It's worth to lay out detailed derivation of Lorentz transformation to grasp this concept deeply. So Lorentz Transformation is a linear transformation between inertial frames. Let's assume the object is moving at constant relative velocity along the z-axis to make it simple. Note the lambda here is basically the Jacobian matrix to transform in various … Continue reading Lorentz Transformation Detailed Derivation

The nature lets us observe ψˉ​ψ,ψˉ​γμψ,ψˉ​σμνψ, it's from Born's rule equipped by operator's property of eigen state and eigen value.

We're told how mysterious spinors are, they are not observable, to dymystefy spinor, I'd like to compare Dirac spinor to Spin-0 and spin-1, these two are actually not spinors at all, but the name is sort of misguiding. The key difference is how they transform! Spinor transform is not a coordinate change — it’s a … Continue reading Spinors Are Unobservable

Now we have the solution to Dirac Equation, but experiments return real numbers for energy, momentum, charge etc. so we need to find the mathematical object that eats a complex field/solution and outputs a real number! These mathematical objects have to be Hermitian Operators. from previous blog, we know energy operator is generator of time … Continue reading From Solution to Dirac Equation to Compute Measurables

I am greatly interested in learning how spinors, antimatters surface out after solving Dirac Equation. Let's use the simplest case, rest frame to start. The full positive-energy solution is So the final complete wavefunction solution is It contains the 4 dimensions to describe the quantum state of the particle/wave/quantum and turns out it's a spinor … Continue reading Dirac Equation Solution

Why Dirac wanted to create the Dirac equation and solve it? Because he wants an equation that describes matter in a world where: Probability is conserved Spacetime is Lorentzian (special relativity is non-negotiable) States superpose (quantum mechanics) Time evolution is causal and first-order Special Relativity wants E2=p2+m2E^2 = p^2 + m^2 and Quantum mechanics wants … Continue reading Dirac Equation

It's because of how identical particles and spacetime symmetry work — let's unpack it. In quantum physics: identical particles are indistinguishable exchanging two identical particles cannot produce a new physical state So the state must be: unchanged, or changed only by a phase Fermions are antisymmetry: You may ask why fermions are antisymmetry, it relates … Continue reading Why Two Fermions Are Exclusive

When we think about fields, it always means something broad, wavy and unreal, it's such a big stretch to connect it to form the rich world we live in where concrete objects are everywhere. We need to know that Concrete objects are stable field configurations. There are three fundamental reasons: First, Fields are quantized, so … Continue reading If Everything is just fields, why does anything become solid, stable, and concrete — including our own bodies?

What is a generator? A generator is the object that tells you how something changes under an infinitesimal symmetry transformation. We need to entirely understand this via the lens of Lie Group and Lie Algebra. generator lives in the tangent vector space and is making the rotation on infinitesimal scale. The laws of nature are … Continue reading Energy is the Generator of Time Change

Recent news comes out that Meta is acquiring Manus for approximately $2 billion, a move that appears to lack technical rationale. What Manus really has is not some breakthrough AI. It is mostly a large amount of prompting and detailed instruction layered on top of the same commodity LLMs everyone else uses. They are good … Continue reading Meta Acquiring Manus for Billions Seems Like a Joke