Reference Frame - Two Case

1. Inertial Reference Frame

An inertial reference frame is either at rest or moves with a constant velocity.

2. Non-Inertial Frame

Non−inertial reference frame is a reference frame that is accelerating either in linear fashion or rotating around some axis

Event

In physics, and in particular relativity, an event is the instantaneous physical situation or occurrence associated with a point in spacetime (that is, a specific place and time). For example, a glass breaking on the floor is an event; it occurs at a unique place and a unique time.

Variant & Invariant in both Mechanics

In classical mechanics and relativistic mechanics, “invariant” and “variant” are terms used to describe physical quantities or properties that remain constant or change, respectively, under certain transformations.

  1. Invariant: In classical mechanics and relativistic mechanics, an “invariant” is a physical quantity or property that remains constant, independent of the coordinate system or frame of reference used to describe it. In other words, an invariant quantity does not change under certain transformations, such as rotations, translations, or Lorentz transformations in relativistic mechanics.

For example, in classical mechanics, the total mechanical energy of a system (kinetic energy + potential energy) is an invariant. Regardless of the reference frame from which it is observed, the total mechanical energy remains the same as long as no external forces act on the system.

In relativistic mechanics, the spacetime interval (a combination of time and space intervals) between two events is an invariant quantity. Different observers moving at different velocities will measure different time and space intervals between the events, but the spacetime interval remains constant for all observers.

  1. Variant: A “variant” in classical mechanics and relativistic mechanics refers to a physical quantity or property that changes under certain transformations or changes of the coordinate system or frame of reference.

For example, in classical mechanics, the velocity of an object is a variant. The velocity of an object depends on the choice of reference frame, and different observers moving at different velocities will measure different values for the object’s velocity.

In relativistic mechanics, the relativistic mass of an object is a variant. The mass of an object is dependent on its velocity relative to the observer’s frame of reference. As an object’s velocity approaches the speed of light, its relativistic mass increases, which is a unique feature of relativistic mechanics.

Understanding invariants and variants is essential in analyzing physical phenomena and making predictions in different reference frames, whether in classical mechanics or relativistic mechanics. The presence of invariant quantities often provides valuable insights into the fundamental laws of physics and helps simplify complex calculations and analyses.

Is Energy Invariant in relativity?

The relativistic mass corresponds to the energy, so conservation of energy automatically means that relativistic mass is conserved for any given observer and inertial frame. However, this quantity, like the total energy of a particle, is not invariant.