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关于固有时及其变换关系
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昨天躺床上想了想，23楼昨天最后给出的思路具有以下特点：
1.由于使用固有时作为参量，四维间隔作为考量标准，这两者都是四维标量，所以自然满足洛伦兹协变。
2.它在低速情况下的确可以变成牛顿力学中的刚体，因为此时坐标时与固有时相同，而四维间隔的相等也就意味着三维空间距离的相等。
3.这种刚体在物理上具有的一个明显特性是，在刚体的随动系看来，物体不会发生任何形变。
1.由于使用固有时作为参量，四维间隔作为考量标准，这两者都是四维标量，所以自然满足洛伦兹协变。
2.它在低速情况下的确可以变成牛顿力学中的刚体，因为此时坐标时与固有时相同，而四维间隔的相等也就意味着三维空间距离的相等。
3.这种刚体在物理上具有的一个明显特性是，在刚体的随动系看来，物体不会发生任何形变。
- 坂上中微子: 回复 fishwoodok :不，这里说的是物质，不是时空。因为有“固有时”作为量度物理进程的参量，这个概念只能针对质点或物质场定义。
关于固有时及其变换关系
有博主要求我解释固有时及其变换关系。首先申明一下：在文献中和在网上，存在着对固有时的不同定义及对其变换关系的不同解释。我不打算列举这些不同定义及对其变换关系的不同解释，也无意去评论它们的是非。我只谈自己的看法，也不强求别人接受我的看法，我也不打算参与网上的争论。为了解释得更清楚，要较多地用到相对论的数学关系。如果反对这些关系，就不必往下看了。
我是在时空事件及时空间隔概念的基础上来定义固有时的，我是在时空坐标的洛伦兹变换的基础上来讨论固有时的变换关系的。为简单起见，本文只写出时轴和x 轴坐标。本文所讨论的内容与马青山博士的博文相类似。
设有t时位于 x 处的事件（ct,x)，及t+dt时位于 x+dx 处的事件（c(t+dt),x+dt),这两个事件之间的时空间隔的平方为 ds2= c2dt2-dx2 。进行洛伦兹变换，事件（ct,x)变换为（ct’,x’),事件（c(t+dt),x+dt)变换为（c(t’+dt’),x’+dx’),这两个事件之间的时空间隔的平方变为为 ds’2= c2dt’2-dx’2 ,并且ds’= ds ,即两个事件之间的时空间隔是洛伦兹变换不变量。
在上述关系中，当dx=0 (或dx’=0）时，ds= cdt （或 ds’= cdt’）,常用 τ 表示t，即 ds= cdτ （或 ds’= cdτ’）；τ （或τ’) 被称为固有时 。这就是我所采用的固有时的定义。必须注意固有时概念得以成立的条件是时钟的位置固定不变，即dx=0 (或dx’=0）。
现在来讨论对钟后A 钟的读数，由于A钟静止在不带撇参照系，它的读数是固有时。当其读数为dτ时 ,所对应的事件为（0+dτ,0+0),进行洛伦兹变换，变到带撇参照系，该事件变为（ct’,x’)。其中，ct’= cdτ/(1-v2/c2)1/2 , x’= - vdτ/(1-v2/c2)1/2 。由于A钟不静止在带撇参照系，在带撇参照系它的读数不是固有时。B钟静止在带撇参照系，它的读数是固有时,但静止在不带撇参照系的A钟的读数不可能变换成为静止在带撇参照系的B钟的读数。
另一方面，ds= cdτ （或 ds’= cdτ’）也是个时空间隔，也是个标量，在坐标变换下，数值不变，但这种不变，不能作为用固有时计时的理由。
The first ever photograph of light as both a particle and wave
March 2, 2015
(Phys.org)—Light behaves both as a particle and as a wave. Since the days of Einstein, scientists have been trying to directly observe both of these aspects of light at the same time. Now, scientists at EPFL have succeeded in capturing the first-ever snapshot of this dual behavior.
Quantum mechanics tells us that light can behave simultaneously as a particle or a wave. However, there has never been an experiment able to capture both natures of light at the same time; the closest we have come is seeing either wave or particle, but always at different times. Taking a radically different experimental approach, EPFL scientists have now been able to take the first ever snapshot of light behaving both as a wave and as a particle. The breakthrough work is published in Nature Communications.
When UV light hits a metal surface, it causes an emission ofelectrons. Albert Einstein explained this "photoelectric" effect by proposing that light – thought to only be a wave – is also a stream of particles. Even though a variety of experiments have successfully observed both the particle- and wave-like behaviors of light, they have never been able to observe both at the same time.
A research team led by Fabrizio Carbone at EPFL has now carried out an experiment with a clever twist: using electrons to image light. The researchers have captured, for the first time ever, a single snapshot of light behaving simultaneously as both a wave and a stream of particles.
The experiment is set up like this: A pulse of laser light is fired at a tiny metallic nanowire. The laser adds energy to the charged particles in the nanowire, causing them to vibrate. Light travels along this tiny wire in two possible directions, like cars on a highway. When waves traveling in opposite directions meet each other they form a new wave that looks like it is standing in place. Here, this standing wave becomes the source of light for the experiment, radiating around the nanowire.
This is where the experiment's trick comes in: The scientists shot a stream of electrons close to the nanowire, using them to image the standing wave of light. As the electrons interacted with the confined light on the nanowire, they either sped up or slowed down. Using the ultrafast microscope to image the position where this change in speed occurred, Carbone's team could now visualize the standing wave, which acts as a fingerprint of the wave-nature of light.
While this phenomenon shows the wave-like nature of light, it simultaneously demonstrated its particle aspect as well. As the electrons pass close to the standing wave of light, they "hit" the light's particles, the photons. As mentioned above, this affects their speed, making them move faster or slower. This change in speed appears as an exchange of energy "packets" (quanta) between electrons and photons. The very occurrence of these energy packets shows that the light on the nanowire behaves as a particle.
"This experiment demonstrates that, for the first time ever, we can film quantum mechanics – and its paradoxical nature – directly," says Fabrizio Carbone. In addition, the importance of this pioneering work can extend beyond fundamental science and to future technologies. As Carbone explains: "Being able to image and control quantum phenomena at the nanometer scale like this opens up a new route towards quantum computing."
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