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History of Bitcoin Updated 2025-07-16
- 2008-08-18: bitcoin.org registered
- 2008-10-31: first public announcement at www.metzdowd.com/pipermail/cryptography/2008-October/014810.html by satoshi@vistomail.com
- 2009-01-03: Genesis block mined
- 2009-01-11: First block not mined by Satoshi
- 2009-01-12: First Bitcoin transactoin
- 2010-05-18: the first of Laszlo's pizzas at about $0.0045 / BTC
- 2010-07-17: first trade happes on Mt. Gox at $0.04951 / BTC: cryptopotato.com/10-years-ago-first-bitcoin-trade-on-mt-gox-for-0-05-per-btc/
- 2014: OP_RETURN goes live
Quantum electrodynamics Lagrangian Updated 2025-07-16
where:
- is the electromagnetic tensor
Note that this is the sum of the:Note that the relationship between and is not explicit. However, if we knew what type of particle we were talking about, e.g. electron, then the knowledge of psi would also give the charge distribution and therefore
- Dirac Lagrangian, which only describes the "inertia of bodies" part of the equation
- the electromagnetic interaction term , which describes term describes forces
As mentioned at the beginning of Quantum Field Theory lecture notes by David Tong (2007):
- by "Lagrangian" we mean Lagrangian density
- the generalized coordinates of the Lagrangian are fields
History of Facebook Updated 2025-09-09
Facebook's original niche was college, and that was cool. Then it became this more diluted and irrelevant thing. If only they had added knowledge sharing to it, OurBigBook would have been done then and there.
From 2005: Four young internet entrepreneurs by CBS Sunday Morning
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Schrödinger picture Updated 2025-07-16
To better understand the discussion below, the best thing to do is to read it in parallel with the simplest possible example: Schrödinger picture example: quantum harmonic oscillator.
"Making a measurement" for an observable means applying a self-adjoint operator to the state, and after a measurement is done:Those last two rules are also known as the Born rule.
- the state collapses to an eigenvector of the self adjoint operator
- the result of the measurement is the eigenvalue of the self adjoint operator
- the probability of a given result happening when the spectrum is discrete is proportional to the modulus of the projection on that eigenvector.For continuous spectra such as that of the position operator in most systems, e.g. Schrödinger equation for a free one dimensional particle, the projection on each individual eigenvalue is zero, i.e. the probability of one absolutely exact position is zero. To get a non-zero result, measurement has to be done on a continuous range of eigenvectors (e.g. for position: "is the particle present between x=0 and x=1?"), and you have to integrate the probability over the projection on a continuous range of eigenvalues.In such continuous cases, the probability collapses to an uniform distribution on the range after measurement.The continuous position operator case is well illustrated at: Video "Visualization of Quantum Physics (Quantum Mechanics) by udiprod (2017)"
Self adjoint operators are chosen because they have the following key properties:
- their eigenvalues form an orthonormal basis
- they are diagonalizable
Perhaps the easiest case to understand this for is that of spin, which has only a finite number of eigenvalues. Although it is a shame that fully understanding that requires a relativistic quantum theory such as the Dirac equation.
The next steps are to look at simple 1D bound states such as particle in a box and quantum harmonic oscillator.
This naturally generalizes to Schrödinger equation solution for the hydrogen atom.
The solution to the Schrödinger equation for a free one dimensional particle is a bit harder since the possible energies do not make up a countable set.
This formulation was apparently called more precisely Dirac-von Neumann axioms, but it because so dominant we just call it "the" formulation.
Quantum Field Theory lecture notes by David Tong (2007) mentions that:
if you were to write the wavefunction in quantum field theory, it would be a functional, that is a function of every possible configuration of the field .
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Craig Steven Wright meme Updated 2025-07-16
TODO find the Shroud of Turin one.
- twitter.com/digitalnaut/status/1757464079076098212 vampire killed by cross of cryptographic evidence
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Scientific Autobiography by Max Planck translated by Frank Gaynor (1949) Updated 2025-07-16
Published as Scientific Autobiography and Other Papers by Max Planck translated by Frank Gaynor (1949) which also contained other papers.
This section refers just to the translation of Scientific autobiography by Max Planck (1948).
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