
#19
Jun411, 05:30 PM

P: 5,462

Consider this quote form another thread:
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'. 



#20
Jun411, 06:31 PM

Sci Advisor
P: 8,007

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. 



#21
Jun411, 09:09 PM

P: 46

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 180degrees in any triangle?)—but, later, nonEuclidian geometry was born from the assumption that one of his axioms was unjustified, thus, not necessarily true. 



#22
Jun411, 10:15 PM

Sci Advisor
P: 8,007

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.) 



#23
Jun511, 12:13 PM

P: 46

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.




#24
Jun511, 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'. 



#25
Jun511, 01:48 PM

Sci Advisor
P: 8,007

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. 



#26
Jun511, 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. 



#27
Jun511, 02:56 PM

P: 834

When I look up the axioms of quantum mechanics, I see nothing about assuming charge or matter are fundamental properties. 



#28
Jun511, 03:07 PM

P: 5,462

Shrug, sigh, I've wasted enough time on semantic nit picking.




#29
Jun511, 07:17 PM

Sci Advisor
P: 8,007




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