What is the blackbody problem and the ultraviolet catastrophe?

[kweba]

Hello! I'm trying to research about the history and development of Quantum theory, especially with regards to Max Planck's energy quanta.

I don't understand what was the problem in classical physics that required Planck to formulate quantum theory/energy quanta, which seemed to have revolutionized physics at the time.

I read about the blackbody radiation problem and the ultraviolet catastrophe that Planck had tackled on, but I'm having a hard time understanding it. All I could pick up is about some infinite energy in the body's system when it absorbs all incoming radiation. I don't know if that's even right.

Anyway, if somebody could explain it to in layman's terms (if possible, with analogies), as I don't really have a working technical knowledge of physics and mathematics. Thanks you very much!

 

[256bits]

According to Wiki
http://en.wikipedia.org/wiki/Ultraviolet_catastrophe
Plank did not develop his theory in response.

Many popular histories of physics, as well as a number of physics textbooks, present an incorrect version of the history of the ultraviolet catastrophe. In this version, the "catastrophe" was first noticed by Planck, who developed his formula in response. In fact Planck never concerned himself with this aspect of the problem, because he did not believe that the equipartition theorem was fundamental – his motivation for introducing "quanta" was entirely different. That Planck's proposal happened to provide a solution for it was realized much later, as stated above.[3] Though this has been known by historians for many decades, the historically incorrect version persists, in part because Planck's actual motivations for the proposal of the quantum are complicated and difficult to summarize to a lay audience.

So, for historical accuracy, you might want to investigate that aspect.

 

[ShayanJ]

Here's the Planck's paper.
And here's a paper which may be useful.

 

[kweba]

according to wiki
http://en.wikipedia.org/wiki/ultraviolet_catastrophe
plank did not develop his theory in response.

Many popular histories of physics, as well as a number of physics textbooks, present an incorrect version of the history of the ultraviolet catastrophe. In this version, the "catastrophe" was first noticed by Planck, who developed his formula in response. In fact Planck never concerned himself with this aspect of the problem, because he did not believe that the equipartition theorem was fundamental – his motivation for introducing "quanta" was entirely different. That Planck's proposal happened to provide a solution for it was realized much later, as stated above.[3] Though this has been known by historians for many decades, the historically incorrect version persists, in part because Planck's actual motivations for the proposal of the quantum are complicated and difficult to summarize to a lay audience.

So, for historical accuracy, you might want to investigate that aspect.

I knew I was being inaccurate somehow and was missing something, thank you!

So the blackbody problem/UV catastrophe had nothing to do with Planck and the development of "quanta"?

But still, my question remains, what was the motivation of Planck behind introducing the concept of "quanta"? Did it stil have something to do with rising problems in classical physics? I know you said in your quote that Planck's actual motivations are difficult to explain to a lay audience, but maybe you (or somebody out there :D) could give a general idea? Thanks so much, sorry for my persistence. :)

 

[kweba]

Here's the Planck's paper.
And here's a paper which may be useful.

Thank you very much! This is a great article! Happened to also come across this at their website: http://physicsworld.com/cws/article/print/2000/dec/01/max-planck-the-reluctant-revolutionary

Why was he called the "reluctant revolutionary?", just to be sure?

 

[ShayanJ]

Thank you very much! This is a great article! Happened to also come across this at their website: http://physicsworld.com/cws/article/print/2000/dec/01/max-planck-the-reluctant-revolutionary

Why was he called the "reluctant revolutionary?", just to be sure?

I think its because some of the views that Planck was opposing,are widely accepted views nowadays.

 

[kweba]

Okay, I think I just found the answer to my own question from this website/blog:

http://www.daviddarling.info/encyclopedia/Q/quantum_theory_origins.html

As it turned out, Max Planck was really "into" the concept of Entropy and the 2nd law of Thermodynamics, and the Time's arrow (the Universe only going forward in one direction); and that he doubted the existence of atoms (which is pretty ironic considering the concept of "quanta").

To quote the site/blog post:

http://www.daviddarling.info/encyclopedia/Q/quantum_theory_origins.html]...Planck[/PLAIN] had held the chair in theoretical physics at the University of Berlin since 1889, specializing in thermodynamics...
...For Max Planck, the second law and the concept of entropy held an irresistible attraction – the prospect of an ultimate truth from which all other aspects of the external world could be understood. These ideas formed the subject of his doctoral dissertation at Munich and lay at the core of almost all his work until about 1905. It was a fascination that impelled him toward the discovery for which he became famous.
...His unswerving belief in the absoluteness of the entropy version of the second law, which he shared with few others, left him in a small minority in the scientific community. It also, curiously, led him to doubt the existence of atoms, and that was another irony given how events turned out.

Like other scientists of his day, Planck was intrigued by why the universe seemed to run in only one direction, why time had an arrow, why nature was apparently irreversible and always running down. He was convinced that this cosmic one-way street could be understood on the basis of the absolute validity of the entropy law.
...In fact, as early as 1882, Planck decided that the atomic model of matter didn't jibe with the law of entropy.

Anyway, it did has "indirectly" something to do with blackbody, but Planck's true motivation behind the concept of "quanta" was to provide a link between irreversibility and the absolute nature of entropy, by using the blackbody formula:

http://www.daviddarling.info/encyclopedia/Q/quantum_theory_origins.html]...While[/PLAIN] a student at Berlin from 1877 to 1878, Planck had been taught by Gustav Kirchhoff who,...proved that the amount of energy a blackbody radiates from each square centimeter of its surface hinges on just two factors: the frequency of the radiation and the temperature of the blackbody. He challenged other physicists to figure out the exact nature of this dependency: What formula accurately tells how much energy a blackbody emits at a given temperature and frequency?

Experiments were carried out, using apparatus that behaved almost like a blackbody (a hot hollow cavity with a small opening), and equations were devised to try to match theory to observation...The sticking point was to find a formula, rooted in known physics, that matched these experimental curves across the whole frequency range.

Planck believed that such a formula might provide the link between irreversibility and the absolute nature of entropy: his scientific holy grail.

So is this right? Planck's goal was to study more about Entropy and the arrow of time, and its related concepts?

Finally, Planck's "quanta" was not in fact a direct response to the Ultraviolet Catastrophe:

http://www.daviddarling.info/encyclopedia/Q/quantum_theory_origins.html]One[/PLAIN] of the myths of physics, which is echoed time and again in books, both academic and popular, and in college courses, even today, is that Planck's blackbody formula had something to do with what's called the "ultraviolet catastrophe."...The name "ultraviolet catastrophe,"...wasn't coined until 1911 by the Austrian physicist Paul Ehrenfest. None of this had any bearing on Planck's blackbody work. Planck hadn't heard of Rayleigh's June 1900 comments when he came up with his new blackbody formula in October In any case, it wouldn't have mattered: Planck didn't accept the equipartition theorem as fundamental. So the "ultraviolet catastrophe," which sounds very dramatic and as if it were a turning point in physics, doesn't really play a part in the revolution that Planck ignited.

But Planck's formulation of the "quanta" and the Planck's Constant & Law, did turn out to resolve the UV Catastrophe issue (accidentally, if that's safe to say)?

 

[256bits]

That is a Wiki quote - their words, not mine.

This should give you an insight and make some sense out of it, contrary to what wiki says.
http://www.daviddarling.info/encyclopedia/Q/quantum_theory_origins.html

a few paragraphs down,

One of the myths of physics, which is echoed time and again in books, both academic and popular, and in college courses, even today, is that Planck's blackbody formula had something to do with what's called the "ultraviolet catastrophe." It didn't. This business of the ultraviolet catastrophe is a bit of a red herring (to mix colorful metaphors), worthwhile mentioning here only to set the record straight. In June 1900, the eminent English physicist Lord Rayleigh (plain John Strutt before he became a baron) pointed out that if you assume something known as the equipartition of energy, which has to do with how energy is distributed among a bunch of molecules, then classical mechanics blows up in the face of blackbody radiation. The amount of energy a blackbody emits just shoots off the scale at the high frequency end – utterly in conflict with the experimental data. Five years later, Rayleigh and his fellow countryman James Jeans came up with a formula, afterward known as the Rayleigh-Jeans law, that shows exactly how blackbody energy is tied to frequency if you buy into the equipartition of energy. The name "ultraviolet catastrophe," inspired by the hopelessly wrong prediction at high frequencies, wasn't coined until 1911 by the Austrian physicist Paul Ehrenfest. None of this had any bearing on Planck's blackbody work. Planck hadn't heard of Rayleigh's June 1900 comments when he came up with his new blackbody formula in October In any case, it wouldn't have mattered: Planck didn't accept the equipartition theorem as fundamental. So the "ultraviolet catastrophe," which sounds very dramatic and as if it were a turning point in physics, doesn't really play a part in the revolution that Planck ignited.

Mostly Planck was trying to work from a thermodynamics point of view and comprise entropy and the second law. The breakdown of Wein's law for a blackbody gave him impetus for his endevour. He actually was not trying to solve the ultraviolet catastrophe per se - it just so happened that he did. It is ironic that Planck, who did not believe in tiny bits of matter called atoms, actually proved that energy came in tiny bits, subsequently called quanta.

EDIT: I see you found the same reference.

 

[kweba]

I think its because some of the views that Planck was opposing,are widely accepted views nowadays.

Or maybe is it because Planck himself was not even sure what his suggestion of quantum energy had meant?

Because he "really did not give it much thought" except to bring a positive result, and that he didn't see his work at the time as representing any kind of threat to classical mechanics or electrodynamics. That's why some historians question whether Planck really ought to be considered the founder of quantum theory, that it wasn't until years later when the "physical"concept of energy quanta was fully realized, when Albert Einstein published his Nobel-winning work on the Photoelectric effect (where he quantized light as packets called photons).

To quote:

http://www.daviddarling.info/encyclopedia/Q/quantum_theory_origins.html]...Physicists,[/PLAIN] especially Planck (the "reluctant revolutionary" as one historian called him), didn't quite know what to make of this bizarre suggestion of the graininess of energy. In truth, compared with all the attention given to the new radiation law, this weird quantization business at its heart was pretty much overlooked. Planck certainly didn't pay it much heed. He said he was driven to it in an "act of despair" and that "a theoretical interpretation had to be found at any price." To him, it was hardly more than a mathematical trick, a theorist's sleight of hand. As he explained in a letter written in 1931, the introduction of energy quanta was "a purely formal assumption and I really did not give it much thought except that no matter what the cost, I must bring about a positive end." Far more significant to him than the strange quantum discontinuity (whatever it meant) was the impressive accuracy of his new radiation law and the new basic constant it contained. This lack of interest in the strange energy elements has led some historians to question whether Planck really ought to be considered the founder of quantum theory. Certainly, he didn't see his work at the time as representing any kind of threat to classical mechanics or electrodynamics. On the other hand, he did win the 1918 Nobel Prize in Physics for his "discovery of energy quanta." Perhaps it would be best to say that Planck lit the spark and then withdrew. At any rate, the reality of energy quanta was definitely put on a firm footing a few years later, in 1905 – by the greatest genius of the age, Albert Einstein.

Source:
http://www.daviddarling.info/encyclopedia/Q/quantum_theory_origins.html

 

[kweba]

That is a Wiki quote - their words, not mine.

Point taken, thanks. But where can we find reliable sources? I checked out the Wikipedia page, and it led me to an "offical" article by Physics world: http://physicsworld.com/cws/article/print/2000/dec/01/max-planck-the-reluctant-revolutionary , which is the same article Shyan posted above as PDF.

This should give you an insight and make some sense out of it, contrary to what wiki says. http://www.daviddarling.info/encyclopedia/Q/quantum_theory_origins.html

EDIT: I see you found the same reference.

Thanks :D Yes, I'm as surprised as you are. Too bad there are only few written works/articles about this subject made available online. Seemed we must have come across it coinidentally from the search engines.

Mostly Planck was trying to work from a thermodynamics point of view and comprise entropy and the second law.

I see. This is also from the "daviddarling" source:

Planck believed that such a formula (blackbody) might provide the link between irreversibility and the absolute nature of entropy: his scientific holy grail.

But what was the "problem" or "idea" about Entropy/2nd law of Thermo, that he intended to "solve" or "achieve"?

The breakdown of Wein's law for a blackbody gave him impetus for his endevour. He actually was not trying to solve the ultraviolet catastrophe per se - it just so happened that he did.

I see thanks! Helped a lot.

Our source also explained it in detail: (Note the bold's)

"..Wien's law" agreed well with the experimental data that had been gathered up to that point and it drew the attention of Planck who time and again, tried to reach Wien's formula using the second law of thermodynamics as a springboard. It wasn't that Planck didn't have faith in the formula that Wien had found. He did. But he wasn't interested in a law that was merely empirically correct, or an equation that had been tailored to fit experimental results. He wanted to build Wien's law up from pure theory and thereby, hopefully, justify the entropy law.In 1899, Planck thought he'd succeeded. By assuming that blackbody radiation is produced by lots of little oscillators like miniature antennae on the surface of the blackbody, he found a mathematical expression for the entropy of these oscillators from which Wien's law followed.

...By the autumn of 1900, it was clear that Wien's law broke down at lower frequencies – ...and beyond. On that fateful afternoon of October 7, Herr Doktor Rubens and his wife visited the Planck home and...gave Planck the bad news about Wien's law. After his guests left, Planck set to thinking where the problem might lie. He knew how the blackbody formula...had to look mathematically at the high-frequency end of the spectrum given that Wien's law seemed to work well in this region. And he knew, from the experimental results, how a blackbody was supposed to behave in the low-frequency regime. So, he took the step of putting these relationships together in the simplest possible way. It was a guess, no more – a "lucky intuition," as Planck put it – but it turned out to be absolutely dead on. Between tea and supper, Planck had the formula in his hands that told how the energy of blackbody radiation is related to frequency. He let Rubens know by postcard the same evening and announced his formula to the world at a meeting of the German Physical Society on October 19."

Is it true that he just "guessed" the formula, without formal derivation or possibly rigorous math proofing?

He actually was not trying to solve the ultraviolet catastrophe per se - it just so happened that he did.

Oh wow okay, that's so cool for Planck! (forgive my rather informal/juvenile-like remark). I see now why they chose the UV Issue as a historical basis to introduce and explain Planck's physics.

But anyway, I still don't understand the problem behind the UV Issue, and how his quantum energy had resolved it. So maybe, if it's okay with you to explain it to me briefly and simply? I'd appreciate it.

It is ironic that Planck, who did not believe in tiny bits of matter called atoms, actually proved that energy came in tiny bits, subsequently called quanta.

Yes, I find that very ironic, yet also funny.

Thanks very much for posting and your help!

 

[256bits]

Loosely described, and baring the actual physics, which I think you can look up Wein, Raleigh, and some of the other terms that you have seen, it became apparent that a radiating body due to the classical investigation of radiation, that a blackbody should emit energy at all wavelengths, and more so at the shorter wavelengths on into an emission of energy on into infinity. Of course, if you take a blackbody, the emission spectrum does not behave that way, but has a peak at a certain frequency, and falls lower at higher and lower wavelengths.

Wiki uses an analogy as a vibrating string, onto of which countless standing waves could be imposed, with each standing wave wavelength, or frequency, if you prefer, as having equal energies. The string would then have limitless energy as the number of standing waves would also be limitless.

You could relate it to sound waves also. A musical instrument giving a note, emits that note, and harmonics, the strength of which is less than the previous harmonic (or note). The sound level of the harmonic(s) decays the farther it is from the basic note. That is the reality.

For an "ultraviolet catastrophe" of the musical instrument, each harmonic would not be at a lessor strength but of the same level as the basic note. Since there are many harmonics, a musician playing an "ultraviolet catastrophe" musical instrument, would have the sound levels of each harmonic add ( which is not additive in the usual sense but of some formula ), and you and your fellow audience members would not enjoy having your eardrums burst with a high decibel output.

For sure there are some analogical errors there, but I hope you get the sense of it.

PS. Re-reading that, it sounds like someone writing from the 1880's

 

[jtbell]

<nitpick> That guy's name was Wien, not Wein. </nitpick>

 

[hjelmgart]

Hehe, I think we once derived both results in a statistical mechanics class, the Rayleigh-Jean and Plancks law. I think deriving them will let you understand why one is wrong and the other isn't - or just finding the deriviation in a book with some good explanations, of why they did as they did, and which assumptions they made (and thus which were wrong).

 

[256bits]

<nitpick> That guy's name was Wien, not Wein. </nitpick>

Ha. That's a hooch. How did any grapes get tossed in there?

( yes. I looked up wein - grape, wine in german and Yidish )