Grade 12
  1. Advanced mechanics  1.1. Dynamics  1.1.1. Motion in two and three dimensions  1.1.2. Advanced Projectile Motion and Range Equations  1.1.3. Relative motion in different reference frames  1.1.4. Motion of charged particles in electric and magnetic fields  1.1.5. Non-uniformly accelerated motion in multiple dimensions  1.2. Dynamics  1.2.1. Newton's laws and applications in non-inertial frames  1.2.2. Dynamics of particle systems  1.2.3. Non-conservative forces and energy dissipation  1.2.4. Momentum in variable mass systems (rocket momentum)  1.2.5. Lagrangian and Hamiltonian Mechanics (Introduction)  1.3. Work, Energy and Power  1.3.1. Work done by non-conservative forces  1.3.2. Power in rotational and translational motion  1.3.3. Advanced Conservation Laws and Applications  1.3.4. Potential energy surface and stability  1.4. Advanced rotational speed  1.4.1. Torque in three dimensions  1.4.2. Moment of inertia for irregular bodies  1.4.3. Gyroscopic motion and precession  1.4.4. Rotational work–energy theorem  1.4.5. Euler's equations of rotational motion  1.5. Gravitational force  1.5.1. Advanced Orbital Mechanics  1.5.2. Lagrange points and stability of orbits  1.5.3. Gravitational time dilation  1.5.4. Escape velocity and energy considerations  1.5.5. Tidal force and the Roche limit
  2. Fluid mechanics and thermodynamics  2.1. Fluid dynamics  2.1.1. Applications of Bernoulli's Principle  2.1.2. Navier-Stokes equations and fluid resistance  2.1.3. Turbulent vs. Laminar Flow  2.1.4. Surface tension and capillary action  2.2. Advanced Thermal Physics  2.2.1. Thermodynamic equilibrium and heat engines  2.2.2. Entropy and the Second Law of Thermodynamics  2.2.3. Maxwell's demon and statistical thermodynamics  2.2.4. Thermodynamic potential and free energy
  3. Oscillations and waves  3.1. Advanced Simple Harmonic Motion  3.1.1. Coupled oscillations and common modes  3.1.2. Damped and driven oscillations  3.1.3. Phase space and resonance  3.1.4. Anharmonic oscillations  3.2. Wave motion  3.2.1. Advanced wave equations and dispersion  3.2.2. Shock Waves and Sonic Booms  3.2.3. Doppler effect in electromagnetic waves  3.2.4. Wave–particle duality
  4. Electromagnetism  4.1. Electrostatics  4.1.1. Gauss's law in unilateral charge distribution  4.1.2. Electric potential for complex charge configuration  4.1.3. Electrostatic energy and self-energy of a system  4.1.4. Dielectrics and Polarization  4.2. Current Electricity  4.2.1. Advanced Circuit Analysis (Thevenin and Norton theorems)  4.2.2. RC, RL and RLC circuits in AC and DC  4.2.3. Superconductivity and applications  4.3. Advanced Magnetism and Electromagnetic Induction  4.3.1. Magnetic fields in conductors and plasma  4.3.2. Lenz's law in time-dependent magnetic fields  4.3.3. Eddy Currents and Applications  4.3.4. Magnetic dipole moment and torque on electric current loops  4.4. Alternating Current and Electromagnetic Waves  4.4.1. LC Circuits and Resonance  4.4.2. Maxwell's equations and electromagnetic wave transmission  4.4.3. Applications of Electromagnetic Waves  4.4.4. Polarization and reflection of EM waves
  5. Optics  5.1. Geometrical Optics  5.1.1. Aberrations in optical systems  5.1.2. Advanced lens and mirror formulas  5.1.3. Optical Instruments and Adaptive Optics  5.2. Wave optics  5.2.1. Diffraction at single and multiple slits  5.2.2. Optical Coherence and Interferometry  5.2.3. Holography and applications
  6. Modern and quantum physics  6.1. Special relativity  6.1.1. Time expansion and length contraction  6.1.2. Relativistic energy and mass  6.1.3. Relativistic Doppler effect  6.2. Quantum mechanics  6.2.1. Schrödinger equation and wave function  6.2.2. Quantum tunneling and applications  6.2.3. Heisenberg uncertainty principle  6.2.4. Quantum superposition and entanglement  6.3. Nuclear physics  6.3.1. Binding energy and mass defect  6.3.2. Neutrino physics and beta decay  6.3.3. Nuclear Fission and Fusion  6.4. Particle physics  6.4.1. Standard Model and fundamental interactions  6.4.2. The Higgs boson and symmetry breaking  6.4.3. Antimatter and CP violation
  7. Astrophysics and cosmology  7.1. General relativity and gravity  7.1.1. Einstein's field equations  7.1.2. Gravitational waves and their detection  7.1.3. Black holes and event horizons  7.2. Cosmology  7.2.1. Dark matter and dark energy  7.2.2. Cosmic microwave background radiation  7.2.3. The expansion of the universe and Hubble's law

Grade 12 ↓


Modern and quantum physics


Modern physics focuses on two major breakthroughs of the early 20th century: relativity and quantum mechanics. Classical physics, which includes Newton's laws of motion and Maxwell's electromagnetism, is extremely effective at describing everyday phenomena. However, it begins to break down when dealing with the very fast, the very large, the very small, or the very intense. In modern physics, we venture into these areas to understand how nature behaves in these extreme cases.

Relativity

Albert Einstein's theory of relativity revolutionized our understanding of space, time, and gravity. There are two parts of relativity: special relativity and general relativity.

Special relativity

The special theory of relativity, introduced by Albert Einstein in 1905, addresses the behavior of objects traveling at high speeds. It is based on two principles:

  • The laws of physics are the same for all observers, regardless of their relative speed.
  • The speed of light in a vacuum remains constant for all observers, regardless of their relative speed or the speed of the light source.

A major consequence of these notions is time dilation, which means that time passes slower for moving objects than for a stationary observer.

Δt' = Δt / √(1 - v²/c²)

In this equation:

  • Δt' is the time interval measured by a moving observer.
  • Δt is the time interval measured by a stationary observer.
  • v is the velocity of the moving object.
  • c is the speed of light.

Example

Imagine a spaceship passing the Earth at 90% of the speed of light. An hour passes on the spaceship, but much longer has passed on Earth. This shows how time slows down for a fast-moving object.

General relativity

General relativity, proposed by Einstein in 1915, explains gravity not as a force, as Newton did, but as a curvature of spacetime due to mass. According to this theory, massive objects such as planets and stars distort the fabric of spacetime, and these distortions guide the motion of smaller objects.

Visualization of curved spacetime

In this simple diagram, the circle represents a massive object, and the line represents how spacetime is curved around it.

Quantum physics

Quantum physics, developed in the early 20th century, is the branch of physics that deals with the behavior of very small particles. It challenges many classical intuitions with surprising predictions about the nature of reality.

Wave–particle duality

One of the most fascinating aspects of quantum physics is wave-particle duality. This theory states that every particle, like an electron or a photon, can exhibit both wave-like and particle-like properties, depending on how it is viewed.

Double slit experiment

In a double slit experiment, light or electrons are fired through two parallel slits. On the other side, a screen shows an interference pattern of multiple bands, indicating wave-like behavior. However, when the particles are observed passing through one slit, they behave like particles.

In the SVG above, particles come in from the left, pass through the slits, and create an interference pattern on the right.

Quantum entanglement

Quantum entanglement describes a phenomenon in which two particles become intertwined, such that the state of one particle instantaneously affects the state of the other, no matter how much distance there is between them. This was one of the ideas that puzzled Einstein, leading him to describe it as "spooky action at a distance."

Visualization of entangled particles

This image shows two entangled particles, one blue and one red, connected by entanglement (dashed line).

Fundamentals of quantum mechanics

Uncertainty principle

The uncertainty principle, formulated by Werner Heisenberg, states that certain pairs of physical properties, such as position and momentum, cannot both be known precisely at the same time. The more precisely one is known, the less precisely the other can be known.

Δx * Δp ≥ ħ/2

Here:

  • Δx is the uncertainty in position.
  • Δp is the uncertainty in momentum.
  • ħ is the decreasing Planck constant, h divided by 2π.

Quantum superposition

According to quantum superposition a particle exists in all of its possible states simultaneously until it is measured, after which it 'chooses' a state. A famous example of this concept is Schrödinger's cat, a thought experiment depicting a cat that is both alive and dead until it is observed.

Schrödinger's cat thought experiment

A cat is placed in a sealed box containing a poison that can be released by a random quantum event. According to quantum mechanics, until the box is opened, the cat is in a state of being both alive and dead. This thought experiment highlights the unique nature of quantum superposition.

Conclusion

Modern and quantum physics have vastly enhanced our understanding of the universe. By exploring the minuteness of particles and the vastness of space, these theories provide a foundation for technological advancement and deepen our understanding of the physical world. Although often contradictory, these fields depict a universe that is far richer and more complex than what can be seen through the lens of classical physics. Both relativity and quantum mechanics challenge, enlighten, and inspire us, giving us a deeper understanding of the complexities of our universe.


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