J. Rogers, SE Ohio, 30 Jan 2025, 2157
Abstract:
This paper proposes a though experiment of a redefinition of the kilogram (kg) unit, anchoring it to the fundamental relationship between mass and frequency as expressed through Planck's constant and a photon of 1Hz frequency. By setting the kg to be equal to the mass of a 1 Hz photon, and also setting the speed of light to unity (c=1), we demonstrate that mass, energy, and frequency become numerically equivalent. This simplification illuminates the fundamental unity of these quantities, traditionally treated as distinct entities. Furthermore, this framework extends to massive particles and connects the concepts of mass, frequency, and the curvature of spacetime, suggesting a more integrated view of quantum mechanics and general relativity.
1. Introduction:
The conventional system of units, while practically useful, often obscures the fundamental unity of physical quantities. Our current definitions of the kilogram, meter, and second have historical origins and are not necessarily aligned with the underlying structure of physical reality. The current system requires many conversion constants that hide the underlying relations in equations. This paper explores an alternative approach, motivated by Planck's constant and the connection between energy and frequency, and suggests a more fundamental relationship where mass, energy, and frequency are effectively the same thing when given a better unit system.
2. Unit Redefinitions:
We propose the following redefinitions:
Kilogram (kg): Define 1 kg to be equal to the mass of a photon with a frequency of exactly 1 Hz. This directly ties the unit of mass to the fundamental relationship encoded in Planck's constant (h), and removes the need for Planck's constant by encoding this scale directly into the kg unit.
Speed of Light (c): Set the speed of light c to 1, making the meter and second equivalent.
These choices are not arbitrary, but designed to reveal the natural relationships between fundamental quantities.
3. Implications for Fundamental Equations:
E = mc² Becomes E = m: By setting c = 1, Einstein's mass-energy equivalence equation simplifies to E = m, where both E and m are now in the same units. This demonstrates the fundamental interchangeability of mass and energy.
E = hf Becomes E = f: With the redefined kilogram, the energy of a photon with a frequency of 1Hz would be 1 in the redefined kg units, and thus Planck's constant h effectively becomes unity and can be removed from the equation. Thus, E = hf is reduced to E = f.
Mass, Energy, and Frequency as Equivalent: Combining the above, we have E = m, and E = f, thus m = f. This highlights that mass, energy, and frequency are fundamentally the same quantity, expressed in different units and scales.
4. Extension to Massive Particles:
This frequency-based perspective is not limited to photons. All quantum mechanical objects are associated with a fundamental oscillation in their quantum fields, that are directly related to their mass, even if not directly visible as an oscillation. We propose that:
Mass is Frequency: Mass is a direct expression of the fundamental oscillation or frequency of a particle's quantum field. A higher frequency corresponds to greater mass.
Hidden Frequencies: Massive particles have very high, hidden frequencies associated with their fundamental mass.
5. Connection to Spacetime Curvature:
We now extend this frequency-based view to general relativity. We consider that:
Mass Curves Spacetime: In general relativity, mass is the source of spacetime curvature.
Additive Curvature: The curvature caused by multiple masses is additive. The combined spacetime curvature due to many objects is equivalent to what a single mass would create if all the masses were in the same place.
Curvature as Frequency: Because mass and frequency are equivalent, the curvature of spacetime can also be viewed as an expression of the collective oscillation frequencies of all the masses contributing to it.
Unified Perspective: The total spacetime curvature has a corresponding mass, which means that it also has a corresponding frequency. Thus, the curvature of spacetime is the sum of the underlying frequency of objects, which all have their fundamental oscillation. Thus, spacetime itself can be viewed as being fundamentally linked to frequency.
6. Discussion:
The redefinitions proposed in this paper demonstrate that our current unit system is concealing an underlying simplicity in the universe. By redefining the kilogram to be tied to a fundamental connection between mass and frequency, and by setting c = 1, we have shown a direct equivalence between mass, energy, and frequency (m=E=f). This also extends to massive particles and has links to spacetime curvature.
This approach highlights:
Underlying Simplicity: The universe may be simpler than what our conventional unit system reveals.
Natural Units: These units based on fundamental relations and constants are more aligned with the underlying physics.
Unified View: The relationships reveal a deep connection between quantum mechanics and general relativity.
Removed Complexity: The unit redefinition removes the need for constants such as h and c by encoding them into the fundamental units themselves.
7. Conclusion:
By choosing our units more carefully, we have removed much of the complexity that comes from arbitrary unit definitions. The simple relationship that is revealed demonstrates that the universe may have an underlying structure that can be expressed in the simple equation of E=f. These ideas can pave the way for us to more clearly see the unified nature of our universe.
Further Research:
Future work could explore how other fundamental constants, like the gravitational constant (G), might fit within this framework. Further investigation into how the concept of frequency applies to spacetime itself is also warranted.
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