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Electric charge is a theoretical given . . .

by AmagicalFishy
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Studiot
#19
Jun4-11, 05:30 PM
P: 5,462
Consider this quote form another thread:

Charge, like mass, is a property of matter.
It is more complicated than mass because simple experiments show that there are two types or polarities.
All matter possesses mass, but not all matter possesses charge.

Experiments show that uncharged (neutral) matter exerts a force of attraction between two masses and that this force is governed by the inverse square law. We call this gravitational attraction.

Work is therefore done on the mass of any matter moved against this force.

Further experiments show that an additional force exists between charged matter, over and above that exerted by gravity. It is further observed that the direction of this force depends upon the relative polarities of the participating charges. We call this electrostatic attraction or repulsion.

Work is therefore done on the mass of any matter that we move against this force.

It is often stated, rather loosely, that work is done on the charge. This is not so. Work is done on the mass of the matter. So you will find the mass of the charged particle appear in many equations.
This 'definition' is the one that leads to the establishment of a unit of charge.
It also explains why we have introduced the concept of charge.

This is a very important distinction. The experiment came first, the concept followed, not the other way around.

But the definition is mute on the subject of why it is necessary for charge to exist at all it simply accepts that it must be so to explain an observation and gives it a name.
It is not 'proven'. To prove something you must have a hypothesis to prove ie you must have a charge hypothesis before the observation.

I call that a 'given'.
atyy
#20
Jun4-11, 06:31 PM
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What is a "point"? "That which has no part." http://aleph0.clarku.edu/~djoyce/jav...okI/defI1.html

Euclid seems nowadays to be criticized by pure mathematicians for that. Apparently "that which has no part" was meaningless, and a point is a fundamental given, and known only by the axioms relating points and lines. (And I think there's some duality between points and lines too.)

So maybe Euclid was doing physics there. He meant the theoretical given is a model of a pencil mark, which of course makes it unaxiomatic, since he didn't define pencil. Also, just like the standard model of particle physics, Euclid's model is only an effective theory, since a pencil mark is not an exact point.

In electrostatics, we also have charge and field as fundamental givens. What is a charge? A thing that is affected by a field. What is a field? A thing that affects a charge.

But now we have to say in "real life" what a charge is. Then we have to bring in things like "gold leaf", which is undefined in classical electrostatics.
AmagicalFishy
#21
Jun4-11, 09:09 PM
P: 48
Well, what I think Euclid meant by "that which has no part" was a simple way of describing something which is completely and totally indivisible. A point has no length, width, volume, etc. If I'm not mistaken, I believe that's the definition of a point still used today. Similarly, "A line is the shortest distance between two points," is still the definition of a line. I'm not aware of any intention to model a pencil mark.

The link you pointed out says something about Euclid failing to realize that a certain few of his axioms were unjustified. I do not think it's referring to his definitions of a point and line. Unfortunately, I don't remember exactly which axiom it was that was unjustified (I believe it may have been something with there being 180-degrees in any triangle?)—but, later, non-Euclidian geometry was born from the assumption that one of his axioms was unjustified, thus, not necessarily true.
atyy
#22
Jun4-11, 10:15 PM
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Quote Quote by AmagicalFishy View Post
Well, what I think Euclid meant by "that which has no part" was a simple way of describing something which is completely and totally indivisible. A point has no length, width, volume, etc. If I'm not mistaken, I believe that's the definition of a point still used today. Similarly, "A line is the shortest distance between two points," is still the definition of a line. I'm not aware of any intention to model a pencil mark.

The link you pointed out says something about Euclid failing to realize that a certain few of his axioms were unjustified. I do not think it's referring to his definitions of a point and line. Unfortunately, I don't remember exactly which axiom it was that was unjustified (I believe it may have been something with there being 180-degrees in any triangle?)—but, later, non-Euclidian geometry was born from the assumption that one of his axioms was unjustified, thus, not necessarily true.
Yes, of course there was no intention to model a pencil mark - that was my interpretation of what it is

OK, if a point has no parts, and by http://en.wikipedia.org/wiki/Duality...ve_geometry%29, incidence relations can be preserved by switching lines and points, then a line also has no parts, no? (Concretely, let a point model a pencil mark. By duality, the pencil mark can also be represented by a line. Hence the two different mathematical objects represent the same physical object.)
AmagicalFishy
#23
Jun5-11, 12:13 PM
P: 48
I'm not exactly sure that's what duality means. From what I know, a line is constructed of an infinite number of points. I'm having a hard time explaining duality to myself, though, so I guess at this point I can't really comment any further.
Studiot
#24
Jun5-11, 12:37 PM
P: 5,462
This discussion is growing ever more whimsical.

I thought you wanted hard science?

Neither points nor lines are axioms in Euclid's 'Elements'.
atyy
#25
Jun5-11, 01:48 PM
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Quote Quote by Studiot View Post
This discussion is growing ever more whimsical.

I thought you wanted hard science?

Neither points nor lines are axioms in Euclid's 'Elements'.
http://aleph0.clarku.edu/~djoyce/jav...ookI.html#defs

They are definitions. Would you say that's a "theoretical given"?

The idea here in making an analogy with Euclid's definitions and axioms and what we draw on paper was to make things more concrete. Instead of discussing theoretical electrodynamics and its experimental basis, let's simplify to Euclidean geometry and something which it models.
Studiot
#26
Jun5-11, 02:17 PM
P: 5,462
No I'd say that Euclid first of all collects/defines/lists a set of geometrical objects with which he is going to work.

Points and lines are such.

Then he makes assertions without proof about all points and lines.

These are axioms.

You cannot have axioms about nothing you must have some working material.

Then he goes on to develop (ie lemmas and proofs) his system of geometry using these axioms and applying them to the working material (the points and lines).

**

In Physics we introduce some working material such as matter, energy, space etc.

Then we introduce properties of our working material - electric force, gravitational force etc

Then we develop relationships between them - Maxwell's equations, Schroedinger's equation and so on.

I think the parallel is a fair one.
DragonPetter
#27
Jun5-11, 02:56 PM
P: 834
Quote Quote by Studiot View Post
No I'd say that Euclid first of all collects/defines/lists a set of geometrical objects with which he is going to work.

Points and lines are such.

Then he makes assertions without proof about all points and lines.

These are axioms.

You cannot have axioms about nothing you must have some working material.

Then he goes on to develop (ie lemmas and proofs) his system of geometry using these axioms and applying them to the working material (the points and lines).

**

In Physics we introduce some working material such as matter, energy, space etc.

Then we introduce properties of our working material - electric force, gravitational force etc

Then we develop relationships between them - Maxwell's equations, Schroedinger's equation and so on.

I think the parallel is a fair one.
I don't think it is a parallel. You're trying to compare purely mathematical concepts like points to physical concepts. We can come up with many mathematical generalizations, idealizations, and even impossibilities that don't necessarily match with reality yet still work nicely in theory, but we can't make up things like charge and expect it to match reality. Charge is a concrete real property, it is not a theoretical given or a purely mathematical concept that we made up because it fits nicely into models.

When I look up the axioms of quantum mechanics, I see nothing about assuming charge or matter are fundamental properties.
Studiot
#28
Jun5-11, 03:07 PM
P: 5,462
Shrug, sigh, I've wasted enough time on semantic nit picking.
atyy
#29
Jun5-11, 07:17 PM
Sci Advisor
P: 8,636
Quote Quote by Studiot View Post
No I'd say that Euclid first of all collects/defines/lists a set of geometrical objects with which he is going to work.

Points and lines are such.

Then he makes assertions without proof about all points and lines.

These are axioms.

You cannot have axioms about nothing you must have some working material.

Then he goes on to develop (ie lemmas and proofs) his system of geometry using these axioms and applying them to the working material (the points and lines).

**

In Physics we introduce some working material such as matter, energy, space etc.

Then we introduce properties of our working material - electric force, gravitational force etc

Then we develop relationships between them - Maxwell's equations, Schroedinger's equation and so on.

I think the parallel is a fair one.
But he never deduces anything using "that which has no part". So points and lines are known only by their incidence relations, and other axioms. Similarly, charge is known only by its effect on a field, and a field is known only by its effect on a charge.


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