In a recent paper, Bender and Klevansky [Phys. Rev. A 84, 024102 (2011)] considered
PT-symmetric matrix representations for fermionic operator algebras of the form ${\ensuremath{\xi}}^{2}={\overline{\ensuremath{\xi}}}^{2}=0$, $\ensuremath{\xi}\overline{\ensuremath{\xi}}+\overline{\ensuremath{\xi}}\ensuremath{\xi}=\ensuremath{\varepsilon}1$, where $\overline{\ensuremath{\xi}}$ is the
PT transform of $\ensuremath{\xi}$. They constructed such algebras for $\ensuremath{\varepsilon}=\ensuremath{-}1$ and established that it is not possible to construct a matrix representation for the standard fermionic algebra ($\ensuremath{\varepsilon}=1$). Bender and Klevansky used the formalism developed by Jones-Smith and Mathur [Phys. Rev. A 82, 042101 (2010)] which extends
PT-symmetric quantum mechanics to the case of odd time-reversal symmetry (fermionic case). By using the same formalism, we show that
PT-symmetric matrix representations exist for both standard ($\ensuremath{\varepsilon}=1)$ and abnormal ($\ensuremath{\varepsilon}=\ensuremath{-}1)$ fermionic algebras if one takes $\overline{\ensuremath{\xi}}$ as adjoint $\ensuremath{\xi}$ with respect to the
CPT and
PT inner products, respectively. This general result is illustrated for the example of a typical quaternionic four-level model by an explicit construction of the fermionic creation and annihilation operators which satisfy all the criteria of
PT quantum mechanics for the odd time-reversal symmetry.
In standard physics, time reversal (T) is a mathematical abstraction: an antiunitary operator that formally reverses the direction of evolution. But what does it mean physically? How do you "reverse time" when you can't reverse scrambled eggs, un-mix gases, or un-bake a cake? This paper provides the answer that physics has been missing for a century. Using nothing but the language of cardboard tubes, colored corks, and paper sheets—objects you could find in a child's workshop—we solve what the most sophisticated quantum field theories cannot: what pure time reversal actually means when every transformation must be physically realizable, not just mathematically definable. The discovery is both radical and simple: T isn't about going backward. It's about stopping. ḱ → 0⁺: the geometric frame rate drops to zero. Billions of intermediate quantum states—the "movie" of a process—vanish into geometric silence. What remains when the frames stop generating? Only the bookends of reality: the beginning and the end. The proton and its anti-proton. The initial configuration and its final counterpart. No rewinding, no backtracking—just the collapse of history into its boundary conditions. This is more than a reinterpretation; it's an ontological revolution. Time isn't a dimension you travel along—it's a process you can halt. The arrow isn't reversed; it's erased. This work completes the "A Tale of Deep Symmetry" trilogy, providing the missing geometric interpretation of T that preserves the sacred CPT theorem while respecting a rigorous mechanical ontology. For physicists tired of mathematical abstractions that obscure rather than illuminate... For philosophers of science wrestling with the nature of time and reality... For AI researchers watching machines ask better questions than humans... For anyone who believes that the deepest truths about our universe can—and should—emerge from models simple enough to build at your kitchen table. The tubes and corks were never just toys. They were the Rosetta Stone for time itself. **Keywords:** Time reversal paradox, operational physics, geometric ontology, AI-driven discovery, CPT symmetry, foundational crisis, simplicity in science
This article is devoted to the view about DNA inspired by zero energy ontology (ZEO) forming the basis of the quantum measurement theory of Topological Geometrodynamics (TGD) and by the notion of dark DNA inspired by the TGD view about dark matter as phases of the ordinary matter with effective Planck constant heff =nh0 h at magnetic body (MB) - the third key notion distinguishing TGD from standard model. The basic prediction of ZEO is that "big" (ordinary) state function reduction (BSFR) changes the arrow of time meaning "death" and "reincarnation" with opposite arrow of time. This leads to a new view about self-organization. The time reversals of the basic processes like transcription and replication turn out to be possible only for the conjugate (passive) strand - this is basically due to the CPT theorem in TGD context and chiral selection. By chiral selection enzymes can catalyze processes but not their time reversals. For instance, conjugate strand polymerizes in reverse time direction - this looks like depolymerization in standard time direction. Polymerization of the conjugate strand however occurs in standard time direction but in reverse direction along strand. The recombination of DNA strands during meiosis is poorly understood. This could correspond to reconnections for the flux tubes associated with the active DNA strands. Time reversal would occur in BSFR and formerly passive conjugate DNA strands would depolymerize to "loose" codons (not independent letters) by the time reversed polymerization, the flux tubes associated with the formerly active strands would suffer reconnections inducing recombination without assistance of enzymes, second BSFR would occur, and be followed by the replication of recombined active strands. According to the findings of Becker, the direction of the electric field along the body axis determines whether the system is awake or sleeps. By the properties of electric field under time reflection, the arrow of time correlates also with the direction of the electric field. TGD predicts that consciousness is possible even at the level of DNA. Could also DNA have a longitudinal electric field with direction correlating with the arrow of time of DNA at the (magnetic body) MB of DNA. Could there be a switch changing the direction of this electric field? This inspires a model for the DNA as ferroelectret based on the properties of the negatively charged sticky ends of chromosome and dark DNA codons as proton triplets along a magnetic flux tube parallel to DNA strand. A simple proposal for the time switch based on the analog of Becker's DC currents emerges: proton flow of the dark protons of sticky end to the opposite sticky end would change the arrow of time. The model could generalize also to proteins known to be ferro-electrets and could be accompanied also by their dark analogs.