DOI: 10.5281/zenodo.16934558
title: Atharv's Angle

description:  

Atharv’s Angle: A Proposed Fundamental Limit to Angular Resolution

 

 

Author: Atharv Tiwari

 

 

 

 

Abstract

 

 

In current physics, the angle is treated as a continuous, dimensionless quantity that can be divided indefinitely. However, if space itself is quantized at the Planck scale, then angular measurement should also be fundamentally limited. I propose the existence of a minimum resolvable angle, defined by the ratio of the Planck length to the distance of observation. This lower bound, hereafter referred to as Atharv’s Angle, introduces a natural cutoff to angular divisibility in nature.

 

 

 

 

1. Introduction

 

 

Physics has repeatedly shown that quantities once assumed to be continuous are in fact discrete. Matter was once thought infinitely divisible until the discovery of atoms; later, subatomic particles were revealed to be composed of quarks. Similarly, distance was believed continuous until quantum gravity introduced the concept of the Planck length (approximately 1.616 × 10⁻³⁵ m) as the smallest meaningful unit of length.

 

By analogy, angle is traditionally considered infinitely divisible. Yet if space itself has a discrete structure at the Planck scale, then angular resolution too must have a limit. This work proposes such a limit, termed Atharv’s Angle.

 

 

 

 

2. Theoretical Formulation

 

 

Angle is defined as the ratio of arc length to radius:

 

θ = s / R

 

If the smallest measurable arc length is the Planck length (lₚ), then the minimum resolvable angle at a distance R is:

 

θₘᵢₙ(R) = lₚ / R

 

This means angular resolution is scale-dependent, but never infinite. No matter how far two directions extend, their separation can never be smaller than θₘᵢₙ.

 

 

 

 

3. Implications and Discussion

 

 

(a) Quantum Gravity Connection

Loop Quantum Gravity and related approaches already suggest that area and volume are quantized. Atharv’s Angle naturally extends this principle to directional resolution.

 

(b) Cosmological Implications

For an observer looking across the observable universe (R ≈ 10²⁶ m), the minimum angle is:

 

θₘᵢₙ ≈ (10⁻³⁵) / (10²⁶) ≈ 10⁻⁶¹ radians

 

This provides a finite lower bound to cosmic angular resolution.

 

(c) Information Limits

The Holographic Principle suggests that information content is bounded by surface area in Planck units. Atharv’s Angle could represent an equivalent bound on directional information.

 

 

 

 

4. Proposed Principle

 

 

Atharv’s Minimum Angle Principle:

In any physical observation at distance R, the smallest resolvable angle is given by:

 

θₘᵢₙ = lₚ / R

 

This principle implies that angles are not infinitely divisible, but constrained by the quantization of space at the Planck scale.

 

 

 

 

5. Conclusion

 

 

If distance is limited by the Planck length, then angular resolution must also be limited. Atharv’s Angle introduces this limit formally as θₘᵢₙ = lₚ / R. This proposal provides a new perspective on the quantization of geometry and could inspire future work in quantum gravity, cosmology, and fundamental physics.

 

 

 

 

Acknowledgment

 

 

This work was independently conceived and written by Atharv Tiwari, with the intention of contributing to the exploration of fundamental limits in physics.