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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