According to the theory of special relativity, the phenomena of time dilation and length contraction occur simultaneously for an observer who is moving relative to another reference frame. However, the variation of mass with velocity, often referred to as relativistic mass, is a concept that is no longer commonly used in modern physics. Instead, the invariant mass, also known as rest mass, is considered as the intrinsic property of an object and does not change with velocity.
When an observer is in motion relative to another observer, they will experience time dilation, where time appears to run slower for the moving observer compared to the stationary observer. Simultaneously, the moving observer will also perceive a contraction of lengths in the direction of motion. This is known as length contraction, where objects in the direction of motion appear shorter when measured by the moving observer.
It's important to note that time dilation and length contraction are reciprocal effects. Each observer will perceive the other's time to be dilated and length to be contracted. This reciprocity is a fundamental principle of special relativity known as the relativity of simultaneity.
However, the concept of relativistic mass is no longer widely used because it can lead to confusion and is not as conceptually consistent as using invariant mass. In modern physics, mass is considered as an invariant property of an object and does not depend on its velocity. Instead, the energy of an object is related to its mass through the famous equation E = mc², where E is the energy, m is the invariant mass, and c is the speed of light.
So, to summarize, time dilation and length contraction occur simultaneously for an observer in motion relative to another reference frame, but the concept of mass variation with velocity is no longer commonly used in modern physics.