How Does Verlinde's Theory Link LQG with Newtonian Gravity?

[tom.stoer]

One has to make very clear what is meant by gravitons:
- physical particles that can be detected experimentally?
- certain states in a Hilbert space?
- idealized plane wave states in a Feynman diagram used to do pertutbation theory?
- ...

One must not mix the plane-wave concept with something like physical existence. The plane waves are a mathematical tool that does not directly fit to experiments. In experiments you detect localized particles, whereas planes waves are certainly not localized. So the problem you observe in QG is implicitly there in ordinary QFT as well, but you are used to hide it behind hand waving arguments going back to the Kopenhagen interpretation.

I don't think that renormalization group theory depends on the existence of plane wave solutions! Neither do Feynman diagrams; they can e.g. be formulated with distorted waves, even if this is less well-known and more complicated.

Look at QCD: you can formulate QCD (at least in a certain regime - e.g. deep inelastic scattering) based on gluons, but that concepts FAILES completely when it comes to hadron physics.

So I don't see why we should insist on a theory that relies on a perturbative concept only. If string theory can be completed non-perturbatively then I expect that something different from plane wave state must emerge.

 

[atyy]

One has to make very clear what is meant by gravitons

Yes, that's why I take language about a theory in which gravitons are fundamental to be shorthand for a theory whose fundamental high energy action is based on the metric field and has the property of general covariance.

 

[tom.stoer]

so if we agree that plane wave states are useless in quantum gravity ... what are gravitons?

 

[marcus]

Yes, that's why I take language about a theory in which gravitons are fundamental to be shorthand for a theory whose fundamental high energy action is based on the metric field and has the property of general covariance.

This is somewhat of a hodgepodge of criteria. You are trying to say "non-emergent" I think. But general covariance does not belong in the list.
Lots of very different theories can have diffeo invariance aka general covariance. Not a very discriminating criterion.

In LQG, for example, gravitons are definitely not fundamental, you have to artificially "flatten" the theory to force a graviton propagator to appear. LQG is kind of a paragon of an emergent spacetime theory. Which is why the LQG community is already all over the Verlinde paper.

We already have a paper by Smolin and a new one by Modesto that came out today And Verlinde's paper has not even been out 3 weeks.

There is a backlog of LQG stuff having to do with holography black holes and thermodynamics, Smolin, Ted Jacobson, Kirill Krasnov, Rovelli. Modesto draws on this and on his own work with the LQG black hole.

so if we agree that plane wave states are useless in quantum gravity ... what are gravitons?

I think you may be suggesting gravitons are a useful mathematical convention. Useful in certain limited circumstances. Sometimes a good way to think about propagating disturbances in the field.

Not sure what you have in mind, so I will state that as my opinion only. In any case we don't have to include gravitons in the discussion.

 

[Physics Monkey]

Should we really think of LQG of a theory of emergent spacetime? I already argued that Verlinde has background dependence in much of his paper. LQG is considerably more background independent that Verlinde's proposal at this point, but even LQG is deeply rooted in the mathematics of manifolds (without a prior metric of course). I'm skeptical of calling a theory that starts from manifolds a theory of emergent spacetime. Perhaps we will understand later that manifolds weren't essential, that it the manifold will fall away as physically irrelevant, but I don't think anyone is in a position to claim that right now in LQG. Or am I wrong?

 

[Physics Monkey]

so if we agree that plane wave states are useless in quantum gravity ... what are gravitons?

I wouldn't say plane wave states are useless. On a conceptual level they allow you to see that a string coupled to a non-trivial background metric is like a string moving in a coherent state of its own flat space gravitons. The graviton vertex operator is precisely a plane wave state as is appropriate in flat space. I'm not claiming that this is the only way to see the connection, only that this way is simple and useful. Of course, one has to be careful about the difference between an exact plane wave state and a sharply peaked (in momentum) wavepacket, but I think this subtle distinction is understood.

 

[marcus]

Should we really think of LQG of a theory of emergent spacetime? I already argued that Verlinde has background dependence in much of his paper. LQG is considerably more background independent that Verlinde's proposal at this point, but even LQG is deeply rooted in the mathematics of manifolds (without a prior metric of course). I'm skeptical of calling a theory that starts from manifolds a theory of emergent spacetime. Perhaps we will understand later that manifolds weren't essential, that it the manifold will fall away as physically irrelevant, but I don't think anyone is in a position to claim that right now in LQG. Or am I wrong?

The theory starts with a manifold but moves on to dispense with it. It does not assume the physical existence of a continuum. Nor does it assume the physical existence of loops, spin networks, foams, 4-simplices or tetrahedra.
This is an interesting and fairly high-level question which Rovelli gave the definitive word on last summer in about twelve slides of a May 2009 seminar talk.
http://relativity.phys.lsu.edu/ilqgs/panel050509.pdf

This file begins with a dozen or so slides from Ashtekar, and then a series from Carlo, and finishes with some from Laurent Freidel. It was not prepared for wide distribution but is primarily a discussion among a small group of colleagues about issues of ontology and interpretation which arose two weeks earlier when John Barrett (Nottingham, UK) gave a talk to the same group.

My crude summary: LQG is not talking about what Nature is "made of" but about how Nature responds to measurements.
It uses various formalisms---the simplices of Group Field Theory (GFT), the networks and foams of the canonical and covariant versions of LQG---as alternative ways of imagining and calculating which the researchers have discovered are consistent.

So one is looking for deeper systems of description, a deeper layer of degrees of freedom from which familiar spacetime emerges. But one does not re-ify these deeper d.o.f.
In LQG the geometry of spacetime is certainly emergent, but in LQG one does not, at least as yet, say from what it is emergent.

The best is to read the dozen or so slides, because they say more than the one-slide summary at the end. But I will quote the summary slide:

==Rovelli 5 May 2009 seminar slide 12==
Summary

1. “Loopy, polymer, triangulated” spaces are helps for intuition, not descriptions of reality. No incompatibility between them.

2. In quantum gravity, flat space is neither many small Planck scale things not few big large-spin 4 simplices. It is a process with a transition amplitudes. We can represent it with different pictures, according to the measurements we are considering, the calculation scheme, and the approximation scheme.

3. We must compute diff-invariant amplitudes, including when dealing with excitations over a flat space. The only way of doing so that I know is to code the background into the boundary space. (Boundary formalism.)

4. We need an approximation scheme. For scattering amplitudes, we can truncate degrees of freedom to a finite number, very much like is done in computing in QED and QCD. (Vertex expansion.)

5. Regime of validity of the vertex expansion: processes whose size L is not much larger than the minimal relevant wavelength λ. Includes the large distance behavior of the scattering amplitudes in coordinate space.

6. At given ratio λ/L, the Large-spin Limit captures processes at scales larger than the Planck length. It gives the semiclassical limit.
→ This does not mean that flat space is “made out of large 4-simplices”!
→ It means that we describe measurements performed at scales larger that the
Planck scale, at low order.
==endquote==

Some of these points specifically address questions raised in the discussion of John Barrett's talk, two weeks earlier.

 

[atyy]

Should we really think of LQG of a theory of emergent spacetime? I already argued that Verlinde has background dependence in much of his paper. LQG is considerably more background independent that Verlinde's proposal at this point, but even LQG is deeply rooted in the mathematics of manifolds (without a prior metric of course). I'm skeptical of calling a theory that starts from manifolds a theory of emergent spacetime. Perhaps we will understand later that manifolds weren't essential, that it the manifold will fall away as physically irrelevant, but I don't think anyone is in a position to claim that right now in LQG. Or am I wrong?

One of the LQG-related formalisms I find fascinating is group field theory. Apparently, all spin foams are related to some GFT - Rovelli likens this to the Maldacena duality http://relativity.livingreviews.org/Articles/lrr-2008-5/ .

A GFT has a manifold and fixed metric. "Quantum Gravity is described by an (almost) ordinary QFT, although with peculiar structure, and one that uses even a background metric "spacetime" (although here interpreted as an internal space only), given by a group manifold ... http://arxiv.org/abs/0903.3970 "

 

[marcus]

A GFT has a manifold and fixed metric...

That could be misleading if one gets the impression that the manifold used in GFT somehow represents spacetime.

The manifold is the cartesian product of N copies of a Lie group G. Think of a fixed geometrical structure like a simplex, or a spin network with N edges. To complete the specification of a geometry this structure needs to be labeled with, say, elements of G.
One can represent "all the possible labelings" by the cartestian product G^N.

One way to think of quantizing "all the possible labelings" is to construct a quantum field theory on G^N. That is a field theory defined on a group manifold---called a group field theory or GFT.

The GFT construction is widely applicable---to covariant LQG (spin foams) and to simplicial quantum gravity (e.g. Regge) and I forget what else. LQG papers use GFT for calculation.
Obviously the group manifold of all possible labelings has no direct relation to what we live in and move around in and experience as space and time.

The fact that GFT techniques of calculation are applied to simplicial QG, and that Rovelli for example, uses GFT uses GFT for spin foam calculations, does not mean that any theory thinks the world is made of simplices, or that the a cartesian product of groups exists in nature. I tried to suggest this a couple of posts back, where I quoted a seminar talk slide in blue bold. The idea, one which LQG can serve as paradigm or prime example, is of emergence from unspecified degrees of freedom---a number of ways of calculating which are shown to be equivalent.
In other words, don't say what the world is made of (whether spin networks or simplices or whatnot). Try to describe how it responds to measurement.

 

[tom.stoer]

I wouldn't say plane wave states are useless. On a conceptual level they allow you to see that a string coupled to a non-trivial background metric is like a string moving in a coherent state of its own flat space gravitons. The graviton vertex operator is precisely a plane wave state as is appropriate in flat space. I'm not claiming that this is the only way to see the connection, only that this way is simple and useful.

You are right, string theory provides already in its perturbative formulation interesting hints regarding the nature of gravity.

Nevertheless I would claim that perturbative string theory is doomed to fail, especially as there is no hint that the perturbation series is finite (there are other reasons as well); therefore one needs a non-perturbative concept. And I am pretty sure that this non-perturbative theory will not be based on "gravitons" or "plane-waves". Instead I expect that "gravitons" will emerge in some limit only. But to be honest I don't think that this limit is physically relevant.

So in contradistinction to QCD there will be no regime in QG where you have experimental access to gravitons.

 

[czes]

You are right, string theory provides already in its perturbative formulation interesting hints regarding the nature of gravity.

Nevertheless I would claim that perturbative string theory is doomed to fail, especially as there is no hint that the perturbation series is finite (there are other reasons as well); therefore one needs a non-perturbative concept. And I am pretty sure that this non-perturbative theory will not be based on "gravitons" or "plane-waves". Instead I expect that "gravitons" will emerge in some limit only. But to be honest I don't think that this limit is physically relevant.

So in contradistinction to QCD there will be no regime in QG where you have experimental access to gravitons.

I looked for a forum where the background independent ideas are discussed and I found it here. I am not a professional physicist and I just walk between Loop Quantum Gravity, Cramer's Transactional Interpretation and Quantum Decoherence approach.
I did some trivial transformations of the equations of gravity and quantum mechanics which suggest the space is created of the interactions (cross product) of the quantum information.

Since some days I repeat my question:

Each particle oscillate (Schrodinger's Zitterbewegung) due to Compton wave length and its frequency. If the information of the oscillation is non-local it has interact with the information from another particles and create a spatial lattice like a quantum network in LQG. The space would be there just a standing wave made of emitted and absorbed information. A graviton might be derived here as a distortion in the network (a mathematical picture of the quantum vacuum density), something like a photon.
What creates a space in LQG if not an information of the oscillating particle ?

 

[Haelfix]

You are right, string theory provides already in its perturbative formulation interesting hints regarding the nature of gravity.

Nevertheless I would claim that perturbative string theory is doomed to fail, especially as there is no hint that the perturbation series is finite (there are other reasons as well); therefore one needs a non-perturbative concept. And I am pretty sure that this non-perturbative theory will not be based on "gravitons" or "plane-waves". Instead I expect that "gravitons" will emerge in some limit only. But to be honest I don't think that this limit is physically relevant.

So in contradistinction to QCD there will be no regime in QG where you have experimental access to gravitons.

Kind of preaching to the choir I think. Most of the advances in string theory since the mid 90s are nonperturbative in nature. Whether its dualities, Ads/Cft or matrix theory. It's far from complete, but the whole 'emergent spacetime' concept very much comes from work done there.

 

[Hans de Vries]

Since some days I repeat my question:

Each particle oscillate (Schrodinger's Zitterbewegung) due to Compton wave length and its frequency.

The Zitterbewegung is a rather outdated concept, that is, there is nothing physically
vibrating and certainly not at c. It is the propagation which is composed out of two
light-like propagators, The Left and Right Chiral components.

Both these components do propagate individually at c but they are coupled together
via the mass term m. Each field is a source of the other enabling propagation speeds
anywhere between 0 and c.

To understand this better one can linearize the Klein Gordon equation, which is possible
in 1+1d, into a Left and Right moving component which are both moving at c but are
coupled via the mass term allowing propagation speeds lower than c.

I did this here: (in sections 16.1 through 16.4)
http://physics-quest.org/Book_Chapter_Dirac.pdf

There are computer simulations shown in figures 16.4 and 16.5. which obtain the
propagation of a Klein Gordon particle's wave-packet in this way.Regards, Hans

 

[MTd2]

My crude summary: LQG is not talking about what Nature is "made of" but about how Nature responds to measurements.
It uses various formalisms---the simplices of Group Field Theory (GFT), the networks and foams of the canonical and covariant versions of LQG---as alternative ways of imagining and calculating which the researchers have discovered are consistent.

You should see the paper I pointed out a few days ago:

http://arxiv.org/abs/1001.4364

Quantum Tetrahedra

Mauro Carfora, Annalisa Marzuoli, Mario Rasetti
(Submitted on 25 Jan 2010)
We discuss in details the role of Wigner 6j symbol as the basic building block unifying such different fields as state sum models for quantum geometry, topological quantum field theory, statistical lattice models and quantum computing. The apparent twofold nature of the 6j symbol displayed in quantum field theory and quantum computing -a quantum tetrahedron and a computational gate- is shown to merge together in a unified quantum-computational SU(2)-state sum framework.

 

[Orbb]

The Zitterbewegung is a rather outdated concept, that is, there is nothing physically
vibrating and certainly not at c.

Just a note: the recent paper

http://www.nature.com/nature/journal/v463/n7277/abs/nature08688.html
Quantum Simulation of the Dirac equation
"[...]We measure the particle position as a function of time and study Zitterbewegung for different initial superpositions of positive- and negative-energy spinor states, [...]"

where Zitterbewegung is experimentally observed.

 

[Hans de Vries]

Just a note: the recent paper

http://www.nature.com/nature/journal/v463/n7277/abs/nature08688.html
Quantum Simulation of the Dirac equation
"[...]We measure the particle position as a function of time and study Zitterbewegung for different initial superpositions of positive- and negative-energy spinor states, [...]"where Zitterbewegung is experimentally observed.

They did a "quantum" simulation of the 1d Dirac equation in a physical system which
they assume to be equivalent in behavior. Certainly they did not experimentally
observe the position of an electron while "Zittering" at c.

If you do a simple computer simulation of the 1d Dirac equation (which is the same
as the 1d linearized Klein Gordon equation) then there is no zittering at all but just
a wave packet moving at a constant speed. This is what is shown in figure 16.4.Regards, Hans

 

[Hans de Vries]

I shouldn't lead this thread into an off-topic direction. (sorry)
Maybe I should give my personal feelings about Erik Verlinde's paper instead.The first thing what game to my mind were the Neutron interference experiments
under gravity (Apparently Lubos Motl did so as well)
(http://motls.blogspot.com/2010/01/erik-verlinde-why-gravity-cant-be.html#more) Acceleration from force is to be understood as wave behavior, phase change
rates, Huygens principle, Wilson loops. Not only in field theory but also in gravity
as the neutron experiments prove. I did put quite some effort in the visualization
the EM case step by step in the following chapter of my book here:

"The Lorentz force derived from the interacting Klein Gordon equation"
(via Wilson Loops) see for instance images 11.3 through 11.6
http://www.physics-quest.org/Book_Lorentz_force_from_Klein_Gordon.pdf

It may be me but I can't find anything in the idea of "entropic force" which fits
into a wave behavior picture...Regards, Hans

 

[tom.stoer]

... I can't find anything ... which fits
into a wave behavior picture...

Why do you think it should fit into the material wave interpretation?

 

[Hans de Vries]

Why do you think it should fit into the material wave interpretation?

Well, the material wave interpretation is proven experimentally...

because of the success of molecular modeling software which threats
the wave function as a continues distribution of charge/current density
and spin density. $$\bar{\psi}\gamma^\mu\psi$$ and $$\bar{\psi}\gamma^5\gamma^\mu\psi$$Regards, Hans

 

[ccdantas]

Good point on neutron interferometer.

At some point, I still believe that one should use a generalization of quantum concurrence for computing microstates. Information should not be equally "available", but under causality should be locally constrained by "shared resources"; concurrence should appear in the calculation.

(...) my book(...)

Nice! I'll take a look at your book.Christine

 

[MTd2]

It may be me but I can't find anything in the idea of "entropic force" which fits into a wave behavior picture...

There is no equivalence principle issue here because in the paper by Verlinde, is about Newtonian gravity. So equivalence principle IS violated. But the quantum corrections due entropy that makes Newtonian gravity in the problem arise are of much larger magnitude or relevance than GR or interference patterns of neutrons.

And even so, I don't really see any issue here. In this set up, gravity is not a force, there is no particle to create gravity, if this were a paper on GR, you could say that geometry is bent by entropy. So, there is not an interference from gravity, because there is simply no gravity. It is exactly like if you used mirrors inside experiments to study coherence. The path is changed, but not the other states of the particle.

Let me put in other way. Entropy, here, is more like a new kind of mass.

 

[czes]

The Zitterbewegung is a rather outdated concept, that is, there is nothing physically
vibrating and certainly not at c. To understand this better one can linearize the Klein Gordon equation, which is possible
in 1+1d, into a Left and Right moving component which are both moving at c but are
coupled via the mass term allowing propagation speeds lower than c.
I did this here: (in sections 16.1 through 16.4)
http://physics-quest.org/Book_Chapter_Dirac.pdf

There are computer simulations shown in figures 16.4 and 16.5. which obtain the
propagation of a Klein Gordon particle's wave-packet in this way.
Regards, Hans

Thank you Hans for the link of your book. I have printed it for me.
I agree there isn't a motion on a quantum fundamental level but there is a wave function which is an information any way. We do not observe a wave function alone as we do not observe an information alone either. We observe an interaction between wave functions. It is shown as a probable information of the particle due a squared wave function in Copenhagen. In other interpretations wave function is more real. This information shows a Compton wave length L=h/mc shown in Klein -Gordon equation.

A. We observe the indirect effects of the wave function as the existence of the particle so it has interact with an environment.
B. If the Compton wave length is a quantum information it has to be non-local due to Bell's theory

If the wave functions interact with each other and are non-local it has to represent something.
I assume it is distributed inversely proportional to the distance from a source of the oscillation represent a background information space.

 

[marcus]

Nice! I'll take a look at your book.Christine

Impressive work in progress, Hans!
Online introduction to relativistic quantum field theory with lots of illustrations, aids to intuition.
It looks like your plan is to cover the subject in 30 chapters, and you already have 14 chapters (all or part) filled in.
In case anyone didn't check it out already, the main chapter menu is here:
http://physics-quest.org/
This has links to the 14-or-so chapters which are all or part completed.

 

[marcus]

Ted Jacobson's 1995 paper is in some sense seminal here---at the root of all this discussion.
I thought it would be good for people to have a glimpse of the actual person:
http://math.ucr.edu/home/baez/marseille/jacobson_rovelli.jpg

This is Jacobson at the first Loops conference, Loops 2004, having a quiet conversation with Carlo Rovelli.

 

[czes]

Ted Jacobson wrote yesterday an article:
Extended Horava gravity and Einstein-aether theory
http://arxiv.org/abs/1001.4823

I think, we may use here a non-local information of the particles oscillation as a physical example of a matter field in Jacobsons theory.

 

[MTd2]

Hi Marcus, check your PMs! :)

 

[Fra]

I share some of these objections/comments...

Fwiw, I'll interject some of my personal views on this.

But I don't really know what "sides" means in a world without geometry.

Good point. One certainly wonders what "distance" means.

In my a the screen can be loosely defined informationally by means of what's predictable and what's not. I envision it like this. Prediction relate to a an observing system, making a prediction. This observer has a complexity. At some point, the predictability of constructed events are so small that it can not be distinguished from zero by a code of limited complexity - here is a natural "relative" horizon of measureable events.

This relates to the problem of how to conceptually handle the meaning of events with zero probability happen? - as I see it, yes then can, but that's irrelevant from the point of view of the ACTION of the observing system, the _expected_ action is invariant with respect to zero probability events, this is am abstract form of "locality". Instead this is where undecidability comes in. Part of the action is always undecidably as I see it - this is where the evolutionary parts comes in. This certainly limits the possibility of making certain predictions of anything. But I still think acknowledging this may improve our undertanding.

He also seems to assume that one side has "already emerged", but how did this happen? Smolin assumes the same thing in his paper, which is quite strange in my opinion.

I can't accept that either. But, I like to "read it" as a temporary working premise in order to show the implications.

I've encounted this exact problem in my own thinking, and the best resolution out of it I have found is to complement this "statistical information view" with an evolutionary view in darwinian style.

So this is why I think we need to start a the smallest complexity scale - which should be unique, and then ponder how higher order organization emerges as complexity increases.

I think his starting points, must in a satisfactoty future treatment be a result of such a process. It's that process I I also need to understand. I think there is a more information theoretical possibility to this than smolins CNS. Something that is formulated in terms of more abstraction "information channels" or screens, rather than explicit black holes.

/Fredrik

 

[Physics Monkey]

I can't accept that either. But, I like to "read it" as a temporary working premise in order to show the implications.

I certainly agree with you here. I have no logical problem with taking some of the space as emergent and trying to show that more "emerges". I'm not sure how natural a starting point this is, but regardless of my opinion, it indicates that Verlinde and Smolin both use background notions to make progress.

One place where your discussion of minimal complexity, etc strikes me as especially relevant is the case of our own universe (roughly de Sitter). A de Sitter spacetime contains a horizon that apparently limits the size of the physical HIlbert space available to observers in the space. Similarly, observers in de Sitter have limitations on how precisely they can measure various physical quantities. A classic reference is the article of Witten http://arxiv.org/abs/hep-th/0106109

 

[atyy]

Similarly, observers in de Sitter have limitations on how precisely they can measure various physical quantities. A classic reference is the article of Witten http://arxiv.org/abs/hep-th/0106109

"For life itself is only an approximation, valid in the limit of a complex organism or civilization." He means this to be true in any physics, not just in asymptotically ds Sitter spacetimes, right?

 

[Physics Monkey]

"For life itself is only an approximation, valid in the limit of a complex organism or civilization." He means this to be true in any physics, not just in asymptotically ds Sitter spacetimes, right?

Haha, yes, I would assume so. It's a pretty vague comment though, so who knows what he really means.

 

[marcus]

http://pirsa.org/06090001/

Ted Jacobson gave a 1-hour video lecture on his 1995 paper deriving the Einstein equation from thermodynamics (essentially the Clausius relation) and
including some more recent results, as of 2006.
He gives some conjectures about possible meanings.
I hadn't watched this talk before, for some reason didn't know it existed.

 

[Hans de Vries]

Nice! I'll take a look at your book.


Christine

Hi, Christine (Obrigado!)

Impressive work in progress, Hans!
Online introduction to relativistic quantum field theory with lots of illustrations, aids to intuition.
It looks like your plan is to cover the subject in 30 chapters, and you already have 14 chapters (all or part) filled in.
In case anyone didn't check it out already, the main chapter menu is here:
http://physics-quest.org/
This has links to the 14-or-so chapters which are all or part completed.

Thank you Marcus.

It's more work as I expected I'm currently at 700 pages including the
unfinished chapters and suspect to end up with something like 1100..

 

[Hans de Vries]

There is no equivalence principle issue here because in the paper by Verlinde, is about Newtonian gravity. So equivalence principle IS violated. But the quantum corrections due entropy that makes Newtonian gravity in the problem arise are of much larger magnitude or relevance than GR or interference patterns of neutrons.

And even so, I don't really see any issue here. In this set up, gravity is not a force, there is no particle to create gravity, if this were a paper on GR, you could say that geometry is bent by entropy. So, there is not an interference from gravity, because there is simply no gravity. It is exactly like if you used mirrors inside experiments to study coherence. The path is changed, but not the other states of the particle.

Let me put in other way. Entropy, here, is more like a new kind of mass.

Question: Why do things fall down according to General Relativity?

Answer: Elementary Wave behavior!

Gravitational time dilation causes the higher part of the wavepacket to oscillate
faster as the lower part and as a result the vertical spatial frequency increases,
corresponding to a continuous increasing momentum and (according to Fourier)
a downward accelerating wave packet.

Regards, Hans

 

[MTd2]

That doesn't look like general relativity, but some sort of argument to put quantum mechanics, with resort to wave mechanics, in the context. In general relativity gravity is caused because locally the shortest path between two points is parametrized by, and equated to, the momentum energy tensor. In the entropic case, by Jacobson, that is not equated with the energy tensor, but to where entropy is minimized.

Perhaps, here, you could apply your reasoning given that the highest part would be "hotter" than the lower and thus pushing the object.

 

[MTd2]

I still don't see why any interference pattern would be destroyed of the neutron experiment would be destroyed, given that no state relevant to the particles, in the experiment, was changed. Geometry follows the difference of perceived entropy in the environment, not the entropy in the object, in this case, the particles.