1. What is Time Dilation?

Time dilation is a phenomenon predicted by Einstein's theory of special relativity where time passes at different rates for observers in different inertial frames of reference, particularly when there is relative motion between them.

2. How Does the Calculator Work?

The calculator uses the time dilation formula:

Where:

• \( t' \) — Dilated time (s)
• \( t \) — Proper time (s)
• \( v \) — Relative velocity (m/s)
• \( c \) — Speed of light (3×10⁸ m/s)

Explanation: The equation shows how time measured in a moving frame (t') expands relative to the proper time (t) measured in the stationary frame, with the effect becoming significant as velocity approaches the speed of light.

3. Importance of Time Dilation

Details: Time dilation has been experimentally verified and has practical applications in GPS satellite systems, particle accelerators, and understanding cosmic phenomena. It fundamentally changes our understanding of time and space.

4. Using the Calculator

Tips: Enter proper time in seconds, velocity in m/s, and speed of light in m/s (default is 300,000,000 m/s). Velocity must be less than the speed of light for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is proper time?
A: Proper time is the time interval measured by an observer at rest relative to the event being measured.

Q2: At what speeds does time dilation become noticeable?
A: Time dilation effects become significant only at velocities approaching the speed of light (typically above 10% of c).

Q3: Has time dilation been experimentally verified?
A: Yes, through experiments with atomic clocks on airplanes and in particle accelerators with unstable particles.

Q4: What happens if v = c?
A: The denominator becomes zero, making the equation undefined. According to relativity, objects with mass cannot reach the speed of light.

Q5: Does time dilation affect aging?
A: Yes, this is known as the twin paradox - a traveling twin would age slower than their Earth-bound sibling.