Beyond the Speed of Light: Quantum Verification through Folded Dimensional Topologies

 

In this article, I present a possible solution to the problem of classical verification in quantum teleportation protocols, based on a theoretical framework grounded in M-theory and the geometry of folded dimensions at the Planck scale. The approach I propose enables quantum verification without classical channels, overcoming the limitations imposed by the speed of light and the causal structures of traditional spacetime.

1. Introduction

Quantum teleportation, as formulated in the model by Bennett et al. (1993), requires a classical channel for the verification and reconstruction of the quantum state at the receiver. This imposes a fundamental constraint: the speed of light as the upper limit for the transmission of verifiable information.

In this work, I propose an alternative based on M-theory, which postulates the existence of additional dimensions compactified at the Planck scale. In this context, I argue that quantum information can be encoded in the topological structures of these dimensions, allowing simultaneous verification at spatially separated points in ordinary spacetime, without the need for a classical channel.

2. Theoretical Foundations

2.1. Compactified Dimensions and String Topology

I build on M-theory, which unifies various versions of string theory within an 11-dimensional framework, seven of which are folded into structures such as Calabi–Yau manifolds. I consider that certain string vibrations can remain entangled through these dimensions, forming a resonant network that is independent of Euclidean space.

2.2. Quantum Topological Weaving

The system I propose is based on pairs of resonant vibrational strings anchored at different points in classical spacetime, but joined through their extradimensional topological continuity. I suggest that information is encoded as a phase shift or geometric deformation in the string, whose counterpart responds simultaneously by being connected through the same fundamental topology.

3. Teleportation–Verification Process Without Classical Channels

• Preparation: Two entangled quantum strings are generated, each located in a different spacetime region (A and B).

• Encoding: A quantum state is transformed into a specific topological deformation of the string at location A.

• Resonance: Due to the extradimensional connection, the string at location B instantly adopts the same deformation.

• Verification: A reader of extradimensional geometry detects the topological shape at B. If it matches the expected invariants (such as knot polynomials or homotopy classes), the verification is considered successful.

Implications for Causality and Communication

Since no information is transmitted through a traditional channel, causality in classical spacetime is not violated. The connection is geometric and simultaneous from an extradimensional frame. In this sense, it is a kind of "topological entanglement," not conventional transmission.

Conclusions and Future Directions

I propose that using folded dimensions as a medium for verification opens a new path for developing communication and information transfer protocols beyond relativistic limits. Although speculative, this proposal aligns with frameworks such as quantum gravity, holographic information, and topological computation.

I believe that developing a rigorous mathematical model and computational simulations within frameworks such as string geometry, quantum topology, and tensor networks could be the next step in validating or refining this proposal.

References:

• Bennett et al. (1993). Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels.

• Witten, E. (1995). String theory dynamics in various dimensions.

• Maldacena, J. (1997). The large-N limit of superconformal field theories and supergravity.

• Preskill, J. (2018). Quantum Computing in the NISQ era and beyond.

• Freedman, M. et al. (2002). Topological quantum computation.