So i read somewhere that Schrodinger had him some calculations pertaining to quantum physics wherein you had to assume there are 10^70 (thats ten to the seventyith power) dimentions. I recall thinking that that sounds like an awful lot of dimentions. Then i realized why there being this many dimentions should matter in any kind of calculations, or even what the hell a dimention is. Then i believe i was distracted by something shiney. Does anyone have any sort of education that might have taught them something about quantum physics, like why exactly everyone is so sure those particles cant be predicted, or what all of those dimentions are all about?
Well there is a theory that there were 11 dimensions before the big bang and apprently something went wrong and only 4 expanded when all 11 should have. The other seven still exist today in there normal size (astronmically smaller than an atom) and they are all around us. There is also a theory that these dimensions halp run the universe smoothly by helping out. There are theories that predict up to 30 dimensions....it's all very theortical really at this stage and time.
To OverTheStars Or -1 + 1=zero.... gravity + mass = zero Re: sargentlard I think a lot of work has gone into applying Lie group mathmatics into the superstring theorys...
SpyMoose: <i>So i read somewhere that Schrodinger had him some calculations pertaining to quantum physics wherein you had to assume there are 10^70 (thats ten to the seventyith power) dimentions.</i> I doubt it, unless it was in the context of Hilbert spaces (which are mathematical constructions - nothing to do with our 4D universe).
So that mathematicians can do what philosphers do: show off. The theory goes that in the beginning the universe was a multidimensional blob of 20 or so dimensions. Some seconds after the Big Ban all the rest fizzled but 3 -length, width, height. Of course there's the less boring one "time" that the modern physists tries to worm in there as valid but I don't buy into it because this means time dilation. In math you can tag on any number of dimensions (thousands even) but then if you dare ask a mathematician what the use of calculating thousands of fucking dimensions is for he'd punch you in the nose. So why does it even matter? Kill time. Not really, but from what I gather, someting called the Heisenberg principle means that on the quantum scale, things being so small, you can't look at photon and see where its going at the same time because it takes a photon to see a photon. This means immediate displacement so you can never, ever pinpoint a particle's position and velocity at the same time. Odd, yes? But incredibly interesting. Spymoose: Ha. At least you're honest James: Don't just give us a taste and then leave. Tell me about Hibert spaces.
gendanken: The dimension of a vector space tells you the maximum number of vectors which are needed to construct any vector in the space. A <b>basis</b> for a vector space contains a number of vectors equal to the dimension of the space. Combinations of those vectors can make any vector in the space. For example, if I take the space of all 3-component vectors, one basis is the following set of vectors: (1,0,0), (0,1,0), (0,0,1) I can make any 3-component vector (x,y,z) from these by taking a linear combination: x(1,0,0) + y(0,1,0) + z(0,0,1) = (x,y,z) A Hilbert space is technically a vector space with an infinite number of dimensions. That means that, in principle, there are vectors in the space which can only be written as linear combinations of an infinite number of basis vectors. Hope this helps!
So in essence Hilbert spaces are just another means by which mathematicians work out those horrible problems of dimensional fields in the thousands? And all you're using there are standard Cartesian coordinates?
What you need to realise is that the mathematical definition of a dimension need have nothing to do with physical dimensions in space. Cartesian coordinates are just one way of specifying locations in space. General vector spaces are much more general. For example, here's another basis for the set of all 3 component vectors: (1,1,0), (0,1,1), (1,0,1) Again, any vector (x,y,z) can be expressed as some combination of these three vectors. In fact, the space of all 3 component vectors has an infinite number of possible bases, or, if you prefer, coordinate systems. But the mathematical dimension of that space is the same no matter which basis (system of coordinates) you choose. So, vector spaces can tell us many useful things about a space (mathematical or real) by generalising the idea of what a space actually is.
