The Matochkin Strait is a waterway located in the Russian Arctic, separating the Novaya Zemlya archipelago into two main parts: Severny (Northern) Island to the west and Yuzhny (Southern) Island to the east. The strait connects the Barents Sea to the Kara Sea and serves as an important navigational route in the region. Its waters are characterized by polar conditions, with ice cover occurring for much of the year, making navigation challenging.
Lamb shift by Ciro Santilli 40 Updated 2025-07-16
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.
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?
Video 1.
Lamb shift by Dr. Nissar Ahmad (2020)
Source. Whiteboard Lecture about the phenomena, includes description of the experiment. Seems quite good.
Video 2.
Murray Gell-Mann - The race to calculate the relativistic Lamb shift by Web of Stories (1997)
Source. Quick historical overview. Mentions that Richard Feynman and Julian Schwinger were using mass renormalization and cancellation if infinities. He says that French and Weisskopf actually managed to do the correct calculations first with a less elegant method.
www.mdpi.com/2624-8174/2/2/8/pdf History and Some Aspects of the Lamb Shift by G. Jordan Maclay (2019)
Video 3. 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.
Video 4.
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.
Video 5.
Lamb shift by Vidya-mitra (2018)
Source.
Sphuṭacandrāpti is a Sanskrit term used in the context of Indian philosophy and logic, particularly in the study of epistemology and rational inquiry. The term can be broken down into two components: "Sphuṭa," meaning clear or distinct, and "candrāpti," which may refer to the attainment or realization of a quality or truth. The concept is often associated with discussions on the clarity of knowledge or cognition.
"Quantity" refers to a measurable property or attribute of an object or phenomenon that can be expressed numerically. It indicates how much of something exists and can apply to a wide range of subjects, including physical objects, time, volume, weight, distance, and more. In mathematics and science, quantities can often be classified as: 1. **Scalar Quantities**: These are quantities that have magnitude only and no direction. Examples include temperature, mass, and speed.
The value of science is multifaceted, touching on various aspects of human existence, knowledge, and societal development. Here are several key points that highlight its significance: 1. **Understanding the Natural World**: Science provides a systematic way to explore and understand the universe, from the smallest particles to the vastness of galaxies. It helps us uncover the laws of nature and the principles that govern life.
This was one of the first two great successes of quantum electrodynamics, the other one being the Lamb shift.
In youtu.be/UKbp85zpdcY?t=52 from freeman Dyson Web of Stories interview (1998) Dyson mentions that the original key experiment was from Kusch and Foley from Columbia University, and that in 1948, Julian Schwinger reached the correct value from his calculations.
Bibliography:
Olog is a term that can refer to several different concepts depending on the context. Here are a few possible interpretations: 1. **Olog (Ology)**: In a more informal or humorous sense, "olog" is often used as a suffix to create playful names for various fields of study (like "biolog" for biology, "geolog" for geology, etc.), especially in discussions of pseudo-disciplines or in casual contexts.
In mathematics, the term "degeneracy" can have several meanings depending on the context in which it is used. Here are a few common interpretations across different areas of mathematics: 1. **Linear Algebra:** In the context of linear algebra, degeneracy often refers to a situation where a certain set of vectors does not span the entire space or fails to be linearly independent.
Boolean-valued refers to the notion of values and operations that are based on Boolean logic, a binary system that deals with truth values. In Boolean logic, there are only two possible values: "true" (often represented as 1) and "false" (often represented as 0). The primary operations in Boolean algebra include: - **AND** (conjunction): The result is true only when both operands are true.
The 97.5th percentile point in a dataset or distribution is the value below which 97.5% of the observations fall. In other words, if you were to rank all the data points in ascending order, the 97.5th percentile would be the point at which only 2.5% of the data points are higher.
The "magic angle" is a term used primarily in the context of nuclear magnetic resonance (NMR) spectroscopy and solid-state NMR. It refers to a specific angle, approximately 54.74 degrees (or arccos(1/√3)), at which the anisotropic interactions in a solid sample can be effectively averaged out. This is particularly relevant for studying solid materials where the molecular orientations can lead to broadening of NMR signals.
A mathematical constant is a fixed, well-defined number that is significant in mathematics. Unlike variables, which can change values, constants remain the same. They often arise in various mathematical contexts and can represent fundamentally important quantities. Examples of widely known mathematical constants include: 1. **Pi (\( \pi \))**: Approximately equal to 3.14159, it represents the ratio of the circumference of a circle to its diameter.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
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    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
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    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
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