The Energy Rest Frame: A Unified Approach to Fundamental Constants

James Rogers, SE Ohio, 03 Dec 2024 1300

Abstract

The concept of the energy rest frame, where a photon completes one rotation per second, provides a novel framework for understanding and unifying several fundamental constants in physics. This paper explores how defining the energy rest frame as $\mathrm{one\; rotation\; per\; second,\; or\; 2}\pi$ radians per second, ties together rotation, frequency, wavelength, energy, momentum, and mass in a coherent and intuitive manner. The implications of this approach simplify the relationships among these constants, offering a new perspective on their interdependence.

Introduction

• Background: Science often teaches the concepts presented here as separate unconnected concepts. By seeing that these concepts are all just related aspects of an energy rest frame we can see how these concepts all directly relate to each other.

• Objective: Introduce the energy rest frame concept and outline its potential to unify these constants, with an emphasis on the rotational aspect.

• Why this was not seen before:  E = h (1 Hz) and E =hc/c are both trivial identities that hid the profound truth that h is the energy at a specific frequency of 1 Hz.

Energy Rest Frame Concept

• Definition: The energy rest frame is a state where a photon undergoes one rotation per second (1 Hz), corresponding to $2\pi$ radians.

• Fundamental Quantities:

  • Rotation ($2\pi f f$ radians): The basis for all scaling in the energy rest frame.

  • Frequency ($f$): 1 Hz

  • Wavelength ($\lambda$): Equals the speed of light ($c$)

  • Energy ($E$): Given by $E=h\cdot f=h\cdot 1\text{Hz}=hE\; =\; h\; \backslash cdot\; f\; =\; h\; \backslash cdot\; 1\; \backslash ,\; \backslash text\{Hz\}\; =\; h$

  • Momentum ($p$): Given by $p=\frac{h}{\lambda }=\frac{h}{c}p\; =\; \backslash frac\{h\}\{\backslash lambda\}\; =\; \backslash frac\{h\}\{c\}$

  • Mass ($m$): Given by $m=\frac{E}{c^2}=\frac{h}{c^2}m\; =\; \backslash frac\{E\}\{c^2\}\; =\; \backslash frac\{h\}\{c^2\}$

Scaling with Observed Frequency

• General Scaling: These quantities scale from the energy rest frame with the observed frequency $f$.

  • Rotation: $2\pi f f$ radians per cycle.

  • Energy: $E=h\cdot f$

  • Wavelength: $\lambda =\frac{c}{f}$

  • Momentum: $p=\frac{h\cdot \mathrm{f/}}{c}$

  • Mass: $m=\frac{h\cdot \mathrm{f/}}{{\mathrm{c^}}^2}$

Unified Framework

• Interconnectedness: The energy rest frame unifies these constants, making their relationships clear and intuitive.  At the energy rest frame all these concepts are just different aspects of the speed of light seen from different ways.

• Rotational Symmetry: The importance of $2\pi f f$ rotation in this framework is that it shows that 2pi is the rotation a photon with a wavelength of c.  This means that 2pi is another way of saying c. This is why you see 2pi in so many formulas, it is being scaled from the energy rest frame.

• Consistency: Every one of these features of a particle at the energy rest frame is scaled by the observed frequency of a photon.  There are no exceptions to this rule.

Educational and Practical Implications

• Simplified Learning: By showing how all these concepts are related to each other at the inherent energy level of all particles we can see how these values are scaled by their motion, the space time the particle travels through, and the motion relative to the observer. The observed frequency of a photon is scaled by each of these interactions to the observed value we observe, and we can calculate the other properties like energy or wavelength from the way the frequency was scaled by the combination of all these different motions. This same concept across all these properties is a clear teaching moment that will make these often disjointed topics clear and easy for students.   

• Practical Applications: This explains why the formula E = hf works, because h is the energy in the energy rest frame and the frequency is scaled by the motion of all the particles involved.  This explains why all these features of a photon all scale this same way. 

• Geometric Insight: At this energy rest frame there is a very geometric relationship between energy, momentum, and mass. Using my new unit system science the following is true:
  
      E = (s_length * s_mass) / c
      p = (s_length * s_mass) / c^2
      m = (s_length * s_mass) / c^3
  
  This is a cube with all edges c, mass is inverse of the volume of the cube, momentum is inverse of the area of one side, and energy is inverse length of one edge. All times the same unit scaling of a single dimension of that cube. 
  
  But what we are really saying is:
  
      E = (s_length * s_mass) / λ
      p = (s_length * s_mass) / λ*c
      m = (s_length * s_mass) / λ*c^2
  
  It is only at the energy rest frame wavelength is equal to c.  As motion in 4D space time scales the appearance of the wavelength, these geometric projections of wavelength also appear to scale along with the wavelength. But only one dimension scales. This could point to a higher dimension that is invariant everywhere in our space time. Could motion in this higher dimension be what is causing rest mass. 
  
  What the formula E =hf has always been doing has been to scale this wavelength because of the scaling of the frequency.  The 1/c inside h has always been converting this to the apparent wavelength all along, scaling this cube and the properties that are dependent on this geometric relationship to wavelength. 

• Since all these constants are related to c which is invariant in all frames, then they will scale properly to all frames by the frequency by scaling the wavelength. 

Conclusion

• Summary: The energy rest frame concept establishes a coherent framework where a photon’s intrinsic rotation, wavelength, energy, momentum, and mass all emerge as interdependent aspects of its motion in spacetime. This insight ties together constants like h, c, and 2π into a single geometric perspective. By scaling these properties with observed frequency, determined by spacetime curvature, particle motion, and relative motion, this framework bridges gaps between quantum mechanics and relativity. Its simplicity and clarity make it a valuable teaching tool and a potential foundation for deeper explorations into the nature of spacetime and fundamental particles.