The Measurement Problem and Ontology

[Iskar]

I have recently read a book called "Philosophie der Physik" ["Philosophy of Physics"] (Ed. by Michael Elsfeld, Suhrkamp, 2012) and came across a number of essays of philosophers (or people claiming they did philosophy) that desperately tried to make quantum mechanics compatible with ontology, especially struggling to "solve" the measurement problem or advancing it as a reason as to why quantum mechanics are flawed (rather than questioning their ontological presuppositions).

In short the measurement problem arises from two basic principles of quantum mechanics:
A) The development of a(n undisturbed) quantum system over time is described by a wave function that satisfies the Schrödinger equation. This treats the system as being to different degrees in all possible states at the same time.
B) When a measurement is conducted only one of a discrete spectrum of macroscopically observable states of the system is measured, commonly known as the "collapse of the wave function".
The first problem/question is now whether this collapse is actually a "physical" process and how the quantum system gets back to being described by a wave function after the measurement collapse.
As second order questions arise a number of issues as to the role of the measurement apparatus, considered as a large quantum system itself, the scale on which quantum and classical phenomena couple and why quantum phenomena never seem to reach our scale even though we can couple them to macroscopic objects.

There is a very good article on a website of Stanford University, that describes the issue in more detail. I found it very readable and can only recommend it.

By ontology as an umbrella term I mean any philosophical ansatz that presupposes the existence of the world (as entirety of all objects) independent of perception or claims the necessity to identify such ontic objects in any scientific theory. In some cases these positions are also referred to as different variations of realism.

The questions I'd like to hear your (well founded) opinions about are the following:

While a simple Kantian (veil of perception) or Cartesian (deceiving god/demon) argument shows that ontology makes untenable assumptions and cannot be proven true, the question remains whether we can prove it false, or at least render it unlikely to be true by showing that it conflicts irresolvably with our empirically supported theories of physics.
Of course quantum mechanics in its particular form is not strictly necessary, so the question amounts to asking: Does any theory that is in good accordance with our quantum level experiments necessarily contain an element that conflicts with ontology?

And secondly, can a careful epistemological analysis of the concepts used in the formulation of quantum mechanics resolve the measurement problem or is it a fundamental logical flaw of the theory? This entails the question in what way it even makes sense to speak of something as a physical process that we do not observe, the prime example being the development of a quantum system according to the wave function only when it is not being observed.

I haven't really made up my mind on this subject yet and I would be interested in what you think about it.

[Sphere]

It is also interesting to look at the similar issues surrounding string theory.

In QM you're only dealing with the wave function, and how "real" it is when you're not measuring it. But at least the wave function can only be formulated in one way. It is rather rigid mathematically if you want to match data.

In the mathematics of string theory there are many different (perhaps infinite) ways of matching data. This is because string theory assumes extra dimensions, and interactions between these hidden dimensions and ours. You have many ways to calibrate the extra-dimensional framework and still match the data we can observe in our 3+time. So the question comes up how "real" are all these things going on in the other dimensions? Is string theory even scientific?

But then again why should you be more or less okay with the wave function doing non-measurable things, but not be okay with non-measurable things going on in other dimensions, if all you're worried about is matching data? I think there is a difference, but it isn't easy to describe.

[Iskar]

I think there are two important differences between QM and ST:

In contrast to string theory, QM makes falsifiable predictions about the outcome of experiments that directly relate to the mathematical objects of the theory, which is crucial for a scientific theory.

The other point is less scientific, but string theory so far does not explain more than QM (or its derivatives quantum chromo/electro/etc. dynamics) and hence falls prey to Ockham's razor.

Apart from hijacking my thread to talk about string theory, any thoughts on the original questions?

[Kyriakos]

Shouldn't you also provide a definition of the concept of ontology, given you did so for so many other terms in the OP?

In very modern philosophy there is a 'catchy' distinction between ontology and phenomenology, ie that the first means (examining) things that "exist", the second means examining things which "appear" as something.
Both terms (on, phenomenon) are Greek, and mean "being" and "appearance".

So an ontology is mostly supposed to be an examination of whether things (notions or objects of other kind) actually exist regardless/independent of any system of perception which has to be there so as to pick them up as appearances.

This is not really a question tied to physics, almost at all, cause (as early as Parmenides at least, and likely a lot earlier- eg Heraklitos or Pythagoras) arguably the more elaborate view in Philosophy is that it is one thing to examine something via thought or thought tied more directly to a sense of it, and a very very different (or all-together different) thing to speak of that something as it is "by itself".

The notion of "a thing by itself" is again in existence in philosophy at least as early as Heraklitos, ie late 6th century BC. It also is notably one of the most used terms in Plato.

*

So, to be more brief still, in my view your question is not examinable in Philosophy, cause what you mean by "Ontology" is a watered-down version of the debate on things existing or not, much like modern notions such as 'idealism' are equally watered down versions of eleatic theories of complete break between finite (eg human) intellect and some supposed "absolute" existent "reality".

[Iskar]

Thanks for pointing out the missing clarification. I inserted a paragraph in the OP.

This is not really a question tied to physics, almost at all, cause (as early as Parmenides at least, and likely a lot earlier- eg Heraklitos or Pythagoras) arguably the more elaborate view in Philosophy is that it is one thing to examine something via thought or thought tied more directly to a sense of it, and a very very different (or all-together different) thing to speak of that something as it is "by itself".

That is precisely the position that I challenge. I would argue that it is impossible to examine something via thought without being tied to a sense of it, for what is "something" if not a bundle of perceptions that we have labelled by a name? Finally to consider something as it is "by itself" is yet to be made understandable to me (feel free to undertake this endeavour).

If you still do not like the questions from the OP you might consider the alternate question whether accepting QM as a viable and in a wide vairety of settings experimentally well supported theory has any implications on philosophical reasoning a posteriori.

[Kyriakos]

Thanks for pointing out the missing clarification. I inserted a paragraph in the OP.



That is precisely the position that I challenge. I would argue that it is impossible to examine something via thought without being tied to a sense of it, for what is "something" if not a bundle of perceptions that we have labelled by a name? Finally to consider something as it is "by itself" is yet to be made understandable to me (feel free to undertake this endeavour).

If you still do not like the questions from the OP you might consider the alternate question whether accepting QM as a viable and in a wide vairety of settings experimentally well supported theory has any implications on philosophical reasoning a posteriori.

I should note that i never like editing my own posts, which is why i did not edit my own here a bit so as to sound not hostile (which i suppose i did, sorry about that! it was not my intention).
Now to go on to your new post, and the "thing in itself" etc:

One is not supposed to examine what a "thing in itself" is. You cannot. It is axiomatically (and logically) merely a dot in the horizon of our thought, cause it means what something would be if it was not inevitably picked up/examined/sensed through particular impressions and mechanisms we have which form them.

In ancient Greek philosophy one of the distinctions of paramount importance is the one between so-called Substance (Ousia in Greek), and Eidos/Archetype (Eidos means type of something). Most of the philosophers prior to Socrates were of the view that there isn't a 'reality' by itself, or at least that would not be in existence or would not be in any human grasp or meter. So the notion of the Substance is there to mean that "if something IS something (eg if it is sensed as something, in one context, but also if it "is" in more absolute ways) then it is that something because it has the substance of being that. This is not circular, though, cause substance has a very special element to the notion: Substance is something formed only when a being able to sense an object and that object come into some kind of contact. Eg if i see a chair i am the being which has the ability to see it (thus), and the chair is something which has the ability to be seen. So for me it appears in that form and with some traits. But Substance exactly connotes that this examination or sense is only 'real' in the context of a balance of different powers, an observer and the observed.

By contrast, Eidos (a Socratic notion) is tied to the Parmenidian way of arguments, ie that ultimately there is some stable and eternal Reality, which is independent of human views. Plato/Socrates water that down a bit to claim that through philosophy we can at least observe a shadow of a shadow of that reality. Parmenides claims we are utterly locked out of that Reality.

Also recall the famous line by Protagoras, that "Man is the meter of all things" etc

[Sphere]

Apart from hijacking my thread to talk about string theory, any thoughts on the original questions?

The more I wrangle with it, the more I come back to Heisenberg. Measurement has to anchor our understanding of reality. At the same time, we have to accept that our understanding will always be flawed.

That being said, from a purely aesthetic viewpoint I find Everett-Wheeler (i.e. many worlds) incredibly elegant. The Wave function itself is elegant, but wave function collapse is ugly. Everett-Wheeler gets rid of the need for collapse without adding on any junk to the wave function. You just need infinite universes which we cannot interact with.

[Iskar]

You just need infinite universes which we cannot interact with.

"just"...

I agree that it is a very elegant way to get rid of the collapse, but to me it seems like it would very quickly succumb to a philosophy-of-science-version of Ockham's razor. Also, solving an intrinsic problem by postulating something extrinsic seems to be less elegant on the meta-level of the question. If we cannot measure this (probably even uncountably) infinite number of universes in any way, then the concept itself is of no scientific relevance whatsoever and seems to veer off to the religious sphere: Saying "God fixes the wave function." (maybe I should have waited for basics to say so to save me the writing, heh) is not qualitatively different from claiming infinitely many, unmeasurable universes, although the latter is more sophisticated.

[Sphere]

I agree that it is a very elegant way to get rid of the collapse, but to me it seems like it would very quickly succumb to a philosophy-of-science-version of Ockham's razor.

It depends on what you are trying to minimize in Ockham's razor. Are you trying to minimize equations or universes? Everett-Wheeler is mathematically simple, it is basically one equation. And in terms of infinite universes, QM is half-way there already. When you do a Feynman sum over all possible histories, those histories are in some sense "real". The split is in how "real" they really are. Whether many-worlds is just a trivial restatement of QM, or revolutionary.

But that's neither here nor there in terms of the aesthetics. Everett-Wheeler allows a determinate and complete description of the entire universe using one wave function. That is elegant, even if it's scientific validity/falsifiability is questionable.

[Kyriakos]

^It is the issue of wanting to form any part of the system through fundamentals of the system being synthesised or altered in other "basic" manners, but this always means you have to set some stable axioms which are not meant to be examined in the system anyway (do not follow from the system; they are its basis, and in a sense they exist just after a limit to reach there).

Parmenides (the dialogue) goes to length about that.

The only other way indeed is to have some extrinsic postulate being used as somehow co-existing with the system. But that means you now use things not following from each other in a way which itself is not an axiom, and moreso you now have moving axioms inside your system apart from immobile base-axioms.

[Iskar]

I have been thinking about the Everett-Wheeler solution and there is one thing that bothers me in particular.

We have that very fruitful paradigm in science that when you find a valid mathematical representation of a physical phenomenon and then apply mathematically valid operations to that representation, then the resulting mathematical expressions should still/again correspond to a meaningful physical concept. (One of the most beautiful examples of this being Dirac's prediction of antimatter from the negative solutions of a quadratic energy equation.)

Now, if there is one wave function representing the entire universe, then this function gives rise to a at least one dimensional vector space of wave functions, namely the (complex, real, quaternionic?) multiples of that function. What do they represent, however? In particular, what would the zero wave function stand for?

[Kyriakos]

I have been thinking about the Everett-Wheeler solution and there is one thing that bothers me in particular.

We have that very fruitful paradigm in science that when you find a valid mathematical representation of a physical phenomenon and then apply mathematically valid operations to that representation, then the resulting mathematical expressions should still/again correspond to a meaningful physical concept. (One of the most beautiful examples of this being Dirac's prediction of antimatter from the negative solutions of a quadratic energy equation.)

Now, if there is one wave function representing the entire universe, then this function gives rise to a at least one dimensional vector space of wave functions, namely the (complex, real, quaternionic?) multiples of that function. What do they represent, however? In particular, what would the zero wave function stand for?

Why would a math construction or system have to represent a physical phenomenon in the first place?

Unless you do not ask about a 'reality' anymore, but about specific phenomena for a human intellect, where math is obviously a tool to define or model stuff, including our human impressions of external phenomena or material qualities. Matter is obviously picked up by our senses, in some measures of it. This doesn't mean it has to be real outside of the human senses and notions tied to those. Maybe 'matter' is not real at all for an equally intelligent alien observer, who just has no sense of matter.

[Iskar]

Why would a math construction or system have to represent a physical phenomenon in the first place?

It does not have to, but once you have found a viable mathematical representation of a physical phenomenon by the interaction of hypothesis and experiment, then a valid mathematical operation on the representation should - within a certain expectable deviation - again represent a physical phenomenon.
E.g. Dirac solved the relativistic energy equation for the electron, which is a quadratic equation and hence yields two solutions, in that case one of positive and of negative energy. While the former one represented the energy of an electron, the latter, negative, one did not seem to have any physical correspondence, but later turned out to accurately predict positrons, the anti-particle of the electron.

Unless you do not ask about a 'reality' anymore, but about specific phenomena for a human intellect, where math is obviously a tool to define or model stuff, including our human impressions of external phenomena or material qualities. Matter is obviously picked up by our senses, in some measures of it. This doesn't mean it has to be real outside of the human senses and notions tied to those. Maybe 'matter' is not real at all for an equally intelligent alien observer, who just has no sense of matter.

What is a reality if not a collection of phenomena for a human intellect?
What is matter supposed to be, except a physical concept?

[Kyriakos]

It does not have to, but once you have found a viable mathematical representation of a physical phenomenon by the interaction of hypothesis and experiment, then a valid mathematical operation on the representation should - within a certain expectable deviation - again represent a physical phenomenon.
E.g. Dirac solved the relativistic energy equation for the electron, which is a quadratic equation and hence yields two solutions, in that case one of positive and of negative energy. While the former one represented the energy of an electron, the latter, negative, one did not seem to have any physical correspondence, but later turned out to accurately predict positrons, the anti-particle of the electron.

Let's use an example from physics more people who are laymen would know of readily, ie the one in Newton and identities about gravitational force and momentum. You there use some identity having to do with relatively simple stables, powers of squares, and concepts of energy due to position and due to ability to alter to other states. (also derivatives and antiderivatives, but those are approximations as well, and i doubt they need to be in this discussion- let alone i am not that well-versed in those ).
All that is ok, but it is entirely tied to concepts you have due to having a sense of more primary qualities, such as matter, weight, movement, fall, alteration by spinning or changing position, and any erosion of the objects states. All that is not there because it was picked up in math, but because they are mental impressions of sensory stuff. The math, on the other hand, is more purely a mental system of thought. This already means you translate something not specifically mental (physical world) to something mental but a specific and bounded system from axioms (math systems). To try to use this math system and models to present a reality of physical objects is analogous to trying to ask a child who doesn't speak english to write his life story in english; the child may start writing if it can at least understand what you are asking, but it definitely won't be in english.
But you asked for english. Much like you asked for a math account. What you will get can either be nothing (no examination), or something in english, but evidently that something will be inherently impossible to be what you asked for (a depiciton of a reality of the external object which would not be entirely particular to the non-isomorphic language you want to use, math for external things).

What is a reality if not a collection of phenomena for a human intellect?
What is matter supposed to be, except a physical concept?

Yes, human science is examining the above reality (including math, which has a slightly different position, but is still human-tied), and only that one. I am not claiming it should not. I am noting that it is a human reality, and objects are not really having to do with humans in the first place. You can shape a statue out of copper, and the form of the statue has an intended meaning for humans. This does not mean that the copper also does. Nor that the copper has any property humans pick up in it through senses or following mental examination. It is examined as a reality with humans as the meter of a reality.

[Sphere]

Why would a math construction or system have to represent a physical phenomenon in the first place?

Why was God a mathematician? There isn't an answer to that.

[Kyriakos]

Why was God a mathematician? There isn't an answer to that.

I don't think a god is a mathematician. If a god exists (it might, given what one means by it, of course ) i think it is likelier that the god would not be distinct from anything 'real', and so could not be making something either. If a god was creating things then that god would have a reason to create them, either a reason as we deem reasons, or a reason in a manner which renders reason a non-deliberating ability, AND more crucially that new ability we cannot grasp again cannot be just a next level above just us, but all next levels.
But if something is 'all next levels', then it is also all levels, lest we have to use at least a dualism (just one parameter is different than the others). If something is all levels then it is not a level, cause a level rises from separation from something. Either something that the thing is already, or something it is not yet. In both cases, again, the level is at One (wait, too much Parmenidian stuff for tonight, it is 11.10 here and i will go to sleep ).

My own general feeling is that if something worth to be termed a god does exist, that something is in no way conscious as we use that term.

[Iskar]

All that is ok, but it is entirely tied to concepts you have due to having a sense of more primary qualities, such as matter, weight, movement, fall, alteration by spinning or changing position, and any erosion of the objects states. All that is not there because it was picked up in math, but because they are mental impressions of sensory stuff. The math, on the other hand, is more purely a mental system of thought. This already means you translate something not specifically mental (physical world) to something mental but a specific and bounded system from axioms (math systems).

I should probably be clearer here, so as not to cause confusion:

We use physical concepts such as matter, weight, movement, etc. to first describe something we perceive, then we quantify this description, i.e. we formulate it mathematically and assign mathematical objects (usually represented by variables) to the physical concepts/observables. Once we have obtained a working mathematical model this way we can work with this model and correct mathematical operations of the model are supposed to lead to new mathematical statements, containing the same or some of the variables representing physical observables. The paradigm is now that these new mathematical statements, when reinterpreted as statements about the physical observables that initially gave rise to the first mathematical statement, give a new, valid statement about the physical observables.

E.g. you have, by quantifying observation of movement obtained an equation that involves the distance covered by a piece of matter. If you now apply a time derivative to the entire equation, which is a purely mathematical operation, then the result is supposed to give you a reliable prediction of the physically observable time derivative of the position, i.e. the velocity.

This already means you translate something not specifically mental (physical world) to something mental but a specific and bounded system from axioms (math systems).

There is no qualitative difference between perceptions of physical "objects" and mathematical considerations. None can escape the immanence of the mind. Supposing an independent physical world is an untenable ontic presupposition.

[Gaidin]

All that is ok, but it is entirely tied to concepts you have due to having a sense of more primary qualities, such as matter, weight, movement, fall, alteration by spinning or changing position, and any erosion of the objects states. All that is not there because it was picked up in math, but because they are mental impressions of sensory stuff. The math, on the other hand, is more purely a mental system of thought. This already means you translate something not specifically mental (physical world) to something mental but a specific and bounded system from axioms (math systems).

Which system are we using? The finite one, the countably infinite one, or the uncountably infinite one?

[Kyriakos]

I should probably be clearer here, so as not to cause confusion:

We use physical concepts such as matter, weight, movement, etc. to first describe something we perceive, then we quantify this description, i.e. we formulate it mathematically and assign mathematical objects (usually represented by variables) to the physical concepts/observables. Once we have obtained a working mathematical model this way we can work with this model and correct mathematical operations of the model are supposed to lead to new mathematical statements, containing the same or some of the variables representing physical observables. The paradigm is now that these new mathematical statements, when reinterpreted as statements about the physical observables that initially gave rise to the first mathematical statement, give a new, valid statement about the physical observables.

E.g. you have, by quantifying observation of movement obtained an equation that involves the distance covered by a piece of matter. If you now apply a time derivative to the entire equation, which is a purely mathematical operation, then the result is supposed to give you a reliable prediction of the physically observable time derivative of the position, i.e. the velocity.


There is no qualitative difference between perceptions of physical "objects" and mathematical considerations. None can escape the immanence of the mind. Supposing an independent physical world is an untenable ontic presupposition.

I am of the view that there is partially qualitative difference between perceptions through senses, and mathematical presentation. Yes, both are parts of our human intelligence/being. But the former is a routine running without the code being an axiom set by us, the latter is an examination of what setting a code by axioms leads to.
As for beings existing in some 'reality' independent of any sensed/examined by specific observers: They might exist in such a reality, or they might not. But surely in either case it is evident that our own reality of them is particular to us and thus not some kind of archetype or connection to a reality stable for any being?

@Gaidin: Do elaborate. The concept of infinity itself is something placed in set systems, as a sense of limit to or away from them you can keep observing or theorising. If you refer to Cantor, then what are you suggesting about the differently deemed progressions of infinite things?

[Gaidin]

@Gaidin: Do elaborate. The concept of infinity itself is something placed in set systems, as a sense of limit to or away from them you can keep observing or theorising. If you refer to Cantor, then what are you suggesting about the differently deemed progressions of infinite things?

I'm talking about applied mathematics insofar as the qualities you listed that I quoted.