The black line represents a familiar ray trace that we should know from high school science : a ray of light travelling from point A hits the glass block, then refracts and changes direction and reaches point B. Fermat's Principle of Least Time explains it this way : the path taken (black line) is the fastest route available.
Btw : speed of light through glass is slower than through air.
If the light had decided to take the direct path (the dotted blue line) it would spend a larger proportion of time travelling through the glass, and arrive at destination B slower. If the light ray decided to take the path that minimized its slow travel through the glass (the dotted red line) it would also arrive slower at destinaton B because the detour would have been too great to justify the smaller distanced traversed through the glass.
We previously understood this as the ray of light traveling in a straight path from A until it hits the glass block, then according to Snell's Law it gets refracted and changes direction until it reaches destination B. Action reaction principle.
But really, where did Snell's Law come from? In fact it is derived from Fermat's Principle of Least time. Fermat's Principle of Least Time is not a happy coincidence that happens to occur because known optics laws make it so : this principle was the one that built up our understand of optics and laws in the first place. This is a "purposeful" interpretation of light path rather than a helpless "action reaction" interpretation we are familiar with, the version we obtain from secondary school education.
The idea of a ray of light knowing "in advance" all the variables is seems kind of illogical. (remember the light has to know all the variables of the materials and path, and even changes in the positions after it starts moving). I guess this hints at some larger explanation : that time does not flow sequentially, and that all events have been laid out from the past to the future. (general relativity and space time continuum ideas lend some credence to this at least).
And perhaps that our experience of time is merely an evolutionary advantage of our brains. (it would be counterproductive to experience time with a lag / in advance / all at once).
3 comments:
OOOhhhh ok... i get your point about 'the ray of light knowing where it was supposed to go before it got there'.
But see, if you have another dimension of time, say we call it hyper-time ^_^... and you're looking at the whole space-time continuum from God's atemporal perspective, then observing that the whole space-time thing is like a picture drawn according to certain laws, the future and past - all of time - is locked already in a determinate, patterned relationship. But for those of us moving through time, with our cognitive limitations... it can seem surprising that the light beam 'knows where its going before it gets there'.
i.e. this is an example of what we would normally think of as causation, being shown to be... illusory. The bending of the light is not caused by knowledge of where it is heading, rather... all is already 'designed' or 'determined' according to natural law. (this is a crude form... but it should suffice)
gotta love logic, causality is always very interesting when studying not only science but also human nature.
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