Colby Serpa 🧬 on Nostr: It does indeed suggests a deeper underlying symmetry in the fabric of the universe. ...

It does indeed suggests a deeper underlying symmetry in the fabric of the universe. Space-time scales invariantly.

Here’s how the curving of space-time creates the wavelength that the particle is nested within. Curious of your thoughts!

“\section{Incremental Torque Of Space-Time Evokes The Curved Waves Of Quantum Particles}
\label{sec:IncrementalTorque}

\subsection{Modeling Wave Behavior Through Incremental Torque}

In quantum mechanics, particles like photons exhibit wave-particle duality, a phenomenon best demonstrated in the double-slit experiment. Here, particles create interference patterns, behaving like waves, yet they also manifest as distinct particles when observed. This wave-like behavior poses a stark contrast to the predictions of classical physics, particularly general relativity, which describes gravity as the curvature of spacetime.

To reconcile these seemingly disparate behaviors, we introduce \textit{incremental torque} within a modified framework of general relativity. This new approach incorporates the constant \( O \), linking energy and wavelength and introducing torque as a rotational force that accumulates along a particle's path through spacetime. This torque provides a mechanism by which particles can exhibit wave-like trajectories, represented as helical paths, without violating the principles of general relativity.

\subsection{Conceptualizing Incremental Torque and Its Effects}

\subsubsection{Torque as a Rotational Curvature}

In classical general relativity, spacetime curvature influences the trajectory of particles. However, by introducing the concept of incremental torque within the \( O \) field framework, we add a rotational element to this curvature. Instead of merely bending spacetime, torque implies a twisting motion that accumulates over time, potentially causing particles to spiral or move in a helical path, rather than simply following a curved line.

\subsubsection{Helical Patterns in 3D Space}

The wave-like behavior observed in quantum mechanics can be conceptualized as a helical structure in three-dimensional space. The peaks and troughs of a wave correspond to the turns of this helix, which arises from the continuous application of small rotational forces, or torque, as the particle moves.

\subsubsection{Incremental Accumulation of Torque}

As a particle, such as a photon, travels through spacetime, the applied torque gradually changes its direction. This incremental accumulation of rotational force causes the particle to follow a spiral path. When summed over a full wavelength, this motion reproduces the wave-like behavior observed in quantum systems.

\subsection{Implementing Incremental Torque in the Model}

\subsubsection{Step 1: Define the Incremental Torque Function}

We define the torque function \( \tau(x) \) that introduces a small rotation in the particle's path:

\[
\tau(x) = \alpha \cdot \frac{O}{\lambda^2} \cos\left(\frac{2\pi x}{\lambda}\right)
\]

where:
\begin{itemize}
\item \( \alpha \) is a proportionality constant.
\item \( O \) is the constant that links energy \(E\) and wavelength \(\lambda\).
\item \(\lambda\) is the wavelength of the particle.
\item \(x\) is the position along the particle's path.
\end{itemize}

\subsubsection{Step 2: Integrate the Torque to Create a Helical Path}

The cumulative effect of this torque can be calculated by integrating \( \tau(x) \) over the particle's trajectory, resulting in a helical path:

\[
\text{Path}(x) = \int \tau(x) \, dx
\]

This path represents the particle's movement in three-dimensional space, where the torque causes the particle to spiral as it moves through spacetime. This helical path corresponds to the wave's peaks and troughs. The helical path demonstrates how the cumulative effect of torque twists the particle's trajectory incrementally as it moves through spacetime. This spiral motion correlates with the peaks and troughs observed in quantum waves but is now represented in 3D space as a helical path.

This model suggests that the wave-like behavior seen in quantum mechanics could be a physical spiral in spacetime, driven by the interaction of energy and wavelength through the \( O \) field and incremental torque.”