Each elliptic space can be modelled with a real projective space. The best thing is to just start thinking about the real projective plane.
Adds up chemical energy and kinetic energy.
Wikipedia mentions however that the kinetic energy is often negligible, even for gases.
The sum is of interest when thinking about reactions because chemical reactions can change the number of molecules involved, and therefore the pressure.
To predict if a reaction is spontaneous or not, negative enthalpy is not enough, we must also consider entropy via Gibbs free energy.
The first diodes. These were apparently incredibly unreliable, especially for portable radios, as you had to randomly search for the best contact point you could find in a random polycrystalline material!!
And also quality was highly dependant on where the material was sourced from as that affected the impurities present in the material. Later this was understood to be an issue of doping.
It was so unreliable that vacuum tube diodes overtook them in many applications, even though crystal detectors are actually semiconductor diodes, which eventually won over!
For a long time, before artificial semiconductors kicked in, people just didn't know the underlying physical working principle of these detectors. What I cannot create, I do not understand basically.
A measurable function defined on a closed interval is square integrable (and therefore in ) if and only if Fourier series converges in norm the function:
Ciro Santilli started taking some notes at: github.com/cirosantilli/awesome-whole-cell-simulation. but they are going to be all migrated here.
It is interesting to note how one talks about single cell analysis, in contrast to whole cell simulation: experimentally it is hard to analyse a single cell. But theoretically, it is hard to simulate a single cell. This mismatch is perhaps the ultimate frontier of molecular biology.
A Computational Whole-Cell Model Predicts Genotype From Phenotype by Markus Covert (2013)
Source. Theory that describes electrons and photons really well, and as Feynman puts it "accounts very precisely for all physical phenomena we have ever observed, except for gravity and nuclear physics" ("including the laughter of the crowd" ;-)).
Learning it is one of Ciro Santilli's main intellectual fetishes.
While Ciro acknowledges that QED is intrinsically challenging due to the wide range or requirements (quantum mechanics, special relativity and electromagnetism), Ciro feels that there is a glaring gap in this moneyless market for a learning material that follows the Middle Way as mentioned at: the missing link between basic and advanced. Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) is one of the best attempts so far, but it falls a bit too close to the superficial side of things, if only Feynman hadn't assumed that the audience doesn't know any mathematics...
The funny thing is that when Ciro Santilli's mother retired, learning it (or as she put it: "how photons and electrons interact") was also one of her retirement plans. She is a pharmacist by training, and doesn't know much mathematics, and her English was somewhat limited. Oh, she also wanted to learn how photosynthesis works (possibly not fully understood by science as that time, 2020). Ambitious old lady!!!
Experiments: quantum electrodynamics experiments.
Combines special relativity with more classical quantum mechanics, but further generalizing the Dirac equation, which also does that: Dirac equation vs quantum electrodynamics. The name "relativistic" likely doesn't need to appear on the title of QED because Maxwell's equations require special relativity, so just having "electro-" in the title is enough.
Before QED, the most advanced theory was that of the Dirac equation, which was already relativistic but TODO what was missing there exactly?
As summarized at: youtube.com/watch?v=_AZdvtf6hPU?t=305 Quantum Field Theory lecture at the African Summer Theory Institute 1 of 4 by Anthony Zee (2004):
- classical mechanics describes large and slow objects
- special relativity describes large and fast objects (they are getting close to the speed of light, so we have to consider relativity)
- classical quantum mechanics describes small and slow objects.
- QED describes objects that are both small and fast
That video also mentions the interesting idea that:Therefore, for small timescales, energy can vary a lot. But mass is equivalent to energy. Therefore, for small time scale, particles can appear and disappear wildly.
- in special relativity, we have the mass-energy equivalence
- in quantum mechanics, thinking along the time-energy uncertainty principle,
QED is the first quantum field theory fully developed. That framework was later extended to also include the weak interaction and strong interaction. As a result, it is perhaps easier to just Google for "Quantum Field Theory" if you want to learn QED, since QFT is more general and has more resources available generally.
Like in more general quantum field theory, there is on field for each particle type. In quantum field theory, there are only two fields to worry about:
- photon field
- electromagnetism field
Lecture 01 | Overview of Quantum Field Theory by Markus Luty (2013)
Source. This takes quite a direct approach, one cool thing he says is how we have to be careful with adding special relativity to the Schrödinger equation to avoid faster-than-light information.Gospel of Matthew 4 King James Version:
18 And Jesus, walking by the sea of Galilee, saw two brethren, Simon called Peter, and andrew the Apostle his brother, casting a net into the sea: for they were fishers.19 And he saith unto them, Follow me, and I will make you fishers of men.
There are unlisted articles, also show them or only show them.