Metagenomics Updated 2025-07-16
Experiments that involve sequencing bulk DNA found in a sample to determine what species are present, as opposed to sequencing just a single specific specimen. Examples of samples that are often used:
- river water to determine which bacteria are present, notably to determine if the water is free of dangerous bacteria. A concrete example is shown at: Section "How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it".
- sea water biodiversity: ocean-microbiome.embl.de/companion.html
- food, including searching for desirable microorganisms such as in cheese or bread yeast
- poo, e.g. to study how the human microbiome influences health. There are companies actively working on this, e.g.: www.microbiotica.com/
One related application which most people would not consider metagenomics, is that of finding circulating tumor DNA in blood to detect tumors.
Short-read DNA sequencing Updated 2025-07-16
RNA-Seq Updated 2025-07-16
DNA sequencing company Updated 2025-07-16
- techcrunch.com/2022/05/31/ultima-genomics-claims-100-full-genome-sequencing-after-stealth-600m-raise/ Ultima genomics TODO technology? Promises 100 USD genome, 600M funding out of stealth...
Origin of replication Updated 2025-07-16
oriC = Origin of Chromosomal replication.
Variable number tandem repeat Updated 2025-07-16
Caused by slipped strand mispairing.
Polymerase chain reaction Updated 2025-07-16
This is an extremely widely used technique as of 2020 and much earlier.
If allows you to amplify "any" sequence of choice (TODO length limitations) between a start and end sequences of interest which you synthesize.
If the sequence of interest is present, it gets amplified exponentially, and you end up with a bunch of DNA at the end.
You can then measure the DNA concentration based on simple light refraction methods to see if there is a lot of DNA or not in the post-processed sample.
Even Ciro Santilli had some contact with it at: Section "How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it", see: PCR!
One common problem that happens with PCR if you don't design your primers right is: en.wikipedia.org/wiki/Primer_dimer
Sometime it fails: www.reddit.com/r/molecularbiology/comments/1kouomw/when_your_pcr_fails_again_and_you_start/and a comment:
Nothing humbles you faster than a bandless gel. One minute you’re a scientist, the next you’re just a pipette-wielding wizard casting spells that don’t work. Meanwhile, physicists are out there acting like gravity always behaves. Smash that upvote if your reagents have ever gaslit you.
PCR = Pray, Cry, Repeat
Fog computing Updated 2025-07-16
Our definition of fog computing: a system that uses the computational resources of individuals who volunteer their own devices, in which you give each of the volunteers part of a computational problem that you want to solve.
Blinkenlights Updated 2025-07-16
E Ink Updated 2025-07-16
Electronic Ink such as that found on Amazon Kindle is the greatest invention ever made by man.
Once E Ink reaches reasonable refresh rates to replace liquid crystal displays, the world will finally be saved.
It would allow Ciro Santilli to spend his entire life in front of a screen rather in the real world without getting tired eyes, and even if it is sunny outside.
Ciro stopped reading non-code non-news a while back though, so the current refresh rates are useless, what a shame.
OMG, this is amazing: getfreewrite.com/
Absorption, spontaneous and stimulated emission Updated 2025-07-16
The Dirac equation predicts spin Updated 2025-07-16
Antimatter Updated 2025-07-16
Predicted by the Dirac equation.
Can be easily seen from the solution of Equation "Expanded Dirac equation in Planck units" when the particle is at rest as shown at Video "Quantum Mechanics 12b - Dirac Equation II by ViaScience (2015)".
Particle creation and annihilation Updated 2025-07-16
Predicted by the Dirac equation.
We've likely known since forever that photons are created: just turn on a light and see gazillion of them come out!
Photon creation is easy because photons are massless, so there is not minimum energy to create them.
The creation of other particles is much rarer however, and took longer to be discovered, one notable milestone being the discovery of the positron.
The Dirac equation is consistent with special relativity Updated 2025-07-16
TODO, including why the Schrodinger equation is not.
Derivation of the Dirac equation Updated 2025-07-16
The Dirac equation can be derived basically "directly" from the Representation theory of the Lorentz group for the spin half representation, this is shown for example at Physics from Symmetry by Jakob Schwichtenberg (2015) 6.3 "Dirac Equation".
The Diract equation is the spacetime symmetry part of the quantum electrodynamics Lagrangian, i.e. is describes how spin half particles behave without interactions. The full quantum electrodynamics Lagrangian can then be reached by adding the internal symmetry.
As mentioned at spin comes naturally when adding relativity to quantum mechanics, this same method allows us to analogously derive the equations for other spin numbers.
Bibliography:
Deriving The Dirac equation by Andrew Dotson (2019)
Source. Pauli equation Updated 2025-07-16
Bibliography:
- www.youtube.com/watch?v=Fu1BGGeyqHQ&list=PL54DF0652B30D99A4&index=63 "K6. The Pauli Equation" by doctorphys
Klein-Gordon equation Updated 2025-07-16
A relativistic version of the Schrödinger equation.
Correctly describes spin 0 particles.
The most memorable version of the equation can be written as shown at Section "Klein-Gordon equation in Einstein notation" with Einstein notation and Planck units:
Has some issues which are solved by the Dirac equation:
- it has a second time derivative of the wave function. Therefore, to solve it we must specify not only the initial value of the wave equation, but also the derivative of the wave equation,As mentioned at Advanced quantum mechanics by Freeman Dyson (1951) and further clarified at: physics.stackexchange.com/questions/340023/cant-the-negative-probabilities-of-klein-gordon-equation-be-avoided, this would lead to negative probabilities.
- the modulus of the wave function is not constant and therefore not always one, and therefore cannot be interpreted as a probability density anymore
- since we are working with the square of the energy, we have both positive and negative value solutions. This is also a features of the Dirac equation however.
Bibliography:
- Video "Quantum Mechanics 12a - Dirac Equation I by ViaScience (2015)" at youtu.be/OCuaBmAzqek?t=600
- An Introduction to QED and QCD by Jeff Forshaw (1997) 1.2 "Relativistic Wave Equations" and 1.4 "The Klein Gordon Equation" gives some key ideas
- 2011 PHYS 485 lecture videos by Roger Moore from the University of Alberta at around 7:30
- www.youtube.com/watch?v=WqoIW85xwoU&list=PL54DF0652B30D99A4&index=65 "L2. The Klein-Gordon Equation" by doctorphys
- sites.ualberta.ca/~gingrich/courses/phys512/node21.html from Advanced quantum mechanics II by Douglas Gingrich (2004)
Solutions of the Dirac equation Updated 2025-07-16
- youtu.be/tR6UebCvFqE?t=23 particle at rest
- youtu.be/tR6UebCvFqE?t=322 unidirectional movement without a potential
- youtu.be/tR6UebCvFqE?t=507 shows that observers in different frames of reference also see different spin. We are reminded of how magnetism is just a side effect of special-relativity.
- youtu.be/tR6UebCvFqE?t=549 Dirac equation solution for the hydrogen atom, final result only + mentions fine structure prediction.
Spin (physics) Updated 2025-07-16
Spin is one of the defining properties of elementary particles, i.e. number that describes how an elementary particle behaves, much like electric charge and mass.
The approach shown in this section: Section "Spin comes naturally when adding relativity to quantum mechanics" shows what the spin number actually means in general. As shown there, the spin number it is a direct consequence of having the laws of nature be Lorentz invariant. Different spin numbers are just different ways in which this can be achieved as per different Representation of the Lorentz group.
Video 1. "Quantum Mechanics 9a - Photon Spin and Schrodinger's Cat I by ViaScience (2013)" explains nicely how:
- incorporated into the Dirac equation as a natural consequence of special relativity corrections, but not naturally present in the Schrödinger equation, see also: the Dirac equation predicts spin
- photon spin can be either linear or circular
- the linear one can be made from a superposition of circular ones
- straight antennas produce linearly polarized photos, and Helical antennas circularly polarized ones
- a jump between 2s and 2p in an atom changes angular momentum. Therefore, the photon must carry angular momentum as well as energy.
- cannot be classically explained, because even for a very large estimate of the electron size, its surface would have to spin faster than light to achieve that magnetic momentum with the known electron charge
- as shown at Video "Quantum Mechanics 12b - Dirac Equation II by ViaScience (2015)", observers in different frames of reference see different spin states
Quantum Spin - Visualizing the physics and mathematics by Physics Videos by Eugene Khutoryansky (2016)
Source. There are unlisted articles, also show them or only show them.