Thinks of these as abstract constructs that help model problems in physics and do calculation using math.
Vectors: Vectors are abstract Physics/Mathematical objects or constructs that help physicist explain some phenomenon and do calculations.
They have certain mathematical laws and operations.
For example:
* Forces acting on Newtonian body
* Particle motion in Magnetic field
* Gravity acting on body
* Velocity of body
Tensors: Types of constructs which is used explain certain exotic phenomenon. They are generalized form of vectors (rank and dimension) and can cover a wide rage of uses cases than just plain vectors. The tensors can have transformations such as translation, shear, twist, stretch etc.
- Stress tensors to explain the forces within the body
* Electromagnetic Tensor
* Ball rolling on floor can be modeled by Rank-1 Tensor (Rank-1 Tensor = Vector)
* Einstein used Rank-1 4D tensors to explain the theory of relativity. Frame of reference: Our choice of co-ordinate must have no effect on reality.
Note: Programming tensors (Machine learning) are not Physics tensors.
Phasors: Yet another special kind of complex number vectors that deal with phase (angle) and amplitude. They live in complex plane and have relation with sine waves, unlike the vectors in XY plane which have direction and magnitude. Think of these as having some relation to rotating stuff in circle.
- Used in RLC circuits and electrical engineering
Spinors:
Paul Dirac and Pauli used this kind of constructs to explain the why electrons (hence) don’t pass into each other like ghosts.
It has something to do with quantum mechanics.
* Every Point in Electromagnetic field is treated as spinor
* Modeling of sub atomic particle
Bottom note: We common humans are not very good at understanding universe or reality from the perspective of modeling a physics problem into complicated mathematical objects which then can be used to explain how the things in reality work, why they work and what implications they have on current understanding.
Its like inventing a new sort of programming language that could help us do difficult stuff more easily. So keep inventing new physical /mathematical constructs who knows may be one day we will solve some interesting problems.
And yes, calculus is awesome. Wish we humans used these as much as we used TikTocs in daily life.
