A different and more elegant way to express Maxwell's equations by using the:instead of the:
E.g. thinking about the electric potential alone, you could set the zero anywhere, and everything would remain be the same.
The Lorentz gauge is just one such choice. It is however a very popular one, because it is also manifestly Lorentz invariant.
Alternative to the Lorentz gauge, but less used in general as it is not as nice for relativity invariance.
This single experimental observation/idea is the basis for all of special relativity.
Special relativity is the direct result of people bending their backs to accommodate for this really weird fact.
Bibliography:
- Subtle is the Lord by Abraham Pais (1982) chapter III "Relativity, the special theory" has a good sketch as you may imagine.
Can you just imagine what if luminiferous aether was one single fixed rigid body? This is apparently what Maxwell believed, Subtle is the Lord by Abraham Pais (1982) page 111 quoting his entry to Encyclopedia Britannica:Then it would provide a natural space coordinate for the entire universe!
There can be no doubt that the interplanetary and interstellar spaces are not empty but are occupied by a material substance or body, which is certainly the largest, and probably the most uniform, body of which we have any knowledge.
Given experiments such as the Fizeau experiment and the Michelson-Morley experiment that couldn't really detect the Earth's movement across aether, people started to wonder if the Earth wasn't dragging the luminiferous aether.
- moving magnet and conductor problem: the more experiments confirm Maxwell's equations, the more special relativity has to be correct
- aberration TODO more precisely how it is evidence.
Michelson Interferometer by Amrita Vlab (2013)
Source. Shows the optical controls and alignment in more detail.Michelson Interferometer by TSG Physics (2012)
Source. TSG PHysiQuantum electrodynamics bibliographycs is the channel from the MIT Department of Physics Technical Services Group. In the video they produce a very clear round interference pattern.Can be used to detect single photons.
Richard Feynman likes them, he describes the tube at Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) at one point.
It uses the photoelectric effect multiple times to produce a chain reaction. In particular, as mentioned at youtu.be/5V8VCFkAd0A?t=74 from Video 1. "Using a Photomultiplier to Detect single photons by Huygens Optics" this means that the device has a lowest sensitive light frequency, beyond which photons don't have enough energy to eject any electrons.
Same motivation as Galilean invariance, but relativistic version of that: we want the laws of physics to have the same form on all inertial frames, so we really want to write them in a way that is Lorentz covariant.
This is just the relativistic version of that which takes the Lorentz transformation into account instead of just the old Galilean transformation.
Lorentz transform consequence: everyone sees the same speed of light by 
Ciro Santilli 37 Updated 2025-07-16
Ciro Santilli 37 Updated 2025-07-16OK, so let's verify the main desired consequence of the Lorentz transformation: that everyone observes the same speed of light.
Observers will measure the speed of light by calculating how long it takes the light going towards cross a rod of length laid in the x axis at position .
Each observer will observe two events:
Supposing that the standing observer measures the speed of light as and that light hits the left side of the rod at time , then he observes the coordinates:
Now, if we transform for the moving observer:and so the moving observer measures the speed of light as:
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
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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. 
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