Theoretical mathematics postulates ... what are they up to, 11 dimensions?
You just hit a big red hot button.
So, just because we can't imagine the dimensions doesn't mean they can't or don't exist.
It also doesn’t mean that they can and do exist.
The rest of this is (somewhat) off-topic.
Theodor Kaluza took the equations of General Relativity and, as an intellectual exercise, manipulated them in a 5d spacetime. To his surprise his manipulations turned up equations that mimicked Maxwell’s differential equations. Since GR is the general state of SR and SR is a more robust and exact follow-on of Maxwell hindsight says this should not be all that surprising, but it was a big hit at the time and then was promptly forgotten.
Along come string theory, which isn’t a theory at all, and in order to get the equations of the vibrating strings to mimic the quantum values of the standard model of particles, which they wouldn’t do in 4d spacetime, string theorists took a page from Kaluza and added more and more dimensions for the strings to vibrate in to get the numbers to come out right.
First, since the strings are speculated to be planck-sized objects there is no known, nor even reasonably speculated, way to detect their existence. Second, the shapes of the extra dimensions vary greatly and the shape to be chosen in any working of the string equations must be chosen carefully to achieve the desired results. The extra dimensions and their shapes do not flow naturally from any formulation of string equation. They must be chosen and forced upon the situation. To their benefit, if chosen appropriately, the equations do produce models roughly equivalent to the standard model of particles with the addition of a spin-2 particle for the graviton, as posited in Quantum Field Theory, and a whole slew of additional particles (supersymmetric particles) not known in the standard model.
None of these dimensions or particles from any of the complicated models from string theory (or, more accurately these days, M-theory) have been shown to be real. They may indeed be found in the new higher energies of the Large Hadron Collider, and if not it may be because the LHC is still under-powered to find them, but at present none of the predictions of M-theory has been verified.
The only reason M-theory has been elevated above speculation to hypothesis is because the math, even as complex as it presently is, can be manipulated to produce models of what we presently know to exist. By strict scientific standards M-theory is not a theory at all. None of its predictions have been verified.
Someone once said, Observation over theory. Except theory is a well-substantiated explanation based on a body of facts that have been repeatedly confirmed through observation and experiment. In science theory explains observation and experiment. M-theory does neither.
Still, we shall see.
[abe]
Just thought of something I said that may be misinterpreted.
"Observation over theory", mickechell, is correct. I did not mean to be seen as challenging that. If an observation conflicts with a theory, the observation wins. I just thought it was a nice segue into ending my personal rant.
Edited by AZPaul3, : clarify
Edited by AZPaul3, : No reason given.
Edited by AZPaul3, : spln