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As most people said already here, physics advances comes with the creations of narratives and concepts that explain a particular behavior (which allows for more narratives and more beahvior to be uncovered with mroe experiments that cen be better understood with theprevious narratives and symbols).

So why oh why did physicist chose the terms positive and negative instead of good and evil directly or black and white for the two complementary elements you need in the lectromagnetic force?

I have not the foggiest idea. My suggestion is that you make a feeling map. Some thing like.. now posstive and negative are not clear cut things. Sometimes positive stuff gives bad results, sometimes negative stuff produces good results in the log term. So basically you can construct a history for each of the different possible chemichal reactions.

A pleasure


I therefore claim to show, not how men think in myths, but how myths operate in men's minds without their being aware of the fact. Levi-Strauss, Claude

by kcurie on Sun Mar 23rd, 2008 at 08:42:57 AM EST
That's clear: the model is (signed) numbers because charge is something that can be added and subtracted, and of which there can be an excess or a deficit.

One problem is that the same words positive/negative, used in a different domain have moral implications, and rg cannot seem to separate the different domains.

The other problem is that charge is signed but not ordered, unlike signed numbers which in addition to sign have a linear order (greater than/lesser than).

So, actually, modelling charge as signed numbers is a bad thing to do.

Technically, one can say that the irreducible representations of U(1) are isomorphic to the signed integers Z, but that is incorrect. The are isomorphic to the additive group of the integers, forgetting multiplication. If you don't have multiplication you have no way to distinguish +1 and -1.

So one possible solution is to write 1 for +1 and 1 for -1, so that

1 + 1 = 2
1 + 1 = 2
1 + 1 = 0

and there is no operation of subtraction and no negative (or positive) numbers.

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris

by Migeru (migeru at eurotrib dot com) on Sun Mar 23rd, 2008 at 08:54:32 AM EST
[ Parent ]
So, actually, modelling charge as signed numbers is a bad thing to do.

How do you view charge--what is the model you use?  I think I'm missing some simple and fundamental point about the attraction / repulsion of equal/opposite charges.

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Sun Mar 23rd, 2008 at 10:24:23 AM EST
[ Parent ]
The key is to separate the various meanings of symbols. '-' has a number of different meanings. In algebra, it can be a unary or a binary operator.

As a unary operator, '-' represents the operation of "opposite": -x is the opposite of x.

As a binary operator, '-' represents the operation of "subtraction": x - y is the operation of subtracting y from x.

There is no value attached to "opposite".

You seem to have a value attached to addition and subtraction: addition:good, subtraction:bad. I can't help you there, you have to learn to separate domains by, every time you catch yourself making the association, consciously telling yourself that's not right. Eventually you just won't make the association.

One way to think about positive and negative charge is that they are related to clockwise and counter-clockwise rotation. But notice that if you look at a rotating disk from the other side, clockwise and counter-clockwise trade places. So there is not a preferred sense of rotation: there are just two opposite senses of rotation. You can choose to associate the words "positive", "clockwise" and "right-handed" to one of them and "negative", "counterclockwise" and "left-handed" to the other.

Now, if you accept as a given that net charge has energy, then you will see that putting together two similar charges will have more energy than putting together two dissimilar charges. That is: n + m or n + m have more energy than n + m. Mechanical forces tend to go towards lower energy states, so it follows that similar charges don't like to be together (more energy) and dissimilar charges do like to be together (less energy).

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris

by Migeru (migeru at eurotrib dot com) on Sun Mar 23rd, 2008 at 10:48:21 AM EST
[ Parent ]
putting together two similar charges will have more energy than putting together two dissimilar charges.

Okay...but...(I have a horrible feeling I'm about to fall into the deep end)...

net charge has energy

single charge = energy.  Two charges interact and the result (the net) = energy (maybe reduced or amplified--more or less energy)

Opposite charges cancel out (less energy); same charges amplify...

...so it's not that two similar charges (two negative charges, say) repulse each other--it's that they generate more energy, energy which seeks to dissipate into the anti-itself sink of either nothingness (escape into emptiness of space > move away > e.g. heat radiation?  Ach...surely not) or--even better--to fly towards that which will suck energy out of it--

So 'negative' energy (or A energy) finds energy is sucked out of it by 'positive' energy (B energy) and vice versa, such that A + A is more energy, more instability, more energy needs to escape, while A + B means less energy, somehow the energy cancels out, A can absorb B energy and B can absorb A energy--

?

(I'm still missing something.)

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Sun Mar 23rd, 2008 at 11:01:18 AM EST
[ Parent ]
Okay, assume that the energy of a charge inside a small volume goes as the square of the charge.

Then, 2 = 1 + 1 has an energy of 4, and 2 = 1 + 1 has an energy of 4 as well. But 0 = 1 + 1 has an energy of 0.

The energy of 1 or 1 is 1. If two unit charges are very widely spatially separated, than their joint energy is 1 + 1 = 2, regardless of the signs.

But if the two charges are together, the energy can be 4 if they are similarly charged or 0 is they are oppositely charged.

So, similar charges will increase their energy if brought together, and opposite charges will decrease their energy if brought together. Mechanics then dictates that opposite charges attract and similar charges repel.

Note how I avoided the use of the '-' sign by recourse to underlining.

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris

by Migeru (migeru at eurotrib dot com) on Sun Mar 23rd, 2008 at 11:09:21 AM EST
[ Parent ]

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