I Why randomness means incomplete understanding

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A. Neumaier

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a basis of mutually exclusive sequences of events
Well, into which basis? If any basis is allowed, then anything can happen. But then it is not determined by the simulation of the wave function but by the additional choice of the basis. This would mean that in our real universe, what happens depends not only on the Schrödinger dynamics but also on choosing a basis. in other words, the basis elements constitute additional hidden variables needed to get real events from quantum mechanics.
 
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It is important to be clear about the concepts. Quantum theory is completely causal, even in a strong sense: Knowing the state at time ##t_0## and knowing the Hamiltonian of the system, you know the state at any time ##t>t_0##.
The wave packet of a particle without interaction/measurement can spread throughout the universe.

/Patrick
 

vanhees71

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Absolutely not. The prediction of quantum mechanics, in general, is not based on knowledge of the past, as far as measurement is concerned.

What would be the usefulness of a predictive theory that would not require any measures?

/Patrick
I'm not sure what you are asking. Quantum mechanics (which applies to everything as long as you can use non-relativistic physics) just predicts the outcome of experiments. What do you mean by "from the past"? As any dynamical theory QT starts from the description of the state the system is prepared in (or is observed to be prepared in) at time ##t_0## and provides via the dynamical laws what's to be expected to be observed later in a measurement, and that it does, within its realm of applicability, very well.
 

vanhees71

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The wave packet of a particle without interaction/measurement can spread throughout the universe.

/Patrick
Yes, of course, that what comes out of a calculation you do in the QM 1 lecture in the first or 2nd week. So what?
 
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I'm not sure what you are asking. Quantum mechanics (which applies to everything as long as you can use non-relativistic physics) just predicts the outcome of experiments. What do you mean by "from the past"? As any dynamical theory QT starts from the description of the state the system is prepared in (or is observed to be prepared in) at time ##t_0## and provides via the dynamical laws what's to be expected to be observed later in a measurement, and that it does, within its realm of applicability, very well.
Pictures are often worth more than speeches :

Classical Mechanics

1564649148871.png


Quantum Mechanics

1564649984512.png


1564649581658.png

That what comes out of a presentation you can have in the QM 1 lecture in the first or 2nd week. Did you miss this passage during your studies?

Without measurements, it is only possible to predict probabilities as if the properties are only accessible through measurement operations that at least disturb them or at most generate them. They are not deduced from the past in a deterministic way.

/Patrick
 

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vanhees71

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That's a quite nice summary of QT, though I don't like the very problematic collapse postulate. What I meant with my statement was the spread of a free wave packet in non-relativistic QT. Usually you get the propagation of a Gaussian wave packet according to the Schrödinger equation as a problem in the first few recitation sessions. It's meaning is of course given as on your French slide: ##|\psi(t,x)|^2## is the position-probability distribution at time ##t##, i.e., it gives the probability for a detector to click at time ##t## when sitting at the point ##x## per (small) detector volume. That's all you need to know to make predictions concerning this position measurement.

What the particle does after detection is a question that cannot be part of the general formalism. If you have a von Neumann filter measurement indeed you have to adapt the wave function due to the interaction of the particle with the measurement device based on the knowledge that it registered the particle at at time ##t## at a place ##x## with some uncertainty given by the position resolution of the detector. In this (and only in this) case the "collapse postulate" is a valid FAPP description of a state-preparation procdedure, but no more.
 
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Well, into which basis? If any basis is allowed, then anything can happen. But then it is not determined by the simulation of the wave function but by the additional choice of the basis. This would mean that in our real universe, what happens depends not only on the Schrödinger dynamics but also on choosing a basis. in other words, the basis elements constitute additional hidden variables needed to get real events from quantum mechanics.
The quantum theory of the miniverse is in the dynamics and the initial conditions, but not the choice of basis. Different bases make clear different features of the miniverse we might wish to understand. They are not separate, alternative theories of the miniverse.

The theory does constrain our choice insofar as our decomposition has to be one that returns approximately standard probabilities, which is the case if ##Re[\mathbf{Tr}[C_{\alpha'}\rho C^\dagger_\alpha]]\approx 0## for ##\alpha'\neq\alpha##. But this is a feature, not a bug, as it ensures our physical understanding of the miniverse is always logically valid.
 

A. Neumaier

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Quantum mechanics (which applies to everything as long as you can use non-relativistic physics) just predicts the outcome of experiments.
No. It leaves most details about the outcomes of experiments undetermined; only their gross statistics is determined.

According to all traditional interpretations, quantum mechanics alone does never predict the outcomes of any single experiment but only the statistics of a large ensemble of similarly prepared experiments.

In contrast, the thermal interpretation predicts the outcomes of experiments individually (from the state of the universe) in terms of the quantum formalism alone, and only our limited knowledge of the latter forces us to statistical considerations.
 
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A. Neumaier

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The quantum theory of the miniverse is in the dynamics and the initial conditions, but not the choice of basis. Different bases make clear different features of the miniverse we might wish to understand. They are not separate, alternative theories of the miniverse.

The theory does constrain our choice insofar as our decomposition has to be one that returns approximately standard probabilities, which is the case if ##Re[\mathbf{Tr}[C_{\alpha'}\rho C^\dagger_\alpha]]\approx 0## for ##\alpha'\neq\alpha##. But this is a feature, not a bug, as it ensures our physical understanding of the miniverse is always logically valid.
So to predict/simulate events you need quantum mechanics plus a basis that must be added externally, though in reality, things happen without having to specify a basis. Since according to you these additional choices are necessay (rather than implied by the quantum formalism), quantum mechanics alone is incomplete.
 

vanhees71

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No. It leaves most details about the outcomes of experiments undetermined; only their gross statistics is determined.

According to all traditional interpretations, quantum mechanics alone does never predict the outcomes of any single experiment but only the statistics of a large ensemble of similarly prepared experiments.

In contrast, the thermal interpretation predicts the outcomes of experiments individually (from the state of the universe) from the quantum formalism alone, and only our ignorance of the latter forces us to statistical considerations.
Well, then can you explain to me, why QT is considered the most successful physical theory ever? What is undetermined in your opinion?

You say, it's "only the statistics". But that's the point! Nature is not deterministic on the fundamental level according to QT. E.g., if you have a single radioactive atom (and today you can deal with single atoms, e.g., in traps or storage rings) there's no way to predict the precise time, when it decays (given it is "here" now).

Of course, there's always the possibility that QT is not complete, and we simply do not know the complete set of observables which might determine the precise time, when the atom decays, but so far we don't have any hint that this might be true, and from the various Bell experiments, all confirming QT but disprove any local deterministic HV theories, I tend to believe that QT is rather complete (despite the description of gravity, which is today the only clear indication that QT is not complete). That's of course a believe, I can't prove, but under this assumption, QT tells us that nature is inherently probabilistic, i.e., certain things like the decay of the instable atom simply are random. I don't see, where a problem with this might be. It's rather amazing how accurately we are able to describe this inherent randomness with probability theory (a mathematical axiomatic system, which doesn't tell anything about the concrete probability measure for a given real-world situation) together with QT (a physical theory that provides precise predictions for probabilities of the inherently random processes observed in nature).

I think there's no reason to think that nature may not be random at the most fundamental level of describability.
 

A. Neumaier

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Well, then can you explain to me, why QT is considered the most successful physical theory ever?
Because it actually determines the statistics with phenomenal success. This is quite a feat!
What is undetermined in your opinion?
Each single outcome, and all details of the fluctuations. Thus most of the stuff that is observed.
But only in the traditional interpretations.

In my opinion, the true, complete quantum physics is the quantum formalism plus the thermal interpretation. It accounts for each single outcome, and for all details of the fluctuations.
 

A. Neumaier

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I think there's no reason to think that nature may not be random at the most fundamental level of describability.
This is a completely unverifiable statement of your faith in the traditional quantum philosophy.
 

Lord Jestocost

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Nature is not deterministic on the fundamental level......
To my mind, there is need to more profound thinking. The onsets of individual clicks in a counter seem to be totally lawless events, coming by themselves and thus being uncaused. Or can one denote a cause which compels these individual effects?
 
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Randonmess is an artifact of measurables. Its not to say it didnt exist for lack of a better word. It is effective in its domain-- dynamics/relation-- average outcome. Like how flatspace is treated in geometry--GR. TI accounts for both. I bare lack of confidence in the unmaleability/universality of time in QM which accounts for every predictive values and observables in S/GR domain-- even the weird ones. I can only suspect that randonmess/indeterminism is not the underlying factor but mere artifacts of probabilty. In the same manner that flatspace is not observable.
 
The statistical character is not something we can get away from. This statistical behavior is described by the partition function

∫ dφ eφT = (2π)n/2(det D)-1/2 = exp -1/2 Tr ln D

where F = 1/2 Tr ln D is the free energy. The first integral is the path integral

∫ e-S = e-F

where F is the free energy and the action is S = φTDφ. The formal similarity to thermodynamics is something that tells us that these expressions can only be interpreted statistically. The free energy is defined as a legendre transform in terms of the conjugate variables J and φ. Expressions such as S = Tr ρ ln ρ cannot interpreted in terms of usual microstates because they are defined through wick rotation.
 
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A. Neumaier

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The formal similarity to thermodynamics is something that tells us that these expressions can only be interpreted statistically.
No. There are many formal similarities in mathematics and physics that cannot be ascribed to a similar interpretation.

The formal similarity only tells that there is a possibility of interpreting it statistically.
 
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At least intuitively any model involving randomness can be replaced with a deterministic model with extra variables controlling that randomness. Not knowing those variables can be called "incomplete understanding", though I think I'd be content and even consider our understanding complete for such models where certain variables are not even theoretically knowable, as long as their effect is well defined.

Problem with QM is that even such hidden variable models are proven to not work. For me my "incomplete understanding" stems not from the randomness itself, but from the way the random outcomes under different parameters are related. But I guess this is a whole other topic.
 

vanhees71

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Because it actually determines the statistics with phenomenal success. This is quite a feat!

Each single outcome, and all details of the fluctuations. Thus most of the stuff that is observed.
But only in the traditional interpretations.

In my opinion, the true, complete quantum physics is the quantum formalism plus the thermal interpretation. It accounts for each single outcome, and for all details of the fluctuations.
Ok, so we agree on the basic facts concerning QT as a very successful physical theory.

Now, it is obviously difficult, even after all this decades, to simply accept the simple conclusion that nature behaves inherently random. If this is true, as strongly suggested by QT and the strong successful experimental tests it has survived up to this day, then there's no way to predict a single measurement's outcome with certainty (of course except in the case, where the system is prepared in a state, where the measured observable takes a certain determined value), because the observable doesn't take a determined value. Then the complete description are indeed probabilities, and to test these probabilities you need an ensemble. Fluctuations are also referring to an ensemble. So if you accept the probabilistic description as complete, there's nothing lacking with QT simply because the outcome of an individual measurment is inherently random.

I still don't understand the thermal interpretion: Recently you claimed within the thermal interpretation the observables are what's in the usual interpretation of QT is called the expectation value of the observable given the state, i.e., ##\langle O \rangle = \mathrm{Tr}(\hat{\rho} \hat{O})##. This is a single value, i.e., it's determined, given the state. Now you claim, there are fluctuations. How do you define them. In the usual interpretations, where the state is interpreted probabilistically, it's clear: The fluctuations are determined by the moments or cumulants of the probability distribution or, equivalently, all expectation values of powers of ##O##, i.e., ##O_n =\mathrm{Tr} (\hat{\rho} \hat{O}^n)##, ##n \in \mathbb{N}##. But then you have again the usual probabilistic interpretation back (no matter, which flavor of additional "ontology" and "metaphysics" you prefer). Just renaming a probabilistic theory avoiding the words statistics, randomness and probability, does not change the mathematical content, as you well know!

So why then call it "thermal" (which is misleading anyway, because it seems to be your intention to provide a generally valid reinterpretation and not just one for thermal equilibrium).
 
No. There are many formal similarities in mathematics and physics that cannot be ascribed to a similar interpretation.

The formal similarity only tells that there is a possibility of interpreting it statistically.
This is more than a formal similarity. The euclidean action essentially is the entropy.
 

vanhees71

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To my mind, there is need to more profound thinking. The onsets of individual clicks in a counter seem to be totally lawless events, coming by themselves and thus being uncaused. Or can one denote a cause which compels these individual effects?
That's precisely my point (take the example of radioactive decay and a Geiger counter): The individual clicks ARE random according to QT. In lack of any deterministic explanation (in view of all these accurate Bell tests confirming QT) my conclusion simply is that nature is inherently random, i.e., when the individual atom decays and thus the Geiger counter clicks, is random.

The mathematical model to describe random events is probability theory, and QT is another theory providing the probability measures to be used to describe measurement outcomes in experiments (which are necessarily random experiments due to the inherent randomness of nature), and as it turns out everything else than "lawless". To the contrary QT provides the best estimates of probabilities for a vast number of observations (in fact all observations so far!) ever. I don't know a single other application of probability theory/applied stastistics, which gives as accurate preditions for probabilities/ statistics than QT! Thus we have a precise probabilistic description of the "inherent randomness of nature". No more no less.
 

vanhees71

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At least intuitively any model involving randomness can be replaced with a deterministic model with extra variables controlling that randomness. Not knowing those variables can be called "incomplete understanding", though I think I'd be content and even consider our understanding complete for such models where certain variables are not even theoretically knowable, as long as their effect is well defined.

Problem with QM is that even such hidden variable models are proven to not work. For me my "incomplete understanding" stems not from the randomness itself, but from the way the random outcomes under different parameters are related. But I guess this is a whole other topic.
It's not all hidden-variable models that are proven to not work to be honest. E.g., the Bohmian interpretation of non-relativistic QM is a deterministic non-local interpretation. There are no hidden variables thought. The well-known ones are sufficient ;-)).

Only any local deterministic hidden-variable theory, as defined by Bell, is ruled out by the may Bell tests done up to now. All demonstrate the violation of Bell's inequality with astonishing significance and confirm the predictions of QT. The problem with non-local deterministic HV theories is to formulate them in accordance with (special) relativity. That's the reason, why Bohmian QT is not (yet?) satisfactorily formulated for relativistic QFT. It's of course not clear, whether there's some non-local deterministic HV theory consistent with relativity. At least there seems to be no proof for such a no-go theorem. On the other hand up to now nobody has found any such non-local theory yet.
 

A. Neumaier

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it is obviously difficult, even after all this decades, to simply accept the simple conclusion that nature behaves inherently random.
It will always be, because your conclusion does not follow logically from the phenomenal success of quantum physics. Thus whether or not someone accepts it is a matter of interpretation and philosophical preferences.

In particular, I do not think it is true because the thermal interpretation explains the randomness in quantum objects in precisely the same way as Laplace explained the randomness in classical objects.
Now you claim, there are fluctuations. How do you define them.
What is usually called fluctuations are just q-correlations, which the thermal interpretation handles as nonlocal properties of the system, just like the diameter or volume of a classical object is a nonlocal property.
Just renaming a probabilistic theory avoiding the words statistics, randomness and probability, does not change the mathematical content, as you well know!
Just having something that follows the axioms of probability theory does not make it a true probability in the sense of experiment, either. It is no more the case than a function is a vector pointing somewhere simply because it belongs to a vector space of functions.
So why then call it "thermal" (which is misleading anyway, because it seems to be your intention to provide a generally valid reinterpretation and not just one for thermal equilibrium).
The word 'thermal' was never just a shorthand for thermal equilibrium.

This label for my interpretation emphasizes the motivation that comes from the fact that the observable quantities of nonequilibrium thermodynamics (i.e., hydromechanics and elasticity theory) appear in statistical mechanics as q-expectation values, and that this observation is generalized to arbitrary quantum systems, rather than only those with a thermodynamical interpretation.
 

A. Neumaier

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This is more than a formal similarity. The euclidean action essentially is the entropy.
No. The Euclidean action is an unphysical tool to get S-matrix elements, and is only formally analogous to the entropy.
 
No. The Euclidean action is an unphysical tool to get S-matrix elements, and is only formally analogous to the entropy.
It is more than formal. For example, the entropy of a black hole is equal to the Euclidean action.
 

vanhees71

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It will always be, because your conclusion does not follow logically from the phenomenal success of quantum physics. Thus whether or not someone accepts it is a matter of interpretation and philosophical preferences.
I don't claim it's a logical conclusion from the success of QT, but I claim that also the assumption that the world "in reality" behaves deterministic and thus incompleteness of QT is no logical conclusion from our experience with physics either.

Indeed, whether or not someone accepts it is a matter of interpretation and [individual!] philosophical preferences [prejudices?]. As religious belief it's something personal of any individual and thus irrelevant and unrelated to the realm of science.

I still have no clue, what the correct interpretation of your "thermal interpretation" is:

What is usually called fluctuations are just q-correlations, which the thermal interpretation handles as nonlocal properties of the system, just like the diameter or volume of a classical object is a nonlocal property.
Just to call fluctuations (a probabilistic notion) now "q-correlations" without giving a meaning to this word, is just empty phrasing.
 

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