Matter as excitations of spacetime lattice?

In summary, there is a common theme among background independent quantum gravity theories that suggests a discretization or fuzziness of the spacetime manifold on Planckian scales. One idea is to represent this discretization as a lattice and describe matter on this spacetime through lattice excitations or vibrations, similar to how particles are described in crystal lattices. This idea has been explored in the loop quantum gravity approach, which uses spin networks to represent spacetime and has shown promising results in connecting with the standard model of particle physics. Further research and exploration of this concept is ongoing, with some speculating that it may lead to a deeper understanding of the relationship between geometry and matter.
  • #1
ericbrown86
2
0
It is a common theme among background independent quantum gravity theories that there should be some sort of discretization, or fuzziness, of the spacetime manifold occurring on Planckian scales.

It has occurred to me that if we take this discretization to consist of a lattice of sorts, might matter on this spacetime not be described via some sort of lattice excitation or vibration, in the same way that vibrations of a crystal lattice allows a particle description (i.e. the phonon)? Of course one would have to figure out, for example, how these excitations could induce a global curvature to the manifold, etc. But even so, it seems to me an interesting idea.

I was just wondering if anyone here knows of any research that has been done regarding this idea, or has any insights they with to discuss. I would love to see if anyone has worked on this.

Thanks!
- Eric
 
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  • #2
ericbrown86 said:
It is a common theme among background independent quantum gravity theories that there should be some sort of discretization, or fuzziness, of the spacetime manifold occurring on Planckian scales.

It has occurred to me that if we take this discretization to consist of a lattice of sorts, might matter on this spacetime not be described via some sort of lattice excitation or vibration, in the same way that vibrations of a crystal lattice allows a particle description (i.e. the phonon)?
One must not think about spacetime as a lattice; this would violate several symmetries, e.g. diff. inv. So the picture is definately more complex.

One idea is the loop quantum gravity (LQG) approach which is based on so-called spin networks. Edges connecting vertices carrying SU(2) degrees of freedom which are coupled at the vertices by intertwining operators. Edges and vertices are representing area and volume operators with quantized spectrum. LQG is a rather promising approach towards QG.

There is an idea that these spin-networks can be generalized and that some kind of "braiding" and "twisting" of the generalized edges (ribbons) can occure. These topologically stable configurations can be combined to objects carrying algebraic properties similar to particles known from the standard model. Moves on these braids may correspond to interactions of elementary particles.

Attention: this is a rather speculative idea - but fascinating as it may point towards particles entirely based on space-time.

http://arxiv.org/abs/hep-th/0603022
Quantum gravity and the standard model
Sundance O. Bilson-Thompson, Fotini Markopoulou, Lee Smolin
(Submitted on 3 Mar 2006 (v1), last revised 21 Apr 2007 (this version, v2))
Abstract: We show that a class of background independent models of quantum spacetime have local excitations that can be mapped to the first generation fermions of the standard model of particle physics. These states propagate coherently as they can be shown to be noiseless subsystems of the microscopic quantum dynamics. These are identified in terms of certain patterns of braiding of graphs, thus giving a quantum gravitational foundation for the topological preon model proposed by one of us.
These results apply to a large class of theories in which the Hilbert space has a basis of states given by ribbon graphs embedded in a three-dimensional manifold up to diffeomorphisms, and the dynamics is given by local moves on the graphs, such as arise in the representation theory of quantum groups. For such models, matter appears to be already included in the microscopic kinematics and dynamics.


http://arxiv.org/abs/1002.1462
Embedding the Bilson-Thompson model in an LQG-like framework
Deepak Vaid
(Submitted on 8 Feb 2010)
Abstract: We argue that the Quadratic Spinor Lagrangian approach allows us to approach the problem of forming a geometrical condensate of spinorial tetrads in a natural manner. This, along with considerations involving the discrete symmetries of lattice triangulations, lead us to discover that the quasiparticles of such a condensate are tetrahedra with braids attached to its faces and that these braid attachments correspond to the preons in Bilson-Thompson's model of elementary particles. These "spatoms" can then be put together in a tiling to form more complex structures which encode both geometry and matter in a natural manner. We conclude with some speculations on the relation between this picture and the computational universe hypothesis.
 
  • #3
Some other sources:
(Rovelli)
http://relativity.livingreviews.org/Articles/lrr-2008-5/ [Broken]


The video and slides of Carlo Rovelli's talk at Strings 2008 provides a good introductory overview of LQG.
Here are the links:
Video:
http://cdsweb.cern.ch/record/1121957?ln=en
Slides:
http://indico.cern.ch/getFile.py/acc...s&confId=21917 [Broken]

An early draft of Rovelli's book online free for anyone who doesn't have the published version:
http://www.cpt.univ-mrs.fr/~rovelli/book.pdf

Another good overview of the whole field of quantum geometry/gravity, Rovelli's chapter in Oriti's book:
http://arxiv.org/abs/gr-qc/0604045

Rovelli:
Interestingly, LQG predicts that when areas and volumes of physical objects are measured they will come out in quantized levels, like the energy levels of a hydrogen atom. The area and volume operators have discrete spectrum. This is not put in by defining the theory on a lattice, it comes out as an advanced result, because the geometric operators corresponding to measurements are part of a quantum theory. Discrete spectra of operators is a kind of discreteness, and it turns out to be entirely compatible with Lorentz symmetry! Rovelli had a paper about that in 2002 or 2003. It's actually kind of neat how it works out. I will get the link for that in case you want to pursue it further.
http://arxiv.org/abs/gr-qc/0205108
Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction
////////////

"A Planck-scale minimal observable length appears in many approaches to quantum gravity. It is sometimes argued that this minimal length might conflict with Lorentz invariance, because a boosted observer could see the minimal length further Lorentz contracted. We show that this is not the case within loop quantum gravity. In loop quantum gravity the minimal length (more precisely, minimal area) does not appear as a fixed property of geometry, but rather as the minimal (nonzero) eigenvalue of a quantum observable. The boosted observer can see the same observable spectrum, with the same minimal area. What changes continuously in the boost transformation is not the value of the minimal length: it is the probability distribution of seeing one or the other of the discrete eigenvalues of the area. We discuss several difficulties associated with boosts and area measurement in quantum gravity.
http://arxiv.org/abs/gr-qc/0205108
 
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  • #4
tom.stoer said:
Attention: this is a rather speculative idea - but fascinating as it may point towards particles entirely based on space-time.

Isn't this now a fairly standard mental picture of things?

It seems natural to take a top-down constraints-based approach as modeled in condensed matter physics. Spacetime is a "stuff" that can develop local knots or trapped resonances in soliton like fashion.

But then it is hard to turn this intuitive vision into a mathematical model as maths needs to construct from the bottom-up. To compute, you need a discrete description. So in the move from intuition to the practical modelling, you have to use lattices, loops, strings, networks, infomation bits - something with essential "grain".

So the situation would seem to be intuitively that grain, in the guise of particles and other local features, arises as a limit to a continuity of interactions. But practically, we have to come at the modelling from the other direction - assuming the grain to be what fundamentally exists, and then building up the continuous background that in fact gave rise to it.
 
  • #5
Naty1 said:
Some other sources:
(Rovelli)
http://relativity.livingreviews.org/Articles/lrr-2008-5/ [Broken]


The video and slides of Carlo Rovelli's talk at Strings 2008 provides a good introductory overview of LQG.
Here are the links:
Video:
http://cdsweb.cern.ch/record/1121957?ln=en
Slides:
http://indico.cern.ch/getFile.py/acc...s&confId=21917 [Broken]

An early draft of Rovelli's book online free for anyone who doesn't have the published version:
http://www.cpt.univ-mrs.fr/~rovelli/book.pdf

Another good overview of the whole field of quantum geometry/gravity, Rovelli's chapter in Oriti's book:
http://arxiv.org/abs/gr-qc/0604045

Rovelli:
Interestingly, LQG predicts that when areas and volumes of physical objects are measured they will come out in quantized levels, like the energy levels of a hydrogen atom. The area and volume operators have discrete spectrum. This is not put in by defining the theory on a lattice, it comes out as an advanced result, because the geometric operators corresponding to measurements are part of a quantum theory. Discrete spectra of operators is a kind of discreteness, and it turns out to be entirely compatible with Lorentz symmetry! Rovelli had a paper about that in 2002 or 2003. It's actually kind of neat how it works out. I will get the link for that in case you want to pursue it further.
http://arxiv.org/abs/gr-qc/0205108
Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction
////////////

"A Planck-scale minimal observable length appears in many approaches to quantum gravity. It is sometimes argued that this minimal length might conflict with Lorentz invariance, because a boosted observer could see the minimal length further Lorentz contracted. We show that this is not the case within loop quantum gravity. In loop quantum gravity the minimal length (more precisely, minimal area) does not appear as a fixed property of geometry, but rather as the minimal (nonzero) eigenvalue of a quantum observable. The boosted observer can see the same observable spectrum, with the same minimal area. What changes continuously in the boost transformation is not the value of the minimal length: it is the probability distribution of seeing one or the other of the discrete eigenvalues of the area. We discuss several difficulties associated with boosts and area measurement in quantum gravity.
http://arxiv.org/abs/gr-qc/0205108

@ericbrown86: These are nice LQG references, not for this ribbon-like braiding and twisting stuff.
 
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  • #6
apeiron said:
Isn't this now a fairly standard mental picture of things?

It seems natural to take a top-down constraints-based approach as modeled in condensed matter physics. Spacetime is a "stuff" that can develop local knots or trapped resonances in soliton like fashion.
With the statement that this is a rather speculative idea - but fascinating as it may point towards particles entirely based on space-time I meant the ribbon idea, not spacetime discreteness. The latter one is somehow common to many approaches regarding QG, even if they differ in the details (effective two-dim. spacetime in the UV has been derived in CDT, asymptotic safety and Horava gravity; ST, AdS/CFT and LQG agree mostly on BH entropy; so there are some common features).

But the main question is if this spacetime discreteness provides a structure from which matter degrees of freedom may emerge. This is certainly not standard. In standard spin networks the knotting of the graph doesn't matter, only its coloring is relevant. So standard LQG w/o ribbons is not sufficient.
 
  • #7
tom.stoer said:
With the statement that this is a rather speculative idea - but fascinating as it may point towards particles entirely based on space-time I meant the ribbon idea, not spacetime discreteness. The latter one is somehow common to many approaches regarding QG, even if they differ in the details (effective two-dim. spacetime in the UV has been derived in CDT, asymptotic safety and Horava gravity; ST, AdS/CFT and LQG agree mostly on BH entropy; so there are some common features).

But the main question is if this spacetime discreteness provides a structure from which matter degrees of freedom may emerge. This is certainly not standard. In standard spin networks the knotting of the graph doesn't matter, only its coloring is relevant. So standard LQG w/o ribbons is not sufficient.

Sorry, I missed that you were talking about braids as a particular approach.

But you would agree with the general situation? Many would see locally fundamental features like particles as emergent in the fashion of solitons in condensed matter physics. Yet still the best approach to modelling such a reality remains one that starts with these local features simply existing as discrete entities, and then building upwards from them to a continuous fabric of reality.

Braids for example would express certain degrees of freedom as a physical shape. It would take the shapes as having brute existence (not asking how they might in fact have emerged via global constraints) and then model how reality could be woven from the interactions the basic shapes make possible.
 
  • #8
tom.stoer said:
With the statement that this is a rather speculative idea - but fascinating as it may point towards particles entirely based on space-time I meant the ribbon idea, not spacetime discreteness. The latter one is somehow common to many approaches regarding QG, even if they differ in the details (effective two-dim. spacetime in the UV has been derived in CDT, asymptotic safety and Horava gravity; ST, AdS/CFT and LQG agree mostly on BH entropy; so there are some common features).

But the main question is if this spacetime discreteness provides a structure from which matter degrees of freedom may emerge. This is certainly not standard. In standard spin networks the knotting of the graph doesn't matter, only its coloring is relevant. So standard LQG w/o ribbons is not sufficient.

What are elementary particles in NCG? Has Connes or others provided a Planck scale picture of what SM in NCG?
 
  • #9
ensabah6 said:
What are elementary particles in NCG? Has Connes or others provided a Planck scale picture of what SM in NCG?

As far as I understand (and I do not understand much about NCG) particles (or fields)emergy as some fluctuations in a fundamental dirac operator. I don't think that this is a "physical" picture.
 
  • #10
tom.stoer said:
As far as I understand (and I do not understand much about NCG) particles (or fields)emergy as some fluctuations in a fundamental dirac operator. I don't think that this is a "physical" picture.

One interpretation of a particle is that it is a localized interaction of a field. Is this "field as fundamental" interpretation of particles compatible with things like strings and braiding or excitation of spacetime?
 
  • #11
ensabah6 said:
One interpretation of a particle is that it is a localized interaction of a field. Is this "field as fundamental" interpretation of particles compatible with things like strings and braiding or excitation of spacetime?
Are you referring to standard quantum field theory here?

In string theory particles are something different (vibrating strings); in the low-energy effective models derived from strings a picture like standard quantum field theory emerges. So yes, there's compatibility.

It is much too early to judge if and how standard quantum field theory and the above mentioned braids are related.
 
  • #12
tom.stoer said:
Are you referring to standard quantum field theory here?

In string theory particles are something different (vibrating strings); in the low-energy effective models derived from strings a picture like standard quantum field theory emerges. So yes, there's compatibility.

It is much too early to judge if and how standard quantum field theory and the above mentioned braids are related.

standard quantum field theory - but I've wondered as much with preons, braiding, etc. And the interpretation of particles in NCG. What is spacetime fundamentally in NCG?
 
  • #13
Fundamentally there is no spacetime in NCG.

Usually one takes a manifold M and defines operators (Laplacian, Dirac, ...) on top of it. This results in a so-called spectral triple (A, H, D) with a C* algebra A, a Hilbert space H on which A acts and a differential operator D. One can then show that one can re-construct the metric properties on M by using eigenfunctions of D living in H.

One can turn this round and start with a spectral triple (A, H, D) w/o underlying manifold! Again the reconstruction of the metric works, therefore something like a manifold emerges from (A, H, D).

If this program is successfull the world is just a special (A, H, D)
 
  • #14
ericbrown86 said:
It is a common theme among background independent quantum gravity theories that there should be some sort of discretization, or fuzziness, of the spacetime manifold occurring on Planckian scales.

It has occurred to me that if we take this discretization to consist of a lattice of sorts, might matter on this spacetime not be described via some sort of lattice excitation or vibration, in the same way that vibrations of a crystal lattice allows a particle description (i.e. the phonon)? Of course one would have to figure out, for example, how these excitations could induce a global curvature to the manifold, etc. But even so, it seems to me an interesting idea.

I was just wondering if anyone here knows of any research that has been done regarding this idea, or has any insights they with to discuss. I would love to see if anyone has worked on this.

Thanks!
- Eric

In my theory QSA space itself is defined by energy lines which the ends of one side accumulate to form particle position(Born’s rule) and the other end goes all over the universe. So in this theory space itself is defined by the particles, i.e. no energy lines defining particles no space defined.
The theory unifies concepts of mass, charge, particle probability position, force/momentum (interactions), space and time all in one unified concept based on the random length of lines and their positions. The theory goes very well with Smolin’s comment that the concept of particles as end of lines should be studied.
It is one example of what is possible. http://www.qsa.netne.net
More info about QSA on http://fqxi.org/community/forum/topic/639
 
  • #15
Another example ... from marcus posts


http://arxiv.org/abs/1006.2230

On the geometrization of matter by exotic smoothness

Torsten Asselmeyer-Maluga, Helge Rose
17 pages
(Submitted on 11 Jun 2010)
"Clifford's hypothesis is investigated: A particle is made up of nothing but a distinct type of a space manifold, differing from the surrounding manifold of empty space. It is shown that this distinct space manifold representing matter differs from the surrounding vacuum by the exotic smoothness of its spacetime. The smoothness structure of spacetime can be described by a tree-like subset -- the Casson handle -- consisting of immersed discs and connecting tubes between them. The Weierstrass representation shows that the immersed discs are represented by spinors fulfilling the Dirac equation and leading to a mass-less Dirac term in the Einstein-Hilbert action. The connecting tubes between the discs realize an action term of a gauge field. Both terms are purly geometrical and characterized by the mean curvature of the components of the Casson handle. This gives a good support to Clifford's conjecture that matter is nothing more but an exotic kind of space."
 
  • #16
tom.stoer said:
One can turn this round and start with a spectral triple (A, H, D) w/o underlying manifold! Again the reconstruction of the metric works, therefore something like a manifold emerges from (A, H, D).

Damn! I finally understood what Conne's Spectral Triple is about! I never understood even the basic idea! Thank you!

Now, it makes sense to try to implement it with LQG, since both start without a manifold.
 
  • #17
tom.stoer said:
Fundamentally there is no spacetime in NCG.

Usually one takes a manifold M and defines operators (Laplacian, Dirac, ...) on top of it. This results in a so-called spectral triple (A, H, D) with a C* algebra A, a Hilbert space H on which A acts and a differential operator D. One can then show that one can re-construct the metric properties on M by using eigenfunctions of D living in H.

One can turn this round and start with a spectral triple (A, H, D) w/o underlying manifold! Again the reconstruction of the metric works, therefore something like a manifold emerges from (A, H, D).

If this program is successfull the world is just a special (A, H, D)

MTd2 said:
Damn! I finally understood what Conne's Spectral Triple is about! I never understood even the basic idea! Thank you!

Now, it makes sense to try to implement it with LQG, since both start without a manifold.
Since the SM exists, and background independent GR exist, shouldn't the entire research be devoted to LQG+NCG?

i.e loop non commutative geometry. LNG Noncommutative quantum geometery NQG noncommutative loop geometery NLG
 
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  • #18
ensabah6 said:
Since the SM exists, and background independent GR exist, shouldn't the entire research be devoted to LQG+NCG?

i.e loop non commutative geometry. LNG Noncommutative quantum geometery NQG noncommutative loop geometery NLG
In order to harmonize bot approaches they have to be cropped.

LQG starts with a manifold and eventually arrives at spin networks. Spin networks are not present in NCG. NCG starts with a spectral triple which in itself is already an effective theory; can it be based on spin networks? LQG is compatible with aditionaly matter fields living on the vertices and links (additional coloring). NCG comes with its own idea how matter can emerge. LQG may provide braided SFs with "topologically emergent matter", but NGC wants to do that, too. NCG does not explain the nc space it si based (afaik), so it translates the unknown symmetry group of the SM to an unknwon nc space w/o explanation why this space.

It is definately a very interesting approach, but unfortunately both research programs are nearly complete; so technically they have not much in common, but regarding their features they have a huge overlap.
 
  • #19
Oh, right. I just checked the sources. A spin network starts without a manifold since it lacks the concept of neighborhood, all that exists are vertexes that connects. The challenge is to find a set of rules that makes the wave function of spin foams, that is, spin networks evolving in space time, be the same of LQG, and so, be sure that gravity can be defined not only background independently, but also out of (almost) nothing.

NCG seems to follow the same path, a spectral triple, which is almost nothing, into something real.

So, I guess the cool thing is to start with a spectral triple spin network .
 
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  • #20
Afaik the spectral triple is based on an algebra of functions on top of "something"; this "something" need not be a manifold (but one can reconstruct certain aspects of a manifold like a metric using the spectral triple).

So one needs at least "something", which could be a spin network. But I think the structure of a spin network is already "too rich" to be interesting. The NCG approach is nicest if the "something" has almost no structure.
 
  • #21
tom.stoer said:
Afaik the spectral triple is based on an algebra of functions on top of "something"; this "something" need not be a manifold (but one can reconstruct certain aspects of a manifold like a metric using the spectral triple).

So one needs at least "something", which could be a spin network. But I think the structure of a spin network is already "too rich" to be interesting. The NCG approach is nicest if the "something" has almost no structure.

How impressed are you with previous papers on the subject, for example,


http://arxiv.org/abs/0802.1783
On Spectral Triples in Quantum Gravity I
Johannes Aastrup, Jesper M. Grimstrup, Ryszard Nest
84 pages, 8 figures
(Submitted on 13 Feb 2008)

"This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator which resembles a global functional derivation operator. The interaction between the Dirac operator and the algebra reproduces the Poisson structure of General Relativity. Moreover, the associated Hilbert space corresponds, up to a discrete symmetry group, to the Hilbert space of diffeomorphism invariant states known from Loop Quantum Gravity. Correspondingly, the square of the Dirac operator has, in terms of canonical quantum gravity, the form of a global area-squared operator. Furthermore, the spectral action resembles a partition function of Quantum Gravity. The construction is background independent and is based on an inductive system of triangulations. This paper is the first of two papers on the subject."


http://arxiv.org/abs/0802.1784
On Spectral Triples in Quantum Gravity II
Johannes Aastrup, Jesper M. Grimstrup, Ryszard Nest
43 pages, 1 figure
(Submitted on 13 Feb 2008)

"A semifinite spectral triple for an algebra canonically associated to canonical quantum gravity is constructed. The algebra is generated by based loops in a triangulation and its barycentric subdivisions. The underlying space can be seen as a gauge fixing of the unconstrained state space of Loop Quantum Gravity. This paper is the second of two papers on the subject."
 
  • #22
ensabah6 said:
How impressed are you with previous papers on the subject, ...
I will try to understand the details.

I know that both approaches (LQG and NCG) are work in progress, so is their combination. As I said:what I expect eventually is a kind of harmonization on a rather low level. So instead of adding even more powerfull math the combination should look simpler and more natural than the two individual approaches (I don't want to be arrogant to advise these excellent people!)
 
  • #23
tom.stoer said:
One must not think about spacetime as a lattice; this would violate several symmetries, e.g. diff. inv. So the picture is definately more complex.

I know this thread is a bit old, but I was hoping that someone would elaborate on tom.stoer's comment here.

What property of a lattice-based spacetime would violate diffeomorphism invariance?
 
  • #24
Diffeomorphism invariance is about coordinate changes. It relies on concepts like manifolds, infinitesimal changes, smooth (or at least differentiable) functions of coordinates etc. But a lattice is fundamentally discrete, so you can't define diffeomorphisms on a fixed lattice.

What LQG does is to "fix" diffeomorphism invariance completely; just like gauge fixing. After you have done that the symmetry has been reduced to the identity. That's why the symmetry is not violated. The theory is trivially invariant as you can't break the symmetry w.r.t. to the identity transformation. But in order to achieve hat all coordinates must go away. Coordinates are unphysical, so they ave to vanish completely. And in that sense the discrete structure in LQG is not a lattice of spacetime points.
 
  • #25
tom.stoer said:
Diffeomorphism invariance is about coordinate changes. It relies on concepts like manifolds, infinitesimal changes, smooth (or at least differentiable) functions of coordinates etc. But a lattice is fundamentally discrete, so you can't define diffeomorphisms on a fixed lattice.

Thanks. Okay, I was thinking of the term lattice incorrectly, when I read this I was thinking more of a big stretchy mesh rather than something that was fixed. I was thinking that if matter was composed of excitations on a lattice then this implied to me that the lattice is continuous and excitable and more like a moving membrane than a fixed immovable structure. So this was wrong.

So perhaps the very ideas of excitations and lattice are incompatible since lattices are discrete by definition and I'm not sure how you'd get excitations on a discrete entity without breaking the nature of the lattice itself. Which is probably what you were getting at in your reply to the OP.
 
  • #26
Think about the surface of a lake. It looks like a smooth manifold. If you look closer, you will find water molecules or even H and O atomes. So it seems as if the surface consists of H and O atoms. But in principle the very concept of "manifold", "surface", "water waves" has disappeared. There are only atoms.

It's the same with the spin network in LQG. There is not space between the "lattice points" - just as there is no water between the atoms. The water "is" the atoms - or the other way round "the atoms are the water".
 
  • #27
tom.stoer said:
Think about the surface of a lake. It looks like a smooth manifold. If you look closer, you will find water molecules or even H and O atomes. So it seems as if the surface consists of H and O atoms. But in principle the very concept of "manifold", "surface", "water waves" has disappeared. There are only atoms.

It's the same with the spin network in LQG. There is not space between the "lattice points" - just as there is no water between the atoms. The water "is" the atoms - or the other way round "the atoms are the water".

Classic. I like how these 7 words have some resonance: "There is no water between the atoms."
There should be a short introductory QG book written in such clear style.
 
  • #28
tom.stoer said:
It's the same with the spin network in LQG. There is not space between the "lattice points" - just as there is no water between the atoms. The water "is" the atoms - or the other way round "the atoms are the water".

Okay, so the interactions that allow things like waves are modeled by adjacent "lattice points" bumping up against each other in some well defined but chaotic manner? Or is there some rules built into any particular LQG model to account for the interactions of adjacent lattice points.
 
  • #29
The dynamics of LQG is well-defined. It's based on so-called spin networks. Every link (edge) in the network carries something like a spin; of course nothing really "spins", but it's similar in the mathematical language used. At every vertex, where different links (spins) meet, they are "intertwined". The spin network therefore carries additional information in its vertices and edges. There are well-defined rules how these spins interact; there are rules how additional vertices and links can be created. Each vertex represents an "atom of space" - a minimal volume. Each link represents a minimal surface.

On this level the mathematical structure is rather clear. One big question is how matter could emerge from these structures w/o additional input. Another question is how the well-known spacetimewe observe (the "water") emerges from these structures.

There is some progress especially regarding the second problem, but the whole picture is not complete - it's work in progress.
 

1. What is a spacetime lattice?

A spacetime lattice is a theoretical framework that suggests that at the smallest scales of space and time, the universe is made up of a discrete, grid-like structure. This lattice is thought to underlie the fabric of spacetime and could potentially explain some of the fundamental properties and behaviors of matter and energy.

2. How are matter and excitations of the spacetime lattice related?

In this theory, matter is considered to be excitations or disturbances in the spacetime lattice. Just as a wave moving through water causes ripples and disturbances in the water's surface, matter moving through the lattice creates excitations in the lattice itself. These excitations are what we perceive as particles and energy.

3. Can the spacetime lattice theory be tested?

Currently, there is no experimental evidence to support the spacetime lattice theory. However, some researchers are working on developing experiments and techniques to potentially test and validate this theory. It is still a highly theoretical concept and much more research is needed before any definitive conclusions can be made.

4. How does this theory relate to other theories of the universe?

The spacetime lattice theory is still a relatively new and unproven concept, so its relationship to other theories of the universe is still being explored. Some scientists believe that this theory could potentially bridge the gap between quantum mechanics and general relativity, as it offers a way to unify these two seemingly incompatible theories.

5. What implications does this theory have for our understanding of the universe?

If the spacetime lattice theory is proven to be true, it would have significant implications for our understanding of the universe. It could potentially explain the origins of matter and energy, and provide a deeper understanding of the fundamental forces and interactions at play in the universe. It could also have practical applications, such as helping to develop new technologies and improve our understanding of cosmology and the early universe.

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