Did Planck think the light emitted from black bodies to be quantised?

[pkc111]

However I need to know whether Planck also had to assume that emitted light was quantised to make his model work? I need to teach this topic in the context of how different experiments shaped our understanding of the light model. I have found 2 sources which seem to contradict each other:(

This one says he didnt assume the light was quantised: https://en.wikipedia.org/wiki/Planc...rBpNiBO6CR8o2mZNXzPXNf67mCDfD6LYNWWyiFCkHz5dk

This one seems to say he did: https://en.m.wikipedia.org/wiki/Ult...X5HUoENqcfb4nCjJDEEtgFi5PD8z3CUr1Bc7D_k_hwrg4 Many thanks

 

[Delta2]

I am not an expert in this but the way I know it, Einstein was the first that argued that light is quantized.

Planck argued something in between (a semiclassical model for light) that light seems to be quantized only during its interaction with matter(that is when it is absorbed or emitted by matter), and when light doesn't interact with matter and it travels in free space it behaves as a classical wave.

 

[vanhees71]

Planck was very reluctant against his own discovery. As a very conservative men he tried for the rest of his life to somehow describe his radiation law from classical physics.

The history is very interesting: The question about the correct blackbody radiation law, which was known to be a universal function of temperature alone, i.e., independent of the material of the cavity walls. That's and because it's about thermodynamics is, why Planck got interested in it in the first place. He already investigated the problem for many years before 1900. The breakthrough came in this year, because at the Physikalisch Technische Reichsanstalt Kurlbaum et al measured the black-body spectrum over a large interval of wavelengths and at various temperatures. Their motivation was to find an accurate measure for the luminosity of all kinds of light sources (gas as well as the very new electric lightning), and there the black-body radiation is an ideal candidate, because it's universal. Planck's first paper, delivered at the academy of sciences, was phenomenological. Ingneously he interpolated between two expressions for the entropy leading to the Raleigh-Jeans and the Wien law for low/high frequencies, from which the correct radiation law, valid for all frequency ranges followed. Then he wanted to get a theoretical derivation from Maxwell electrodynamics and thermodynamics. In his earlier works he already worked out the idea that he can use the most simple model for the container walls, i.e., harmonic oscillators and investigated the exchange of radiation energy with these oscillators. Then he used (also reluctantly, because he was rather a proponent of the phenomenological thermodynamics than of kinetic theory a la Boltzmann) statistical physics to get the radiation law. The ingenious idea indeed was to first "quantize the energy". From the generally valid Wien-displacement law it's clear that the energy quanta must be in multiples of $\hbar \omega$ (where $\hbar$ is the modern name for his new fundamental constant, the quantum of action; he rather wrote $h f$). The other ingenious idea was to use a stochastics of how to distribute wave modes over the oscillators to count the microstates, thereby introducing the famous formula $S=k_{\text{B}} \ln \Omega$, in a way we call today "Bose-Einstein statistics". Of course his idea was to make the discrete energy quanta continuous again at the end of the calculation, but he found that he only got the correct radiation law leaving the energy quantized in the specific way he did, based on the Wien displacement law. Reluctantly Planck accepted the finding that electromagnetic energy of radiation at a certain frequency seems to be exchanged with matter in discrete quanta of the size $\hbar \omega$, but he never accepted Einstein's light-quanta hypothesis.

In a sense Planck was right, seen from the modern perspective, where we have (cavity) QED at hand. Einstein's idea that light quanta can be interpreted as localized point-like particles is flawed in any respect. Particularly in the case of black-body radiation when realized as thermal radiation within a cavity that's a completely wrong picture, but the photons describe quantized energy eigenmodes of the quantized electromagnetic field, and these eigenmodes lead not to locally peaked energy-density distributions but these are spread over the entire cavity.

 

[pkc111]

Interesting thank you vanhees71.
Im not sure how Planck could have stopped at modelling the energy being released from matter in discrete packets, and in particular reconciled that with a view that the light energy was being released as a wave? How else could he have imagined the light energy leaving the matter in that way other than as photons? Would he have imagined them as wave pulses? would the pulses then join up to form a continuous wave that left the material?

 

[pkc111]

I am not an expert in this but the way I know it, Einstein was the first that argued that light is quantized.

Planck argued something in between (a semiclassical model for light) that light seems to be quantized only during its interaction with matter(that is when it is absorbed or emitted by matter), and when light doesn't interact with matter and it travels in free space it behaves as a classical wave.

Thanks Delta2 that makes sense.

 

[vanhees71]

Interesting thank you vanhees71.
Im not sure how Planck could have stopped at modelling the energy being released from matter in discrete packets, and in particular reconciled that with a view that the light energy was being released as a wave? How else could he have imagined the light energy leaving the matter in that way other than as photons? Would he have imagined them as wave pulses? would the pulses then join up to form a continuous wave that left the material?

That was a big trouble for Planck. First he introduced the discrete energy exchange between matter and em. field as a calculational tool and then realized that he had to keep it quantized in order to get his radiation law which he knew to be in complete agreement with the high-precision measurements of Rubens and Kurlbaum.

It was Einstein, who introduced in one of his famous papers of 1905 the "heuristic point of view" of "light quanta". Famously, Planck wanted to hire Einstein somehow to Berlin, because of his relativity theory and for sure also his work on fluctuations in thermodynamics (among which is the famous paper about Brownian motion also of 1905). He felt he had to find excuses for Einstein's light-quantum paper. He argued that a young man as Einstein was must also be allowed to be courageous and make some bold claims ;-).

As I wrote above, I think, Planck was partially right, because today we know that the idea of photons as point-like particle objects is completely wrong. They are certain states of the quantized electromagnetic field (one-photon Fock states), and these indeed do not have an interpretation in terms of localizable objects. Photons in this modern sense do not even have a proper position observable! The particle-like aspects, i.e., the discreteness of registering photons with, e.g., a photoplate is rather an effect of the interaction of the em. field with matter, and this is indeed all Planck needed to assume. From the modern point of view of QED all there is as a well-defined localization of a photon is the probability to have an interaction event with a detector at the place defined by the latter. This probability is proportional to the energy density of the electromagnetic field, which indeed is a proper (gauge-invariant and local!) observable within QED. This follows immediately from the fact that most photodetectors work with the photoeletric effect, i.e., a photon gets absorbed by an atom making within the detector. This can be described in the well-known way in first-order perturbation theory in the electric-dipole approximation, which immediately shows that the detection probability for a single photon at a given place (with always finite position resolution of course) is proportional to the energy density of the electromagnetic field.

I think there's not a single subject in "modern physics" that's more misrepresented by popular-science and sometimes even by introductory university textbooks than the idea of photons!

 

[pkc111]

Amazing ! thanks vanhees71
If light was imagined to leave with energies of discrete amounts, how did he end up with a continuous blackbody curve as a predicted result (rather than a series of points)?

 

[vanhees71]

The discrete amounts refer to radiation of a given frequency. The frequency is continuous. It can take any positive real value.

 

[Mister T]

Summary:: I understand that he solved the ultraviolet catastrophe by assuming that the atoms were oscillators permitted to vibrate at particular frequencies. I understand that he also had to dismiss the equipartition model assumptions to make his model work.

I need to teach this topic in the context of how different experiments shaped our understanding of the light model.

It's best to use the photoelectric effect to teach beginners about the quantization of light. The blackbody issue is by far more difficult to understand.

 

[vanhees71]

No, that's the worst approach. The photoelectric effect is entirely explained by the semiclassical theory, i.e., a classical electromagnetic wave field interacting with a bound electron and calculating the transition probability rate for a transition to a scattering state.

If you have QED at hand, and that's the ONLY legitimate way to treat photons in the 21st century, the blackbody case is a piece of cake. It's just summing a geometric series!