Torsion On My Mind

8 min readAug 7, 2023

Clearly, for a system which is still evolving towards a MaxEnt state, additional data (in the form of relevant boundary conditions) are required to specify a solution for the entropic Liouville PDE (Eq. (3) with N>1). Fortunately, exploiting the comprehensive isomorphism between the kinematic (energy) and entropic quantities outlined in PJ2019 and discussed further here, we can see that many of the PDE solutions directly applicable in this entropic context are explicitly treated by Courant & Hilbert [27].
M. Parker and C. Jeynes, Entropic Uncertainty Principle, Partition Function, and Holographic Principle Derived from Liouville’s Theorem [1]

The above image is from Claude Swanson, The Torsion Field and The Aura [2] and describes a couple of simple torsion experiments conducted in the 1950’s (replicated many times since) by the Russian astrophysicist Nikolai Kozyrev. If you will notice, both torsion pendulums are suspended in thoroughly evacuated vacuum chambers which are thermally and electromagnetically shielded. Either an entropy increasing (evaporating acetone) or decreasing (freezing water) source is strategically placed outside the vacuum chamber. The increasing source repells the asymmetric torsion arm and causes the circular disc to rotate clockwise as viewed from the source location; the decreasing source attracts the asymmetric torsion arm and causes a counter-clockwise rotation in the disc. William Tiller analyzes these experiments mathematically in Some Initial Comparisons Between the Russian Research on “The Nature of Torsion” and the Tiller Model of “Psychoenergetic Science”: Part I [3] and while his analysis is quite rigorous his conclusions are not quantitative due to lacking a sufficient theoretical understanding of his coupling variable:

To evaluate the interaction between the R-space entropy conjugate of the small mass sphere inside the vacuum chamber with the R-space entropy conjugate of either the water freezing vessel or the acetone evaporation vessel located outside the vacuum chamber, we must use the Equation 3e formula modified by the Equation 5a factor to obtain for the system of two vectors, g_S(k_t), shown in Equation 7 as
g_S(k_t) = γg_{Sphere}(k_t) + g’_{vessel}(k_t). (7a)
Here, γ is the constant thermodynamic entropy per unit volume value for the D-space sphere and g’_{vessel} is Equation 3c modified according to Equation 5a. If g_S(k_t) is greater than γg_{Sphere}(k_t) then the vectors add which means that the non-local force is attractive. If instead, g_S(k_t) is less than γg_{Sphere}(k_t), the two vectors subtract and a repulsive force is operating. The difficulty we have in making a final evaluation is that although the parameter B switches from being negative for the freezing water case to positive for the evaporating acetone case, α_eff can in general be of a mathematically complex form, α_eff = α_0 + iα_1, with the coefficients either positive or negative and we have no experimental data to decide which is operational in either case.

These experiments seem ideally suited for an entropic analysis using the Quantitative Geometric Thermodynamics [4] of Parker and Jeynes. The circular disc already has the requisite symmetry (at least C2) and it would seem that one could surround an info-entropic “mass” with asymmetric torsion pendulum constructs situated according to the n^{th} roots of unity, giving it at least C2 symmetry as well. With the sensitivity of modern gauges, we should be able to extract very precise information from these experiments and it would also be interesting, perhaps even informative, to conduct experiments in both “unconditioned” and “conditioned” spaces, using Tiller’s Intention Host Device (IHD); in fact, it could be interesting to simply utilize an activated IHD AS the info-entropic “mass,” just to see what might happen.

Parker and Jeynes present the relevant mathematics in Maximum Entropy (Most Likely) Double Helical and Double Logarithmic Spiral Trajectories in Spacetime [4], in their section titled, The Double — Armed Logarithmic Spiral. The Double Helix is a special case of the Double Logarithmic Spiral with the helix seemingly representing reversible processes and the logarithmic irreversible. The essential parameters are “the logarithmic radial parameter Λ given by the requirement that the galactic radius R_G and the Schwarzschild radius r_{BH} are related logarithmically by the half — thickness

Λ = (2/L)ln (R_G/r_{BH});

the pitch at the info-entropic source, which informs (or is informed by) the entropic “mass”; and the coupling coefficient informed by the “mass” and radial parameter. The entropic potential is proportional to the entropic “mass” and the force is given by the potential. The info-entropic field is holomorphic (analytic), its component elements harmonic conjugates. So, what am I missing?

Evidently, the intrinsic complex structure inherent to the geometry of spacetime has deep and perhaps under-appreciated consequences for even our classical field theories.
J. Dressel, et. al., Spacetime Algebra as a Powerful Tool for Electromagnetism [5]

Entanglement at the microscopic scale is currently well understood. But the galactic scale also appears to us to have some properties which seem similar. It is clear that our idealised spiral galaxy, expressed as a (holomorphic) double-logarithmic spiral, is treated by the QGT formalism as an object whose entropy is given holographically, just like the entropy of its central supermassive black hole. But then, should the galaxy not also be considered as entangled, just as are quantum things like atoms and atomic nuclei? After all, entanglement represents another way to speak of non-local influence, and what could be more non-local than the symmetry of well-formed spiral galaxies, which are common in the Universe?
C. Jeynes, et. al., The Poetics of Physics [6]

What do the authors of [5] mean by “complex structure inherent to the geometry of spacetime?” It appears to me that they ultimately mean “holomorphic structure” or, perhaps more precisely, that the geometry of spacetime is inherently holographic. But meta-ultimately, once again, they must be referring to William Tiller’s Macroscopic Information Entanglement, hence the mention of classical field theories. Tiller’s Macroscopic Information Entanglement manifests due to wave/particle duality with its mathematical origins being what may be called “Fourier Transform structure.” My conjecture is, the holographic nature of spacetime also manifests due to wave/particle duality and its mathematical origins most certainly being holomorphic structure.

Consistent with Real Analysis, in Complex Analysis the derivative is defined on limits

lim_(h → 0) (f(z_0 + h) − f(z_0))/h

where z_0 and h are complex numbers. In Real Analysis, for a limit and, hence, a derivative, to exist at a point x_0 in the domain of a function f, it must take the same value regardless of whether you approach x_0 from x < x_0 or from x_0 < x. The same applies in Complex Analysis, but here z_0 can be approached from numerous directions. This leads immediately to the Cauchy — Riemann Equations.

A function defined on complex variables which is differentiable at each point in its domain is called analytic (but see the Wikipedia link above). Oftentimes the complex variables themselves are composed of functions also defined on complex variables and which also satisfy Laplace’s Equation

Δu = ∂²u/∂x² + ∂²u/∂y² = 0

where z = (x, y) = x + iy. Such functions are called harmonic conjugates and are frequently utilized in physics to model fields and flows. Generally, harmonic conjugates are used to couple a potential function with its kinematics, but they can also be used to model orthogonally coupled fields, such as electromagnetism or, in the case of Parker’s and Jeynes’ QGT, info-entropic fields.

At any rate, let f = u +iv, u and v harmonic conjugates, be analytic on a domain D. Then across all of D

∂u/∂x = ∂v/∂y and ∂u/∂y = −∂v/∂x.

The proof of this follows immediately from calculating the above limit, lim_(h → 0) (f(z_0 + h) − f(z_0))/h, which defines the derivative of f, as h → 0 from its real component

f’(z_0) = ∂u/∂x + i∂v/∂x

and again as h → 0 from its imaginary component

f”(z_0) = 1/i ∂u/∂y + ∂v/∂y

and then equating the real and imaginary parts of these derivatives. This is an early example of what is called separating and equating grades in Geometric Algebra/Calculus. Now, Green’s theorem on line integrals applied to the Cauchy — Reimann equations leads immediately to the Cauchy Formula, an integral representation formula which is important for solving boundary-value problems.

This says that a holomorphic (analytic) function is completely determined by its boundary-values. Boundary-values can be either temporal, i. e. predator/prey relation, or spatial, i. e. electrostatic field. If spatial, the actual boundary can be physical or idealized — abstract. It seems to me that this is intimately correlated with the Holographic Principle and is what is ultimately meant by “the intrinsic complex structure inherent to the geometry of spacetime.”

Complex variables are the earliest instantiation of multivectors, composed of a scalar component and a bivector component. The complex algebra is ring isomorphic to the even sub-algebra (G_+)² of G². The quaternion division algebra is ring isomorphic to the even sub-algebra (G_+)³ of G³. These earlier algebras provided the motivation for William Clifford’s development of the fully general case. A modern result is David Hestenes’ Spacetime Algebra with its inherent “complex structure.” Geometric derivatives, which generalize the gradient, and directed integrals, which generalize line and flux integrals, enable a full generalization of the Cauchy Formula, called the Clifford-Cauchy Integral Formula

The expression under the integral is the geometric product, which is unavailable in any other form of analysis. The geometric product enables the pseudoscalar and these two together enable the full generalization of these derivatives and integrals. And note that these integrals are over the boundary of what amounts to a manifold embedded in R^m and where the functions are defined on multivectors, i. e. they define multivector fields. One would think that this should be useful for extending QGT to the non-equilibrium domain. I, for one, am highly interested in their entropic force and would really like to see a QGT analysis of those Kozyrev torsion experiments, a non-equilibrium analysis eventually.

It is worth pointing out that Bohm’s recognition of a “quantum-mechanical” potential U(x) exerting a “quantum-mechanical” force “analogous to, but not identical with” the conventional strong force on a nucleon ([Bohm 1952] his Equation (8)), can now be understood to be a prescient anticipation of our entropic force, familiar from our previous discussion of galactic geometry ([Parker and Jeynes 2019, their Equation (23)).
C. Jeynes, et. al., [6]

David Bohm’s quantum potential seems, at the very least, conceptually related to William Tiller’s coupling field and with modern technology those torsion experiments should provide precise, low-cost information regarding any “entropic forces,’ which appears to be the causal agent here, or, at the very least, an info-entropic field appears strongly correlated with the causal agent. They should provide valuable insight into the physical nature of info-entropic fields. Perhaps I’m misunderstanding something, but these torsion pendulums, viewed properly, have the requisite symmetry (at least C2) and one is led to believe that the QGT formalism could model what essentially amounts to a source generated potential acting on a body.

See also my Medium article, Searching for New Physics with Precision Clocks, which is about a low-cost augmentation to a precision clock experiment already underway in England, the QSNET consortium.

Torsion On My Mind

Written by Wes Hansen