Torsion Waves

The query “What exactly are torsion waves?” opens a door into one of the most fascinating and deeply divided subjects at the periphery of modern physics. The term itself is a source of profound ambiguity, referring to two entirely separate concepts that, despite sharing a name, occupy opposite ends of the scientific spectrum. On one side lies a legitimate, albeit speculative, area of theoretical physics rooted in the rigorous mathematics of differential geometry. Here, torsion is a potential property of the fabric of spacetime, a geometric “twist” that exists alongside the more familiar concept of curvature. The possibility of “torsion waves” in this context is a theoretical outgrowth of certain extensions to Einstein's theory of General Relativity, a subject of active research and debate among physicists.  

On the other side lies a world of pseudoscience, a collection of extraordinary claims involving faster-than-light communication, paranormal phenomena, and exotic energy sources, all attributed to so-called “torsion fields” or “torsion waves”. This version of torsion, popularized by figures such as Nikolai Kozyrev, Anatoly Akimov, and Gennady Shipov, has been widely and repeatedly refuted by the mainstream scientific community, its proponents often accused of fraud and its experimental evidence shown to be non-existent or attributable to mundane causes.  

To answer the central question with the required precision, it is therefore essential to navigate both of these worlds. A complete understanding demands a clear demarcation between the rigorously defined mathematical object of theoretical physics and its misappropriated namesake in the realm of pseudoscience.

A Roadmap for Clarity

This report will embark on a systematic exploration of torsion, designed to build a clear and comprehensive understanding from the ground up. The structure is designed to first establish a solid foundation in the legitimate science before critically examining the pseudoscientific claims that have muddled public understanding.

• In the first section, we will lay the scientific groundwork, beginning with the mathematical definition and geometric meaning of the torsion tensor. It will then explore the first and most natural physical theory to incorporate torsion: the Einstein-Cartan-Sciama-Kibble (ECSK) theory of gravity.

• The mid-article will address the core question of propagation. It will explain why torsion does not form waves in the standard ECSK framework, and what modifications to the theory are required to allow for hypothetical “torsion waves.” This section will include a detailed comparison with the well-understood phenomena of electromagnetic and gravitational waves and review the current status of experimental searches for any sign of spacetime torsion.

• After propagation, we will turn a critical eye to the pseudoscientific narrative. It will trace the origins of these ideas, detail the extraordinary claims made, and present the overwhelming scientific evidence and formal refutations that place these concepts firmly outside the bounds of credible science.

• Finally, we will conclude by synthesizing these disparate threads, providing a definitive answer to the titular question and offering a look at the future of legitimate torsion research in the ongoing quest for a theory of quantum gravity.

Why Torsion Matters

Before delving into the technical details, it is worth asking why the concept of torsion holds a persistent intellectual appeal for physicists. Its importance stems from several key ideas. First, torsion represents the most natural generalization of the geometry that underpins Einstein's General Relativity. Standard GR is built on Riemannian geometry, which makes the simplifying assumption that a property known as the affine connection is symmetric, thereby forcing torsion to be zero by definition. Relaxing this single assumption opens the door to a richer, more general geometric landscape known as Riemann-Cartan spacetime.  

Second, this generalized geometry provides an elegant and natural home for one of the most fundamental properties of matter: quantum spin. In the Einstein-Cartan-Sciama-Kibble (ECSK) theory, the intrinsic angular momentum of elementary particles, like electrons and quarks, acts as the source for spacetime torsion, just as mass and energy act as the source for spacetime curvature. This elevates spin from a mere quantum number to a dynamic participant in the architecture of the cosmos.  

Finally, this spin-torsion coupling, though predicted to be incredibly weak under normal conditions, could have profound consequences in the most extreme environments in the universe. Theoretical models suggest that the repulsive forces generated by torsion at ultra-high densities could prevent the formation of gravitational singularities, potentially replacing the Big Bang with a “Big Bounce” and resolving the paradox of the infinite density at the heart of black holes.It is this potential to solve some of the deepest puzzles in cosmology and fundamental physics that keeps torsion an active, if speculative, field of study.  

Understanding the Torsion Tensor

To grasp the physical concept of torsion, one must first understand its mathematical origins in the field of differential geometry. Torsion is not an arbitrary addition to physics; it is a fundamental property of geometric spaces that is explicitly removed in the simplified framework used by standard General Relativity.

Beyond Riemannian Geometry

Einstein's theory of General Relativity describes gravity as the curvature of spacetime. The mathematical framework for this is Riemannian geometry, a powerful tool for describing curved spaces. A key feature of Riemannian geometry is the Levi-Civita connection, which is the rule for how to “parallel transport” a vector along a curve. This connection is uniquely defined by two conditions: it must be compatible with the metric (meaning lengths and angles are preserved during transport), and it must be torsion-free. The torsion-free condition is an explicit assumption, a mathematical choice made for simplicity that is equivalent to stating that the connection is symmetric in its lower indices.  

The entire field of torsion research stems from relaxing this single assumption. By allowing the connection to be asymmetric, we move from the specific case of a Riemannian manifold to the more general case of a Riemann-Cartan manifold. In this broader framework, torsion emerges naturally as a measure of the connection's asymmetry. This reveals that the absence of torsion in General Relativity is not a fundamental law of nature, but a simplifying postulate of that particular theory.  

The Formal Definition of Torsion

In differential geometry, the torsion tensor, T, is a quantity associated with any affine connection, ∇. It is formally defined as a vector-valued 2-form that takes two vector fields, X and Y, as inputs and produces a vector as an output. The definition is given by :  

$$ T(X, Y) = \nabla_X Y - \nabla_Y X - [X, Y] $$

Here, ∇X​Y represents the covariant derivative of the vector field Y in the direction of the vector field X. It describes how Y changes as one moves along the integral curves of X. The term in the Lie bracket of the two vector fields, which measures the intrinsic failure of the flows generated by X and Y to commute. In essence, the torsion tensor T(X,Y) quantifies the difference between how the connection “twists” the vector fields relative to each other (∇X​Y−∇Y​X) and how they intrinsically fail to commute on the manifold.

This definition can be expressed more concretely in a local coordinate basis. The connection ∇ is characterized by its connection coefficients, Γjki​ (which are known as Christoffel symbols in the special case of the Levi-Civita connection). The components of the torsion tensor, Tjki​, are then given by the antisymmetric part of these connection coefficients :  

$$ Tjki​=Γjki​−Γkji​ $$

This coordinate-based definition makes the core concept exceptionally clear: torsion is precisely the measure of the asymmetry of the connection. If the connection is symmetric in its lower indices, as is assumed for the Levi-Civita connection in General Relativity, the torsion tensor is identically zero. Therefore, any theory that allows for a non-zero torsion is a theory that utilizes an asymmetric connection.  

The Geometric Interpretation and A Failure to Close

While the formal definition is precise, the geometric intuition behind torsion is more vivid. It can be understood as a measure of “closure failure” when attempting to construct an infinitesimal parallelogram on a manifold.  

Imagine a point on a manifold and two small, independent vector directions, v and w. One can construct an infinitesimal parallelogram by moving a distance along v, then a distance along w, then back along −v, and finally back along −w. In a simple flat space, this path forms a closed loop, returning precisely to the starting point.

However, in a space with torsion, this is not guaranteed. A more sophisticated way to visualize this is by “developing” or “rolling” the tangent space along the sides of this parallelogram. Imagine the tangent space at the starting point as a flat sheet of paper. As you move along the vector v, you roll this flat sheet without slipping along the curve. When you reach the next corner, you then roll it along the direction of w, and so on for all four sides. When you complete the circuit and return the tangent space to its original location, the point of contact on the paper will have been displaced from its starting position. This displacement vector is a direct manifestation of the torsion tensor, T(v,w). The fact that traversing the circuit in the opposite direction (along −w, then −v, etc.) undoes the displacement highlights the skew-symmetric nature of the torsion tensor: T(v,w)=−T(w,v).  

This concept is analogous to the idea of a dislocation in solid-state physics. In a perfect crystal lattice, moving along lattice vectors forms closed loops. However, in the presence of a dislocation (a missing or extra plane of atoms), tracing a similar path around the dislocation results in a “closure failure” quantified by the Burgers vector. In this analogy, the torsion tensor plays the role of the dislocation density.  

Torsion vs. Curvature

Torsion and curvature are the two fundamental ways a space can deviate from being flat, but they represent distinct geometric properties.

• Curvature measures the failure of a vector to return to its original orientation after being parallel-transported around a closed loop. It is associated with the commutator of covariant derivatives acting on a vector, [∇μ​,∇ν​], and describes a rotation of the vector.  

  $$ Vρ=Rλμνρ​Vλ $$

• Torsion, as described above, measures the failure of an infinitesimal parallelogram to close, resulting in a translational displacement or dislocation.  

A key way to distinguish them is through handedness. Torsion imparts a detectable handedness, or chirality, to a space. For example, the effect of torsion might be different for a right-handed path versus a left-handed path. Mathematically, this is reflected in the fact that the torsion tensor is an odd-rank tensor that is odd under parity (PT) transformations.Curvature, described by the even-rank Riemann tensor, has no such intrinsic handedness.  

This distinction has a profound impact on the motion of objects. In a torsion-free space like that of General Relativity, the “straightest possible path” (an autoparallel, which parallel-transports its own tangent vector) is identical to the “shortest path” between two points (a geodesic). In a space with torsion, these two concepts diverge. The geodesic equation depends only on the symmetric part of the connection, while the autoparallel equation depends on the full, asymmetric connection. Thus, the presence of torsion can cause the straightest path to deviate from the shortest one.  

Decomposition of the Torsion Tensor

For physical applications, it is useful to decompose the torsion tensor into its irreducible components regarding the Lorentz group. At any point in spacetime, the torsion tensor Tbca​ can be broken down into three independent pieces :  

1. The Trace Vector (Vectorial Torsion): Tb​=Tbaa​. This is a vector component that captures one part of the torsion.

2. The Axial Vector (Totally Antisymmetric Part):

   $$ S_a = \epsilon_{abcd}T^{bcd} $$

   This component, also known as “skew torsion,” is a pseudovector and is particularly important as it is the only part that couples to Dirac fermions in the simplest theories.

3. The Tensor Part (Trace-Free Part): The remaining component is a tensor qbca​ that is trace-free and has more complex symmetries.

This decomposition is not merely a mathematical exercise. Different physical theories may predict that only certain components of torsion are non-zero. For example, the simplest version of the ECSK theory sourced by Dirac fermions generates only the axial vector component. This classification helps physicists categorize and study the potential physical effects of different types of torsion.  

The Einstein-Cartan-Sciama-Kibble (ECSK) Theory

While torsion is a well-defined mathematical concept, its journey into physics has been a long and intermittent one. The most direct and compelling physical application of torsion is found in the Einstein-Cartan-Sciama-Kibble (ECSK) theory, which provides a natural geometric home for the quantum mechanical property of spin.

From Cartan to Sciama and Kibble

The story of torsion in gravity begins with the French mathematician Élie Cartan. In the early 1920s, shortly after Einstein finalized his theory of General Relativity, Cartan proposed a “generalisation de la notion de courbure” (generalization of the notion of curvature). Inspired by the work of the Cosserat brothers on generalized theories of elasticity, which involved media with internal rotational degrees of freedom, Cartan developed the mathematics of spaces with both curvature and torsion. He formulated a gravitational theory on this more general geometric stage, but his work went largely unnoticed for several decades. There were several reasons for this: the modern concept of intrinsic quantum spin had not yet been discovered, making a physical source for torsion unclear, and Cartan's mathematical formalism, based on differential forms and moving frames, was unfamiliar to most physicists of the era.  

The theory was independently rediscovered and revitalized in the late 1950s and early 1960s, most notably by Dennis Sciama and T.W.B. Kibble. By this time, the intrinsic spin of elementary particles was a cornerstone of quantum mechanics. Sciama and Kibble, working independently, laid the modern foundations of the theory, clarifying the physical connection between spin and torsion and establishing what is now commonly known as the Einstein-Cartan-Sciama-Kibble (ECSK) theory. Their work brought Cartan's visionary ideas into the mainstream of theoretical physics, establishing a viable alternative to standard General Relativity.  

Intrinsic Spin Density

The central postulate of ECSK theory is both simple and profound: just as the density and flow of mass-energy (described by the energy-momentum tensor) act as the source for the curvature of spacetime, the density of intrinsic angular momentum, or spin, acts as the source for the torsion of spacetime.  

In General Relativity, the fundamental properties of matter that shape geometry are mass and momentum. In ECSK theory, spin is elevated to an equally fundamental role. This is deeply satisfying from a theoretical standpoint, as relativistic quantum theory shows that elementary particles are fundamentally characterized by two key invariants of the Poincaré group (the symmetry group of special relativity): mass and spin. ECSK theory restores a symmetry between these two properties, giving both a direct dynamical role in the structure of spacetime.  

This physical principle is formalized in the Cartan field equations. The theory is derived from the same Einstein-Hilbert action as General Relativity, but it is formulated on a Riemann-Cartan manifold where the connection (and thus torsion) is treated as an independent variable. The variation of the action leads to two sets of equations:

1. The Einstein-Cartan Equation: This is a generalization of Einstein's field equation. It looks similar, but the Ricci tensor on the left-hand side is now built from the full, asymmetric connection and is therefore no longer symmetric. This allows it to be equated to a possibly asymmetric energy-momentum tensor.  

2. The Cartan Equation: This is a new equation that arises from varying the action regarding the connection. It establishes a direct, algebraic relationship between the torsion tensor and the spin density tensor, σabc​, of the matter fields :  

   $$ T_{abc} + \delta_{ac} T_{bdd} - \delta_{bc} T_{add} = \kappa \sigma_{abc} $$

   where κ is a constant related to Newton's gravitational constant, G. This equation is the mathematical heart of the theory, explicitly stating that torsion is directly proportional to the spin density of matter.

The Non-Propagating Nature of Torsion in ECSK

A critical and often misunderstood feature of ECSK theory arises directly from the algebraic nature of the Cartan equation. Unlike the Maxwell equations for electromagnetism or the Einstein field equations for curvature, which are partial differential equations, the Cartan equation for torsion contains no derivatives in relation to time or space.  

This has a profound consequence: torsion in ECSK theory is a non-propagating field. An algebraic relationship means that the value of the torsion field at a given point in spacetime is determined solely by the value of the spin density at that exact same point. There is no mechanism for a disturbance in the torsion field to travel from one point to another.  

Therefore, if the spin density is zero (as it is in a vacuum), the torsion tensor must also be identically zero. Torsion is “stuck” to its source. The effects of torsion are confined entirely to the interior of matter distributions with a net spin density. Outside these sources, the spacetime of ECSK theory is identical to the vacuum solutions of standard General Relativity, such as the Schwarzschild and Kerr metrics. This means that propagating “torsion waves” that travel through a vacuum do not exist in standard ECSK theory. The theory modifies gravity inside matter, but not outside.

Physical Consequences of Spin-Torsion Coupling

Despite being non-propagating, the presence of torsion inside matter leads to significant physical predictions, particularly in regimes of extreme density.

• Repulsive Interaction at High Densities: The minimal coupling between torsion and fermionic matter (particles with half-integer spin like electrons and quarks, described by the Dirac equation) generates an effective nonlinear spin-spin self-interaction. This interaction term, which appears when the theory is expressed in the familiar language of Riemannian geometry, is equivalent to adding a term proportional to  

  $$ (\bar{\psi} \gamma_5 \gamma_a \psi)^2 $$

  to the Lagrangian, where ψ is the fermion field. This term corresponds to a repulsive force that becomes significant only at extraordinarily high fermion densities, such as those predicted to exist in the very early universe or inside black holes. This repulsion arises fundamentally from the interplay between spin and geometry, providing a gravitational effect rooted in the quantum nature of matter.  

• Avoiding Singularities: This powerful repulsive force offers a potential solution to one of the most persistent problems in General Relativity: the prediction of singularities.

  • The Big Bounce: In standard cosmology, the universe begins from a point of infinite density and temperature—the Big Bang singularity. In ECSK cosmology, as the universe contracts to an incredibly dense state, the spin-torsion repulsion would overwhelm gravity, halting the collapse and causing a “bounce.” This “Big Bounce” model replaces the singularity with a regular, albeit extreme, transition from a contracting phase to our current expanding phase.  

  • Regular Black Holes: Similarly, the gravitational collapse of a massive star is predicted to halt before a singularity can form. Instead of an infinitely dense point, the matter would reach a maximum density and form a regular structure. Some models suggest this could be an Einstein-Rosen bridge (a type of wormhole) leading to a new, expanding universe on the “other side” of the event horizon.  

• Modified Dirac Equation: When the Dirac equation for a fermion is written in a spacetime with torsion, it acquires an additional, non-linear cubic term. This modified equation is known as the Hehl-Datta equation. It represents the back-reaction of the fermion's own spin on its motion through the torsion it generates.  

The Gauge Theory Perspective

The ECSK theory gains further theoretical support from its formulation as a gauge theory. General Relativity can be understood as a gauge theory of the Lorentz group, which describes rotations and boosts. ECSK theory can be formulated as a gauge theory of the full Poincaré group, which includes not only Lorentz transformations but also spacetime translations.  

In this elegant picture, the fundamental fields of gravity are the gauge potentials associated with these symmetries. The potential associated with local Lorentz rotations gives rise to curvature, while the potential associated with local translations gives rise to torsion. This framework provides a deep, first-principles motivation for including torsion in a theory of gravity, suggesting that it is the natural geometric consequence of making the symmetries of special relativity local.  

The Emergence of Torsion Waves in Modified Gravity

The standard Einstein-Cartan-Sciama-Kibble (ECSK) theory, while providing a compelling geometric role for spin, does not predict propagating torsion waves. Torsion is algebraically tied to its source and vanishes in a vacuum. To generate a scenario where torsion can ripple through spacetime as a wave, one must move beyond ECSK to more speculative, modified theories of gravity.

Making Torsion Propagate and Theories Beyond ECSK

Why ECSK is Not Enough for Waves

As established, the algebraic nature of the Cartan field equations is the mathematical reason why torsion is non-propagating in ECSK theory. A field that propagates must have dynamics governed by a differential equation, allowing a disturbance at one point to influence another point at a later time. The ECSK equations lack the necessary derivative terms for this to occur.  

Therefore, the existence of propagating torsion waves is not a hidden feature of the simplest extension of General Relativity. Instead, it requires a deliberate modification of the underlying theory by adding new terms to the gravitational action. This places the concept of torsion waves on a much more speculative footing than gravitational waves, which are an unavoidable prediction of standard, unmodified General Relativity.

The Key to Propagation

To transform a non-dynamical field into a dynamical, propagating one, its Lagrangian must include kinetic terms—terms that involve derivatives of the field. For torsion, this means adding terms to the gravitational action that are quadratic in the derivatives of the torsion tensor (e.g., of the form (∇T)2) or quadratic in the torsion tensor itself (T2) and the curvature tensor (R2).  

When such terms are included, the variation of the action regarding the connection no longer yields a simple algebraic equation. Instead, it produces a full-fledged partial differential equation for the torsion field. If this equation takes the form of a wave equation, it will admit solutions that describe propagating disturbances, or “torsion waves.” These hypothetical quanta of the torsion field are sometimes referred to as “tordions”. The existence and specific properties of these waves are entirely dependent on the choice of these additional, non-minimal terms and their associated coupling constants.  

Poincaré Gauge Theory and Metric-Affine Gravity

The frameworks that accommodate these modifications are broader and more general than ECSK theory. The two most prominent are Poincaré Gauge Theory (PGT) and Metric-Affine Gravity (MAG).

• Poincaré Gauge Theory (PGT): As an extension of the gauge principle discussed for ECSK, PGT allows for a Lagrangian that is quadratic in the gauge field strengths—that is, quadratic in both curvature and torsion. This naturally introduces kinetic terms for torsion.  

• Metric-Affine Gravity (MAG): This is an even more general framework where the metric and the connection are treated as completely independent geometric fields. In MAG, one can also have nonmetricity, which is the covariant derivative of the metric and measures how lengths change during parallel transport. By constructing Lagrangians with various combinations of curvature, torsion, and nonmetricity, a vast landscape of modified gravity theories can be explored, many of which feature propagating torsion modes.  

The Properties of Propagating Torsion

Within these modified theories, the predicted properties of torsion waves are highly model-dependent.

• Massive vs. Massless: Propagating torsion can be either massive or massless. For instance, in a framework known as Covariant Canonical Gauge Theory of Gravity (CCGG), which adds quadratic terms to the action, the axial vector part of torsion is found to obey a wave equation analogous to that of a massive Proca field, implying a massive propagating mode. Other models can be constructed to yield massless modes.  

• Spin Content: The propagating “tordions” can have different quantum spins. Depending on which irreducible part of the torsion tensor is made dynamic, these theories can predict the existence of new massive or massless particles with spin-0 (scalar), spin-1 (vector), or spin-2 (tensor).  

• Ghosts and Tachyons: A major theoretical hurdle for these models is physical consistency. The introduction of higher-derivative terms into a theory of gravity is notorious for creating pathologies. Many choices of parameters in PGT and MAG lead to:

  • Ghosts: Particles with negative kinetic energy, which would lead to a catastrophically unstable vacuum and violate the principle of unitarity (conservation of probability).  

  • Tachyons: Particles with imaginary mass that would propagate faster than light, violating causality.  

A significant portion of modern research in this area is dedicated to identifying specific combinations of Lagrangian terms and coupling constants that result in “ghost-free” and “tachyon-free” theories, which propagate only healthy degrees of freedom alongside the standard graviton.  

Torsion Waves vs. Gravitational and Electromagnetic Waves

To understand what hypothetical torsion waves are, it is instructive to compare them with the two types of physical waves that are well-established: electromagnetic waves and gravitational waves. This comparison highlights the unique nature of torsion and the challenges associated with its potential detection.

Fundamental Nature and Sources

• Electromagnetic Waves (EMWs): These are propagating disturbances in the electromagnetic field. They are sourced by the acceleration of electric charges, with the dominant mode of radiation being dipolar.  

• Gravitational Waves (GWs): These are propagating ripples in the curvature of spacetime itself. As predicted by General Relativity, they are sourced by the accelerating quadrupole moment of mass-energy, such as in the case of two black holes orbiting each other.  

• Torsion Waves (TWs): These are hypothetical propagating ripples in the torsion of spacetime. In the modified gravity theories that permit them, they would be sourced by the dynamics of spin density or other new physical phenomena, not simply by accelerating mass or charge. Their radiation pattern (dipolar, quadrupolar, etc.) is model-dependent.  

Propagation and Interaction with Matter

• EMWs: Propagate at the speed of light, c, in a vacuum. They are transverse waves that interact strongly with matter containing electric charges. This strong interaction makes them easy to detect but also means they are easily absorbed, scattered, or shielded.  

• GWs: Also propagate at the speed of light, c. They are transverse waves with two distinct polarization modes (“plus” and “cross”). Their defining characteristic is their extraordinarily weak interaction with matter. This makes them incredibly difficult to detect, but it also allows them to travel across the universe almost entirely unimpeded, carrying information from the most violent cosmic events.  

• TWs: The propagation speed is model-dependent but is generally assumed to be c. Their interaction with matter would be fundamentally different from the other two. Since torsion couples to spin, torsion waves would primarily interact with the intrinsic angular momentum of particles. This is a much more specific and likely even weaker interaction than that of gravity with mass-energy. Some models predict additional polarization modes beyond the two of gravity, such as scalar or vector modes, which would produce different effects on detectors.  

Detection Principles

The different ways these waves interact with matter dictate entirely different strategies for their detection.

• EMWs: Are detected by measuring the forces they exert on charged particles (e.g., in an antenna) or the energy they deposit in a material (e.g., in a CCD camera or a photomultiplier tube).  

• GWs: Are detected by measuring the minuscule, differential strain they induce in spacetime. Detectors like LIGO and Virgo use laser interferometry to measure the tiny, oscillating changes in distance between freely falling test masses separated by several kilometres.  

• TWs: The detection of hypothetical torsion waves would require a device sensitive to their primary coupling—spin. Proposed detection schemes involve looking for anomalous torques or precessional effects on ultra-sensitive gyroscopes or spin-polarized materials. Some studies suggest that certain types of torsion waves could also induce a strain in gravitational wave detectors, but with a characteristic phase shift in the response that would distinguish it from a standard gravitational wave.  

Potential Signatures and Experimental Searches for Spacetime Torsion

While propagating torsion waves remain a theoretical speculation, the broader concept of spacetime torsion—whether propagating or not—is subject to experimental investigation. Physicists have devised a range of experiments and observational strategies to search for any evidence of torsion's existence. The consistent outcome of these searches has been a series of null results, which, while not disproving the concept, place increasingly stringent limits on the parameters of any theory that includes it.

The Challenge of Detection

The primary difficulty in searching for torsion is the predicted weakness of its effects. In the most plausible theories, spin-torsion interactions are suppressed by powers of the Planck mass, making them utterly negligible except in the most extreme physical environments, such as the interiors of neutron stars or the first moments of the universe. The coupling constant for torsion-spin interactions is expected to be incredibly small, meaning any detector must have extraordinary sensitivity to have a chance of seeing a signal.  

Cosmological and Astrophysical Signatures

Some of the most promising avenues for constraining torsion come from cosmology and astrophysics, where extreme conditions and vast distances can amplify subtle effects.

• Cosmic Microwave Background (CMB): The primordial light from the early universe could carry an imprint of torsion. Some modified gravity models predict that torsion fields present during cosmic inflation could have sourced a unique stochastic gravitational wave background (SGWB). This background would be characterized by an extremely “red-tilted” spectrum (meaning its power is much greater at larger scales), a feature that could be detected by next-generation CMB polarization experiments like LiteBIRD. Other theories predict that a background torsion field could cause cosmological birefringence, a rotation of the polarization plane of CMB photons as they travel across the cosmos.  

• Gravitational Wave Propagation: While torsion in ECSK theory does not propagate, a static background torsion field (perhaps sourced by dark matter) could, in principle, affect the propagation of standard gravitational waves. This could manifest as an anomalous dampening or amplification of the GW amplitude over cosmological distances. However, detailed calculations indicate that this effect is likely far too small to be detected with current or near-future instruments like LISA.  

• Neutrino Oscillations: The interaction between neutrinos and a background torsion field could modify the probabilities of neutrino oscillations. This would lead to new, spin-dependent terms in the oscillation formulae. Future experiments designed to study the cosmic neutrino background, such as PTOLEMY, could potentially probe such effects.  

Laboratory and Accelerator Experiments

Direct searches in controlled laboratory settings provide some of the tightest constraints on torsion.

• Torsion Pendulums: These exquisitely sensitive devices, capable of measuring minute forces and torques, are a primary tool for testing fundamental physics. In the context of torsion, they are used to search for new, long-range, spin-dependent forces that could be mediated by torsion-like particles (such as axions). Decades of experiments have found no evidence for such forces, placing stringent limits on their possible strength and range.Modern torsion balance experiments, while often designed to test the Equivalence Principle or search for dark matter, can be repurposed to set the world's leading constraints on certain types of torsion interactions.  

• Neutron Spin Rotation: A direct way to probe in-matter torsion is to measure the rotation of the spin axis of polarized neutrons as they pass through a material. Since torsion couples to spin, a background torsion field within the material would cause the neutron spins to precess. An experiment measuring neutron spin rotation in liquid Helium-4 found no such effect, placing the first direct experimental upper bound on a specific combination of parity-violating torsion coupling parameters.  

• Particle Colliders: High-energy physics offers another window. If torsion manifests as a new, heavy particle (a “tordion”), it could be produced in the violent collisions at the Large Hadron Collider (LHC). Such a particle would be expected to decay into Standard Model particles, particularly those with strong couplings, like the top quark. Searches at the ATLAS and CMS experiments for new resonances decaying into top-antitop quark pairs have found no evidence for tordions, thereby excluding them up to masses of several TeV, depending on their assumed coupling strength.  

Null Results and Upper Limits

The collective result from this wide-ranging experimental program is unambiguous: to date, there is no credible, reproducible evidence for the existence of spacetime torsion. This does not mean torsion is definitively proven not to exist. Rather, the null results systematically shrink the available parameter space, forcing any viable theory of torsion to predict effects that are even weaker or occur at even higher energies than previously thought. Each new experiment that finds nothing tightens the constraints, making the concept of physical torsion increasingly elusive.  

The Pseudoscience of “Torsion Fields”

Parallel to the legitimate scientific investigation of spacetime torsion, a separate and scientifically baseless narrative has developed. This narrative, originating primarily in the Soviet Union and post-Soviet Russia, co-opted the language of theoretical physics to promote a range of pseudoscientific and paranormal claims. Understanding this history is crucial to fully answering the question “What exactly are torsion waves?” as it is the source of most public confusion on the topic.

Kozyrev, Akimov, and Shipov

The intellectual lineage of pseudoscientific torsion fields can be traced from the speculative theories of an astronomer to their repackaging by a group of physicists seeking state funding for fringe research.

Nikolai Kozyrev's “Causal Mechanics”

Nikolai A. Kozyrev (1908-1983) was a Russian astronomer who made some legitimate contributions to science, including providing the first spectroscopic evidence for volcanic activity on the Moon. However, he is more widely known for his highly controversial and unorthodox theories about the nature of time.  

In his “Causal Mechanics,” Kozyrev proposed that time itself is not merely a coordinate but a physical entity with active properties. He claimed that time possesses a form of energy that flows through the universe, can have a variable “density,” and can be actively manipulated. He conducted a series of experiments using sensitive torsion balances and gyroscopes, claiming to have measured anomalous weight changes and forces arising from various processes like stretching elastic, dissolving sugar, or even human thought. He attributed these effects to the action of his “time energy,” which he claimed did not propagate like a wave but appeared “everywhere at once,” instantly connecting cause and effect across any distance.  

Akimov and Shipov's “Torsion Fields”

In the 1980s, a group of Russian researchers, led by Anatoly Akimov and Gennady Shipov, took up Kozyrev's mantle.They performed a crucial act of rebranding: Kozyrev's mystical “flow of time” was repackaged with a more scientific-sounding name: “torsion fields.” This terminological substitution was the key to their narrative. They borrowed the term “torsion” from legitimate differential geometry and “spin” from quantum mechanics, but fused them in a manner completely divorced from their actual physical meaning.  

There is a clear intellectual lineage here. Kozyrev's experiments involving rotation (gyroscopes) and other processes were re-interpreted by Akimov and Shipov as being sourced by “spin,” and the resulting anomalous force was labelled “torsion.” This allowed them to frame their research in the language of advanced physics, making it sound more plausible to non-experts and potential funding bodies, even though the core claims remained as extraordinary as Kozyrev's.

Their central assertions were a dramatic departure from all known physics:

• Information without Energy: They claimed that torsion fields transmit information but no energy.  

• Superluminal Propagation: They asserted that these fields propagate billions of times faster than the speed of light, allowing for instantaneous communication across the galaxy and even communication with the past and future.  

• Unshieldable Waves: They claimed that torsion fields could not be shielded by any known material, passing through any obstacle unimpeded.  

• Paranormal and Exotic Phenomena: They explicitly linked their “torsion fields” to paranormal phenomena like telepathy, psychokinesis (PK), and clairvoyance. Furthermore, they claimed that “torsion generators” could be built to achieve fantastical technological feats, including free energy, antigravity propulsion, and miracle medical devices.  

A Scientific Critique and Refutation

The claims of the Kozyrev-Akimov-Shipov school stand in stark opposition to the principles of modern physics and have been thoroughly debunked through theoretical analysis, formal review, and failed experimental replication.

Contradictions with Fundamental Physics

The pseudoscientific torsion field theory is not a viable physical theory because it fundamentally contradicts well-established laws of nature.

• Violation of Special Relativity: The central claim of faster-than-light (FTL) propagation is a direct and fatal violation of Einstein's Special Theory of Relativity. The principle of causality, which states that an effect cannot precede its cause, is a cornerstone of physics and is inextricably linked to the existence of a maximum speed limit, the speed of light. Any FTL communication would allow for paradoxes where information is sent back in time to alter the past, a scenario that is logically and physically incoherent.  

• Contradiction with Legitimate Torsion Theory: The properties claimed by Akimov and Shipov are the opposite of those predicted by the legitimate ECSK theory. As established in Part I, real theoretical torsion is non-propagating and confined to matter. The pseudoscientific version is superluminal and unshieldable. This direct comparison reveals that the latter is not an extension of the former, but a complete fabrication that merely borrows its name.  

• Internal Inconsistencies: The theory is riddled with nonsensical internal contradictions. For example, proponents claim the fields are carried by neutrinos but simultaneously do not interact with matter, which is false, as neutrinos interact via the weak force. They claim the fields transmit no energy but can cause physical effects like moving pendulums or curing diseases, which violates the conservation of energy.

Formal Refutation and Failed Replications

The scientific community has formally and experimentally rejected these claims on multiple occasions.

• The Soviet Academy of Sciences Commission (1960): An official commission was appointed to investigate Kozyrev's work. Their conclusions were damning. They found that his theory was not based on clear axioms and was not developed with sufficient mathematical or logical rigour. They determined that the quality and accuracy of his laboratory experiments were too poor to draw any specific conclusions. Finally, they refuted his astronomical “evidence,” finding no geometric asymmetry in Saturn and attributing the appearance of it in Jupiter to its cloud bands, not the planet's shape.  

• The “Commission to Combat Pseudoscience”: In the post-Soviet era, the Russian Academy of Sciences established a commission to combat the rise of pseudoscience. This commission, led by figures like Nobel laureate Vitaly Ginzburg and physicist Eduard Kruglyakov, explicitly identified the torsion field research of Akimov and Shipov as pseudoscience, a fraud, and an embezzlement of state funds.  

• Failed Experimental Replications: The specific technological claims made by torsion field proponents have failed under independent scrutiny.

  • An experiment claiming to dramatically reduce the electrical resistivity of copper using a torsion generator was independently tested and found to be false; the treated and untreated samples had identical resistivity.  

  • A “reactionless drive” based on torsion field technology was installed on the Russian Yubileiny satellite in 2008. After launch, it was determined that the engine had failed to change the satellite's orbit by even a micron, demonstrating its complete ineffectiveness.  

  • Other researchers who attempted to replicate Kozyrev's sensitive pendulum experiments found that the observed effects could be fully explained by mundane thermal gradients and air currents, factors that Kozyrev had not adequately controlled for. The general lack of standardized protocols, sensors, and reproducible results is a hallmark of this fringe field.  

The Hallmarks of Pseudoscience

The narrative of “torsion fields” exhibits all the classic characteristics of pseudoscience. The claims are made in isolation from the broader scientific community and are not published in reputable peer-reviewed journals. The “evidence” consists of anecdotes, poorly controlled experiments, and appeals to authority rather than reproducible data. The theory is used as a catch-all explanation for a vast range of unrelated and often paranormal phenomena, from telepathy to alternative medicine.

A notable example is the “Kozyrev mirror,” a device made of polished aluminum sheets, often in a spiral shape, which is claimed to focus “time energy” and produce altered states of consciousness. Research into this device is emblematic of the field's unscientific nature. In 2012, Austrian skeptics awarded the “Goldenes Brett” (Golden Plank), a negative prize for the “most astonishing pseudo-scientific nuisance” of the year, in part for a master's thesis on the Kozyrev mirror that was widely condemned as unscientific.  

The persistence of these ideas, despite overwhelming refutation, can be understood partly through the sociology of science. The initial research by Akimov and Shipov was fuelled by promises of breakthrough military technology to state funders in a secretive environment. Even after being discredited scientifically, they continued to receive funding from government ministries. This narrative was later exported to fringe communities in the West, often presented as “suppressed Russian science,” tapping into conspiracy theories and a distrust of mainstream institutions to ensure its survival.  

Synthesizing the Science and Pseudoscience

What Exactly Are Torsion Waves?

After this comprehensive analysis, a definitive answer to the central question can be formulated. “Torsion waves” can mean one of two things, and the distinction is absolute.

1. In the context of established, experimentally verified physics (General Relativity and the Standard Model of Particle Physics), torsion waves do not exist. The geometry of General Relativity is, by postulate, torsion-free.

2. In the context of theoretical physics, the concept is more nuanced.

   • In the most natural and well-studied extension of General Relativity, the Einstein-Cartan-Sciama-Kibble (ECSK) theory, spacetime possesses torsion, which is sourced by the intrinsic spin of matter. However, this torsion is non-propagating; it is algebraically tied to its source and cannot radiate away as a wave.

   • In more speculative modified theories of gravity (such as certain Poincaré Gauge or Metric-Affine theories), propagating torsion waves are a theoretical possibility. Their existence depends on adding specific, non-minimal kinetic terms to the gravitational action. These waves remain entirely hypothetical, are subject to increasingly stringent experimental constraints, and are not a prediction of any standard theory.

3. In the context of popular discussion and fringe science, the term “torsion waves” or “torsion fields” refers to a pseudoscientific concept with no basis in physical reality. These claims of superluminal, unshieldable, paranormal information fields have been thoroughly debunked and are contradicted by fundamental principles of physics.

The Great Divide

There is an unbridgeable chasm between the scientific concept of torsion and its pseudoscientific counterpart. The former is a subtle, rigorously defined geometric property whose physical effects, if they exist at all, are predicted to be extraordinarily weak and confined to the most extreme physical regimes. The latter is a fantastical notion of a powerful, all-pervading force capable of explaining paranormal phenomena. The two are linked only by the misappropriation of a scientific term. Any discussion of “torsion waves” that involves faster-than-light travel, telepathy, or free energy is unequivocally in the realm of pseudoscience.  

The Future of Torsion Research

Despite the null experimental results and the noise from pseudoscience, the concept of spacetime torsion continues to play a role on the legitimate frontiers of theoretical physics. Its future lies not in the pursuit of exotic technologies, but in the painstaking work of fundamental research and precision measurement.

Quantum Gravity and Cosmology

Torsion remains a compelling idea in the search for a unified theory of quantum gravity, as it offers a geometric way to incorporate the quantum property of spin into a gravitational framework. Active and future research directions include: 

• Early Universe Cosmology: Theorists continue to explore the role that torsion could have played during the inflationary epoch or in a “Big Bounce” scenario. The potential for torsion to leave faint, but detectable, signatures in the Cosmic Microwave Background or a primordial gravitational wave background remains a key motivator for developing next-generation cosmological observatories.  

• Dark Matter and Dark Energy: Some models propose that torsion could be related to the dark sector of the universe. This could be through a new particle associated with a propagating torsion field acting as a dark matter candidate, or through torsion's influence on the cosmological constant and the nature of dark energy.  

• Fundamental Theory: Torsion arises naturally in some approaches to quantum gravity, such as certain formulations of string theory or loop quantum gravity, where it may appear as a necessary component of the spacetime structure at the Planck scale. Recent work has explored unifying Bohmian mechanics and ECSK gravity, with the quantum potential emerging from torsional curvature.  

• Precision Optomechanics: A promising experimental frontier involves the use of highly sensitive, laser-cooled mechanical systems, such as torsional oscillators. While not designed to detect torsion directly, these experiments probe the quantum nature of gravity itself. By pushing the boundaries of precision measurement at the interface of the quantum and gravitational realms, they could reveal or constrain new physics, including any potential torsion-like effects.  

The Path Forward with Precision Measurement

The future of legitimate torsion research is one of incremental progress and extreme precision. If spacetime torsion is a real feature of our universe, its effects are subtle and deeply hidden. The path forward lies in continuing to push the limits of measurement in every available domain: improving the sensitivity of gravitational wave detectors, launching more advanced CMB telescopes, building larger particle colliders, and developing novel quantum sensors. Each null result is not a failure, but a valuable piece of information that refines our understanding of fundamental physics and guides the ongoing search for a complete theory of the universe.