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

[Demystifier]

Inertial mass!

Both inertial and gravitational mass are coupling constants in classical Newtonian mechanics, but that's not really important here.

 

[Demystifier]

So does "ontic" mean dynamical variable in a Lagrangian?

No.

and I'm not aware of physically relevant cases where acceleration shows up in the Lagrangian.

Second time derivatives of metric appear in the Einstein-Hilbert Lagrangian for gravity. But the second derivative terms can be written as a total derivative, so they don't contribute to the equations of motion.

 

[TeethWhitener]

The point is this: If you know the trajectory of the particle ##x(t)##, then knowledge of mass ##m## serves no purpose. The mass only serves to find ##x(t)## by solving a dynamical equation of motion, such as the Newton equation
$$m\ddot{x}=F(x)$$
In fact, ##m## can be eliminated by defining ##f(x)\equiv F(x)/m##, in which case the Newton equation becomes
$$\ddot{x}=f(x)$$

More generally, dynamics of a point particle is defined by a Lagrangian ##L(x,\dot{x})## and the equation of motion
$$\frac{d}{dt}\frac{\partial L}{\partial\dot{x}}=\frac{\partial L}{\partial {x}}$$
In general, ##L## does not need to depend on the mass ##m##. In this sense, classical mechanics is not about ##m##. It is about ##x(t)##.

I admit, this is all very confusing. In general, ##L## doesn't depend on ##x## or ##t##, unless spatial or temporal symmetry is broken. And if you know the trajectory of the particle, why would the velocity serve any purpose?

Can you provide me with an ontic quantity that is not a dynamical variable of the Lagrangian or its time derivative?

 

[martinbn]

Both inertial and gravitational mass are coupling constants in classical Newtonian mechanics, but that's not really important here.

For which interaction?

 

[Demystifier]

Can you provide me with an ontic quantity that is not a dynamical variable of the Lagrangian or its time derivative?

In classical mechanics, no. In Bohmian mechanics, particle trajectory ##x(t)##.

 

[Demystifier]

For which interaction?

How would that help you to grasp the notion of "ontic"?

 

[Demystifier]

And if you know the trajectory of the particle, why would the velocity serve any purpose?

See item 2. in post #1. It doesn't serve any additional purpose, but it's directly encoded in the ontic trajectory so it's ontic itself.

 

[A. Neumaier]

I see position, I don't see momentum.

I never saw position. I see extended objects in space. I feel forces.

Have you ever seen a real particle constrained to move along a circle? I did, in a roulette. It had well defined all three position coordinates ##x,y,z##.

These are not well-defined real numbers (as in Bohmian mechanics) but are both observer-dependent and inaccurate.

 

[martinbn]

How would that help you to grasp the notion of "ontic"?

And you not answering will help how? In any case you brought it up!

So far what i understand is that ontic must include particle position, and must exclude momentum. That's the only reason, that I can see, you so strongly insist that mass is not ontic. And the whole purpose is that it helps you to think about some questions.

Are you eventually going to talk about classical fields too. For example what is ontic for the electromagnetic field? The ##E## and ##B##? Or for a scalor field.

 

[Demystifier]

I never saw position. I see extended objects in space.

Fair enough, it can be a good motivation for introducing field ontology instead of particle ontology. (As you might know, some versions of Bohmian QFT are based on field ontology instead of particle ontology.)

I feel forces.

Yes, but feelings cannot be measured. Treating feelings as ontic generalizes to treating qualia as ontic, which is fine, but probably doesn't help much in understanding physics (unless you accept that wf collapse is related to consciousness).

 

[A. Neumaier]

Yes, but feelings cannot be measured.

A spring feels forces, too, which is used to measure them.

 

[Demystifier]

A spring feels forces, too, which is used to measure them.

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

Alternatively, to avoid a use of that word, I would say that the spring just moves the way it moves and a regularity of this motion can be described by an abstract mathematical quantity we call force.

 

[gentzen]

So far what i understand is that ontic must include particle position, and must exclude momentum. That's the only reason, that I can see, you so strongly insist that mass is not ontic.

I would say that in classical mechanic, momentum will be ontic for some formulations, and not ontic for others. But independent of this, mass would not be ontic. It is not ontic, because it is just some constant in some law. But if you include relativistic effects, then mass becomes more than just a constant, therefore mass might become ontic for some formulation.

 

[martinbn]

I would say that in classical mechanic, momentum will be ontic for some formulations, and not ontic for others.

I think @Demystifier will disagree. To me it seems that for him it is very important that momentum is not ontic.

But independent of this, mass would not be ontic. It is not ontic, because it is just some constant in some

But that constant characterises the object in a way that almost means "amount of stuff". Why would that not be ontic!?

But if you include relativistic effects, then mass becomes more than just a constant, therefore mass might become ontic for some formulation.

Invariant mass is still just a constant. But if you include relativity, then coordinates seem not ontic.

 

[Jarvis323]

I am trying to underand more. So ontic is not a word you can use in physics independent of the theory that sets the context right.

Is there value in classical physics to ask what is ontic beyond as a mental excersize and to understand the concept? Or do we need it as a way to have a common sense picture of classical physics that assigns physical meaning to the mathematical objects.

Say we then move on to the theory of relativity. Now we think about what is ontic again, and we have our commen sense picture that assigns physical meaning. We will have a new meaning of ontic as well. Does it matter if the common sense picture we have now contradicts the one we had with classical physics?

Our common sense picture needs to be right? Or is just an exersize, and/or for comfort, or entertainment?

Now we do the same in QT. Because QT is supposed to describe the microscopic world on a fundamental level, ontic now has more weight? We are talking again just about common sense pictures of the mathematical objects with the same motivation and goal? Or, if we assumed that QT were the complete lowest level description of reality, does this imply that what is ontic in QT is absolutely real? This is what I don't understand the most, what is the end game. If we prove QT is complete, and we prove A is ontic in QT, then we've proven something about the true physical meaning and existence of A?

 

[Killtech]

Even in pure math, if I say "The set exists", no mathematician will ask me to define "The", to define "set" or to define "exists"

Hmm, well Bourbaki would disagree as their starting point in discussing mathematics was... we need to define the word "set" first before we can talk anything else. Also "exist" implies the prior is well defined. There was enough discussion in mathematical logic to what that means so everyone could start on the same page. But fair point, frequently used worlds in mathematical language like "the" or "let" and alike are never formally defined.

1. In classical mechanics, the particle position as a function of time x(t) is ontic. Its Fourier transform x~(ω) is not ontic.
2. In classical mechanics, anything that can directly be derived from x(t) is ontic

These two statements sound like a contradiction to me?

The meaning of "directly" also has to be learned through examples. For instance, the velocity x˙(t) and acceleration x¨(t) are directly derived from x(t). The momentum p(t)=mx˙(t) and the force F(x) are not directly derived from x(t).

I'd rather say that would be a convention. I don't think classical mechanics states what is ontic or not. You could just as well assume the momentum is ontic instead of the velocity.

Think of it this way: if you had to code a simulation of classical mechanics, then all the objects that your application will store in RAM memory could be considered ontic (their information exists in a very direct way). In this scenario, you will find there are very many possible implementations that yield the same simulation and each uses very different convention of what to make ontic. And you can either save the velocity or momentum in memory - or you could take both, which however is likely to run into consistency bugs, so it's better not to have such redundancy.

In principle any minimal implementation could decide to store any (bijective) transformations of the quantities you described above as it's fundamental objects it deals with - instead of what you called ontic. If we really lived in the Matrix as in the films, how would you really know it's not implemented via Fourier transforms of everything? Don't make the mistake of common sense: it is merely a representation of our primary perception (our eyes) and the neural net in our brain to process the data from it. So if you would question blind people you may very easily encounter a different common sense then yours. In particular, they will probably perceive momentum as much more impactful then velocity.

From those examples, one can use intelligent extrapolation to determine whether many other concepts in classical physics are ontic or not. (But in some cases it may not be obvious, so we may have have different interpretations of classical physics. That's particularly true in the theory of relativity.)

I don't think you can uniquely attribute concepts like "ontic" to a quantity in general due to the problem above. You require some additional convention to fix it. Consider choice of ontic quantities being like a specification of coordinates for your theory. That analogy shows the problem: any choice works.

 

[gentzen]

I think @Demystifier will disagree. To me it seems that for him it is very important that momentum is not ontic.

Fine, maybe he will disagree. Perhaps he has good reasons why. I would first have to hear them, before I consider changing my opinion. To me it seems that for him, being able to use words like ontic, ontology, ontologial, or nomological (or rather the concepts corresponding to those words) and be properly understood is what is very important. My impression is that he uses momentum just as an example to clarify his understanding of those words.

Invariant mass is still just a constant.

But for the non-relativistic approximation, the invariant mass is not helpful, neither for Newton's law of gravitation, nor for the relation between velocity and momentum.

 

[Fra]

As mass is somehow confined energy in space, "reconstructing" a mass concept properly first needs a proper reconstruction of both space and energy concepts. And constructing space from distinguishable events, would involve both some embedding dimensionality and a metric.

If we think of the ##x(t)## as the basic kinematical variables, maybe this is the logic of Demystifier?

Mass would instantly bring us into dynamics, which is a more complex matter.

Even in my abstract agent interpretation, the set of distinguishable events, is the absolute most basic thing. But next up, one wants to construct various counts and measures of this, to form "expectations", and one then soon find that one needs to introduce a concept of "amount of evidence" ~ memory, that effectively works as an "inertia" in the information revision process.

/Fredrik

 

[Fra]

Invariant mass is still just a constant.

This is one of the problem of mathematical models, a lot of things are just empirical "parameters". These you tune/calibrate = determine experimentally. But once one starts to ask what is the origin of mass (ie what determines the VALUES of the "parameters"), then one needs a deeper grip of things to add explanatory value. Like what is the conceptual function of mass? What we know is that it relates to inertia and gravitation, so we apparently need to understand intertia and gravitation to get deeper.

/Fredrik

 

[Demystifier]

If we think of x(t) the as the basic kinematical variables, maybe this is the logic of Demystifier?

Yes.

 

[Demystifier]

Hmm, well Bourbaki would disagree as their starting point in discussing mathematics was... we need to define the word "set" first before we can talk anything else.

Offtopic, but what's their definition of set? I think set in set theory is primitive, i.e. cannot be defined precisely in terms of something more elementary. There are axioms (ZF) of set theory, but they don't tell what a set is.

 

[Minnesota Joe]

From those examples, one can use intelligent extrapolation to determine whether many other concepts in classical physics are ontic or not. (But in some cases it may not be obvious, so we may have have different interpretations of classical physics. That's particularly true in the theory of relativity.)

When one grasped the meaning of "ontic" in classical physics, one can start to think and talk about "ontic" in quantum physics.

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

 

[Killtech]

Offtopic, but what's their definition of set? I think set in set theory is primitive, i.e. cannot be defined precisely in terms of something more elementary. There are axioms (ZF) of set theory, but they don't tell what a set is.

Sets are defined in an axiomatic way, but it is a definition. Algebraic objects (groups, rings, fields, ...) are usually defined in a similar fashion. What you mean is that sets are not constructed out of something else and that is true. There is the {} symbol notation to define set expressions which does not have it's own rigorous definition i think, though all elements one can use there are logical symbols and "element of" relation. It however allows you to write down Russels paradox. Generally the expressions that are not enough to satisfy being sets yet well defined to accept them anyway are named classes.

So sets are logical expressions that additionally satisfy set theory axioms. the "element of" relation is implicitly defined along with sets by the same axioms.

Sets therefore initiate the transition from logical expressions to working with mathematical objects. But each mathematical object still represents a very lengthy list of logical expression that define it. Elements of a set inherit a huge part of that list allowing for a very handy notation to say so much about a thing by writing so little (maths are lazy). And that makes us not think of it in such a way and perceive it as an actual object.

Hmm, as such set theory maybe allows for an analogy: It is similar in function to a C++ compiler (or other language) that allows us to write higher language code that is nicely understandable for humanes but that still evaluates to a very nasty assembler / machine language expressions composed of only very elemental/basic operations so the code still can be evaluated by simple Touring machines.

 

[Fra]

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

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

 

[gentzen]

Generally the expressions that are not enough to satisfy being sets yet well defined to accept them anyway are named classes.

So sets are logical expressions that additionally satisfy set theory axioms. the "element of" relation is implicitly defined along with sets by the same axioms.

I would say that Demystifier is right, both with "Offtopic" and with "set in set theory is primitive, ... 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.

 

[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.