The typical and the exceptional in physics

[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!

 

[rubi]

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

Klauders states are preserved. Maybe you are confusing them with Schrödingers states for the harmonic oscillator?

 

[A. Neumaier]

Klauders states are preserved.

Please give a reference for your statement. To my knowledge there are no constant variance coherent states of any kind that are conserved under a dynamics with a Coulomb potential.

 

[rubi]

Please give a reference for your statement. To my knowledge there are no constant variance coherent states of any kind that are conserved under a dynamics with a Coulomb potential.

http://cds.cern.ch/record/523392/files/0110108.pdf
http://info.phys.unm.edu/~ideutsch/classes/Phys566F99/566_Journal/Articles/Schneibner.pdf
By the way, the variance needn't be constant. It would also suffice if it were bounded by a small number.

 

[Ken G]

Or what the approximations are approximating.

It's obvious what the approximations are approximating, all you have to do is look at the process of deciding that an approximation has occurred. Pick any example you like, call it "situation A', where you would say an approximation has occurred. I will show you what you mean, by simply looking at the two quantities that you regard as "close". Done, that's what the approximation is approximating-- the one quantity is approximating the other. Epistemology is always pretty easy.

 

[ddd123]

It's obvious what the approximations are approximating, all you have to do is look at the process of deciding that an approximation has occurred. Pick any example you like, call it "situation A', where you would say an approximation has occurred. I will show you what you mean, by simply looking at the two quantities that you regard as "close". Done, that's what the approximation is approximating-- the one quantity is approximating the other. Epistemology is always pretty easy.

I have to say I disagree with this way of conceiving epistemic operations "without an object", other than it being inconsistent it's unnecessary if you just want to avoid an ontology. What you approximate are the results of experiments wrt predictions. And the same goes with understanding, modeling, mapping, handling information etc... You can't "just approximate", it's devoid of meaning to say that without saying what you are approximating. It ends up with the earlier conundrum of information about nothing.

 

[Ken G]

What you approximate are the results of experiments wrt predictions.

I think if you read what I said again, you will see that is exactly what I said. But there is not some "independent reality" that is being approximated, there are experiments, and there are predictions, and if they are close, we say there is an approximation going on. One is free to believe there is an independent reality if one chooses, and many do, but it has nothing to do with the scientific process, and it is clearly not being approximated. One cannot say that a prediction approximates an apple, that would be a category error.

You can't "just approximate", it's devoid of meaning to say that without saying what you are approximating. It ends up with the earlier conundrum of information about nothing.

Not at all-- the information is about other information. What else can you say is being approximated?

 

[ddd123]

Not at all-- the information is about other information. What else can you say is being approximated?

I simply said that when you use concepts like those there is always an object (which doesn't imply an ontology, it's simply the object of epistemology which is the content and its meaning). You approximate the (information on the) measurement results. There's the development of the theory, the information it carries and that which it wants to explain, and the semantics related with that information: so here we have a few things that go into epistemology that cannot be reduced to just information as if it was some pure substance of thinking.

 

[Ken G]

I simply said that when you use concepts like those there is always an object (which doesn't imply an ontology, it's simply the object of epistemology which is the content and its meaning).

Then we aren't disagreeing-- if someone says that when you compare a predicted quantity to an observed quantity, then the quantities are "things", there's not much point in disputing that. My issue is about the so-called "things" underneath the quantities, the ontology that the quantities are blamed on. Those are the things that cannot be approximated, nor indeed tested at all. We test the success of the epistemology, and the ontology applied is just the way we like to think about what we are doing-- which makes it just more epistemology because it is clearly our minds that are doing the ontology.

You approximate the (information on the) measurement results. There's the development of the theory, the information it carries and that which it wants to explain, and the semantics related with that information: so here we have a few things that go into epistemology that cannot be reduced to just information as if it was some pure substance of thinking.

Claiming that epistemology was a pure substance of thinking would be falling into ontology once again! I'm as skeptical that there is a pure substance of thinking as I am that there is a pure substance of an apple. I just go with what I see-- manipulation of information, all over the show. Watch a scientist use a wavefunction, and you will see the manipulation of information. Watch a scientist carry out an experiment, and you will see more manipulation of information. The information may have a different character, but a string of zeroes has a different character from an alternating series of 1s and 0s-- we are good at noticing the attributes of information, and all we are really capable of doing is noticing samenesses and differences. What else can the intellect do?

 

[Simon Phoenix]

But there is not some "independent reality" that is being approximated

I was walking across the golf course the other day and then suddenly this golf ball hit me right between the eyes. My doctor told me not to worry about the huge lump on my forehead as it was only epistemic

 

[ddd123]

I just go with what I see-- manipulation of information, all over the show. Watch a scientist use a wavefunction, and you will see the manipulation of information. Watch a scientist carry out an experiment, and you will see more manipulation of information. The information may have a different character, but a string of zeroes has a different character from an alternating series of 1s and 0s-- we are good at noticing the attributes of information, and all we are really capable of doing is noticing samenesses and differences. What else can the intellect do?

I don't see how paradigm building and shifts, or even just mathematical intuition, could be reduced to noticing sameness and differences... it's a variety of qualitatively different operations that come into play.

Actually I don't see why, in this context, we should worry about the nature of thinking itself! All we need to know about epistemology is that it concerns our ways of knowing, which involves a plurality of factors. We refer to that knowing with respect to the operations we perform in the lab: we can leave it at intuition, it's even simpler than having an ontology to worry about. We don't need a theory of mind to do physics, why are you worrying about it?

 

[A. Neumaier]

http://cds.cern.ch/record/523392/files/0110108.pdf
http://info.phys.unm.edu/~ideutsch/classes/Phys566F99/566_Journal/Articles/Schneibner.pdf
By the way, the variance needn't be constant. It would also suffice if it were bounded by a small number.

Thanks for the papers. I knew Rydberg states, but their variance is not even bounded.

Note that the first paper only treats a 1D mock version of hydrogen, with bounded variance. The second paper treats the real thing and points out: ''That means that there will be a total dephasing in $\phi$''. The reference [3] of the second paper from which this information is taken is R.F. Fox, Phys. Rev. A 59, 3241 (1998).

Fox discusses the variance in Section G for celestial bodies and concludes that

for the Earth the variance grows by a factor of about 1422$\times$(square of the number of periods). Since each period is a year, the variance will not reach order unity [...] until about $10^{36}$ years have elapsed. This is so much longer than the age of the universe that we can conclude that a Rydberg coherent state treatment of the Sun-Earth system yields a compact, localized state in all three spherical polar coordinates for the entire lifetime of the system.

Thus although the variance is unbounded, the quantum description is very accurate.

 

[vanhees71]

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.Okay, I see.

I thought Hawking radiation is radiation due to quantum fluctuations around the event horizon of a black hole. Where do you need the wave function of the universe for that?

 

[Demystifier]

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

That's very difficult, because vanhees71 has a very complex personality. By applying some amateur psychoanalysis on him, I arrived at the following conclusions:
1. No doubt, he is a very smart guy.
2. He is excellent in the shut-up-and-calculate "interpretation", and when he sticks to that kind of business he is usually consistent.
3. However, he is not completely satisfied with the shut-up-and-calculate business. He has a need to say something more about interpretations.
4. He also thinks that interpretations are irrelevant to physics.
5. Unfortunately, the facts 3. and 4. constitute a contradiction. This contradiction is the main source of complexity in his personality.
6. He tries to reconcile the contradiction between 3. and 4. by defending a sort of minimal interpretation.
7. However, the minimal interpretation does not really satisfy him, so sometimes in his arguments he goes beyond the minimal interpretation. This further increases inconsistency of his arguments and complexity of his personality.
8. Of course, it is very unlikely that he would admit that the above is true (except 1. and 2.)

In short, an interesting combination of high intelligence and unsharp views on quantum interpretations makes the discussions with him very challenging.

 

[A. Neumaier]

high intelligence and unsharp views

Isn't that a consequence of the Heisenberg uncertainty principle? I find that nobody here has both high intelligence and completely sharp views. These are strictly complementary variables.

 

[vanhees71]

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.

Well, of course you use the FLRW metric to describe a very coarse-grained view of the universe and then assume homogeneity and istropy (cosmological principle). Then you are able to make predictions about local observations by considering small fluctuations. This leads to predictions for the pattern of the CMBR fluctuations and structure formation that can be tested with local observables. This model works pretty well (under the assumption of the existence of cold dark matter and adjusting the cosmological constant; then there's a pretty convincing model called inflation that can be used to explain the necessary finetuning of the parameters). In any case the cosmological standard model $\Lambda$CDM is a model that admits its test against observations, and thus it's science (although a lot of untestable assumptions, including the cosmological principle itself go into it).

Black holes are predictions of GR, and here the issue is a bit more critical. The point is that inevitably compact objects must collapse under the gravitational interaction if no other forces prevent this collapse. In normal stars it's the thermal pressure due to nuclear-fusion processes, in neutron stars it's the pressure due to nuclear forces leading to a hadronic equation of state, maybe with the possibility of quark cores, etc. etc. Now there are objects observed in the universe like the one in the center of our own galaxy SGR A where the mass is larger than any mass thinkable for a compact stable object to be possible given the known forms of matter and their corresponding equations of state. From this one concludes that SGR A should be a black hole. Whether it's really a black hole is not proven. There may be other kinds of matter that may explain the high-mass objects without the conjecture that they are black holes. On the other hand a black hole is also observable in principle, as this example shows. GR predicts that from outside I can only know its fundamental constants (mass, spin, electric charge), and what's "inside" (i.e., beyond the horizon) is unobservable. Another way to observe such massive objects are the recently seen gravitational waves, which also were predicted by GR simulations. So there are at least some observable and testable consequences of the prediction of black holes (space-time singularities), and thus it's science.

The universe as a whole is unobservable and thus not subject of science in the usual sense, where you should be able to test predictions about an entity conjectured. It's not clear to me, how you can observe the universe as a whole. All we can do are pretty local observations and then extrapolate using assumptions as in standard cosmology.

For the "wave function of the whole universe" (I'd prefer to talk about the quantum state of the universe, because it's not clear whether a naive wave-function picture is adequate of maybe it's a mixed rather than pure state) it's even worse. You cannot even describe it. The best you can do is to invent some effective description which is testable only in the sense that the partial traces to get the relevant subsystems we are able to observe lead to a correct description of these observations.