Thursday, December 19, 2013

Searching for Spacetime Defects

Defects in graphene.
Image source: IOP.
Whether or not space and time are fundamentally discrete is one of the central questions of quantum gravity. Discretization is a powerful method to tame divergences that plague the quantization of gravity, and it is thus not surprising that many approaches to quantum gravity rely on some discrete structure, may that be condensed matter analogies, triangulations, or approaches based on networks. One expects that discretization explains the occurrence of singularities in general relativity as unphysical, much like singularities in hydrodynamics are merely mathematical artifacts that appear because on short distances the fluid approximation for collections of atoms is no longer applicable.

But finding experimental evidence for space-time discreteness is difficult because this structure is at the Planck scale and thus way beyond what we can directly probe. The best tests for such discrete approaches thus do not rely on the discreteness itself but on the baggage it brings, such as violations or deformations of Lorentz-symmetry that can be very precisely tested. Alas, what if the discrete structure does not violate Lorentz-symmetry? That is the question I have addressed in my two recent papers.

In discrete approaches to quantum gravity, space-time is not, fundamentally, a smooth background. Instead, the smooth background that we use in general relativity – the rubber sheet on which the marbles roll – is only an approximation that becomes useful at long distances. The discrete structure itself may be hard to test, but in any such discrete approach one expects the approximation of the smooth background to be imperfect. The discrete structure will have defects, much like crystals have defects, just because perfection would require additional explanation.

The presence of space-time defects affects how particles travel through the background, and the defects thus become potentially observable, constituting indirect evidence for space-time discreteness.To be able to quantify the effects, one needs a phenomenological model that connects the number and type of defects to observables, and can in return serve to derive constraints on the prevalence and properties of the defects.

In my papers, I distinguished two different types of defects: local defects and non-local defects. The requirement that Lorentz-invariance is maintained (on the average) turned out to be very restrictive on what these defects can possibly do.

The local defects are similar to defects in crystals, except that they are localized both in space and in time. These local defects essentially induce a violation of momentum conservation. This leads to a fairly straight-forward modification of particle interactions whenever a defect is encountered that makes the defects potentially observable even if they are very sparse.

The non-local defects are less intuitive from the particle-physics point of view. They were motivated by what Markopoulou and Smolin called ‘disordered locality’ in spin-networks, just that I did not, try as I might, succeed in constructing a version of disordered locality compatible with Lorentz-invariance. The non-local defects in my paper are thus essentially the dual of the local defects, which renders them Lorentz-invariant (on the average). Non-local defects induce a shift in position space in the same way that the local defects induce a shift in momentum space.

I looked at a bunch of observable effects that the presence of defects of either type would lead to, such as CMB heating (from photon decay induced by scattering on the local defects) or the blurring of distant astrophysical sources (from deviations of photons from the lightcone caused by non-local defects). It turns out that generally the constraints are stronger for low-energetic particles, in constrast to what one finds in deformations of Lorentz-invariance.

Existing data give some pretty good constraints on the density of defects and the parameters that quantify the scattering process. In the case of local defects, the density is roughly speaking less than one per fm4. That’s an exponent, not a footnote: It has to be a four-volume, otherwise it wouldn’t be Lorentz-invariant. For the non-local defects the constraints cannot as easily be summarized in a single number because they depend on several parameters, but there are contour plots in my papers.

The constraints so far are interesting, but not overwhelmingly exciting. The reason is that the models are only for flat space and thus not suitable to study cosmological data. To make progress, I'll have to generalize them to curved backgrounds. I also would like to combine both types of defects in a single model. I am presently quite excited about this because there is basically nobody who has previously looked at space-time defects, and there’s thus a real possibility that analyzing the data the right way might reveal something unexpected. And into the other direction, I am looking into a way to connect this phenomenological model to approaches to quantum gravity by extracting the parameters that I have used. So, you see, more work to do...


  1. Bee:much like singularities in hydrodynamics are merely mathematical artifacts that appear because on short distances the fluid approximation for collections of atoms is no longer applicable.

    Any papers showing this?

    Not that, such a singularity has been proven not to exist in terms of the fluid approximation, yes?


  2. In AWT the question, whether the space-time is continuous is analogous to question, whether the water surface continuous, if we would observe it with its own surface ripples at small scales?

    black hole

    If we define the space-time like the environment for spreading of transverse waves, then at both small or large scales such an environment will become discontinuous and fragmented into many density fluctuations. But this is just a local perspective of us, human observers.

    If we would shrink/expand into scale of space-time fluctuations, then the scale of space-time fluctuations would shrink accordingly. This is just another example of relative reality concept.

  3. I really do not have a pet theory but do appreciate that if any approximation could lead to something correlated in the very nature of QGP, as to it's fluid design, it is held in context as continuity? This could be a mistake on my part.

    Then, this would further correspond to development and continuity of lets say, when jets are produced?


    1. Gee, I had a great reply for you. Looks like it didn't go thru
      Great essay even without equations in it. :-)

  4. Edgar, There's nothing in the spam filter from you, seems it got lost indeed. Sorry about that, very annoying :(

  5. Plato,

    Not sure what you are asking for. If you're on distances comparable to the size of an atom a continuum approximation clearly doesn't make sense anymore. You can look at it this way: In the hydrodynamical description you find singular solutions, but if you were to zoom in around the singularity, you'd eventually start seeing the 'grainy' (atomic) structure of the fluid. Best,


  6. Hi Bee,

    In the QGP is there a point to point measure?

    I guess at Planck scale should you choose to use discreteness as a model.....


  7. BEE:For example, in General Relativity, Einstein's field equations when applied to the gravitational collapse of a very massive star develop infinities in density and curvature at the centre of the system. Singularities in your Kitchen

  8. 12 pentagons close an unlimited hexagon tessellation into an elliptic surface. 12 heptagons do what hyperbolically? Equal numbers cancel even if non-adjacent. Discrete spacetime is incompatible with vacuum isotropy and conservation of angular momentum, arXiv:1109.1963 Suppose the tessellation is nothing but defects! A quasitiling is aperiodic (periodic in 5D) but has a sharp spot diffraction. They have assigned space groups,

    "But finding experimental evidence for space-time discreteness is difficulty" Measurable Lorentz-symmetry violation need only occur where physics refuses to look. Green's function removes physical chirality from Newton. Green's function is not within GR. The universe is not mirror-symmetric toward fermionic matter (quarks): parity violations, chiral anomalies, symmetry breakings; Chern-Simons repair of Einstein-Hilbert action. Physics has been burned for denying chirality,

    Phys. Rev. 104(1) 254 (1956) Heretical, stupid idea...
    Phys. Rev. 105(4) 1413 (1957) ...that is observed...
    Phys. Rev. 105(4) 1415 (1957) ...and independently confirmed...
    PNAS 14(7) 544 (1928) ...28 years after it was observed and rejected for being impossible.

    Do discretized spaces have torsion? If so, they are chiral or racemic, crystallography's screw axes (A + B = N-fold axis). An -even numbered N-fold screw axis has a racemic version N/2, e.g 6(1),6(5); 6(2)6(4); 6(3). A pair's lowest number is right-handed. Paired enantiomorphic space groups are mathematically chiral independent of contents, Section 2 Section 3ff.

    "Wick-rotation" Projecting graphs down by one dimension (cf: Schlegel diagrams) bumps into Kuratowski's theorem (e.g,, knots). There are more than 66 million organic compounds in the CAS Registry. About a dozen are K(5) molecules. Organic chemistry is flat, even the fullerenes and other bubbles.

    Empirical not quite exact angular momentum conservation is MoND's Milgrom acceleration uncreating dark matter. Any Lorentz-symmetry violation is detected by a geometric Eötvös experiment.
    The apparatus. Load the image in a separate frame for a much larger view,

    insert visually and chemically identical, single crystal test masses in enantiomorphic space groups, such as P3(1)21 versus P3(2)21 alpha-quartz (about 20,000 tonnes/year commercially grown for crystal oscillator chips). Given 0.113 nm^3 volume/alpha-quartz unit cell, the 40 gram net load as 8 single crystal test masses compares 6.68×10^22 pairs of opposite shoes (pairs of enantiomorphic unit cells). One vertical side of the test mass cubic array is left-handed, the other right-handed. Differential vacuum free fall (bets are on divergent speeds not directions) is torque bringing that interferometer leg (plane mirrors) out of null into a single photon counter.

    Symmetry "problems" in discretized spaces are natural evolution. Their presence is measurable vs. isotropic vacuum to one part in 20 trillion difference/average on a bench top within 90 days. Derive your theory, model its chiral divergence, tell the U/Washington Physics Department/CENPA to run a geometric Eötvös experiment

  9. All very interesting.

  10. PhysRevD - Wow - congratulations!

  11. forgot to mention 't Hooft's recent preprint, promoting his discrete determistic Hamiltonian formulation of QM

  12. The search for space-time defects may not be a difficult task, until we consider all forces violating the inverse square law (with exception of gravity) into account. The various dipole and dispersion forces, Casimir force and magnetic forces may affect the geodesic motion of massive bodies across space-time and as such they can be considered a space-time defects too.

    Alternatively you may want to define the space-time just with light spreading and after then we can consider all gravitational lensing and dark matter effects as a manifestation of space-time defects. If you decide not to consider them as a space-time defect violating the dimensionality of space-time, then indeed some more detailed criterion of "space-time defect" would be welcomed here.

  13. In another words, most of problems of contemporary physics are just a problem of vague terminology.

  14. Jaybeegee,

    Thanks for mentioning 't Hooft's paper, I had missed it! Should probably have a look. (Unfortunately, this just reminded me there's a proceedings deadline at the end of the month.) Best,


  15. "A particle that encounters a nonlocal defect continues its path in space-time elsewhere, but with the same momentum"

    Seems you 've just invented the absolute space-time travel mechanism!

  16. Well, the interaction probability for localized states is basically zero. So there's not much travel that you can do with these defects, unless you can cook up a mechanism to collect them.

  17. IMO magnetic motors work on this principle. They're collecting magnetic monopoles and harnessing negentropic work from them. The ensembles of Dirac fermions inside of superconductors and topological insulators can violate the gravitational law instead.

  18. Bee - " I am presently quite excited about this because there is basically nobody who has previously looked at space-time defects, and there’s thus a real possibility that analyzing the data the right way might reveal something unexpected. "

    Well now you've done gone and done it.. there will soon be a stampede of researchers chasing your lead!

    Congrats though on PRD .. haven't picked up a copy in quite some time, even before I switched from APS to IOP

  19. "a mechanism to collect them", that's exactly what crossed my mind! I just couldn't figure out what such mechanism would based upon as there was no evidence on your papers for possible interaction mechanisms between such defects so that I could set up a bait to lure some of them nasty beasts to make them gather! But you are so much more clever and I trust that you could figure out a plan for this...

  20. As a chemist,
    one thinks of C60, when looking at that graphite monolayer with pentagon defects.

  21. @Georg An unlimited size graphene sheet closes to an elliptic surface given 12 internal regular pentagons. The smallest example is dodecahedrane, C_20H_20. A C_260 fullerene,
    (View with CHIME plug-in)

    is point group I (not I_h) and is calculated to be perfectly mathematically chiral. Petitjean's CHI = 0, COR = 1, DSI = 0, J. Math. Phys. 40, 4587 (1999). The fun question is, what hyperbolic shape is chicken wire incorporating 12 heptagons?

  22. Bee is moving on up and Congratulations! Today a D (Physical Review D), not the best grade, but tomorrow an A (Physical Review A)!

  23. This comment has been removed by the author.

  24. Bee can you kindly update on what will be needed to experimentally test Doubly Special Relativity and Discrete Spacetime theories? Can they be tested today, or do we need tomorrow's technology?

    You are obviously very familiar with Giovanni Amelino-Camelia's work (and have cited him in your PRD paper too). In 2001 he wrote the paper "Testable scenario for Relativity with minimum-length." That paper says: "[O]ne might be tempted to assume that none of these effects could be tested in the near future. However, this is not true, at least not for" [part of what he theorizes in his paper].

    Thanks in advance for any information you can provide regarding experiments that can be done or are in planning.

  25. Basically, I said your phenomenological approach is a more advanced way to explore the cosmological question as physics. Just as Crick and Watson asked facing models to assemble of DNA with due regard for Rosylin's data from the crystal structure.
    A minimum distance concept needs to consider the relation to min duration (divided by c) beyond linear. This a long standing foundational early proposal.
    How they test the Casmir thus a relation to the cosmological constant I do not know the tech. But instead of two planes of metal use graphine more than five atoms close.
    As we can think of such forces as particals, in the apparent nonlinear of it all shoot particles (leptons? ) through it with sensors that encode the landscape.
    It may take biochemistry to simplify the design as it encounters issues of theory in its complexity. Uncle Al has some very relavant ideas for this.
    Then again there is QM logic to consider in polarization. Maybe sets of double planes in sets.
    But of the three great arguments for the existince (of God) or some yet unknown as dispassionate Ontology, I feel Teleology should fit in somewhere
    if a poet may speak. Best..

    1. I want to add some consequences should such an experiment work.
      Crick et al in perfecting their model took the cosmological answer to be its role of replication. So they thought of hydrogen bonding.
      If the experiments work it would make more natural ways to intervine to aid globally from a higher stance of Phenomenology methods and self repair of errors by code buildt already into the generation problem answered as general to DNA topology.
      This could lead to whole new areas of physics as that essential distinction between codons (36) on 3D and the rest reaching into 4D of the 64.
      New classes of "particles " will be found. (Cosmons, Melissons, Over such abstract unified sheets ...quasons but -on or -inorganic are not good suffixes)
      Nor Vanderaals as force, Uncle Bob.
      Such fields or "particles" like a living cell may balance over min space time higherGR analog for micro errors too at a local or reached spacious singularity. Laws again as life (mind) everywhere uniform.

    2. Interesting, the idea of collecting such singularities. Where it may be the linear position (or non-linear, non-local superposition) may be a fixed number coordinate code such as holes involving Goldbach's conjecture.
      Time travel may be limited over a quantum span both ways into the past of future as QM theory seems to suggest
      At spacious field of zero D as rest we see duration as nature solving and adapting a unique existential code which can be similar to Newtonian aether ideas in the sense as Einstein said we may as well use the term as a hyponym.
      A possible consequence of this enquiry is a need for abstract Labeling (theory) as a standard choice independent but by the same methods a neutral reference frame.
      (You go girl! What the heck is gravity? Melission means honey Bee and it is more than issues of subjective statistics or terminology. How fitting you would think about the honeycomb or seek the spiral symmetry of sunflowers following the sun then try to see more than a wax cell as accidental measure in our models of prophilis and pressure. Thanks for your gift of new inspiration.)

  26. REF:

    Think bigger! Defects (voids) in a granular spacetime equals wormholes?

  27. Think about this Frank: no matter how many millions some agency throws or wastes to strengthen encryption it will not work unless they understood on a higher level the very question you asked us to think about.

  28. Frank,

    I thought about this, but couldn't make sense of it. Best,


  29. Hi - I'm not a physicist, but very interested in these questions and love perusing this blog. My question is, space-time defects seem IMHO much more question-begging than perfection. Because if space-time geometry is the essential substrate of reality, what could intervene into it to create a defect? That would seem to presuppose something external to that geometry that could cause a defect.

  30. Unknown artist from another artist interested in these questions :
    Perhaps the essence as an underlying perfection is the question. How art relates reflecting and influencing the other would views or the world.
    An artist friend (we were so young then) saw me making a Pauling dodecahedron of straws and jacks from an inorganic chemistry set then asked me if I could make a ball of hexagons. I said no but let him try. After he convinced himself there was some sort of restrictions he became free to make some intricate structures quite independent of the underlying organic chemistry (perhaps? ) and they were beautiful.
    In the Gothic West grotesque gargoyles were added to cathedrals as a token of humility that there may be more than we know pointing or reaching for the stars.

    Or in the East a work of carving with long intricate perfected steps adds a defect (wabi) . Or in the beads in beads of finer colors and ink the paintings come alive beyond projection to an ideal point that these can fill the plane everywhere.

    We can of course choose to seek higher art so prove its limitations or copy the iron work on a Singer sewing machine down to errors in the mould

    In the calligraphy of our scribbles we can take a lifetime to draw the same circle or line segment in black on white. But even Zen masters do not try to do both in pursuit of perfection.

    This may change with our generation.

  31. Unknown,

    You're confused because you got the premise up-side down. In this scenario geometry is *not* the 'essential substrate of reality'. Instead, the fundamental structure is something entirely different, some kind of network, something that's discrete and just approximates a smooth background. Best,



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