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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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