"... In retrospect, Riemann's famous lecture was popularized to a wide audience via mystics, philosophers and artists, but did little to further our understanding of nature ... First, there was no attempt to use hyperspace to simplify the laws of nature. Without Riemann's original guiding principle -- that the laws of nature become simple in higher dimensions -- scientists during this period were groping in the dark. Riemann's seminal idea of using geometry -- that is, crumpled hyperspace -- to explain the essence of a a force' was forgotten during those years ... The mathematical apparatus developed by Riemann became a province of pure mathematics, contrary to Riemann's original intentions. Without field theory, you cannot make any predictions with hyperspace [emphasis added]..."
Since ingesting Einstein's relativity theory 50 years ago, physics fell down a quantum rabbit hole and, ever since, physicists' reports to the world of popular science have been curiouser and curiouser. This version, from the author of the graduate text Quantum Field Theory , is very curious as he delineates the "delicious contradictions" of the quantum revolution: that the new paradigms of subatomic matter require the existence of "hyperspace," an ultimate universe of many dimensions, to accomodate their mostly mathematical behaviors.
Unified field theory as it is currently understood does not preclude any of the hypotheses that Kaku invites to this Mad Hatter's Theory Party: superstrings, parallel universes and, his centerpiece, time travel. Although occasionally facile, Kaku remains on solid theoretical ground up to the point of his untestable hypotheses, which lead to his more abstract arguments. In the past decade particle physics has lurched to astonishing contradictions and Kaku's adventurous, tantalizing book should not be penalized for promising more than present technology can test. His intellectual perceptions will thrill lay readers, SF fans and the physics-literate.
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