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Grandpa -

The law of conservation of energy states that matter can neither be
created nor destroyed.  Waves carry energy.  If two sound waves cancel each other out (undergo destructive interference) the energy changes to heat.  But if two light waves cancel each other out in a vacuum, what happens to the energy of the light?

- Kurt Einfeldt

Kurt -  It's an interesting question - and it has an interesting "answer."

We know, of course, that sound cannot travel in a vacuum - and travels faster usually in denser media.  Sound travels much faster down a steel railroad track than it does in air, for example. But light travels best with no medium at all - in a vacuum, and we know it can't travel at all through a railroad track. Light evidently has a dual personality.  There is much we don't know about light. In some calculations, we must assume that light is a wave phenomenon and not particles for the calculations to make any sense. Then in other calculations, we must assume the opposite, that light is made up of particles and is not a wave, or those calculations don't make any sense.  

Your case is one of those wherein our results will make no sense if we assume the wave theory of light instead of the particle theory of light.  We can't know that either of these theories is completely correct.  The fact that we need both verifies for us that we don't really know what the character of light is.  Often, theories are used because they allow us to accomplish things.  What works, in a way, is true.  Looking critically at these theories, we can find inconsistencies.  They prove we don't know the whole story, but they don't make the theories less valuable.  What you have discovered with your Gedankin helps you to understand lots of these principles.  I find "Gedankin" is not in my dictionary - roughly, it means "mind experiment."  We use them when we can't do an actual physical experiment.  Einstein much favored Gedankins.

It's interesting to note that Albert Einstein did not win a Nobel Prize for either of his two greatest discoveries - special relativity and general relativity.  This is because few others could, at that time, grasp the probable truth of it.  To them, it was just one of Einstein's Gedankins.  They might have thought, " What a wonderful and delightful mind he has, but how can we use this ? "  That is, they might have thought this way until atomic energy proved a few points.

When Einstein did win the prize, it was for the Photo-Electric Effect, which deals with this very problem of the dual nature of light.  If you do a search on that discovery, you may then have some more questions.  This remarkable insight into what's going on suggests that light is really neither particle nor wave, but is at the same time both - and also that many other phenomena must also have this dual nature. 

A link to a good photoelectric effect article:

http://physics.bu.edu/py106/notes/PhotoelectricEffect.html  

- Grandpa

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