The unit of electrical inductance is the henry (symbol: H). One henry is defined as the amount of inductance in a circuit in which a change in current of one ampere per second induces an electromotive force of one volt. Mathematically, this can be expressed as: 1 H = 1 V·s/A Where: - V is volts, - s is seconds, - A is amperes.
Classic theory predicts that the output frequency must be the same as the input one since the electromagnetic wave makes the electron vibrate with same frequency as itself, which then irradiates further waves.
But the output waves are longer because photons are discrete and energy is proportional to frequency:
The formula is exactly that of two relativistic billiard balls colliding.
Compton Scattering by Compton Scattering (2017)
Source. Experiment with a caesium-137 source.As seen from explicit scalar form of the Maxwell's equations, this expands to 8 equations, so the question arises if the system is over-determined because it only has 6 functions to be determined.
As explained on the Wikipedia page however, this is not the case, because if the first two equations hold for the initial condition, then the othe six equations imply that they also hold for all time, so they can be essentially omitted.
It is also worth noting that the first two equations don't involve time derivatives. Therefore, they can be seen as spacial constraints.
TODO: the electric field and magnetic field can be expressed in terms of the electric potential and magnetic vector potential. So then we only need 4 variables?
A (multi-user) blog is the hello world of the web, so creating one of those is the best way to quickly evaluate web technology, i.e. time to Hello World.
Some new frameworks like FeathersJS are making a chat app instead, as that highlights the push notifications a bit better.
Suppose that a rod has is length measured on a rest frame (or maybe even better: two identical rulers were manufactured, and one is taken on a spaceship, a bit like the twin paradox).
Question: what is the length than an observer in frame moving relative to as speed observe the rod to be?
The key idea is that there are two events to consider in each frame, which we call 1 and 2:Note that what you visually observe on a photograph is a different measurement to the more precise/easy to calculate two event measurement. On a photograph, it seems you might not even see the contraction in some cases as mentioned at en.wikipedia.org/wiki/Terrell_rotation
- the left end of the rod is an observation event at a given position at a given time: and for or and for
- the right end of the rod is an observation event at a given position at a given time : and for or and for
By plugging those values into the Lorentz transformation, we can eliminate , and conclude that for any , the length contraction relation holds:
The key question that needs intuitive clarification then is: but how can this be symmetric? How can both observers see each other's rulers shrink?
And the key answer is: because to the second observer, the measurements made by the first observer are not simultaneous. Notably, the two measurement events are obviously spacelike-separated events by looking at the light cone, and therefore can be measured even in different orders by different observers.
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.
- 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.
Animation showing how space-separated events can be observed to happen in different orders by observers in different frames of reference
. Source. Due to the failures of earlier generations, which believed that would quickly achieve AGI, leading to the AI winters, 21st researchers have been very afraid of even trying it, rather going only for smaller subste problems like better neural network designs, at the risk of being considered a crank.
While there is fundamental value in such subset problems, the general view to the final goal is also very important, we will likely never reach AI without it.
This is voiced for example in Superintelligence by Nick Bostrom (2014) section "Opinions about the future of machine intelligence" which in turn quotes Nils Nilsson:
There may, however, be a residual cultural effect on the AI community of its earlier history that makes many mainstream researchers reluctant to align themselves with over-grand ambition. Thus Nils Nilsson, one of the old-timers in the field, complains that his present-day colleagues lack the boldness of spirit that propelled the pioneers of his own generation:Nilsson’s sentiment has been echoed by several others of the founders, including Marvin Minsky, John McCarthy, and Patrick Winston.Concern for "respectability" has had, I think, a stultifying effect on some AI researchers. I hear them saying things like, "AI used to be criticized for its flossiness. Now that we have made solid progress, let us not risk losing our respectability." One result of this conservatism has been increased concentration on "weak AI" - the variety devoted to providing aids to human
thought - and away from "strong AI" - the variety that attempts to mechanize human-level intelligence
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!
Intro to OurBigBook
. Source. We have two killer features:
- 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-calculusArticles 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/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either: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.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
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. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact