[hamdani yusuf (OP)]

In Planck's formula for radiation from black bodies, Boltzmann's constant somehow appears.


https://en.m.wikipedia.org/wiki/Boltzmann_constant

Macroscopically, the ideal gas law states that, for an ideal gas, the product of pressure p and volume V is proportional to the product of amount of substance n and absolute temperature T:
 pV=nRT,
where R is the molar gas constant (8.31446261815324 J⋅K−1⋅mol−1).[3] Introducing the Boltzmann constant as the gas constant per molecule[4] k = R/NA transforms the ideal gas law into an alternative form:
 pV=NkT,
where N is the number of molecules of gas.

It implies the quantization of oscillating electric charges producing the radiation,  which is related to the definition of temperature itself.

[alancalverd]

No such implication. k_B derives from classical statistical mechanics.

[hamdani yusuf (OP)]

k_B derives from classical statistical mechanics.

Do you meant it's no longer needed?

[alancalverd]

Of course it's needed. How else can you describe the Boltzmann distribution, rationalise the gas laws, or do thermodynamics?

Quantum mechanics doesn't displace classical mechanics, any more than relativity displaces newtonian physics. The test of both is that they degenerate to the classical formula for large or slow systems.

[hamdani yusuf (OP)]

Of course it's needed. How else can you describe the Boltzmann distribution, rationalise the gas laws, or do thermodynamics?

Quantum mechanics doesn't displace classical mechanics, any more than relativity displaces newtonian physics. The test of both is that they degenerate to the classical formula for large or slow systems.

How does Boltzmann's constant relate to black body radiation?

[hamdani yusuf (OP)]

I asked Gemini. What is the difference between planck's formula for black body radiation and wien's approximation?

Planck's formula and Wien's approximation both attempt to describe the spectrum of black body radiation, the characteristic energy distribution emitted by an ideal perfect absorber at a given temperature. However, they differ in their accuracy and underlying assumptions.
...
In conclusion, Planck's formula is the more general and accurate description of black body radiation, thanks to its inclusion of energy quantization. Wien's approximation provides a useful simplification for shorter wavelengths but is not sufficient for the entire spectrum.

Can you write the equations side by side?

Planck's Formula   B(ν, T) = (2 * h * ν^3) / (c^2 * (e^(h * ν / (k_B * T)) - 1))
Wien's Approximation   B(ν, T) = (2 * h * ν^3) / (c^2 * e^(h * ν / (k_B * T)))

It seems like planck only adds -1 term to wien's formula.

You're right, at first glance, the equations might seem very similar, with Planck's formula just adding a -1 term to Wien's approximation. However, that seemingly small addition has a profound impact:

The -1 term accounts for quantization: This term incorporates the revolutionary idea that energy can only be emitted or absorbed in discrete packets. This concept of quantized energy levels was a major breakthrough in physics and went beyond the classical framework used in Wien's approximation.

[alancalverd]

Just shows why you shouldn't use ChatGPT as a source of scientific information. It displays all the insight and understanding of a politician.

[hamdani yusuf (OP)]

Just shows why you shouldn't use ChatGPT as a source of scientific information. It displays all the insight and understanding of a politician.

It reflects the quality of training data sources. It seems like it hasn't been equipped with the tools to filter out incorrect statements.

[alancalverd]

My point exactly!

[hamdani yusuf (OP)]

Just shows why you shouldn't use ChatGPT as a source of scientific information. It displays all the insight and understanding of a politician.

It reflects the quality of training data sources. It seems like it hasn't been equipped with the tools to filter out incorrect statements.

When the AI models still depend on their human supervisors to select which data sources are more accurate and reliable than the others, then the quality of those supervisors will determine the quality of responses that they'll produce. Leaving their current mistakes uncorrected will make it harder and more expensive to correct them in the future.

[alancalverd]

So the only trustworthy answers come from human judgement, and may become more trustworthy as humans test their hypotheses by experiment (science) but anything from an AI source may be infected by untruth, and any such infection is potentially malignant because the whole point of AI is that it can collect inputs (including its own output) and synthesise outputs quicker than a human. Which puts AI on a par with religion.

[hamdani yusuf (OP)]

anything from an AI source may be infected by untruth

Human sources are not immune from falsehood either. The probabilities for their occurrence can only be reduced by more check and recheck, compared to observations.

[alancalverd]

But humans tend to conduct experiments or simply ask "does that seem reasonable?"   AI just goes on regurgitating any old rubbish because it doesn't care about the consequences of its output.

[hamdani yusuf (OP)]

But humans tend to conduct experiments or simply ask "does that seem reasonable?"   AI just goes on regurgitating any old rubbish because it doesn't care about the consequences of its output.

But the developers do care about the accuracy of their AI models. It determines whether or not they can get their return of investment.

[alancalverd]

The model may be 100% accurate and quote Donald Trump's authoritative speech to the letter, but I wouldn't want anyone to inject themselves with hydrochloroquinone.

[hamdani yusuf (OP)]

The model may be 100% accurate and quote Donald Trump's authoritative speech to the letter, but I wouldn't want anyone to inject themselves with hydrochloroquinone.

New AI models will be able to filter out misinformation, based on previously accumulated information, and comparison with various other information sources, including their own sensors.

[alancalverd]

If all the previously accumulated information is the Bible, AI will reject any scientific statement as unreliable and the world will regress to the intellectual level of the Republican Party.

Science is all about challenging consensus, not nurturing it.

[hamdani yusuf (OP)]

If all the previously accumulated information is the Bible, AI will reject any scientific statement as unreliable and the world will regress to the intellectual level of the Republican Party.

That's a big if. And fortunately it's not true.

[alancalverd]

It was once. Similar problems have been found where all the permitted truth was all in Mao's Little Red Book, or Lysenko's state-approved botany papers.

Problem with the internet as a source is that there is only one right answer to scientific question, but an infinite number of wrong ones, and the internet grants allows them equal weight.

[hamdani yusuf (OP)]

It was once. Similar problems have been found where all the permitted truth was all in Mao's Little Red Book, or Lysenko's state-approved botany papers.

Problem with the internet as a source is that there is only one right answer to scientific question, but an infinite number of wrong ones, and the internet grants allows them equal weight.

It would be harder to censor worldwide openly accessible information sources. Especially with VPN and satellite connection.

Internet doesn't give equal weight for different sources. Traditional search engines like Google prioritize most referred sources.