In physics, we often treat Planck's constant (h) as a mysterious fundamental constant of quantum mechanics, while treating the speed of light (c) as the fundamental constant of special relativity. But what if they're actually the same thing, just viewed from different angles? Through a simple thought experiment involving unit adjustments, we can reveal a profound truth: Planck's constant might not be a new fundamental constant at all, but simply the inverse of the speed of light, disguised by our human choice of units.
I am having to modify this paper, because I didn't understand that if the meter is redefined that would change things with J as well. and change them as m^2 while speed of light is moving at just the change for m. I had to write a program to perform a search for the correct values. The program may need more refinement, but the fact that the two units move at different speeds means you can match them up to make K = 1 J m. The new values for h and 1/c are as follows.
New meter length: 1.713856368228e+08 old meters
Final h: 1.946278004282e-17 J·s
Final c: 51380121329003624.000000000000 m/s
1/c: 1.946278004282e-17
Relative difference between h and 1/c: 2.404990513452e-13
The Thought Experiment
Let's start by defining a constant K as the product of h and c:
K = hc
In conventional units, this gives us a value in Joule-meters (J⋅m). Now, here's where things get interesting. What if we adjust our units for meter slightly to make K exactly equal to 10^-25 J⋅m? This seemingly arbitrary choice leads to something remarkable.
When we do this and calculate the new speed of light (c = 10^-25 J⋅m / h), something fascinating emerges: the inverse of this new speed of light (1/c) has exactly the same digits as Planck's constant, just scaled differently by K. The new value for c is 1.5091901796×10^8.
The Natural Units Revelation
But we can go further. What if we set K = 1 J⋅m? This choice of "natural units" reveals something profound:
- The speed of light becomes c ≈ 1.50919 × 10^34 m/s
- Planck's constant becomes exactly 1/c
- Energy and wavelength become directly related: E = 1 J m λ
In this system, h isn't some mysterious quantum constant - it's literally just 1 J⋅m divided by c. The famous value of h (6.626 × 10^-34 J⋅s) is simply what you get when you express this relationship in our conventional units.
Why This Matters
This revelation suggests several profound insights:
- Unit Artifacts: The "mysterious" value of Planck's constant is just an artifact of how we chose to define joules, seconds, and meters.
- Unified Physics: Quantum mechanics and special relativity might be more deeply unified than we thought - they're just different perspectives on the same fundamental relationship between energy-distance and velocity.
- Natural Relationships: When we strip away our arbitrary unit choices, we see that energy and wavelength have a direct inverse relationship (E = 1/λ in natural units).
- Simplified Understanding: Many quantum mechanical relationships might be simpler than they appear - they've just been obscured by our choice of units.
The Mathematics Made Clear
Let's break down what we discovered:
- h is scaled by joule-seconds (J⋅s)
- c is scaled by meters/second (m/s)
- K is scaled by joule-meters (J⋅m)
When we set K = 1 J⋅m, we remove this artificial scaling and see the true relationships:
- h becomes simply 1/c
- Quantum wavelength-energy relationships become direct inverse relationships
- The "quantum" nature of reality might simply be another manifestation of having a universal speed limit
Why Wasn't This Seen Before?
This insight remained hidden because no one thought to:
- Treat K = hc as meaningful in itself
- Adjust units to make K a round number
- Notice that doing so would make 1/c match h's digits
- Consider what would happen if we set K = 1 J⋅m
Implications
This perspective suggests that quantum mechanics might not be as mysterious as we thought. Many of its seemingly bizarre features might simply be consequences of having a universal speed limit, viewed through the lens of our arbitrary unit choices.
The wave-particle duality, the uncertainty principle, and other quantum phenomena might be better understood when viewed through this lens of natural units where h is simply 1/c.
Conclusion
Sometimes the deepest insights come not from complex mathematics or elaborate experiments, but from simply looking at familiar things in a new way. By questioning our unit choices and following the implications of setting K = 1 J⋅m, we've uncovered a simpler way to understand some of the most fundamental relationships in physics.
This doesn't make quantum mechanics any less remarkable - if anything, it makes it more profound by showing how deeply it's connected to the basic structure of spacetime through the speed of light. It just shows that some of what we thought was mysterious might have been obscured by our human choices of measurement units.
The universe, it seems, might be simpler than we imagined. We just needed to look at it through the right lens.
Appendex 1/c=h search program.
import numpy as np
initial_h = 6.62607015e-34 # Planck's constant in J·s
initial_c = 299792458 # Speed of light in m/s
def adjust_values(initial_h, initial_c, meter_factor):
new_c = initial_c / meter_factor
new_h = initial_h / (meter_factor**2)
return new_h, new_c
def find_matching_values(initial_h, initial_c, tolerance=1e-12, max_iterations=1000000):
meter_factor = 1.0
step_size = 0.5
direction = 1
prev_difference = float('inf')
for iteration in range(max_iterations):
h, c = adjust_values(initial_h, initial_c, meter_factor)
difference = h - 1/c
if np.isclose(h, 1/c, rtol=tolerance, atol=0):
return meter_factor, h, c
if np.sign(difference) != np.sign(prev_difference):
direction *= -1
step_size /= 2
meter_factor *= (1 + direction * step_size)
prev_difference = difference
if iteration % 1000 == 0:
print(f"Iteration {iteration}: difference = {difference:.6e}, step_size = {step_size:.6e}, meter_factor = {meter_factor:.6e}")
raise ValueError("Convergence not achieved within maximum iterations")
try:
meter_factor, final_h, final_c = find_matching_values(initial_h, initial_c)
print(f"Meter factor: {meter_factor:.12e}")
print(f"New meter length: {1/meter_factor:.12e} old meters")
print(f"Final h: {final_h:.12e} J·s")
print(f"Final c: {final_c:.12f} m/s")
print(f"1/c: {1/final_c:.12e}")
print(f"Relative difference between h and 1/c: {abs(final_h - 1/final_c)/final_h:.12e}")
except ValueError as e:
print(f"Error: {e}")
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