I Why randomness means incomplete understanding

[Stephen Tashi]

Of course you cannot describe macroscopic systems in all microscopic detail.

I think that you are speaking in a practical sense - i.e. such a task is too complex to be done in practice. However, what I am suggesting is that, in addition to being impractical, the task may be theoretically impossible. For example, to define theoretically and microscopically the macroscopic event "I go to the grocery store" presupposes there is some algorithm that can look at a subsequence of microscopic events and declare that it represents "I go to the grocery store".

 

[PAllen]

I think that you are speaking in a practical sense - i.e. such a task is too complex to be done in practice. However, what I am suggesting is that, in addition to being impractical, the task may be theoretically impossible. For example, to define theoretically and microscopically the macroscopic event "I go to the grocery store" presupposes there is some algorithm that can look at a subsequence of microscopic events and declare that it represents "I go to the grocery store".

Why would you think this is theoretically impossible? The only reason I can think of is that you believe there is no such subsequence - that is that such a statement has no microscopic underpinning. More specifically, that you believe the microscopic representation of this, by itself, does not represent the macroscopic event; that there is something fundamentally missing, in principle, from any microscopic description. This would imply that if you took all the atoms and states involved, they would not implement the macroscopic event unless you added something else. Do you have any suggestion of what that something else is?

 

[microsansfil]

Hi,

Why randomness means incomplete understanding: it is a point of view that stems, in my opinion, from the fact that quantum mechanics is an essentially predictive theory. It's not an explanatory theory, hence a large number of interpretations. A scientific explanation is traditionally defined as a causal assignment, but quantum mechanics challenges our commonsense picture of causality. For example by implying that some things happen at random, with no apparent cause.

Heisenberg : We have to relearn what understanding really means.

/Patrick

 

[vanhees71]

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 difference to classical physics is that QT is indeterministic, i.e., having prepared a system in a minimum-entropy state (i.e., a pure state) doesn't imply that all observables take determined values. All the tests of QT indicate that this is not due to some incompleteness of possible knowledge but an inherent feature of nature.

 

[A. Neumaier]

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 difference to classical physics is that QT is indeterministic, i.e., having prepared a system in a minimum-entropy state (i.e., a pure state) doesn't imply that all observables take determined values. All the tests of QT indicate that this is not due to some incompleteness of possible knowledge but an inherent feature of nature.

Elsewhere you said that quantum mechanics is solely about predicting experiments. In that sense it predicts nothing in the microscopic domain in a causal fashion. This was the view of Heisenberg at the time he wrote his paper about the uncertainty relation [referred to as equation (1) below], directly opposing what you wrote above:

Da nun der statistische Charakter der Quantentheorie so eng an die Ungenauigkeit aller Wahrnehmung geknüpft ist, könnte man zu der Vermutung verleitet werden, daß sich hinter der wahrgenommenen statistischen Welt noch eine ,,wirkliche'' Welt verberge, in der das Kausalgesetz gilt. Aber solche Spekulationen scheinen uns, das betonen wir ausdrücklich, unfruchtbar und sinnlos. Die Physik soll nur den Zusammenhang der Wahrnehmungen formal beschreiben. Vielmehr kann man den wahren Sachverhalt viel besser so charakterisieren: Weil alle Experimente den Gesetzen der Quantenmechanik und damlt der Gleichung (1) unterworfen sind, so wird durch die Quantenmechanik die Ungültigkeit des Kausalgesetzes definitiv festgestellt.

(Maybe someone can find an English translation.)

 

[vanhees71]

Sure, QT is about predicting the outcome of experiments, as any theory in physics. I've no clue how you come to the conclusion that it predicts nothing in the microscopic domain in a causal fashion. In fact it does precisely this. If that was not the case, we'd be in need of a new theory, and if there were an observation, for which QT fails to predict the outcome accurately we maybe already had a hint, how to modify it.

I don't think that Heisenberg is a good source concerning discussions about the interpretation. He's one of the main culprits leading to all this fuss about this topic, and the above quote again shows that he didn't understand Bohr's very important correction of his flawed view on the uncertainty relation in his first paper, which he published without first discussing it with Bohr: The uncertainty is not due to the "measurability" of observables but due to the "preparationability" of systems. The last sentence is also very revealing: Heisenberg also fails to clearly distinguish between causality and determinism. Though he is right, more today than in his time after all the investigations following Bell's important insights, in saying that it's highly speculative to think that there may be a "hidden determinism" (again to refer to "causality" is wrong though).

As long as there is not a clear contradiction between QT and observations, I'd say it's indeed highly speculative to think that there may be a deterministic, necessarily non-local, (hidden-variable?) theory behind the probabilistic nature of the quantum description.

 

[OCR]

It now seems that in the simulation according to your recipe, nothing happens at all.

Oh, interesting!. . . a simulation that simulates nothing ?? .

That couldn't even simulate a no bel prize. . . .

.

 

[A. Neumaier]

Bohr's very important correction

So let me quote Bohr (Nature 1928) on causality:

This postulate implies a renunciation as regards the causal space-time co-ordination of atomic processes. [...] there can be no question of causality in the ordinary sense of the word. [...] we learn from the quantum theory that the appropriateness of our usual causal space-time description depends entirely upon the small value of the quantum of action as compared to the actions involved in ordinary sense perceptions. [...] the radical departure from the causal description of Nature met with in radiation phenomena, to which we have referred above in connexion with the excitation of spectra. [...] Thus we see at once that no causal connexion can be obtained between observations leading to the fixation of a stationary state and earlier observations on the behaviour of the separate particles in the atom.

Probably you'll reply that you don't think that Bohr is a good source concerning discussions about the interpretation. Nobody is, since nobody has your views. Your views about interpretation are in many respects a minority view.

I don't think that Heisenberg is a good source concerning discussions about the interpretation.

Since you speak by argument from authority, let me emphasize that I consider Heisenberg to be a more important authority than you. His views are not antiquated at all.

 

[A. Neumaier]

Oh, interesting!. . . a simulation that simulates nothing ?? .

That couldn't even simulate a nobel prize. . .

It simulates a wave function, but no events. Thus one gets a huge amount of data, but nothing happens.

 

[vanhees71]

So let me quote Bohr (Nature 1928) on causality:

Probably you'll reply that you don't think that Bohr is a good source concerning discussions about the interpretation. Nobody is, since nobody has your views. Your views about interpretation are in many respects a minority view.

Since you speak by argument from authority, let me emphasize that I consider Heisenberg to be a more important authority than you. His views are not antiquated at all.

That's your decision to follow "authorities". I don't claim to be an authority in any respect, but I don't think that my view on interpretation is a minority view. In my environment I don't know any physicist who doesn't share this view, i.e., does not follow the "orthodox interpretation" of QT. That may be due to the fact that our topic of theoretical-physics research (relativistic heavy-ion collisions) is very close to phenomenology and experiments, i.e., we have contact with real-world physics in the lab rather than overly philosophical speculations.

That said, I indeed consider Bohr a better source for discussions on interpretation than Heisenberg, though I don't share your enthusiasm for his writings about the subject which tend to be more confusing than necessary, but Heisenberg tops him in this respect.

Among the best writings on interpretation is the "Prologue" in the book

J. Schwinger, Quantum Mechanics, Symbolism for atomic measurements, Springer Verlag

 

[A. Neumaier]

In my environment I don't know any physicist who doesn't share this view

Everyone shares the math of quantum physics and the intuition for how to apply it.

But ask anyone about the details about how they interpret things and one finds huge differences. In fact one tends to find more views than people asked, since the same persons' views are different when asked in different contexts.

 

[OCR]

That couldn't even simulate a no bel prize. . .

The space in "no bel" was not a simulation. . . it was deliberate. .

.

 

[A. Neumaier]

The space in "no bel" was not a simulation. . . it was deliberate. .

This revealed a limitation in my biological OCR routine !-)

 

[Stephen Tashi]

Why would you think this is theoretically impossible?

Perhaps it's a delicate mathematical point. To define "I go to the grocery store" requires that "I" do it. But "I" am not a well defined subset of events in the universe. (E.g. atoms come and go from "me", but "I" remain, in the judgement of myself, "the same".)

Macroscopic events are judged by macroscopic beings. Attempts to define them in micrscopic detail are circular since both the event and the definer of the event are not microscopically defined. A definition of "I go to the grocery store" in terms of microscopic events that "I" judge to be correct would be one where "I" agreed that the definition worked. But "I" am not microscopically defined - unless "I" succeed in defining "I" microscopically. That attempt at self-definition is utterly circular.

I don't know whether @A. Neumaier is saying something along these lines, but it seems relevant to the objection that known dynamical laws do not model the macroscopic events of measurements being taken.

 

[A. Neumaier]

I don't know whether @A. Neumaier is saying something along these lines

No. You are nitpicking.

To work on the theoretical level, one doesn't need to specify a macroscopic object (such as 'You') to the last detail, knowing precisely which atoms belong to it. One just needs an approximate model that captures the relevant features. (All our models in physics are approximate!) To define "You go to the grocery store" it is enough to have a stick model of you with movable joints, knowledge of the location of all joints and the door of grocery store, and a lattice quantum model of the material of which the sticks and joints are made, to be able to work from first principles.

 

[Stephen Tashi]

No. You are nitpicking.

To work on the theoretical level, one doesn't need to specify a macroscopic object (such as 'You') to the last detail, knowing precisely which atoms belong to it. One just needs an approximate model that captures the relevant features.

I agree I'm nitpicking, but notice that "one just needs" implies a judgement by a macroscopic being concerning whether needs are met.

The assertion that a system of dynamical laws doesn't model the macroscopic events of measurements being taken is an example of the familiar saying "It's hard to prove a negative case". People can respond along the lines of "Of course it does. We let X be the subset of microscopic events that define 'Bob takes a a measurement' and there you have it."

If we grant that macroscopic events can be defined as subsets of microscopic events in a dynamical system, then we cannot object that the system does not represent macroscopic measurements. We can only object that the system does not tell us "naturally" or by some convenient general definition which microscopic events represent macroscopic measurements.

Your assertion that "randomness mean incomplete understanding" is more subtle than the above points - and apparently not specific to macroscopic events. However, some responses say, in effect, "What's the problem? We define 'Bob takes a measurement' as a set of microscopic events and run a simulation where we draw simulated random numbers at appropriate times and there you have it."

I don't understand your reply to this type of argument. You issue challenges like " This still does not say what an event is, and how a quantum detector in the miniverse would recognize it.". This seems to require that a proposed model include a general definition of "what an event is". Is that your requirement? You would object to people defining the events in a model on case-by-case basis? Perhaps your objection is that there is no general rule telling where to draw the random numbers.

 

[A. Neumaier]

"one just needs" implies a judgement by a macroscopic being concerning whether needs are met.

This is needed for all of science. With your argument you should stop being interested in it.

 

[A. Neumaier]

You issue challenges like " This still does not say what an event is, and how a quantum detector in the miniverse would recognize it.". This seems to require that a proposed model include a general definition of "what an event is". Is that your requirement? You would object to people defining the events in a model on case-by-case basis?

If there is no formal meaning to the notion of events in terms of wave functions, one cannot simulate events by simulating wave functions. Since what happens is constituted of events, nothing happens in such a simulation.

Therefore a formal notion of event is needed to be able to simulate what happens. Of course it cannot depend on a case by case basis, since what happens in reality also happens without us having made up cases. Special cases can be distinguished on the basis of the general notion, just as special molecules make sense only with a concept of a molecule.

 

[microsansfil]

Sure, QT is about predicting the outcome of experiments, as any theory in physics.

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

 

[Morbert]

But then how does the simulation proceed in such a way that each simulated detector knows which value it has to display at which time (so that an event happens), while only propagating the wave function of the total system?

It now seems that in the simulation according to your recipe, nothing happens at all.

It simulates a wave function, but no events.

You are free to evolve the wavefunction, but that doesn't commit you to a statement like "nothing happens".

You could also, for example, decompose the wavefunction into a basis of mutually exclusive sequences of events $|\Psi\rangle = \sum_\alpha C_\alpha|\Psi\rangle$ and compute the aforementioned probabilities $||C_\alpha |\Psi\rangle||^2$ or, more generally, $\mathbf{Tr}[C_\alpha\rho C_\alpha^\dagger]$.

Quantum mechanics let's you use whichever treatment of the system is most suitable for your purposes.

 

[A. Neumaier]

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.

 

[microsansfil]

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]

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]

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?

 

[microsansfil]

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

Quantum Mechanics

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

 

[vanhees71]

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.

 

[Morbert]

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]

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.

 

[A. Neumaier]

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]

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.