# I Why randomness means incomplete understanding

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#### A. Neumaier

An event which occurs at some time $t$ is a property that obtains at time $t$, under a consistent quantum description of the system. A detector in the miniverse measures an event if the history of the detector is correlated with the occurrence of the event. Measurement itself isn't the event. It's the correlation between histories of events.
So everything measures everything, to some extent, since zero correlations are the exception. And all events happen all the time simultaneously. A very strange miniverse! What then guarantees the coherence of behavior of the objects? How to select one reasonable scenario from the chaos where everything happens?

#### DennisN

This is not really true. You can create a pseudo-random generator, but it needs to be seeded with an outside source of randomness, otherwise you'll get deterministic behavior.
Good point, that is correct.
A definition of "random" that has advantages is if it is not possible to compress the series at all. With that definition, most computer pseudo-random number generators are not random, regardless of how they are seeded.
Yes. Shannon's information entropy can be used the evaluate the "randomness". A stream of data that has maximum information entropy (which is 8 if each symbol is coded with 8 bits) is random. If the entropy is less than 8, it's not random. I should also add that here I assume that the sample size, i.e. the length of the stream of data, is sufficiently long to make an accurate calculation of the entropy.

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#### vanhees71

Gold Member
The experimenters don't actually know to describe their detectors in atom-by-atom detail. The macroscopic experimenter can give a macroscopic description of a detector.

If we use a moderate dose of pure mathematics, we can simply assert that there is a subset of S of the set of all "real" trajectories of the universe through its possible states and this set S consists exactly of those where "I go to the grocery store". But a heavy does of pure mathematics may question whether this approach does define a set. After all, it assumes the macroscopic judgement "I go to the grocery store" is unambiguous . So there is circular procedure used in defining the set.
Of course you cannot describe macroscopic systems in all microscopic detail. As the application of the standard many-body treatments show the macroscopic "relevant observables" tend to behave in a way well-described by classical physics.

To the contrary it's pretty difficult to observe the quantum behavior of macroscopic observables, though this is possible today thanks to refined technique; these days the have counted single phonons of a nano-mechanical oscillator:

#### Morbert

And all events happen all the time simultaneously. A very strange miniverse!
Not all events happen, simultaneously or otherwise. Quantum mechanics will assign probabilities to mutually exclusive sequences of events. If one sequence happens, the others won't. Quantum mechanics won't tell you which sequence actually happens, of course. But that's to be expected if the world really is probabilistic.

#### A. Neumaier

Not all events happen, simultaneously or otherwise. Quantum mechanics will assign probabilities to mutually exclusive sequences of events. If one sequence happens, the others won't. Quantum mechanics won't tell you which sequence actually happens, of course. But that's to be expected if the world really is probabilistic.
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.

OCR

#### 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

Gold Member
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:
Werner Heisenberg said:
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

Gold Member
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:
Niels Bohr said:
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.

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#### vanhees71

Gold Member
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.

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#### 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 !-)

OCR

#### 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.

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#### 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.