What is a particle?

Increasingly, I hear about incompleteness theorems and conjectures in
physics. There was an interesting article in AJP a while back by Hecht
that made the point that the term "mass" has no firm meaning in
physics. As another example, I'll point out that the concept of
"particle" is pretty poorly captured at both the classical level and
at the quantum level.

Classically, a particle is something that carries linear momentum and
linear kinetic energy but has no internal or rotational degrees of
freedom. Strictly speaking, in classical terms this is anathema,
because anything that has mass classically also has volume and
therefore has both rotational and internal degrees of freedom and thus
in any real interaction would carry both angular and rotational
kinetic energy. I don't believe it is sufficient to say that
classically a particle is a real object in which we ignore the effects
of rotational and internal degrees of freedom. To me this simply means
we are classically approximating a real object with something that has
no meaning classically.

Similarly, in the quantum world, we run into a "well-I-don't-mean-
quite-that" problem. It's simpler in the quantum world to label a
particle by its properties, and here it is entirely possible for a
particle to carry, say, mass without carrying volume as a label.
However, at the very least one would expect that a particle would be
distinguishable as a single entity that carries these properties and
is at least conceptually separable from its surroundings. But, as we
know, a quantum mechanical particle is *not* separable from its
surroundings. At the very least, it carries (and in fact is in some
ways *defined* by) a sea of particles that helps carry some of those
properties, and that sea has no finite spacetime extent. So we can't
really say in any meaningful way that the thing that passed from
*this* emission event observed to *that* absorption event observed,
was a particle. The best we can say is that it seemed to be a particle
when it left and seemed to be a particle when it arrived, but that in
between it was something remarkably different.

And so we run into a simple but recurring problem in physics, that we
use many concepts which have *suggestive* meaning but are in no way
complete descriptions of anything in particular. The reason I bring
this up is that the so-called dual or complementary descriptions of
nature (neither description being complete but the total of two
incompatible concepts seeming to collectively map to nature) I thought
was restricted to quantum mechanics, but it appears to be much more
pervasive than I thought.

PD

.

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