Incoming links: Electron
Starting in the 2019 redefinition of the SI base units, the elementary charge is assigned a fixed number, and the Ampere is based on it and on the second, which is beautiful.
This choice is not because we attempt to count individual electrons going through a wire, as it would be far too many to count!
Rather, it is because because there are two crazy quantum mechanical effects that give us macroscopic measures that are directly related to the electron charge. www.nist.gov/si-redefinition/ampere/ampere-quantum-metrology-triangle by the NIST explains that the two effects are:
- quantum Hall effect, which has discrete resistances of type:for integer values of .
- Josephson effect, used in the Josephson voltage standard. With the Inverse AC Josephson effect we are able to produce:per Josephson junction. This is about 2 microvolt / GHz, where GHz is a practical input frequency. Video "The evolution of voltage metrology to the latest generation of JVSs by Alain Rüfenacht" mentions that a typical operating frequency is 20 GHz.Therefore to attain a good 10 V, we need something in the order of a million Josephson junctions.But this is possible to implement in a single chip with existing micro fabrication techniques, and is exactly what the Josephson voltage standard does!
Those effect work because they also involve dividing by the Planck constant, the fundamental constant of quantum mechanics, which is also tiny, and thus brings values into a much more measurable order of size.
"Barys" means "heavy" in Greek, because protons and neutrons was what made most of the mass of known ordinary matter, as opposed notably to electrons.
Baryons can be contrasted with:
- mesons, which have an even number of elementary particles. The name meson comes from "medium" since their most common examples have two quarks rather than three as the most common baryons such as protons. So they have less mass than a proton, but more than an electron, this medium mass.
- leptons, which are much lighter particles such as the electron. "Leptos" means "fine, small, thin".
Uranium emits them, you can see their mass to charge ratio under magnetic field and so deduce that they are electrons.
Caused by weak interaction TODO why/how.
The emitted electron kinetic energy is random from zero to a maximum value. The rest goes into a neutrino. This is how the neutrino was first discovered/observed indirectly. This is well illustrated in a decay scheme such as Figure "caesium-137 decay scheme".
Was the first model to explain the Balmer series, notably linking atomic spectra to the Planck constant and therefore to other initial quantum mechanical observations.
This was one of the first major models that just said:
I give up, I can't tie this to classical physics in any way, let's just roll with it, OK?
It still treats electrons as little points spinning around the nucleus, but it makes the non-classical postulate that only certain angular momentums (and therefore energies) are allowed.
Bibliography:
- Inward Bound by Abraham Pais (1988) Chapter 9.e Atomic structure and spectral lines - Niels Bohr
- The Quantum Story by Jim Baggott (2011) Chapter 3 A Little Bit of Reality
The fundamental intuition about capacitors is that they never let electrons through.
They can only absorb electrons up to a certain point, but then the pushback becomes too strong, and current stops.
Therefore, they cannot conduct direct current long term.
For alternating current however, things are different, because in alternating current, electrons are just jiggling back and forward a little bit around a center point. So you can send alternating current power across a capacitor.
The key equation that relates Voltage to electric current in the capacitor is:So if a voltage Heavyside step function is applied what happens is:More realistically, one may consider the behavior or the series RC circuit to see what happens without infinities when a capacitor is involved as in the step response of the series RC circuit.
- the capacitor fills up instantly with an infinite current
- the current then stops instantly
Finding capacitance with an oscilloscope by Jacob Watts (2020)
Source. Good experiment.Capacitors Explained by The Engineering Mindset
. Source. 2019.Condensed matter physics is one of the best examples of emergence. We start with a bunch of small elements which we understand fully at the required level (atoms, electrons, quantum mechanics) but then there are complex properties that show up when we put a bunch of them together.
Includes fun things like:
As of 2020, this is the other "fundamental branch of physics" besides to particle physics/nuclear physics.
Condensed matter is basically chemistry but without reactions: you study a fixed state of matter, not a reaction in which compositions change with time.
Just like in chemistry, you end up getting some very well defined substance properties due to the incredibly large number of atoms.
Just like chemistry, the ultimate goal is to do de-novo computational chemistry to predict those properties.
And just like chemistry, what we can actually is actually very limited in part due to the exponential nature of quantum mechanics.
Also since chemistry involves reactions, chemistry puts a huge focus on liquids and solutions, which is the simplest state of matter to do reactions in.
Condensed matter however can put a lot more emphasis on solids than chemistry, notably because solids are what we generally want in end products, no one likes stuff leaking right?
But it also studies liquids, e.g. notably superfluidity.
One thing condensed matter is particularly obsessed with is the fascinating phenomena of phase transition.
What Is Condensed matter physics? by Erica Calman
. Source. Cute. Overview of the main fields of physics research. Quick mention of his field, quantum wells, but not enough details.A suggested at Physics from Symmetry by Jakob Schwichtenberg (2015) chapter 3.9 "Elementary particles", it appears that in the Standard Model, the behaviour of each particle can be uniquely defined by the following five numbers:
E.g. for the electron we have:
- mass:
- spin: 1/2
- electric charge:
- weak charge: -1/2
- color charge: 0
Once you specify these properties, you could in theory just pluck them into the Standard Model Lagrangian and you could simulate what happens.
Setting new random values for those properties would also allow us to create new particles. It appears unknown why we only see the particles that we do, and why they have the values of properties they have.
Predicts fine structure.
Bibliography:
How To Solve The Dirac Equation For The Hydrogen Atom | Relativistic Quantum Mechanics by Dietterich Labs (2018)
Source. Amazingly confirms the wave particle duality of quantum mechanics.
The effect is even more remarkable when done with individual particles such individual photons or electrons.
Richard Feynman liked to stress how this experiment can illustrate the core ideas of quantum mechanics. Notably, he night have created the infinitely many slits thought experiment which illustrates the path integral formulation.
The discovery of the photon was one of the major initiators of quantum mechanics.
Light was very well known to be a wave through diffraction experiments. So how could it also be a particle???
This was a key development for people to eventually notice that the electron is also a wave.
This process "started" in 1900 with Planck's law which was based on discrete energy packets being exchanged as exposed at On the Theory of the Energy Distribution Law of the Normal Spectrum by Max Planck (1900).
This ideas was reinforced by Einstein's explanation of the photoelectric effect in 1905 in terms of photon.
In the next big development was the Bohr model in 1913, which supposed non-classical physics new quantization rules for the electron which explained the hydrogen emission spectrum. The quantization rule used made use of the Planck constant, and so served an initial link between the emerging quantized nature of light, and that of the electron.
The final phase started in 1923, when Louis de Broglie proposed that in analogy to photons, electrons might also be waves, a statement made more precise through the de Broglie relations.
This event opened the floodgates, and soon matrix mechanics was published in quantum mechanical re-interpretation of kinematic and mechanical relations by Heisenberg (1925), as the first coherent formulation of quantum mechanics.
It was followed by the Schrödinger equation in 1926, which proposed an equivalent partial differential equation formulation to matrix mechanics, a mathematical formulation that was more familiar to physicists than the matrix ideas of Heisenberg.
Inward Bound by Abraham Pais (1988) summarizes his views of the main developments of the subjectit:
- Planck's on the discovery of the quantum theory (1900);
- Einstein's on the light-quantum (1905);
- Bohr's on the hydrogen atom (1913);
- Bose's on what came to be called quantum statistics (1924);
- Heisenberg's on what came to be known as matrix mechanics (1925);
- and Schroedinger's on wave mechanics (1926).
Bibliography:
- physics.stackexchange.com/questions/18632/good-book-on-the-history-of-quantum-mechanics on Physics Stack Exchange
- www.youtube.com/watch?v=5hVmeOCJjOU A Brief History of Quantum Mechanics by Sean Carroll (2020) Given at the Royal Institution.
2s/2p energy split in the hydrogen emission spectrum, not predicted by the Dirac equation, but explained by quantum electrodynamics, which is one of the first great triumphs of that theory.
Note that for atoms with multiple electrons, 2s/2p shifts are expected: Why does 2s have less energy than 1s if they have the same principal quantum number?. The surprise was observing that on hydrogen which only has one electron.
Initial experiment: Lamb-Retherford experiment.
On the return from the train from the Shelter Island Conference in New York, Hans Bethe managed to do a non-relativistic calculation of the Lamb shift. He then published as The Electromagnetic Shift of Energy Levels by Hans Bethe (1947) which is still paywalled as of 2021, fuck me: journals.aps.org/pr/abstract/10.1103/PhysRev.72.339 by Physical Review.
The Electromagnetic Shift of Energy Levels Freeman Dyson (1948) published on Physical Review is apparently a relativistic analysis of the same: journals.aps.org/pr/abstract/10.1103/PhysRev.73.617 also paywalled as of 2021.
TODO how do the infinities show up, and how did people solve them?
Lamb shift by Dr. Nissar Ahmad (2020)
Source. Whiteboard Lecture about the phenomena, includes description of the experiment. Seems quite good.www.mdpi.com/2624-8174/2/2/8/pdf History and Some Aspects of the Lamb Shift by G. Jordan Maclay (2019)
Freeman Dyson - The Lamb shift by Web of Stories (1998)
Source. Mentions that he moved to the USA from the United Kingdom specifically because great experiments were being carried at Columbia University, which is where the Lamb-Retherford experiment was done, and that Isidor Isaac Rabi was the head at the time.
He then explains mass renormalization briefly: instead of calculating from scratch, you just compare the raw electron to the bound electron and take the difference. Both of those have infinities in them, but the difference between them cancels out those infinities.
Hans Bethe - The Lamb shift (1996)
Source. Ahh, Hans is so old in that video, it is sad to see. He did live a lot tough. Mentions that the shift is of about 1000 MHz.
The following video: www.youtube.com/watch?v=vZvQg3bkV7s Hans Bethe - Calculating the Lamb shift.
Lamb shift by Vidya-mitra (2018)
Source. Looking at the energy level of the Schrödinger equation solution for the hydrogen atom, you would guess that for multi-electron atoms that only the principal quantum number would matter, azimuthal quantum number getting filled randomly.
However, orbitals energies for large atoms don't increase in energy like those of hydrogen due to electron-electron interactions.
In particular, the following would not be naively expected:
- 2s fills up before 2p. From the hydrogen solution, you might guess that they would randomly go into either one as they'd have the same energy
- in potassium fills up before 3d, even though it has a higher principal quantum number!
This rule is only an approximation, there exist exceptions to the Madelung energy ordering rule.
A tiny idealized magnet! It is a very good model if you have a small strong magnet interacting with objects that are far away, notably other magnetic dipoles or a constant magnetic field.
The cool thing about this model is that we have simple explicit formulas for the magnetic field it produces, and for how this little magnet is affected by a magnetic field or by another magnetic dipole.
This is the perfect model for electron spin, but it can also be representative of macroscopic systems in the right circumstances.
The intuition for the name is likely that "dipole" means "both poles are on the same spot".
Different macroscopic magnets can be approximated by a magnetic dipole when shrunk seen from far away
. Source. 