Comment by rndphs
4 years ago
> If spacetime is continuous you effectively get infinite precision -> information density - at every point (of which there are an infinite number).
This would be true if objects existed at perfectly local points. However we know that a perfectly localised wavefunction has spatial frequency components that add up to infinite energy. Any wavefunction with finite energy is band-limited. At non-zero temperature the Shannon-Hartley theorem will give a finite bit rate density over frequencies, and since the wavefunction is band limited it will therefore only have the ability to carry a finite amount of information.
This and the comment under it are making my point for me. Relativity assumes spacetime is continuous. Quantum theory implies that quantum phenomena are bandlimited and therefore the information spacetime can hold is limited.
The difference is we know what the quantised components of field theory are. We don't have any idea what the quantised components of spacetime are supposed to be, or how they operate.
The various causal propagation theories (like causal dynamical triangulation) may be the first attempts at this, but it's going to be hard to get further without experiments that can probe that level - which is very difficult given the energies involved. Without that, we're just guessing.