The logic of modern physicsBridgman, P. W. (Percy Williams)
Philosophy
The logic of modern physics
Bridgman, P. W. (Percy Williams)
Physics -- Philosophy
By procedures exactly like those outlined above, we may treat all the
corresponding magnetic quantities; there is formal parallelism between
the two sets of phenomena, but there is the physical difference that we
have to realize a single magnetic pole by the device of using a very
long slender magnet.
We now give our electrical system more freedom, in that we allow the
charges to be in motion with respect to each other. Perhaps the most
immediate question which we now have to ask is whether charge continues
to be conserved when set in motion, or whether the total charge on an
isolated body is a function of its velocity? To answer this question we
must generalize the procedure by which we assigned a numerical value to
a stationary charge. Perhaps the simplest way is to allow two unit
charges each to move with constant velocity, remaining at unit distance
apart, and measure with a spring balance the force required to keep them
at constant distance apart. Now we immediately find that the force is
altered under these conditions, so that our first impulse is to say that
the charge is a function of the velocity. But as we experiment further,
we find that the state of affairs is very complicated; the force between
the two charges at any moment of their motion depends not only on the
charges, their distance apart, and their velocities, but also on the
angle between the line joining them and the direction of motion in the
lines. Further experiment of other kinds yields other information; it
requires a force to maintain a charge in uniform motion in a magnetic
field, or to maintain a magnetic pole in motion in an electric field. A
moving electric charge exerts a force on a stationary magnetic pole, so
that by definition the moving charge is surrounded by a magnetic field,
and similarly a moving magnetic pole is surrounded by an electric field.
Returning to our two moving electric charges, we are impelled to ask
whether, if all these complications are possible, the numerical constant
(unity for static charges) in the inverse square law of force is a
function of velocity as well as the magnitude of the charges themselves?
If we broaden the question in this way, as we apparently must, our
problem becomes indeterminate, for we are trying to answer two different
questions with a single kind of measurement, namely of the force between
moving charges. I have had no better luck on trying other methods of
measurement. Apparently the operations do not exist by which unique
meaning can be given to the question of whether the magnitude of a
charge is a function of its velocity. On realizing this situation, we
are at first embarrassed to know how to proceed, but we reflect that the
embarrassment is not of our own making, but corresponds to a physical
fact. The concept of charge as a unique and independent thing
essentially pertains only to static systems. We may extend the concept
to moving systems if we wish, as a matter of convenience to ourselves,
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