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Robert Shaw
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If the universe was in an energy eigenstate then d<A>/dt = 0 for any dynamic variable A. Stuff moves which implies that the Universe isn't in an eigenstate. What factors drive the energy spread?
I don't think this is an informative way to look at it. Rather, I think it makes more sense to consider the fact that the entropy of the universe is increasing over time (indicating a low-entropy state in the past). When entropy is maximized, the universe will no longer by dynamic. So the question becomes: how did that low-entropy state in the early universe occur? Unfortunately, we don't yet know the answer.Robert Shaw said:If the universe was in an energy eigenstate then d<A>/dt = 0 for any dynamic variable A. Stuff moves which implies that the Universe isn't in an eigenstate. What factors drive the energy spread?
Please would you suggest what law/equation guides the evolution of the quantum state of the Universe?kimbyd said:I don't think this is an informative way to look at it. Rather, I think it makes more sense to consider the fact that the entropy of the universe is increasing over time (indicating a low-entropy state in the past). When entropy is maximized, the universe will no longer by dynamic. So the question becomes: how did that low-entropy state in the early universe occur? Unfortunately, we don't yet know the answer.
Robert Shaw said:If the universe was in an energy eigenstate then d<A>/dt = 0 for any dynamic variable A. Stuff moves which implies that the Universe isn't in an eigenstate. What factors drive the energy spread?
For toy universe models such as the neo-classical harmonic oscillator, non-stationary state solutions exist which are superpositions of energy states.
What about bigger systems, the Universe for instance?
Robert Shaw said:Does QM apply to things that were not prepared in laboratories?
If so what does QM say about states not prepared in laboratories?
Does the preparation have to be carried out by a trained physicist?
In that case QM can be used to describe the universe. If <universe| H |universe> = constant but <A>≠constant then it follows |universe> is not an eigenstate of H but must be a superposition.PeroK said:QM applies to everything, essentially. The question is how you use QM to study and explain things. You can explain a hydrogen atom, whether or not it was created in a laborary or not.
Robert Shaw said:Energy eigenstates "the averages and probabilities of all dynamical variables are independent of time" (Ballentine p72). Any QM textbook will say the same.
Robert Shaw said:In that case QM can be used to describe the universe. If <universe| H |universe> = constant but <A>≠constant then it follows |universe> is not an eigenstate of H but must be a superposition.
PeroK said:Yes, but how?
There is an extensive literature on Quantum Cosmology in which some authors say the state of the universe is a pure state (vector) and others say it is non-pure (density matrix). The universe has a state and the state is represented by a state function.PeroK said:Let me give you an example. Suppose you hit a tennis ball. You can measure the velocity, say. That is not an expected value. That is a single velocity, ##v##.
But, if you have a machine that fires out tennis balls, you can measure the velocity of each and talk about the expected value of the velocity ##\langle v \rangle##.
In QM, when you use the quantity ##\langle A \rangle## you must, by definition, be talking about the second scenario. You must be talking about the expected value of a large number of identically prepared systems. In this case, an ensemble of tennis balls emerging from a machine.
In the case of the universe, therefore, you can talk about a quantity ##A##. But, there is literally no way to talk about a quantity ##\langle A \rangle##. For that, you would need a "universe machine" spitting out identically prepared universes. And that is at least one problem with trying to apply QM to the whole universe.
Energy eigenstates are solutions to the time independent Schrodinger equation. Since the universe is growing, it isn't represented by a time independent Hamiltonian. There is not necessarily a conserved energy function.Robert Shaw said:On a larger scale, if stuff in the universe is non stationary then the overall state cannot be an eigenstate of total energy, it must be a superposition.
We need a quantum theory of gravity before we can say that.Robert Shaw said:It would be absurd to suggest that there is a scale above which QM is inaccurate
Robert Shaw said:There is an extensive literature on Quantum Cosmology in which some authors say the state of the universe is a pure state (vector) and others say it is non-pure (density matrix). The universe has a state and the state is represented by a state function.
Robert Shaw said:Solar systems have states. Planets too. It would be absurd to suggest that there is a scale above which QM is inaccurate...in what way would the inaccuracy be manifested?
Most quantum cosmologists do not concur with your assertion that the universe as a whole is in a mixed (density matrix) state. The consensus is that it's in a pure state overall but the substates are mixedKhashishi said:Energy eigenstates are solutions to the time independent Schrodinger equation. Since the universe is growing, it isn't represented by a time independent Hamiltonian. There is not necessarily a conserved energy function.
Anything macroscopic with a finite temperature is not going to be in a pure state. If we want to treat the universe as a thermodynamic system (and we should), then we need to use a mixed state.We need a quantum theory of gravity before we can say that.
There's two kinds of mixed state. If two objects are entangled, a subsystem containing just one object is in a mixed state. You must be referring to this in your post. Perhaps everything in the universe is entangled, so any subsystem is necessarily mixed.Robert Shaw said:Most quantum cosmologists do not concur with your assertion that the universe as a whole is in a mixed (density matrix) state. The consensus is that it's in a pure state overall but the substates are mixed
That's just the quantum field equations. In the classical approximation, Schrodinger's equation.Robert Shaw said:Please would you suggest what law/equation guides the evolution of the quantum state of the Universe?
It's the property that is the most relevant to your statement. What you're asking, ultimately, is how the universe is in a state that is not equilibrium. And that's a question related to entropy.Robert Shaw said:You've commented on entropy which is one property of the state but not the only property.
...what about the state itself, how does it develop?
Robert Shaw said:Most quantum cosmologists do not concur with your assertion that the universe as a whole is in a mixed (density matrix) state. The consensus is that it's in a pure state overall but the substates are mixed
Rather than be defeatist why not start with a toy model and then scale it up?PeterDonis said:The "consensus" is not worth much if there is no experimental support. And as @PeroK has pointed out, we can't run repeated experiments on the universe to collect statistics and determine expectation values for observables that can be compared to theoretical predictions. So all the "consensus" of quantum cosmologists amounts to at this point is personal opinions. At some point we might be able to test some of the theoretical claims being made, but right now we can't.
At its simplest the toy universe could be an isolated harmonic oscillator.Robert Shaw said:Rather than be defeatist why not start with a toy model and then scale it up?
Begin with an isolated toy universe which is a box of photons. It might be a coherent state (as studied by Glauber et al) and in that case the variance and average total energy are known precisely. Alternatively it might be a Fock state in which case the energy is sharp. This toy universe is amenable to your preparation and ensemble conditions.
Now let's scale the model up, all the time keeping it a closed system.
As we get bigger, how does the sharpness of energy change? If the stuff in our toy universe approximates to the stuff in the real universe, what if anything can we say about the total energy distribution.
Remember the toy universe is perfectly isolated so there is no outside world with which it can decohereRobert Shaw said:At its simplest the toy universe could be an isolated harmonic oscillator.
State prep A gives an energy eigenstate.
State prep B gives a coherent state which has a spectrum of total energies; measurement of its energy would result in different values. This is not because the prep method is in some way crude but a quantum phenomenon associated with superposition.
As we scale our procedure up, to real matter, say a cup of tea, what can we say about the spread of total energy of the whole state (I'm not asking about the spread of energy of the components).
Remember, coherent states of the oscillator are pure states.Robert Shaw said:Remember the toy universe is perfectly isolated so there is no outside world with which it can decohere
Robert Shaw said:Does QM apply to things that were not prepared in laboratories?
Robert Shaw said:In that case QM can be used to describe the universe.
I can see no reason why the universe should be in a eigenstate of energy.kimbyd said:That's just the quantum field equations. In the classical approximation, Schrodinger's equation.It's the property that is the most relevant to your statement. What you're asking, ultimately, is how the universe is in a state that is not equilibrium. And that's a question related to entropy.
Redefining your question in terms of entropy is a bit broader, but it serves the same point because the equilibrium state for our observable universe is empty space (so far as we can tell), which is an eigenstate of energy.
I can make no sense of your claim that any state "preparation procedure" is relevant.bhobba said:Of course it does - its any preparation procedure at all.
The real issue is applying it to the universe - what prepares the universe.
Deep question - but best to start another thread to discuss it.
That I think is debatable - but as said above best to start a new thread.
Thanks
Bill
I am very confused as to what you are asking, then.Robert Shaw said:I can see no reason why the universe should be in a eigenstate of energy.
And the spread of energy in a quantum state has nothing to do with entropy.
Robert Shaw said:I can make no sense of your claim that any state "preparation procedure" is relevant.
For any state to manifest motion, there must be a mixture of energy eigenstates (energy eigenstates are by definition stationary).kimbyd said:I am very confused as to what you are asking, then.
Your original question seemed to be asking why the universe isn't in an eigenstate, expressed as a statement that the universe changes over time and thus must not be in an eigenstate. I pointed out that the change of the universe over time is better-represented by examining entropy rather than energy.
But now you seem to be suggesting that the universe not being in an eigenstate is the natural state that doesn't need any explanation. So what are you asking?
Happy to start a new thread on state preparation proceduresbhobba said:Depending on interpretation state preparation procedure and state are generally considered synonymous.
What prepares the state of the universe?
A state preparation procedure is something like passing an electron through a slit. We know behind the slit it is in a state of definite position - that is a preparation procedure - you need to interact a quantum system with something to prepare it - what do you interact the universe with?
Here is a state preparation that occurs in nature. It is well known that a few stray photons from the cosmic microwave background radiation is enough to give a dust particle a define position.
Yes even your nose is subject to a preparation procedure - it is constantly interacting with its environment which, without going into technical details, is why your nose acts classically ie is a classical object and not a quantum one - of course like everything is made of quantum stuff, but due to that interaction can be considered classical - like just about everything around us.
But please, as previously requested, if you want to discuss that start a new thread.
Thanks
Bill
Robert Shaw said:For any state to manifest motion, there must be a mixture of energy eigenstates (energy eigenstates are by definition stationary).
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To be clear I am making the simplifying assumptions:Robert Shaw said:For any state to manifest motion, there must be a mixture of energy eigenstates (energy eigenstates are by definition stationary).
From this it follows that the state of the Universe is a superposition of energy states. I'd like to restrict the discussion by assuming the total state begins in a pure state.
So the interesting question is whether the width of the energy variance has any physical significance.
Robert Shaw said:To be clear I am making the simplifying assumptions:
1) Universe is a closed quantum system
2) there is motion in the universe
From these it follows that the state of the Universe cannot be an energy eigenstate.
My question is whether the spread of the mixture of energy levels has physical significance.