Quantum mechanics and light behaviors in daily life

2 min read

Light travels in a straight line. When light is reflected by a mirror, the incoming angle is equal to the reflection angle. When light enters water, it changes its directions according to Snell’s law. …

Or does it?

These light behaviors are not as intuitive as we think if we really want to explain them in quantum mechanics. We have to keep in mind, when a light particle – photon – travels from point A to point B, the photon takes all paths available in the universe! Correct, not just the straight line between A and B, but also any weird curves you can imagine starting from A to B.

“Photon Dance 8” by zwopper, Deviant Art

First, let’s show that photons actually travel in non-classical paths. In the setting below, light is emitted from the left and received by the small “black hole” on the right. There is a wall between them so the light can’t travel in the straight line. A mirror is placed at the bottom. You might think, the only way for the light to reach the “black hole” is to travel in the classical path shown below.

Light is reflected at the center of the mirror

Now, if one removes the central and right part of the mirror, and also removes some parts on the left, as shown in the figure below, you would think that there is no light reaching the black hole. After all, the central part of the mirrow is where the light get reflected and reach the black hole.

Light also takes other paths

Contrary to what we believe, some light does reach the “black hole”! This demonstrates that the photons take all paths!

(The examples/figures above are from video by The Science Asylum. Another equally interesting video from the same channel is https://www.youtube.com/watch?v=cep6eECGtw4 )

The Science Asylum’s Youtube video

Next, a natural question is, why we see the light travels in straight line? Why it is reflected by the mirror with equal incoming and reflecting angle?

We will have to understand that a photon has “phases”. The term “phase” is familiar to us when we study “waves”. In a nutshell, if two waves have aligned phases, when they come together they will form a bigger wave; if the phases are not aligned, then the final wave will be smaller or even disappears!

Aligned and anti-aligned phases
https://wiki.anton-paar.com/en/double-slit-experiment/

It turns out while the photons do take all the paths, only the “classical” paths are where the photons have aligned phases! To work this out, we really need to do some calculations. Here are the steps copied from https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Quantum_Behaviour

  1. Define the light source.
  2. Work out the frequency of the photon.
  3. Define any objects which the light cannot pass through.
  4. Define the first point you wish to consider.
  5. Define a set of paths from the source to the point being considered, the more, the better.
  6. Work out the time taken to traverse one of the paths.
  7. Work out how many phasor rotations this corresponds to.
  8. Draw an arrow representing the final phasor arrow.
  9. Repeat steps 6-8 for each of the paths.
  10. Add all the phasor arrows together, tip-to-tail.
  11. Square the amplitude of this resultant phasor arrow to gain the intensity of the light at this point. It may help to imagine a square rotating around, instead of an arrow.
  12. Repeat steps 4-11 for every point you wish to consider. The more points you consider, the more accurate your probability distribution will be.
  13. Compare all the resultant intensities to gain a probability distribution which describes the probabilities of a photon arriving at one point to another. For example, if the intensity of light at one point is two times the intensity of light at another, then it is twice as likely that a photon will arrive at the first point than the second.
  14. If all the points being considered were on a screen, the intensities show you the relative brightnesses of light at each of the points.

I admit it’s not very easy calculations. But what matters is that we understand photons do take all the paths available, and when there are no photons, it’s only because the phases of the photons are misaligned.

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穷书生宋登阁,一心想当官。可惜考了八年,还是没中。最后,连买包子的钱都没有。在包子铺,济公看他可怜,就点拨他,帮他写了篇文章。靠这篇文章宋登阁果然考中,当上了县官。济公还为他介绍了一位贤惠美女为妻。实现了过去的梦想。 可是当了官才知道官小。开始也有心为老百姓做事,但为了仕途,宋登阁不听济公的劝告,一次次降低自己的道德底线,也一次次升官进爵。一次,为了能娶京城高官的女儿,他还无情地把原配夫人休掉。夫人伤心欲绝。这时,济公来了劝她。 夫人:“活佛,妾身如今已难在这个世上为人了。” 济公:“这个世上不行,还有那个世上啊。只是你尘缘未尽,事情还没办完哪能就去啊?” 夫人:“可是妾身如今已无存身之所。” 济公:“那你就哪里来到哪里去吧。” 夫人:“为什么叫我哪儿来到哪儿去?” 济公:“是啊。我看你还是先回去挂起来。” 这女子一愣,然后笑了,说:“妾身险些忘了,是该挂起来。” 几十年很快就过去。宋登阁官越做越大,成为朝中重臣,对济公也越来越嫌弃,甚至还想毒死他。最后,宋登阁因为争权失败,被送上了断头台。斩首之前,夫人突然出现,两人抱头痛哭,夫人给他留下一个黄手巾。宋登阁就被砍头了。 这时宋登阁惊醒,自己竟然还在包子铺,脖子也没被砍。这一辈子原来只是黄粱一梦。可是身边的确有一个黄手巾。看墙上,有个美女画。这个美女明明刚才还是年轻女子,现在也白发苍苍了。宋登阁懵懵懂懂,出了包子铺。 上面的故事是《济公游记》中的《醉官图》。我很喜欢,看了多遍。我佩服那个夫人。她原本就是包子铺里的画,济公让她活到宋登阁的梦里。在被休伤心欲绝的时候,济公说让它挂起来,她竟然立刻想起来了自己本来就只是一幅画而已,马上就挂起来,退出历史舞台。这等觉性,让人赞叹。 不知道宋登阁梦醒之后会做什么。是继续考试当官吗?还是做个小买卖安心过小日子?或者,他是否也会突然明白,自己只是某个电视剧里的人物而已?唉,我还不如宋登阁。活了几十年,满脑子都是功名,心里全部是欲望。“为世界做贡献”、“成功”、“有出息”,高尚的口号下,只是要做“人上人”而已;而最终,还是来自面对自己什么都不是这个真相的恐惧。我要学习宋登阁夫人,明白自己什么都不是,安心把自己“挂起来”。
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当年禅宗五祖弘忍要把衣钵传下去,就让弟子们做一首能显示自己体悟的偈子。五祖的高徒神秀就在墙壁上写了下面的诗: 身是菩提树心如明镜台时时勤拂拭莫使惹尘埃 慧能当时也在五祖门下,不过他不识字。有天听到别人念神秀的诗,就说,我也有个偈子,请那人代他写到墙上。诗云: 菩提本无树明镜亦非台本来无一物何处惹尘埃 大家都很惊奇,没想到其貌不扬的慧能还能写出这样的诗。五祖知道慧能已经悟道,便将衣钵传给他。于是,慧能就成了六祖。不过他还不能暴露身份,就悄悄到了南方。有次,他到了广州法性寺,赶上印宗法师在讲经,听到两个和尚讲话。当时风吹着旗子在动,一个和尚说,是风在动;另一个和尚说,是旗在动。慧能听到,说,不是风动,也不是旗动,而是您两位的心在动。大家都很惊讶,印宗法师请他上座,才了解这就是六祖。而慧能从此开始传法。 上面的故事是超简版,如果要了解详情,可以读六祖坛经。我第一次听到慧能的偈子以及他的“不是风动不是旗动而是心动”的言论,是在高中的政治课上。当时我们的老师很年轻,估计也就二十来岁,看我们理科班上政治课一点都不积极(政治不列入理科的高考),有时就给我们聊一些有意思的哲学,比如白马非马、特殊包含一般等等。政治课我几乎没及格过,对这些我倒是特别感兴趣,听得津津有味。多年之后,每次我再读起慧能的偈子,总觉得倍感亲切。回头看,这是当年老师给我播下了种子。
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