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From: tomyee3@gmail.com (ProkaryoticCaspaseHomolog)
Newsgroups: sci.physics.relativity
Subject: Re: Want to prove =?UTF-8?B?RT1tY8KyPyBVbml2ZXJzaXR5IGxhYnMgc2hvdWxkIHRy?=
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Date: Thu, 28 Nov 2024 17:50:52 +0000
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On Thu, 28 Nov 2024 3:23:14 +0000, Ross Finlayson wrote:

> On 11/27/2024 04:09 PM, rhertz wrote:
>> On Wed, 27 Nov 2024 4:18:19 +0000, ProkaryoticCaspaseHomolog wrote:
>>
>> <snip>
>>
>>> In class some 55 or so years ago, we derived Planck's Law using
>>> Einstein's method. We also derived various consequences of the law,
>>> including the formula for energy density u. I won't claim that I
>>> would be able to re-derive the formulas without a lot of review, but
>>> the basic skills still lie dormant within my skull. So don't try to
>>> snow me. You are only a former electrical engineer, a highly competent
>>> one, but untrained in physics, as is evident by the types of mistakes
>>> that you have been making.

At the time, our first and second-year physics textbooks were the
Feynman Lectures on Physics. The derivation of Planck's radiation law
will be found in 42-5 of volume one:
https://www.feynmanlectures.caltech.edu/I_42.html

I am unhappy with Feynman's derivation because of a couple of errors
which significantly lessen Einstein's accomplishment:
1) Feynman mistakenly implied that Einstein's derivation was dependent
   on Planck's work. For instance, he stated that Einstein deduced the
   equality of B_nm and B_mn by comparing his equation with Planck’s
   formula: "But Planck has already told us that the formula must be
   (42.12). Therefore we can deduce something: First, that B_nm must
   equal B_mn, since otherwise we cannot get the(e^(ω/kT)−1)."
   Instead, Einstein found that B_nm = B_mn simply results from the
   denominator going to zero as T approaches infinity.
2) Likewise, a second place where Feynman mistakenly implied a
   dependence of Einstein's derivation on Planck's formula was where
   he stated that Einstein obtained the form of A_mn/B_mn by equating
   the numerator of his derivation with Planck’s formula. Instead,
   Einstein obtained the expression for A_mn/B_mn as following
   immediately from Wien's distribution law.

We were the last class to use the Feynman lectures for first and
second year physics. They are a marvelous set of texts, but not
really suited for an introductory course. The next crop of freshmen
used Halliday and Resnick. They are less useful for getting basic
insights into physics and much more useful in learning how to
calculate.

>>> For example, no competent physics student would mix up his units in
>>> the manner that you have been doing.
>>>
>>> No competent physicist would write "ΔT = 2E/(3 PV)" and then claim
>>> that the only thing he did wrong was to leave out n.
>>>
>>> If I do something silly like goof up by a factor of 10, I own up to
>>> my mistake. You seem almost incapable of admitting error.
>>
>> <snip>
>>
>>> I don't see much point in reading an article about radiometry from
>>> somebody who doesn't check his units.
>>>
>>> There are several related terms that should be distinguished.
>>> Radiant exitance (radiant emittance) has units of W/m^2
>>> Spectral exitance in wavelength has units of W/m^3
>>>
>>> The formula u = 4 σ T^4/c, which you claim that I used incorrectly,
>>> has units of Joules/m^3
>>>
>>> They aren't the same thing.
>>
>> <snip>
>>
>>> Your perpetual motion device, whereby you use a 5 W laser to heat
>>> up a 5 cm radius sphere to 707 K, would be quite impressive if it
>>> worked.
>>
>> <snip>
>>
>> I'm sorry that you went mad with my previous post. At any case, it
>> served for you displaying your true colors.

What do you claim those colors to be? I was being plain-spoken in
warning you to _always be skiptical of what ChatGPT tells you._

>> I've been careful to maintain discussions with you, avoiding any
>> downplaying or personal attacks. Quite a different attitude that I have
>> with Paul, which is mostly boy's game interchange insults.

As I stated, I used somewhat harsh language to get you to be more
critical in your thinking. I have always tried to be careful in
attacking the message, never the messenger. With its alluring manner
of stringing together phrases into seemingly authoritative sentences,
ChatGPT has deceived many into thinking that its output can be
trusted. ChatGPT has led many users off precipices. You were merely
a victim of ChatGPT's siren call. Don't be a victim in the future.

>> You are not JUST a physicist either, and you're very far from being one.
>>
>> Here is how you described yourself two years ago:
>>
>> *********************************************************
>> "Posted: Thu, 29 Dec 2022 09:49 by: Prokaryotic Capase H
>>
>> Hey, don't knock Halliday & Resnick! That's about as far as -I- ever
>> got, since my undergraduate degree was in biology. In graduate school, I
>> studied molecular biology, and for my postdoc, I studied bacterial
>> replication origins. I've spent the last quarter century in software
>> engineering, and my favorite websites are ....."
>> ********************************************************
>>
>> Your comments:
>>
>> "For example, no competent physics student would mix up his units in
>> the manner that you have been doing".
>>
>> "You seem almost incapable of admitting error."
>>
>> "So don't try to snow me. You are only a former electrical engineer..."
>>
>> "Your perpetual motion device, whereby you use a 5 W laser to heat
>> up a 5 cm radius sphere to 707 K, would be quite impressive if it
>> worked."
>>
>>
>> show how far are you willing to go in the heat of a discussion: You LIED
>> (I told you that the 707 K were from a ChatGPT, not me. I CONSULTED YOU
>> ABOUT IT, and you didn't care),

I was upset that you didn't realize the absurdity yourself. You were
still in ChatGPT's thrall, and only harsh language would serve to
shake you out of it.

>> you downplayed me and, for worse, you
>> are somehow PRETENDING that you're closer to physics than me.
>>
>> Actually, I'm not just an engineer. I have also two master degrees, and
>> I didn't pursue a PhD because I considered it was A STUPID THING TO DO,
>> even when many advised me to go for it. I'm not a person that lives from
>> flashing academic degrees or achievements. Furthermore, I'm sure that,
>> in the last 50 years, the number of theoretical and experimental
>> realizations that I did EXCEED yours by 10x. I was a prolific achiever,
>> but I never wanted to show off it, nor at the university or places of
>> work. I refused to publish for general audience, as I didn't want to
>> seek for fame/glory. I'm THE ONLY JUDGE that I accept, and I'm immune to
>> any praise or prize since I was a little kid.

For what it's worth, a paper that I wrote 35+ years ago and which was
ignored for many years has in the last decade received more citations
that in all the years previous, because the satellite DNA that I
discovered has proven useful in genetic engineering.

>> I'm going to tell this one more time, because it's the center of the
>> problem:
>>
>>
>> Using a modified Stefan's formula (by 4/c) to calculate the internal
>> temperature of a small aluminum cavity IS AN ABERRATION OF COMMON SENSE.

You don't get the radiation density formula by simply multiplying the
Stefan-Boltzmann equation by 4c.

As seen in Wikipedia, you start with Planck's equation which gives
the spectral radiance of black body radiation. The MKS units of
spectral radiance (in terms of frequency) are watts per steradian
per square meter per hertz (W·sr^-1·m^-2·Hz^-1)

You get the energy density at a given frequency by accounting for the
spectral radiance in all directions 4π. You get the energy density
by dividing the energy flux by c.
u_ν = 4π/c B_ν

Integrate this over all frequencies to get the total energy density u.
After simplifying the expression, WolframAlpha handles the integration
easily. Un-simplify the integration result, and you are back to a bit
of a mess which you can resolve by collecting all the messy stuff
into the "radiation constant" denoted by the letter "a", which is
closely related to the Stefan-Boltzmann constant "σ".

So that's where you get
u = aT^4 = 4σT^4/c
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