What are invariants, in relation to special relativity?

I'm a first year physics undergrad and in the lecures on relativity the lecturer briefly spoke about invariants but gave no detail. What are they?|||There are different types of quantities in relativity: Scalars, vectors, and tensors. Each has certain associated "invariants". By invariant is meant the value does not change when you change your inertial frame. Any relativistic scalar has a value which is invariant, like the rest mass of a particle or the speed of light. Any relativistic vector has one invariant: its length. For example, a vector connecting two points (or "events) in spacetime has an invariant length. (e.g. it two events occur at (x1,y1,z1,t1) and (x2,y2,z2,t2) then the square of the spacetime distance between them is c^2(t2-t1)^2-(x2-x1)^2-(y2-y1)^2-(z2-z1)… There is also a momentum vector mo g ( vx, vy, vz, c) where g is "gamma" and mo is the rest mass and (vx,vy,vz) is the velocity vector. So that means m^2g^2(v^2-c^2)= m^2c^2 is invariant (mo^c^2) is the total energy of the particle, which is therefore also invariant). There is an electromagnetic charge-current vector, and an electromagnetic potential vector, and their lengths are invariant also. Most tensors in relativity are antisymmetric tensors. An antisymmetric tensor in spacetime has three invariants (three might not be the right number, I forget). That means there are three invariants associated with the stress-energy tensor, and three associated with the electromagnetic field tensor. There are more, but they are all of this type.|||C for example (Speed of light in a vacuum)|||Quantities which are the same in all (inertial) reference frames.





Measured velocity of an object depends on the frame of reference. So velocity is not an invariant. But mass is invariant (what used to be called "rest mass").





Energy and momentum are frame-dependent, because energy includes kinetic energy. But the quantity E^2 - (pc)^2 is invariant and equal to (mc^2)^2.