Fundamental reality: Hilbert space

[Giulio Prisco]

What do you guys think of this soberly elegant proposal by Sean Carroll?

Reality as a Vector in Hilbert Space

Fundamental reality lives in Hilbert space and everything else (space, fields, particles...) is emergent. Seems to me a step in the right conceptual direction.

 

[A. Neumaier]

Fundamental reality lives in Hilbert space and everything else (space, fields, particles...) is emergent.

It is a well-known fact that the opposite holds:

Hilbert space emerged in the 1920s from the more fundamental reality of having to understand quantum mechanics.

Mathematical concepts can describe aspects of, but they can never be physical reality.

 

[martinbn]

It is so sketchy that I am not even sure if it makes any sense. Just because one can form gramatically correct sentances, it doesn't mean that it has any content.

 

[Giulio Prisco]

Mathematical concepts can describe aspects of, but they can never be physical reality.

Well it seems to me that if an abstract mathematical concept seems to provide a correct description of physical reality, and if any more intuitive description seems to fail, and if all that is repeatedly confirmed without exceptions, then the mathematical concept itself is the only statement that we can make about physical reality. Whether this means that the mathematical concept is physical reality, I don't know.

 

[PeterDonis]

What do you guys think of this soberly elegant proposal by Sean Carroll?

I think his description of this as an "extremist" position is correct.

 

[A. Neumaier]

the mathematical concept itself is the only statement that we can make about physical reality.

A concept is not a statement about reality but a language construct.

We know that space and time are real (in the ordinary sense of the word) since we live in it, and these concepts were there long before mathematics. The mathematical description of it had to wait till the 1600s.

On the other hand, nobody has ever seen a physical Hilbert space. Calling it more real than the physical space we live in is selfdelusion.

 

[Giulio Prisco]

It is so sketchy that I am not even sure if it makes any sense.

Sketchy it certainly is. This is a research program, not a research result.

But I think it does make sense.

Think of field vs. particle ontologies in quantum field theory. Particles are easier to visualize and the theory was built up with particles in mind, at least at the beginning. But today there seems to be ample consensus on the idea that fields are fundamental, and particles are an emerging aspect of reality that we observe when we do this or that to observe the field.

It seems to me that Carroll is just pushing this approach one step further down. What really is, the thing itself, is a vector in Hilbert space. Our current description of the world, with fields and particles and things and all that including you and me, is emergent.

For those who like Everett's interpretation, in his last book Carroll argues that all Everett worlds live in the universal reality vector, and the "many worlds" of the popular interpretation of Everett's interpretation are emergent.

It seems to me that this sketchy preliminary proposal could be pursued further to define our description of the world in terms of the universal reality vector and show how it emerges.

See also this post by Scott Aaronson, which seems related.

 

[Giulio Prisco]

We know that space and time are real... On the other hand, nobody has ever seen a physical Hilbert space. Calling it more real than the physical space we live in is selfdelusion.

Didn't they use to say exactly the same thing about atoms?

Yet today atoms (and subatomic entities) form the basis of our consensual understanding of reality.

 

[vanhees71]

A concept is not a statement about reality but a language construct.

We know that space and time are real (in the ordinary sense of the word) since we live in it, and these concepts were there long before mathematics. The mathematical description of it had to wait till the 1600s.

On the other hand, nobody has ever seen a physical Hilbert space. Calling it more real than the physical space we live in is selfdelusion.

Well, know enter this debate about the meaning of the words "real" or "reality". I think there are as many different meanings of this word as there are philosophers using it.

I'd say for the standard bread-and-butter physics all what's real are obejctively observable phenomena. Mathematics is used to describe these phenomena. Why should be Euclidean 3D affine space (a purely matheamtical construct of the human mind) be "more real" than a separable Hilbert space (another purely mathematical construct of the human mind)? Both mathematical constructs are used successfully in the mathematical description of the observable phenomena on different levels of such a description and with different realms of validity.

 

[A. Neumaier]

Didn't they use to say exactly the same thing about atoms?

Yet today atoms (and subatomic entities) form the basis of our consensual understanding of reality.

For the understanding of reality, but not for reality itself. This makes a big difference!

Why should be Euclidean 3D affine space (a purely mathematical construct of the human mind) be "more real" than a separable Hilbert space

Both are just concepts. Real (in the ordinary sense of the word; I don't care about the philosopher's Spitzfindigkeiten) are space and time, not their description in terms of mathematical concepts.

 

[Giulio Prisco]

Real (in the ordinary sense of the word; I don't care about the philosopher's Spitzfindigkeiten) are space and time...

I don't disagree, but are you conflating the concepts of ordinary and fundamental reality? I'm trying (at least here) to keep them separate. Fundamental reality is that thing from which you can derive a complete and consistent description of ordinary reality, but not the other way around.

 

[A. Neumaier]

I don't disagree, but are you conflating the concepts of ordinary and fundamental reality? I'm trying (at least here) to keep them separate. Fundamental reality is that thing from which you can derive a complete and consistent description of ordinary reality, but not the other way around.

You are conflating descriptions of reality with reality itself.

Of course it is very likely that a Hilbert space figures in the description of fundamental reality, but it remains only a description, not the reality behind it.

What really is, the thing itself, is a vector in Hilbert space.

You are not even consistent about what 'is' (or better 'describes') reality in your proposal - a Hilbert space or a vector?

 

[Giulio Prisco]

You are conflating descriptions of reality with reality itself.

Of course it is very likely that a Hilbert space figures in the description of fundamental reality, but it remains only a description, not the reality behind it.

You are not even consistent about what 'is' (or better 'describes') reality in your proposal - a Hilbert space or a vector?

Not my proposal (though I like it).
A vector.
If a description is the best we can do, how do you define the concept of "reality behind it" ?
For example, what is a particle? Is it a little ball with a position that varies in time (like all the little balls that I have seen) ?
But our best theory of particles says that there's no such thing.
So what is a particle?
Is it an excitation of a quantum field?
But quantum field theory says that individual excitations of quantum fields can be defined only in certain cases.
And besides that, what is a quantum field?
It would be nice to have an answer, but does one necessarily exist?
"Imaginability must not be made the test for ontology" (Ernan McMullin)
Isn't it good enough to have a mathematical model, call it reality, and derive ordinary reality from it?

 

[pinball1970]

You are conflating descriptions of reality with reality itself.

Of course it is very likely that a Hilbert space figures in the description of fundamental reality, but it remains only a description, not the reality behind it.

You are not even consistent about what 'is' (or better 'describes') reality in your proposal - a Hilbert space or a vector?

As an interested observer (with my head spinning a little)

When you guys get there i.e. find out what reality actually is at the fundamental level and work out how everything else is emergent, what words will you use to describe it?

If it is “like” a Hilbert space will you just invent another word?

If it is something else then will the terminology start to become irrelevant since the you cannot peel away another layer?

How would you start to describe the stuff of the fundamental reality?

When you cannot go past stuff?

 

[A. Neumaier]

Isn't it good enough to have a mathematical model, call it reality, and derive ordinary reality from it?

A mathematical model is a model of reality, not reality. Just as a position and momentum vector together are a comprehensive model of a classical point particle, but they are not a particle.

How would you start to describe the stuff of the fundamental reality?

I would call the fundamental reality the universe, and our description of it a mathematical model. The description would involve many other concepts, primarily fields, and particles would be a semiclassical approximate concept valid under certain conditions.

 

[Lord Jestocost]

What do you guys think of this soberly elegant proposal by Sean Carroll?

Reality as a Vector in Hilbert Space

Fundamental reality lives in Hilbert space and everything else (space, fields, particles...) is emergent. Seems to me a step in the right conceptual direction.

I would call this "ironic sciene", a term coined by John Horgan:

"Ironic science resembles literary criticism or philosophy or theology in that it offers points of view, opinions, which are, at best, "interesting," and which provoke further comment. But ironic science does not converge on the truth." https://www.aps.org/publications/apsnews/199612/backpage.cfm

 

[EPR]

What do you guys think of this soberly elegant proposal by Sean Carroll?

Reality as a Vector in Hilbert Space

Fundamental reality lives in Hilbert space and everything else (space, fields, particles...) is emergent. Seems to me a step in the right conceptual direction.

Google the MWI.

 

[Demystifier]

I think there are as many different meanings of this word as there are philosophers using it.

No, there are more meanings used by philosophers than there are philosophers using it.

 

[Demystifier]

What do you guys think of this soberly elegant proposal by Sean Carroll?

 

[Giulio Prisco]

A mathematical model is a model of reality, not reality. Just as a position and momentum vector together are a comprehensive model of a classical point particle, but they are not a particle.

So *what is* a classical particle besides that? Does the question even make sense?

Also, in this specific case, since classical particles don't exist, there's no "element of fundamental reality" behind the mathematical description.

 

[Giulio Prisco]

Nice picture!

Of course, counterintuitive doesn't mean wrong. If the theory is correct (within its limits of validity and all that) it can only confirm the information from the senses. Otherwise the theory is not correct.

 

[A. Neumaier]

So *what is* a classical particle besides that? Does the question even make sense?

A classical particle is a miniature version of a planet or a cannon ball., from whose motions the concept was abstracted.

 

[atyy]

For those who like Everett's interpretation, in his last book Carroll argues that all Everett worlds live in the universal reality vector, and the "many worlds" of the popular interpretation of Everett's interpretation are emergent.

Isn't this just standard MWI?

 

[Giulio Prisco]

Isn't this just standard MWI?

Yes but no :-) This is what Everett meant and what many experts (eg Carroll, Wallace) think, but the simplified picture of splitting worlds and the MWI label make one tend to forget that the world is One Big World, not many small worlds.

 

[DennisN]

Mathematical concepts can describe aspects of, but they can never be physical reality.

Which to my ears is very similar to the saying "the map is not the territory."

 

[strangerep]

I don't care about the philosopher's Spitzfindigkeiten

TIL a new German word...

 

[PeroK]

On the other hand, nobody has ever seen a physical Hilbert space. Calling it more real than the physical space we live in is selfdelusion.

Being completely agnostic on these questions, I might say that anyone who thinks they know what must and what cannot be is deluded.

Could we with all our senses and intelligence actually be the product of a purely mathematical system? It sounds mad but on what grounds can it be dismissed - notwithstanding a priori faith in the opposite?

 

[A. Neumaier]

Could we with all our senses and intelligence actually be the product of a purely mathematical system? It sounds mad but on what grounds can it be dismissed - notwithstanding a priori faith in the opposite?

That it sounds mad is sufficient for dismissal.

We could be an implementation of a mathematical algorithm, but not a mathematical system, since the latter is an object in nonphysical, timeless Platonic reality.

 

[PeroK]

That it sounds mad is sufficient for dismissal.

We could be an implementation of a mathematical algorithm, but not a mathematical system, since the latter is an object in nonphysical, timeless Platonic reality.

Die Glaube ist immer maechtiger als der Zweifel.

Hermann Hesse

 

[Prishon]

What do you guys think of this soberly elegant proposal by Sean Carroll?

Reality as a Vector in Hilbert Space

Fundamental reality lives in Hilbert space and everything else (space, fields, particles...) is emergent. Seems to me a step in the right conceptual direction.

Complete nonsense. But if he wants to believe that...

 

[A. Neumaier]

Die Glaube is immer maechtiger als der Zweifel.

And rightly so. Without an implementation to carry out mathematics, it is just a collection of true statements, nothing happening.

 

[PeterDonis]

Moderator's note: Thread moved to the QM interpretations forum.

 

[PeroK]

And rightly so. Without an implementation to carry out mathematics, it is just a collection of true statements, nothing happening.

I think the quotation was intended as ironic resignation, rather than a celebration of dogma!

 

[Prishon]

I think the quotation was intended as ironic resignation, rather than a celebration of dogma!

Why should nothing happen? Happen in what sense? Can you give an example? Is it like the central dogma of biology?

 

[PeterDonis]

Moderator's note: A number of off topic posts have been deleted. Please keep the thread discussion focused on the specific paper referenced in the OP.