I know what Gauss's law is (vaguely), what exactly is undefined by Coulomb's law that cannot be a result without the use of Gauss's law? That is what I asked for.
Everything, if you take Maxwell's equations (including Gauss's law) as your starting point. In that case, Coulomb's law becomes a derived result, rather than a basic assumption. Just as p=mv can be a derived result rather than a basic assumption.
You know very well what I meant by "undefined". And that is 1/0 = undefined NOT, well I just chose to not define something... BS.
Sorry, Aer. Where are you going with this? If you want a particular point where Coulomb's law is undefined, take r=0 in the formula F=kQq/r<sup>2</sup>, for example.
r is the spacial difference between two particles, I know of no case where one particle exists exactly where another particle exists. This is not physical or real. A photon is physical and real and has pc=hf which is undefined in relativity because fundamentally, p=γmv. That was the discussion and always has been.
What about a boson with integral spin? Is that "not physical or real"? It seems you've forgotten the conversation we've been having. Oh well.
Are any two bostons ever located in exactly the same space? I believe their state is only a range of possible location, correct? Two bosons could be in the same range and not occupy the exact same space. I didn't forget. I've been talking to many people - from my memory, I was talking to Pete about pi and randomness or something, then QQ came along and said 360/0 = 360 which SL said was infinity. Then shmoe made the smartass comment that 360/0 was undefined and insisted that since 0 was a real number, N/0 was undefined. I qualified that to say that unless you know 0 to be exactly 0, then N/0 is infinity. Then you decided to come along and defend shmoe by disagree with me (seems like the popular thing to do Please Register or Log in to view the hidden image!). Then I brought up your little γm example for a photon in which you said 1/0 was infinity. You retracted. I lambasted you. And here we are talking about QM.
I might add in here and just complicate things even more than my naive 360/0 = 360 comment, having had some time to see the cafuffle that I generated over definitions. If you have a sphere and note that an infinite number of spheres can exist within that sphere how many spheres are you looing at when you look at the sphere....so by this logic every object is infinite. How many ones are there in the number one....answer infinite number of ones....so by definition everything is infinite..... There was ages ago reference made somewhere to the development of 4 dimensional calculus or maths.....but was disbanded due to complexity i think... As I don't have the math background I can't really comment with out it being speculative but I get the impression that math is sort of a linear expression and to progress into a more realistic expression the math has to have 3 dimensions to it.....don't ask me to explain further than that except to say that I think what they meant was the math flow of logic should be spherical rather than point to pont. The logic expands in all directions rather than moving in a line.... Just a point of interest.......
No, the position is described by the wavefunction which is only a probability. They are not in the exact same position.
Which means their postion is only known as a probability. You cannot say definitely from this that they occupy the exact same space.
James, I understand that postion. but 1=1=1=1=1=1=1=1=1=1=1 ~ also I object multiplied by same object still equals 1 object. Using this logic 10 objects multiplied by the same 10 objects = ten objects..... thus 10 *10 = 10 in this context as each object is still 1 object..... Of course this is contraversial to the usual use of math.... I understand this..... A while ago MacM argued that Mass ^2 made no sense in the E=mc^2 equation. And in using this logic it makes perfect sense mass ^ 2 = one mass. An apple times itself still equals that apple. However when you throw in c^2 the use of m makes more sense.
You're losing track of the discussion again. You asserted, with your open mind, that nothing in the universe could possibly exist in the same space at the same time. I've given your an example of something that you could well measure to be in exactly the same place at the same time, which disproves your statement.
You jest? No, you are violating the Heisenberg Uncertainty Principle because you are claiming to know the exact position of two bosons. Bosons move around and the best we can do is give a probability of where they are at any time. While two bosons may have the same probability function, that doesn't mean they ever exist at the same position at any point in time. You are assuming that they could exist in the same place at the same time because the wavefunction gives the same probability for each.
