# Clarifying the Meaning of "Random" in Quantum Physics

This might be a silly question but when people say that something on the quantum level is completely "random," (except for general probability) does that mean, according to theory at least, if you were to go back in time and repeat an experiment exactly that the results could just as easily be different as the same, or that the results of a given experiment are unpredictable beforehand aside form general likeliness of many different possible events but the results would still be the same in the aforementioned scenario? Or, I suppose, do currently accepted theories not have an answer for this?

Staff Emeritus
I don't think anyone is thinking about time travel.

What they mean is that if you have N identically prepared systems, the number x with a particular outcome approaches Np for large N, if p is the probability of that outcome.

The result of experiment X at time T was x.
In a hypothetical parallel universe, doing the same experiment at time T might result in y.
However this does not alter the fact the in the original universe the result was x.

bhobba
Mentor
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zonde
Gold Member
when people say that something on the quantum level is completely "random," (except for general probability) does that mean, according to theory at least, if you were to go back in time and repeat an experiment exactly that the results could just as easily be different as the same
People sometimes say that quantum randomness is fundamental and then I believe they mean what you said. Bet you have to leave out "according to theory" phrase because theory is silent about it.

Clarifying the meaning of randomnes in quantum theory as opposed to randomness in classical physics is tricky. Traditionally it has been considered as fundamental and thus quantum theory is considered as an indeterministic theory, but if you read the answer by V50 for instance, he is describing classical probability, since by the Born rule postulate that is the way we must think of predictions in quantum physics. Classical probability is obviously compatible with classical physics and it is not from that point of view definitory of a random theory.

It is often argued that the difference lies in probabilities being the only result obtainable in quantum physics, but that is not exactly true as many results, like those using the time independent Schrodinger equation or many in QFT are not in the form of probabilities. Others center on the lack of trajectories for particles but that is just a side effect of not being "classical particles" so it is kind of tautological to give it as a reason for fundamental randomness of the theory.

More paradoxical features of quantum physics wrt the meaning of randomness and its fundamental or not character: As is well known QM is often split attending to time evolution in a purely deterministic evolution (Schrodinger equation) between measurements that is reversible(unitary) and a random one that is irreversible(non-unitary) related to observation-measurement, with people giving more weight to one or the other kind depending on their interpretation. But ironically for the interpretations that admit this cut, the random part is the one corresponding to classical(and therefore classically deterministic)macroscopic observation. And interpretations like many worlds that deny the cut are purely deterministic like the SE.

So it is important to realize that the presence of randomness per se does not mean all kinds of determinism are discarded, although I tend to think that the specific form of classical determinism is. Causal determinism I would say is not.

On the other hand relativistic quantum field theory in as much a it follows the SR ontology is local and classical deterministic since it is set in Minkowski spacetime. How is that compatible with the quantum part in view of the Bell type quantum experiments outcomes is not clearly explained or even addressed in general.
Also the basic tenets of particle physics when it talks about matter constituents or ultimate building blocks or the distinction between elementary and composite particles according to their internal structure in Democritus atomism fashion follow classical determinism.

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A. Neumaier
On the other hand relativistic quantum field theory in as much as it follows the SR ontology is local and classical deterministic since it is set in Minkowski spacetime. How is that compatible with the quantum part in view of the Bell type quantum experiments outcomes is not clearly explained or even addressed in general.
The latter is explained in the discussion here (and its context, starting at #153 there).

atyy
This might be a silly question but when people say that something on the quantum level is completely "random," (except for general probability) does that mean, according to theory at least, if you were to go back in time and repeat an experiment exactly that the results could just as easily be different as the same, or that the results of a given experiment are unpredictable beforehand aside form general likeliness of many different possible events but the results would still be the same in the aforementioned scenario? Or, I suppose, do currently accepted theories not have an answer for this?
The "going back in time" is conceptually more or less right, but a better way to put it is "identically prepared" (as Vanadium 50 says above).

Within quantum theory, the theory itself says that even if we prepare systems "identically", the result will usually be different for each "identical" preparation. In the Copenhagen interpretation, this means that a pure state is the complete specification of everything we can know about a single system, but the theory only makes statistical predictions even if the pure state of a single system is completely specified (as bhobba mentions above).

It may be that we will discover that quantum theory is not the most fundamental theory, and there could be a more fundamental theory in which identical preparations do give identical results. Relative to such a more fundamental theory, the "identical" preparations of quantum theory would correspond to non-identical preparations.

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A. Neumaier
Relative to such a more fundamental theory, the "identical" preparations of quantum theory would correspond to non-identical preparations.
Not really. ''identically prepared'' means no more and no less than ''prepared in the same pure state'', and hence is relative to the model of the physical system. Of course, only very small and discrete quantum systems can be truly identically prepared. Thus in most cases there is in addition to the randomness according to born's rule another source of unrepeatability, due to our inability to reproduce a state exactly.

atyy
Not really. ''identically prepared'' means no more and no less than ''prepared in the same pure state'', and hence is relative to the model of the physical system. Of course, only very small and discrete quantum systems can be truly identically prepared. Thus in most cases there is in addition to the randomness according to born's rule another source of unrepeatability, due to our inability to reproduce a state exactly.
I don't think we disagree. You are talking about "identically prepared" within the Copenhagen interpretation, which is what I am referring to by quantum mechanics. By "relative to a more fundamental theory", I mean a theory in which the pure state is not the most complete specification of the state of an individual system, for example Bohmian mechanics. In Bohmian mechanics, quantum theory is not fundamental, and the "identical preparations" of quantum theory corresponds to a distribution over different initial conditions.

A. Neumaier
You are talking about "identically prepared" within the Copenhagen interpretation
I am not talking about the Copenhagen interpretation.

The term "identically prepared'' is not specific to an interpretation, since the Born rule, of which it is part, must hold in any interpretation of quantum mechanics that deserves this name. Even in Bohmian mechanics, one can derive the Born rule only if one first gives an explanation what it means in the Bohmian setting to prepare a system in a pure quantum state ##\psi## (in the sense of an operational Born rule). Otherwise we do not have an interpretation of quantum mechanics (with its notion of pure state) but a completely different theory.

atyy
I am not talking about the Copenhagen interpretation.

The term "identically prepared'' is not specific to an interpretation, since the Born rule, of which it is part, must hold in any interpretation of quantum mechanics that deserves this name. Even in Bohmian mechanics, one can derive the Born rule only if one first gives an explanation what it means in the Bohmian setting to prepare a system in a pure quantum state ##\psi## (in the sense of an operational Born rule). Otherwise we do not have an interpretation of quantum mechanics (with its notion of pure state) but a completely different theory.
Sure. I mean Bohmian mechanics as a completely different theory.

The latter is explained in the discussion here (and its context, starting at #153 there).
Almost every nonlinear deterministic system is chaotic, in a precise mathematical sense of ''almost'' and ''chaotic''. It ultimately comes from the fact that already for the simplest differential equation ##\dot x = ax## with ##a>0##, the result at time ##t\gg 0## depends very sensitively on the initial value at time zero, together with the fact that nonlinearities scramble up things. Look up the baker's map if this is new to you.
So I also find useful to distinguish between a linear classical determinism and a nonlinear determinism. Can you expand on how the nonlinearity enters in quantum microscopic systems?
All arguments I have seen against hidden variable theories - without exception - assume a particle picture; they become vacuous for fields.

The problems of few particle detection arise because their traditional treatment idealizes the detector (a complex quantum field system) to a simple classical object with a discrete random response to very low intensity field input. It is like measuring the volume of a hydrodynamic system (a little pond) in terms of the number of buckets you need to empty the pond - it will invariably result in integral results unless you model the measuring device (the bucket) in sufficient detail to get a continuously defined response.
I agree with this.
It follows that quantum field theory is not affected by the extended literature on hidden variables.
The problem is that currently QFT as applied to high energy physics and the standard model of particle physics relies on a classical atomistic particles ontology(even to define elementary particles wich is its fundamental goal, the search of the universe ultimate constituents or building blocks associated to ever bigger energies) and in that sense it is indeed quite affected by hidden variables literature since atomism is deterministic in the classical sense.

zonde
Gold Member
The latter is explained in the discussion here (and its context, starting at #153 there).
All arguments I have seen against hidden variable theories - without exception - assume a particle picture; they become vacuous for fields.
You can replace particles with clicks in detectors and the arguments remains the same. So Bell inequality applies to fields just as well.
This can be easily argued based on this model:

You can replace particles with clicks in detectors and the arguments remains the same.
Clicks in detectors IS what's normally interpreted as the particle picture so it replaces nothing. It is an assumption of the inequalities that goes by the name of local hidden variables a.k.a. classical determinism, wich is local and linear. An what is violated in the experiments.

A. Neumaier
The problem is that currently QFT as applied to high energy physics and the standard model of particle physics relies on a classical atomistic particles ontology
Not really. One can interpret everything in QFT in terms of densities and currents only; indeed, this is how much of QFT is related to experimental results. The particle terminology is to a large extent historicial baggage. It is not needed for the interpretation. In typical high-energy experiments, one measures tracks of energy deposits; their interpretation as particle tracks is optional though common.

So Bell inequality applies to fields just as well.
[old & incorrect quick answer - I confused satisfied and violated] Of course. Nobody disputes that. But there is not the slightest argument suggesting that a hidden-variable field theory would have to satisfy the Bell inequalities, while a hidden-variable particle theory provably does so, unless one allows for all sorts of weird behavior that is inconsistent with an intuitive notion of a particle.

[new and valid answer] A hidden-variable particle theory provably satisfies Bell inequalities known to be violated by quantum mechanics, unless one allows for all sorts of weird behavior that is inconsistent with an intuitive notion of a particle. On the other hand, a hidden-variable field theory is so nonlocal from the start that none of the assumptions used to justify Bell type inequalities are satisfied, hence the Bell inequalities cannot be derived.

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bhobba
..Box apparatus Color/Hardness 50/50's
-Operational Result

Summary: +22:00 - non corellation
+24:38 - Bells inequality, unpredictable, non deterministic, random. Probability is forced upon us by observations.
+29:00 - Uncertainty Principle
+43:38 - Empirical vs principle argument
+1:1:08 - Test/Operational conclusion on superposition
Moral: Deal with it...

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zonde
Gold Member
Clicks in detectors IS what's normally interpreted as the particle picture so it replaces nothing. It is an assumption of the inequalities that goes by the name of local hidden variables a.k.a. classical determinism, wich is local and linear. An what is violated in the experiments.
Clicks in detectors is a physical fact (direct observation) and not subject to interpretation.
So if we base inequality argument on clicks of detectors we simply bypass any interpretation about what is causing them.

zonde
Gold Member
Of course. Nobody disputes that. But there is not the slightest argument suggesting that a hidden-variable field theory would have to violate the Bell inequalities, while a hidden-variable particle theory provably does so, unless one allows for all sorts of weird behavior that is inconsistent with an intuitive notion of a particle.
You lost me here.
What do you mean by "hidden-variable particle theory"?
Do you mean that QM predicts violation of Bell inequalities because it clings to particle idea?

Clicks in detectors is a physical fact (direct observation) and not subject to interpretation.
So if we base inequality argument on clicks of detectors we simply bypass any interpretation about what is causing them.
Not subject to interpretation? Are you serious? Apples falling down are also physical direct observation facts, interpreting this has produced two different theories by Newton and Einstein, but hey, they are not subject to interpretation according to you.

zonde
Gold Member
Not subject to interpretation? Are you serious? Apples falling down are also physical direct observation facts, interpreting this has produced two different theories by Newton and Einstein, but hey, they are not subject to interpretation according to you.
Neither Newton's nor Einstein's theory of gravity dispute the physical direct observation fact of apples falling down. They give slightly different reasons why they are falling down.

Not really. One can interpret everything in QFT in terms of densities and currents only; indeed, this is how much of QFT is related to experimental results. The particle terminology is to a large extent historicial baggage. It is not needed for the interpretation. In typical high-energy experiments, one measures tracks of energy deposits; their interpretation as particle tracks is optional though common.
This is a true to a certain extent, but the LHC search for the fundamental building blocks and the fact that they are defined depending on internal structure(wich only admits an interpretation in terms of the classical atomistic particle picture) doesn't seem to be just historical baggage judging by the cost of the enterprise and doesn't seem to allow an optional interpretation.

Neither Newton's nor Einstein's theory of gravity dispute the physical direct observation fact of apples falling down. They give slightly different reasons why they are falling down.
Nothing I said disputes that clics are produced. Only the physical interpretation of those clics wich you claim doesn't exist.

zonde
Gold Member
Nothing I said disputes that clics are produced. Only the physical interpretation of those clics wich you claim doesn't exist.
Hmm maybe my statement was sloppy.
But now I do not understand your point. My argument was that we can base Bell type inequality on physical fact that clicks are produced. So we do not have to interpret clicks in any way to produce the inequality.

A. Neumaier