The typical and the exceptional in physics

[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.

 

[vanhees71]

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.

I don't see, why it is a contradiction that my interests go beyond physics. I also think that the minimal interpretation is the only consistent one, but it's interesting to discuss other interpretations as well. So I agree with everything except 5 since it's no contradiction to consider something as irrelevant for science but being nevertheless interested in it ;-).

 

[Demystifier]

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.

That's correct. But some of the people here are not so far from a coherent state, which is a state that minimizes the product of uncertainties (product of inverse intelligence and unsharpness). vanhees71 is not close to a coherent state, which is probably good for creativity.

 

[A. Neumaier]

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

There are at least some observables of the universe as a whole, for example the mass density in the observable part. There are also testable consequences, obtained by restriction of its unitary dynamics to some observable part and a semiclassical FLRW approximation for the remainder, which produces enough dissipation to decohere everything, and the framework for inflation studies that can be tested through observation of the microwave background.

Thus according to your criterion for black holes, its science, too.

 

[atyy]

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.

I believe the wave function of vanhees71 is real :)

 

[Demystifier]

So I agree with everything except 5

So, you agree that you are not completely satisfied with the minimal (ensemble) interpretation?

 

[rubi]

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 $\phi$''.

Well, the second paper treats Klauder's hydrogen coherent states (see the link in my post #296) and you're ignoring half of the paper. It also states that $\theta$, $r$, the Lenz-Runge vector and the eccentricity vector have bounded variance. Moreover, the first paper, which explains Klauder's construction, says that the energy has bounded variance for high quantum numbers. $\phi$ is the only variable that has unbounded variance, but it grows very slowly for celestial bodies. This is what I said in post #299.

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?

No, there is no derivation of Hawking radiation that goes like this. For some reason, however, popularizers explain it this way. The actual derivation of the Hawking effect is not even close. What Hawking really does is decompose the wave function of the universe into field modes that end up in the black hole and modes that reach future infinity. He then traces out the modes that end up in the black hole and finds a thermal state. Hawking's original paper is a bit dense, but it's explained well in Fabbri's book "Modeling black hole evaporation".

 

[Simon Phoenix]

I believe the wave function of vanhees71 is real :)

As far as I can tell he hasn't collapsed yet

 

[Demystifier]

I don't see, why it is a contradiction that my interests go beyond physics.

OK, perhaps I should have say "tension" (rather than contradiction).

 

[atyy]

I don't see, why it is a contradiction that my interests go beyond physics. I also think that the minimal interpretation is the only consistent one, but it's interesting to discuss other interpretations as well. So I agree with everything except 5 since it's no contradiction to consider something as irrelevant for science but being nevertheless interested in it ;-).

Well, the disagreement is sharper than that.

You think that the locality of relativistic QFT is inconsistent with collapse.

While I am agnostic about the reality of collapse, all evidence I know of shows that the nonlocality of collapse is consistent with the locality of relativistic QFT.

So we reach the point in the discussion where I show that collapse does not affect the Hamiltonian of the system, and does not allow superluminal transmission, which you agree with.

So you criticize that I am not including the measurement apparatus in the Hamiltonian. But we are at the point where you haven't indicated whether there is a quantum state of the LHC (the measurement apparatus).

Other sharp points of disagreement are that I understand the minimal interpretation to have a collapse (or updating) and a Heisenberg cut, whereas it is not clear whether you believe there should be a Heisenberg cut or not. My minimal interpretation is agreed upon by Landau and Lifshitz, and by Weinberg.

 

[A. Neumaier]

It also states that θ, r, the Lenz-Runge vector and the eccentricity vector have bounded variance.

But this alone doesn't make the motion classical. The variance of all variables must be bounded for that, and you had erroneously claimed that in post #296.

 

[A. Neumaier]

I show that collapse does not affect the Hamiltonian of the system.

There is nothing to show here, as the Hamiltonian of a system is fixed and whatever the state is, it cannot affect the Hamiltonian. The only affection goes in the other direction.

 

[vanhees71]

Well, the disagreement is sharper than that.

You think that the locality of relativistic QFT is inconsistent with collapse.

While I am agnostic about the reality of collapse, all evidence I know of shows that the nonlocality of collapse is consistent with the locality of relativistic QFT.

So we reach the point in the discussion where I show that collapse does not affect the Hamiltonian of the system, and does not allow superluminal transmission, which you agree with.

So you criticize that I am not including the measurement apparatus in the Hamiltonian. But we are at the point where you haven't indicated whether there is a quantum state of the LHC (the measurement apparatus).

Other sharp points of disagreement are that I understand the minimal interpretation to have a collapse (or updating) and a Heisenberg cut, whereas it is not clear whether you believe there should be a Heisenberg cut or not. My minimal interpretation is agreed upon by Landau and Lifshitz, and by Weinberg.

As I said before, in Landau Lifshitz I cannot find the word collapse (by searching the electronic copy I have ;-)), and Weinberg holds the view that the question in interpretational issues is undecided (after a brilliant analysis in an early chapter of his QM lectures book). Then he happily goes on using the standard representation.

I don't think that a Heisenberg cut is in any way justified by the formalism of QT nor is it in anyway justified by observations. It's just a matter of technological challenge how to sufficiently isolate macroscopic systems from perturbations to avoid decoherence to demonstrate quantum effects also on them. You have to decide from case to case at which point in an experimental setup you can treat things (semi-)classically. I think that Bohr was right saying that a measurement apparatus should be within the validity of the semi-classical description. It must be an open system such that you can store the information on the measurements made, which is an irreversible process.

The interaction between measured object and the macroscopic measurement device are part of the Hamiltonian and as such, according to the successful relativistic QFT, a local interaction. The assumption that such a local interaction can cause far-distant instantaneous responses is thus a contradiction in adjecto. According to the standard (minimal) interpretation there's also no need to explain it by far-distant correlations as described by entanglement. It's all standard QT (or functional analysis if you wish).

 

[rubi]

But this alone doesn't make the motion classical. The variance of all variables must be bounded for that.

Well either that or it must grow very slowly as you indicated.

We will never be able to construct coherent states that have bounded variance for all possible observables. One must always pick some small set of observables that should have this property. It's true that bounded variance for $\phi$ is desirable, but sufficiently slow growth of the variance for large quantum numbers makes the system just as classical as bounded variance. Since hydrogen atoms behave very non-classical for low quantum numbers, it's not to be expected that the dynamics behaves classically in that case. After all, electrons apparently don't actually revolve around the nucleus on elliptic orbits.

 

[atyy]

As I said before, in Landau Lifshitz I cannot find the word collapse (by searching the electronic copy I have ;-)), and Weinberg holds the view that the question in interpretational issues is undecided (after a brilliant analysis in an early chapter of his QM lectures book). Then he happily goes on using the standard representation.

I don't think that a Heisenberg cut is in any way justified by the formalism of QT nor is it in anyway justified by observations. It's just a matter of technological challenge how to sufficiently isolate macroscopic systems from perturbations to avoid decoherence to demonstrate quantum effects also on them. You have to decide from case to case at which point in an experimental setup you can treat things (semi-)classically. I think that Bohr was right saying that a measurement apparatus should be within the validity of the semi-classical description. It must be an open system such that you can store the information on the measurements made, which is an irreversible process.

The interaction between measured object and the macroscopic measurement device are part of the Hamiltonian and as such, according to the successful relativistic QFT, a local interaction. The assumption that such a local interaction can cause far-distant instantaneous responses is thus a contradiction in adjecto. According to the standard (minimal) interpretation there's also no need to explain it by far-distant correlations as described by entanglement. It's all standard QT (or functional analysis if you wish).

LL give the update rule, which I and many others call collapse. LL also don't use the term "Heisenberg cut", but they describe it.

Weinberg, although he says interpretation is not settled, still says the minimal interpretation has a Heisenberg cut and collapse.

 

[atyy]

There is nothing to show here, as the Hamiltonian of a system is fixed and whatever the state is, it cannot affect the Hamiltonian. The only affection goes in the other direction.

Yes, that's how I showed it:)