The only way I know to answer shminux’s question rigorously (with the decoherence time scale) in MWI is to make the assumption that a diagonal density of states of represents a classical ensemble of worlds (with weights corresponding to probabilities)- which means explicitly talking about worlds.
Then you can define a decoherence time-scale of some sort. To the best of my knowledge, without some rule-of-thumb for what a world is, all you can say is that “the system evolves to a a density matrix that has 1/sqrt(2) Aligned on one diagonal element, and 1/sqrt(2) anti-aligned on the other.”
The only way I know to answer shminux’s question rigorously (with the decoherence time scale) in MWI is to make the assumption that a diagonal density of states of represents a classical ensemble of worlds (with weights corresponding to probabilities)- which means explicitly talking about worlds.
Yeah, that’s a cool realization: “Hey, this all works if we assume that a density matrix is what an entangled state looks like from inside!” And this happens to be pretty true, though if it’s your definition of “world” then there will be different “worlds” from different perspectives.
But anyhow, to answer shminux I wouldn’t use worlds, I’d just give the decay rate of the top state coupled to a photon mode, to the bottom state plus a photon. The assumption there is not about worlds, but simply that the amplitude-squared measure should be used to describe the properties of the atom.
And this happens to be pretty true, though if it’s your definition of “world” then there will be different “worlds” from different perspectives.
I can’t parse what you mean by perspectives here- do you mean different non-relativistic observers (no relativity, we are using Schroedinger quantum), or do you mean putting a different basis on the Hilbert space?
But anyhow, to answer shminux I wouldn’t use worlds, I’d just give the decay rate of the top state coupled to a photon mode, to the bottom state plus a photon.
Shminux’s question involves an unpolarized beam entering a magnetic field and aligning, not polarized atoms flipping state. These are very different problems.
In the shminux question, you have an entirely off-diagonal density matrix that evolves toward diagonal very quickly when the system becomes entangled with the screen. To extract information, you implicitly or explicitly assume that a diagonal density of states represents an ensemble of classical worlds.
In the question you are answering, you start with only one diagonal element in the density matrix non-zero, and over time the amplitude of that element shrinks while the element of the other diagonal element grows. This is a totally different problem. You still are implicitly thinking about worlds, you’ve just created a different problem where there is no entanglement so it dodges the messy question.
I can’t parse what you mean by perspectives here- do you mean different non-relativistic observers (no relativity, we are using Schroedinger quantum), or do you mean putting a different basis on the Hilbert space?
Hm. So what I mean is that if you have several particles entangled with each other, and you want to know what that “looks like” to one subsystem (or, experimentally, if you’re going to produce a beam of these particles and do a bunch of single-particle measurements), then you have to trace over the other particles in the entangled state. This gives you a reduced density matrix, which is then interpreted as a mixed state. A mixed state between what? Well, “worlds,” of course.
This the definition of “world” I meant when I said “if that’s your definition of world...”
But anyhow, why did I say that different observers will see different lists of worlds? Well, because when you take the partial trace, what you trace over depends on which perspective you want (experimentally, what partial measurement you’re making). If you’re an electron, your worlds are boring—we traced all the complicated externals away and now your perspective just looks like a distribution over single-electron states. If you’re a person, your perspective is much more interesting, your density matrix is much bigger. Or to put it another way, you have more “worlds” to have a distribution over.
You still are implicitly thinking about worlds,
And you’re implicitly thinking about waterfalls, because every cognitive algorithm is isomorphic to a thoght about a waterfall :P
The only way I know to answer shminux’s question rigorously (with the decoherence time scale) in MWI is to make the assumption that a diagonal density of states of represents a classical ensemble of worlds (with weights corresponding to probabilities)- which means explicitly talking about worlds.
Then you can define a decoherence time-scale of some sort. To the best of my knowledge, without some rule-of-thumb for what a world is, all you can say is that “the system evolves to a a density matrix that has 1/sqrt(2) Aligned on one diagonal element, and 1/sqrt(2) anti-aligned on the other.”
Yeah, that’s a cool realization: “Hey, this all works if we assume that a density matrix is what an entangled state looks like from inside!” And this happens to be pretty true, though if it’s your definition of “world” then there will be different “worlds” from different perspectives.
But anyhow, to answer shminux I wouldn’t use worlds, I’d just give the decay rate of the top state coupled to a photon mode, to the bottom state plus a photon. The assumption there is not about worlds, but simply that the amplitude-squared measure should be used to describe the properties of the atom.
I can’t parse what you mean by perspectives here- do you mean different non-relativistic observers (no relativity, we are using Schroedinger quantum), or do you mean putting a different basis on the Hilbert space?
Shminux’s question involves an unpolarized beam entering a magnetic field and aligning, not polarized atoms flipping state. These are very different problems.
In the shminux question, you have an entirely off-diagonal density matrix that evolves toward diagonal very quickly when the system becomes entangled with the screen. To extract information, you implicitly or explicitly assume that a diagonal density of states represents an ensemble of classical worlds.
In the question you are answering, you start with only one diagonal element in the density matrix non-zero, and over time the amplitude of that element shrinks while the element of the other diagonal element grows. This is a totally different problem. You still are implicitly thinking about worlds, you’ve just created a different problem where there is no entanglement so it dodges the messy question.
Hm. So what I mean is that if you have several particles entangled with each other, and you want to know what that “looks like” to one subsystem (or, experimentally, if you’re going to produce a beam of these particles and do a bunch of single-particle measurements), then you have to trace over the other particles in the entangled state. This gives you a reduced density matrix, which is then interpreted as a mixed state. A mixed state between what? Well, “worlds,” of course.
This the definition of “world” I meant when I said “if that’s your definition of world...”
But anyhow, why did I say that different observers will see different lists of worlds? Well, because when you take the partial trace, what you trace over depends on which perspective you want (experimentally, what partial measurement you’re making). If you’re an electron, your worlds are boring—we traced all the complicated externals away and now your perspective just looks like a distribution over single-electron states. If you’re a person, your perspective is much more interesting, your density matrix is much bigger. Or to put it another way, you have more “worlds” to have a distribution over.
And you’re implicitly thinking about waterfalls, because every cognitive algorithm is isomorphic to a thoght about a waterfall :P