Do Planck length and Planck time imply that spacetime is not continuous?
In: Physics
No. Even in quantum mechanics, position is continuous.
The Planck length is the smallest width that can be detected, because it takes progressively more and more energy to probe progressively smaller distances. Concentrating enough energy to detect a Planck-length-scale object would create a black hole and thus render the object unobservable anyway. It’s also roughly the length at which the energy present in the vacuum itself (and the uncertainty in that energy) produces distortions to space-time in the same way that massive objects do at more familiar length scales.
…except that’s not really likely to be true anyway, because it assumes general relativity is valid at those energy and length scales, which it almost certainly is not. The behavior of gravity at very high energy and very short lengths is not currently understood, and it’s likely that a full theory of quantum gravity will change if not entirely eliminate these characterizations. But as no one has a damn clue how quantum gravity works yet, exactly how it will do so is currently unknown.
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