Naked Science Forum
On the Lighter Side => New Theories => Topic started by: hamdani yusuf on 14/01/2024 08:17:55
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I've been interested in Planck's law for years, and tried to understand the equation using various interpretations by trying to relate it to various statistical distribution curves. I was intrigued by the resemblance of Planck's equation to inverse gamma distribution.
https://en.m.wikipedia.org/wiki/Planck's_law
https://en.m.wikipedia.org/wiki/Inverse-gamma_distribution
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I asked Google Bard about it, and got interesting answers.
Curve of planck's equation looks similar to inverse gamma distribution. Is there any meaningful relationships between them?
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What's planck's law?
My apologies for the earlier confusion. You're right, I'm able to help with your question about Planck's law.
Planck's law, also known as the Planck radiation law, describes the way a perfect absorber of light, called a blackbody, emits electromagnetic radiation at different wavelengths or frequencies when heated to a specific temperature.
Here are some key points about Planck's law:
Quantization: It revolutionized physics by proposing that energy isn't emitted or absorbed continuously, but in discrete packets called quanta. Each quantum of energy is proportional to the frequency of the radiation emitted or absorbed by the blackbody.
Mathematical Equation: Planck derived a mathematical equation to describe the relationship between the intensity of the emitted radiation at each wavelength and the blackbody's temperature. This equation involves Planck's constant, a fundamental physical constant.
Impact on Quantum Theory: Planck's law marked a crucial turning point in physics, paving the way for the development of quantum mechanics. It challenged the classical understanding of light and energy, leading to the concept of energy quantization and laying the foundation for further discoveries in atomic and nuclear physics.
Now, regarding your question about the similarity between the curve of Planck's equation and the inverse gamma distribution, you're correct that there is a resemblance. Both curves exhibit a peak at a certain point and then decrease asymptotically on either side.
However, it's important to note that while there may be a visual similarity, the physical interpretations of these curves are very different. Planck's law reflects the fundamental nature of light and energy in the context of blackbody radiation, while the inverse gamma distribution is a statistical tool used to analyze data with skewed tails.
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I followed up with other question.
Did Planck mention anything about inverse gamma distribution in his writing?
No, Max Planck did not mention the inverse gamma distribution in his writings. In fact, the inverse gamma distribution wasn't formally defined until well after Planck's death in 1947. While the visual similarity between the curve of Planck's equation and the inverse gamma distribution exists, they arose from different theoretical contexts and mathematical frameworks.
Planck's equation emerged from his investigation of blackbody radiation and the revolutionary concept of energy quantization. He proposed that energy wasn't emitted or absorbed continuously, but in discrete packets, paving the way for quantum mechanics. His equation relates the intensity of blackbody radiation at different wavelengths to the temperature, utilizing his newly discovered constant ("Planck's constant").
On the other hand, the inverse gamma distribution belongs to the realm of statistics and probability theory. It serves as a mathematical model for certain types of data that exhibit skewness and an extended tail in one direction. Its formalization came much later, not directly connected to Planck's work.
So, while the resemblance in their curves might be intriguing, it's a superficial similarity arising from two entirely different domains. There's no known theoretical connection between the two concepts in Planck's original work.
Afaik, Planck developed his law based on Maxwell-Boltzmann statistical mechanics. That's why Boltzmann's constant appears in his equation.