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This is possibly one of the most intrigue paper at the end of the year presented by Sir Roy Patrick Kerr (still an archive, I guess it must be an extensive work for the reviewer and editor to review the paper😆
Looking at the first sentence of the abstract, this paper is not going to be nice to the current proposal of the singularity theorem by the late Stephen Hawking and Sir Roger Penrose. The discussion in the paper is way beyond my capability to simplify and share with you all. So I will attach a few links that include discussion, explanation for the topic. Hope it could sparks your interest and welcome to discuss. (Link in comment section)
References
1. Standard Solar Spectra | PVEDucation. (n.d.). https://www.pveducation.org/pvcdrom/appendices/standard-solar-spectra
2. Thornton, S. T., & Rex, A. (2012). Modern physics for scientists and engineers. Cengage Learning.
3. Serway, R. A., Moses, C. J., & Moyer, C. A. (2005). Modern Physics.
4. Young, H. D., Freedman, R. A., & Ford, A. L. (2012). Sears and Zemansky’s University Physics: With Modern Physics.
5. Krane, K. S. (2012). Modern Physics. Wiley.
6. Young, D. P., Cutnell, J. D., & Stadler, S. (2018). Cutnell & Johnson Physics.
7. Halliday, D., Resnick, R., & Walker, J. (2018). Fundamentals of Physics: Extended. Wiley.
8. Eisberg, R. M., & Resnick, R. (1985). Quantum Physics of atoms, molecules, solids, nuclei, and particles. John Wiley & Sons.
9. Giancoli, D. C. (2014). Physics: Principles with Applications. Addison-Wesley.
10. Planck, M. (1900). On an Improvement of Wien’s Equation for the Spectrum. Ann. Physik, 1, 719-721.
11. Wien, W. (1897). XXX. On the division of energy in the emission-spectrum of a black body. The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, 43(262), 214–220. https://doi.org/10.1080/14786449708620983
12. Blackbody radiation. (n.d.). http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html
13. Wikipedia contributors. (2023). Planck’s law. Wikipedia. https://en.wikipedia.org/wiki/Planck%27s_law
14. Carson, T. R. (2000). Steps to the Planck Function: A Centenary Reflection. arXiv preprint astro-ph/0011219.
Planck’s Law
In 1900, when Planck tried to fit for the curve, he knew that Wien’s approach is in a correct direction but couldn’t fit for data at longer wavelengths. He continued Wien’s work and made a “crazy” assumption. He assumed that the energy comes in quanta but not continuous and introduced a constant (Planck’s constant) where he regarded it as a calculational trick rather than a fundamental principle. Luckily, 5 years later, Albert Einstein successfully proved his quantization of energy level when trying to explain photoelectric effect.
The final form of Planck’s function is as below:
(Appendix 1)
Appendix 2 shows fitting using T = 5525 K.
This function is so powerful that it could reach to the function we mentioned earlier in the post.
If we take the derivation of the equation equal to zero to work out the peak wavelength, we will reach to a value in close agreement to Wien’s displacement law.
If we apply the function for short wavelengths, we will reach Wien’s distribution function.
If we apply the function for long wavelengths, we will reach Rayleigh-Jeans function.
If we integrate the function over all wavelengths, we will reach to Stefan-Boltzmann Law.
All workings are shown in Appendix 3.
