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Re: [Phys-L] conservation laws (was: photoelectric effect)

There's a lesson here about style of thinking.

To my way of thinking, the conservation laws are the
flesh and bones of physics. Charge is conserved.
That's a really big deal. It pays to pay attention
to the conservation laws.

Charge is conserved *more strictly* than electrons are
conserved. Electrons can turn into other things, e.g.
muons ... or they can annihilate against positrons ...
but in all cases charge is conserved. I am quite tired
of textbooks that get this wrong:

There's a proverb that says "education is the process
of cultivating your intuition". If there's an argument
that says the charge Q is conserved, and the current is
I = Q dot, that's a really big deal. That's bedrock physics.

If that conflicts with your intuition, it's time to
revise and upgrade your intuition.


Analogous situations show up All The Time in electronics.
For example, the carrier density in a semiconductor is
orders of magnitude less than in a metal. So if you hook
a chunk of semiconductor in series with metal wires, the
current is the same everywhere in the series circuit (by
conservation of charge!). In places where the density is
lower, those carriers will just have to move faster.

Analogous situations show up All The Time in fluid dynamics.
In the introductory course, if fluids are mentioned at all,
it is typically assumed that the density is constant ...
but in the real world there are mucho plenty of situations
where the density is not constant. For starters, consider
a vacuum pump. By definition, the whole point of a vacuum
pump is to have a much lower density on the input, compared
to the output. So the rate in terms of moles per second is
wildly different from the rate in terms of liters per second.

Also steam engines and gas turbine engines and nozzles on
the end of hose and ..........

Also cars on the freeway. This leads to infamous instabilities.
Cars are conserved as they flow down the road, or at least you
hope so; you hope that not too many are created or destroyed
along the road. So if for any reason they decide to go slower,
the density goes up. That's interesting, because if the density
goes up, people tend to drive slower, because they don't want
to crash. So there is tremendous positive feedback. In some
places they regulate the onramps to keep the density down in
order to optimize the flux. You are better off waiting your
turn to enter the roadway and then going fast, as opposed to
entering an unregulated roadway and getting stuck in a traffic

Also bazillions of other manifestations of the idea.