Blackbody Radiation: Explaining Integer Frequencies

[BioMatrix]

I guess this is supposed to be here... I dunno. Anyhoo, I understand this concept intuitively, but why do frequencies have to have integer values? Is that true of all waves, or just electromagnetic waves? Could a wave have 33.43 Hz, for example? Please explain!

 

[chroot]

Whoever said that all frequencies were integers?!

The second is an arbitrarily defined unit, after all -- if mankind chose a different length of time for a unit, the numerical value of all frequencies would change.

What's quantized is the energy in each photon, in units of h-bar, which is a fundamental unit like G or alpha. Frequencies are not quantized to integral Hz.

- Warren

 

[BioMatrix]

So you're saying that only frequency in terms of Planck's constant is necessarily integral?

 

[lalbatros]

All sorts of photon are possible: any frequency or wavelength.
But the light -or electromagnetic- energy can only go by chunks, called photons. This chunk of energy depends on the color -or frequency- of the photon(s):

E(one chunk) = hf​

If you measure (count more properly) the energy in the basket for photons of frequency f , you can only find an integer number of chunks "hf" for these sort of photons. That means the energy will be

E(basket) = n E(one chunk) = n hf​

where n can only be an integer number.

For human beings, photons are very small quantities of energy. Even the gamma-rays photons have very small energies compared to the energies involved in our human lifes. A small light that can be observed by naked eye usually emits a huge number of photons. Still photons can be detected individually with special equipments.

Michel

 

[BioMatrix]

If you measure (count more properly) the energy in the basket for photons of frequency f , you can only find an integer number of chunks "hf" for these sort of photons. That means the energy will be

E(basket) = n E(one chunk) = n hf​

where n can only be an integer number.

So energy must be an integral value in terms of h*f, but f can be whatever? I was under the impression that frequency could be integral values in terms of the Planck length, i.e., it couldn't be 2.3 Planck lengths / s. This is because the .3 Planck lengths has no meaning, as 1 Planck length is the smallest length that has any meaning.

 

[lalbatros]

BioMatrix,

The "planck length" has nothing to do with the black body radiation story neither with the basics of quantum mechanics. The "planck length" comes on stage when one tries to unify all current theories of physics, because somehow space may then also show some quantum behaviour. Only very extreme physical situation are involved.

Now, concerning the frequencies. Note that in many familar situations they also need to be related to integer multiples. But this is another story:

Take a string from a guitar for example. You can look at the oscillations of the string with a stroboscope tuned on the oscillation frequency. What you will see is an integer number of oscillations on the length of the string. At both ends, the string cannot oscillate, and in between it will show an integer number of stationary waves. You will also be able to see the harmonics by tuning the stroboscope on multiples of the 'fundamental' frequency.

There are many similar systems in physics, specially in electronics and optics. Concerning the blackbody radiation, this come theoretically into play also because the light inside the "oven" for this experiment is constrained in a way very similar to the string of a guitar in between the walls. However, this does not play any real role in the end. This is because this constraint cuts off the possibility of black-body radiation in the very low frequency domain (wavelengths larger than the oven inside). The radiations that made the history of physics with the BB radiation where in the visible range, rather short wavelength. To understand the measured spectra emitted by a (black body) oven, Planck had to introduce the famous formula E=hf and assumes that only chunks (called photons later) can exist in the radiation.

Note, however, that at low temepratures this 'size' effect may come into play since the wavelengths considered then are large. For example this may be of interrest when studying thermal noise in radar(-like) systems (in atronomy for example). Radars work with frequencies much lower than visible light.

Michel

 

[CarlB]

In this world, it's going to be difficult to distinguish between some of these things. Integers are very exact mathematical objects. Since the universe is finite in size and has only existed for a finite length of time, it is not possible to create photons with frequencies that are exact, in ratios or any way else.

Carl