A subset of Spacetime diagram.
The key insights that it gives are:
- future and past are well defined: every reference frame sees your future in your future cone, and your past in your past coneOtherwise causality could be violated, and then things would go really bad, you could tell your past self to tell your past self to tell your past self to do something.You can only affect the outcome of events in your future cone, and you can only be affected by events in your past cone. You can't travel fast enough to affect.Two spacetime events with such fixed causality are called timelike-separated events.
- every other event (to right and left, known as spacelike-separated events) can be measured to happen before or after your current spacetime event by different observers.But that does not violate causality, because you just can't reach those spacetime points anyways to affect them.
Animation showing how space-separated events can be observed to happen in different orders by observers in different frames of reference
. Source. Split in the spectral line when a magnetic field is applied.
Non-anomalous: number of splits matches predictions of the Schrödinger equation about the number of possible states with a given angular momentum. TODO does it make numerical predictions?
www.pas.rochester.edu/~blackman/ast104/zeeman-split.html contains the hello world that everyone should know: 2p splits into 3 energy levels, so you see 3 spectral lines from 1s to 2p rather than just one.
p splits into 3, d into 5, f into 7 and so on, i.e. one for each possible azimuthal quantum number.
It also mentions that polarization effects become visible from this: each line is polarized in a different way. TODO more details as in an experiment to observe this.
Well explained at: Video "Quantum Mechanics 7a - Angular Momentum I by ViaScience (2013)".
Experimental physics - IV: 22 - Zeeman effect by Lehrportal Uni Gottingen (2020)
Source. This one is decent. Uses a cadmium lamp and an etalon on an optical table. They see a more or less clear 3-split in a circular interference pattern,
They filter out all but the transition of interest.
- youtu.be/ZmObNFAqkBE?t=165 passes the lines through a polarizer, which shows how orbital angular momentum is carried by photon polarization
- youtu.be/ZmObNFAqkBE?t=370 says they are looking at 1D2 to 1P1 changes.
Zeeman Effect - Control light with magnetic fields by Applied Science (2018)
Source. Does not appear to achieve a crystal clear split unfortunately.If you shine microwave radiation on a Josephson junction, it produces a fixed average voltage that depends only on the frequency of the microwave. TODO how is that done more precisely? How to you produce and inject microwaves into the thing?
It acts therefore as a perfect frequency to voltage converter.
The Wiki page gives the formula: en.wikipedia.org/wiki/Josephson_effect#The_inverse_AC_Josephson_effect You get several sinusoidal harmonics, so the output is not a perfect sine. But the infinite sum of the harmonics has a fixed average voltage value.
And en.wikipedia.org/wiki/Josephson_voltage_standard#Josephson_effect mentions that the effect is independent of the junction material, physical dimension or temperature.
All of the above, compounded with the fact that we are able to generate microwaves with extremely precise frequency with an atomic clock, makes this phenomenon perfect as a Volt standard, the Josephson voltage standard.
TODO understand how/why it works better.
Highlighted at the Origins of Precision by Machine Thinking (2017).
The 3D structure of GFP is so cool. It is so clearly a bottle with a fluorescent bit well isolated right in the middle. Like a little lamp.
Experiments explained by QED but not by the Dirac equation:
- Lamb shift: by far the most famous one
- hyperfine structure TODO confirm
- anomalous magnetic dipole moment of the electron
This point is beautifully argued in lots of different sources, and is clearly a pillar of AGI.
Perhaps one may argue that our deep learning layers do form some kind of hierarchy, e.g. this is very clear in certain models such as convolutional neural network. But many of those models cannot have arbitrarily deep hierarchies, which appears to be a fundamental aspect of intelligence.
How to Create a Mind:
The lists of steps in my mind are organized in hierarchies. I follow a routine procedure before going to sleep. The first step is to brush my teeth. But this action is in turn broken into a smaller series of steps, the first of which is to put toothpaste on the toothbrush. That step in turn is made up of yet smaller steps, such as finding the toothpaste, removing the cap, and so on. The step of finding the toothpaste also has steps, the first of which is to open the bathroom cabinet. That step in turn requires steps, the first of which is to grab the outside of the cabinet door. This nesting actually continues down to a very fine grain of movements, so that there are literally thousands of little actions constituting my nighttime routine. Although I may have difficulty remembering details of a walk I took just a few hours ago, I have no difficulty recalling all of these many steps in preparing for bed - so much so that I am able to think about other things while I go through these procedures. It is important to point out that this list is not stored as one long list of thousands of steps - rather, each of our routine procedures is remembered as an elaborate hierarchy of nested activities.
Human Compatible: TODO get exact quote. It was something along: life goal: save world from hunger. Subgoal: apply for some grant. Sub-sub-goal: eat, sleep, take shower. Sub-sub-sub-goal: move muscles to get me to table and open a can.
The one parameter subgroup of a Lie group for a given element of its Lie algebra is a subgroup of given by:
Intuitively, is a direction, and is how far we move along a given direction. This intuition is especially vivid in for example in the case of the Lie algebra of , the rotation group.
One parameter subgroups can be seen as the continuous analogue to the cycle of an element of a group.
Huge interest overlap with Ciro Santilli, e.g. he's into
- molecular biology in general: I should have loved biology by James Somers
- JCVI-syn3.0: www.newyorker.com/magazine/2022/03/07/a-journey-to-the-center-of-our-cells
- cryo-EM: www.newyorker.com/magazine/2022/03/07/a-journey-to-the-center-of-our-cells
- David Goodsell: www.newyorker.com/magazine/2022/03/07/a-journey-to-the-center-of-our-cells
- History of Google: www.newyorker.com/magazine/2018/12/10/the-friendship-that-made-google-huge
TODO: in high level terms, why is QED more general than just solving the Dirac equation, and therefore explaining quantum electrodynamics experiments?
Also, is it just a bunch of differential equation (like the Dirac equation itself), or does it have some other more complicated mathematical formulation, as seems to be the case? Why do we need something more complicated than
Advanced quantum mechanics by Freeman Dyson (1951) mentions:
A Relativistic Quantum Theory of a Finite Number of Particles is Impossible.
Bibliography:
- physics.stackexchange.com/questions/101307/dirac-equation-in-qft-vs-relativistic-qm
- physics.stackexchange.com/questions/44188/what-is-the-relativistic-particle-in-a-box/44309#44309 says:
By several reasons explained in textbooks, the Dirac equation is not a valid wavefunction equation. You can solve it and find solutions, but those solutions cannot be interpreted as wavefunctions for a particle
- physics.stackexchange.com/questions/64206/why-is-the-dirac-equation-not-used-for-calculations
- www.physicsforums.com/threads/is-diracs-equation-still-useful-after-qed-is-developed.663994/
- drive.google.com/file/d/1JTPVd09NPaGH-KzGv2jU3XXcFiJAoUjw/view some crazy due investigating, let's see how long until it goes down, posted at: Points to:"Alex Conferno" is also brought up: twitter.com/conferno
- www.reddit.com/r/DataHoarder/comments/12trawt/has_anyone_ever_actually_spoken_to_denis_petrov/
- gyrovague.com/2023/08/05/archive-today-on-the-trail-of-the-mysterious-guerrilla-archivist-of-the-internet/. Trended on Hacker News: news.ycombinator.com/item?id=37009598
- gigazine.net/gsc_news/en/20240326-archive-today/
Other mentions of "Denis Petrov":
Man-made virus!
TODO: if we had cheap de novo DNA synthesis, how hard would it be to bootstrap a virus culture from that? github.com/cirosantilli/cirosantilli.github.io/issues/60
Is it easy to transfect a cell with the synthesized DNA, and get it to generate full infectious viral particles?
If so, then de novo DNA synthesis would be very similar to 3D printed guns: en.wikipedia.org/wiki/3D_printed_firearms.
It might already be possible to order dissimulated sequences online:
Contains the first sporadic groups discovered by far: 11 and 12 in 1861, and 22, 23 and 24 in 1973. And therefore presumably the simplest! The next sporadic ones discovered were the Janko groups, only in 1965!
Each is a permutation group on elements. There isn't an obvious algorithmic relationship between and the actual group.
TODO initial motivation? Why did Mathieu care about k-transitive groups?
Their; k-transitive group properties seem to be the main characterization, according to Wikipedia:Looking at the classification of k-transitive groups we see that the Mathieu groups are the only families of 4 and 5 transitive groups other than symmetric groups and alternating groups. 3-transitive is not as nice, so let's just say it is the stabilizer of and be done with it.
- 22 is 3-transitive but not 4-transitive.
- four of them (11, 12, 23 and 24) are the only sporadic 4-transitive groups as per the classification of 4-transitive groups (no known simpler proof as of 2021), which sounds like a reasonable characterization. Note that 12 and 25 are also 5 transitive.
Mathieu group section of Why Do Sporadic Groups Exist? by Another Roof (2023)
Source. Only discusses Mathieu group but is very good at that. Rich people who create charitable prizes are often crooked Updated 2024-12-23 +Created 1970-01-01
A friend of mine who's a rich man - he invented some kind of simple digital switch - tells me about these people who contribute money to make prizes or give lectures: "You always look at them carefully to find out what crookery they're trying to absolve their conscience of."
TODO who was he talking about? Robert Noyce or Gordon Moore feel likely candidates:
But do you know what, Cirism is totally fine with taking indulgences to absolve someone from their past sins, so long as they have repented. Everyone deserves a second chance.
A quantum version of the LC circuit!
TODO are there experiments, or just theoretical?
OMG, Ciro Santilli only learned about this in 2021 after: twitter.com/ryancdotorg/status/1375484757916672000
Unlisted articles are being shown, click here to show only listed articles.