[Paper Review] Quantum mechanical observer and superstring/M theory

M.J. Dance|ArXiv.org|Dec 31, 2008

Quantum Mechanics and Applications14 references3 citations

TL;DR

This paper proposes that the Lagrangian density of superstring/M theory may emerge from the quantum dynamics of a first-stage observer O1, as perceived by a later observer O2. By incorporating both O1’s center-of-mass kinetic energy and a fermionic internal degree of freedom, and accounting for quantum uncertainties in reference frame transformations, the resulting effective Lagrangian resembles superstring theory, suggesting that observer dynamics could underlie fundamental physics.

ABSTRACT

Terms are suggested for inclusion in a Lagrangian density as seen by an observer O2, to represent the dynamics of a quantum mechanical observer O1 that is an initial stage in an observation process. This paper extends an earlier paper which suggested that the centre-of-mass kinetic energy of O1 could correspond to, and possibly underlie, the Lagrangian density for bosonic string theory, where the worldsheet coordinates are the coordinates which O1 can observe. The present paper considers a fermion internal to O1, in addition to O1's centre of mass. It is suggested that quantum mechanical uncertainties in the transformation between O1's and O2's reference systems might require O2 to use $d$ spinor fields for this fermion, where $d$ is the number of spacetime dimensions. If this is the case, and if the symmetry/observability arguments in arXiv:hep-th/0601104 apply, the resulting Lagrangian density for the dynamics of O1 might resemble, or even underlie, superstring/M theory.

Motivation & Objective

• To extend prior work linking observer center-of-mass motion to bosonic string theory by including internal fermionic degrees of freedom in the observer O1.
• To investigate how quantum uncertainties in the transformation between observers O1 and O2 might necessitate d spinor fields in spacetime dimensions d, leading to a richer field structure.
• To explore whether the resulting Lagrangian density, combining O1’s center-of-mass and fermionic dynamics, resembles or underlies superstring/M theory.
• To provide a physical interpretation of superstring theory’s Feynman diagrams as arising from observer-based information processing and reference frame uncertainty.
• To examine the role of symmetry and observability constraints in restricting observable coordinates, leading to a worldsheet-like structure.

Proposed method

• Introduce a Lagrangian density for observer O1’s center-of-mass motion as seen by observer O2, using the nonrelativistic kinetic energy term $ \mathcal{L}^{EK}_{\text{obs}} = \frac{1}{2}m\kappa^{\alpha\beta}\eta_{\mu\nu}\frac{\partial X^{\mu}}{\partial x^{\alpha}}\frac{\partial X^{\nu}}{\partial x^{\beta}} $, with $ x^{\alpha} $ as O1’s internal coordinates.
• Extend the model by adding a fermionic term $ i\bar{\psi}^{\mu}\gamma^{\alpha}\partial_{\alpha}\psi_{\mu} $, representing the electron’s kinetic energy relative to O1’s center of mass.
• Argue that quantum uncertainties in the O1–O2 reference frame transformation necessitate d spinor fields $ \psi_{\mu} $, where d is the number of spacetime dimensions.
• Apply symmetry and observability constraints: O1 cannot measure radial coordinate r or angular coordinates θ, φ, leading to identification of worldsheet coordinates τ = t and σ = φ.
• Restrict the resulting Lagrangian to a 2D worldsheet structure, yielding a form analogous to superstring theory Lagrangians.
• Interpret the topology of superstring Feynman diagrams (e.g., genus-L Riemann surfaces) as representing O1’s self-interaction and reference frame uncertainty, with external lines puncturing the central surface due to O2’s knowledge being filtered through O1.

Experimental results

Research questions

• RQ1 Can the dynamics of a quantum mechanical observer O1, including its center-of-mass motion and internal fermionic degrees of freedom, give rise to a Lagrangian resembling superstring theory?
• RQ2 How do quantum uncertainties in the transformation between observers O1 and O2 lead to the need for d spinor fields in d-dimensional spacetime?
• RQ3 What role do symmetry and observability constraints play in reducing the effective dimensionality of the observer’s dynamics to a 2D worldsheet?
• RQ4 How might the topology of superstring theory’s perturbative Feynman diagrams (e.g., Riemann surfaces with handles) be interpreted as arising from observer-based information processing?
• RQ5 Is it possible that M-theory’s underlying structure emerges not from fundamental strings, but from the quantum measurement process involving sequential observers?

Key findings

• The inclusion of a fermionic term $ i\bar{\psi}^{\mu}\gamma^{\alpha}\partial_{\alpha}\psi_{\mu} $ in the Lagrangian density, alongside O1’s center-of-mass kinetic energy, leads to a structure resembling the action of superstring theory.
• Quantum uncertainties in the O1–O2 reference frame transformation are argued to necessitate d spinor fields $ \psi_{\mu} $, effectively embedding spacetime dimensionality into the field content.
• By postulating that O1 cannot measure the radial coordinate r and lacks observability of certain angular coordinates, the worldsheet coordinates τ = t and σ = φ are selected, reducing the dynamics to a 2D effective theory.
• The resulting Lagrangian density under these constraints takes a form structurally similar to that of superstring theory, particularly in its worldsheet action and field content.
• The topology of superstring perturbation theory diagrams—such as closed orientable Riemann surfaces with L handles—can be interpreted as representing O1’s self-interaction and the uncertainty in reference frame transformation, with external lines puncturing the central surface due to O2’s knowledge being mediated through O1.
• The paper tentatively suggests that the foundation of M-theory may not be fundamental strings, but rather the quantum dynamics and information-processing capacity of a first-stage observer O1.