The Phenomenon of Time Dilation

Time Dilation is a consequence of Albert Einstein's Special Theory of Relativity. It states that time passes differently for observers who are moving relative to each other, or for observers in different gravitational fields (though this calculator focuses on velocity-based time dilation).

Specifically, a clock that is moving relative to an observer will be measured to tick slower than a clock that is at rest with respect to that observer. The faster the relative velocity, the greater the time dilation effect.

How to use this calculator:

1. Enter the Proper Time (t₀). This is the time interval measured by an observer in the moving reference frame (e.g., an astronaut on a fast spaceship measuring time with their own clock).
2. Enter the Relative Velocity (v) of the moving reference frame with respect to a stationary observer. This can be entered directly in m/s or as a fraction/percentage of the speed of light (c).
3. Click "Calculate Time Dilation".
4. The results will display the Dilated Time (time measured by the stationary observer), the difference in time, and the Lorentz Factor.

Theory & Formulas

The key principles for understanding time dilation due to relative velocity are:

1. Proper Time (t₀):

Proper time is the time interval between two events occurring at the same location in a given reference frame. It's the shortest possible time interval measured between those two events.

2. Lorentz Factor (γ - Gamma):

The Lorentz factor is a fundamental quantity in special relativity that appears in several relativistic formulas, including time dilation and length contraction. It is defined as:

3. Dilated Time (t):

The time interval (t) measured by an observer in a stationary reference frame, for events occurring in a frame moving at velocity (v) relative to them, is longer than the proper time (t₀) measured in the moving frame. This is given by:

This means that from the perspective of the stationary observer, the moving clock runs slow.

Variables:

• t: Dilated time, measured by the stationary observer (same units as t₀)
• t₀: Proper time, measured in the moving reference frame (e.g., seconds, minutes, years)
• v: Relative velocity between the two reference frames (m/s)
• c: Speed of light in a vacuum (approximately 299,792,458 m/s).
• γ: Lorentz factor (dimensionless).

Calculator Inputs

Calculation Results

Dilated Time (t):

Time Difference (t - t₀):

Lorentz Factor (γ):

Step-by-Step Solution