Jan 13 2009, 09:39 AM
Ok I can add to this, but I just woke up so I may have to come back and edit this later.
QUOTE (Yannick @ Jan 13 2009, 02:56 AM)
In a discussion about whether or not negative speed is possible (no definite answer yet, but I said yes, in the sense of deceleration, but you can't really have a negative speed, so no), we got a bit off topic and started talking about whether negative things are conceivable at all. So this guy started saying stuff about negative charges, and I replied with:
Ok, firstly: you can distinguish between two types of quantities: scalar and vector. The difference is that vectors have a direction associated with them and scalars don't.
Speed is a scalar, and as far as I know negative speed doesn't have any physical meaning... however it has a vector equivalent called velocity. You may hear speed and velocity interchangeably but there is a difference. You can't just say something is moving at a velocity of 10m/s, because then you don't know which direction its moving. You need to know the speed and the direction to get its velocity. You could give the direction as an angle from an established direction, or if you have defined a coordinate system (lets say that the y direction is north of where I am and x direction is east) then through the magic of trigonometry its possible to break it down into 2 numbers: the x component of the velocity and the y component. i.e. if you have a velocity of [2,1] this is telling you that for each unit of time, you are moving 2 units in the x direction and 1 in the y direction. If you imagine a flat 2D world you can describe any direction in this way. So if you know somethings position and velocity you have everything you need to know to track how it moves with time, but if you just knew that the speed was 5 you'd have no clue because it could be moving in any old direction. Anyways what I'm getting at is that with velocity you can have a negative number, because it just means you're moving in the opposite direction.
Oh, forgot about those. We've not done much on magnetism in school, but when charges are said to be negative and positive, are they actually, or is it just like "This one has this type of charge, and this one has the opposite of that, so they must be positive and negative!"
Oh man, I think my brain just like, exploded. Do you know how difficult it is to comprehend that we can have negative charges? I mean, how is that measurable? It totally just stopped making sense to me. (This isn't to say I've stopped believing in it, but woah, brain ache.) Here's my attempt (mostly for myself) to make it make sense again...
It's completely arbitrary which one is positive and which one is negative, the important thing is that they have opposite charges, so if you force an equal amount of positive and negative charges together, like in an atom, from far away it looks like a big neutral charge.
but what if like, there's a 0, and there's really no such thing as negative and positive, just directions from 0? Not necessarily only two (like on a number line), but an infinite amount of directions? Negative and positive are just opposite directions, and it really has nothing to do with a number being below zero, just the absolute value from it? It makes it make sense! Sort of. To me anyway.
Ok, you're mixing math-land with reality again. What does "direction" mean in your hypothetical number-plane? With a line of numbers theres a simple way of getting to the next and previous number, you either add or subtract 1. How would you get from 0 to the next number in one of the other directions?
QUOTE (CheeseMoose @ Jan 13 2009, 04:08 AM)
The second paragraph is better. The charge on an electron is not less than the charge on a proton, it's the same, but in the opposite direction. It's just convenient (and makes the adding up work out) to label those directions as positive and negative.
Actually charges don't have a direction - it's the electric field of the charge which is the opposite direction.
The value of the electric field at some point in space tells you the force a positive charge at that point would feel from the electron or whatever. (Again we could switch everything positive to negative and vice versa and it wouldn't make a difference, as long as you're consistent)
The equation for the electric field for itty-bitty things like electrons is called Coulombs law, which is:
Electric field at some point = (a bunch of constants) * the charge / the square of the distance from that point to the charge * a unit vector pointing from the charge to that point.
A unit vector = vector with magnitude of 1. This gives the electric field it's direction. Now, if the charge is positive, the direction of the electric field is the same as the unit vector: away from the charge, so it will repel a positive charge. But if it's negative, the electric field is in the opposite direction, so it attracts. Eek gotta go sorry if this isconfusingbye