[Paper Review] Reciprocal Symmetry and Equivalence between Relativistic and Quantum Mechanical Concepts

Mushfiq Ahmad|ArXiv.org|Nov 11, 2006

Relativity and Gravitational Theory1 references3 citations

TL;DR

This paper introduces a reciprocal symmetry framework where velocity and slowness (c²/v) are dual concepts, enabling derivation of relativistic and quantum mechanical laws from symmetric postulates. It derives the relativistic velocity addition law from a postulate on minimum slowness of light and Planck's blackbody radiation law from a maximum energy postulate, establishing equivalence between relativistic and quantum concepts through duality.

ABSTRACT

We have defined slowness (or reciprocal velocity) corresponding to v as cc/v, where c is the speed of light and v is the corresponding velocity. Velocity and slowness are images of each other. Reciprocal symmetric law of addition of velocities fulfils the requirement that the sum (or the difference) of velocities remains unchanged if velocities are replaced by the corresponding slownesses. We have postulated reciprocal symmetry, which states that every valid statement has an equally valid (reciprocal) image statement. The postulate has allowed us to derive: (1). Relativistic law of addition of velocities from Einstein's image postulate that no physical body can travel with a slowness less than the slowness of light. (2). Black body radiation formula from Planck's image postulate that no body can attain a level of energy higher than an upper limit value 2W.

Motivation & Objective

• To establish a reciprocal symmetry principle where every physical statement has a dual image statement.
• To derive the relativistic law of velocity addition using a postulate that no physical body can travel with slowness less than that of light.
• To derive Planck's blackbody radiation formula using an image postulate that no body can exceed an upper energy limit of 2W.
• To demonstrate equivalence between relativistic and quantum mechanical concepts through reciprocal duality.
• To unify foundational principles of relativity and quantum mechanics via a symmetric mathematical framework.

Proposed method

• Define slowness as c²/v, establishing a reciprocal relationship between velocity and slowness.
• Postulate reciprocal symmetry: every valid physical statement has an equally valid dual statement in the reciprocal domain.
• Derive the relativistic velocity addition law from the postulate that no body can have a slowness less than c²/c = c.
• Derive Planck's radiation formula from the postulate that no body can attain energy higher than 2W, the upper energy limit.
• Use the duality between velocity and slowness to map relativistic concepts into quantum-like frameworks and vice versa.
• Apply the reciprocal symmetry principle to transform postulates and derive laws in both domains consistently.

Experimental results

Research questions

• RQ1 Can the relativistic law of velocity addition be derived from a postulate involving the minimum slowness of light?
• RQ2 Can Planck's blackbody radiation formula be derived from a postulate imposing an upper bound on energy, specifically 2W?
• RQ3 Is there a symmetric duality between relativistic and quantum mechanical concepts through the reciprocal transformation of velocity into slowness?
• RQ4 Does the reciprocal symmetry postulate lead to equivalent formulations of fundamental physical laws in both domains?
• RQ5 Can the unification of relativity and quantum mechanics be achieved through a reciprocal transformation of physical quantities like velocity and energy?

Key findings

• The relativistic law of velocity addition is successfully derived from the postulate that no physical body can travel with a slowness less than that of light, i.e., c²/c = c.
• Planck's blackbody radiation formula is derived from the postulate that no body can attain an energy level higher than 2W, the upper energy limit.
• The reciprocal symmetry principle ensures that the laws of physics remain invariant under the transformation of velocity to slowness (c²/v).
• The duality between velocity and slowness enables a symmetric formulation of both relativistic and quantum mechanical laws.
• The framework establishes an equivalence between relativistic and quantum mechanical concepts through the use of reciprocal postulates and transformations.
• The paper demonstrates that fundamental physical laws can be derived from symmetric, dual postulates in velocity and slowness spaces.