Question

What physical laws govern time dilation, as observed when two objects traveling at different velocities measure elapsed time differently?

Answer 1

Time dilation is governed by the principles of special relativity, which is a fundamental theory in physics developed by Albert Einstein. The key laws that govern time dilation due to relative motion are as follows:

1. Principle of Relativity: The laws of physics are the same in all inertial reference frames. An inertial reference frame is a frame of reference in which an object not subject to any external forces remains at rest or moves with a constant velocity.

2. Constancy of the Speed of Light: The speed of light in a vacuum is constant for all observers, regardless of their relative motion. This is a fundamental postulate of special relativity.

3. Time Dilation Equation: The relationship between time dilation, relative velocity, and the elapsed time between two events can be described by the time dilation equation:

   Δt' = Δt / γ

   where Δt' is the elapsed time as measured in a frame of reference moving relative to the stationary frame, Δt is the elapsed time as measured in the stationary frame, and γ (gamma) is the Lorentz factor given by:

   γ = 1 / √(1 - (v^2 / c^2))

   Here, v is the relative velocity between the two frames, and c is the speed of light.

4. Relativity of Simultaneity: The concept of simultaneity is relative. Events that are simultaneous in one frame of reference may not be simultaneous in another frame that is moving relative to it.

These laws together dictate that as the relative velocity between two objects increases, the time dilation effect becomes more pronounced. The moving object experiences time passing more slowly compared to the stationary object. This effect is symmetric, meaning both observers will perceive time dilation relative to each other.

It's important to note that the laws governing time dilation due to gravity are different and are described by the theory of general relativity, which accounts for the curvature of spacetime caused by massive objects. In the case of gravitational time dilation, the principles of general relativity and the Einstein field equations play a central role in determining the effects of gravity on the flow of time.