Undergrad Is GRW theory an interpretation of quantum mechanics or a rival theory?

[Killtech]

There are axioms (ZF) of set theory, but they don't tell what a set is". For example, an inaccessible cardinal is a set, but there are no logical expressions that could define a specific inaccessible cardinal.

I'm not sure what you mean by "what a set is"? What isn't clear about a set from the axioms? Well, okay, in terms of ontology as the question of "what is", sets aren't made for this purpose, so they don't define a relation for such questions. But i am not aware of any definitions in math that handle it... so no different to any other objects in math.

not sure what you mean by a specific inaccessible cardinal set. Cardinality number of the real numbers can be written by a set and therefore represents a logical expression for it. Sure it's most probably not complete enough to decide all kind of statements about (like AC or NAC) it but it is a definition. The class of all cardinal numbers i think isn't a set but a class. Even so, it's still well defined but that definition will leave even more statements about it undecided.

 

[Jarvis323]

I would say no.

As I see it, in classical mechanics and in the basic kinematics, t is just a parameter in the model, that serves the purpose of indexing the order of events. Other than that, time is not something you can observe in itself. The only way to distinguish $t_{1}$ from $t_{2}$ is by means of some change, which is a measure defined in terms of some various $x$ (as that is the basics).

If one starts to question the metric in the time dimension, I think it's again is getting more complex.

From an abstract agent perspective of $x_{t}$ as just a set of distinguishable events, the $x$ are in my view just LABELS. ie. there is no intrinsic justification for imaginig a continuum of these events. It's easy to intuitively think of $x$ as real numbers. But in the reconstruction, they are to me nothing by labels. The continuum is something that needs motivation. Same with the index $t$, it's initially just an index defining and ORDER of the events. NO need to jump into thinking about a continuum as distinguishable events as something that makes sense. In fact I think there is a lot that would speak against this.

So the embedding of these lables into the continuum mathematics, is practical but I think can fool us. We are dressing things up, witout justification, and then forgets about what are the core and what's just a gauged dresssing.

/Fredrik

Intuitively, based on my limited understanding, the set of ontic mathematical objects in any dynamical theory should be sufficient to recover the state spaces of the systems.

 

[gentzen]

I'm not sure what you mean by "what a set is"? What isn't clear about a set from the axioms? ... But i am not aware of any definitions in math that handle it... so no different to any other objects in math.

not sure what you mean by a specific inaccessible cardinal set. Cardinality number of the real numbers can be written by a set and therefore represents a logical expression for it.

Even if you don't believe me, your questions have answers, at least answers which are accepted in certain communities. (Those communities don't especially like the Bourbaki treatment of set theory.) However, I would say this is offtopic here. There is a Set Theory, Logic, Probability, Statistics Forum. If you want, we can discuss it there.

 

[PeterDonis]

not sure what you mean by a specific inaccessible cardinal set.

It's a topic that belongs in the math forum on set theory, not here:

https://en.wikipedia.org/wiki/Inaccessible_cardinal

 

[PeterDonis]

There is a Set Theory, Logic, Probability, Statistics Forum. If you want, we can discuss it there.

Yes, please take discussion of set theory to a separate thread in that forum. It is off topic here.

 

[Demystifier]

What about time in $x(t)$ and $\phi(x,t)$? Is time considered ontic?

Good question! I would say yes, but in relativistic physics that's debatable.

 

[A. Neumaier]

I guess now we would need a new thread entitled "Learning the word "feels"", because obviously this word cannot be defined precisely.

Well, it is learned by osmosis... The human body responds to forces in a similar way as the spring; no qualia are needed!
The point is that forces are more real than position, and hence qualify more as being ontic, according to your defence of why position is ontic.

 

[Demystifier]

The point is that forces are more real than position, and hence qualify more as being ontic, according to your defence of why position is ontic.

I think you took one of my defences out of the context.

 

[A. Neumaier]

I think you took one of my defences out of the context.

Well, you said that you ''see position'' (though in fact you don't) to justify its ontic-ness. I didn't see a context that would remove the force of the argument (if it woukd have applied).

But I guess the real reason you consider position as ontic is because it is needed for Bohmian mechanics...

 

[Demystifier]

Well, you said that you ''see position'' (though in fact you don't) to justify its ontic-ness. I didn't see a context that would remove the force of the argument (if it woukd have applied).

The context is that it was only one in a series of hand-waving arguments, neither of which is sufficiently convincing by itself.

But I guess the real reason you consider position as ontic is because it is needed for Bohmian mechanics...

Actually, it's the other way around. The idea that position is ontic in classical mechanics is much older, from which Bohmian mechanics looks like a natural extension.

 

[Minnesota Joe]

Actually, it's the other way around. The idea that position is ontic in classical mechanics is much older, from which Bohmian mechanics looks like a natural extension.

Given this interesting information and given the Dürr and Teufel quote in post #21, I have another question if you don't mind. They wrote: "They must be there: a particle theory without particle positions is inconceivable." [emphasis mine]

If I take that claim literally, they are stating a necessary condition to have a particle theory. That seems to imply that "ontic" is the name for this relationship of necessity and that would explain why it is narrower than "real".

But that also seems to imply that what fixes the ontic quantities is what you take to be real in the first place (e.g. particles or fields or...)

What do you think of this?

 

[martinbn]

Actually, it's the other way around. The idea that position is ontic in classical mechanics is much older, from which Bohmian mechanics looks like a natural extension.

This is what you want, not necessarily what is. That's why your arguments are not convincing. You started with the conclusion (that you wish to be true) and then you try to find support for it.

You still haven't answered some of my questions. For example what is the ontology in classical field theory?

 

[Demystifier]

But that also seems to imply that what fixes the ontic quantities is what you take to be real in the first place (e.g. particles or fields or...)

What do you think of this?

Yes, but it's relative to a theory. Late Durr would say that you can't have a physical theory if you have not fixed what is your theory about. For instance, if you propose a speculative theory of unicorns, then, within the theory, unicorns are treated as ontic.

 

[Demystifier]

For example what is the ontology in classical field theory?

A field, e.g. scalar field $\phi(x,t)$. (In gauge theories it's a bit more complicated.)

 

[Demystifier]

This is what you want, not necessarily what is. That's why your arguments are not convincing. You started with the conclusion (that you wish to be true) and then you try to find support for it.

Suppose that you don't know what "beauty" means, so I try to explain it to you through an example. For example, cat is beautiful and cockroach isn't. Would you object that this is what I want, not necessarily what is? If you would you would miss the point, because the point is only to explain what the beauty means, not to decide which animals are beautiful and which aren't.

Or perhaps you have a better way to explain what "beauty" means?

And if you have no idea how is that related to "ontic", then you missed the point of the entire thread.

 

[martinbn]

Yes, but it's relative to a theory. Late Durr would say that you can't have a physical theory if you have not fixed what is your theory about. For instance, if you propose a speculative theory of unicorns, then, within the theory, unicorns are treated as ontic.

Then in the classical particle theory, it is the particles that are ontic.

A field, e.g. scalar field $\phi(x,t)$. (In gauge theories it's a bit more complicated.)

Which one? What if there are more than one way of describing the physical field in terms of mathematical fields? In classical electrodynamics what is ontic, $E$, $B$, $H$, $D$, $F_{\mu\nu}$,...?

 

[martinbn]

Suppose that you don't know what "beauty" means, so I try to explain it to you through an example. For example, cat is beautiful and cockroach isn't. Would you object that this is what I want, not necessarily what is? If you would you would miss the point, because the point is only to explain what the beauty means, not to decide which animals are beautiful and which aren't.

Or perhaps you have a better way to explain what "beauty" means?

And if you have no idea how is that related to "ontic", then you missed the point of the entire thread.

My problem is that you are not discussing like a scientist. You are not interested in finding things out. You are discussing like a member of school debate team. You simply want, through rhetoric, to present the best possible argument to support your position. You don't really care what is ontic or not, what you care about is how to make your case, which is BM is the way to go. As I said, I am probably wrong, but that's how it seems to me, and that's why I find it dificult to follow your reasoning. By the way is there anyone, who is not a BM supporter, who finds your arguments convincing?

 

[Demystifier]

Then in the classical particle theory, it is the particles that are ontic.

Yes. And the mathematical object that most directly represents the particle is $x(t)$. Unless you know an even better mathematical object, in which case I am ready to revise my claim above.

In classical electrodynamics what is ontic, $E$, $B$, $H$, $D$, $F_{\mu\nu}$,...?

In the theory before relativity theory, it was $E$ and $B$. In the modern relativistic version it's $F_{\mu\nu}$.

 

[Demystifier]

As I said, I am probably wrong, but that's how it seems to me, and that's why I find it dificult to follow your reasoning. By the way is there anyone, who is not a BM supporter, who finds your arguments convincing?

I believe that most supporters of ontic interpretations of QM would find my arguments convincing. This includes supporters of many worlds and objective collapse (GRW), who would not agree that particle positions are ontic in QM (and which I don't even claim in this thread), but would agree that particle positions are ontic in classical mechanics. That's because they understand what ontic means. On the other hand, supporters of non-ontic interpretations (shut up and calculate, Copenhagen, minimal statistical, QBism, relational, ...) have problems with understanding what ontic means, and contrary to my hopes, it seems that this thread does not help them much.

 

[Demystifier]

My problem is that you are not discussing like a scientist.

My problem is that there is no scientific definition of "ontic", so I must use more basic methods of teaching new words, through examples like in kindergarden.

 

[Minnesota Joe]

I believe that most supporters of ontic interpretations of QM would find my arguments convincing. This includes supporters of many worlds and objective collapse (GRW), who would not agree that particle positions are ontic in QM (and which I don't even claim in this thread), but would agree that particle positions are ontic in classical mechanics. That's because they understand what ontic means. On the other hand, supporters of non-ontic interpretations (shut up and calculate, Copenhagen, minimal statistical, QBism, relational, ...) have problems with understanding what ontic means, and contrary to my hopes, it seems that this thread does not help them much.

Well, if it's any consolation, it also helps kindergarteners like me who are trying to learn about physical theories in quantum foundations!

 

[PeterDonis]

It's compatible with common sense and basic intuition.

I don't think I agree. If an object hits me and knocks me off my feet, it's not the object's position that did it, it's the object's momentum. If I focus sunlight on a leaf with a magnifying glass and set the leaf on fire, it's not the position of the sunlight that did it, it's the sunlight's energy. If I put two objects in the two pans of a balance and watch what happens, it's not the positions of the two objects that determines what the balance does, it's their masses.

So my intuition says that all of those things are "ontic". Which may just mean that my preferred meaning of "ontic" is different from yours; but that just raises the question of why I should care about yours.

 

[TeethWhitener]

My problem is that there is no scientific definition of "ontic", so I must use more basic methods of teaching new words, through examples like in kindergarden.

There’s a philosophical distinction here that makes this assertion problematic. It seems like you’re saying that “ontic” has an extension (there is a list of things that are ontic) but not an intension (that list of ontic things might have nothing else in common with each other than simply being ontic).

The problem here is when we ask how the term ontic is any more useful than a made-up term like blergian. Typically, the usefulness of a term comes in its intension. Consider a famous example: analytic functions vs holomorphic functions. The two terms have the same extension (all and only analytic functions are holomorphic) but not the same intension (“analytic” does not mean the same thing as “holomorphic”). So without an intensional definition of ontic, it just seems like ontic is an arbitrary list.

 

[Demystifier]

I don't think I agree. If an object hits me and knocks me off my feet, it's not the object's position that did it, it's the object's momentum. If I focus sunlight on a leaf with a magnifying glass and set the leaf on fire, it's not the position of the sunlight that did it, it's the sunlight's energy. If I put two objects in the two pans of a balance and watch what happens, it's not the positions of the two objects that determines what the balance does, it's their masses.

So my intuition says that all of those things are "ontic". Which may just mean that my preferred meaning of "ontic" is different from yours; but that just raises the question of why I should care about yours.

I said basic intuition. Trained physicists have good intuition about momentum, energy and mass, but most people on the street don't. Yet all people have intuition about object's position. I can easily imagine a non-human civilization that did not develop concepts analog to our momentum, energy and mass, but I cannot easily imagine that such a civilization did not develop a concept analog to our position.

If I wanted to be more dramatic, perhaps I would even dare to paraphrase Kronecker by saying: God created positions, all else is the work of man.

 

[vanhees71]

I think this thread proves by empirical evidence that "ontic" is a completely irrelevant property, because it's not defined at all what it means. All that's relevant is what's observable, and all you need for a theory is that describes the observable facts (usually within a limited realm of applicability) correctly.

 

[Demystifier]

and all you need for a theory is that describes the observable facts

No, that's all what you need. As for ontic, some physicists need it, some don't.

 

[PeterDonis]

I said basic intuition. Trained physicists have good intuition about momentum, energy and mass, but most people on the street don't.

I disagree. I think the ordinary person on the street would understand the things I wrote about the real world effects of momentum, energy, and mass just fine, and would consider your claim that those things are not "ontic" to be daft. Your arguments about why position alone should be ontic are not based on "basic intuition", but on complicated physical theories that took centuries to develop and many expensive experiments to confirm.

 

[Demystifier]

I think this thread proves by empirical evidence that "ontic" is a completely irrelevant property, because it's not defined at all what it means.

People need a lot of concepts that are not defined at all. I already mentioned the concept of "beauty". Even in your sentence above, the words "I", "think", "irrelevant" and many others are not defined at all.

 

[Demystifier]

I disagree. I think the ordinary person on the street would understand the things I wrote about the real world effects of momentum, energy, and mass just fine, and would consider your claim that those things are not "ontic" to be daft. Your arguments about why position alone should be ontic are not based on "basic intuition", but on complicated physical theories that took centuries to develop and many expensive experiments to confirm.

OK, another try! I hope we all know what's the difference between kinematics and dynamics:
http://www.differencebetween.info/difference-between-kinematics-and-dynamics
What if I define ontic objects as objects that are studied by kinematics?

 

[physika]

One cubic metre of iron has more mass than one cubic metre of plastic. Explain that intuitively!

...well, space (volume) is not mass !

rather M=E/C²

.