Discrete Photon Levels and Atomic Spectra: A Worldline Perspective on Quantum Transitions and Entanglement

 J. Rogers, SE Ohio, 26 Feb 2025, 1353 

Abstract:

This paper proposes a novel perspective on atomic spectra and quantum entanglement based on the concept of electron worldlines within spacetime. We posit that discrete electron energy levels in atoms correspond to distinct, allowed worldline configurations within the atom's spacetime environment. Quantum jumps between these energy levels are interpreted as transitions between these allowed worldlines. We argue that the emitted photon during such a transition embodies the spacetime "difference" between the initial and final electron worldlines, with its own worldline reflecting this difference. Furthermore, we suggest that entanglement can be understood as a consequence of photon-mediated "worldline sharing" between particles, providing a geometric interpretation for this enigmatic quantum phenomenon. This framework offers a potentially unifying perspective on quantum mechanics and spacetime, grounded in the fundamental equivalence of energy, mass, and frequency.

1. Introduction: The Puzzle of Discrete Spectra and Entanglement

Atomic spectra, characterized by discrete emission and absorption lines, are a cornerstone of quantum mechanics. The Bohr model and subsequent quantum theories successfully explained these discrete energy levels by postulating quantized electron orbits and energy transitions. However, the underlying nature of these quantized levels and the mechanism of photon emission remain somewhat abstract, often described in terms of energy levels and probabilities. Simultaneously, quantum entanglement, with its non-local correlations and "spooky action at a distance," continues to challenge our classical intuitions about space, time, and locality.

This paper seeks to offer a fresh perspective by re-examining atomic spectra and entanglement through the lens of electron worldlines within spacetime. Building upon the fundamental equivalence of energy, mass, and frequency [1], we propose that discrete energy levels are manifestations of allowed, quantized electron worldlines in the spacetime environment of an atom. We explore how photon emission can be understood as a consequence of transitions between these worldlines, and how this worldline perspective might illuminate the nature of quantum entanglement.

2. Foundation: Mass-Frequency-Spacetime Equivalence and Planck's Constant

Our framework rests on the premise that energy (E), mass (m), and frequency (f) are fundamentally equivalent and represent different facets of the same underlying reality, intrinsically linked to spacetime. We adopt the perspective that Planck's constant (h), traditionally seen as a fundamental constant of nature, can be understood as a unit conversion factor arising from our chosen systems of measurement [1]. Specifically, we posit:

• Q_m = h/c²: Defining Q_m as the mass equivalent of a 1Hz photon, where 'c' is the speed of light. Thus, h = Q_m * c².

• E = hf = (Q_m * c²) * f: Re-expressing the Planck-Einstein relation, highlighting that photon energy is fundamentally proportional to frequency and scaled by Q_m and c².

• m = Q_m * f: Extending the equivalence to mass and frequency, suggesting that mass itself is fundamentally linked to frequency, with Q_m as the conversion factor.

Within this framework, we interpret the seemingly disparate equations E=mc² and E=hf as different expressions of the same underlying equivalence, emphasizing that mass, frequency, and energy are ultimately interchangeable.  This means that it is the worldline of a photon that scales it own intrinsic values in lock step with each other. 

3. Discrete Electron Worldlines and Atomic Energy Levels

Instead of visualizing electrons in discrete "orbits" in space alone, we propose considering their "worldlines" – their trajectories through spacetime. We hypothesize that within the spacetime environment of an atom (influenced by the nucleus and other electrons), electrons are constrained to exist in specific, allowed worldline configurations.

• Allowed Worldlines: Analogous to standing waves or resonant modes, we suggest that only certain "stable" or "resonant" worldline patterns are permitted for electrons within the atom. These allowed worldlines are characterized by specific spacetime curvatures, oscillations, or geometric configurations.

• Discrete Energy Levels as Worldline States: Each allowed electron worldline configuration corresponds to a discrete energy level. Higher energy levels are associated with more "energetic" worldlines – perhaps characterized by greater spacetime curvature, higher frequency oscillations along the worldline, or more complex geometric patterns. These discrete energy levels are not arbitrary but are determined by the allowed, quantized spacetime configurations for electron worldlines within the atomic environment.

4. Photon Emission as Worldline Transition and Difference

Quantum jumps between electron energy levels, leading to photon emission, are reinterpreted as transitions between these allowed electron worldlines.

• Worldline Transition: When an electron transitions from a higher energy level (and its associated "energetic" worldline) to a lower energy level (and its "less energetic" worldline), it undergoes a shift in its spacetime trajectory.

• Photon as Worldline "Difference": We propose that the emitted photon embodies the spacetime "difference" between the initial (higher energy) and final (lower energy) electron worldlines. The photon's own worldline is not arbitrarily determined but is a manifestation of this spacetime transition. Its properties – energy, momentum, and frequency – are directly related to the magnitude and characteristics of this worldline difference.

• Photon Worldline Reflects Energy Difference: The energy of the emitted photon (E=hf) is thus directly linked to the "magnitude" of the change in the electron's worldline. A larger energy difference between electron levels corresponds to a more significant shift in worldlines and a higher frequency photon.

• Discrete Photon Spectra: The discrete nature of electron energy levels naturally leads to discrete differences in allowed worldlines, resulting in the emission of photons with discrete energies and frequencies, thus explaining the observed atomic spectra.

5. Entanglement as Shared Worldlines Mediated by Photons

Extending this worldline perspective, we propose a novel interpretation of quantum entanglement.

• Photons as Worldline Mediators: We suggest that photons, beyond being energy carriers, can act as mediators that establish "worldline sharing" between particles. When particles interact and exchange photons, they are, in effect, intertwining aspects of their spacetime trajectories.

• Entangled State = Shared Worldlines: Quantum entanglement arises when two or more particles are in a state of "shared worldlines," facilitated by photon interaction. In an entangled state, the particles are not merely correlated in their properties; they are fundamentally linked at the level of their spacetime existence. Their worldlines are intertwined, creating a non-separable spacetime configuration.

• Non-Local Correlations from Shared Trajectories: The seemingly non-local correlations observed in entangled particles become less paradoxical when viewed through this lens. If entangled particles are sharing worldlines, changes affecting one particle's "worldline aspect" would instantaneously influence the entire shared worldline configuration, affecting the other particle regardless of spatial separation. The correlation is not "spooky action at a distance," but rather a consequence of their fundamental spacetime linkage.

• Photon Exchange as Entanglement Mechanism: Photon exchange, in this framework, is the fundamental process that generates entanglement by establishing these shared worldlines. The properties of the exchanged photon, including its worldline implications, are crucial for understanding the nature and strength of the entanglement.

6. Discussion and Implications

This worldline perspective on atomic spectra and entanglement carries significant implications:

• Geometric Quantum Mechanics: It strongly suggests a geometric interpretation of quantum mechanics, where quantum phenomena are fundamentally rooted in the geometry of spacetime and particle worldlines. Quantum states are not just abstract mathematical entities, but represent distinct spacetime configurations.

• Unification of Quantum Mechanics and Relativity: By grounding quantum phenomena in spacetime geometry and emphasizing the equivalence of energy, mass, and frequency, this framework moves towards a potential unification of quantum mechanics and general relativity.

• New Understanding of Quantum Gravity: If quantum phenomena are inherently linked to spacetime geometry and worldlines, it might offer new insights into the nature of quantum gravity, suggesting that gravity is not a separate force to be quantized, but rather emerges from the quantized spacetime itself.

• Further Research Directions: This framework necessitates developing a rigorous mathematical formalism to describe allowed electron worldlines, photon worldline differences, and the mechanics of worldline sharing in entanglement. Experimental investigations aimed at probing the spacetime aspects of quantum transitions and entanglement could provide further validation or refinement of this perspective.

7. Conclusion

This paper proposes a novel worldline framework for understanding discrete photon levels in atoms and quantum entanglement. By interpreting electron energy levels as manifestations of allowed electron worldlines in spacetime, and photon emission as a consequence of transitions between these worldlines, we offer a geometric and potentially more intuitive understanding of atomic spectra. Furthermore, the concept of photon-mediated "worldline sharing" provides a fresh perspective on entanglement, suggesting that entangled particles are fundamentally linked through their spacetime trajectories. While requiring further development and rigorous mathematical formulation, this framework offers a promising avenue for exploring the deep connections between quantum mechanics, spacetime, and the fundamental nature of reality.