Justification for a Starting Point for Energy, Wavelength, Frequency in Photons

 

In the study of photons, it's crucial to understand how their energy, frequency, and wavelength are perceived differently across various observers and frames of reference. However, in order for this scaling to occur, we must first recognize that photons, as quantum entities, must have a baseline or starting energy from which all these observed changes can be measured. Each frame of reference and the photons own worldline scale the energy.  But for this scaling to happen there has to be a default and that default level would be the same in every photon. 

In effect, to be scaled a photon has to have a rest state.  If it started as zero, it would be zero in every frame, because no matter how you scale zero you get zero. 

The idea behind this justification is rooted in the understanding that all photons are inherently identical in terms of their fundamental properties. Their energy and frequency are not fundamentally different in nature but appear to change based on their interaction with various frames of reference. This is a direct consequence of relativistic effects like Doppler shifts and time dilation, but the critical point is that in order for these effects to be meaningful, there must be a starting energy—a baseline—from which these shifts can scale.

1. Photons Are Inherently Identical:

At their core, all photons are the same—regardless of their frequency, energy, or observed wavelength. This suggests that photons share an underlying, fundamental property that remains constant across all frames of reference. However, when we observe photons from different frames of reference, their frequency and wavelength change depending on the relative motion of the observer. This phenomenon is explained by relativistic effects, but it raises the question: what is the photon’s inherent state of energy before these relativistic shifts occur? It is not zero, and we know it is the same in all photons.

2. The Need for a Starting Energy:

In the context of energy and frequency scaling, the photon must have a non-zero starting energy. This is because, for any energy to be scaled by different frames of reference, there must be a default value that all photons share in their own worldline before interaction with any observer’s frame. Without this initial energy, we wouldn't have a reference point to apply the observed shifts.

• Energy Scaling: A photon’s energy is relative to the observer’s frame, meaning its frequency can be perceived as higher or lower depending on the relative motion between the photon and the observer. But for this scaling to make sense, we must start with a base energy. This base energy is not arbitrary; it represents the photon's "default" state in its own frame, the value that all observers can scale from.

3. The Worldline of the Photon:

The worldline of a photon—the path it traces through spacetime—is fundamental in determining its observed energy. The photon’s worldline interacts with other reference frames, and its energy changes as a result of this interaction. This energy is scaled based on the relative motion between the photon and the observer, but the photon must have a starting energy from which this scaling occurs.

While photons do not experience time in the traditional sense (that time is experienced in its worldline, the same as for massive particles), the concept of a "rest frame" for the photon is useful in this context: the rest frame is not a literal rest frame, but a reference point where the photon has a known, fixed energy (which can be tied to Planck’s constant at 1 Hz frequency).  1 Hz frequency, at speed of light wavelength has Planck's constant energy.  (E=h 1 Hz)  This starting energy becomes the reference energy that all observers can measure, and that is scaled according to their relative motion.

4. The Role of Planck’s Constant:

The Planck constant ($h$) plays a crucial role in this justification. In the model proposed, the default energy of the photon is exactly Planck’s constant at a frequency of 1 Hz with a wavelength equal to the speed of light ($c$). This defines the photon's "starting" state. The energy of a photon can then be scaled based on the frames of reference of the observer, but this starting energy serves as a reference point.

Thus, Planck’s constant becomes the energy of the photon at this baseline. This constant defines the energy at 1 Hz, serving as a fundamental "unit" or default energy for the photon. As the photon interacts with different frames of reference, its energy and frequency are modified according to relativistic principles, but always starting from this baseline energy.

5. Energy Scaling in Different Frames:

Once we define this starting energy, we can scale the energy observed by different observers using Doppler shifts, time dilation, and other relativistic effects. The frequency of the photon may appear to increase or decrease depending on the observer's motion relative to the photon, but in all cases, the photon’s energy is a scaled version of its baseline energy, which is governed by its worldline.

This scaling depends on the relative motion between the photon and the observer. However, without this default, non-zero energy, the concept of energy scaling in relativistic frames would not be possible.

6. Conclusion:

In summary, all photons must have a starting energy that is non-zero, which serves as the reference point for scaling the energy and frequency across different frames of reference. This starting energy is Planck's constant at 1 Hz with a wavelength equal to $c$, and it represents the default energy that all photons share. From this point, their energy can be modified according to the frames they interact with, but this baseline energy is essential for meaningful energy scaling.

This interpretation provides a new way to view photons: not as entities without a baseline energy, but as quantum particles with a default state of energy that can then be scaled based on the relative motion between the photon and different observers. This new perspective on photon energy brings clarity to how we understand energy scaling across different reference frames in relativistic physics.