Does the Schrodinger equation tell us how to increase the relative probability of interacting with an almost completely orthogonal Everett Branch?
“Almost completely orthogonal” here bears qualifying: In classical thermodynamics, the concept of entropy is sometimes taught by appealing to the probability of all of the gas in a room happening to end up in a configuration where one half of the room is vacuum, and the other half of the room contains gas. After some calculation, we see that the probability of this happening ends up being (effectively) on the order of 10^(-10^23), give or take several orders of magnitude (not like it matters at that point).
Now, that said, how confident are you that different Everettian earths are even at the same point of space time we are, given a branching, say, 10 seconds ago? Pick an atom before the split and pick its two copies after. Are they still within a Bohr radii of each other after after even a nanosecond? Their phases are already scrambled all to hell, so that’s a fun unitary transformation to figure out.
Sure, you can prepare highly quantum mechanical sources and demonstrate interference effects, but “interuniversal travel” for any meaningful sense of the word, is about as hard as simply transforming the universe itself, subatomically, atom for atom, controllably into a different reality.
So in that sense, Schrodinger’s equation tells us as much about trans-universe physics as the second law of thermodynamics tells us about building large scale Maxwell’s Demons.
So in that sense, Schrodinger’s equation tells us as much about trans-universe physics as the second law of thermodynamics tells us about building large scale Maxwell’s Demons.
The second law of thermodynamics tells us everything there is to know about building large scale Maxwell’s Demons. You can’t. What else is there to it?
Schroedinger’s equation isn’t quite as good. It’s not quite impossible. But it is enough to tell us that there’s no way we’ll ever be able to do it.
The Schrodinger equation is not even at the right level of the relevant physics. It applies to non-relativistic QM. My guess is that DanielLC simply read the QM sequence and memorized the teacher’s password. World splitting, if some day confirmed experimentally, requires at least QFT or deeper, maybe some version of the Wheeler-deWitt equation.
General form the Schrodinger Equation: dPsi/dt = -iH/hbar Psi
Quantum Field theories are not usually presented in this form because it’s intrinsically nonrelativistic, but if you pick a reference frame, you can dump the time derivative on the left and everything else on the right as part of H and there you go.
So it’s equivalent. As calef says, there are good reasons not to actually do anything with it in that form.
This is a little chicken-or-the-egg in terms of “what’s more fundamental?”, but nonrelativistic QFT really is just the Schrodinger equation with some sparkles.
For example, the language electronic structure theorists use to talk about electronic excitations in insert-your-favorite-solid-state-system-here really is quantum field theoretic—excited electronic states are just quantized excitations about some vacuum (usually, the many-body ground state wavefunction).
You could switch to a purely Schrodinger-Equation-motivated way of writing everything out, but you would quickly find that it’s extremely cumbersome, and it’s not terribly straightforward how to treat creation and annihilation of particles by hand.
Does the Schrodinger equation tell us how to increase the relative probability of interacting with an almost completely orthogonal Everett Branch?
“Almost completely orthogonal” here bears qualifying: In classical thermodynamics, the concept of entropy is sometimes taught by appealing to the probability of all of the gas in a room happening to end up in a configuration where one half of the room is vacuum, and the other half of the room contains gas. After some calculation, we see that the probability of this happening ends up being (effectively) on the order of 10^(-10^23), give or take several orders of magnitude (not like it matters at that point).
Now, that said, how confident are you that different Everettian earths are even at the same point of space time we are, given a branching, say, 10 seconds ago? Pick an atom before the split and pick its two copies after. Are they still within a Bohr radii of each other after after even a nanosecond? Their phases are already scrambled all to hell, so that’s a fun unitary transformation to figure out.
Sure, you can prepare highly quantum mechanical sources and demonstrate interference effects, but “interuniversal travel” for any meaningful sense of the word, is about as hard as simply transforming the universe itself, subatomically, atom for atom, controllably into a different reality.
So in that sense, Schrodinger’s equation tells us as much about trans-universe physics as the second law of thermodynamics tells us about building large scale Maxwell’s Demons.
The second law of thermodynamics tells us everything there is to know about building large scale Maxwell’s Demons. You can’t. What else is there to it?
Schroedinger’s equation isn’t quite as good. It’s not quite impossible. But it is enough to tell us that there’s no way we’ll ever be able to do it.
The Schrodinger equation is not even at the right level of the relevant physics. It applies to non-relativistic QM. My guess is that DanielLC simply read the QM sequence and memorized the teacher’s password. World splitting, if some day confirmed experimentally, requires at least QFT or deeper, maybe some version of the Wheeler-deWitt equation.
The Schroedinger equation is sufficient for world splitting. It’s just entanglement at a massive scale.
QFT is a special case of the general form of the Schrodinger equation.
Link?
General form the Schrodinger Equation: dPsi/dt = -iH/hbar Psi
Quantum Field theories are not usually presented in this form because it’s intrinsically nonrelativistic, but if you pick a reference frame, you can dump the time derivative on the left and everything else on the right as part of H and there you go.
So it’s equivalent. As calef says, there are good reasons not to actually do anything with it in that form.
This is a little chicken-or-the-egg in terms of “what’s more fundamental?”, but nonrelativistic QFT really is just the Schrodinger equation with some sparkles.
For example, the language electronic structure theorists use to talk about electronic excitations in insert-your-favorite-solid-state-system-here really is quantum field theoretic—excited electronic states are just quantized excitations about some vacuum (usually, the many-body ground state wavefunction).
Another example: http://en.wikipedia.org/wiki/Kondo_model
You could switch to a purely Schrodinger-Equation-motivated way of writing everything out, but you would quickly find that it’s extremely cumbersome, and it’s not terribly straightforward how to treat creation and annihilation of particles by hand.