Way back in the day, Laplace’s Demon was concieved of as a creature that knows the position and momentum of every particle in the universe.
These days, I hear, we don’t think the universe is made of particles anymore but rather waves of… something… probability or something or other.
So what would be the right way to characterize Laplace’s Demons in contemporary terms?
(And does wave/particle duality maybe let us go ahead and formulate it in terms of particles after all?)
You’d have to do it in a way that’s compatible with the uncertainty principle and the fact that information can’t travel faster than light. I’m not quite brave enough to say that you can’t do it, but it sure seems like Laplace’s demon has been pretty thoroughly neutered by modern physics.
In quantum mechanics, all behavior is reduced to a mathematical representation, i.e. information and a set of rules. This should not be construed to mean that the universe is made of waves of probability or anysuch, but merely that these are the rules that precisely (albeit stochastically) describe all interactions, and that any interactions between local fields are interlinked, and interactions between distant (non-local) fields can be either connected via some kind of remote link (entanglement) or obey a set of rules that are not available to the observer embedded in that universe (non-local hidden variables). The idea that information cannot travel faster than light is an assumption in special and general relativity, but does not hold in most interpretations of quantum mechanics, or at least, not without a lot of additional gyrations to explain transactional mechanics (the apparent non-causal interactions) in a way that doesn’t violate local causality or local reality.
In QM terms, Laplace’s Daemon, containing all the information of the universe, would in essence be the universe itself. That is to say, in order to embed all the information to describe the universe it would have to have at least the same information volume and complexity as the universe, and therefore functionally indistinguishable from it. There is no possibility of representing the universe in toto as a synecdoche of itself, any more than you could have an exact copy of the Empire State Building down to the last fastener, brick, and window that would take any less information to replicate than building the Empire State Building itself, even if it physically occupied less room.
Stranger
The closest analogue to Laplace’s Demon would be a creature that knew the wave function of the Universe (to arbitrary precision.) If this demon knew what the wave function was at all points in space, he/she would be able to predict the future evolution of the wavefunction via the Schrödinger equation, just as Laplace’s Demon could predict the future motion of all classical particles by knowing their initial positions, initial velocities, and how they interacted.
The problem with this, of course, is that the Quantum Laplace’s Demon has more information than we can ever have about the state of the Universe. The laws of special relativity imply that the volume of space that we can know about is perforce limited, and the laws of quantum mechanics place a fundamental limit on what aspects of the wavefunction we can know about. Before quantum mechanics and special relativity, we might have imagined that we mere mortals could aspire to obtain the perfect knowledge of Laplace’s Demon. Nowadays, we know that it’s not possible; Laplace’s demon has become metaphysical rather than physical.