I understood the “right now” part. What I guess I was getting at is that critics of String Theory claim the theory is so ill-defined and mutable that the answer to the question “can this be disproven” might not be “yes, in the future” but “never”. I don’t claim myself this is right, I’m just wondering what others might think of this critique. Obviously, you don’t think much of it, but I’ve yet to hear of experiments that don’t involve galaxy-sized (or bigger) accelerators that would do the trick. So, I guess, in the minds of the critics, if one can’t disprove the existence of compactified dimensions without building such fantastically large instruments, does that make the theory “safe from science”? I mean, are String Theorists expecting their critics to essentially prove a negative? You know: “Critic: Prove that there are extra dimensions! String Theorist: No, you prove that there aren’t!” Just because something could be there if you squiched it down to the plank length isn’t an argument that it is there. String Theorists, I guess, counter that the maths are so beautiful, the aesthetics are compelling enough. The critics then retort asthetics aren’t science. This doesn’t seem to me to be such an unreasonable debate. You appear to suggest that critics of String Theory are using “rhetorical bullshit”, motivated by professional jealousy and covetousness of resources, to unfairly discredit the pursuit of String/M Theory. It’s at least as bold an accusation as has been levelled at the String Theorists, so I wanted to be clear on that.
As for competing theories, the critics might again say they don’t just propose a different path to quantum gravity, they propose a more economical and modest path that also happens to better-resemble the real world, as opposed to the unreachably-plank-scale-buffered fantasy realm of higher dimensions. Hence, these approaches are patently more reasonable. More rhetorical bullshit? If so, why?
Like I said before, I just ask questions. I don’t claim to know the answers. I have an interest as a spectator, so I hope you don’t read my statements as some kind of personal attack on somebody. You’re obviously peeved by this line of questioning (though I don’t mean offense), and perhaps you find me almost too dense to dignify with responses. Pity the dense, then, if you can, because we are still curious.
But any of your forward-back/right-left points can still be described by my own forward-back/right-left points. Still only two dimensions.
Our daily observations are consistent with a three-spatial-dimensional universe. In a small enough neighborhood (say, a ball one meter in diameter) everything can be determined with three coordinates, no matter what orientation is picked for the axes.
In Euclidean space the metric simply takes the form of the Kronecker delta, thus the components of a vector and it’s one-form are the same. In Minkowski spacetime there are four dimensions; the three spatial dimensions and time. The metric used to describe Minkowski spacetime is the Minkowski metric η[sub]αβ[/sub] which is simply defined (though it can be defined in other equivalent ways) as: η[sub]00[/sub] = -1, η[sub]0i[/sub] = 0, η[sub]ij[/sub] = δ[sub]ij[/sub], (by convention time is the zeroth dimension) so the components of a vector and it’s one-form are same except that, for an arbitary four-vector A, A[sup]0[/sup] = -A[sub]0[/sub]. So when working out the square norm of a vector you take away the square of the time component rather than adding it as you would if you were working out the square norm of a vector in Euclidean space. The reason for the choice of Minkowski spacetime is that it it is invariant under a homogenous Lorentz transformation, with Lorentz boost becoming a hyperbolic rotation.
It’s certainly not arbitary, real space forms a vector space and the number of dimensions in a vector space is the maximum number of linearly independent vectors. Any less dimensions you lose the abilty to describe all the vectors in real space, any more and you have vectors that don’t exist in real space.
Thanks, that helps. Perhaps I was confusing dimensions with directions, which would be infinite, but still describable in terms of three relative (not absolute) dimensions. With your explanation it becomes harder to conceive of a physical dimension other than the three we observe relative to our ‘self-point.’