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[Phys-l] perpetual motion machine: splitter



Suppose I have a "3dB splitter" as shown in this diagram:
_
| |------------ B
A ===================| |
|_|------------ C

such that if I put in 1 watt via port A, I get out 1/2 watt via port B
and 1/2 watt via port C.

Now consider energy flow in the other direction, i.e. the right-to-left
direction. Ports B and C are mutually isolated; in no case does energy
entering port B exit via port C or vice versa.

All energy flowing in via port B flows out via port A, and all energy flowing
in via port C also flows out via port A.

****************************************************

Assigment:

1) Prove that the device described above does not exist and cannot exist.
That is, show that at least one of the statements above the row of asterisks
is false. Show that it is not just a little bit false; there is something
fundamentally and categorically wrong.

Huge hint: Show that the device would violate the second law of thermodynamics.

Note: Pointing out small engineering imperfections is *not* the answer. I
know that you won't get "exactly" 1/2 the power out of each port. Please
recognize that any value anywhere near 1/2 suffices to build the perpetual
motion machine.


2) Explain what is really going on.

Hint: The optical version (i.e. a beamsplitter) is conceptuatlly equivalent but
may be easier to analyze.

=======================

This is very relevant to two recent threads: the "fire starter" thread and the
"energy equation" thread. There is some very useful, profound, and elegant
physics involved.