Defining the Energy Rest Frame of a Photon and the Energy Relationship to Planck’s Constant

Introduction

In the context of modern physics, the concept of a "rest frame" for a photon has been traditionally elusive. Since photons travel at the speed of light, $c$, and do not experience time in the same way as massive particles, they are typically said to have no rest frame. However, for the purpose of exploring the energy-frequency relationship of photons and their fundamental constants, we will define a conceptual "energy rest frame" for a photon and for matter, where the photon has a frequency of 1 Hz and a wavelength equal to the speed of light, $c$.

The important thing to remember is that this rest frame is the energy rest frame for both massless and massive particles.  The Higgs field gives enough of an imbalance to matter's inertia so it can't immediately shoot off at light speed.  This pins energy(time dimension) to motion (3D space) in massive particles, but the photons energy is always equal to its momentum so it goes light speed no matter its energy level. Don't confuse motion in 3d space with motion in time.  These are two independent quantities unless you have a mechanism to tie them together, like matter does with Higgs. 

What we see as energy is the motion we see in the time dimension, and as the photon shows, this experience of time in the worldline of photon can affect the perception we have of its wavelength, frequency and energy.  Worldlines of both massive and massless particles are identical in the time dimension, it is just taht motion in 3D space is tied to energy by the Higgs particle making an imbalance of inertia.  Even though photons are moving at the speed of light in 3D space they are not moving at maximum speed in the time dimension, and this is why its frequency is independent of 3D motion.

So when we are talking about a rest frames we are not talking about motion, we are talking about a lowest energy level allowed. The photon does have a rest frame for its energy, for its base that is then scaled by its worldline.  

This theoretical framework allows us to demonstrate how the default energy in this rest frame corresponds exactly to Planck's constant, $h$.

Defining the Photon’s Rest Frame

• Rest frame: In this theoretical model, we define the photon’s rest frame not as a true stationary state, but as a reference point where the photon has a frequency of 1 Hz. The wavelength associated with this frequency is chosen to be the speed of light, $c$. This results in a specific energy value that will be shown to correspond to Planck’s constant.

• Frequency ($f$): The frequency of a photon is defined as the number of oscillations per second. In this model, we set the frequency of the photon in the rest frame to 1 Hz.

• Wavelength ($\lambda$): The wavelength is the spatial period of the photon’s oscillation. For our rest frame, we define the wavelength as $\lambda = c$, where $c$ is the speed of light in a vacuum.

Energy of a Photon

The energy of a photon is related to its frequency by the equation:

$$E = h f$$

Where:

• $E$ is the energy of the photon.
• $h$ is Planck's constant.
• $f$ is the frequency of the photon.

Since we have defined the frequency of the photon in this rest frame as 1 Hz, the energy of the photon becomes:

$$E = h \times 1 \, \text{Hz}$$

Thus, the energy of the photon in this rest frame is exactly equal to Planck’s constant:

$$E = h$$

Relationship Between Frequency, Wavelength, and Energy

Now, we use the relationship between wavelength and frequency for a photon:

$$c = f \lambda$$

Where:

• $c$ is the speed of light in vacuum.
• $f$ is the frequency of the photon.
• $\lambda$ is the wavelength of the photon.

For the defined rest frame, we have:

• $f = 1 \, \text{Hz}$
  
• $\lambda = c$
  

Substituting these values into the equation:

$$c = 1 \, \text{Hz} \times c$$

This confirms that the photon in the defined rest frame has a wavelength of $c$ and a frequency of 1 Hz, and the energy associated with this photon is $h$.

Implications of the Rest Frame Definition

By defining the photon’s rest frame in this way, we gain a direct understanding of the fundamental energy associated with the photon at its baseline state. Here are the key takeaways:

1. Planck’s constant as energy: In this framework, Planck's constant is not just a fundamental constant in quantum mechanics, but is directly the energy of a photon in this theoretical "rest frame" (at 1 Hz and wavelength $c$).

2. Energy scaling: As the frequency of the photon changes, so too does the energy, in accordance with $E = h f$. For frequencies higher than 1 Hz, the energy increases linearly, while for frequencies lower than 1 Hz, the energy decreases. This is a direct result of the frequency-wavelength-energy relationship.

3. Quantum nature of the photon: The energy of the photon, as derived from the frequency-wavelength relation, shows the inherent quantization of energy in the photon’s behavior. This reinforces the idea that the quantum of energy is tied to Planck's constant, and any deviation in the frequency corresponds to a change in energy.

4. Rest frame of the photon: The rest frame, as defined here, offers a conceptual way to understand the photon’s intrinsic properties, even though traditional relativity asserts that a true rest frame for a photon doesn’t exist due to its constant motion at the speed of light.
   

5. Speed of Light Contraction: The rest wavelength defined here, corresponding to a frequency of 1 Hz and a wavelength of $c$, naturally leads to the observed speed of light. As the photon’s frequency increases (and energy increases), the wavelength contracts, while massive particles approach the speed of light. This contraction from the rest wavelength effectively sets the speed of light as a universal constant. The observed value of the speed of light arises from this fundamental relationship, maintaining its constancy in all inertial frames, regardless of the energy of the photon. This illustrates how the photon’s energy (and frequency) influences its observed properties, but the speed of light remains invariant in all frames due to this natural contraction.

If there is a rest frame how does frequency of light change

It is true that the photon itself experiences no time, it is always at 1 Hz, have a wavelength equal to c and have Planck's constant as the energy.  That can never change.  

What can change is the frame of reference of its worldline.  The photon never experiences any changes, but its path through space time can change and that path can interact with other frames of reference, making this rest frame of the photon appear to be any other energy level.  So it is not the photon changing, it is its geodesic in space time that is experiences changes in time experience.

Conclusion

In this theoretical framework, we have defined the "rest frame" of a photon as having a frequency of 1 Hz and a wavelength equal to the speed of light. This yields an energy that corresponds exactly to Planck’s constant, $h$, which is the fundamental quantum of energy in this framework.

This provides a clear and intuitive way to understand Planck’s constant not just as an abstract constant in quantum mechanics, but as the energy of a photon in its rest frame at 1 Hz frequency and $c$-wavelength. This perspective helps demystify the significance of $h$ and offers insights into the energy-frequency relationship of photons within the context of their worldline and relativistic properties.