What Is the Role of Ontology in the Interpretations of Quantum Mechanics?

[ftr]

It seems that the word ontology which suppose to be about the most concrete object we can come up with is itself not well defined.
Take for example this post

I would categorize all the interpretations into 3 categories:
1) Interpretations without ontology (most variants of Copenhagenish interpretations)
2) Interpretations with ontology but without primitive ontology (consistent histories, thermal interpretation)
3) Interpretations with primitive ontology (Bohmian, many worlds, objective collapse)

Primitive ontology is the fundamental ontological quantity to which all other ontological quantities can be reduced. In Bohmian mechanics it is particle positions of all particles in the Universe. In many worlds it is the wave function of the multiverse.

Which alludes to primitive ontology as a property and not "what" is actually there(ontology proper) as the ultimate ontology which we seek. even particle is not well defined in relativistic QFT. Even so how do we seek explanation for what a particle is by saying things like ontology of BM is particle position.
With QFT it is even more mysteries, the field is just numbers/functions and you are not allowed to speculate about there origin. You get the real, not real(mathematical) reaction, and if you ask if they are real that should mean they are ontological but you will get a blank face since no one wants to believe that numbers are all there is.
I mean it seems none of the interpretations are really about ontology proper even TI(which is based on field). So what good are they, is foundation about ontology proper or not?

 

[vanhees71]

"Ontology" is just an empty phrase of philosophers. Literally "it's what is".

From a physicist's point of view, physics deals with observational objective facts and theoretical models describing general rules they follow. It's and empirical fact itself that such rules exist at all to begin with.

Within standard relativistic QFT a particle is an asymptotic free single-quantum Fock state with specific quantum numbers defined by the standard model (mass, spin, various charges of the gauge interactions). It can be observed using all kinds of sophisticated detectors which allow to measure the particle's momentum, and all the intrinsic properties mentioned above. In this sense it's a well defined object (in the sense of an objectively observable fact).

Only when you leave this simple scientific point of view you enter the realm of mystery and esoterics. Where to draw the distinction between mystery and esoterics on the one side and philsophy on the other is a question I'm not able to answer ;-)).

 

[hilbert2]

Well, one could ask whether numbers and mathematical theorems somehow "exist", even without any intelligent being thinking about them, given that they are so useful in formulating the properties of physical objects. But there's no experiment that could prove this either way, so a physicist could just say that it's a linguistic matter (what we decide to mean with the word "exist" ?).

 

[phinds]

"Ontology" is just an empty phrase of philosophers. Literally "it's what is".

+1 on that

 

[PeterDonis]

a physicist could just say that it's a linguistic matter (what we decide to mean with the word "exist" ?)

Exactly. Or, to put it another way, when people ask a question like "do numbers exist?", they may think they're asking a question about reality, but they're actually only asking a question about how we choose to use words.

 

[kith]

In quantum foundations, a couple of precise definitions related to ontology are used. They were introduced in
"Einstein, incompleteness, and the epistemic view of quantum states". N Harrigan and RW Spekkens. Found. Phys. 40, 125 (2010), arXiv:0706.2661.

There's also a nice review article from Matt Leifer which discusses many results using this terminology:
"Is the Quantum State Real? An Extended Review of ψ-ontology Theorems". Matthew Saul Leifer. Quanta 2014; 3:67--155, arxiv:1409.1570.

 

[ftr]

Exactly. Or, to put it another way, when people ask a question like "do numbers exist?", they may think they're asking a question about reality, but they're actually only asking a question about how we choose to use words.

As you know being a science oriented person( you may say Geeky ) we dislike words and prefer numbers and symbols, hence our disdain for philosophy where they play on made up ugly looking words with multi meanings attached.
My intention is simple down to earth. Just as the book on my shelf is made of atoms and atoms are made of electrons and protons I want to know what is an electron made of. Ok, it is a fundamental particle described by spin/charge/mass ..., but surely the properties for the electron and other particles and space must arise from some more fundamental entity that some different relations between a bunch of them, isn't that what we really mean by ontology. I am demanding a very simple explanation, why do people think I have lost it.

As a matter of fact the standard theories like QFT already point to that by postulating the harmonic oscillator as being the basic ingredient of the fields that make up everything else. So, I am not demanding something exotic, we already have a good example of it. we need something like it but it must produce all of physics. All this is in contrast to all of the QM interpretations which do nothing fundamental( just like a hillbilly putting on a fancy suit) although I must admit that it pushes our understanding just a tad further.

I guess what I am saying is that such program at least should be part of the foundation program.

 

[PeterDonis]

My intention is simple down to earth. Just as the book on my shelf is made of atoms and atoms are made of electrons and protons I want to know what is an electron made of.

I understand the intuitive appeal of the question. I'm just saying that the answer won't come from philosophy (for example, by asking what the word "ontology" means). It will come from scientific experiments. We didn't learn that the book on your shelf was made of atoms, or that atoms are made of electrons and nuclei, from philosophy. We learned it from scientific experiments that probed the structure of matter and the structure of atoms.

The problem today is that so far our experiments have told us nothing about any level of structure below what is described by the Standard Model of particle physics (leptons, quarks, and gauge bosons) and General Relativity. The star candidate from a few decades back, supersymmetry, is now pretty unlikely based on the lack of any evidence for it appearing so far in the LHC experiments. And nobody has any other candidate that predicts anything useful from observation for many orders of magnitude beyond the level we can currently probe.

Some people respond to this vacuum by insisting on philosophical speculations. Others, like me, just accept that there are limits to our ability to probe and move on to other areas where we have a greater expectation of useful results.

I am demanding a very simple explanation

No, you're not, because the simple explanation you're demanding is that electrons are fundamental--they aren't made of anything, they're the lowest level of structure there is--because that's what all of our current evidence says. And you are clearly not accepting that explanation because you ask what electrons are made of.

standard theories like QFT already point to that by postulating the harmonic oscillator as being the basic ingredient of the fields that make up everything else

No, that's not correct, because not all fields in QFT have an interpretation as harmonic oscillators. Only free fields do, but free fields are useless by themselves because we observe interactions.

 

[ftr]

No, you're not, because the simple explanation you're demanding is that electrons are fundamental--they aren't made of anything, they're the lowest level of structure there is--because that's what all of our current evidence says. And you are clearly not accepting that explanation because you ask what electrons are made of.

I do think it is fundamental as a particle, however, there been many ideas like string theory and string nets for example. But I lean toward more QED picture of the electron as noting but some entity that emits and absorbs photons but not sure if it is the right/left part dance or with other particles.

No, that's not correct, because not all fields in QFT have an interpretation as harmonic oscillators. Only free fields do, but free fields are useless by themselves because we observe interactions.

I just mentioned it as an example.

 

[PeterDonis]

I do think it is fundamental as a particle

It's not a particle, it's a quantum field. "Particle" is just a term for some particular states of quantum fields.

I lean toward more QED

QED is a subset of the Standard Model of particle physics, which is our best current model of the electron, yes.

 

[lodbrok]

It seems that the word ontology which suppose to be about the most concrete object we can come up with is itself not well defined.

I think the issue is not with the definition of ontology, but with understanding of what it means.

Ontology deals with "existence" and "being", "what is"? Contrary to some claims, to say the meaning of ontology is clear is not the same thing as saying there is a clear "ontology" in a specific theory.

Almost all theories in physics have an ontology. This means simply that the theories have in them some understanding of what they claim exists or is real, that they are trying to model/explain/predict etc? Even a theory that claims electrons are not real, has an ontology. Another theory may claim that the only thing that is real is the wave-function or field -- that is still an ontology. Whatever it is the theory claims "exists" is the ontology for that theory. This is quite a separate question from whether the ontology of a theory is the true one, or which ontology is correct, because even alchemy had an ontology that the fundamental elements of existence were "fire", "water", "earth" and "air".

There can be no physics without ontology, because that is what physics is, the study of stuff that exists such as objects, their behaviours, phenomena and their occurrences. Even those who dismiss "ontology" as just "philosophy" unknowingly rely on it in their practice of physics -- unless they are just mathematicians pretending to be physicists.

 

[Demystifier]

"Ontology" is just an empty phrase of philosophers. Literally "it's what is".

"Measurement" is just an empty phrase of instrumentalists. Literally "it's the process in which something is measured".

Now seriously. Even most physicists who despise philosophy believe that the Moon is there when nobody observes it. (Mermin, for instance, doesn't believe it, but most physicists do.) And the statement that "the Moon is there when nobody observes it" is an ontological statement. So even physicists who proudly claim that ontology is a meaningless word - do have ontological beliefs. True, the word "ontology" is not precisely defined (except in the work by Harriagan and Spekkens), but it doesn't mean that it doesn't have any meaning at all.

In fact, in any scientific or mathematical theory it is impossible to give a precise definition of all words, simply because any definition requires a use of some words which also need to be defined, but one cannot have an infinite regress and circular definitions are not allowed. So some words must remain undefined, which are called primitive. For instance, in the standard minimal interpretation of QM which denies the existence of the measurement problem, the notion of measurement itself is primitive. This means that adherents of this interpretation think that the notion of measurement is clear intuitively, so that it doesn't need to be precisely defined. Likewise, adherents of some other interpretations (e.g. Bohmian or many-world) often think that the notion of ontology is clear intuitively, so that it doesn't need to be precisely defined. Similarly, a QBist may think that the notion of information is clear intuitively, etc. Different interpretations can therefore be reduced to what notion one thinks to be clear intuitively so that it can be considered primitive.

 

[vanhees71]

The claim that the statement that the moon exists independent of whether one observes it or not is something contradicting any laws of physics or being a problem in our current understanding of physics is simply nonsense. To the contrary physics tells us that, as soon as we have verified by observation that there's a moon out there, it's following from the contemporary known laws of nature that it is there, whether or not somebody is looking. You can even predict with a high accuracy where you can see it at a given point of time (though the moon is not particularly easy to describe as poor Kepler realized already more than 400 years ago). This is all some hype in socalled popular-science media, which think it's better to tell people that there are mysteries about and esoterics in quantum theory though to the contrary it's the best description of matter ever. There's no single indication from solid science that it is contradicting any empirical accurate evidence. It's incomplete in the respect that there's no working QT of gravity yet, but this doesn't affect the fact that the moon is there whether or not anybody looks at it in any way.

Then indeed, what's a measurement is simply defined by measuring things in the lab, and it's the best defined thing ever, because to measure something you have to understand the issue about what's measured and how it can be meausured to a degree that let's you build the necessary measurement devices. This is applied science called engineering, and an engineer doesn't need to bother whether something has an "ontology" or other empty phrases from philosophy, but he has to know how the laws of nature work to get the desired functioning of his (measurement) devices. Philosophy won't help him at all but the well-established theories of physics do!

 

[Lord Jestocost]

Statements like “the moon is there when nobody observes it” or “the moon isn’t there when nobody observes it” express nothing else but belief or nonbelief, thus leaving the realm of empirical science. An instrumentalist would murmur: "You can even never be certain whether all of your putative outer experience is not mere imagining."

 

[lodbrok]

This is applied science called engineering, and an engineer doesn't need to bother whether something has an "ontology" or other empty phrases from philosophy, but he has to know how the laws of nature work to get the desired functioning of his (measurement) devices. Philosophy won't help him at all but the well-established theories of physics do!

Scientists don't have to bother with the word "ontology" but they have to bother about ontology. What was the thing again you were trying to measure? -- that is ontology. It is fine if you never call it "ontology" and you don't have to understand the meaning of the word to practice physics, but you do indeed bother about ontology. Philosophy tells me that you are doing that, and perhaps you do not realize you are doing that because you have a faulty notion of what philosophy is all about.

I also have to take issue with the suggestion that Philosophy can't help physicists do physics. Any discipline that deals with concepts and how they relate with each other and how to reason properly from those concepts to make conclusions will benefit tremendously from philosophy. It is unfortunate some of the caricatures that are painted of philosophy in the physics community. Some of the current problems in physics would not exist if physicists had a better grounding of philosophy and I would encourage any serious student of physics who is able to do so, to learn a bit of philosophy.

 

[vanhees71]

It's never wrong to learn things outside your own specialization, but I'd really like to know which current problems in physics could be solved by a better grounding of (in?) philosophy. I've tried to read several books and papers on the philosophy of physics, and at best I got some interesting metaphysical aspects about well-established theories (like SR, GR, Q(F)T) from it, e.g., the meaning of the spacetime manifold in GR or the meaning of particles within relativistic QFT etc. This however is only an a-posteriori analysis of existing well-established theories or models of physics, and the merit of this is to get a better understanding about the meaning of the notions of the theory in relation to "what is", i.e., in this sense there's some merit in clarifying the "ontology" underlying these well-established theories. These sort of books/papers, however, seems to be pretty rare.

A great deal of philosophy-of-physics writings make up problems which are not even there in physics. One of them is the "measurement problem" of QT. I never figured out what the heck this should be, given the fact that QT is the most comprehensive and most accurate theory applied to the description of the results of real-lab experiments and observations ever. There's not a single "measurement problem" out there! To the contrary, e.g., the HEP physicists are really desperately looking for "physics beyond the Standard Model". So far without any success, i.e., all "candidates" for "beyond-the-standard-model physics" in the recent years at the end have vanished in the statistical noise, i.e., as soon as the "promising BSM signals" reached the $5 \sigma$ significance level, the signals were gone and correspondingly the SM prediction verified on this significance level. So there's no "measurement problem" whatsoever, and this on the other hand indeed is a problem, because it's almost sure that the SM is not a complete description of the particle content of nature due to the missing candidates for particles making up "dark matter", which seems to be needed to describe many astronomical and cosmological phenomena (if not on the other hand GR is proven to be only approximately valid, which however has not happened yet either though the observational tests of GR became a high-precision science in the recent decades, including the recent discovery and description (prediction!) of gravitational-wave forms for black-hole and neutron-star mergers).

Another shortcoming of the SM is of course that hitherto it could not be extended to the gravitational interaction, and also there we lack foremost any empirical evidence for "quantum-gravity effects", which could guide the theorists in formulating a satisfactory theory of quantum gravity that is applicable to the phenomena.

 

[Demystifier]

I'd really like to know which current problems in physics could be solved by a better grounding of (in?) philosophy

- the measurement problem in QM (provided that one accepts that it is a problem in physics)
- causal paradoxes associated with time travel allowed by certain solutions in general relativity (provided that one accepts that those paradoxes are a problem in physics)

Of course, you can always say that in such problems it is not well defined, in physical terms, what exactly the problem is, and consequently that those problems are not physical problems. But even if they are not purely physical problems, they are still problems on which physics has something to say. Hence it's natural for (at least some) physicists to work on them. If physicists can work, for instance, on protein folding, which is not a purely physical problem (but involves also biology), then I don't see why physicists couldn't work on problems which involve some philosophy.

One of them is the "measurement problem" of QT. I never figured out what the heck this should be, given the fact that QT is the most comprehensive and most accurate theory applied to the description of the results of real-lab experiments and observations ever.

In your case, you don't need philosophy to solve the measurement problem. You need philosophy to understand what the heck the measurement problem is.

 

[vanhees71]

Well, there may be philosophical problems with measurement in QT, but I don't see any physical one and I obviously don't understand, why the philosophical problems are problems to begin with.

 

[haushofer]

In your case, you don't need philosophy to solve the measurement problem. You need philosophy to understand what the heck the measurement problem is.

Maybe physicists sometimes have the wrong expectations from philosophy: it most often helps to raise the right questions instead of answering them.

 

[Demystifier]

I obviously don't understand, why the philosophical problems are problems to begin with.

Don't blame philosophy for that.

 

[Demystifier]

Well, there may be philosophical problems with measurement in QT, but I don't see any physical one

In the first attachment in https://www.physicsforums.com/threads/reading-materials-on-quantum-foundations.963543/post-6270768 I have explained what the measurement problem is from the point of view that can make sense to mathematical physicists. Since you are good in mathematical physics, perhaps that explanation of the measurement problem can make more sense to you.

 

[Lord Jestocost]

(PDF) An Interview with Sir Anthony Leggett - ResearchGate

In this interview, Anthony J. Leggett puts the value of philosophy for physicists in a nutshell:

“Yes, it was very useful. In some sense, all of it was useful and particularly useful was the philosophy part. I think that if you go through a course of analytical philosophy – I’m very conscious that philosophy means different things in different parts of the world – but in the Anglo-Saxon tradition, a degree in philosophy is very highly analytical, and if you go through it you do became much more conscious of the implicit assumptions that you’re making in your work. I do feel that one benefit I had from this is that – more than a lot of my colleagues in physics who hadn’t had this kind experience – I’m conscious of the implicit assumptions I’m making.” [in bold by LJ]

 

[A. Neumaier]

when people ask a question like "do numbers exist?", they may think they're asking a question about reality,

''Do numbers exist?'' is a perfectly valid question about reality (or what ''reality'' is supposed to mean), though it is answered differently by Platonists and others.

but they're actually only asking a question about how we choose to use words.

In this sense, everything asked is just a question about how we choose to use words. This empties questions of their essence, and language of its expressibility. Though the term ''reality'' may have multiple meanings (and hence needs a philosophical analysis to disentangle their various uses), it is a term needed - even though people like @vanhees71 substitute it by phrasing things in terms of ''observational objective facts'' rather than ''reality''. But this compound term is not really less ambiguous. Are electrons factually emitted by a source though we only observe pointer readings?

"Ontology" is just an empty phrase of philosophers. Literally "it's what is".

From a physicist's point of view, physics deals with observational objective facts and theoretical models describing general rules they follow. It's and empirical fact itself that such rules exist at all to begin with.

You also have an ontology - that the only things that exist are observational objective facts, and everything else is just a tool to describe and predict these.

But taken for themselves, observational objective facts are just a huge mess of numbers that don't make sense without interpretation through theory and informal rules for how to apply it. That this works is completely unexplained by such a philosophy as yours.

A great deal of philosophy-of-physics writings make up problems which are not even there in physics. One of them is the "measurement problem" of QT. I never figured out what the heck this should be, given the fact that QT is the most comprehensive and most accurate theory applied to the description of the results of real-lab experiments and observations ever. There's not a single "measurement problem" out there!

The measurement problem has nothing to do with experimental practice, so your arguments against it are pushing a straw man.

The measurement problem is a problem in theoretical physics - that of making the description on the microscopic level and that on the macroscopic level compatible with a view of quantum physics that applies in precisely the same way to all levels of resolution. This is needed for consistency since there is no empirically visible borderline between the microscopic and the macroscopic.

You use two different ontologies for the macroscopic reality (observational objective facts = what is read from instruments) and for the microscopic reality (electrons are not read from instruments but inferred by theory), related by philosophy-free (= made with an unreflected philosophy) ad hoc arguments. You don't even try to understand the views of those who apply more stringent criteria for logical coherence - you are satisfied with making derisive comments!

 

[vanhees71]

In the first attachment in https://www.physicsforums.com/threads/reading-materials-on-quantum-foundations.963543/post-6270768 I have explained what the measurement problem is from the point of view that can make sense to mathematical physicists. Since you are good in mathematical physics, perhaps that explanation of the measurement problem can make more sense to you.

Yes, but there you claim that it would be problematic to define, what "meaurement" means, but that's the least of all problems, because a "meausurement" is simply what experimentalists do in their labs (or astronomers with the telescopes, satellites, and space stations).

The theory or mathematical physics provides a mathematical description for the outcomes of measurements, and in QT it's a probabilistic/statistical description. There's not a single case known, where the predictions of the properly applied mathematical description fail, and what's claimed "random" by QT so far has ever been found random (e.g., the place an electron hits the screen when running through a double slit). So where's the problem?

The measurement problem is a problem in theoretical physics - that of making the description on the microscopic level and that on the macroscopic level compatible with a view of quantum physics that applies in precisely the same way to all levels of resolution. This is needed for consistency since there is no empirically visible borderline between the microscopic and the macroscopic.

But that's the point! The macroscopic classical behavior of macroscopic objects is understood by coarse graining. This behavior is only valid on a limit level of resolution. At sufficiently finer resolution you observe the various fluctuations, including irreducible quantum fluctuations. This also implies that there's no borderline between microscopic and macroscopic behavior, the latter being a coarse grained observation of the latter. I thought that's the very point of your "thermal interpretation", but of course only as soon as I'm allowed to interpret the mathematical operations (particularly the trace rule to evaluate expectation values) statistically (and in the sense of information theory).

 

[A. Neumaier]

But that's the point! The macroscopic classical behavior of macroscopic objects is understood by coarse graining. This behavior is only valid on a limit level of resolution.

Yes, that's the point! You apply only classical reasoning to the quantum systems called laboratories, not your own postulates of quantum mechanics. You don't have a logically consistent way of deriving this classical reasoning from your postulates - because this is impossible. You cannot prepare ensembles of laboratories, making enough independent copies to get their statistics. This gap is the measurement problem. Here you have a blind spot.

 

[vanhees71]

I don't get it. Of course, one can derive the macroscopic behavior of many-body systems, including all kinds of lab equipment from many-body quantum theory. An entire big branch of theoretical physics, known as condensed-matter physics is doing that the whole day!

 

[A. Neumaier]

I don't get it. Of course, one can derive the macroscopic behavior of many-body systems, including all kinds of lab equipment from many-body quantum theory. An entire big branch of theoretical physics, known as condensed-matter physics is doing that the whole day!

But not using your quantum postulates!

Instead one uses the identification of macroscopic measurement results with q-expectations of smeared fields and currents, and the q-expectations of operator products (which are nonhermitian, hence do not even admit an interpretation as statistical expectations) to formulate their dynamics.

 

[Demystifier]

Yes, but there you claim that it would be problematic to define, what "meaurement" means, but that's the least of all problems, because a "meausurement" is simply what experimentalists do in their labs (or astronomers with the telescopes, satellites, and space stations).

But as someone with good understanding of mathematical physics, you will agree that the statement "meausurement is simply what experimentalists do in their labs" is not very precise in the mathematical sense. Bohmian mechanics, for instance, gives a much more precise mathematical definition of the notion of measurement. If that is not a good motivation for studying Bohmian mechanics, then I don't know what is.

 

[PeterDonis]

''Do numbers exist?'' is a perfectly valid question about reality (or what ''reality'' is supposed to mean), though it is answered differently by Platonists and others.

When Platonists answer "yes" to this question, what difference does it make? What expectations should I have about possible future events, that I would not have if the answer were "no"? Or, to put it another way, if you claim that numbers exist, I should be able to test that claim somehow. How would I test it?

 

[PeterDonis]

Are electrons factually emitted by a source though we only observe pointer readings?

The pointer readings don't tell me how or where the electron was emitted, they tell me where the electron was detected. If I want to know where an electron was emitted, I design a source that tells me. If the source tells me an electron was emitted, yes, I will believe an electron was emitted even if I can't directly observe it--in short, I will believe that electrons exist.

Now compare this with "numbers exist". How can I build a "number source" or "number detector" analogous to the electron source and electron detector above?

 

[MathematicalPhysicist]

"Measurement" is just an empty phrase of instrumentalists. Literally "it's the process in which something is measured".

Now seriously. Even most physicists who despise philosophy believe that the Moon is there when nobody observes it. (Mermin, for instance, doesn't believe it, but most physicists do.) And the statement that "the Moon is there when nobody observes it" is an ontological statement. So even physicists who proudly claim that ontology is a meaningless word - do have ontological beliefs. True, the word "ontology" is not precisely defined (except in the work by Harriagan and Spekkens), but it doesn't mean that it doesn't have any meaning at all.

In fact, in any scientific or mathematical theory it is impossible to give a precise definition of all words, simply because any definition requires a use of some words which also need to be defined, but one cannot have an infinite regress and circular definitions are not allowed. So some words must remain undefined, which are called primitive. For instance, in the standard minimal interpretation of QM which denies the existence of the measurement problem, the notion of measurement itself is primitive. This means that adherents of this interpretation think that the notion of measurement is clear intuitively, so that it doesn't need to be precisely defined. Likewise, adherents of some other interpretations (e.g. Bohmian or many-world) often think that the notion of ontology is clear intuitively, so that it doesn't need to be precisely defined. Similarly, a QBist may think that the notion of information is clear intuitively, etc. Different interpretations can therefore be reduced to what notion one thinks to be clear intuitively so that it can be considered primitive.

You are bound to have primitive objects.
In set theory the "set" is that primitive in Category theory "Category" is that object.

But you still have circularity, since those objects define themselves, you can't escape circularity and infinite regress in science and philosophy and also in life.

 

[A. Neumaier]

When Platonists answer "yes" to this question, what difference does it make? What expectations should I have about possible future events, that I would not have if the answer were "no"? Or, to put it another way, if you claim that numbers exist, I should be able to test that claim somehow. How would I test it?

I didn't claim that metaphysical statements can be empirically tested. Their purpose is to organize understanding, not to enhance predictability.

 

[A. Neumaier]

If I want to know where an electron was emitted, I design a source that tells me. If the source tells me an electron was emitted,

How does a source tell you this? Just because a manufacturer claims it does?

Now compare this with "numbers exist". How can I build a "number source" or "number detector" analogous to the electron source and electron detector above?

Any random number generator provides a source of numbers.

 

[hilbert2]

In Euclid's Elements there's an attempt to define things like points and lines, which in modern thinking make no sense to attempt to define. "A point is something that has no parts".

Maybe in some language there's a different word 'exist' for something that exists physically and something that exists as a concept. But I think the existence of numbers is a bit more concrete than that of many other things people imagine. There can be a surprisingly good agreement about properties of numbers, at least if you discuss them with someone who can understand them to the same level.

 

[lavinia]

One meaning of ontology in Physics is the study of the nature space. I believe this has a long history but perhaps the modern ideas began with Newton's argument for Absolute Space, a preferred frame of reference in which the laws of Physics hold. While I do not know the physics it would seems that this would include all inertial frames of reference - in the sense of Galileo. I believe that Leibniz argued against Absolute space and used philosophical arguments to show that Absolute Space should not exist.

Newton also believed in Absolute Time.

Here is an article on Leibniz's philosophy. Take a look at section 5 Leibniz on Space and Time.

https://plato.stanford.edu/entries/leibniz-physics/#AgaAbsSpaTim

The article says that Newton called Absolute Space the sensorium of God. Leibniz countered that since space has parts that would mean that God has parts and this is not possible.

One question I would have for physicists is whether the idea of space as a manifold is a modified idea of Absolute Space. It seems that gravity is not intrinsic to the manifold itself but is a metrical relation that depends of the distribution of matter and energy and which is imposed on the underlying manifold. So while there is no preferred frame of reference there is nevertheless an underlying space.