I Ontology of wavefunction vs. ontology of electric field

[greypilgrim]

Hi.

Different interpretations of QM have different opinions about the ontology of the wavefunction, i.e. if it really, physically exists or if it is "just" a mathematical tool needed to calculate the outcome of measurements. The QM interpretations comparison table on Wikipedia summarises the answer to this question in the "Wavefunction real?" column.

So far I haven't seen similar discussions about the existence of classical fields, e.g. the electric field. It is defined at every point in space as the force that would act on a small charged test particle, divided by its charge. An analogous question now could be if the electric field really, physically exists in empty space or if it is only a mathematical tool.
Is there a definite answer to this question?

If not, in what way do the concepts "wavefunction" and "electric field" differ such that the question about existence seems to be much more debatable for the former?

 

[A. Neumaier]

in what way do the concepts "wavefunction" and "electric field" differ

One can probe by a single measurement the value of the electric field in a small region where it does not vary much, whereas one cannot do the same for the value of a wave function.

 

[greypilgrim]

But this is a property of probability and also applicable to classical probability distributions.

So why aren't we debating if the probability distribution of a classical coin flip really, physically exists or if it is just a mathematical tool, but we are when it comes to a wavefunction describing a spin 1/2?

 

[A. Neumaier]

But this is a property of probability and also applicable to classical probability distributions.

Yes. And indeed there is disagreement whether probabilities are real (a property of a physical system) or subjective (just mathematical tools). This shows that (potential) direct observability makes the difference.

 

[Nugatory]

But this is a property of probability and also applicable to classical probability distributions.

Surely you are not suggesting that "can probe by a single measurement" is a property of probability and classical property distributions?

So why aren't we debating if the probability distribution of a classical coin flip really, physically exists or if it is just a mathematical tool, but we are when it comes to a wavefunction describing a spin 1/2?

I have no idea, but then again I'm not sure who this "we" that you're talking about is.

 

[greypilgrim]

Ah, this makes sense.

And indeed there is disagreement whether probabilities are real (a property of a physical system) or subjective (just mathematical tools).

So am I correct if I say:
The reason this question isn't much debated in classical (deterministic) theories is because probabilities only enter those due to a lack of knowledge, which is subjective. So in classical theories, probabilities are only mathematical tools.

 

[greypilgrim]

Surely you are not suggesting that "can probe by a single measurement" is a property of probability and classical property distributions?

No, I was referring to

whereas one cannot do the same for the value of a wave function.

 

[Nugatory]

No, I was referring to...

Ah - got it - thx.

 

[A. Neumaier]

Ah, this makes sense.

So am I correct if I say:
The reason this question isn't much debated in classical (deterministic) theories is because probabilities only enter those due to a lack of knowledge, which is subjective. So in classical theories, probabilities are only mathematical tools.

No. I said there is disagreement about the reality status of classical probability. Thre are objective (frequency) schools and subjective (Bayesian) schools, and shades in between. It is nearly as controversial and problem-ridden as quantum mechanics interpretations, though not as fiercly debated.