星空浩淼
发表文章数: 1743
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Different notions of nonlocality appearing in phys
1. Aharonov-Bohm-like interactions;
2. Einstein-Podolsky-Rosen Paradox (EPR) correlations;
3. the impossibility to localize a particle. that is, delta functions are not the eigenfunctions of a position operator;
4. the field equation contains an arbitrary order of derivatives;
5. coupling of a field to derivatives of potentials, e.g., Darwin-like terms;
6. locality conditions in quantized theories, that is, the commutator of field vanishes for sapce-like distances, are violated.
唯有与时间赛跑，方可维持一息尚存
| 发表时间：2005-07-06, 09:47:15 |
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sage
发表文章数: 1125
武功等级: 天山六阳掌
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内力值: 535/535
Re: Different notions of nonlocality appearing in
1. Aharonov-Bohm-like interactions;
2. Einstein-Podolsky-Rosen Paradox (EPR) correlations;
3. the impossibility to localize a particle. that is, delta functions are not the eigenfunctions of a position operator;
4. the field equation contains an arbitrary order of derivatives;
5. coupling of a field to derivatives of potentials, e.g., Darwin-like terms;
6. locality conditions in quantized theories, that is, the commutator of field vanishes for sapce-like distances, are violated.
================================================================
you have to define what you mean by non-locality. There is a presice definition in terms of cluster decomposition.
6. is roughly a definition of non-locality. 4 is a way to construct an example. one way to get 4 from a local theory is to integrate out a massless field, such as photon in QED. this is somewhat related to 5.
1,2,3 are not non-locality.
delta function should be understood as a eigen-function of the position operator.
| 发表时间：2005-07-06, 16:11:16 |
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No-go
发表文章数: 369
武功等级: 太极剑法
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Re: Different notions of nonlocality appearing in
And why 4, 5 are non-locality?
| 发表时间：2005-07-06, 17:07:51 |
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sage
发表文章数: 1125
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Re: Different notions of nonlocality appearing in
And why 4, 5 are non-locality?
============================================================
locality in field theory means the lagrangian is local. This means that any operator in the lagrangian is local.
a set of operator with arbiturary number of derivatives is not local. an example of this is
exp( i a \partial_x)
expanding the exponantial gives arbiturary number of derivatives. using this, one can write down operators like
\phi(a+x) exp(i a \partial_x) \phi(x)
with \phi(x) being local fields. This is non-local because it has an instantaneous interaction between \phi(x) and \phi(x+a).
One way to get a non-local lagrangian is integrate out a massless field. That field, being massless, will include modes with arbiturarily large wavelength. in order to take this into account in a theory without the massless field, a non-local lagrangian must be used.
the case of a darwin term is not clear to me. however, integrating out photon in QED will be a way to generate a non-local lagrangian.
| 发表时间：2005-07-06, 19:44:31 |
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No-go
发表文章数: 369
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Re: Different notions of nonlocality appearing in
Oh, I see it means there exists non-local interaction. How about
\phi(a+x) exp(a \partial_x) \phi(x)? Should it be a local one, since
exp(a \partial_x) \phi(x)=\phi(a+x) ?
| 发表时间：2005-07-06, 20:27:46 |
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卢昌海
发表文章数: 1617
武功等级: 北冥神功
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内力值: 602/602
Re: Different notions of nonlocality appearing in
If everything is about \phi(x+a) and if that's the only type of term in the Lagrangian, then it is identical to a (local) Lagrangian contains \phi(x) only. Nonlocal lagrangian contains both \phi(x) and \phi(x+a).
BTW, I guess what sage meant by exp(i a \partial_x) is the same as what you wrote as exp(a \partial_x) (although he typed an extra "i"). And the term he wrote: \phi(a+x) exp(i a \partial_x) \phi(x) probably meant to be \phi(x) exp(a \partial_x) \phi(x).
宠辱不惊，看庭前花开花落
去留无意，望天空云卷云舒
| 发表时间：2005-07-06, 20:47:01 |
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No-go
发表文章数: 369
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Re: Different notions of nonlocality appearing in
Means it should be Hermitian? Then what it the difference between
\phi(a+x) exp(a \partial_x) \phi(x) and \phi(a+x) \phi(a+x) in a field theory?
| 发表时间：2005-07-06, 20:55:32 |
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sage
发表文章数: 1125
武功等级: 天山六阳掌
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Re: Different notions of nonlocality appearing in
sorry. many typos and confusions.
I actually mean to write
exp(a \partial_x) which is exp(-ip a).
The non-local lagrangian term should be
\phi(x) exp(a \partial_x) \phi(x).
by the way, we could do another simple excercise (I cannot be sure about all the factors and signs). suppose we have a massless field \phi, it only has a kinetic term
L=(\partial \phi)^2
suppose such a field mediate has an interaction \phi \psi \psi
the equation of motion is then \phi = \partial^-2 \psi \psi. Integrating out \phi, which mention substitute the equation of motion, generates a term
\partial^-2 \psi^4
which is manifestily non-local. this is the statement that integrating out a massless field gives a non-local interaction.
| 发表时间：2005-07-06, 20:58:13 |
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卢昌海
发表文章数: 1617
武功等级: 北冥神功
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Re: Different notions of nonlocality appearing in
::what it the difference between \phi(a+x) exp(a \partial_x) \phi(x)
::and \phi(a+x) \phi(a+x) in a field theory?
\phi(a+x) exp(a \partial_x) \phi(x) and \phi(a+x) \phi(a+x) are the same.
\phi(x) exp(a \partial_x) \phi(x) is a coupling between \phi(x) and \phi(x+a), which is nonlocal.
宠辱不惊，看庭前花开花落
去留无意，望天空云卷云舒
| 发表时间：2005-07-06, 21:06:18 |
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元江
发表文章数: 228
武功等级: 逍遥拳
(第五重)
内力值: 200/200
Re: Different notions of nonlocality appearing in phys
这个题目很有意思，星空列出的几点很好。
我现在经常想得是比较普通的，与EPR有关的非局域性。
非局域性有两种(？)
一种是与空间范围有关，一个物理量只与空间一点有关还是与其周围
一个空间范围有关。
另一种是与因果性有关的，如EPR中的非局域性。
让我对后一种发些议论：-)
与因果性有关的非局域性似乎可以以两种面目出现。
一种是我们认定的客体是不是非局域，另一种是这些
客体是不是有非局域的关系。
我的看法是，如果我们承认我们关注的客体(如单色平面波函数)
是真实的(对应真实物质，如自由粒子)，那么量子力学就是非局
域的，我们甚至不用考察非局域的关系。
如果我们认为平面波函数仅仅是用来描述对象的一种方便，没有
可以真正对应平面波函数的自由粒子，任何粒子都是限制在一定
空间范围内的波包，那么，我们就可以进一步考察量子力学里的
非局域关系。
我的看法是因果律不能在任何程度上被违反，但是在一定的范围
内，比如局域的波函数范围内，由于我们的知识或手段的局限，
使我们观察到因果律被违反的现象。
道可道非常道
名可名非常名
| 发表时间：2005-07-06, 21:15:15 |
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No-go
发表文章数: 369
武功等级: 太极剑法
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内力值: 242/242
Re: Different notions of nonlocality appearing in
That is because \partial^-2... effects like an integral. Right?
| 发表时间：2005-07-06, 21:18:07 |
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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: Different notions of nonlocality appearing in
这个题目很有意思，星空列出的几点很好。
我现在经常想得是比较普通的，与EPR有关的非局域性。
非局域性有两种(？)
一种是与空间范围有关，一个物理量只与空间一点有关还是与其周围
一个空间范围有关。
另一种是与因果性有关的，如EPR中的非局域性。
让我对后一种发些议论：-)
与因果性有关的非局域性似乎可以以两种面目出现。
一种是我们认定的客体是不是非局域，另一种是这些
客体是不是有非局域的关系。
我的看法是，如果我们承认我们关注的客体(如单色平面波函数)
是真实的(对应真实物质，如自由粒子)，那么量子力学就是非局
域的，我们甚至不用考察非局域的关系。
如果我们认为平面波函数仅仅是用来描述对象的一种方便，没有
可以真正对应平面波函数的自由粒子，任何粒子都是限制在一定
空间范围内的波包，那么，我们就可以进一步考察量子力学里的
非局域关系。
我的看法是因果律不能在任何程度上被违反，但是在一定的范围
内，比如局域的波函数范围内，由于我们的知识或手段的局限，
使我们观察到因果律被违反的现象。
=================================================
non-locality should be only defined on observables. It has no definite meaning on something which is not a direct observable. Therefore, in this sense, there is no non-locality in quantum mehanics. EPR is not non-locality.
Non-locality is not acausal. non-locality conceptually means that one can influence things very far away. it roughly means that one can send a signal infinitely fast. however, causality is totally different. it means that there is a closed geodesic (or time-like curve). in plain words, this means A can send a signal (does not matter how fast) to A, and A can send the signal back before A send that signal. one cannot achieve this even if locality is maximally violated. Newtonian gravity, for example, is instantaneous. however, it is causal.
| 发表时间：2005-07-06, 21:24:17 |
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元江
发表文章数: 228
武功等级: 逍遥拳
(第五重)
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Re: Different notions of nonlocality appearing in phys
To sage, 不太能理解你说的这些道理
让我每次问一点点，
你以为按量子力学的解释，平面波所对应的粒子位置
怎样确定呢？
道可道非常道
名可名非常名
| 发表时间：2005-07-06, 21:31:44 |
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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
Re: Different notions of nonlocality appearing in phys
谢谢以上各位，尤其是sage兄的回答令我知道更多。这让我深刻明白什么叫做
“throw out a brick to attract a jade”，or
“I offer a few commonplace remarks by way of introduction so that your come up with many valuable opinions”
-:)
在一门学科中，同一个名词术语在不同场合有时候可能有不同的含义，这使得初学者常常搞混淆和弄糊涂。
尽管sage兄不承认类似EPR佯谬或AB效应这些东西体现nonlocality，但人们早已经习惯了这种说法，至于到底算不算某种类型的nonlocality，各人理解不一，人们争论不休。象AB效应那样的东西，甚至象双缝干涉实验所体现出来的东西（同时经过两个缝），这里的所谓nonlocality，更有点holism、integrity、 entirety、wholeness那样的含义。
粒子的位置呈现某种“弥散性”在大量文献中也是被称为“非定域性”的。
元江兄用平面波来理解nonlocality，实则有误：且不管平面波是一个理想概念，平面波只是表明粒子处于所有位置的概率是相同的，但在某个时刻对粒子位置进行测量，则会发现粒子必处于某个确定的位置。与此相关地，在凝聚态物理中，局域态和扩散态的含义则是：前者表示粒子被束缚在某个有限的空间范围之内，只有在这里找到粒子的概率不为零；后者表示粒子可以在任何地方出现，在每个地方出现的概率不为零。
正如sage兄所说，因果律违背与nonlocality是两码事，尽管后者可能导致前者，但物理允许的nonlocality，必定不违背因果律。不过，superluminal有时候会被作为对nonlocality的狭义理解，此时的nonlocality成为人们对量子力学“不完备性”进行攻击的口实，在我看来，这里是一种误解。
质量为零的场，例如电磁场，如果试图用分数阶微分来构造光子波函数，则导致nonlocality，这个跟昌海兄补充解释的那种nonlocality密切相关。
（好象还没有说完，但忘了还想说些什么）。
唯有与时间赛跑，方可维持一息尚存
| 发表时间：2005-07-06, 22:38:38 |
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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: Different notions of nonlocality appearing in
OK, let's go slowly
你以为按量子力学的解释，平面波所对应的粒子位置
怎样确定呢？
it is not a eigenstate of position. therefore, there is no obvious meaning of position for such a state.
it just means that if you measure position, you will have equal probability to find it anywhere.
| 发表时间：2005-07-06, 23:15:10 |
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元江
发表文章数: 228
武功等级: 逍遥拳
(第五重)
内力值: 200/200
Re: Different notions of nonlocality appearing in phys
先举一个例子
在美国一个实验室内(A)，我用光电效应从金属中打出电子。
于是，电子自由了，在空间以一定的动量传播。
如果我要描写其中一个电子的状态，我可以用两种图像，
经典图像好理解，就是一个“粒子”作匀速直线运动。
量子图像下，我们说这个粒子由一个单色平面波描述。
因为单色平面波的幅度是常数，而且我们也没有边界
来限止这个电子(在这之前，金属提供了边界)，所以
按量子力学的几率波解释：这个电子在空间任何一点
出现的概率是相等的。也就是说，假定我在电子逸出
金属的同时在六十万公里外的一个地点测这个电子，我
与实验室(A)内的人测到这个电子的几率是一样的。
按因果律和经典图像，这是不可能的，即使电子以光速
运动，也要两秒后才有可能在六十万公里外的一个地点
测到这个电子。所以这个
“电子可以同时等概率地出现在空间任何一点”的量子力学
陈述是违背因果律的。
我倾向于承认因果律，所以我认为用单色平面波来描述一个自由
粒子的运动只有数学上的方便，而没有物理上的意义：-)
(我讲得绝对一点：-))
道可道非常道
名可名非常名
| 发表时间：2005-07-07, 09:01:59 |
作者资料
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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: Different notions of nonlocality appearing in
先举一个例子
在美国一个实验室内(A)，我用光电效应从金属中打出电子。
于是，电子自由了，在空间以一定的动量传播。
如果我要描写其中一个电子的状态，我可以用两种图像，
经典图像好理解，就是一个“粒子”作匀速直线运动。
量子图像下，我们说这个粒子由一个单色平面波描述。
因为单色平面波的幅度是常数，而且我们也没有边界
来限止这个电子(在这之前，金属提供了边界)，所以
按量子力学的几率波解释：这个电子在空间任何一点
出现的概率是相等的。也就是说，假定我在电子逸出
金属的同时在六十万公里外的一个地点测这个电子，我
与实验室(A)内的人测到这个电子的几率是一样的。
按因果律和经典图像，这是不可能的，即使电子以光速
运动，也要两秒后才有可能在六十万公里外的一个地点
测到这个电子。所以这个
“电子可以同时等概率地出现在空间任何一点”的量子力学
陈述是违背因果律的。
我倾向于承认因果律，所以我认为用单色平面波来描述一个自由
粒子的运动只有数学上的方便，而没有物理上的意义：-)
(我讲得绝对一点：-))
the point is that you cannot make such a plane-wave. suppose you prepare such a plane-wave in a cavity. to make it very extened, you have to make it very much peaked at a single momentum. however, this will require you to have a extremely long cavity.
| 发表时间：2005-07-07, 09:27:45 |
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: Different notions of nonlocality appearing in
按因果律和经典图像，这是不可能的，即使电子以光速
运动，也要两秒后才有可能在六十万公里外的一个地点
测到这个电子。所以这个
“电子可以同时等概率地出现在空间任何一点”的量子力学
陈述是违背因果律的。
even that electron is indeed travel faster than light, it is not against causality.
something instantaneous is only a violation of special relativity, not causality.
I have explained causality in my earlier post. the point is that one cannot send your signal back before you send it. in principle, being able to travel outside of the lightcone does not necessarily mean a violation of causality.
| 发表时间：2005-07-07, 09:31:32 |
作者资料
|
元江
发表文章数: 228
武功等级: 逍遥拳
(第五重)
内力值: 200/200
Re: Different notions of nonlocality appearing in phys
所谓“你不能make such a plane wave” 是否就是
量子力学中的平面波不对应一个经典意义下的自由粒子？
作为数学式子，我总可以写下一个平面波，我的问题是
当把这个平面波去对应经典意义下的自由粒子时冒出来的。
我没有说我要make such a plane wave，我是说在电子逸出
金属表面后，我们可不可以把波函数的概念应用到电子上去，
如果波函数的概念应用到电子上去，此后产生的疑问怎样
解释？
到底怎样来定义因果律是另一回事。
以特例讲，电子逸出金属表面后，距金属六十万
公里处有没有可能立即测到这个电子？
道可道非常道
名可名非常名
| 发表时间：2005-07-07, 11:01:29 |
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: Different notions of nonlocality appearing in
所谓“你不能make such a plane wave” 是否就是
量子力学中的平面波不对应一个经典意义下的自由粒子？
作为数学式子，我总可以写下一个平面波，我的问题是
当把这个平面波去对应经典意义下的自由粒子时冒出来的。
我没有说我要make such a plane wave，我是说在电子逸出
金属表面后，我们可不可以把波函数的概念应用到电子上去，
如果波函数的概念应用到电子上去，此后产生的疑问怎样
解释？
the point is the following
1) for a true plane wave, there is only one momentum. it is also infinitely long.
2) when you get something out of a metal, the maximal size of the wave-packet is roughly set by the size of that piece of metal. it is not a plane-wave.
3) in reality, sometimes you can see the electron out of a metal as plane wave because the size of the wave-packet is much longer than the size that you care about. for example, you can do interference experiment with those electrons out of the metal. you can use plane wave APPROXIMATELY as long as the size of the wave packet (the size of the metal) is much larger than the distance between the two slits.
however, such an approximation certainly fails when you talk about miliions of kilometers away.
到底怎样来定义因果律是另一回事。
以特例讲，电子逸出金属表面后，距金属六十万
公里处有没有可能立即测到这个电子？
as i said, in this example, you could not.
even if it is possible, even if you can map classical particle to plane wave, it is not a violation of causality.
| 发表时间：2005-07-07, 11:46:02 |
作者资料
|
元江
发表文章数: 228
武功等级: 逍遥拳
(第五重)
内力值: 200/200
Re: Different notions of nonlocality appearing in phys
1) for a true plane wave, there is only one momentum. it is also infinitely
long.
我不理解这句话的意思。我知道一个平面波只对应一个动量，
而且一旦动量完全确定之后，按量子力学，粒子坐标完全不确定。
粒子坐标完全不确定与这个粒子可以等几率的出现在空间任意一点
是一致的。
我的问题是，量子力学的这些说法应用到一个自由粒子上时是否
能让人信服？或者量子力学就不能用到自由粒子状态？
2) when you get something out of a metal, the maximal size of the wave-packet
is roughly set by the size of that piece of metal. it is not a plane-wave.
这个回答的意思似乎在回避量子力学中的问题，也就是说
“虽然自由粒子和平面波的图像会有麻烦，但实际上没有真正的
自由粒子，所以也没有真正的平面波”，所以we are OK.:-)
道可道非常道
名可名非常名
| 发表时间：2005-07-07, 13:07:20 |
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: Different notions of nonlocality appearing in
我不理解这句话的意思。我知道一个平面波只对应一个动量，
而且一旦动量完全确定之后，按量子力学，粒子坐标完全不确定。
粒子坐标完全不确定与这个粒子可以等几率的出现在空间任意一点
是一致的。
我的问题是，量子力学的这些说法应用到一个自由粒子上时是否
能让人信服？或者量子力学就不能用到自由粒子状态？
why not?
这个回答的意思似乎在回避量子力学中的问题，也就是说
“虽然自由粒子和平面波的图像会有麻烦，但实际上没有真正的
自由粒子，所以也没有真正的平面波”，所以we are OK.:-)
it is not. let me repeat,
here is the reply to your metal example
1) a plane-wave is infinitely long. (or like you said, the position is completely uncertain)
2) therefore, in order to prepare a plane, you have to have an infinitely long device.
3) in reality, you cannot have an infinitely long device, therefore, there is no plane-wave.
4) in your example, the wave-packet is the size of the metal. it is not plane-wave. therefore, there is no contradiction in your example.
here is the comment to your statement on free particle.
5) free particle does not have to be simple plane-wave. what define a free-particle is that energy exchange with enviroment is much less than its own energy. electron outside metal could probably consider to be free. however, it could at the same time be a wave packet.
here is the reply to the true plane wave case
6) let's go beyond your example. say, we have a plane-wave. in order to have that, we have an infinitely large device. in it, we prepare the plane-wave. notice that in the infinitely large device, prepring a state here and there lose its meaning. you have to prepare it everrywhere.
therefore, statement like preparing a plane-wave here and measure it there lost its meaning.
therefore, you cannot use plane-wave for your argument.
| 发表时间：2005-07-07, 13:22:58 |
作者资料
|
元江
发表文章数: 228
武功等级: 逍遥拳
(第五重)
内力值: 200/200
Re: Different notions of nonlocality appearing in phys
here is the reply to your metal example
1) a plane-wave is infinitely long. (or like you said, the position is completely uncertain)
Agree.
2) therefore, in order to prepare a plane, you have to have an infinitely long device.
Hehe, I do not want to prepare a plane-wave, the burden is not on my shoulder
:-), I am OK with the picture of a particle, it has a position, it has a definite momentum and it just ran away from a metal.
Now, there is someone coming to me and said that,
"you know, this particle can be described by a plane-wave, that plane-wave possesses the same momentum as you see it as a particle."
"Really, what about the position of THIS particle?"
"Well, it can be anywhere in the universe, what you see it here now because you are lucky."
3) in reality, you cannot have an infinitely long device, therefore, there is no plane-wave.
Does that mean that, all the filed theories, either in condensed matter or particle physics, when we use plane-wave solution as H_0 and subsequently do pertubation calculation relative to this H_0, we are actually based on a collection of non-existent thing?
道可道非常道
名可名非常名
| 发表时间：2005-07-07, 16:23:41 |
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: Different notions of nonlocality appearing in
>Hehe, I do not want to prepare a plane-wave, the burden is not on my shoulder
I think the burden is on your shoulder. we are trying to see if Quantum Mechanics is consistent. I claim it is. you tried to use that metal example to say it has something wierd. I claim it is a bad example since what you get from it is not a plane-wave. therefore, your argument does not apply.
>I am OK with the picture of a particle, it has a position, it has a definite momentum and it just >ran away from a metal.
you should not be OK with that. this classical picture does not give you, for example, interference.
>Now, there is someone coming to me and said that,
>"you know, this particle can be described by a plane-wave, that plane-wave possesses the >same momentum as you see it as a particle."
>"Really, what about the position of THIS particle?"
>"Well, it can be anywhere in the universe, what you see it here now because you are lucky."
so what? it is true when we have a true plane-wave.
>Does that mean that, all the filed theories, either in condensed matter or particle physics, >when we use plane-wave solution as H_0 and subsequently do pertubation calculation >relative to this H_0, we are actually based on a collection of non-existent thing?
No. as I have explained above, plane-wave is a very good approximation in many circumstances as long as the size of the wave packet is much larger than the scale of the experiment. I did not see anything wrong of using that.
maybe we need to go even slower. I am not sure I understand your logic. could you please repeat what exactly you mean?
| 发表时间：2005-07-07, 17:01:20 |
作者资料
|
元江
发表文章数: 228
武功等级: 逍遥拳
(第五重)
内力值: 200/200
Re: Different notions of nonlocality appearing in phys
让我再理一下思路
1) 在我的实验室空间有一个电子在做匀速直线运动，它有确定的
动量，能量和坐标。
如果你认为这个物理状态不可能存在。那么我们可以把讨论停在这儿。
2)按德。布罗意关系，这个粒子对应物质波。由德。布罗意关系
我们得到平面波。这个平面波有确定的传播方向(波矢)和波长(能量)，
因此，电子的动量和能量保存了下来。但是电子的坐标没有解释。
3)按几率解释，物质波的模平方是粒子在空间分布的概率。平面波
的幅度弥散在整个宇宙，模平方是常数。于是，此电子的坐标可以是
在宇宙间的任意一点，而且从一点到另一点的轨迹不可追踪，从一点
到另一点不需要时间。
我对这第三点感到不可接受。
道可道非常道
名可名非常名
| 发表时间：2005-07-07, 19:11:58 |
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: Different notions of nonlocality appearing in
1) 在我的实验室空间有一个电子在做匀速直线运动，它有确定的
动量，能量和坐标。
如果你认为这个物理状态不可能存在。那么我们可以把讨论停在这儿。
correct. strictly speaking, there is not such a state in quantum mechanics.
2)按德。布罗意关系，这个粒子对应物质波。由德。布罗意关系
我们得到平面波。这个平面波有确定的传播方向(波矢)和波长(能量)，
因此，电子的动量和能量保存了下来。但是电子的坐标没有解释。
3)按几率解释，物质波的模平方是粒子在空间分布的概率。平面波
的幅度弥散在整个宇宙，模平方是常数。于是，此电子的坐标可以是
在宇宙间的任意一点，而且从一点到另一点的轨迹不可追踪，从一点
到另一点不需要时间。
the state of plane-wave exists. however, in such a state, there is no coordinate for the particle. therefore, the statement of from this point to the other point has no meaning since it is not correct to think about a particle to be at some point to begin with. it is not correct to say that the particle is at this point and then at the other point in a plane wave state.
this is the statement of uncertainty principle, something cannot have both precise momentum and position. when you aare in plane-wave state, you have precise momentum. the notion of position loses meaning in such a state.
| 发表时间：2005-07-07, 21:58:13 |
作者资料
|
元江
发表文章数: 228
武功等级: 逍遥拳
(第五重)
内力值: 200/200
Re: Different notions of nonlocality appearing in phys
好，我想我们的讨论可以停在这儿了
我试着小结一下：
看这一段对话，
-----------------------------------------------------------------------------
---------------------------
1) 在我的实验室空间有一个电子在做匀速直线运动，它有确定的
动量，能量和坐标。
如果你认为这个物理状态不可能存在。那么我们可以把讨论停在这儿。
correct. strictly speaking, there is not such a state in quantum mechanics.
-----------------------------------------------------------------------------
----------
据说在量子力学(量子物理)开始之初，概念很混乱，于是有一种说法，
星期一，三，五用量子力学，星期二，四，六用经典力学。
这么多年过去了，量子力学越来越完善，但是量子力学到底在什么
范围下适用似乎仍然是个问题。一般讲，量子力学用在微观物理
现象上，但是象这样一个微观粒子但存在于宏观空间的问题，量子力学
不能给出令人满意的答复。对于我来说，我的疑惑已经在前面说明。对
sage学友来说，这样一个问题对量子力学而言根本不存在，因此是在
量子力学意义上的伪问题。
不知道其他学友是否有不同看法？
这个问题其实是很重要的。用平面波来描述自由粒子，然后用自恰场或
微扰方法计入相互作用来研究体系行为几乎是一切现代物理理论的出发点。
难道那希奇古怪的发散和重整化不会是我们采用了平面波而付出的代价么？
道可道非常道
名可名非常名
| 发表时间：2005-07-08, 09:14:40 |
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: Different notions of nonlocality appearing in
据说在量子力学(量子物理)开始之初，概念很混乱，于是有一种说法，
星期一，三，五用量子力学，星期二，四，六用经典力学。
这么多年过去了，量子力学越来越完善，但是量子力学到底在什么
范围下适用似乎仍然是个问题。
there is a very well defined classical limit of quantum mechanics. So the answer is that quantum mechanics applys to everybody and everything. however, when we are considering classical situation, it is convenient technically for us to take the classical limit of quantum mechanics (which we call classical mechanics)
一般讲，量子力学用在微观物理
现象上，但是象这样一个微观粒子但存在于宏观空间的问题，量子力学
不能给出令人满意的答复。
quantum mechanics shows that classical intuition of precise momentum and precise position is not correct. It tells us what is the correct way of thinking about position and momentum.
it also tells us why the classical intuition of momentum and position is APPROXIMATELY correct by taking classical limit. This is typical why a more fundamental theory replace an older one. it contains the older one as an approximation.
I am not sure what more you can possibly want.
这个问题其实是很重要的。用平面波来描述自由粒子，然后用自恰场或
微扰方法计入相互作用来研究体系行为几乎是一切现代物理理论的出发点。
I have said many times that plane-wave exists as quantum mechanical state. it describs the free particle. it is perfectly OK to use it to describe free-particle.
难道那希奇古怪的发散和重整化不会是我们采用了平面波而付出的代价么？
No. it is not. divergence comes from the fact that we have local interactions. and, the divergence is not a price. it is completely physical. It teaches us real physical effect. it is not a problem.
| 发表时间：2005-07-08, 10:47:38 |
作者资料
|
元江
发表文章数: 228
武功等级: 逍遥拳
(第五重)
内力值: 200/200
Re: Different notions of nonlocality appearing in phys
sage学友, I understand the statements you made about Quantum Mechanics. They are what I read and hear everywhere, my problem is that, I feel , they are not as obviously right as other physics laws.
Let me go back the example again.
a electron just leave a metal, it has momentum (velocity) and position,
this is how our experiment can be performed. Since I have to put an electrons collector somewhere in the Lab (so position is necessary) and I am expecting the electron will hit my collector (so momentum is necessary).
Now, here is the question
a) To my mind, QM would treat this electron as a plane-wave since it is a free particle. If so, I lost the position and I do not know where I should place my electron collector.
b) You said, it is not a plane-wave. It is a wave packet. It is fine to treat it as a wave packet so that within the precision we can accept, we can say it has a momutum and position in both quantum mechanics and classic mechanics.
However, the b) will lead another question, how can we treat electrons inside a metal as plane-wave if we even can not treat the electron in the air as plane-wave?
道可道非常道
名可名非常名
| 发表时间：2005-07-09, 10:40:25 |
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: Different notions of nonlocality appearing in
>Let me go back the example again.
=============================================
OK. let's just talk about your example.
I believe that you do not interpret your example correctly, as I have said many times.
>a electron just leave a metal, it has momentum (velocity) and position,
>this is how our experiment can be performed. Since I have to put an electrons >collector somewhere in the Lab (so position is necessary) and I am expecting >the electron will hit my collector (so momentum is necessary).
very good. just remember you prepare it in a collector with finite size.
>Now, here is the question
>a) To my mind, QM would treat this electron as a plane-wave since it is a >free particle.
there are two mistakes here.
first, free particle does not have to be plane-wave.
second, in principle, what you have is not a plane wave since your wave-packet has a finite size.
>If so, I lost the position and I do not know where I should place >my >electron collector.
>b) You said, it is not a plane-wave. It is a wave packet. It is fine to treat it >as a wave packet so that within the precision we can accept, we can say it >has a momutum and position in both quantum mechanics and classic >mechanics.
a wave-packet is something neither with a definite position (uncertainty of position is the size of the wave packet) nor definite momentum (uncertainty of the momentum is set by the inverse of the size of the wave-packet).
>However, the b) will lead another question, how can we treat electrons inside >a metal as plane-wave if we even can not treat the electron in the air as >plane-wave?
again, in principle, it is NOT a plane-wave inside or outside of the metal. however, in practice, it is a good APPROXIMATION since the size of the wave packet is much larger than the size of the lattice space.
again, you can use plane-wave as a approximation as long as the size of the wave-packet is much larger than the character size of the experiment.
| 发表时间：2005-07-09, 12:19:27 |
作者资料
|
元江
发表文章数: 228
武功等级: 逍遥拳
(第五重)
内力值: 200/200
Re: Different notions of nonlocality appearing in phys
sage,
between my collector and the metal is air(vacumn)
道可道非常道
名可名非常名
| 发表时间：2005-07-09, 12:35:11 |
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: Different notions of nonlocality appearing in
>between my collector and the metal is air(vacumn)
the detail of your setup does not matter. in vacuum, the electron you have will still be a finite size wave-packet. its size could not be bigger than the typical size of your equipment, collector, metal, the distance between metal and collector, whatever.
are you thinking an electron in vacuum has to be a plane-wave?
| 发表时间：2005-07-09, 21:51:55 |
作者资料
|
元江
发表文章数: 228
武功等级: 逍遥拳
(第五重)
内力值: 200/200
Re: Different notions of nonlocality appearing in phys
the detail of your setup does not matter. in vacuum, the electron you have will still be a finite size wave-packet. its size could not be bigger than the typical size of your equipment, collector, metal, the distance between metal and collector, whatever.
are you thinking an electron in vacuum has to be a plane-wave?
---------------------------
I agree with you here that the electron in between a metal and a collector is
a wave-packet. Only this can explain why we can arrange our experiment based on the concepts of position and momentum.
My question is then, under what circumstances, we do have a free particle which can be described by a plane-wave? or may be there is no such thing as a plane-wave in qunatum mechanics, it is merely a mathematical method.
道可道非常道
名可名非常名
| 发表时间：2005-07-09, 22:03:19 |
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: Different notions of nonlocality appearing in
I agree with you here that the electron in between a metal and a collector is
a wave-packet. Only this can explain why we can arrange our experiment based on the concepts of position and momentum.
My question is then, under what circumstances, we do have a free particle which can be described by a plane-wave? or may be there is no such thing as a plane-wave in qunatum mechanics, it is merely a mathematical method.
==================================================================
there are several layers of answers, please read them carefully.
1) as an state in the Hilbert space, plane-wave exists.
2) in reality, in a lab environment, there is no exact plane-wave, since we have to have a infinitely large equipment in order to prepare a real plane-wave. so, if you want, this is the ONLY condition under which we have a true plane-wave.
3) however, we do use plane-wave in many places. this is because plane wave is a very good approximation in a lot of situations. The condition for plane wave to be a good approximation is that the equipment you use to prepare it is much larger than the characer size of your equipment. If you are interested, do the following excercise:
given a plane-wave passing a double slit (with distance d between the two slits), you will easily derive the interference pattern behind that double slit.
then start with a finite size wave packet (just truncate the plane-wave to a finite size of x ). now, since it is finite sized, you can fourier transform it into a set of plane-waves. Now, work out the interference pattern. you should observe that as x>>d, it is very close to the plane-wave case above.
so, simply put, it exists, it is almost impossible to make in practice, it is a good approximation to use.
| 发表时间：2005-07-09, 22:17:54 |
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|
追忆
发表文章数: 693
武功等级: 般若掌
(第八重)
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Re: Different notions of nonlocality appearing in phys
Sage 兄，could you please explain this question to me ? i do not understand the meaning .
you said ::free particle does not have to be plane-wave.
generally speaking , in vacuum ,what ought we to treat a free particle as ? (and it has no definite position and momentum )
| 发表时间：2005-07-09, 23:25:42 |
作者资料
|
元江
发表文章数: 228
武功等级: 逍遥拳
(第五重)
内力值: 200/200
Re: Different notions of nonlocality appearing in phys
there are several layers of answers, please read them carefully.
1) as an state in the Hilbert space, plane-wave exists.
--Agree. as a mathematical object, plane-wave exists.
2) in reality, in a lab environment, there is no exact plane-wave, since we have to have a infinitely large equipment in order to prepare a real plane-wave. so, if you want, this is the ONLY condition under which we have a true plane-wave.
--Lets say, emitting an electron from a metal to the air and wait for long time for electron to travle a long distance, can I say the whole sky is my equipment to prepare this electron to be a plane-wave and that sky should be large enough?
3) however, we do use plane-wave in many places. this is because plane wave is a very good approximation in a lot of situations. The condition for plane wave to be a good approximation is that the equipment you use to prepare it is much larger than the characer size of your equipment. If you are interested, do the following excercise:
given a plane-wave passing a double slit (with distance d between the two slits), you will easily derive the interference pattern behind that double slit.
--If I can not apply the concept of position, how do I know where should I lay down my double slit? or I can put the double slit anywhere?
then start with a finite size wave packet (just truncate the plane-wave to a finite size of x ). now, since it is finite sized, you can fourier transform it into a set of plane-waves. Now, work out the interference pattern. you should observe that as x>>d, it is very close to the plane-wave case above.
so, simply put, it exists, it is almost impossible to make in practice, it is a good approximation to use.
--If a finite size wave packet is a particle, when you do fourier transform, are you slicing a single particle into many pieces? If not, than the plane-wave is just a math object to do analysis, it does not have a physical realization.
道可道非常道
名可名非常名
| 发表时间：2005-07-09, 23:26:50 |
作者资料
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dolphin
发表文章数: 179
武功等级: 华山剑法
(第一重)
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Re: Different notions of nonlocality appearing in phys
sage 的观点描述的是现今证明是自洽而实用的单粒子数学表示,从计算结果来看大家也认为没有什么问题;元江的质疑还是归结为对量子力学中测不准关系如何理解,以前的一些贴子如波函数坍塌的讨论最后也会归结到这一点.
费曼认为没人真正理解量子力学大概也是说没人真正理解为什么量子力学会有这种不确定性,它的起源又来自哪里?是不是要用更深的理论来解释(或许能根据此理论来重写单粒子数学表示)?但是在找到真正的答案之前,若现有的单粒子数学表示能正确地计算出一些物理结果,那么应该认为现在的数学表示是基本合理的.
| 发表时间：2005-07-10, 03:11:24 |
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|
西门吹牛
发表文章数: 469
武功等级: 空明拳
(第三重)
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Re: Different notions of nonlocality appearing in phys
我个人觉得元江兄的问题，可能更要归结为对量子力学及其各种基本概念的理解问题。
空间位置波函数为平面波时，表示粒子在动量空间的波函数为delta函数，即只有单一的频率成分（或处于某一个确定的动量本征态），而在位置空间的位置则完全不确定，并且在位置空间各处出现的概率都相同。如此而已，跟这里所讲的非定域性扯不上关系。
其实，星空兄和sage兄一开始的回帖就讲得非常清楚了，可惜元江兄可能没有细看啦！
一舞剑气动四方,天下英雄莫能挡
形踪飘忽疑无影,冷面郎君傲雪霜
| 发表时间：2005-07-10, 08:03:56 |
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: Different notions of nonlocality appearing in
>--Lets say, emitting an electron from a metal to the air and wait for long time for electron to >travle a long distance, can I say the whole sky is my equipment to prepare this electron to >be a plane-wave and that sky should be large enough?
notice I said infinite size. in principle, the whole universe is not big enough.
and, as you said, in order to get a very pure plane-wave, you have to use a very big lab and wait for it to propagate for a long time.
--If I can not apply the concept of position, how do I know where should I lay down my double slit? or I can put the double slit anywhere?
You can always apply the concept of position. you just have to be aware of the limit of that concept. a double-slit is usually a classical object with many many particles, so it has a very small spread in position. for plane-wave, you can put the slit anywhere you will still get the same interrference. for a wave-packet of size x, you can put the slit anywhere within x. it is possible since you also know in this case the position of electron within x.
--If a finite size wave packet is a particle, when you do fourier transform, are you slicing a single particle into many pieces? If not, than the plane-wave is just a math object to do analysis, it does not have a physical realization.
superposition principle says that one particle state could be a superposition of many states. A particle could appear in each of those states, it could also be a superpostion of all of those states. all of the states, as well as the superpositions, are all physically possible states.
| 发表时间：2005-07-10, 09:00:38 |
作者资料
|
元江
发表文章数: 228
武功等级: 逍遥拳
(第五重)
内力值: 200/200
Re: Different notions of nonlocality appearing in phys
To have a plane-wave, I need an infinite size device. An electron left from a metal is a wave-packet. I can accept that.
Now, expand the wave-packet with respect to plane-wave as Forier Transformation and the superposition principle says the wave-packet has certain probability to be in one of the plane-waves. If I am not mistaken, that means that a particle does have an opportunity to be in a pure plane-wave state even the device we have is not infinite.
It looks like that there is an inconsistency among the avove statements.
道可道非常道
名可名非常名
| 发表时间：2005-07-10, 10:09:03 |
作者资料
|
元江
发表文章数: 228
武功等级: 逍遥拳
(第五重)
内力值: 200/200
Re: Different notions of nonlocality appearing in phys
今早忙出门，漏看了海豚和西门的帖子
海豚引得费曼的说法我是同意的，我想弄清楚的
是为什么费曼这样说？我在量子力学书上看到的
是从胜利走向胜利，似乎每一个问题都有合理的
答案。那么到底是什么原因使得费曼和其他大师
都说量子力学不好懂呢？这个难点在哪里？
西门说“单频“粒子”在位置空间的位置则完全
不确定，并且在位置空间各处出现的概率都相同。“
这个说法是书上的标准说法，我的疑问就是针对
这个说法来的。“各处出现的概率都相同”这句
话的意思其实是“我们根本不知道这个单频“粒子”
会出现在哪里”。这个说法显然与我们的经验有矛盾，
因为我们做实验时是知道(在一定精度内)“粒子”出
现在哪里的。
那么，似乎只有两种可能：
1)不存在“单频粒子”，sage用的是这个说法吧，即一
个在实验中能跟踪轨迹的，一定是个波包，“单频粒子”
只能在无穷大空间中存在。按这个解释的话，德。布罗意
关系是有问题的，因为德。布罗意是将一个物质粒子作
单频对应得出其波性的。
2)存在“单频粒子”，下面我想不清楚，那位能试试？
道可道非常道
名可名非常名
| 发表时间：2005-07-10, 14:12:31 |
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: Different notions of nonlocality appearing in
To have a plane-wave, I need an infinite size device. An electron left from a metal is a wave-packet. I can accept that.
Now, expand the wave-packet with respect to plane-wave as Forier Transformation and the superposition principle says the wave-packet has certain probability to be in one of the plane-waves. If I am not mistaken, that means that a particle does have an opportunity to be in a pure plane-wave state even the device we have is not infinite.
It looks like that there is an inconsistency among the avove statements.
-------------------------------------------------------------------------------------------------------------------------
fourier transform or not will not change physics.
there is no inconsistency. you can write any localized wave-packet as superposition of plane-waves (the extreme case being a delta-function). however, no matter how you write it, whether you call it a superposition of a set of plane-wave or not, a localized wave-packet is still LOCALIZED. the point is that with a finite size equipment, you can not produce a state that is not localized. ONE SINGLE plane-wave as a state is not localized. therefore, you cannot produce it with a finite size device.
| 发表时间：2005-07-10, 16:41:51 |
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: Different notions of nonlocality appearing in
1)不存在“单频粒子”，sage用的是这个说法吧
I did not say it. I believe I have said many times that plane-wave exists as a state in Hilbert space.
，即一
个在实验中能跟踪轨迹的，一定是个波包，“单频粒子”
只能在无穷大空间中存在。
this is correct.
按这个解释的话，德。布罗意
关系是有问题的，因为德。布罗意是将一个物质粒子作
单频对应得出其波性的。
there is no problem. a particle could be in a plane-wave state, as I have said many many times.
2)存在“单频粒子”，下面我想不清楚，那位能试试？
you seems to think by saying particle, we mean it has momentum and position at the same time. quantum mechanics teachs us this is fundamentally wrong. it is a wrong concept derived from our classical intuition.
| 发表时间：2005-07-10, 16:47:35 |
作者资料
|
元江
发表文章数: 228
武功等级: 逍遥拳
(第五重)
内力值: 200/200
Re: Different notions of nonlocality appearing in phys
想来想去，我想的问题就是
在经典力学中我们同时知道一个粒子精确的坐标和动量。
在量子力学中我们只能同时知道一个粒子不精确的坐标和动量，
这不是测量手段问题，而是原理上不允许同时知道一个粒子精
确的坐标和动量。到这里概念上还可以接受，就是点粒子对应
一个波包。
然而，在极限情况下，波包扩展成一个平面波，在这种状态下，
粒子动量精确而粒子的坐标完全不确定。我以为这样的情况没
有实际的物理对应。或者波包收缩成一个delta函数，这时粒子
坐标精确而粒子的动量完全不确定，我以为这样的情况也没
有实际的物理对应。可是这两种情况都是在用量子力学分析物
理时常用的。对于前者，如果认为平面波的确对应一个真实物
理粒子的话，这个观点本身就意味着量子力学的非定域性，因
为这个粒子可以”同时“出现在无穷大空间中的任何一点。
道可道非常道
名可名非常名
| 发表时间：2005-07-10, 22:01:21 |
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: Different notions of nonlocality appearing in phys
“\phi(x) exp(a \partial_x) \phi(x) is a coupling between \phi(x) and \phi(x+a), which is nonlocal. ”
\phi(x) * \phi(x+a), 这个式子让我联想到关联函数（一阶相关矩），如果它的平均值不为零，这两个场量就是相关的，其中a就是相干长度。
我最近借了一本英文版的nonlocal quantum field theory and 随机量子力学（写不来英文的“随机”这个单词），可惜恐怕没有时间看，一直放在那里，随机微分方程什么的我没有学过，看起来有难度。在那里面好象就是大量用随机过程中的那些平均概念，我现在怀疑，那里可能就是把\phi(x) * \phi(x+a)这样的非定域相互作用理解成有实际意义的关联函数。
sage兄专门从事理论物理，如果有兴趣，不妨专门学学，到时再给我们大家讲讲。
唯有与时间赛跑，方可维持一息尚存
| 发表时间：2005-07-10, 23:30:57 |
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: Different notions of nonlocality appearing in phys
TO元江兄：波函数不能象电磁场强度那样理解成一种物理场，这是量子力学告戒我们的，尽管历史上有人尝试过把它理解成某种实际的物理空间中存在的场，但终归是失败的。到目前为止几率幅解释是最合理的。
如果没有初始条件，空间位置平面波的确不能告诉我们粒子到底在哪里，它只是告诉你，粒子在空间位置出现的概率各处相同，所以说粒子的位置完全不确定。换句话说，粒子位置状态，是所有位置本征态的等权叠加。每个测量，位置状态坍塌到某个位置本征态之一。无数次测量这种状态的粒子，会发现粒子位置在所有位置出现的频次相同。
唯有与时间赛跑，方可维持一息尚存
| 发表时间：2005-07-10, 23:42:09 |
作者资料
|
元江
发表文章数: 228
武功等级: 逍遥拳
(第五重)
内力值: 200/200
Re: Different notions of nonlocality appearing in phys
谢谢参于讨论的各位学友
星空学友：
“TO元江兄：波函数不能象电磁场强度那样理解成一种物理场，
这是量子力学告戒我们的，尽管历史上有人尝试过把它理解
成某种实际的物理空间中存在的场，但终归是失败的。到目
前为止几率幅解释是最合理的。”
是的，按现在的量子力学共识，几率幅解释是最合理，我想了解
的是几率幅解释本身有没有令人疑惑的地方。而我的疑惑就在几
率幅解释的两个极端情况。要注意的是，我不是质疑平面波和delta
函数的数学意义(所以，sage学友说平面波存在于希尔伯特空间里
我是能接受的)，我的疑惑是，平面波的几率解释会导致我们对一个
粒子位置的完全无知，只要想到物理的结论还是需要实验检测的，
我觉得无法接受这个结论；同时平面波的几率解释也同时概括了所有
的非定域性论证，即，如果单个粒子可以在全空间任何一点出现的话，
也就是单个粒子的波幅弥散在全空间的话，那么它与其它粒子，不论
两者相距多远，都有波幅重迭，所以两者一定相干。于是，我们宇宙
中所有的粒子按其自然状态来说都是相干的，于是，自由粒子的存在
是个“错误”的概念。
“如果没有初始条件，空间位置平面波的确不能告诉我们粒子到底在
哪里，它只是告诉你，粒子在空间位置出现的概率各处相同，所以说
粒子的位置完全不确定。换句话说，粒子位置状态，是所有位置本征
态的等权叠加。每个测量，位置状态坍塌到某个位置本征态之一。无
数次测量这种状态的粒子，会发现粒子位置在所有位置出现的频次相
同。”
这个陈述是不是意味着不存在定态的平面波状态？如果有定态的平面波
状态，那么与初始条件无关。星空学友可不可以就这一点再澄清一下？
关于叠加原理，我以为在理解波函数性质本身时应该尽量不去引用它。
叠加是对所有波函数的一种操作，由叠加而来的性质是波函数性质的
集合表现，不应该在这时再转回去解释单个波函数性质。实际上，单
个波函数可以看作叠加的特例。
----------------------------------------------------------
我漏了星空学友的前一帖，你提到了非定域相互作用场论，很有意思，
我的想法与其类似。
1)每一个真实的物理现象一定有至少一个特征长度，物理上有意义的
波函数或场是局限于(定域在)由这个特征长度度量的范围内的。平面波
没有这个特征长度，所以没有真实的物理对应。
2)两个或多个波函数能产生相干(或纠缠)的条件是必需有幅度的直接(或间接的重合
)。这个条件只有在波函数可以不重合下才有意义，也就是波函数满足1)。
道可道非常道
名可名非常名
| 发表时间：2005-07-11, 07:39:42 |
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: Different notions of nonlocality appearing in
同时平面波的几率解释也同时概括了所有
的非定域性论证，
this is at least an abuse of language of nonlocality. strictly speaking, it refers to physical effect propagating outside of the light-cone.
即，如果单个粒子可以在全空间任何一点出现的话，
也就是单个粒子的波幅弥散在全空间的话，那么它与其它粒子，不论
两者相距多远，都有波幅重迭，所以两者一定相干。
correct, if we actually made a plane-wave, which is in principle possible. actually, if there is another electron with overlaping wavefunctions with the one we make, to be technically correct, they should be treated as identical particles.
于是，我们宇宙
中所有的粒子按其自然状态来说都是相干的，于是，自由粒子的存在
是个“错误”的概念。
interference is not interaction. they are two independent concepts. when doing the double slit experiment, the wave-function of the electron interfer with itself to produce interference, and it is a free particle.
关于叠加原理，我以为在理解波函数性质本身时应该尽量不去引用它。
叠加是对所有波函数的一种操作，由叠加而来的性质是波函数性质的
集合表现，不应该在这时再转回去解释单个波函数性质。实际上，单
个波函数可以看作叠加的特例。
no. it is the heart and soul of quantum mechanics. it is not simple addition. it is superposition. if we just add up the physical effect of two waves, you do not get interference.
----------------------------------------------------------
1)每一个真实的物理现象一定有至少一个特征长度，物理上有意义的
波函数或场是局限于(定域在)由这个特征长度度量的范围内的。平面波
没有这个特征长度，所以没有真实的物理对应。
this is not quite true. plane-wave has a character lenght which is inverse of the momentum. this tell us, for example, the size of its interference effect. it does not have a character length in position.
2)两个或多个波函数能产生相干(或纠缠)的条件是必需有幅度的直接(或间接的重合
)。
这个条件只有在波函数可以不重合下才有意义，也就是波函数满足1)。why?
| 发表时间：2005-07-11, 08:23:34 |
作者资料
|
店小二
发表文章数: 79
武功等级: 野球拳
(第八重)
内力值: 138/138
Re: Different notions of nonlocality appearing in phys
这个帖子回帖数太多，为防止国内读者读取速度太慢，请另开一个主题继续讨论吧。
我爱月夜，但我也爱星天。
| 发表时间：2005-07-11, 08:32:18 |
作者资料
|
元江
发表文章数: 228
武功等级: 逍遥拳
(第五重)
内力值: 200/200
Re: Different notions of nonlocality appearing in phys
Well, we are almost there, either we agree each other or leave the topic there to be clarified later.
-----------------------------------------------------------
同时平面波的几率解释也同时概括了所有
的非定域性论证，
this is at least an abuse of language of nonlocality. strictly speaking, it refers to physical effect propagating outside of the light-cone.
即，如果单个粒子可以在全空间任何一点出现的话，
也就是单个粒子的波幅弥散在全空间的话，那么它与其它粒子，不论
两者相距多远，都有波幅重迭，所以两者一定相干。
correct, if we actually made a plane-wave, which is in principle possible. actually, if there is another electron with overlaping wavefunctions with the one we make, to be technically correct, they should be treated as identical particles.
于是，我们宇宙
中所有的粒子按其自然状态来说都是相干的，于是，自由粒子的存在
是个“错误”的概念。
interference is not interaction. they are two independent concepts. when doing the double slit experiment, the wave-function of the electron interfer with itself to produce interference, and it is a free particle.
------------------------------------------------------------------
OK, we have different understand of "free particle". We understand the same way about a "free particle" in classical meaning, i.e. it does not interact with any other particle. Coming to QM, when interference exists, even though a particle does not have energy exchange with other, but the state of a "free particle" needs to be determined bu considering how the other particles "fell", is this still "free"? I do not think so. However, let me re-phrase my statement that
一个不用考虑其它粒子状态的“自由粒子”概念是错误的。
--------------------------------------------------------------
关于叠加原理，我以为在理解波函数性质本身时应该尽量不去引用它。
叠加是对所有波函数的一种操作，由叠加而来的性质是波函数性质的
集合表现，不应该在这时再转回去解释单个波函数性质。实际上，单
个波函数可以看作叠加的特例。
no. it is the heart and soul of quantum mechanics. it is not simple addition. it is superposition. if we just add up the physical effect of two waves, you do not get interference.
-------------------------------------------------------------
OK< which onw is more in the heart and soul of quantum mechanics?:-)
the object we are studing or the relation between those objects?
-----------------------------------------------------------------
----------------------------------------------------------
1)每一个真实的物理现象一定有至少一个特征长度，物理上有意义的
波函数或场是局限于(定域在)由这个特征长度度量的范围内的。平面波
没有这个特征长度，所以没有真实的物理对应。
this is not quite true. plane-wave has a character lenght which is inverse of the momentum. this tell us, for example, the size of its interference effect. it does not have a character length in position.
-------------------------------------------------------------
I did mean a character length in position.
2)两个或多个波函数能产生相干(或纠缠)的条件是必需有幅度的直接(或间接的重合
)。
这个条件只有在波函数可以不重合下才有意义，也就是波函数满足1)。why?
--------------------------------------------------------------
This is my opinion. That is , there has to be something in exchanging between two parts, so that the two parts can interract or interfere. That is all what I can tell.
道可道非常道
名可名非常名
| 发表时间：2005-07-11, 08:49:35 |
作者资料
|