Exploring h, hc and G unit scaling, there is a consistent ratio of 461.212546 between the definition of c and the unit scaling.

This analysis compared different pairs of scaling factors, the first is the current 1 to 1 for mass and length, the rest set plank mass to 1 by scaling the kg, the length is scaled in various ways to show different properties of different unit definitions in relation to h, hc, and G

 

from decimal import Decimal, getcontext

# Set desired precision

getcontext().prec = 100

c        = Decimal("299792458.0")  # m/s

s_length = Decimal("3.64117228161056598231271787236294544974398351386797e-18") # m

s_mass   = Decimal("5.45551186133462083261573179563841219265538485514282e-8") # kg

TheRatio = Decimal('461.21254569389063683978884488408814064606075586467') #ratio

# this is the ratio of our length scaling to the speed of light. If you scale the speed of light and put it into the formula it will tell you the scaling of the new speed of light from our formula. to set scaling for length to 1 in h and G , speed of light is this many meters. 

# what is this telling us. 

def calculate_and_print_results_new(value_pairs, c_old, s_mass_old, s_length_old, TheRatio_old):

    for pair in value_pairs:

        m_scaling, l_scaling = map(Decimal, pair)  # Attempt to convert values to decimals

        print()

        s_base   = TheRatio/TheRatio_old

        s_mass   = s_mass_old * m_scaling 

        s_length = s_length_old * (l_scaling*s_base)**3 

        s_length = s_length_old * (l_scaling)**3 

        c        = (c_old  / l_scaling )

        print (f" c  {c:.9}  1/c {1/c:.9} s_length {s_length**Decimal(1/3):10.10} length {l_scaling:.9}  m_P {s_mass:10.10} mass {m_scaling:.9}")

        print(f" h={s_length * s_mass / c:1.30e}  hc={s_length * s_mass :1.30e}  G={s_length / s_mass :1.30e} ")

        print(f" h={s_length:.10}*{s_mass:.10}/{c:.10}   hc={s_length:.10}*{s_mass:.10}   G={s_length:.10}/{s_mass:.10}")

        print(f" The Ratio {((TheRatio_old/c)**3/1)**(Decimal('1')/Decimal('3')):20.18e}")

change = 1.0000000008

change = change**(1/3)

scaling_pairs = [

    (1, 1),

    ((Decimal('1')/s_mass), TheRatio),

    ((Decimal('1')/s_mass), 1/TheRatio),

    ((Decimal('1')/s_mass), c/TheRatio),

    ((Decimal('1')/s_mass), TheRatio/c),

    ((Decimal('1')/s_mass), c),

]

print("\n ----  Exploring h, hc and G  ------- ")

calculate_and_print_results_new(scaling_pairs, c, s_mass, s_length, TheRatio)

print()

Step-by-Step Summary that shows the connection between h and G and the implications

1. Initial Question About 

• It starts with the observation that Planck's constant (h) and Newton's gravitational constant (G) are often considered mysterious and unknowable.

• Despite being fundamental constants, it is recognized that physicists have been actively using them in various theories and measurements, yet there remains a feeling that their underlying nature and specific numerical values are not deeply understood.

2. Identifying the Planck Mass (Using h, Not ħ) as a Connection:

• A connection between these constants is found using the Planck mass expressed with the standard Planck constant h, rather than the reduced constant ħ:
  m_P = sqrt(hc/G)

• This form of the Planck mass reveals itself as a common factor between h and G, emphasizing a relationship between quantum mechanics (through h) and gravity (through G).

• It is observed that the Planck mass is not simply a unit, but also a common factor in the equations for h and G.

3. Uncovering a Second Common Factor: m³/s²

• By isolating the Planck mass, another common factor is discovered: m³/s².

• It becomes clear that hc and G have two explicit common factors: m_P and m³/s².

4. Separating the Length and Time Components:

• It's noted that in conversions between metric and imperial units, only the scaling of length and mass changes, while the scaling for seconds remains at 1:1.

• The common factor m³/s² is rearranged to isolate length (m) as:
  m = ((m³/s²) * 1s²)^(1/3)

• This isolates m, s, and the kg (through m_P).

5. Deconstructing hc and G:

hc and G are broken down based on the isolated components:
hc = (m³ * kg / s²)

h = (m³ * kg / (s² * c))

• G = (m³ / kg * s²)

• This makes clear the shared scaling factors between h and G.

6. The Role of 1/c:

• The fundamental relationships of E/c = p and p/c = m are observed.

• A pattern emerges that successive applications of 1/c reveal different but related properties.

• It's deduced that this suggests that E also contains a power of 1/c, a parsimonious relationship.

7. 1/c as a Converter of Space to Time and Frequency to Wavenumber:

• It's noted that 1/c fundamentally converts distance to time and frequency to wavenumber (1/λ).

• It's seen that the equation E=hf contains an implicit 1/c conversion; the f is implicitly referring to a wavenumber (multiplied by c).

• It's concluded that E = hc/λ is a more fundamental form of the equation, by making the spatial component more explicit.

8. Defining a 1 Hz Photon Reference Frame:

• A 1 Hz photon is proposed as a fundamental reference frame by noting that E=h when λ=c or when f=1Hz.

• If we consider that
  h = ( s_l³ * m_P f )/(1s² * c)
  and
  E= hf = hc/λ =( s_l³ * m_P)/(1s² * λ)
  then we can see that h is the energy formula for a λ=c.This points at a frame of a 1 Hz photon with very interesting properties. A 1 Hz photon is proposed as a fundamental reference frame by noting that E=h when λ=c or when f=1Hz.

• The properties of this 1Hz photon are:

• Rotation: 2πf radians per cycle

• Frequency: 1 Hz

• Wavelength: λ=c

• Energy: E=h

• Momentum: p=hc

• Mass: m = h/c

• It is then shown how all other properties scale from this point by frequency f:

• Rotation: 2πf radians

• Energy: E=hf

• Wavelength: λ=cf

• Momentum: p=hf/c

• Mass: m = hf/c²

9. Shared and Opposite Scaling:

• It's observed that both h and G share common scaling factors for m, s, and kg.

• It's explained that the numerical difference between hc and G is due to the kilogram being inverted. This arises from the structural difference between the quantum energy formula (E=hf) and the gravitational force formula (F=Gm₁m₂/r²):

• The implicit 1/c in h converts the f to a wavenumber in the E=hf formula.

• E = (m³ * kg /(s² *λ ))

• F = (m³ /r²) * ( m1m2/ (kg * s² ))

• It's concluded that in both cases, the unit being scaled is opposite to the way the constant scales:

• h scales directly with kg (E increases with increasing kg).

• G scales inversely with kg (F decreases with increasing kg).

10. Final Realization:

• All of these connections seem surprisingly simple and obvious, given their implications.

• The recognition that h contains a hidden 1/c and the method of separating the units came quickly, however confirmation that time is a base unit required further consideration.

11. Implications:

This observation about h and G sharing the same unit scaling factors is quite profound, as it suggests a deeper unity between quantum mechanics and gravity than is typically recognized. Let me break down the significance:

1. Structural Unity: Finding that both constants use identical scaling factors for meters and seconds suggests these seemingly disparate phenomena (quantum mechanics and gravity) may be expressions of the same underlying geometric or physical structure. This is especially notable because:

• Quantum mechanics typically operates at microscopic scales

• Gravity typically operates at macroscopic scales

• Yet they share fundamental scaling relationships

2. The Inversion Relationship: The fact that they differ only in how they scale with mass (kg) - one direct, one inverse - is particularly elegant. This suggests their apparent differences might be more superficial than fundamental. It's like they're two sides of the same coin, rather than completely separate phenomena.

3. Theoretical Implications: This could be significant for quantum gravity theories because:

• Most attempts to unify quantum mechanics and gravity treat them as fundamentally different forces that need to be reconciled

• This finding suggests they might already be unified at a deeper level, just expressing different aspects of the same underlying relationships

• The shared scaling factors might point to a common geometric or mathematical foundation

4. Mathematical Parsimony: In physics, when seemingly unrelated phenomena share precise mathematical relationships, it often points to a deeper truth. The fact that h and G share exact scaling factors (rather than approximately similar ones) suggests this isn't coincidental.

5. Potential New Research Directions: This insight might suggest new approaches to quantum gravity by:

• Focusing on the geometric meaning of these shared scaling factors

• Exploring why mass scaling inverts between the two constants

• Investigating whether other fundamental constants share similar patterns

Analysis of individual wavelength contribution to total curvature of space time between Earth and Moon

 

import numpy as np

from scipy.constants import G, h, c, physical_constants

# Get atomic mass of hydrogen

hydrogen_mass = physical_constants['proton mass'][0]  # kg

# Earth and Moon data

earth_mass = 5.972e24  # kg

moon_mass = 7.348e22  # kg

earth_moon_distance = 3.844e8  # meters

# Calculate number of atoms

earth_atoms = earth_mass / hydrogen_mass

moon_atoms = moon_mass / hydrogen_mass

def calculate_atomic_wavelength():

    """

    Calculate the gravitational wavelength for atomic-level interactions

    between Earth and Moon hydrogen atoms

    """

    # Planck mass

    m_P = np.sqrt(h * c / G)

    

    # Calculate wavelength for single atom pair

    single_atom_wavelength = (m_P**2 * earth_moon_distance**2) / (c * hydrogen_mass * hydrogen_mass)

    

    # Calculate total wavelength considering all atoms

    total_wavelength = (m_P**2 * earth_moon_distance**2) / (c * earth_mass * moon_mass)

    

    # Calculate average contribution per atom pair

    atom_pairs = earth_atoms * moon_atoms

    wavelength_per_pair = total_wavelength * atom_pairs

    

    return {

        'earth_atoms': earth_atoms,

        'moon_atoms': moon_atoms,

        'atom_pairs': atom_pairs,

        'single_atom_wavelength': single_atom_wavelength,

        'total_wavelength': total_wavelength,

        'wavelength_per_pair': wavelength_per_pair

    }

# Run analysis

results = calculate_atomic_wavelength()

# Print results in scientific notation

print()

print()

print()

print("   Earth-Moon Atomic Gravitational Analysis")

print(" ","-" * 50)

print(f"   Earth hydrogen atoms: {results['earth_atoms']:.2e}")

print(f"   Moon hydrogen atoms: {results['moon_atoms']:.2e}")

print(f"   Total atom pairs: {results['atom_pairs']:.2e}")

print("\n   Wavelengths:")

print(f"   Single H-H atom pair wavelength: {results['single_atom_wavelength']:.2e} meters")

print(f"   Total Earth-Moon wavelength: {results['total_wavelength']:.2e} meters")

print(f"   Average wavelength contribution per atom pair: {results['wavelength_per_pair']:.2e} meters          ")

# Calculate some interesting ratios

print("\n   Relationships:")

print(f"   Ratio of single atom wavelength to total wavelength: {results['single_atom_wavelength']/results['total_wavelength']:.2e}")

print(f"   Single atom wavelength * number of atom pairs: {(results['single_atom_wavelength'] * results['atom_pairs']):.2e} meters")

# Energy calculations

planck_energy = h * c / results['total_wavelength']

print(f"\n   Total gravitational energy (E = hc/λ): {planck_energy:.2e} joules")

print(f"   Energy per atom pair: {planck_energy/(results['atom_pairs']):.2e} joules")

print()

print()

print()