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Manfred comments on Timeless Physics Question - Less Wrong Discussion
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Comments (30)
This is not possible because different particles oscillate with different frequencies, depending on their energy. And though it would be possible to make a "standing wave universe" work by simply adding a universe to its complex conjugate, writing it as a sum is probably the shortest way to write this universe, so it's not like we actually got rid of complex numbers in any equations.
The universe oscillates with exactly one frequency as it moves through configuration space.
As for why it looks like different particles have different frequencies, I'm not sure. Apparently, I don't understand entanglement as well as I thought I did.
Wouldn't just writing the real parts of the boundary conditions be simpler?
Our universe is not an energy eigenstate, that's why.
I said that wrong.
The universe has exactly one amplitude. It does not have all the amplitudes of the constituent particles. It does not move in all the ways the constituent particles do.
I figured out why it looks like different particles have different frequencies, even if the universe only has one. I don't think I could explain it well though.
How do you know? Each individual particle is not in an energy eigenstate, but that doesn't mean that the system isn't. If you add the waveform of a system where particle a has energy 1 and particle b has energy 2 to a system where particle a has energy 2 and particle b has energy 1, you end up with a system with an energy eigenstate of 3, but each particle is not in an energy eigenstate.
You could, in theory, check whether or not the universe you're in is where you'd expect a node to be, but if I understand this right, the nodes are all within tiny fractions of a Planck length of each other. You'd have to know the position of every particle in the universe with a root mean square error smaller than that.
The short answer is that energy eigenstates don't change over time, while the universe does.
This is a good point. What I said didn't mean what I thought it meant. But this system seems like an example of the power of entanglement. If the particles were unentangled, there would be change over time. But they are entangled, and there isn't any change over time. A computer living in this system would not actually move any electrons around to do any computation.
How do you know? You can only see what's happening now.
If particles "move around," but the state doesn't change at all (because it's an energy eigenstate), then no robot made of particles will ever write anything new to its hard drive. The particles don't remember that they moved around - that's one of the whole points of quantum mechanics.
The particles are in that position. They are in that position because the boundary conditions of the universe are such that them being in that position has a relatively high amplitude.
If it's an energy eigenstate, it still has to work as a universe. It still has to have a past for every future and a future for every past. If it has the big bang, it will still have the people who remember existing that must inextricably follow. It's just that it has them all at once.
So the time-dependent Schroedinger equation is how the world works, but it doesn't do anything, and by some separate miracle the things that exist look like the time-dependent Schroedinger equation? :D
Sounds neat!
What do you mean?
It's only a miracle if it's false. It would be surprising for there to be a simpler explanation than the true one, but it's only expected for there to be a more complex one.