The biggest stumbling block that has traditionally plagued all the unification endeavors has been the simple fact that on the face of it, general relativity and quantum mechanics really appear to be incomprehensible. Recall that the key concept of quantum theory is the uncertainty principle. When you try to probe positions with an ever-increasing magnification power, the momenta {or speeds} start oscillating violently. Below a certain minuscule length known as the Planck length, the entire tenet of a smooth spacetime is lost. This length {equal to 0.000...4 of an inch, where the 4 is at the thirty-fourth decimal place} determines the scale at which gravity has to be treated quantum mechanically. For smaller scales, space turns into an ever-fluctuating "quantum foam." But the very basic premise of general relativity has been the existence of a gently curved spacetime. In other words, the central ideas of general relativity and quantum mechanics clash irreconcilably when it comes to extremely small scales.
( Mario Livio )
[ The Equation That Couldn't Be ]
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