[Paper Review] Ghost spinors, shadow electrons and the Deutsch Multiverse

Elena V. Palesheva|ArXiv.org|Aug 5, 2001

Computational Physics and Python Applications4 references3 citations

TL;DR

This paper proposes that ghost spinors—solutions to the Einstein-Dirac equations with zero stress-energy tensor but non-zero current—represent physical particles in parallel universes, providing a physical basis for David Deutsch's multiverse interpretation of quantum interference. By identifying ghost neutrinos and electrons as shadow particles in the Deutsch multiverse, the work establishes a field-theoretic framework for non-interacting, zero-energy particles that still carry conserved currents, thereby offering a novel physical interpretation of quantum-level multiverse phenomena in flat spacetime.

ABSTRACT

In this article a new solution of the Einstein-Dirac's equations is presented. There are ghost spinors, i.e. the stress-energy tensor is equal to zero and the current of these fields is non-zero vector. Last the ghost neutrino was found. These ghost spinors and shadow particles of Deutsch are identified. And in result the ghost spinors have a physical interpretation and solutions of the field equations for shadow electrons as another shadow particles are found.

Motivation & Objective

• To provide a physical interpretation for ghost spinors—solutions of the Einstein-Dirac equations with vanishing stress-energy tensor but non-zero current.
• To establish a connection between ghost spinors and shadow particles in David Deutsch's multiverse framework.
• To demonstrate that ghost spinors, including ghost electrons, are consistent with field equations in flat spacetime and possess measurable current despite zero energy.
• To resolve conceptual issues in the multiverse interpretation by grounding shadow particles in solutions of relativistic field equations.

Proposed method

• Solving the Einstein-Dirac equations in a flat spacetime with a specific non-diagonal metric $ ds^2 = dx^0{}^2 + 2e^{x^0}dx^0dx^3 - dx^1{}^2 - dx^2{}^2 $, which yields a vanishing Riemann tensor and thus zero Einstein tensor.
• Using a tetrad formalism with Dirac matrices $ \gamma^{(i)} $ and spin connection $ \Gamma_k $, particularly $ \Gamma_0 = \frac{1}{2} \begin{bmatrix} 0 & \sigma_3 \\ \sigma_3 & 0 \end{bmatrix} $, to define the covariant derivative in curved tetrad space.
• Constructing bispinor solutions $ \psi $ with exponential dependence on $ x^0 $ and $ x^2 $, such as $ \psi = \begin{bmatrix} 1 \\ -1 \\ 1 \\ 1 \end{bmatrix} e^{\frac{mc}{\hbar}x^2 + \alpha(x^0)} $, satisfying the Dirac equation with $ m=0 $ (ghost neutrino) or $ m \neq 0 $ (ghost electron).
• Computing the stress-energy tensor $ T_{ik} $ explicitly and showing it vanishes identically for these solutions, confirming their ghost nature.
• Deriving the current density $ j^{(k)} = (4e^{2\frac{mc}{\hbar}x^2 + 2\alpha(x^0)}, 0, 0, 4e^{2\frac{mc}{\hbar}x^2 + 2\alpha(x^0)}) $, which remains non-zero despite zero energy, confirming physical detectability via current.
• Identifying these ghost fields as shadow particles in Deutsch’s multiverse, where their zero stress-energy tensor corresponds to absence of gravitational coupling, while their non-zero current allows for quantum interference effects.

Experimental results

Research questions

• RQ1 Can ghost spinors—solutions with zero stress-energy tensor but non-zero current—be physically interpreted within a relativistic field theory framework?
• RQ2 How do ghost spinors in flat spacetime relate to the concept of shadow particles in David Deutsch’s multiverse model?
• RQ3 What field equations describe shadow electrons, and do they admit consistent solutions with non-zero current and zero energy?
• RQ4 Can the physicality of shadow particles be justified through solutions of the Einstein-Dirac equations rather than ad hoc assumptions?
• RQ5 Is there a consistent field-theoretic mechanism for non-gravitating, non-energy-carrying particles to still influence quantum interference patterns?

Key findings

• Ghost neutrinos are found as solutions to the Einstein-Dirac equations in flat spacetime with $ m=0 $, exhibiting zero stress-energy tensor $ T_{ik} \equiv 0 $, yet non-zero current $ j^{(k)} \neq 0 $, confirming their ghost nature.
• For massive ghost spinors ($ m \neq 0 $), such as ghost electrons, the solution $ \psi = \begin{bmatrix} 1 \\ -1 \\ 1 \\ 1 \end{bmatrix} e^{\frac{mc}{\hbar}x^2 + \alpha(x^0)} $ satisfies the Dirac equation and yields $ T_{ik} \equiv 0 $, confirming their ghost status.
• The current density for ghost electrons is $ j^{(k)} = \left(4e^{2\frac{mc}{\hbar}x^2 + 2\alpha(x^0)}, 0, 0, 4e^{2\frac{mc}{\hbar}x^2 + 2\alpha(x^0)}\right) $, demonstrating measurable flow despite zero energy.
• Ghost spinors are physically interpreted as shadow particles in the Deutsch multiverse, where their zero stress-energy tensor corresponds to no gravitational interaction, yet their current enables quantum interference.
• The paper establishes a field-theoretic foundation for shadow particles by deriving consistent solutions to the Einstein-Dirac equations, resolving the lack of dynamical equations for such particles in previous multiverse models.
• The work redefines the distinction between matter and substance: ghost spinors are matter (carry current) but not substance (zero stress-energy tensor), resolving a conceptual ambiguity in relativistic field theory.