A Geometric Deceleration-Based Model for Blackbody Radiation

Abstract:

This paper presents a novel geometric approach to explaining blackbody radiation based on particle collisions in gases. The model proposes that chains of collisions lead to energy accumulation in a small percentage of particles, which then emit photons at the peak frequency of blackbody radiation. This approach provides a classical-like explanation for the observed spectrum, including its temperature dependence and intensity variations.

Introduction

Blackbody radiation has long been explained using quantum mechanics, but this paper proposes a classical-like model based on particle collisions and energy accumulation. This geometric approach suggests that the observed spectrum results from the statistical distribution of particle energies following chains of collisions.

The Geometric Viewpoint

I am working on a framework that is based entirely on curved space and it is that curved space that give a particle the ability to move along a worldline.  Acceleration at the atomic level require photons to merge their worldlines into the curved space at the nucleons. This increases the curved space and inertia in the atom.   Then by the law of conservation of energy deceleration would require the release of photons that match the rate of deceleration.  That is the basis of this classic description of black body radiation. 

This emission of continuous photons has been observed in bremsstrahlung or electron braking.  An unusually energetic energy release is also seen during the instantaneous deceleration in cavitation. 

The Collision-Chain Model

Energy Accumulation

In a gas, particles undergo frequent collisions. While most collisions result in energy exchange, some lead to a net accumulation of energy in certain particles. These "collision chains" can produce particles with significantly higher energies than the average.

Peak Frequency Emissions

The model proposes that only a small percentage of particles, those that have accumulated sufficient energy through collision chains, can emit photons at the peak frequency of blackbody radiation or above. This rarity explains the observed faintness of blackbody radiation, especially at lower temperatures.

Spectrum Shape

• The shape of the blackbody spectrum can be explained by the distribution of particle energies resulting from collision chains:
• Low-frequency tail: Produced by the more common, lower-energy collisions.
• Peak frequency: Results from the small percentage of particles that have accumulated enough energy through collision chains.
• High-frequency tail: Caused by even rarer, extremely energetic collisions.

Mathematical Analysis

Let's examine this model at 7000K:

Average kinetic energy per particle:

E_avg = (3/2)kT ≈ 1.44968 × 10^-19 J

Peak wavelength of blackbody radiation:

λ_peak = b/T ≈ 4.13967 × 10^-7 m

Peak frequency and energy:

f_peak ≈ 7.24201 × 10^14 Hz

E_photon ≈ 4.79865 × 10^-19 J

Probability of a particle having peak energy:

P ∝ e^(-E_photon / kT) ≈ 0.00701

This calculation shows that approximately 0.701% of particles have energy equal to or greater than the peak energy of blackbody radiation at 7000K.

Discussion

Continuous Nature of the Photon Release

Black body radiation is fully continuous. The photons released from my theory's explanation of deceleration are also continuous, and their energy levels depend on the rate of that deceleration. I am hoping to create a mathematical frameworks with the work I am doing on this theory.

Rarity of Peak Emissions

The calculation demonstrates that only about 0.7% of particles have sufficient energy for peak frequency emissions. This rarity explains the faintness of blackbody radiation and supports the collision-chain model.

Rarity of All Emissions Across the Spectrum

This is further limited by only a certain percentage of collision events emitting a photon that is not absorbed immediately by the particle it is colliding against.  The chances of a photon escaping the system increase with more added energy in the system. Lower energy events, although much more numerous at 99.3% more often, rarely escape because of the low speeds and low energies of the particles involved. 

Temperature Dependence

As temperature increases, the probability of longer collision chains increases, leading to more particles with high energy. This explains the shift in peak frequency and increased intensity of blackbody radiation at higher temperatures.

Spectrum Tails

The low-frequency tail results from the more common, lower-energy collisions but as the energy gets lower less escape.  

The high-frequency tail is produced by the rarest, most energetic collisions. The continuous nature of the spectrum reflects the variety of collision chain lengths possible.  

The highest energy releases are very unlikely to occur. Only if the fastest two particles collide head on can we get to that level of energy release, and even at that energy level is is likely that both photons will be absorbed. 

Ultraviolet Catastrophe

Early theories showed that there should have emissions in the ultraviolet spectrum.  This does not happen. Current standard theories limit it with rules and explanations.  This theory can't physically emit ultraviolet because of physical limitations of the real world. 

 Plasma Deceleration Limits:

• Plasmas have well-established limits on particle deceleration rates.
• This is due to complex interactions between charged particles and electromagnetic fields within the plasma.

Ion Behavior in Plasmas:

• The limited acceleration of ions at higher energies is indeed a known characteristic of plasmas.
• This is often related to phenomena like Debye shielding and the plasma frequency.

Electron Dynamics:

• The limitation on electron speed changes is a fundamental aspect of plasma physics.
• This is related to concepts like electron plasma oscillations and the electron plasma frequency.

Conclusion

This geometric, collision-based model provides a classical-like explanation for blackbody radiation. It accounts for the spectrum shape, temperature dependence, and faintness of radiation through the statistical nature of particle collisions and energy accumulation. While further research is needed, this approach offers a fresh perspective on a fundamental physical phenomenon and potentially bridges classical and quantum concepts.