- #36
Claude Bile
Science Advisor
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JerryMac said:Sorry to dig this thread back up but I have been thinking about this same issue a lot. I wanted to question something further.
The pulse example he gave was something I thought about in particular myself. What confused me is once the waves cancel each other out, what attributes of the system allow them to "know" where to continue after time T where they cancel.
Consider a standing wave on a string; at some time, then the displacement will be zero everywhere. Where has the energy gone? Nowhere, because while the displacement is zero, the velocity is not. You can make a similar argument for EM waves; while the E field may be zero at some time, dE/dt and d^2E/dt^2 are not zero, which is important. (Keep in mind too, that quantities like energy density and Poynting vector are time-averaged, which is why time derivatives do not appear in these expressions).
JerryMac said:In other words if we could freeze a moment in time where they are cancelled, what can we observe to tell us that the two pulses' magnitudes would return and continue on as before? How could we tell the difference between this two pulse system and a system where there were never any pulses at all?
Another way a look at it... even if there was one pulse and I froze time, how could I tell if the pulse was moving in a positive or negative direction along the X axis. If I can't tell, how can the Universe?
The momentum of the wave will determine the direction that it propagates.
JerryMac said:Is this all really a version of the Uncertainty Principal?
Nope, you don't need to resort to quantum physics!
Claude.