Monday, October 21, 2024

Reconciling Planck's Constant with a Fundamental Geometric Relationship between Energy and Wavelength

Abstract:

This paper presents the results of a program that validates the key proposals put forth in the recent work "The True Nature of Planck's Constant: A Fundamental Discovery." The original paper suggested that Planck's constant (h) serves as a scaling factor to reconcile the speed of light (c) with a more fundamental constant of 2 × 10^-25 J·m.

The program implemented in this study demonstrates the mathematical feasibility of this hypothesis. By applying a small adjustment of 0.226% to the definition of the meter, the program was able to show that the product of Planck's constant and the speed of light (hc) becomes exactly equal to 2 × 10^-25 J·m. This allows the energy-wavelength relationship to be simplified to E = 2k × 10^-25 J·m / λ, where k is the scaling factor used to adjust the meter.

Furthermore, the program verified that this geometric formula produces the same energy values as the traditional E = hc/λ equation, using the adjusted values for Planck's constant and the speed of light. This confirms the mathematical consistency of the proposed relationship.

It is important to note that while the program validates the mathematical foundations of the idea presented in the original paper, it does not on its own prove that this new interpretation of Planck's constant and the energy-wavelength relationship is the true underlying fundamental relationship in nature. Further experimental and theoretical work would be required to fully establish the viability of this proposal.  


The results:

New meter length: 0.9932229286 old meters

scale factor: 0.9932229286

New speed of light: 301838035.93 old m/s

New Planck's constant: 6.62607015e-34 J⋅s

Old hc product: 1.98644586e-25 J⋅m

New hc product: 2.00000000e-25 J⋅m

Target value: 2.00000000e-25 J⋅m

Difference from target: 0.00000000%


Energy calculations for 5.00e-07 m wavelength:

Old method: 3.97289171e-19 J

New method: 3.97289171e-19 J

Geometric method: 3.97289171e-19 J


Ratio (old / Geometric): 1.0000000000


***  ***  ***  

 

 Wavelength and Frequency Conversions:


Old wavelength: 1.00e-09 m

New wavelength: 1.01e-09 new_m

Old frequency: 2.9979e+17 Hz

New frequency: 2.9979e+17 Hz

Old energy: 1.9864e-16 J

New energy: 1.9864e-16 J

Energy ratio (new/old): 1.0000000000

Old E = hf check: 1.0000000000

New E = hf check: 1.0000000000

Old E = hc/λ check: 1.0000000000

New E = hc/λ check: 1.0000000000


Old wavelength: 5.00e-07 m

New wavelength: 5.03e-07 new_m

Old frequency: 5.9958e+14 Hz

New frequency: 5.9958e+14 Hz

Old energy: 3.9729e-19 J

New energy: 3.9729e-19 J

Energy ratio (new/old): 1.0000000000

Old E = hf check: 1.0000000000

New E = hf check: 1.0000000000

Old E = hc/λ check: 1.0000000000

New E = hc/λ check: 1.0000000000


Old wavelength: 1.00e-06 m

New wavelength: 1.01e-06 new_m

Old frequency: 2.9979e+14 Hz

New frequency: 2.9979e+14 Hz

Old energy: 1.9864e-19 J

New energy: 1.9864e-19 J

Energy ratio (new/old): 1.0000000000

Old E = hf check: 1.0000000000

New E = hf check: 1.0000000000

Old E = hc/λ check: 1.0000000000

New E = hc/λ check: 1.0000000000

The program: 

import math


# Original constants

old_meter = 1

old_c = 299792458  # speed of light in m/s

old_h = 6.62607015e-34  # Planck's constant in J⋅s


# Step 1: Adjust the meter

#scale_factor = .99322284

scale_factor = 0.99322292857404059774

new_meter = old_meter * scale_factor


print(f"New meter length: {new_meter:.10f} old meters")

print(f"scale factor: {scale_factor:.10f}")


# Step 2: Calculate new speed of light in new meters

# new_c * new_meter = old_c * old_meter

new_c = old_c * old_meter / new_meter


print(f"New speed of light: {new_c:.2f} old m/s")


# Step 3: Calculate new Planck's constant

new_h = 2e-25/new_c


print(f"New Planck's constant: {new_h:.8e} J⋅s")


# Check the hc product

old_hc = old_h * old_c

new_hc = new_h * new_c


print(f"Old hc product: {old_hc:.8e} J⋅m")

print(f"New hc product: {new_hc:.8e} J⋅m")


# Compare with 2e-25 J⋅m

target = 2e-25

print(f"Target value: {target:.8e} J⋅m")

print(f"Difference from target: {(new_hc - target) / target:.8%}")


# Calculate energy for a sample wavelength

wavelength = 500e-9  # 500 nm

new_wl = wavelength / new_meter


old_energy = old_h * old_c / wavelength

new_energy = new_h * new_c / new_wl 

geometric_energy = 2e-25 / new_wl 


print(f"\nEnergy calculations for {wavelength:.2e} m wavelength:")

print(f"Old method: {old_energy:.8e} J")

print(f"New method: {new_energy:.8e} J")

print(f"Geometric method: {geometric_energy:.8e} J")


print(f"\nRatio (old / Geometric): {old_energy / geometric_energy:.10f}")


# New section: Wavelength and frequency conversions

print("\n***  ***  ***  \n \n Wavelength and Frequency Conversions:")


# Test wavelengths

test_wavelengths = [1e-9, 500e-9, 1e-6]  # 1 nm, 500 nm, 1 μm


for old_wavelength in test_wavelengths:

    # Old calculations

    old_frequency = old_c / old_wavelength

    old_energy = old_h * old_frequency


    # New calculations

    new_wavelength = old_wavelength / new_meter

    new_frequency = new_c / new_wavelength

    new_energy = new_h * new_frequency


    print(f"\nOld wavelength: {old_wavelength:.2e} m")

    print(f"New wavelength: {new_wavelength:.2e} new_m")

    print(f"Old frequency: {old_frequency:.4e} Hz")

    print(f"New frequency: {new_frequency:.4e} Hz")

    print(f"Old energy: {old_energy:.4e} J")

    print(f"New energy: {new_energy:.4e} J")

    print(f"Energy ratio (new/old): {new_energy/old_energy:.10f}")


    # Verify E = hf relationship

    print(f"Old E = hf check: {old_energy / (old_h * old_frequency):.10f}")

    print(f"New E = hf check: {new_energy / (new_h * new_frequency):.10f}")


    # Verify E = hc/λ relationship

    print(f"Old E = hc/λ check: {old_energy / (old_h * old_c / old_wavelength):.10f}")

    print(f"New E = hc/λ check: {new_energy / (new_h * new_c / new_wavelength):.10f}")

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