Adds special relativity to the Schrödinger equation, and the following conclusions come basically as a direct consequence of this!
Experiments explained:
Experiments not explained: those that quantum electrodynamics explains like:See also: Dirac equation vs quantum electrodynamics.
- Lamb shift
- TODO: quantization of the electromagnetic field as photons?
The Dirac equation is a set of 4 partial differential equations on 4 complex valued wave functions. The full explicit form in Planck units is shown e.g. in Video 1. "Quantum Mechanics 12a - Dirac Equation I by ViaScience (2015)" at youtu.be/OCuaBmAzqek?t=1010:Then as done at physics.stackexchange.com/questions/32422/qm-without-complex-numbers/557600#557600 from why are complex numbers used in the Schrodinger equation?, we could further split those equations up into a system of 8 equations on 8 real-valued functions.
Equation 1.
Expanded Dirac equation in Planck units
. PHYS 485 Lecture 14: The Dirac Equation by Roger Moore (2016)
Source. Predicts fine structure.
Bibliography:
Dirac equation for the electron and hydrogen Hamiltonian by Barton Zwiebach (2019)
Source. Uses perturbation theory to get to the relativistic corrections of fine structure! Part of MIT 8.06 Quantum Physics III, Spring 2018 by Barton ZwiebachHow To Solve The Dirac Equation For The Hydrogen Atom | Relativistic Quantum Mechanics by Dietterich Labs (2018)
Source. You gotta be born after the year 2000 to understand it.
This is becoming more and more popular as a group chat with channels and threads possibility as of 2020.
Very similar to Slack.
They force your username to have 4 random digits? www.reddit.com/r/discordapp/comments/43kjdl/whats_the_number_next_to_the_username/
Not possible to anonymously join just one server without creating a new account? What's the point of servers then! www.reddit.com/r/discordapp/comments/6gmjl7/changing_nick_before_joining_a_new_server/ Oh, also nicks don't hide your username from the server in any way, you can get the original username by just clicking on the person's username.
No proper threaded discussion without creating new channels? As of 2022 there is kind of a way, but it was a bit obtuse.
As of 2022 they also have a school hub: support.discord.com/hc/en-us/articles/4406046651927-Discord-Student-Hubs-FAQ which auto creates groups by university email access. Good idea, and shows popularity amongst that user group.
Servers don't have an ID to join them? www.reddit.com/r/discordapp/comments/b9zdt6/join_discord_server_from_id/
Can only make public servers if you have 1000 members?? support.discord.com/hc/en-us/articles/360023968311 Why so much bullshit?? www.reddit.com/r/discordapp/comments/6jouf8/how_do_i_make_my_server_public/
Output: another sequence of complex numbers such that:Intuitively, this means that we are braking up the complex signal into sinusoidal frequencies:and is the amplitude of each sine.
- : is kind of magic and ends up being a constant added to the signal because
- : sinusoidal that completes one cycle over the signal. The larger the , the larger the resolution of that sinusoidal. But it completes one cycle regardless.
- : sinusoidal that completes two cycles over the signal
- ...
- : sinusoidal that completes cycles over the signal
Motivation: similar to the Fourier transform:In particular, the discrete Fourier transform is used in signal processing after a analog-to-digital converter. Digital signal processing historically likely grew more and more over analog processing as digital processors got faster and faster as it gives more flexibility in algorithm design.
- compression: a sine would use N points in the time domain, but in the frequency domain just one, so we can throw the rest away. A sum of two sines, only two. So if your signal has periodicity, in general you can compress it with the transform
- noise removal: many systems add noise only at certain frequencies, which are hopefully different from the main frequencies of the actual signal. By doing the transform, we can remove those frequencies to attain a better signal-to-noise
Sample software implementations:
- numpy.fft, notably see the example: numpy/fft.py
DFT of with 25 points
. This is a simple example of a discrete Fourier transform for a real input signal. It illustrates how the DFT takes N complex numbers as input, and produces N complex numbers as output. It also illustrates how the discrete Fourier transform of a real signal is symmetric around the center point.Check which you you have:Tested on Ubuntu 23.10 I see:which means I have GNOME Display Manager.
systemctl status display-manager.service● gdm.service - GNOME Display Manager
Loaded: loaded (/lib/systemd/system/gdm.service; static)
Active: active (running) since Sun 2023-12-24 10:34:50 GMT; 23min ago
Process: 1827 ExecStartPre=/usr/share/gdm/generate-config (code=exited, status=0/SUCCESS)
Main PID: 1850 (gdm3)
Tasks: 4 (limit: 71817)
Memory: 6.8M
CPU: 119ms
CGroup: /system.slice/gdm.service
└─1850 /usr/sbin/gdm3React setups:
This can be used to detect if a given species of microorganism is present in a sample, and is therefore a widely used diagnostics technique to see if someone is infected with a virus.
You could of course do full DNA Sequencing to see everything that is there, but since it is as a more generic procedure, sequencing is more expensive and slow.
The alternative is to use a DNA amplification technique.
Can be seen as a cheap form of DNA sequencing that only test for a few hits. Some major applications:
- gene expression profiling
- single-nucleotide polymorphism: specificity is high enough to detect snips
Most of these are going to be Whole-genome sequencing of some model organism:en.wikipedia.org/wiki/Whole_genome_sequencing#History lists them all. Basically th big "firsts" all happened in the 1990s and early 2000s.
- 1975 by Sanger et al.: 5 kbp of the single-stranded bacteriophage ΦX174 using Sanger's radiolabelling method
- 1981 by Sanger et al.: 17 kbp of human mitochondrial DNA via Sanger method, known as the Cambridge Reference Sequence
- 2003: Human Genome Project (3 Gbp)
Searching for "H" for hydrogen leads to: physics.nist.gov/cgi-bin/ASD/lines1.pl?spectra=H&limits_type=0&low_w=&upp_w=&unit=1&submit=Retrieve+Data&de=0&format=0&line_out=0&en_unit=0&output=0&bibrefs=1&page_size=15&show_obs_wl=1&show_calc_wl=1&unc_out=1&order_out=0&max_low_enrg=&show_av=2&max_upp_enrg=&tsb_value=0&min_str=&A_out=0&intens_out=on&max_str=&allowed_out=1&forbid_out=1&min_accur=&min_intens=&conf_out=on&term_out=on&enrg_out=on&J_out=on
AKA how this GitHub page gets served under the domain: cirosantilli.com
Ciro only touches this very rarely, and always forgets and go into great pain whenever a change needs to done, so it is important to document it.
The last change was of 2019-07-07, when Ciro moved from the www subdomain www.cirosantilli.com to the APEX cirosantilli.com. A redirect is setup from the www subdomain to APEX.
GoDaddy DNS entries:
Type Name Value TTL
A @ 185.199.108.153 1 Hour
A @ 185.199.109.153 1 Hour
A @ 185.199.110.153 1 Hour
A @ 185.199.111.153 1 Hour
CNAME www cirosantilli.github.io 1 HourMoved cirosantilli.com to Porkbun 2022-02, unfortunatly records were not automatically updated and domain went down for a bit, upadded to new entries for IPv6 as well which are not documented by GitHub:
TYPE HOST ANSWER TTL PRIORITY OPTIONS
A cirosantilli.com 185.199.108.153 600
A cirosantilli.com 185.199.109.153 600
A cirosantilli.com 185.199.110.153 600
A cirosantilli.com 185.199.111.153 600
AAAA cirosantilli.com 2606:50c0:8000::153 600
AAAA cirosantilli.com 2606:50c0:8001::153 600
AAAA cirosantilli.com 2606:50c0:8002::153 600
AAAA cirosantilli.com 2606:50c0:8003::153 600
CNAME www.cirosantilli.com cirosantilli.github.io 600where the IPs are obtained from: help.github.com/en/articles/setting-up-an-apex-domain#configuring-a-records-with-your-dns-provider (archive).
- Custom domain:
cirosantilli.com - Enforce HTTPS: checked
And the CNAME file is tracked in this repository: CNAME.
Integer factorization algorithms better than Shor's algorithm Updated 2025-07-11 +Created 1970-01-01
- 2023 www.schneier.com/blog/archives/2023/01/breaking-rsa-with-a-quantum-computer.html comments on "Factoring integers with sublinear resources on a superconducting quantum processor” arxiv.org/pdf/2212.12372.pdf
A group of Chinese researchers have just published a paper claiming that they can—although they have not yet done so—break 2048-bit RSA. This is something to take seriously. It might not be correct, but it’s not obviously wrong.We have long known from Shor’s algorithm that factoring with a quantum computer is easy. But it takes a big quantum computer, on the orders of millions of qbits, to factor anything resembling the key sizes we use today. What the researchers have done is combine classical lattice reduction factoring techniques with a quantum approximate optimization algorithm. This means that they only need a quantum computer with 372 qbits, which is well within what’s possible today. (The IBM Osprey is a 433-qbit quantum computer, for example. Others are on their way as well.)
It is quite amazing to read through books such as The Supermen: The Story of Seymour Cray by Charles J. Murray (1997), as it makes you notice that earlier CPUs (all before the 70's) were not made with integrated circuits, but rather smaller pieces glued up on PCBs! E.g. the arithmetic logic unit was actually a discrete component at one point.
The reason for this can also be understood quite clearly by reading books such as Robert Noyce: The Man Behind the Microchip by Leslie Berlin (2006). The first integrated circuits were just too small for this. It was initially unimaginable that a CPU would fit in a single chip! Even just having a very small number of components on a chip was already revolutionary and enough to kick-start the industry. Just imagine how much money any level of integration saved in those early days for production, e.g. as opposed to manually soldering point-to-point constructions. Also the reliability, size an weight gains were amazing. In particular for military and spacial applications originally.
A briefing on semiconductors by Fairchild Semiconductor (1967)
Source. Uploaded by the Computer History Museum. There is value in tutorials written by early pioneers of the field, this is pure gold.
Shows:
- photomasks
- silicon ingots and wafer processing
Found through Google with no direct relation known to Ciro Santilli:
- en.wikipedia.org/wiki/Santilli: Wikipedia page of the glorious family, Santillis with their own Wikipedia page:
- Ruggero Santilli: "fringe science guy", by far dominates Google as of 2019. Created the respectable R.M. Santilli Foundation
- Ray Santilli made a fake 1995 alien autopsy movie, YouTube sample: www.youtube.com/watch?v=sVcaT2QnoDs
- Ivana Santilli: Canadian singer, pop-electric-chill: www.youtube.com/watch?v=hQRuVN0H8dM
- accounts on important websites
- github.com/santilli anonymous GitHub as of 2019
- santilli.com/ for rent by realnames.com/ (wiki page) as of 2019
- Also Brazilian and tech related like Ciro Santilli.
- www.youtube.com/user/TheOverthrowShow thepetesantillishow.com/ Pete Santilli, American Conservative news commentator show, makes Ciro cringe of boredom. At least he has a passion.
Possibly related variants:
- Santillo:
- Will Santillo who makes somewhat artistic porn photos. His website with several free demos: santillophotography.com/
- www.linkedin.com/in/ciro-santillo-2025a6ba/ a "Ciro Santillo", github.com/Ciruxx, also a programmer
- Santilly, a town in Saône-et-Loire department, France
- santilly.com/ redirects to www.pompes-funebres-santilly.com/fr/, a French funerary service
The key content previously on this page was moved to the following sections:
It was mind blowing when in 2022, after several years of selection, one of the 7 finalists was broken on a classical computer, not even in a quantum computer! news.ycombinator.com/item?id=30466063 | eprint.iacr.org/2022/214 Breaking Rainbow Takes a Weekend on a Laptop by Ward Beullens. Dude announced he had a break a few days before submission: twitter.com/WardBeullens/status/1492780462028300290 On Twitter. He's so young. Epic.
Edit: and then, after the third round, things were a bit unclear, so they made a fourth round with 4 choices out of the 7 from round 3, and in August 2022 one of the four was broken again on a classic CPU!!! OMG: arstechnica.com/information-technology/2022/08/sike-once-a-post-quantum-encryption-contender-is-koed-in-nist-smackdown/
There are unlisted articles, also show them or only show them.