Natural Science Forum / Physics / Relativity / July 2009

What are the spatial dimensions of a *volumeless* object having
mass and charge?

If they are zero, how can such object be different from a mathematical
point?

Hereafter is a summary of Paul Draper's position, where he is
claiming
that 'volumeless' doesn't imply a dimensionless point.
(from http://groups.google.fr/group/sci.physics.relativity/browse_thread/thread/fa0128
76dcdaafae#
)

Marcel Luttgens

Summary:

PD: Well, I didn't say that. What I said is that there appear to be
physical objects for which we have no attributable or measurable
volume, nor is there any reason to expect that they would. This is
not
quite the same as saying that these *physical* objects ARE
mathematical points.

Why do you think mass requires volume?

Note that the definition of matter limits it to composite stuff, by
virtue of bearing both mass and volume. The only substances we know
that have both mass and volume are all composite substances. No
fundamental object has been demonstrated to bear both mass and volume.

Whether fundamental particles have volume or not is *unknown*. We
have
zero evidence that they do have volume, despite looking. It is
therefore inappropriate to DECREE that all things have volume, and by
virtue of that decree declare that the possibility of having no
volume
is nonsense.

It is false to reason that all things must NECESSARILY have volume,
and that therefore mass with no volume is logical nonsense.

Alen:
"There can be no such thing as a
real singularity. Whether you characterise the matter
in terms of intrinsic volume, or interaction distance,
or whatever, these can never be zero if they are to exist
at all. There must always be a minimum possible
quantum of distance or volume, or any measurable
quantity, and this must therefore be associated with
a finite maximum allowable field intensity, etc., that
may be associated with it."

Bell:

From that, I would say a good scientist would conclude fundamental
particles *may or may not* have mass and no volume. But you have
done the same thing you accuse us of, by saying that absolutely,
without a doubt, an electron in the external world is a dot with
mass. I'll throw your very own logic back at you and say, that has
not
been experimentally verified, yet you seem to take it as
absolute fact."

PD: What I said is that the claim that electrons CANNOT be a point
because
it is IMPOSSIBLE for something to have mass and not volume is simply
not supported by experiment.
There is no experimental evidence that everything that has mass has
volume. That statement is only experimentally supported for composite
substances and there is no experimental support for a similar
statement
for fundamental particles.

PD: I did not say they were dimensionless.
What I said was that you could not argue that they NECESSARILY
have volume because they have mass, which is precisely the claim that
was made originally.

PD: Things that have no volume are not necessarily mathematical
abstractions. They are real things. Electrons are real things.
Geometrical points (mathematical abstractions) do not have electrical
charge, do not have weak hypercharge, do not have spin, do not have
parity. Just because two things share the common trait of having no
volume does not make them the same thing!

PD: Well of course. Mathematical structures are necessarily models of
reality and do not belong to reality itself. That's not to say they
aren't useful, because mathematical models allow you to do things to
see features that aren't obvious from looking at the physical objects
themselves, but turn out to be features of the physical objects when
you look. But there will always be features of the physical object
that are never captured by the mathematical model.

ML:
"PD is trying to to sell his dimensionless electron whith the
following reasoning:
Fundamental particles have mass, but *could* be dimensionless because
it has not been shown experimentally that they have volume.
Most of the time, in his posts, he gave the impression that "are"
should be used instead of "could"."

PD: You're not paying attention. I'm not claiming the electron is
known to
be dimensionless. I'm disputing your claim that it MUST have volume.

Yes, that is what I said. From this, you somehow got the impression
that "are" should be used instead of "could".

PD: Nor have I *ever* claimed that they are mathematical points. In
fact,
I went to some length to place a careful distinction between
fundamental particles and mathematical points. Yet you somehow,
through all that, got the impression that I'm claiming fundamental
particles are mathematical points.

PD: Please read again what I said. Never did I say that
mathematical points have physical properties.

ML:
"I retain from your statements that
- whether fundamental particles have volume or not is *unknown*
- you never ever claimed that they are mathematical points
 having physical properties like mass or charge."