Also about the Planck hypothesis

[snoopies622]

These questions are rather like the one mahela007 just asked, but are perhaps a little more specific.

I have never clearly understood how the Planck hypothesis (E=nhf for the oscillators of a black body) fits into the later quantum theory of Schrodinger, Heisenberg, et al. Specifically,

1. Since the year 1900 was before the work of Rutherford and Bohr produced a model of the atom that is similar to the familiar, more modern one (massive positive charges surrounded by light, negative ones), what exactly did Planck think was oscillating at frequency f?

2. Solving the Schrodinger equation for a quantum harmonic oscillator yields descrete energy levels separated by nhf. Is this why the Planck hypothesis works? That is, are the restoring forces between atoms/molecules in a solid body Hooke-like (directly proportional to their displacement from an equilibrium position)?

Thanks.

 

[f95toli]

1. Since the year 1900 was before the work of Rutherford and Bohr produced a model of the atom that is similar to the familiar, more modern one (massive positive charges surrounded by light, negative ones), what exactly did Planck think was oscillating at frequency f?

He didn't. He just realized that it fit experimental data. Note, however, that is was well known that there was something wrong with the classical (non-quantized) approach since it gave unreasonable results; meaning Planck had a good reason for trying "strange" approaches.

2. Solving the Schrodinger equation for a quantum harmonic oscillator yields descrete energy levels separated by nhf. Is this why the Planck hypothesis works? That is, are the restoring forces between atoms/molecules in a solid body Hooke-like (directly proportional to their displacement from an equilibrium position)?

Yes and no. The reason why the approach works is ultimately because photons really exist (whatever that means) and are not just "mathematical constructs", it also turns out they have the properties suggested by Planck and Einstein.
There is a mathematical connection between photons and the "restoring force" in atoms/molecules but the very same connection holds for many other systems. There are a huge number of systems that behave approximately like harmonic oscillators as long as the deviation from equilibrium is small (it is easy to see way if you Taylor expand some common potentials), atoms/molecules are just one example.

 

[snoopies622]

...what exactly did Planck think was oscillating at frequency f?

He didn't. He just realized that it fit experimental data.

So to Planck the f only referred to the frequency of the emitted electromagnetic radiation - and yet he didn't believe that light itself was quantized?

 

[kote]

So to Planck the f only referred to the frequency of the emitted electromagnetic radiation - and yet he didn't believe that light itself was quantized?

I'm going to copy and paste from my thesis here:

In his book, Black-Body Theory and the Quantum Discontinuity 1894 – 1912, Thomas Kuhn discusses the history of the discontinuity, or incompatibility, between quantum and classical mechanics. Kuhn claims that Planck did not recognize quantum mechanics as a new and incompatible theory until nearly a decade after first introducing the quantum concept. Kuhn writes, “Planck himself did not publicly acknowledge the need for discontinuity until 1909, and there is no evidence that he had recognized it until the year before.” James Cushing agrees and writes, “For several years he attempted to fit this new approach into the framework of classical physics, but he finally accepted the reality of quanta.”​

In the same book, Kuhn cites Einstein as introducing the concept of a quantized light-particle in 1906, 3 years before Planck admitted the possibility that such a move away from continuous classical concepts had to be made. Kuhn, regarding this move by Einstein, states, “In a sense, it announces the birth of the quantum theory.”

Edit: I forgot I had some Planck quotes in here too...

Planck, when first proposing the quantization of exchanges of energy with black bodies, offered no interpretation at all. Commenting on his experimentally perfect black body equation, Planck stated that “it could not be expected to possesses more than a formal significance.” He also wrote, “on the very day when I formulated this law, I began to devote myself to the task of investing it with a true physical meaning.”​

 

[Naty1]

Kote's post # 4 tracks with what I have read...that Planck introduced/discovered the mathematical concepts...but Einstein understood the physical phenomena related to theoretical discreteness...that the frequency (color) of light not its total energy controls the ejection of electrons in the photoelectric effect

that's why eventually discrimination the of the day was overcome and Einstein was finally awarded a Nobel... for the photoelectric effect...

 

[f95toli]

So to Planck the f only referred to the frequency of the emitted electromagnetic radiation - and yet he didn't believe that light itself was quantized?

My guess was that he didn't believe anything at first. It is not at all uncommon for scientist to FIRST discover that an expression fits experimental data and THEN figure out what that expression means physically. It is very possible that he simply one day said to himself: "Hmm, I wonder what happens if I let the energy be equal to some constant times the frequency".
Keep in mind here that Planck's constant (obviously) wasn't known at the time, meaning h was -as far as Planck was concerned- initially just a phenomological constant whose value he picked so that his expression matched experimental data.

 

[kote]

My guess was that he didn't believe anything at first.

See above. No need to guess .

 

[snoopies622]

I ask question (1) because my introductory physics books describe the Planck hypothesis as referring to "oscillators", "atomic oscillators", "atomic vibrators", etc. without going into any detail as to what these oscillating things actually are, so I was wondering what Planck himself had in mind. I don't have a copy of his original paper. Has anyone read it?

 

[jtbell]

You have to keep in mind that in Planck's day, physicists knew very little about the structure of matter. The electron had only recently been discovered, and physicists were trying to figure out how to arrange it together with positive charge in a way that would produce stable neutral matter.

They did know, from Maxwell's Equations, supported by experiments by Hertz etc., that oscillating charges produce electromagnetic waves. So it was reasonable for them to assume that light originates in some kind of oscillating-charge phenomenon in matter. In the case of electromagnetic radiation inside a cavity (black-body radiation), those oscillators would have to be in the walls of the cavity. They could take that idea and develop predictions from it, even though they didn't know exactly what those oscillators were.

 

[conway]

I ask question (1) because my introductory physics books describe the Planck hypothesis as referring to "oscillators", "atomic oscillators", "atomic vibrators", etc. without going into any detail as to what these oscillating things actually are, so I was wondering what Planck himself had in mind. I don't have a copy of his original paper. Has anyone read it?

I'm going to put in my two cents here because I don't think this question has been properly answered yet. They key point here is thermodynamics. Thermodynamic laws don't depend on the specific property of any material. So we are free to imagine any material with physically plausible properties, and the laws of thermodynamics should apply to that material. Specifically, the equilibrium energy distribution of radiation within a cavity should be the same no matter what material object is assumed to mediate the distribution. It can be a real atom or it can be a tiny imaginary charged mass-on-a-spring. That is the basis of Planck's approach: that for the purpose of analysis, it doesn't matter if you use real atoms or imaginary oscillators.

By the way, Schroedinger's disccovery twenty-six years later finally showed that the harmonic oscillator is a good model for the atom.