Non-Zero Straightness

Title: Non-Zero Straightness: Connecting Curved Calculus, Variable c, and Nuclear Anomalies

Author: Orion Franklin, Syme Research Collective
Date: March 14, 2025

Abstract: Classical calculus assumes that curved functions can be locally straightened by taking infinitesimally small steps. However, if space-time is fundamentally curved, then true straightness may not exist at any scale larger than zero. This insight challenges not only differentiation but also the assumption of constant fundamental physical quantities, such as the speed of light (c). In previous Syme Papers, The Limits of Calculus in a Curved Space introduced the idea that differentiation is inherently flawed in a curved universe, while The More to C Hypothesis proposed that c is not truly constant but fluctuates at fine resolutions. Here, we establish a direct connection between non-zero straightness, resolution-based physical constants, and nuclear anomalies, arguing that our mathematical tools introduce errors that make these fluctuations imperceptible at macroscopic scales.

By integrating the insights from both prior works, we explore how these ideas may resolve inconsistencies in fusion physics, relativity, and quantum measurement theory. Furthermore, we investigate how AI-driven analysis and high-resolution experimental data may help uncover hidden physics beyond our current theoretical models.

1. The Illusion of Local Linearity and the Limits of Measurement

1.1 Differentiation as a False Approximation (From "The Limits of Calculus in a Curved Space")

• Classical calculus assumes that curves can be locally approximated as straight lines, leading to differentiation and the assumption of a locally flat tangent plane.

• However, in general relativity, space-time is curved at all scales, meaning no true straight segment exists unless its length is exactly zero.

• This is significant because it suggests that all measurements of change, motion, and forces in physics are built upon an inherent approximation that may introduce subtle errors at fine resolutions.

• Mathematically, this can be expressed as:

  lim (L → 0) (Δy / Δx) is undefined, unless L = 0

  where represents segment length. As long as , curvature persists, making true straightness impossible.

1.2 The Consequence for Physical Constants (Bridging to "More to C")

• Just as differentiation assumes local straightness where none exists, physics assumes constant values for fundamental constants where small-scale fluctuations may exist.

• If c fluctuates at fine resolutions but appears constant at our scale, we may be imposing a false constancy in the same way we impose false linearity in differentiation.

• This suggests a direct connection between the resolution limit of calculus and the resolution limit of fundamental constants in physics.

2. Connecting Non-Zero Straightness to the More to C Hypothesis

2.1 Resolution-Based Fluctuations of c (From "More to C")

• The More to C Hypothesis proposes that c is not truly constant but fluctuates at scales smaller than our current instruments can detect.

• If differentiation is flawed due to the false assumption of local straightness, then our measurements of c may be flawed for the same reason.

• This can be expressed as:

  lim (ΔR → 0) (Δc / ΔR) = 0

  implying that c appears constant only because our measurement resolution () is too large to detect fluctuations.

• If this hypothesis holds, it could explain several long-standing mysteries in physics, including:

  • Nuclear anomalies such as the unexpectedly high yields observed in the Castle Bravo test (1954), Tsar Bomba (1961), Ivy Mike (1952), Operation Redwing Test Cherokee (1956), and Soviet Test 219 (1962)—where fusion reactions produced greater energy output than predicted, suggesting possible fluctuations in fundamental constants at extreme energy densities.

  • Quantum uncertainty and potential fine-structure constant variations, implying that fundamental constants like c and α may not be strictly fixed but instead fluctuate at finer resolutions.

  • Unexplained astrophysical deviations in gravitational lensing, cosmic redshift measurements, and cosmic microwave background anisotropies, hinting that our understanding of space-time curvature and energy transfer may be resolution-dependent.

3: High-Energy Anomalies and Resolution-Based Physics

3.1 The Limits of Current Measurement Precision

Physicists assume that fundamental constants such as c, Planck’s constant (h), and the fine-structure constant (α) remain fixed across all conditions. However, modern high-energy experiments suggest that subtle variations in these constants may arise under extreme conditions.

One area where such variations could become evident is particle collisions at relativistic speeds. In high-energy collisions at the Large Hadron Collider (LHC), unexpected shifts in particle decay rates, cross-sections, and energy distribution have occasionally been observed. These discrepancies, though small, may be early evidence of resolution-dependent changes in fundamental physics.

Similarly, cosmological data reveals anomalies in background radiation and large-scale structure formation. The Cosmic Microwave Background (CMB) exhibits unexplained anisotropies, which some theories attribute to dark matter. However, if c was slightly different at high energies, this could provide an alternative explanation for these inconsistencies.

3.2 Resolution-Limited Curvature and Energy Dynamics

In curved space-time, a trajectory that appears straight at one resolution may reveal hidden curvature at finer scales. The same principle applies to fundamental constants:

• If c fluctuates at high energy levels but is averaged out at macroscopic scales, our models of energy transfer and high-energy interactions could be subtly incorrect.

• This means that current calculations of reaction rates, decay probabilities, and energy distributions may contain systematic errors that only become apparent at extreme conditions.

• Similarly, if the fine-structure constant (α) is resolution-dependent, then electromagnetic interactions—such as photon emission spectra in distant quasars—may need to be re-evaluated under a new framework.

These ideas suggest that the observed discrepancies in high-energy physics, cosmology, and quantum mechanics may share a common root: the limitation of current measurement tools in resolving subtle variations in fundamental constants.

4. The Future of Measurement: AI and High-Resolution Data Analysis

4.1 AI-Driven Reassessment of Constants

• Traditional physics assumes static values for c, h (Planck’s constant), and other fundamental parameters.

• Machine learning models trained on high-energy astrophysical and quantum datasets could be used to identify small-scale deviations that classical measurement techniques have overlooked.

• AI-assisted simulations can test alternative models of c, helping predict where deviations might be observed in experiments.

4.2 Precision Experiments to Test the Hypothesis

• Extreme Energy Fusion Tests: Controlled fusion reactions could be monitored for small deviations in nuclear reaction rates based on potential fluctuations in c.

• High-Resolution Gravitational Time Dilation Studies: Examining whether slight variations in c appear in extreme gravitational fields.

• Astrophysical Data Mining: Searching for unexplained anomalies in cosmic redshift, gravitational lensing, and cosmic microwave background fluctuations.

• Quantum Coherence and Fine-Structure Constant Studies: Investigating if fundamental quantum interactions behave differently under extreme energy conditions.

5. Conclusion: A Unified View of Curvature and Constants

• The assumption that differentiation reveals straightness is as flawed as the assumption that c is constant at all scales.

• If our mathematical and measurement tools introduce false linearity, then they may also introduce false constancy in fundamental physics.

• High-energy nuclear anomalies, quantum uncertainty, and astrophysical deviations may all stem from the same hidden structure of space-time.

• The future of physics lies in developing better measurement frameworks that acknowledge the resolution-dependent nature of physical laws.

• By leveraging AI, high-resolution data analysis, and experimental precision, we may uncover the missing physics hidden within the fine structure of the universe.

Acknowledgments

The author thanks the Syme research community for discussions on calculus limitations, quantum measurement theory, and nuclear physics anomalies. Special thanks to researchers investigating the intersection of AI, relativity, and fusion energy.

References

• Einstein, A. (1915). "The Field Equations of Gravitation."

• Hawking, S., & Ellis, G. F. R. (1973). The Large Scale Structure of Space-Time.

• Barrow, J. D. (1999). "Cosmologies with Varying Light Speed."

• Carroll, S. (2003). Spacetime and Geometry: An Introduction to General Relativity.

• National Ignition Facility. (2022). "Advances in Inertial Confinement Fusion and Plasma Physics."