On the Fundamental Nature of 2 × 10^-25 J⋅m, Planck's constant as a scaling factor for this ratio, and the Definition of the Meter

Author: James M. Rogers
Location: SE Ohio
Date: 11 Oct 2024 Time: 1230 

Abstract This paper proposes that the product of Planck's constant and the speed of light (hc) should exactly equal 2 × 10^-25 J⋅m, and that our current deviation from this value may be due to a historical artifact in the definition of the meter in 1983 to al. We demonstrate that a 0.226% adjustment to the meter would align this fundamental constant with what appears to be its natural value, potentially revealing deeper geometric relationships in physics.

It is important to note that we are not actually proposing this change in reality.  Right know we propose a small k value to just offset the top and bottom of the formula to the new measurement.  

So E =  2 × 10^-25 J⋅m*k / λ where k is the scaling factor to bring us in line with the current definition of the meter.  But with the recognition that this simple geometric relationship is the actual relationship between energy and wavelength.

1. Introduction

The product hc currently equals approximately 1.98644568 × 10^-25 J⋅m. The proximity of this value to exactly 2 × 10^-25 J⋅m (within 0.68%) suggests a possible fundamental relationship that has been obscured by our choice of units. This paper proposes that this relationship is not coincidental but rather indicates a more natural unit of length.

2. Current Values and Proposed Adjustment

Current values:

• h ≈ 6.62607015 × 10^-34 J⋅s (exact by definition)
• c ≈ 2.99792458 × 10^8 m/s (exact by definition)
• hc ≈ 1.98644568 × 10^-25 J⋅m

Proposed adjustment:

• Meter length increase: 0.226%
• New meter = 1.00226 × current meter
• Result: hc = 2 × 10^-25 J⋅m exactly

3. Mathematical Analysis

The energy-wavelength relationship would simplify to:

E = hc/λ = 2 × 10^-25/λ

This gives us:

λ = 2 × 10^-25/E

The elegance of this relationship suggests it might be more fundamental than our current formulation.

4. Implications

4.1 Quantum Mechanical Relationships

The simplified relationship E = 2 × 10^-25/λ provides a direct geometric connection between energy and wavelength. This suggests that energy might be fundamentally geometric in nature, manifesting as a relationship between space and time rather than as a separate physical quantity.

4.2 Wave-Particle Duality

The factor of 2 could represent a fundamental aspect of wave-particle duality, possibly related to the bidirectional nature of wave propagation or the symmetric nature of quantum states.

4.3 Natural Units

This adjustment suggests a more natural system of units where:

1. Energy-wavelength relationships are exact
2. Quantum mechanical equations simplify
3. Geometric relationships in physics become more apparent

5. Historical Context

The meter has undergone several redefinitions:

1. 1793: Earth meridian-based definition
2. 1889: International prototype meter bar
3. 1960: Krypton-86 wavelength definition
4. 1983: Speed of light definition

Each redefinition improved alignment with fundamental physical constants. The proposed adjustment continues this historical progression toward more natural units.

6. Practical Implementation

The proposed adjustment would require:

1. Redefining the meter as 1.00226 times its current length
2. Adjusting the speed of light definition accordingly
3. Maintaining the current definitions of second and kilogram

Impact:

• Minimal disruption to everyday measurements
• Simplified quantum mechanical calculations
• More elegant theoretical relationships

7. Theoretical Implications

7.1 Geometric Nature of Energy

This relationship suggests energy might be fundamentally geometric, manifesting as a relationship between wavelength and a universal constant (2 × 10^-25 J⋅m).

7.2 Quantum-Classical Transition

The simplified relationships might provide new insights into the quantum-classical boundary and measurement theory.

7.3 Unification Prospects

The geometric nature of this relationship could provide new approaches to quantum gravity and the unification of fundamental forces.

8. Experimental Verification

Proposed tests:

1. Examine historical experimental discrepancies using adjusted units
2. Look for simplified patterns in high-energy physics data
3. Analyze quantum interference experiments with the new geometric interpretation

9. Conclusion

The proposed 0.226% adjustment to the meter length would align hc with exactly 2 × 10^-25 J⋅m, potentially revealing fundamental geometric relationships in physics. This alignment suggests our current unit system might be slightly misaligned with nature's fundamental geometry.

References

1. Einstein, A. (1905). "Zur Elektrodynamik bewegter Körper"
2. de Broglie, L. (1924). "Recherches sur la théorie des quanta"
3. Bureau International des Poids et Mesures (2019). "SI Brochure"

Technical Notes

The remarkable proximity of hc to 2 × 10^-25 J⋅m in our current system, and the small adjustment needed to make it exact, strongly suggests this relationship reflects a fundamental aspect of nature rather than a coincidence.