The typical and the exceptional in physics

[vanhees71]

OK, so you do believe that there is a wave function of the LHC.

I believe that there is a state in the sense of QT. FAPP it's however described by classical physics (including the protons and heavy ions running through the accelerator ;-)).

 

[A. Neumaier]

your axioms simply ignore this difference because they might be tied to the classical mindframe.

This difference can indeed be ignored since probabilities are a classical concept, if interpreted as relative frequencies.

 

[atyy]

I believe that there is a state in the sense of QT. FAPP it's however described by classical physics (including the protons and heavy ions running through the accelerator ;-)).

OK, so what I don't understand is you believe there is a quantum state of the LHC, but not a quantum state of the universe. What is the largest system with a quantum state?

 

[vanhees71]

It has nothing to do with size. It must refer to situations that can be observed many times under the same circumstances ("preparation") for the probability interpretation to make sense. The universe as a whole can neither be repeatedly prepared nor observed at all (according to the present cosmological model there's a horizon, behind which we can't look). So to associate a state with the universe as a whole is mute since you cannot check its validity by observation.

I don't think that there is any size restriction in the sense that for a sufficiently large system quantum theory breaks down. It's only hard to isolate large (macroscopic) systems sufficiently from interactions with the environment to prevent decoherence. Where possible mesoscopic and even macroscopic objects show quantum behavior, e.g., Zeilinger's bucky-ball double-slit experiment, entanglement of the phonon states of two macrocopic diamonds (at room temperature!), superfluidity of helium,...

 

[A. Neumaier]

The settings of the polarizers is relevant to the outcome and should be included in the Hamiltonian.

In the interaction picture, which is commonly used when describing photons in QM experiments, a spatial path through the experimental setting is effectively the time axis, and the type and density of the material the photons go through determine a time-dependent Hamiltonian. Thus the interaction (i.e., the Hamiltonian in the interaction picture) changes whenever the material properties change. in particular, it changes before and after passing a polarizer. This is just swept under the carpet in the abstract discussion of the experiments, where one treats the polarizer as a black box with known input-output behavior, so that the description of the process no longer has a Hamiltonian formulation.

In general, the details preparing, modifying, and recording quantum systems are all represented in the Hamiltonian the system experiences, and the choices available to the experimenter appear as choices of parameters in this Hamiltonian.

 

[atyy]

It has nothing to do with size. It must refer to situations that can be observed many times under the same circumstances ("preparation") for the probability interpretation to make sense. The universe as a whole can neither be repeatedly prepared nor observed at all (according to the present cosmological model there's a horizon, behind which we can't look). So to associate a state with the universe as a whole is mute since you cannot check its validity by observation.

I don't think that there is any size restriction in the sense that for a sufficiently large system quantum theory breaks down. It's only hard to isolate large (macroscopic) systems sufficiently from interactions with the environment to prevent decoherence. Where possible mesoscopic and even macroscopic objects show quantum behavior, e.g., Zeilinger's bucky-ball double-slit experiment, entanglement of the phonon states of two macrocopic diamonds (at room temperature!), superfluidity of helium,...

But is it possible to check the validity of the existence of a quantum state for the LHC?

 

[vanhees71]

It depends whether you accept the effective classical description of the LHC as describing with the possible and obviously sufficient accuracy this quantum state. If you deny that the classical behavior of macroscopic systems is fully compatible with QT, then of course, you won't accept this (admittedly quite pragmatic) point of view.

 

[atyy]

It depends whether you accept the effective classical description of the LHC as describing with the possible and obviously sufficient accuracy this quantum state. If you deny that the classical behavior of macroscopic systems is fully compatible with QT, then of course, you won't accept this (admittedly quite pragmatic) point of view.

But why can't I use that argument to say that there is a quantum state of the universe?

 

[Demystifier]

But why can't I use that argument to say that there is a quantum state of the universe?

I think you and @vanhees71 are discussing a variant of the heap paradox:
https://en.wikipedia.org/wiki/Sorites_paradox
How big a heap needs to be in order to make sense to think of it as a heap?

This problem is serious only if you think that the concept of a heap (wave function) is something fundamental.

 

[atyy]

I think you and @vanhees71 are discussing a variant of the heap paradox:
https://en.wikipedia.org/wiki/Sorites_paradox
How big a heap needs to be in order to make sense to think of it as a heap?

This problem is serious only if you think that the concept of a heap (wave function) is something fundamental.

I don't remember where I saw this:

If k is small, then k+1 is small.

1 is small.

Hence all numbers are small.

 

[rubi]

As vanhees said correctly, the requirement for the existence of a quantum state is the repeatability of experiments. The quantum state predicts the probabilities for events and science uses a frequentist interpretation of probability, so we can only test probabilities if we can repeat experiments. However, we do have access to "multiple universes". In particular, every observer has access to a region of the universe at each instant of time on his or her clock. The presence of horizons doesn't pose problems to this idea. It just means that one needs to use open quantum systems to describe the physics in the accessible part of the universe.

The wave function of the universe is routinely used in quantum cosmology or quantum black hole physics. For example, Hawking radiation is a consequence of the fact that observers outside of black holes need to use open quantum systems to model their part of the universe. Hawking just takes the wave function of the universe and computes a reduced density matrix from it, which then turns out to be a thermal state.

 

[vanhees71]

Well, a part of the universe is not the universe as a whole. Of course, to talk about observable parts of the universe is a valid subject for physics. Cosmology in the sense it is meant by the scientific community is of course valid physics, but it's not dealing with the universe as a whole but it rather tells us that this is a pure thought product which cannot be treated scientifically.

 

[atyy]

Well, a part of the universe is not the universe as a whole. Of course, to talk about observable parts of the universe is a valid subject for physics. Cosmology in the sense it is meant by the scientific community is of course valid physics, but it's not dealing with the universe as a whole but it rather tells us that this is a pure thought product which cannot be treated scientifically.

But there are not many copies of the LHC either.

 

[rubi]

Well, a part of the universe is not the universe as a whole. Of course, to talk about observable parts of the universe is a valid subject for physics. Cosmology in the sense it is meant by the scientific community is of course valid physics, but it's not dealing with the universe as a whole but it rather tells us that this is a pure thought product which cannot be treated scientifically.

But in order to derive things like the Hawking effect or inflation, you need to talk about the universe as a whole. But that's not problematic. For instance, it is also done routinely in general relativity. Of course, every observer sees a comological horizon, but the FRW solution extends beyond that horizon. Of course, a black hole has an event horizon, but there is also an interior solution. It's just not reasonable to assume that the universe ceases to exist beyond the horizon. Instead, the same physics applies beyond the horizon. i.e. general relativity and quantum theory. Hence, the universe should also have a state beyond the horizon. However, we just take the partial trace with respect to the parts of the universe that are inaccessible to us. Locality guarantees that this is not problematic. Whatever the quantum state is in those inaccessible regions, it will not affect the physics we can observe here on earth, so taking the partial trace with respect to local observables will not depend on the physics of the inaccessible regions.

But there are not many copies of the LHC either.

The same argument also applies to the LHC: There are many copies of the LHC, shifted in time.

 

[vanhees71]

That's true, but you gain a lot of statistics concerning the results by repeating the pp and heavy-ion collisions again and again. That's why the design of the LHC has aimed for "large luminosity" (with great success). In addition there are 4 big experiments (ATLAS, CMS, LHCb, Alice) which measure partially the same observables independently, cross checking the results. Rather than copying the LHC it's for sure more sensible to build some new accelerator that can investigate new things (but also check partially old results).

 

[atyy]

That's true, but you gain a lot of statistics concerning the results by repeating the pp and heavy-ion collisions again and again. That's why the design of the LHC has aimed for "large luminosity" (with great success). In addition there are 4 big experiments (ATLAS, CMS, LHCb, Alice) which measure partially the same observables independently, cross checking the results. Rather than copying the LHC it's for sure more sensible to build some new accelerator that can investigate new things (but also check partially old results).

Yes, but that only means that there is a quantum state of the particles involved in the collisions, since those can be prepared many times.

The LHC cannot be prepared many times, so how could it have a quantum state?

 

[atyy]

The same argument also applies to the LHC: There are many copies of the LHC, shifted in time.

Then there would also be a wave function of the universe.

 

[A. Neumaier]

If k is small, then k+1 is small.

This only holds if smallness has a discrete spectrum. But its spectrum is continuous, so there are degrees of smallness.

Fortunately, quantum mechanics is not affected by this as it holds from the smallest to the largest scales.

 

[rubi]

Then there would also be a wave function of the universe.

Well, as I argued, there is a wave function of the univserse and it is used routinely in quantum cosmology, quantum black hole physics and quantum gravity. Predictions like the Hawking effect and inflation depend on it.

 

[A. Neumaier]

Then there would also be a wave function of the universe.

guaranteed is only a state, not necessarily a pure state.

 

[stevendaryl]

Well, as I argued, there is a wave function of the univserse and it is used routinely in quantum cosmology, quantum black hole physics and quantum gravity. Predictions like the Hawking effect and inflation depend on it.

Okay, but at least some of the people arguing on this thread argue that it is meaningless to talk about the wave function of the universe.

 

[A. Neumaier]

Well, a part of the universe is not the universe as a whole. Of course, to talk about observable parts of the universe is a valid subject for physics. Cosmology in the sense it is meant by the scientific community is of course valid physics, but it's not dealing with the universe as a whole but it rather tells us that this is a pure thought product which cannot be treated scientifically.

Then classical relativity, which makes assertions about the whole universe, would also not be a valid subject of physics. Neither would be black holes, as we cannot observe them - only effects at their horizons. Neither would be the interior of the sun, as we cannot observe it - only effects on its surface.

But being able to observe certain effects suffices for doing valid physics on their causes.

By the same token, the whole universe is a valid subject for physics.

 

[atyy]

Well, as I argued, there is a wave function of the univserse and it is used routinely in quantum cosmology, quantum black hole physics and quantum gravity. Predictions like the Hawking effect and inflation depend on it.

But vanhees71 doesn't agree (I'm trying to figure out his views).

 

[rubi]

Okay, but at least some of the people arguing on this thread argue that it is meaningless to talk about the wave function of the universe.

I would be interested in those peoples opinion on Hawking radiation then. I don't see how one can deny a wave function of the universe without denying Hawking radiation.

But vanhees71 doesn't agree (I'm trying to figure out his views).

Okay, I see.

 

[andrew s 1905]

Fortunately, quantum mechanics is not affected by this as it holds from the smallest to the largest scales

I know about predictions and results at small/medium scales but not at the largest scales can you give me some examples?
Thanks Andrew

 

[rubi]

I know about predictions and results at small/medium scales but not at the largest scales can you give me some examples?
Thanks Andrew

You can describe the motion of the sun and the Earth using the Hamiltonian $\hat H=\frac{\hat P_\text{sun}^2}{2M_\text{sun}}+\frac{\hat P_\text{earth}^2}{2M_\text{earth}} + G\frac{M_\text{sun} M_\text{earth}}{\left|\vec r_\text{sun}-\vec r_\text{earth}\right|}$ and a quantum state that is peaked on a phase cell of the classical sun-earth system. Ehrenfest's theorem guarantees that the expectation values of this quantum system will agree with the motion predicted by the classical equations of motion, i.e. you will get elliptic orbits. There exist coherent states for the this Hamiltonian, so the variance will not grow over time.

 

[A. Neumaier]

I know about predictions and results at small/medium scales but not at the largest scales can you give me some examples?

Baryosynthesis in the early universe is a pure quantum phenomenon. It may need an extension of the standard model to be quantitatively correct. But nothing points to a failure of quantum physics itself at these scales.

 

[A. Neumaier]

There exist coherent states for the this Hamiltonian, so the variance will not grow over time.

The first is valid but not the second! But the time scales involved are horrendous - larger than the age of the Earth, I guess.

 

[rubi]

The first is valid but not the second! But the time scales involved are horrendous - larger than the age of the Earth, I guess.

Well, it depends on the variables you're looking at. Klauder's coherent states have fixed variance for at least some variables. For others, in celestial systems, the time scales are huge, as you said, so the classical-quantum correspondence is still valid.

 

[A. Neumaier]

Well, it depends on the variables you're looking at. Klauder's coherent states have fixed variance for at least some variables.

But Klauder's states are not preserved by the dynamics!