Exploring the Measurability of LQG: Insights from Spinfoam and Spin Networks

[Mike2]

So Loop Quantum Gravity predicts a "spinfoam" which goes from one quantum "spin network" state to another in the fashion of a path integral. And each spin network describes the properties of spacetime and is the eigenstate of the QG Hamiltonion.

OK. But by what process is the spin network actually measured? What "interaction" causes the superposition of spin networks to "colapse" to a particular spin network eigenstate? I have to wonder if such a measurement process can even exist at that level. Since every region of space is always in contact with its neighboring regions in the same way (measurement or not), what special event could cause one region to collapse in a "measurement"? And if it does not collapse, then could it be that by definition spacetime must always be assumed to be in a superposition? And what would be the implications of that?

If there is no measurement process to get the spinfoam wave function to collapse to an eigenstate spin network, then it would seem that we have achieved a realm of unpredictibility/unmeasureability again. Is this right?

 

[selfAdjoint]

I believe the "measurement" or interaction happens with the intertwinors at the vertices. Remember this is all spacetime description so time evolution doesn't come into it explicitly (and is actually problematical!).

 

[marcus]

[edit] didn't see that sA already replied.

So Loop Quantum Gravity predicts a "spinfoam" which goes from one quantum "spin network" state to another in the fashion of a path integral...

OK. But by what process is the spin network actually measured? What "interaction" causes the superposition of spin networks to "collapse" to a particular spin network eigenstate? I have to wonder if such a measurement process can even exist at that level.

thanks for starting this thread, Mike. I hope others besides me think it is interesting and want to reply or contribute questions.

the spin network in canonical LQG is roughly analogous to a WAVE FUNCTION in the simplest schroedinger QM picture of the position of a particle in one dimension.

I guess everyone realizes that you never actually MEASURE the wavefunction in QM. what you observe are OBSERVABLES like POSITION----which occur in the theory as selfadjoint operators on the hilbert statespace.

Analogously, in LQG, you do not expect to observe spin networks, the spinnetworks are a basis of a hilbert of quantum states of (spatial) geometry-----like schroedinger wavefunctions. what you expect to observe are OBSERVABLES -----corresponding to selfadj. operators on that hilbert-----for example observables like AREA and VOLUME.

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In reading your post I am not sure what you are talking about. there are two broadly different types of QG approaches:

1. canonical

2. path integral (also called "sum over histories")

AFAIK, the only place you might expect to see a Hamiltonian operator defined on the statespace is in type 1.

AFAIK, the only place you ever see a spinfoam is in type 2.

But in your question you mention both Hamiltonian and spinfoam, so I am wondering which type of QG you are talking about.

Also, unfortunately, so far in type 1, with canonical LQG, a unique Hamiltonian operator has not been decided on. There is a Hamiltonian in the simplified models used in LQC cosmology which depend on assuming largescale uniformity of the universe, but not in the full theory. I should mention that in canonical LQG the Hamiltonian is expected to occur as a CONSTRAINT, technically not as a time-evolution operator. But that is a secondary issue. In LQC, where the Hamiltonian constraint is defined, they contrive to get a sort of discrete time-evolution out of it and model the evolution of the universe. Because type 1 canonical LQG does not so far have a unique well-defined Hamiltonian constraint, you might get clearer answers if you focused on the other branch.

One thing you could do, to get more definite answers, is to focus your question on the type 2 QG approaches and try to get as straight as possible on them.

Maybe others will have a different idea of how to respond, but that is what i would suggest: focus on path integral QG, at least for now, and get as clear as you can there. If you want to pursue that, let us know.
(even then I couldn't promise entirely satisfactory responses, but at least it narrows things down some)

 

[f-h]

Funny that that should pop up now, I was just discussing this point, among others...

In short, if you have an apparatus meassuring the area of a bit of space, then you get collapse to the respective Area operator eigenstate which is (a superposition of) Spin Networks.

It can be asked if such an appartatus is actually well defined to begin with...

 

[Mike2]

[edit]
But in your question you mention both Hamiltonian and spinfoam, so I am wondering which type of QG you are talking about.

I realize that I may not have gotten the technicalities completely right. But I think that my question still remains:

Since every region of space is always in contact with its neighboring regions in the same way (measurement or not), what special event could cause one region to collapse in a "measurement"? It seems that there can be nothing special to cause collapse.

There seems to be a necessary interaction of particles before information can be extracted in the process of measuring particle properties. There is a wavefunction associated with only the particle to be measured, and this must interact with its surroundings/measureing device before the wavefunction can callapse. But it seems that a wavefunction for space is always in contact with its surrounding space, and so there is no isolated wavefunction to begin with. Or there can be no process to change the relative degree of entanglement with its surroundings to either establish a separate wavefunction to measure, or to increase the entanglement with the surroundings to measure it.

Or perhaps particles themselves are the collapse/measurement of quantum spacetime since there is always a particle associated with a given geometry of spacetime that we are trying to measure.

 

[marcus]

Funny that that should pop up now, I was just discussing this point, among others...

In short, if you have an apparatus meassuring the area of a bit of space, then you get collapse to the respective Area operator eigenstate which is (a superposition of) Spin Networks.

It can be asked if such an appartatus is actually well defined to begin with...

just a remark: whenever I have seen this discussed (e.g. by Rovelli) it is always pointed out that without matter, without actual events, the points of the continuum have no meaning

so one cannot speak of an abstract area, there must be some matter (like a crystal or a wooden desktop) in the picture

I suppose when you investigate if it is well-defined to measure the area of the surface of the desktop, that the physical apparatus must somehow involve the desktop.

but I can only make side comments like this, I cannot help you resolve the problem.

I have a question for you. When I picture the canonical LQG model, I tend to imagine it "Heisenberg style", with a fixed quantum state and operators that perhaps can evolve. Would you say this is the wrong way? Or do you also sometimes picture it like that?

I have difficulty imagining the spinnetwork quantum state physically "collapsing", I only think that one can find out more about the quantum state of spatial geometry. The "wavefunction" is not a physical thing in nature but a summary of the information one has about the world's shape. Is this view mistaken, in your view?

 

[Mike2]

Funny that that should pop up now, I was just discussing this point, among others...

In short, if you have an apparatus meassuring the area of a bit of space, then you get collapse to the respective Area operator eigenstate which is (a superposition of) Spin Networks.

It can be asked if such an appartatus is actually well defined to begin with...

Maybe the particles produced by acceleration in the Unruh effect is a type of space crashing into space, quantum space bits forced to interact with nearby spacetime bits. Each particles (with its associated energy) is a measure of the spacetime eigenstate.

 

[f-h]

There must be some matter, like a meassurement apparatus ;) which furthermore must be considered classical, or we're dragging in the interpretation of Quantum mechanics on top of the conceptional problems as well.

>When I picture the canonical LQG model, I tend to imagine it "Heisenberg style", with a fixed quantum state and operators that perhaps can evolve.<

That's actually a misconception, they evolve in what? External time? In the hardcore Rovelli style canonical picture the space of the universe is a superposition of Spinnetworks annihilated by the Hamiltonian constraint.

The question of how to make sense of this is hard, very hard, and I think your guess is as good as mine.

 

[Careful]

**There must be some matter, like a meassurement apparatus ;) which furthermore must be considered classical, or we're dragging in the interpretation of Quantum mechanics on top of the conceptional problems as well.**

AHA ! Why does this ring a bell to me ?

**
The question of how to make sense of this is hard, very hard, and I think your guess is as good as mine. **

That is why after a certain amount of time you start to wonder whether in standard QM, you interpret the superposition principle correctly in the first place

Careful

 

[Dcase]

Hi all:

Mike2 from one, who is also trying to learn this material, allow me to add my own spin.

Please note that selfAdjoint, marcus, f-h and Careful all probably know this QM material better than I do.

Consider the perspective alluded to by selfAdjoint "time evolution doesn't come into it explicitly" and marcus of "schroedinger wavefunctions' [SW].

From my perspective loops [circles or ellipses] are in a category like time-independent SW.

This is somewhat like f-h "measuring the area of a bit of space".

When one considers Careful "dragging in the interpretation", one may be able to integrate loop areas along the equivalent gauge and period helical trajectory to yield a volume measurement. This would tend to be in the category of time-dependent SW.

In using a perspective such as this, one may be able to place GR planetary orbital loops in the time-independent SW category and the corresponding helical mechanics of planetary orbits in the time-dependent SW category.

After all, loops are simply helices with a zero helical angle.

The f-h "Heisenberg style" has been shown to be equivalent to SW.

 

[Dcase]

Hi all:

I have noticed that rotating objects [moon, planets, stars] tend to have positive Riemannian elliptic curvature while revolving objects [moons around planets, planets around stars, stars around galactic cores] may have negative Gaussian hyperbolic
curvature.

This Japanese website [author: iittoo?] in English possibly has interesting illustrations of a psuedosphere or tractoid and how revolving bodies may be hyperbolic. The circle is a special type of both an ellipse and hyperbola. Rotating tractrix [matrix [loop?] pulled by a string] images are also interesting.
Figures 6, 6’ illustrate how the helix may be a geodesic for the moving tractoid.
Figure 16 is credited to Tore Nordstrand from Gallery of Curved Surfaces [French].
This may illustrate how a solar system or galaxy may retain the logarithmic spiral structure as they move through space-time using the apparent helical geodesic of this hyperbolic curve.
http://www1.kcn.ne.jp/~iittoo/us20_pseu.htm

Since the hyperbola and ellipse has reciprocal eccentricities, this may have a role in the R to 1/R relationship often emphasized in string theories.

Consider the hyperbola with 2^(1/2) [~1.414213562] eccentricity and the ellipse with 1/(2^(1/2)) [~0.707106781] eccentricity.

 

[Mike2]

That's actually a misconception, they evolve in what? External time? In the hardcore Rovelli style canonical picture the space of the universe is a superposition of Spinnetworks annihilated by the Hamiltonian constraint.

Doesn't a measurement itself involve evolutioin, specifically from a superposition to an eigenstate? But if it is not possible to measure it, even remotely from some exotic implication, then doesn't that make the theory untestable, and thus unfalsifiable?

 

[Careful]

**
When one considers Careful "dragging in the interpretation", one may be able to integrate loop areas along the equivalent gauge and period helical trajectory to yield a volume measurement. This would tend to be in the category of time-dependent SW.**


If you think I am simply having problems with the interpretation then you are deeply mistaken All major *technical* problems (quantum covariance, classical limit, sensible definition and *existence* of local observabe, ...) as well as the very much weakened notion of fasifiability of such program are ultimately due to the superposition principle.

Careful

 

[f-h]

That is why after a certain amount of time you start to wonder whether in standard QM, you interpret the superposition principle correctly in the first place

Careful

On a personal note, I actually started out on my journey to studying a bit of QG with a similar conviction, for the moment Rovelli convinced me that these problems can be considered distinctly. We'll see.

 

[Careful]

On a personal note, I actually started out on my journey to studying a bit of QG with a similar conviction, for the moment Rovelli convinced me that these problems can be considered distinctly. We'll see.

Strictly speaking, for local obervables, you can separate them if you consider matter to be different from geometry for example, but this comes at a huge cost (note: you have to accept a non-solution strategy for the measurement problem here)! Although - loosly speaking - the superposition principle is the main source of trouble in the construction of the Hamiltonian constraint (read Kuchar and Isham 1985 and you will see what I mean...). My idea is that QM is a linear approximation to a non-linear local classical field theory ( yep : no entanglement, although you have the same correlation functions - the difference is in the interpretation of single events).

Careful

 

[Mike2]

If you think I am simply having problems with the interpretation then you are deeply mistaken All major *technical* problems (quantum covariance, classical limit, sensible definition and *existence* of local observabe, ...) as well as the very much weakened notion of fasifiability of such program are ultimately due to the superposition principle.

Is it possible that QG could always have to remain in superposition? Could the coefficients of the eigenstates summed up in superposition change continously with position and other physical effects depend on that? Could there be measurable consequence that depend on superposition? Or is that a contradiction of terms?

 

[Careful]

Is it possible that QG could always have to remain in superposition? Could the coefficients of the eigenstates summed up in superposition change continously with position and other physical effects depend on that? Could there be measurable consequence that depend on superposition? Or is that a contradiction of terms?

Ok, I am a bit drunk (my kid has his birthday saturday and we are ``pre-parteeing'' ) but here is a simple albeit adequate argument. Basically, everything in the universe happens only once, quantum mechanics is a statistical theory which implies *repeated* events (in time !). You can only measure a superposition of ``classical'' states if you make a bunch of assumptions and do a series of measurements in advance on the (presumed) *same* sample. Logically, this implies that you can never (in principle) distinguish a superposition of universes from a single universe unless you build in some ``cyclicity'' principle for the quantum state, in other words you assume that the dynamics is such that``locally'' the Poincare recurrency times for your preferred set of observables are very short (which is unlikely as hell). That is why I said that any theory of quantum gravity has a very weak notion of fasifiability since it is never possible to check the statistics of a fundamentally stochastic theory if the latter is dynamical as well !

As a personal note f-h, haha, when I started QG I went of course straight to the superposition principle and knew immediatly that any solution (kinematical or dynamical) for it would be terribly nonlocal (actually I told to some friends three years ago that any discrete lorentz invariant theory of quantum gravity would be necessarily non local). I did not care at the time, since hey QM in the single particle formulation is nonlocal, so one would have no better hope for QG. But (!), I did not want to get out cheaply, by adding something different (no only geometry should do it) - turned out that at the kinematical level a solution exists which is impossible to implement and is only good for mathematicians.

Physics is about finding mechanisms which generate correlations between two local events, basically you can do anything with non-local theories and our only chance for understanding is to figure out a determinstic local theory. If we have to bring in God, consciousness, action at a distance or whatever in physics we are lost from the start and scientific endeavour becomes meaningless. We can only hope that God gave us the power to understand without us having to account for an unexpected intervention from his side.

Nazdrovie

Careful

 

[vanesch]

If we have to bring in God, consciousness, action at a distance or whatever in physics we are lost from the start and scientific endeavour becomes meaningless. We can only hope that God gave us the power to understand without us having to account for an unexpected intervention from his side.

Sounds like the story of the Bable Fish, no ?

 

[Careful]

Sounds like the story of the Bable Fish, no ?

Ah, did not even know about that, you truly scan the web too much