To Learn in Physics

To Learn in Physics

Remember to think freely and not confine to the terminologies!

Quantum Spin - Spinors - Spin Statistic Theorem - Knots (More on this and spinors, on PBS Space Time at YT)
- Premise: Conservation of Angular Momentum
- Einstein de-Haas effect - experiment involving a suspended iron cylinder subjected to a vertical magnetic field causing it to rotate
- Electrons have a spin property, which is conserved when they are aligned by the magnetic field
- Zeeman Effect: Zeeman, Lorentz figured out that while looking at specific wavelengths emitted by electrons when jumping between energy levels, these energy levels split when atoms are put in an external magnetic field
  - Lorentz described this using the ideas of classical physics - that an electron being a spinning ball of charge moving in circles around an atom would lead to a magnetic moment - a dipole magnetic field. The different alignments of that orbital magnetic field relative to the external magnetic field turns one energy level into three.
  - Anomalous Zeeman effect - In some cases the magnetic field causes energy levels to split even further
  - One explanation was that each electron has its own magnetic spin
  - For this, electrons must be spinning balls
  - Pauli pointed out that in that case the electrons must be spinning faster than the speed of light - even if they were particles at all.
  - Pauli's called it classically non-describable two-valuedness
- Quantum spin is therefore an intrinsic angular momentum, unlike classical angular momentum
- Stern-Gelarch Experiment
- Pauli's inclusion of spinors to Schrodinger's Equation
- Dirac found a complete fix of Schrodinger's Equation to make it work with Relativity - it could only work by including spinors.
- Electron spin only corrects orientation every 720 degrees.
  - One rotation causes a twist, another brings it back
  - Technically a spinor wavefunction has a phase that changes with orientation angle, and a 360 degree spin makes it out of phase from the starting point
- Hans Ohanian, author of one of the most used Quantum textbooks, shown that you can derive the angular momentum and magnetic moment by looking at the energy and charge currents in the Dirac field, i.e. the quantum field surrounding the Dirac spinor, or the electron.
- Particle described by spinors have half integer Spin QNs. +/- 1/2. They are fermions.
- Bosons are described by vectors, not spinors. These rotations define how they interact with each other.
Why can't magnetic field be described by applying relativity to electric field? (More: In my Zoho Notebooks)
Poynting Vector - Light and Sound (More: in my journal)
Basic Engineering Physics and Chemistry: Schrodinger's Equation derivation, Degrees of Freedom, Jablonski Diagrams, Quantum Tunneling, etc.
Quantum Field Theory
- Derived because independent particles cannot explain how particles are the same everywhere, and also quantum mechanics does not work well with changing number of particles, e.g. an absorbed photon
- QFT is a new mathematical framework that introduces a field
- A mathematical field is like a fluid that fills spacetime, with each point populated by a mathematical object
- The mathematical objects should obey some symmetries, as restricted by special relativity, called Poincare Symmetries
- These are only respected by certain mathematical objects, and they are classified by a parameter known as spin.
- Numbers - 0, Spinors - 1/2, Vectors - 1, 3/2, 2
- Each symmetry forces the field to respect the conservation of certain quantities over time
  - Conservation of energy, momentum, angular momentum and velocity of the center of mass
- The mathematical objects can contain symmetries of their own (e.g. complex numbers exhibit an internal symmetry, which implies the conservation of another quantity over time, related to the very nature of complex numbers, the electric charge)
- To transform a classical object to a quantum object, we allow it to occupy several positions
- Similarly, to transform a classical field to a quantum field, we allow it to have different configurations that evolve over time (spacetime field). Over time, the field evolves as a superposition of all possible scenarios.
- Just like energy levels for electrons in an atom, a quantum field also has energy levels. It can only contain an integer number of disturbances, or quanta of energy. These are particles, similar to a wave on the surface of water. A particle is simply a disturbance that propagates through the field.
- Quantum field is also agitated by fluctuations which keep popping in and out of existence. These are called virtual particles and are extremely short-lived.
- In our universe several fields coexist and constitute different families of particles. e.g. Vector fields (spin 1), Spinors (spin 1/2), Higgs Field (spin 0)
- Among all these fields, most have internal symmetries which provide them with quantities that are conserved over time, or charges which distinguish their particles between different versions.
  - Fields formed from complex numbers have a symmetry which gives them their electric charge. This gives a positive and negative charge. This is antimatter.
  - Antimatter is the complex conjugate of the ordinary particle.
  - The quark field exhibits a symmetry that assigns them another charge, the colour charge, which must also be conserved over time.
  - The set of all these fields is the standard model of particle physics.
- Interactions
  - e.g. Photon Field and Electron Field
  - We allow an electron to emit or absorb a virtual photon and vice versa.
  - This will cause a problem. For example, we start with two motionless electrons, which progress in a straight line over time.
  - But the fields can evolve in various ways. Sometimes the electrons absorb or emit virtual particles, causing them to diverge or attract in different ways. But the overall sum of interactions is what predicts the state of the real world, in which the electrons diverge. In this way, QFT predicts forces simply from symmetries.
  - If the particles were an electron and a positron, they would attract.
- Therefore, in QFT, the evolution of the universe is described as the synthesis of all possible scenarios in the microscopic scale.
- Problems: This works with special relativity, but not with general relativity.
String Theory
M-Theory
Special Relativity
General Relativity
Fluid Mechanics and Analysis
Solid Mechanics and Analysis
Radio and Signal Processing
Electrical Networks and Analysis
Condensed Matter Physics
Solid State Physics
Thermodynamics
Black Body Radiation and Quantization of Light
Quantum Mechanics and its Interpretations
Chemical Bonding
Organic Chemistry
Biology