Since a photon is emitted from an excited electron, and this electron has rotational motion around itself and the nucleus of an atom, the motion of the emitted photon must be a combination of linear projectile motion and the electron's rotational motions around itself and around the nucleus. The combination of linear motion and the rotation of electron around the nucleus creates a helical motion. When this is combined with the electron's self-rotation, a second helical motion is generated. Hence, a photon released from an electron has a nested helical motion. Initially, we will calculate the speed of the photon in this nested helical path and then use this speed to calculate the classical energy of the photon and its relation to Planck's everlasting energy equation.

1. Introduction

To show the hundred-year-old lost relation between classical energy and Planck’s energy, we first calculate the various speeds of the photon.

1.1 Calculation of the Linear Speed of Photon

In these calculations, we find that if a photon traverses the straight distance between the points O and B (which is the same wavelength λ) in one period T, its speed equals:

However, it has been experimentally proven that this value is indeed C.

1.2 Calculation of the Wave Speed of Photon

If we consider the photon's motion along its curved path, we find that the distance travelled by the photon between points O and B exceeds λ. The actual distance travelled by the photon divided by the time taken T, gives us the photon's wave speed over one complete cycle.

1.3 Calculation of the True Speed of Photon in the First Helix

In its first helical motion, the photon’s speed is the result of its linear speed and its wave speed, which are perpendicular to each other. Therefore, the true speed can be calculated using the following equation:

1.4 Calculation of the Speed of Photon in the Nested Helix

The motion in the nested helix results from the combination of two wave motions and one linear motion. The two wave motions are aligned and perpendicular to the linear motion, so the total speed is:

2. Calculation of the Classical Kinetic Energy of Photons

In this part, we calculate the energy of photon considering its helical motion:

initial total kinetic energy = linear energy + rotational energy = Translational energy + rotational energy

Where E_T is the initial kinetic energy, which is always constant and equals half the mass of the photon m_p times the square of the nested helical speed V_T:

This energy consists of two parts: rotational energy of photon E_R which depends on the constant angular velocity and the variable rotational radius:

The second part is the translational (linear) energy, which equals the same energy measured by Planck in the laboratory, i.e., Planck’s constant times the frequency:

The sum of rotational and translational energy is always constant and equals the total energy, so the following equations can be written:

Now, we divide the first equation by the constant E_T

We define the two variable parameters as follows:

The following result can be derived from the above equations:

In other words, each of the translational energy E_L and rotational energy E_R be considered as a fraction of the total energy E_T

Since the total energy E_T is always constant, it can be understood that as the rotational radius r increases, the rotational energy increases and the translational energy decreases, resulting in a decrease in frequency f, and vice versa. As the rotational radius r decreases, the rotational energy decreases and the translational energy increases, increasing in frequency f.

Thus, the following graphs of the variations in translational energy E_L and rotational energy E_R relative to the rotational radius r can be drawn:

2.1 Calculation of Frequency at the Point of Equality between Translational and Rotational Energy

Now, we calculate the frequency at which the translational energy E_L and rotational energy E_R of the photon are equal:

This frequency f_G corresponds to green light in the visible spectrum. At this frequency, the rotational energy equals the translational energy, and i_R = i_L = 1/2. Considering the frequency range of visible light, it can be said that in the frequency range of 300 THz to 900 THz, the range of 𝑖_𝑅 𝑎𝑛𝑑 𝑖_𝐿 will be as follows:

In fact, the relationship between i_L and f (Terahertz) can be written as follows:

2.2 Relationship between Planck's Energy Equation and Classical Kinetic Energy (Planck-Saleh Energy Equation)

From the equivalence of translational energy with Planck's energy equation, we can write:

We call the constant value the Saleh constant "S" and rewrite the above equation as follows:

This equation is called the Planck-Saleh equation, where S is the Saleh energy constant and i is a variable coefficient equal to i of L and indicates the variations in translational energy.

In previous articles, we calculated the rotational and translational energy of photons using the speed of photons in a nested helical path (V_T = 3.3 C) and we examined its relationship with Planck's energy equation. We now proceed to calculate the constant angular velocity (ω) by equating the translational and rotational energy at a frequency of 600 THz. Subsequently, considering the constancy of the angular velocity across all frequencies, we derive a formula to calculate the radius of the rotation of photons (r) in terms of the variable coefficient of rotational energy (i_R). Finally, we calculate the rotational radius for several frequencies within the range of visible light.

Where a_R is the amplitude of rotational motion and a_L is the amplitude in linear motion. The rotational radius is the vector sum of these two perpendicular quantities. Therefore, we have:

At a frequency of 600 THz, the linear amplitude is one-quarter of the wavelength, so we have:

Now, with the rotational radius for green light at a frequency of 600 THz, we calculate the constant angular velocity of photons:

Using the obtained angular velocity, for the rotational radius of photons, we have:

Now, by substituting different values, we obtain the rotational radius of several visible light spectra:

Finally, we calculate the linear and rotational velocity for the frequency f = 600 THz, where E_R =E_L, using two methods and comparing the results.

On the other hand, for the rotational speed, considering the rotational radius r_G = 1.76 × 10^-7 and ω = 4 × 10¹⁵ so:

By comparing the obtained rotational and linear speeds, it is evident that both values are equal, which serves as proof of the accuracy of the presented calculations.

Utilizing a simple lens, we choose filters at will (red, yellow, green, blue, and violet). Then, we apply the filter to the lens and locate a thermometer at its focal point. It is evident that the temperature shown on the thermometer is lowest when using the red filter, highest with the violet filter, and the green filter falls in the middle.

These results confirm the validity of Planck's universally accepted equation.

Despite our common perception of red light as warm and blue light as cool, the experimental data clearly demonstrate the opposite.

Next, we evaluate the results of two experiments conducted by physicists at the University of Michigan and the Massachusetts Institute of Technology [1,2]. These experiments indicate that Planck's equation does not hold at a very small scale from the light source. The main reason for this is that at very close distances to the source (d=ε or equivalently at t = ε), the amount of energy significantly exceeds the amount of energy that Max Planck predicted. This is because photons exhibit both linear and rotational motions. In the experiments conducted by the University of Michigan and MIT, the total energy was measured, whereas in Planck's experiment, only the linear energy was measured, not the rotational energy. The discrepancy in energy measurements (between the two university experiments and Planck's experiment) indicates the presence of rotational motion of photons or missing rotational energy [3].

Now, let's discuss the first question: why does red light appear warmer and blue light cooler?

A New Explanation for Why the Translational Energy (Derived From Planck’s Equation and Saleh’s Experiment) of Blue Spectrum Is Greater Than That of Red One, While Our Sense of Sight and Touch Perceive Red Light as Warmer, Larger, and Stronger Than Blue Light

Given that the photon traverses in a helical path; it has both linear and rotational motion, the energy of the linear motion (translational energy) can be easily calculated using Planck's equation and Saleh's experiment. Also, as the frequency of blue light is higher than that of red light, all measuring devices demonstrate the energy of blue light is greater than that of red light based on its frequency. When we observe a wave with a helical motion coming towards us from the front, such as the blue and red spectrum, it's clear that because the frequency of blue light is higher, its wavelength, amplitude, and rotational radius (r_m) are smaller than those of red spectrum. Thus, the cross-section area of the blue spectrum is smaller than that of the red one. Consequently, red light stimulates a larger area on the retina or skin, activating more visual and tactile cells, and is perceived as stronger and warmer.

The internal energy of the red spectrum is greater than that of the blue one, and the translational energy of the red spectrum is less than that of the blue.

Overall, we perceive blue light as cold because, although the amount of its translational energy is greater, its rotational energy is less than that of red light. Conversely, we perceive red light as warm because, despite having less translational energy compared to blue light, it possesses greater rotational energy.

Notice:

The speed of a photon has been considered to be "C", the energy of each photon was considered to be E=m_pC² and the classical energy of the photon was E = 1⁄2 m_pC². Where m_p is the mass of the photon ( 𝑚𝑝 = 1.64 × 10⁻³⁶𝑘𝑔). Recent calculations have shown that the speed of a photon is "3.3 C" [4]. Consequently, in the calculation of the photon's kinetic energy, the speed should be considered as v=3.3C. If the new speed is squared, which is 3.3 times the previous speed, the new energy value is approximately 10 times the previous energy. In other words, the new energy value has increased by a factor of 10 compared to the old one, or approximately 1000%, which corresponds to the value obtained in the MIT University experiment at a very small scale from the light source. Hence, the results obtained from the MIT University experiment are also correct and valid.

To enhance comprehension, we will calculate the different energies (translational, rotational, and total) of the end of violet light with a frequency of f=900 THz.

In this example, we used a frequency of 900 THz, for which the energy obtained using Planck's method is at its maximum (within the range of 300 to 900 THz) and its value is as follows:

The obtained classical energy value, using the speed value of v=C, is equals:

These two values show a significant difference. However, the classical energy value, using a speed that is v=3.3C, would be:

If we look at the obtained values, we will demonstrate that the photon's energy at a speed of v=3.3C is very close to the experimentally calculated energy by that of Planck, with a slight difference due to the rotational energy of the photon, which is not measurable in Planck's experimental method. Consequently, the rotational energy of the photon is not accounted for in Planck's relation.

Therefore, it can be stated that the value of the translational energy of a photon equals the established empirical value by Max Planck, which is valid. On the other hand, the energy value obtained from the MIT experiment and Saleh Theory calculations represents the total energy of the photon, and these two are also accurate, real, and acceptable.

In other words, the MIT University experiment demonstrates the total energy value. The empirical energy calculation method of Max Planck indicates the translational energy value, while Saleh Research Group's calculations show the values of translational, rotational, and total energy.

In previous articles, it was stated that the translational energy (E_L) is a fraction of the total energy (E_T), and this fraction for a electromagnetic wave with a frequency of f=900 THz equals i_L = 3/4 [5]. In other words, its translational energy constitutes 75% of the total energy, while the remaining 25% is attributed to its rotational energy.

As evidenced by the observations, the value obtained for translational energy matches the energy obtained from the Planck method.

References:

[1] Chandler, David L. “Breaking the Law, at the Nanoscale.” MIT News | Massachusetts Institute of Technology, news.mit.edu/2009/heat-0729 . Accessed 29 July 2009.

[2] Thompson, Dakotah, et al. " Hundred-fold enhancement in far-field radiative heat transfer over the blackbody limit." Nature 561.7722 (2018): 216-221.

[3] Saleh, Gh. "New Discoveries About the Speed of Electromagnetic Waves 2024 Part C." Saleh Theory, 06 Nov. 2023, https://www.saleh-theory.com/article/new-discoveries-about-the-speed-of-electromagnetic-waves-2024-part-c

[4] Saleh, Gh. "New Discoveries About the Speed of Electromagnetic Waves 2024 Part B." Saleh Theory, 30 Oct. 2023, https://www.saleh-theory.com/article/new-discoveries-about-the-speed-of-electromagnetic-waves-2024-part-b

[5] Saleh, Gh. "Discovery of the Hundred-Year-Old Lost Mathematical and Physical Relationship Between the Classical Kinetic Energy of Photons and Planck's Everlasting Experimental Equation in the Universe (Planck-Saleh Energy Equation)" Saleh Theory, 28 Jun. 2024, https://www.saleh-theory.com/article/discovery-of-the-hundred-year-old-lost-mathematical-and-physical-relationship-between-the-classical-kinetic-energy-of-photons-and-plancks-everlasting-experimental-equation-in-the-universe-planck-saleh-energy-equation