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Let's assume the Maths is all we care about. One way to clear it up is to decide what we would need to give to a computer to figure out the results. Let's assum
by jostylr 8y ago
Let's assume the Maths is all we care about. One way to clear it up is to decide what we would need to give to a computer to figure out the results. Let's assume the computer can solve any equation we give it.
Bohmian Mechanics: Given Schrödinger's equation, Bohm's equation, the initial positions of the experiment and the measuring apparatus (assuming it is set on autopilot) and the initial wavefunction of the joint experiment and apparatus setup, then we evolve the system and the positions of the stuff in the apparatus will tell us the result of the experiment. Done.
Copenhagen Interpretation: We need Schrödinger's equation for the experimental setup, the initial wavefunction of the experiment, and some explicit timing for collapse as well as some stand-in for the eigenstates (we never actually collapse to an eigenstate or anything spiky, but rather to a nearby smooth state, such as a finite sum of Gaussians). We can optionally add-in the apparatus or observer wavefunction and collapse to something with an outcome involving those wavefunctions. It is kind of a mess to tell a computer how to do this, particularly if you have a number of experiments, possibly conditioned on the results of other experiments. It is not an independent time evolution. The Maths fail us in setting up a universe.
One could let this multi-experiment setup evolve until everything is done and then collapse at the very end. That leads to less of a mess of specification, but now one has the fact that we are saying reality does not have, in any, even approximate, sense, a definitive experience such as the one we are used to, at any point except for the last one. In some sense, this is the Many Worlds theory.
GRW is based on the idea of adding automatic collapse into the equations and that's fine and cool; it hits the wavefunction with a gaussian every so often. One also has to add in something else of an ontological nature, but that can be considered a philosophical issue (though it can matter what one chooses, say from a relativistic point of view). We at least have in GRW a Maths based evolution though it is different than the standard one.
The Copenhagen Interpretation is not an actual theory; there is no possible universe where it could be true or implemented. It can be made more specific, but it does require something more and the more one sticks to the Copenhagen spirit, the more of a "on high" specification mess, it becomes.
Both GRW and Bohmian Mechanics at least could be true.