地衣
发表文章数: 53
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等效原理和场方程
等效原理和场方程是什么关系？如果我写出了一个关于场的方程我如何可以看出它已经满足了等效原理。按照我初始的理解，只要方程的量由张量构成，做成了广义的形式，则方程自动满足等效原理。但想想又不对。等效原理是包含了物理含义的，广义协变只是一种形式的要求。例如只要适当选择度规张量，可以将牛顿方程也做成广义协变的形式。
那么，我要如何才能看出一个方程是否满足了等效原理呢，或者说，等效原理是如何体现在Enstein的引力场方程里的呢。
另，我的id青苔不能登陆了。请站长帮忙。
君愁我亦愁
| 发表时间：2005-10-10, 10:27:48 |
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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: 等效原理和场方程
I think it slightly depends on what you mean by equivalence principle.
The ability of going to local Lorentzian frame is general coordinate invariance.
As you said, general coordinate invariance does not completely fix the form of Einstein equation. Actually, we do expect higher order terms in that equation. Einstein just pick the lowest order possible term. From modern point of view, it is the lowest order effective field theory. Weinberg has emphsized this point of view a long time ago.
| 发表时间：2005-10-11, 21:47:32 |
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地衣
发表文章数: 53
武功等级: 野球拳
(第六重)
内力值: 122/122
Re: 等效原理和场方程
sage 所言极是，等效原理是场方程的低阶近似。我想起了书上用等效原理处理了时间膨胀及光线偏转，但处理水星进动是从场方程出发。原因是时间膨胀光线偏转是引力的低阶效应，而进动是引力的高一阶近似？
我曾认为如果通过坐标变换能找到一个局部惯性系则说明等效原理自动得到了满足，这样理解是否不确切？还有sage可不可以用你的理解把马赫原理和等效原理的区别讲一下，这个我一直不很清楚，或者我们可以讨论一下。
站长，可不可以把程序设计为在帖子页面登陆后直接回到要回复的帖子的页面，而不用重新打开帖子再回复？这样更加快捷些。
君愁我亦愁
| 发表时间：2005-10-12, 00:29:21 |
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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: 等效原理和场方程
It is somewhat hard to understand Mach's principle these days since it
was always stated in its original terms, which was originated a long
time ago. It is also particularly for us to understand why Mach's
principle is relevant since we all sort of heard about General
Relativity first, which usually makes much more sense than Mach's
principle, which is usually very vague.
Nevertheless, let me give it a try.
Before I start, I would like to say that everything I said here I
learned from Weinberg's book. So, if you, like some others, considers
Weinberg not understanding Relativity, ignore what I said.
The whole began as to the origin of inertia. Newton claim that an
object like to stay in the state it is in. this is called
inertia. However, it is not true everywhere, such as in an falling
elevator. More specifically, in a accelerated frame, you see things
begin to accelerate, change their state. Newton's answer is that there
is a absolute universal
frame, which is THE inertia frame. In that frame, objects obey
Newton's first law. Moreover, the universe (stars and so on), are
approximately at rest in that frame. Falling elevator is accelerating
respect to those stars, therefore, it is not an inertia frame.
Mach, on the other hand, claimed that the universal frame is not
correct. He, instead, claims that things have inertia because there is
some mysterious connection between them and all the other matter in
the universe. In an accelerated frame, things starts to accelerate.
It is not because it is not an inertia frame, but because somehow the
accelerated motion of your frame respect to the rest of the matter of
the universe changed your inertia property, so that you do want to
accelerate rather than stay in your own state.
According to Mach, such a change in inertia property will depend on
your motion accelerating or not, and direction of the motion. Also, it
will also depends on the distribution of other matter near you, since
that would change the way you want to accelerate.
In short, Mach claimed, if we generalize it a little bit, that the
physical law governing your motion will depends on your motion state
and the distribution of matter around you.
On the other hand, equivalence principle claims something in between
Mach and Newton. It claims that there is no universal frame, in
contrast to Newton. It claims that there is always a locally inertia
frame, in which all the Newtonian notion of inertia applies, the law
of motion in that frame is independent of any other things in the
universe. This is clearly in contrast to Mach, who claims there is a
change of physics depending on other stuff. In general relativity, all
the other matter in the universe does have a role to play, it
determines the transformation we have to use to go to that inertia
frame.
However, once in that inertia frame, the physics is independent of
anybody else.
Of course, experimental evidence support equivalence principle. For
example, if Mach is right, we might expect some direction dependence on
the property of the physical system, such as the energy level in
atoms. There is none observed.
As you might have observed, the contrast between Mach and Einstein is
a bit vague. Actually, from a modern point of view, the original idea
of Mach is too vague to be directly compared with equivalence
principle, which is very precise. We could come up models sort of
mimic Mach effects and compare with GR. Such attempts have been
made. Such models are disfavored by experiments.
| 发表时间：2005-10-12, 21:47:01 |
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孙伊
发表文章数: 48
武功等级: 野球拳
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内力值: 119/119
Re: 等效原理和场方程
Sage老师，看了您的解释，我感觉比Weinberg书里面说的清晰多了！我现在是这么理解的，您看是否贴切呢：
看了Weinberg解释，但跟青苔一样，觉得Weinberg的描述很糊涂。我不明白Weinberg是怎么得出等效原理跟Mach原理·冲突·的结论。在我看来，Mach原理虽然模糊，却涵盖了等效原理。也就是说，如果一个理论是不违背Mach原理的最一般理论（当然，由于Mach原理的模糊性，可能很难找到这种“最一般理论”，我只是假定一下），那么这个理论应该包含许多待定参数，而等效原理就是这众多不违背Mach原理的理论中的一种最特殊形式。而且GR的待定参数很容易确定，就是在极限情况下过渡到牛顿理论。而诸如Brains-Dick理论，即便用牛顿理论作为边界条件，也还剩下一个待定系数ω。别的理论我不知道，但我现在通过您的解释得到的理解是，其它理论都会比GR需要更多的参数，这些参数不能仅仅通过把牛顿理论作为边界条件得到，必须通过额外的实验来测定。但目前的实验精度范围之内，都没有跟GR发生任何偏离，所以即便其它理论正确，也说明理论中那些待定参数必将受到严格的限制，以至于实验结果看上去跟GR没有明显偏离。
↑↑↑↑↑↑↑↑偶瞎猜的，错了请不要骂偶，多谢！↑↑↑↑↑↑↑↑
| 发表时间：2005-10-13, 04:14:49 |
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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: 等效原理和场方程
看了Weinberg解释，但跟青苔一样，觉得Weinberg的描述很糊涂。我不明白Weinberg是怎么得出等效原理跟Mach原理·冲突·的结论。在我看来，Mach原理虽然模糊，却涵盖了等效原理。也就是说，如果一个理论是不违背Mach原理的最一般理论（当然，由于Mach原理的模糊性，可能很难找到这种“最一般理论”，我只是假定一下），那么这个理论应该包含许多待定参数，而等效原理就是这众多不违背Mach原理的理论中的一种最特殊形式。而且GR的待定参数很容易确定，就是在极限情况下过渡到牛顿理论。而诸如Brains-Dick理论，即便用牛顿理论作为边界条件，也还剩下一个待定系数ω。别的理论我不知道，但我现在通过您的解释得到的理解是，其它理论都会比GR需要更多的参数，这些参数不能仅仅通过把牛顿理论作为边界条件得到，必须通过额外的实验来测定。但目前的实验精度范围之内，都没有跟GR发生任何偏离，所以即便其它理论正确，也说明理论中那些待定参数必将受到严格的限制，以至于实验结果看上去跟GR没有明显偏离。
=============================================
Mach's principle is too vague in its original term. A vague principle of course contains everybody. However, it is not very useful. A physics statement must be precise.
My guess is that Weinberg is defining Mach's principle to be a much narrower and more precise thing, and abuse the name a little bit by still calling it Mach's principle.
Actually, the name of something really does not matter. What is really Mach's principle does not matter either. The real question is general relativity vs other equally precise models, such as the version of Brans-Dicke discussed in Weinberg.
By the way, nowadays, we call something Brans-Dicke not only it has a scalar conformally couple to Ricci, but also to matter (trace of the energy momentum tensor).
| 发表时间：2005-10-14, 00:18:23 |
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地衣
发表文章数: 53
武功等级: 野球拳
(第六重)
内力值: 122/122
Re: 等效原理和场方程
many thanks to sage
君愁我亦愁
| 发表时间：2005-10-14, 07:41:13 |
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