fermions, such
as electron and quark. Therefore, let's begin our discussion with
ferion mass.
| 发表时间：2006-05-05, 00:56:39 |
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HPC
发表文章数: 244
武功等级: 逍遥拳
(第七重)
内力值: 206/206
Re: Mass Problem I: Intro
it is nice to read it, but do you think the problem of mass can be really solved only by consideration of gravitation? since mass can produce the gravity.
Faith, Fashion and Fancy.
| 发表时间：2006-05-05, 04:53:20 |
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kanex
发表文章数: 860
武功等级: 弹指神通
(第六重)
内力值: 343/343
Re: Mass Problem I: Intro
I think we can consider the problem of mass without taking into account of GR at all?
ft!
| 发表时间：2006-05-05, 06:08:06 |
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sage
发表文章数: 1125
武功等级: 天山六阳掌
(第六重)
内力值: 535/535
Re: Mass Problem I: Intro
I think we can consider the problem of mass without taking into account of GR at all?
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kanex, HPC and duality:
this is really a very vague question, so is the question whether mass could come from self-interaction of gravity. the short answer is no. at least not from the gravity that we know of. a easy estimate of size of gravitational self-interaction indicates that it is much less than the masses for all known massive particles.
One purpose of the set of articles is to ask the question of mass more precisely.
| 发表时间：2006-05-05, 23:33:27 |
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kanex
发表文章数: 860
武功等级: 弹指神通
(第六重)
内力值: 343/343
Re: Mass Problem I: Intro
Dear sage, I dont think duality's idea is feasible. I think HPC mean something else as well.
What I am thinking is a different issue......
As we know the rest mass comes from unitary irreducible representations of the Poincare group. We work out the Casimir operators of the Lie algebra, and then consider its eigenvalues so that we get some "observables" which commutes with all the generators --- one of the casimir operators is P^2, and its eigenvalue is identified with the rest mass.
However, we know the Poincare group comes from the 10 linearly independent isometries [killing vectors] of the Minkowski spacetime. If we are in a different soluion of the Einstein's Field Equation [which seems to be the case, but I am not familiar with Lamda-CDM], the dimension of the isometry group will be different. In general, the dimension is lower than 10.
The idea is, the rest mass [even the spin] of "particles" may not be an invariant if we want to take GR into account, i.e. in some curved spacetime.
[I am not very sure if what I've written above are correct though.]
ft!
| 发表时间：2006-05-06, 06:58:06 |
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sage
发表文章数: 1125
武功等级: 天山六阳掌
(第六重)
内力值: 535/535
Re: Mass Problem I: Intro
fine. the whole notion of free particle and particle vacuum are different in the de Sitter. On the other hand, the usual notion of free-particle in flat space still makes sense if the scale in our problem is much less than the curvature. Therefore, as far as our problem about the masses of fundamental particles, we could still use the language of flat space (little group of poincare algebra, etc) without problem.
| 发表时间：2006-05-06, 08:19:59 |
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duality
发表文章数: 29
武功等级: 野球拳
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内力值: 103/103
Re: Mass Problem I: Intro
My this idea is very normal, It only depends on what we learned from the studying before.
I am considering that maybe it is fully possible that mass can come from the self-interaction of gravity as the same as self-interaction of electron when I have never none the calculation of it .
a easy estimate of size of gravitational self-interaction indicates that it is much less than the masses for all known massive particles
Well, sage :
Have you ever calculate it detailly?
If we add the self-energe of gravity into the calculation for the origin of mass , then, can this process solve this problem very well?
| 发表时间：2006-05-13, 03:16:55 |
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sage
发表文章数: 1125
武功等级: 天山六阳掌
(第六重)
内力值: 535/535
Re: Mass Problem I: Intro
Well, sage :
Have you ever calculate it detailly?
If we add the self-energe of gravity into the calculation for the origin of mass , then, can this process solve this problem very well?
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it is very similar to the fact that the gravitation binding energy of earth is much smaller than its mass.
| 发表时间：2006-05-22, 14:43:24 |
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