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James Mackey wrote:
Jim Green wrote:
At 13:02 25 03 2005 , the following was received:
Go back to basics, in this case the definition of "field". Charged
objects, in a certain region, experience forces that are proportional to
the charges, and for each object there is a unique force vector at each
point of the region. Divide the force vector by the associated charge on
the object. The resulting set of vectors is called the "vector field in
the region". Is it real?
Well, Jack, one small quibble: We don't discover a "unique force vector";
we invent the idea of a vector with the wild hope that our calculations
will be made easier. If we divide a set "force vectors" by the associated
charge, we have the _invented_ concept of a "vector field." We have
not _discovered_ a field. Nevertheless sometimes we reify the idea of a
field. This is just fine as long as we remember that this is an invention
not a bucket of stuff we have discovered.
We sometimes _reify_ the concept and then argue whether it is "real."
OK, I give up! After reading this thread, my question is, What is real?
I thought the concept and application of vectors was well established
before it was ever applied to the definition of the Electric field.
I don't think we need to pursue the question of "What is real?" in all
its philosophical glory. Simple, common-sense guidelines should be
enough to help us answer our questions. For me, electrons are obviously
real. And anything that can deflect the path of a moving electron is
also obviously real. Granted, that is not a comprehensive treatment of
what is real, but I think it will do for our purposes.
When an electron enters the region between the charged plates of a
parallel-plate capacitor, its path is deflected. If a student asks
"What deflects the electron?", we all say the deflection was caused by
the electric field between the plates. But if the electric field exists
only in our minds the question is still unanswered. What deflects the
path of the electron? If we dispense with the field concept and say the
accumulated charge on the plates deflected the electron (I see no
reasonable alternative), we are left with classical
action-at-a-distance. If we're going to be philosophical, a "real"
electric field is more palatable to me than pure action-at-a-distance.
I also believe my radio antenna is a real thing. I don't think I need a
comprehensive philosophical understanding of "real" to reasonably hold
that belief. I believe that anything that can affect my radio antenna
is also real. I reject out of hand the notion that mere mental
constructs, invented to help us perform calculations, can affect my
radio antenna. But when I tune a particular radio station, I am not
hearing things the instant they are broadcasted by the transmitter.
There is a delay that depends in part on my distance from the
transmitter. Since I believe that time is real, that delay is also
real, even though I cannot put "time" into one of Jim's buckets. Simple
action-at-a-distance does not explain that delay, but a real
electromagnetic field does-- and in a way that makes physical sense. If
the electromagnetic field is not a real thing, then oscillations in the
field aren't real either. But if all that is true, what is reaching out
from the transmitter to my radio antenna, and why does the reach not
Assistant Professor of Physics