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IIUC, quantized doesn't mean finite, it just means discrete. Energy being quantized in bound states in quantum mechanics means that the eigenvalues are discrete
by bobbylarrybobby 3y ago
IIUC, quantized doesn't mean finite, it just means discrete. Energy being quantized in bound states in quantum mechanics means that the eigenvalues are discrete, but a state can still be any linear combination whatsoever of the eigenstates.
And since spacetime is continuous, it's determines by its values on a dense subset, in particular a countable sense subset, which would make both sets of possibilities, gravity and quantum, have cardinality something like R^N.
- eternityforest 3y agoWhat determines the amount of information? Is it the total values the gravity could have had with unlimited mass? The number of values that are less than the one it is observed to be? All the values in the probability distribution for some uncertainty thing? If you have a carbon atom, does it have unlimited information because it theoretically could instead have been some other number of atoms?
- archgoon 3y ago> What determines the amount of information? Noise. Your ability to distinguish between states. > If you have a carbon atom, does it have unlimited information because it theoretically could instead have been some other number of atom You don't even need that. A single hydrogen atom has an infinite number of bounded energy states. In principle, you could store infinite information by putting an electron in the nth energy state and keeping it there. In practice, you can't, due to noise.