| > we think classically of the past as definite and the future in terms of possibilities- but in reality both the future and the past are indeterminate in exactly the same way This has nothing to do with quantum theory. It's from classical physics already, from chaotic systems. For conservative systems, both predicting and retrodicting them is equally hard, due to high sensitivity of both to initial condition which we do not know exactly. > it’s just that typically there are a lot more possible futures for the current state than pasts, because of entropy This holds only in special cases, like when entropy of an isolated system increases (e.g. evolution towards equilibrium). When the system gets into equilibrium, entropy then remains constant, and both past macrostates and future macrostates have the same number of microstates, so for any state after that, "the number of futures" is the same as "the number of pasts". > In fact you could define the past as being the direction in configuration space with the smallest uncertainty In other words, you suggest to define future as that direction in which entropy increases. This is consistent with the usual meaning of future for an isolated thermodynamic system in a non-equilibrium process, evolving towards equilibrium; 2nd law implies entropy cannot decrease when comparing to the past macrostate, and entropy often increases when the new macrostate is reached. But this is not usable definition in general. Earth, Solar System, Galaxy interact with their neighborhood; they are not such isolated systems in a macrostate, moving towards equilibrium. We do not know how to measure their entropy, to find out whether they move towards past or future. And if we somehow found entropy of Earth decreases, nobody would seriously suggest Earth is moving towards the past. Instead, everything moves towards the future, just by definition, because that is how we think for ages. If spilled milk somewhere is observed to jump back into a cup, nobody will think the milk went back in time; instead, we will say that a very improbable thing just happened, violating prior experience and 2nd law, but that process would happen in time just as everything else, from the past towards the future. Redefining "future" as that direction of a process in which "entropy is increasing" is really an unnecessary and flawed idea of future. We knew what future was before people invented kinetic theory and entropy; it's those events which we approach, anticipate, and when they come, we label them with a number for date and time on the clock, which (if it is running correctly) never decreases, only stays the same or increases. What entropy did in the meantime does not matter at all; a good clock does not care. |
Not exactly. What’s important here is that every past is real. In the sense that different paths a particle can take can interfere with each other. It’s not indeterminate in a some fuzzy intuitive sense of “something we don’t know.” every past that matches the current known state of a system is real. That’s something that is included in the package of “quantum weirdness.”
And, if you make the assumption that every future is real in the same way, that’s the many worlds/decoherence interpretation.