Once upon a time there was a guy who knew how to ride a red
bicycle.
Everything was fine until one day somebody showed him a blue
bicycle. "Look!" he cried. "It's different!"
He insisted that he could not ride a blue bicycle, because it
was different from a red bicycle, and it would be an abomination
to treat things as the same when really they are different.
Not only was he unable to ride the blue bicycle, he told the world
that I was unable to ride the blue bicycle, and tried to prevent
my students from riding the blue bicycle. I reminded him of what
H.E. Fosdick said: the person saying it couldn't be done was
liable to be interrupted by the persons doing it.
The rest of us continue to recognize that things can be profoundly
analogous without being identical. Children learn this before the
age of two: As long as the blue tricycle *behaves* the same as
the red tricycle, knowledge of one is transferable to the other.
There is a pedagogical principle that says learning proceeds
from the known to the unknown.
My students have no trouble riding the blue bicycle. Professional
physicists have no trouble riding the blue bicycle. Making a big
fuss about unimportant details is nothing but sophistry and pedantry.
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For the metaphor impaired, here's the key:
Red bicycle = flow of water
Blue bicycle = flow of momentum
Children learn about the conservative flow of water at an early age;
this knowledge is easily and properly transferred to the flow of
momentum.