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朝花夕拾:关于物质系统总能量的一点讨论

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星空浩淼

发表文章数: 1743
武功等级: 九阳神功
     (第五重)
内力值: 617/617

朝花夕拾:关于物质系统总能量的一点讨论



一个物质系统的能量等于各部分能量以及它们之间相互作用之和。

注意,这个“和”是对一定观察者在某一时刻来求的。但是一个物质系统是有空间尺寸的,而“同时”又是相对性的,这样问题就来了:
假定这个物质系统其中有两个部分相隔1光年,系统整体能量守恒,但各个部分不单独守恒。现在,我计算系统能量时,将系统各部分在同一时刻的能量值以及它们之间的相互作用加起来。但是另一个观察者A相对于我以1000米/秒速度运行,则系统的能量,除了按相对论公式变化之外,还因为,例如系统中相隔1光年的两个部分a和b,由于同时的相对性,A求和与我求和采用了不同时刻的两个部分能量之和。例如,用我的钟来看,我将0秒时的a和b能量求和,而观察者A则是将0秒时的a和2秒时的b的能量求和,这样“物质能量”的定义就。。。。

量子力学方程中,如果将时空坐标平等化(注意Dirac方程那里还不算真正的时空坐标平等),则从原量子力学方程出发,表达为四维时空中的三维超曲面坐标微分方程形式,此时原Hamlitonian换成能量动量张量(与两个四维时空单位矢量收缩)。
可惜这个方程除了形式美观,很难解。因此自从Dirac在内的三个诺贝尔奖得主先后提出后,一直没有人理睬。

量子力学运动方程这样处理的好处,我认为有:
1)不存在上述那个有空间分布范围的系统能量定义的问题;
2)向广义相对论推广很自然,因为那是二阶张量形式的——或许是量子力学向广相推广的另一个途径。

谨供大家讨论


持之以恒就是胜利


发表时间:2004-06-25, 02:45:31  作者资料

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: 朝花夕拾:关于物质系统总能量的一点讨论



量子力学方程中,如果将时空坐标平等化(注意Dirac方程那里还不算真正的时空坐标平等),则从原量子
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
I am not sure I understand what you mean. could you please be more specific?

力学方程出发,表达为四维时空中的三维超曲面坐标微分方程形式,此时原Hamlitonian换成能量动量张量(与两个四维时空单位矢量收缩)。
可惜这个方程除了形式美观,很难解。因此自从Dirac在内的三个诺贝尔奖得主先后提出后,一直没有
which equation you actually referring to?
人理睬。



量子力学运动方程这样处理的好处,我认为有:
1)不存在上述那个有空间分布范围的系统能量定义的问题;
2)向广义相对论推广很自然,因为那是二阶张量形式的——或许是量子力学向广相推广的另一个途径。

If you are talking about general covariantize quantum mechanics, it is already done (see for example, the book by paul davies).



谨供大家讨论


发表时间:2004-06-25, 12:55:12  作者资料

星空浩淼

发表文章数: 1743
武功等级: 九阳神功
     (第五重)
内力值: 617/617

Re: 朝花夕拾:关于物质系统总能量的一点讨论



下面用本人过去文章中的一段文字来代替回答一下sage兄:
3. The starting point for introducing the time operator
As mentioned above, an important motive for trying to introduce a time operator lies in that the theory of relativity requires that time and space must be treated on an equal footing. However, the traditional theories treat time and space very differently:
(1) The traditional many-particle system theory has a defect: the system contains only one time variable while there are as many position variables as there are particles which is in contradiction with the relativity of simultaneity. As observed in another reference system,all particles in the system would no longer share a common time coordinate, and the original Hamiltonian would no longer correspond to the total energy, i.e., the sum of the individual energies of all particles at the same moment of time (note that the energy of a single particle in the system is not necessarily conservative). Historically, in view of this unsatisfactory aspect of the traditional theory, people have introduced the many-time formalism theory [32–34] (being equivalent to the Heisenberg–Pauli theory), where for a
system composed of N particles, there corresponds N distinct time and space variables. In this sense, time and space are treated with equality in the many-time formalism [35].
(2) However, even in the many-time formalism of quantum mechanics, for every single particle of a many-particle system, its time and space coordinates are still not equal, namely its space coordinates can be taken as dynamic variables while the time coordinate cannot. This is what we will try to rectify in this paper. In view of what is mentioned above, our discussion would only be limited to the relativistic single-particle and quantum field cases (while the nonrelativistic single-particle theory can be taken as a special case of the former).
Certainly, even in the classical theory of relativity, time and space could not be completely equal because of the law of causality. In other words, in spacetime diagrams, the distribution of the worldline of an arbitrary particle is not symmetrical about the surface of lightcone.
In a word, in order to define a time operator, it is necessary to put the time coordinate on the same footing as position coordinates. For this, we reconstruct the analytical mechanics and the corresponding quantum theories, which are equivalent to the traditional ones.

我讲的是量子力学方程的多时描述(the many-time formalism )
[32] Dirac P M 1932 Proc. R. Soc. A 136 453
[33] Tomonaga S 1946 Prog. Theor. Phys. 1 27
[34] Schwinger J 1948 Phys. Rev. 74 1439
[35] Tomonaga S 1966 Nobel Lecture


量子力学运动方程这样处理的好处,我认为有:
1)不存在上述那个有空间分布范围的系统能量定义的问题;
2)向广义相对论推广很自然,因为那是二阶张量形式的——或许是量子力学向广相推广的另一个途径。

If you are talking about general covariantize quantum mechanics, it is already done (see for example, the book by paul davies).

我的意思是从量子力学的多时描述形式出发的。你说的这个我略知一二,即传统中早已出现的广义协变的或弯曲时空中的量子场论,但没有进去研究过,只知道有这么回事。

由于等会儿我要回家了,这里暂时不多谈


持之以恒就是胜利


发表时间:2004-06-25, 21:16:49  作者资料

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: 朝花夕拾:关于物质系统总能量的一点讨论



Thank you for the reply. I understand now that you are talking about system with many degreesof freedom. in this case, nothing that I know of handles it better than quantum field theory. It handles infinite many degrees of freedom with a space-time dependent field operator. There is a very well defined energy momentum tensor derived from noether's theorem. It is also straight forward to generalized it to curved space-time background.


发表时间:2004-06-26, 13:57:51  作者资料

星空浩淼

发表文章数: 1743
武功等级: 九阳神功
     (第五重)
内力值: 617/617

Re: 朝花夕拾:关于物质系统总能量的一点讨论



sage兄说的极是,由于量子场论的成功(最多再加上量子统计或温度场论),量子力学的多时描述自然而然的就被淘汰了。
可能科学的发展就是这样的,中间有很多分叉,但只有一条路是对的,其他路最后成了盲肠。只有后人一不小心重复前人错误,容易误入进去。


持之以恒就是胜利


发表时间:2004-06-27, 23:41:48  作者资料