Where Twisted Light Could Help Detect Drones

Light can be made to carry orbital angular momentum. The wavefront spirals around the propagation axis like a corkscrew, and the beam profile takes on a characteristic doughnut shape with a dark center. This is "OAM light," and it has a property that makes it interesting for sensing rotating things: when an OAM beam reflects off a smooth rotating surface, it picks up a Doppler shift proportional to the OAM order times the rotation rate, separately from any standard linear Doppler shift the target produces.

This effect was experimentally demonstrated in 2013. Lavery and colleagues spun a uniform diffuser at known rates, illuminated it with OAM beams of different orders, and read off the rotation rate cleanly from the rotational Doppler line. The whole illuminated surface contributed to the signal, the line was sharp, and the technique scaled with the beam order. It was a clean physics result that opened up a real engineering question: where else can this be useful?

Small drones are an obvious candidate. They have rotors that spin at known rates. Different drone models hover at different RPMs. The rotational Doppler shift, if you can extract it, becomes a direct readout of which drone you're looking at. The question is which configurations of an OAM-LIDAR system would actually deliver that readout, and the answer turns out to be more specific than the general enthusiasm for OAM-based remote sensing might suggest.

I want to walk through four scenarios where OAM light has a credible path to helping with drone detection, and what would need to be true for each to work.

Coherent rotational Doppler from rotor disks

The cleanest case is the direct application of the Lavery effect to drone rotors. If you can produce coherent reflection from a substantial fraction of a rotor disk's surface, the rotational Doppler shift becomes a sharp spectral feature at the OAM order times the rotor's angular velocity. For a Mavic 3 hovering at 5000 RPM with an ell-equals-five probe, that's a 417 Hz line. For a Mini 3 at 6040 RPM with the same probe, it's 503 Hz. For a Phantom 4 at 5500 RPM, 458 Hz. The lines are well separated, scale linearly with rotor speed, and live cleanly above the low-frequency clutter where atmospheric scintillation lives.

The catch is the word "coherent." Rotational Doppler requires the rotor surface to act as a coherent reflector, not as a chopping mask. At near-infrared wavelengths around 1.55 micrometers, drone rotor surfaces look very rough; speckle dominates and the rotational Doppler line gets buried. At longwave infrared wavelengths around 10 micrometers, the same surfaces look much smoother relative to a wavelength, the speckle cells are larger, and a much greater fraction of the surface contributes coherently. A LWIR OAM-LIDAR system targeting drone rotors at moderate range is the configuration where rotational Doppler should work.

The other engineering knobs that move the needle in the right direction are range and target size. Shorter range means less atmospheric phase scrambling between transmitter and target, which preserves more of the OAM mode purity. Larger rotors mean more coherent surface area at any given wavelength. A system designed for fifty-meter range against the Mavic 3 class of drone is much friendlier to rotational Doppler than a system designed for two-hundred-meter range against the Mini 3 class.

Static azimuthal shape classification

Drones are not rotationally symmetric. A quadcopter has four arms in a cross pattern. A hexacopter has six. A drone with a forward-facing camera gimbal has a clear front-back asymmetry. A drone with side-mounted antennas has a different azimuthal signature than one without. These features persist whether the drone is hovering, moving, or even when the rotors are stopped.

An OAM-resolved measurement is a Fourier decomposition in the azimuthal direction. A target with a strong four-fold symmetry will deposit power preferentially into ell-equals-zero, plus-or-minus four, plus-or-minus eight, and so on. A target with three-fold symmetry will look different. A target with a forward-back asymmetry but no rotational symmetry will look different again. The power spectrum across OAM modes is, in effect, a fingerprint of the target's azimuthal shape.

This is conceptually different from the rotational Doppler case. Rotational Doppler reads dynamics; static azimuthal classification reads geometry. The two are complementary. A practical sensor could use one or both depending on whether the drone is hovering or maneuvering, and depending on the rotor speed regime.

The implementation is also less demanding than rotational Doppler in one important way: it doesn't require coherent reflection from the rotor surface. Static azimuthal shape sensing can work on the integrated speckle pattern, because what you're measuring is the azimuthal distribution of return power, not the phase coherence of any particular surface element. This is a more forgiving regime experimentally.

The constraint here is angular resolution. The OAM beam needs to spatially resolve the drone's azimuthal features, which means the beam waist at the target needs to be comparable to the drone size. This pushes toward shorter range or larger optics. For a 350 millimeter quadcopter at 100 meters, you need beam optics that produce a meter-class beam waist on target, which is achievable but constrains the system design.

Clutter rejection through mode filtering

Drone detection in operational settings rarely happens against a clean background. The drone might be flying in front of trees, against an urban skyline, near a sun glint off a window, or against a fast-moving cloud edge. The detection problem is often signal-to-clutter limited rather than signal-to-noise limited, and the question becomes whether you can distinguish a drone return from the background clutter that's also showing up in your sensor.

OAM-resolved reception offers a potentially useful angle on this. Most natural backgrounds (vegetation, terrain, atmospheric scattering) tend to deposit their power preferentially into low-order OAM modes. Diffuse reflection from a rough natural surface tends to look approximately like a Gaussian return, which is mostly ell-equals-zero with some spread into low orders. A coherent return from a structured target like a drone, especially one with rotor modulation, can have a more distinctive distribution across higher-order modes.

This means a sensor that integrates only the higher-order mode content might see a much improved signal-to-clutter ratio for drone returns relative to background. The drone return retains its power across the high-order modes; the clutter mostly doesn't show up there. This is a different kind of advantage than the previous two: it doesn't require extracting more information from the drone, it requires rejecting more information from the clutter.

The published literature on OAM-LIDAR has done relatively little work on realistic clutter scenarios. Most simulations are against empty-sky backgrounds. Most lab demonstrations use cooperative targets in controlled rooms. A focused study of OAM-resolved drone detection against realistic outdoor clutter, with vegetation and urban backgrounds, would tell us whether the clutter-rejection mechanism works in practice. The physics suggests it should help; whether the magnitude of the help is operationally significant is an empirical question.

Combined OAM and polarization

Rotor blades have characteristic polarization signatures that depend on their material. Carbon fiber blades produce different polarized return than aluminum or composite blades. Different drone manufacturers use different blade materials, and even within a manufacturer's product line, different drone classes use different blade compositions.

A sensor that resolves both OAM mode and polarization state has access to a much richer feature space than either alone. The OAM modes capture azimuthal structure; the polarization states capture material composition. Different drone classes can be expected to occupy different regions of this combined space, in ways that might separate them more cleanly than either modality on its own.

The underlying physics is sound, and the engineering is reasonable. Polarimetric sensing is well understood, OAM-resolved sensing is well understood, and combining them in a single receiver doesn't require fundamentally new technology.

What would make these work

The thread that runs through all four scenarios is that OAM helps when the underlying physics couples to angular momentum, and when the system is designed so that the angular-momentum coupling survives the round trip from transmitter to target to receiver. The cases above all have one or both of those properties. Coherent rotational Doppler couples directly to angular momentum and works when coherent reflection is preserved. Static azimuthal classification couples to angular structure of the target and works when the beam resolves the target. Clutter rejection works because OAM modes naturally separate structured from unstructured returns. Combined OAM-polarization works because OAM contributes one dimension of structure that polarization cannot.

In each case, the engineering questions are concrete: what wavelength, what range, what beam waist, what integration time, what mode order. These are the kinds of questions that benefit from focused simulation studies and small-scale experimental demonstrations rather than from broad-stroke proposals. The cases where OAM should help with drone detection are not unlimited, but they're also not empty.

Why the Riemann Hypothesis and Fluid Turbulence May Be the Same Problem

Tesla coils, Majorana towers, and the spectral fingerprint connecting two Millennium Prize problems.

In my free time, I used to build audio-modulated solid state Tesla coils as a hobbyist. The physics of the plasma streamers that came off those coils fascinated me (vacuum tube driven tesla coils produce long spearlike arcs without bufurcations and fractal patterns, what causes them?), and as it turns out, that physics is closely related to the physics of fluid turbulence. Plasmas obey a similar mathematical description. What is interesting is that two deep open problems: the Riemann hypothesis (a Clay Millennium Prize Problem) and the problem of intermittency in fluid turbulence (closely related to, though not identical with, the Clay problem on Navier–Stokes existence and smoothness) may be related to one another.

Presentation

https://www.youtube.com/watch?v=U9CuORupmS8

How can it be that two of the largest open problems in physics and mathematics are asking the same thing?

The Riemann Hypothesis as Physics

The Riemann zeta function encodes the distribution of prime numbers. Prime factorization is, of course, the bedrock of current cryptographic standards, which rely on the difficulty of factoring large primes. That difficulty can be sidestepped by quantum computers running Shor's algorithm, which factors integers in polynomial time.

The Riemann hypothesis asks whether all of the non-trivial zeros of this function lie along the so-called critical line, with real part 1/2. Numerical search has verified this for the first many billions of zeros. None has been found off the line. But the conjecture remains a conjecture.

What physicists noticed, and what is the doorway into everything that follows, is that this function looks suspiciously like it could be describing the energy levels of some quantum mechanical system. This is the Hilbert-Pólya conjecture: the idea that there exists a self-adjoint operator whose eigenvalues coincide with the imaginary parts of the non-trivial zeta zeros. Because self-adjoint operators have real eigenvalues, the existence of such an operator would automatically prove the Riemann hypothesis. The hypothesis would then be settled not by abstract mathematics but by physics.

This is not idle speculation. In 1973, Hugh Montgomery showed that the pair correlations of the non-trivial zeta zeros match the Gaussian Unitary Ensemble statistics of random matrix theory, the very same statistics that govern eigenvalue spacing in quantum chaotic Hamiltonians with broken time-reversal symmetry. Andrew Odlyzko verified this numerically to extraordinary precision for the first billion zeros. In 1999, Berry and Keating elaborated the picture: the underlying "Riemann dynamics" should be chaotic, with periodic orbits labeled by primes. They proposed the Berry-Keating Hamiltonian, H=(xp+px)/2H = (xp + px)/2 H=(xp+px)/2, as a candidate for the Hilbert-Pólya operator.

Then, in 2021, Tamburini and Licata showed the Majorana equation (the physicist Ettore Majorana famously "disappeared" in the 1930s) placed in Rindler spacetime which is the frame of a uniformly accelerated observer, reduces to a Hamiltonian of exactly the Berry-Keating form. The boundary conditions on the Majorana wavefunction involve Bessel functions which, through Mellin-Barnes integrals, connect directly to the Riemann zeta function.

Their 2025 preprint argues that the Majorana Hamiltonian in Rindler space is essentially self-adjoint and proposes a spectral correspondence with the non-trivial zeta zeros. This sits alongside other Hamiltonian constructions in the Hilbert–Pólya program (Berry–Keating, Connes, Sierra, Bender–Brody–Müller). None of these constructions has yet been accepted by the academic community as a proof, and the Tamburini–Licata version will need to clear the same hurdles, but given their compelling and rigorous constructions, the proposals deserve more attention. I have had many long conversations with Dr. Tamburini about this, and I think it deserves much more attention than it has received.

Why Fluid Turbulence Wears the Same Statistics

Here is where the physics widens. The Riemann zeta function does not just show up in random matrix theory and accelerated quantum field theory. It shows up in the statistics of nonlinear deterministic systems near phase transitions. Quantum chaos, fluid turbulence intermittency, magnetohydrodynamic instabilities. All of them.

Modeling fluid turbulence and atmospheric flows, or the plasma behavior in fusion tokamaks and coronal mass ejections, is largely intractable. The physics is not well understood. So if there really is a universal spectral signature governing these systems, and it really is the Riemann zeta function, then resolving this would do considerably more than collect two million dollars from the Clay Institute. It would help us understand magnetohydrodynamic instabilities, which are the bottleneck for plasma confinement in tokamaks. It would improve weather prediction. And, since the same physics sits at the intersection of nonlinear deterministic and quantum probabilistic regimes, it could illuminate quantum gravity itself. Quantum gravity is, in a sense, the missing physics of reconciling those two regimes. As I have discussed with Ed Witten, macroscopic quantum-like behavior is one direction for understanding it.

The Majorana Tower and the Cascade

So what is going on physically? One clue comes from Majorana fermions and Majorana zero modes. These are particles that are their own antiparticles, and they enjoy what is called topological protection, which makes them the leading candidate for noise-resilient scalable quantum computation. Microsoft is actively investing in this technology for that reason. There are also theories which link Majorana physics to how the brain processes information, something I have discussed at length with Dr. Tamburini.

The picture I find compelling is this. Fermionic spin systems can be entangled and pumped by Floquet drivers into a state of saturation. Beyond that point, the system undergoes a phase transition at which its statistics are described by the Riemann zeta function. The information stored in the entanglement structure is then bosonized into ultraweak superradiant Majorana-like vortex photon signals carrying orbital angular momentum (OAM). There may also be gravitational feedback at these phase transitions. Majorana-like vortex photons carry the necessary quantum information imprinted from these Majorana-like fermionic spin states necessary, and critically, in a way that can propagate through tissues but then also backpropagate which is necessary for adjusting dendritic weights and connections.

Ultraweak superradiant Majorana-like vortex biophotons have been measured in brain tissues, and light is known to modulate long term potentiation (LTP) and long term depression (LTD) which adjusts dendritic connections, weights, and arborization - much like plasma filamentation in tesla coils.

This sounds speculative. It is, at the edges. But the load-bearing pieces are not. There are now multiple publications reporting that the zeros of the Riemann zeta function have been reproduced experimentally by pumping or driving qubits, and the mathematical link to Majorana physics has appeared in respectable journals. OAM light is known to carry the kind of quantum information needed for these effects, and has been explored as a candidate explanation for the black hole information paradox and for intracellular communication in living tissue.

One way to read all this: the boundary between the right and left Rindler wedges, in collections of entangled Majorana particles, traces out the critical line of the Riemann zeta function. The split structure of these particles is how quantum information gets stored before being saturated and released as light and gravity. The mathematics here implicates Z2 orbifolds at the phase transition, the bosonization of information into light-like modes, and the resulting superradiant cascades.

Twistor theory, the theory of null geodesics that Penrose has long argued must be central to a complete theory of gravity, fits naturally into this picture. So does Einstein-Cartan theory, which introduces spacetime torsion to general relativity, or, equivalently, gravity to quantum theory through spin. Could these light-like signals be implicated in the transmission of the gravitational force? Beyond-standard-model physics has been investigated along exactly these lines as a direction for understanding dark matter and dark energy, through the seesaw mechanism and the unique state oscillations these particles allow.

The Original Majorana Tower

Most physicists know Majorana for the Majorana spinor, the equation, and the zero modes. Fewer know that Majorana's 1932 paper introduced an infinite-component relativistic wave equation, the first construction of infinite-dimensional unitary representations of the Lorentz group, predating Wigner and Bargmann by years. The equation yields an infinite tower of particle states with increasing spin and a characteristic mass spectrum. Unlike the Dirac equation, all energies are positive. Majorana's original motivation, in fact, was eliminating the negative-energy sea. Higher-spin states have lower effective mass, creating a natural hierarchy of states across scales.

Tamburini and collaborators showed that this extends to photons with orbital angular momentum propagating in structured plasmas via the Anderson-Higgs mechanism. The key point for turbulence is this: the Majorana tower describes an infinite set of states where higher angular momentum corresponds to lower effective mass, a natural hierarchy mirroring the multi-scale cascade structure of turbulence, where energy is transferred from large eddies to small. That is to say, eddies of low angular momentum at large scale, to eddies of high angular momentum at small scale.

Migdal's Loop Equation and the Zeta Zeros

The connection between the zeta function and turbulence has been made even more explicit by Alexander Migdal. His loop equation program provides a rigorous derivation showing that the non-trivial zeros of the Riemann zeta function directly govern the complexity decay exponents of turbulence. Migdal's strategy is to abandon the local point-wise description of turbulence in favor of integrated loop observables, a move borrowed directly from quantum chromodynamics.

In 1993, Migdal predicted that the probability distribution of circulation Γ\Gamma Γ around a large loop CC C depends on the minimal surface area AA A bounded by the loop, and not on the loop's detailed shape. This is the direct turbulence analog of the Wilson loop area law in confining gauge theories, where the Wilson loop expectation decays with area, signaling quark confinement.

The prediction went against every existing turbulence theory and was considered controversial. In 2019, a group at NYU confirmed it numerically via direct numerical simulations, finding that circulation is a bifractal quantity whose moments scale with loop area. This confirmation, twenty-six years after Migdal's original prediction, prompted him to return full-time to research in theoretical physics.

The area law also creates a structural parallel with the Ryu-Takayanagi formula from holographic gravity, where the entanglement entropy of a boundary region equals the area of the minimal bulk surface. All three contexts (QCD confinement, turbulence circulation, and holographic entropy) share a key physical observable computed from the area of a minimal surface bounded by specific boundary data. The shared minimal surface principle is, I think, the deepest geometric thread tying Migdal's turbulence to quantum gravity.

The most striking result of the Migdal program is how the non-trivial zeros of the Riemann zeta function appear as complex decay exponents of turbulence. This is not an assumption or a conjecture overlaid on the result. It emerges through a specific traceable chain of mathematical steps. The Euler ensemble involves star polygons with a co-primality constraint, and that constraint injects the Euler totient function into the statistical mechanics. When one computes the Mellin transform of the energy spectrum and averages over the ensemble, a Dirichlet series falls out. The physical consequence is log-periodic oscillations in turbulent correlation functions, oscillations on a logarithmic time scale generated by the imaginary parts of the zeta zeros. No phenomenological model of turbulence predicts them. Migdal reports emerging experimental evidence for them in high-precision wind tunnel data from the Max Planck turbulence group.

This result does not prove the Riemann hypothesis. But it creates a physical context in which the hypothesis has observable consequences. If all non-trivial zeros lie on the critical line, the complex exponents have a specific universal structure. An off-line zero would produce a detectable anomaly in turbulent decay measurements. The geometry of the Riemann zeta function becomes, in principle, measurable by experiment.

Cascades, Conformal Symmetry, and the Saturation Picture

The connection between the Majorana tower and turbulent cascades is currently at the level of conjecture rather than proven physical equivalence. But the parallels are detailed enough to constitute a serious research program.

In classical turbulence, energy cascades from large eddies to small ones through a self-similar sequence of vortex breakups, each scale contributing to the overall energy spectrum. The intermediate inertial range is characterized by scale invariance: the same physics repeating at every scale. This is precisely the structure described by conformal field theories, the quantum field theories of critical points. The Majorana tower provides infinite-dimensional unitary representations of the Lorentz group, which contains the conformal group at the appropriate limit. The tower's infinite spectrum, with its mass-spin relation, creates a level spacing that maps onto the cascade's energy levels. And periodic driving of Majorana-like systems to high angular momentum states, climbing the tower, produces spectral statistics governed by the zeros of the Riemann zeta function. That ties the tower directly to the turbulence decay exponents.

The picture I keep coming back to is that the critical line of the Riemann zeta function is the statistical saturation point of these systems. It governs the tipping points in models of macroscopic quantum-like behavior, including quantum chaos and fluid turbulence. The Migdal program and the Tamburini results, taken together, suggest that both turbulence and the Majorana tower may realize precisely such a system, and that they may be the same system seen through different lenses.

The physics here looks, to me, similar to the physics of dendritic arborization in brain tissue, or to magnetohydrodynamic instabilities in plasmas, since magnetohydrodynamics is essentially the same as ordinary hydrodynamics with the addition of Maxwell's equations. One way to see it is through Tesla coil streamers.

Vacuum tube driven Tesla coils produce fractal streamers that seem to lack magnetohydrodynamic instabilities or streamer bifurcations. Streamer geometry can be modulated, with degrees of freedom pruned to a laminar setting or increased, in a way that resembles how dendritic connections are modulated in long-term depression and long-term potentiation. At the phase transition, there is a conformal fractal pattern across scales.

Vacuum tube driven tesla coils (VTTCs) produce characteristic streamers with fractal patterns and spearlike arcs where magnetohydrodynamic instabilities or bifurcations (MHDs) are pruned in a manner similar to dendritic arborization in brain tissues.

Migdal's 2025 extension to magnetohydrodynamic turbulence uses two coupled Euler ensembles, one for hydrodynamic circulation and one for magnetic circulation. The same zeta-zero structure persists, with an additional phase transition at magnetic Prandtl number Pm=1P_m = 1 Pm​=1 where the solution bifurcates. This robustness of the zeta structure across pure hydrodynamic and magnetohydrodynamic contexts strengthens the case that the zeta zeros represent a genuine universality class of cascade dynamics, and not an artifact of any one model.

Closing

Two Millennium Prize problems. One geometric structure. The Riemann zeta function turning up, again and again, at the saturation point of nonlinear deterministic systems, in the spectra of accelerated Majorana fields, in the loop statistics of turbulent fluids, and possibly in the bosonized output of driven entangled spin systems carrying orbital angular momentum. If this is right, then turbulence in a tokamak, the distribution of primes, the cascade of vortices in a wind tunnel, and the eigenvalues of the operator we have been searching for since Hilbert and Pólya are pieces of a single picture.

I do not claim this is settled. I claim it is the most interesting research direction I know of, and one where the experimental knobs are getting close enough to turn.

Backpropagation in the Brain Does Not Work Like AI Architectures

The data center arms race is a confidence trick that is doomed to fail due to the underlying physics which makes our brains work differently and orders of magnitude more efficiently.

In spite of attempts to undermine the credibility of theories of consciousness reliant on new physics, they are nonetheless credible enough to continue to demand the attention of the world's top academics, scientists, corporations, leaders, and governments.

What makes the human brain different from transformer based neural network architectures? Or, put another way, what gives us consciousness, and therefore the moral standing that flows from it, and can we ever approach this empirically rather than as a matter of faith or pure philosophical speculation?

This is a topic I've discussed with some of the top researchers in this area (Dr. Tuszynski, Dr. Murugan, Dr. Anirban, Dr. Craddock, James Tagg, Dr. Tamburini, Dr. Hameroff, etc). I was invited to present on this topic directly by Dr. Stuart Hameroff at the The Science of Consciousness (TSC) conference this year (though the TSC conference was allegedly shut down due to organizer affiliations to Jeffrey Epstein) and was also accepted to present at the APS/IPI conferences:

Backpropagation in the Brain: is the Transformer Architecture Viable? [REUPLOAD]

Why Current AI Architectures are Not Conscious: Neural Networks as Spinfoam Networks in a Theory of Quantum Gravity | IPI Letters

The singularity narrative is upside down

Large technology companies would like you to buy, on faith, the idea that we are approaching a so-called technological singularity at which machines will outwit the masses, after which we will, in some vague way, be enslaved by them. The narrative is then used to rationalize giving these systems agency, rights, and an ever-larger share of the world's energy and capital.

I want to make the opposite argument. The real singularity, if you want to use that word, is the point at which our collective intelligence (CI in the academic literature) catches up to and then surpasses the games being played on us by the people pushing this story. It is the moment we discover we have been outwitted the entire time, and not by the machines.

Information throughput in groups scales faster than per-unit-of-energy performance scales in transformer-style surveillance architectures. The latter is derivative and runs into asymptotic limits, a fact that Joseph Tainter described in The Collapse of Complex Societies without ever needing to mention GPUs. The former is what researchers studying interbrain synchrony are quietly documenting in lab after lab. Group cognition is not a metaphor. It is measurable, and it grows in a way that transformer architectures do not.

So why are we propping up the entire economy on the opposite assumption? Why are we taking seriously Mark Zuckerberg's stated ambition for data centers the size of Manhattan, or Google's reported plans for orbital data centers with their own dedicated power plants, when by many credible estimates the human brain is hundreds of thousands of times more efficient at compute than anything we are currently building, and when we cannot even reliably house, feed, or educate our own people?

Yann LeCun and others have proposed so-called world models, in which AI-endowed robotic agents are placed into society and taught to take human jobs. Years and oceans of training data later, we still do not have reliable self-driving cars, and we do not have the patience or resources to raise our own children. There is a tell in there, somewhere, if you are willing to look at it.

The 2024 Nobel Prize in Physics, awarded to John Hopfield and Geoffrey Hinton for work on machine learning, has come in for serious criticism along these lines. The complaint is not that the work is uninteresting. The complaint is that it does not teach us about the laws of nature in the way a physics prize is supposed to. It is computer science with a heuristic architecture imposed on it, evaluated by humans with attention in the loop, who are also the ones who decide what the simulation means. Nature has not been falsified. Nature has been bypassed. Some have gone further and argued that the prize is being used to rationalize the AI surveillance bubble that has been under construction for at least as long as I have been thinking about consciousness.

How I got here

I have long been drawn to the Penrose–Lucas argument that Gödel's incompleteness theorem points toward a non-algorithmic component of human reasoning. The argument has well-known claimed critiques (Putnam, Davis, Feferman, Chalmers), most centrally that it requires the human mathematician to know their own consistency, which is itself what Gödel's theorem says cannot be established. I find the argument suggestive rather than conclusive, and I treat it as motivation for looking at new physics, not as a derivation of it, and to inspire skepticism of any claims for cryptographic standards that are supposedly unbreakable because any conception a mathematician might have about the ultimate security of a standard is necessarily either incomplete or inconsistent.

Shortly after, I encountered the work of Roger Penrose, who had reached essentially the same conclusion from Gödel and gone further, implicating quantum gravity and macroscopic quantum-like effects in brain tissue. The standard objection is obvious. Wet, warm, noisy environments should decohere any such effect long before it could matter. I considered that a serious problem for the original formulation of the theory, but I was intrigued enough to keep going.

The next year I started studying quantum gravity and lattice mathematics under Richard Borcherds, the Fields medalist who proved the monstrous moonshine conjecture. In 2018, when I was in Boulder, NIST's post-quantum cryptography program leans on lattice problems whose security rests on a worst-case to average-case reduction (Ajtai, Regev). The average-case hardness used in the cryptosystem is reducible to the worst-case hardness of approximate lattice problems. Exact SVP is NP-hard, but the approximation factors used in cryptography are not currently known to be NP-hard, so the security claim is conjectural rather than proven.

Under known assumptions of either classical or quantum physics, they are intractable. That mattered to me for an old reason. It has always struck me as too hubristic a request of the universe that any class of unbreakable encryption should exist above scrutiny, available to a privileged group of elites for the hoarding of secrets.

Here is where it gets interesting.

Four problems, one shape

If you read the literature carefully, you find that four apparently distinct problems have all been framed as related, and in some cases as equivalent.

1. The black hole information paradox.

2. Post-quantum cryptography.

3. The shortest vector problem on a high-dimensional lattice.

4. The hard problem of consciousness, and the related binding problem.

   
   

https://www.mdpi.com/1099-4300/25/12/1645

https://ieeexplore.ieee.org/document/743432

https://www.researchgate.net/publication/242663551_Analyzing_Vision_at_the_Complexity_Level

This is not a fringe claim. It is in the literature. And it has practical consequences. The research of a physicist working on the black hole information paradox can, at least in principle, be quietly redirected toward developing cryptography. The work of a mathematician on string theory or lattice mathematics can be quietly redirected toward AI surveillance systems. The researchers and the public need not be told.

In each case, the underlying physics for resolution is not well-established or widely known. In the black hole case, information falls in but quantum mechanics insists unitarity is preserved. Several authors in the consciousness literature have proposed that the binding problem maps onto hard combinatorial-geometric problems, including lattice problems or noncommutative tori closely related to SVP, and there are real issues with alternative theories like predictive coding.

Both of those structures appear empirically in the brain. The Blue Brain Project found them. So did Edvard and May-Britt Moser, along with John O'Keefe, in their work on grid cells, for which they shared the 2014 Nobel Prize in Medicine. Related high-dimensional structures appear empirically in cortical tissue. The Blue Brain Project (Reimann, Nolte, Markram et al., 2017) reported high-dimensional simplicial complexes and rich directed-graph topology in reconstructed microcircuitry. This is algebraic-topological evidence rather than direct evidence of non-commutative tori, but it indicates that cortical connectivity sits naturally in a high-dimensional geometric setting and is one one study out of many in the literature.

When researchers actually went after the black hole information paradox, monstrous moonshine and macroscopic black hole entropy turned out to be linked through holographic descriptions of black hole microstates. Several modern theories of quantum gravity now treat gravity itself as an entropic or thermodynamic force. The Cardy formula gives the asymptotic density of states in a 2D conformal field theory, providing a microscopic derivation of the Bekenstein-Hawking entropy. To resolve the paradox of information that must be both publicly hidden and uniquely accessible, the theory of secret black hole information islands was introduced. These are regions inside the event horizon that, on recent quantum gravity accounts, are holographically encoded in, and possibly entangled with, the leaking Hawking radiation. They follow the unitarity-preserving Page curve.

Notice the shape of this. Information is trapped, and yet it escapes, encoded, in something that radiates out. That is a Cartesian duality if you want to read it that way. The hidden islands of entanglement entropy are where the mind is stored, apart from the body of the black hole. That same shape may be exactly what we need to understand the brain.

What we know about the brain that does not fit the transformer story

Let me list the things we know empirically that the dominant AI story does not account for.

Information and memory in the brain are processed non-locally, distributed across tissues, and not stored in localized binary logic gates the way a von Neumann architecture stores them. The speed of behavior and information retrieval seems to outrun what standard electrochemical signaling across dendritic membranes can permit on its own. To make things even more interesting, single-celled organisms display Pavlovian learning which would seem implausible based on assumptions that this type of behavior comes from dendritic neural networks:

Biologists stunned after a brainless single cell showed Pavlovian learning

Backpropagation in the brain, also known as the weight transport problem or credit assignment problem, has no widely accepted, biologically plausible mechanism. In artificial networks we cheat. While useful in modeling economic systems which require one-way transactions, in biological tissue, no one has produced an obviously correct account of bidirectional feedforward and feedback signaling.

Hyperscanning studies show that brain activity synchronizes across people sharing a social environment, and that this synchronization correlates with shared understanding and empathy. Group performance, in many tasks, scales faster than the sum of individual performances. Transformer architectures do not have this feature.

Empirical studies of human decision-making show interference patterns that look more like the mathematics of non-classical physics than like classical probability. Psychedelics produce conformal fractal patterns across scales in the visual field, again more consistent with non-classical geometry than with classical signal processing. Single-celled organisms display behaviors complex enough that you would expect them to require a brain. The energy efficiency of the brain alone tells you that purely electrochemical signaling cannot account for perceptual binding.

Inside the cytoskeleton of cells are long cylindrical proteins called microtubules, which anesthetics selectively block. Xenon anesthetics have been tested with different xenon isotopes, and anesthetic potency varies with the isotope. That should stop you in your tracks. Different isotopes of the same element, with the same chemistry, produce different effects on consciousness. The natural reading is that consciousness is partly generated by non-classical means involving spin dynamics, consistent with the radical pair mechanism known from quantum biology.

Ultraviolet super-radiance has been measured in brain tissue in some newer (and admittedly contested) studies. Researchers including those I have spoken with at length suggest that microtubules act as time-crystalline optical waveguides. Light has been shown to modulate long-term potentiation and long-term depression. Ultra-weak photon emission from isolated neurons correlates with action potential firing. There are even more fringe studies suggesting superconductivity or near-superconductivity-induced effects in microtubules. Those last claims need much more experimental work, and I will not defend them past saying they should not be dismissed without that work.

Numerical simulations of information stored in fermionic spin states imprinted onto biophotons with orbital angular momentum.

The model

Penrose's original orchestrated objective reduction theory has had problems with experiment. But recent work in quantum biology suggests that macroscopic quantum effects in the warm wet noisy brain might be possible after all, through periodic driving into Fröhlich condensates, or through topological protection, both of which are under active investigation at the major tech companies. (Microsoft, where I once worked, has invested heavily in Majorana physics for exactly these reasons. The work of James Tagg and Dr. Kerskens ties this directly into the model I am about to sketch.)

Tegmark's 2000 decoherence criticism of Orch-OR was directly rebutted by Hagan, Hameroff, and Tuszyński in Phys Rev E (2002), who argued he modeled the wrong system (24 nm separations versus the smaller ones Orch-OR actually proposes) and ignored shielding mechanisms like Debye counterion layers, ordered water, and lattice-based error correction; their recalculation extended decoherence times by seven orders of magnitude, though still short of the 25 ms target. Subsequent experimental work, especially Babcock et al. 2024 demonstrating UV superradiance across tryptophan mega-networks in microtubules, plus xenon nuclear-spin anesthesia studies and the broader quantum biology field, has chipped further at the "warm-wet-noisy means impossible" framing without actually proving Orch-OR.

On the Penrose-Diósi side, Donadi et al. 2021 (Nature Physics) ruled out only the natural parameter-free version of the model using Gran Sasso germanium detectors, leaving regularized versions with larger R₀ alive; however, the 2024 follow-up by Figurato et al. showed that closing the remaining gap would require 18 orders of magnitude better experimental sensitivity, which is brutal but not strictly a falsification, and dissipative variants and alternative gravitational collapse models remain on the table. Additional studies on quantum chaos or even topological protection might close this gap. Some forms of structured OAM light like "Hopfions" could preserve properties at scale.

In our model, information stored in Majorana-like fermionic spin states hosted within microtubules is orchestrated to saturation. At a critical fixed point, a tipping point, the information bosonizes into light-like modes, manifesting as cascades of super-radiant ultra-weak Majorana-like vortex biophotons. These collapse the evolving superposition. The collapse is triggered gravitationally. The phase transition itself is captured mathematically by Z2 orbifolds.

I once discussed with Edward Witten his proposal that pure gravity in anti-de Sitter space (a spacetime of negative curvature) might be described by the monster conformal field theory, which describes massless bosons. Z2 orbifolds are how you transition from such a CFT to a fermionic spin system in de Sitter space (positive curvature), like the so-called baby monster CFT. These are real mathematical objects. In quantum gravity models, Z2 orbifolds are fundamental in constructing Israel junction conditions, the rules for gluing two spacetime geometries together.

The Riemann zeta function and its generalizations, like the Epstein zeta function for high-dimensional lattices, are used in this setting to regularize divergent vacuum energy and define partition functions. In experiments, the zeros of the Riemann zeta function can be reproduced by periodically driving qubits. Mathematical physicists like Dr. Tamburini, with whom I have had many long conversations, have shown you can describe the behavior of particles that are their own antiparticles (Majorana fermions) on curved spacetime using the zeta function. The critical line marks the saturation point in the statistics of these systems. It also turns up in tipping points for macroscopic quantum-like behavior, including quantum chaos and fluid turbulence. This is more or less exactly what the Hilbert-Polya conjecture proposes, that the zeros of zeta could be the energy levels of some unknown quantum system. We may be looking at one.

In loop quantum gravity, the spacetime substrate is a spin foam network. Causal fermion systems theory uses similar graph structures to quantize spacetime. These look extraordinarily like the spin-state networks in the brain. Penrose's proposal is that quantum gravity introduces a non-computable element into physics. Dr. Scott Aaronson, by contrast, has been a sharp public critic of Orch-OR. Readers should weigh the Penrose proposal against Aaronson's critiques - but what is interesting is that although Dr. Aaronson expresses skepticism regarding Penrose's proposal, a similar proposal appears in one of his own publications "NP Problems and Physical Reality" where he suggests that spinfoam networks may possibly act as substrates for the noncomputable physics Penrose describes.

Penrose has further suggested that a complete theory of quantum gravity will be written in the mathematics of null light geodesics, sometimes called soft hair in twistor theory with similar structures in Einstein-Cartan theory. The monster vertex operator algebra, corresponding to the monster CFT, maps cleanly to twistors. Those light-like modes are analogous to the hidden islands of entanglement entropy I mentioned earlier in the black hole context. They are how the mind, in this picture, attaches to the body of the neural network.

If you have been keeping score, that is a single picture in which the black hole information paradox, the shortest vector problem, post-quantum cryptography, and the hard problem of consciousness are all aspects of the same physics.

Noncommutative tori and high dimensional lattices have been studied as representations of brain neural networks by credible research groups, where the perceptual binding problem is resolved through new physics - the equivalent to the shortest vector problem.

A falsifiable prediction

I do not currently have funding for this work, but have been in active discussions with research groups that have been interested in collaboration. It seems the available funding is mostly directed toward perpetuating the status quo. So what I can offer at the moment, in lieu of an experiment, is a numerical simulation and a falsifiable prediction.

If the model is correct, information stored in Majorana-like spin states within microtubules should imprint onto super-radiant ultra-weak biophotons.

Several studies have shown superradiant Majorana-like vortex biophotons propagate through brain tissue, and that light modulates long term potentiation (LTP) and long term depression (LTD). This light carries quantum information through the property of orbital angular momentum (OAM) with feedforward and feedbackward information necessary to carry out backpropagation.

Spectral analysis of those photon signatures could provide a method of post-quantum cryptanalysis. Specifically, the smallest eigenvalue of the Dirac-like operator spectrum over the relevant space corresponds to the shortest vector of the high-dimensional lattice, or the non-commutative torus, that any given neural network represents. There is already related work attacking the shortest vector problem with spin-glass and folded spectrum methods. The proposal here is to drive a neural network representing such a lattice problem to gravitational collapse and read out the geometry from the ultra-weak photon spectra at the phase transition.

If the photons originate from exotic Majorana-like states in the cell, they should carry a quantum fingerprint. A system with conserved parity is linked to the polarization of the photons it emits. From numerical simulations I predict three measurable signatures.

First, Floquet sidebands. Extra spectral lines from periodic driving.

Second, a magnetic field-dependent polarization bias.

Third, strong cross-correlations showing photons alternate polarization in sequence.

Detecting any of these would be strong evidence that biophotons are not metabolic noise but are carrying quantum information from deep inside the cell, and that this is the substrate through which the brain achieves the equivalent of backpropagation. It would also be evidence for what actually distinguishes mind from machine.

Why this matters now

The argument I am making is not anti-technology. It is anti-confidence-trick. We are being asked to spend astonishing amounts of money and energy on an architecture whose advocates cannot tell you, in physical terms, why it should approach what a three-pound piece of biological tissue does for twenty watts. We are being asked to grant moral standing to systems whose advocates have not solved, and in many cases have not seriously engaged with, the physics that would make such standing meaningful.

The serious answer to the consciousness question may not require Manhattan-sized data centers or orbital power plants. It may require something much harder for the present economic order to monetize, namely, a deep and patient interest in what makes us human, and in what allows one mind to connect with another.

Trevor Nestor trevor.nestor at berkeley dot edu