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jesch comments on Timeless Physics - Less Wrong
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Years after first reading this, I think I've internalized its central point in a clear-to-me way, and I'd like to post it here in case it's useful to someone else with a similar bent to their thinking.
Without worrying about the specific nature of the Schrodinger equation, we can say the universe is governed by a set of equations of form x, where each x[i] is some variable in the universe's configuration space, each f[i] is some continuous function, and t is a parameter representing time. This would be true even in a classical universe---the configuration space would just look more like the coordinates for a bunch of particles, and less like parameters of a waveform. All this is really saying is that the universe has some configuration at every time.
Now, one thing you can do with parametric equations is eliminate the parameter. If we have, say, 1000 parametric equations relating x[1] through x[1000] to t, we can convert these to 999 equations relating x[1] through x[1000] to one another, and "cut out the middleman" so to speak. Your new equations will define the same curve in configuration space, and you can determine the relative order of events just by tracing along that curve (as long as there are no "singularities"---points where two different values of t gave you the same point in the configuration space).
Moreover, from inside the universe there's no way to tell the difference between these two situations. "Two hours ago" can mean either "at t - 2hr" or it can mean "at the point on this curve in configuration space where the clocks all say it's 7:00 instead of 9:00", and there's no experimental distinction to be made between these meanings. So positing a fundamental thing called "time" doesn't actually have any explanatory power!
From this understanding, timeless physics is better viewed as a more parsimonious way to frame any theory, rather than a part of quantum theory specifically. We could just as well explain Newtonian physics timelessly.
I also understood this using parametric equations, although I simplified to t, x(t) and y(t), to aid in visualization. So then I was looking at my mental image, and I thought "but what About memory?" At any particular point on my curve, the observer in that point knows what the curve looks like in one direction(past), but not the other. I get that both directions along the curve are determined, but why would my mind contain information about exactly one?
This is off the top of my head, so it may be total bullshit. I find the idea of memory in a timeless universe slippery myself, and can only occasionally believe I understand it. But anyway...
If you want to implement a sort of memory in your 2D space with one particle, then for each point (x0,y0) in space you can add a coordinate n(x0,y0), and a differential relation
dn(x0,y0) = δ(x-x0,y-y0) sqrt(dx^2 + dy^2)
where δ is the Dirac delta. Each n(x0,y0) can be thought of as an observer at the point (x0,y0), counting the number of times the particle passes through. There is no reference to a time parameter in this equation, and yet there is a definite direction-of-time, because by moving the particle along a path you can only increase all n(x0,y0) for points (x0,y0) along that path.
A point in this configuration space consists of a "current" point (x,y), along with a local history at each point. If you don't make any other requirements, these local histories won't give you a unique global history, because the points could have been visited in any order. But if you impose smoothness requirements on x and y, and your local histories are consistent with those smoothness requirements, then you will have only one possible global history, or at most a finite number.
one small problem, nothing is moving. how can you have an observer when every bit of that observer is part of the existing static universe... observer implies a moving entity and no motion exists in a static universe.