Incoming links: From first principles
- The Quantum Story by Jim Baggott (2011) page 10 mentions:and the footnote comments:
Early examples of such cavities included rather expensive closed cylinders made from porcelain and platinum.
- 1859-60 Gustav Kirchhoff demonstrated that the ratio of emitted to absorbed energy depends only on the frequency of the radiation and the temperature inside the cavity
- 1896 Wien approximation seems to explain existing curves well
- 1900 expriments by Otto Lummer and Ernst Pringsheim show Wien approximation is bad for lower frequencies
- 1900-10-07 Heinrich Rubens visits Planck in Planck's villa in the Berlin suburb of Grünewald and informs him about new experimental he and Ferdinand Kurlbaum obtained, still showing that Wien approximation is bad
- 1900 Planck's law matches Lummer and Pringsheim's experiments well. Planck forced to make the "desperate" postulate that energy is exchanged in quantized lumps. Not clear that light itself is quantized however, he thinks it might be something to do with allowed vibration modes of the atoms of the cavity rather.
- 1900 Rayleigh-Jeans law derived from classical first principles matches Planck's law for low frequencies, but diverges at higher frequencies.
Black-body Radiation Experiment by sciencesolution (2008)
Source. A modern version of the experiment with a PASCO scientific EX-9920 setup.The opposite of from first principles.
And most important of all: you should not start learning phenomena by reading the from first principles derivation.
Instead, you should see what happens in experiments, and how matches some known formula (which hopefully has been derived from first principles).
Only open the boxes (understand from first principles derivation) if the need is felt!
E.g.:
- you don't need to understand everything about why SQUID devices have their specific I-V curve curve. You have to first of all learn what the I-V curve would be in an experiment!
- you don't need to understand the fine details of how cavity magnetrons work. What you need to understand first is what kind of microwave you get from what kind of input (DC current), and how that compares to other sources of microwaves
- lasers: same
Physics is all about predicting the future. If you can predict the future with an end result, that's already predicting the future, and valid.
Two equations derived from first principles by Brian Josephson that characterize the device, somewhat like an I-V curve:where:
- : Josephson current
- : the Josephson phase, a function defined by the second equation plus initial conditions
- : input voltage of the system
- : current across the junction, determined by the input voltage
Note how these equations are not a typical I-V curve, as they are not an instantaneous dependency between voltage and current: the history of the voltage matters! Or in other words, the system has an internal state, represented by the Josephson phase at a given point in time.
To understand them better, it is important to look at some important cases separately:
- AC Josephson effect: V is a fixed DC voltage
Derived from classical first principles, matches Planck's law for low frequencies, but diverges at higher frequencies.