| MadSci Network: Physics |
Well, quantum mechanics doesn't really address the space time fabric as a whole, and general relativity doesn't really address what happens on a quantum scale (although it does implicitly assume that space time remains smooth). The problem is that quantum mechanics incorporates the Heisenberg uncertainty principle, which says that the uncertainty in a particle's energy multiplied by the time over which that energy is measured cannot be smaller than Planck's constant. This is the source of virtual pair production - as long as a particle-antiparticle pair annihilates quickly enough, the brief violation of the conservation of energy cannot be detected. The existence of virtual pair production has been well-verified by experiment, so this is not in question. The problem comes when we look at shorter and shorter times. The shorter the time they exist, the more massive a particle-antiparticle pair can be. When the time becomes the Planck time (10^-43 sec), the mass of the pair can be as large as the Planck mass (10^-8 kg, or 10^19 GeV/c^2). It is at this point that quantum mechanics and general relativity both break down. Masses this large, this close together, create gravitational fields that need general relativity to be described, but general relativity cannot deal with the very fine structure of space-time that would result if the expected pair production of more and more massive pairs at shorter and shorter time scales actually takes place. This makes the fabric of space-time on very small scales look like "quantum foam" rather than the smooth fabric that general relativity assumes. So on this very fundamental level, quantum mechanics and general relativity cannot coexist. Therefore, one or the other, or both, need to be modified, or a new theory is needed to address what happens at such small scales. Numerous attempts have been made over many decades to deal with this problem; string theory, although proposed initially for different reasons, seems to fit the bill (although it is far from a testable theory at this time). Other possibilities are M-theory (a generalization of string theory) and loop quantum gravity. There are others as well, but these are the most popular at the moment. Here are some references: Virtual pair production: http://zebu.uoregon.edu/~imamura/209/apr14/virtual.html Loop quantum gravity (and other similar efforts: http://relativity.livingreviews.org/Articles/lrr-1998-1/ M-theory: http://www.damtp.cam.ac.uk/user/gr/public/qg_ss.html
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