1. What is Time Dilation?

Time dilation is a phenomenon predicted by Einstein's theory of relativity where time appears to pass at different rates for observers in different inertial frames of reference, especially when those frames are moving at significant fractions of the speed of light relative to each other.

2. How Does the Calculator Work?

The calculator uses the time dilation equation:

Where:

• \( \Delta t \) — Dilated time (observed time)
• \( \Delta t_0 \) — Proper time (time in the rest frame)
• \( v \) — Relative velocity between observers
• \( c \) — Speed of light (299,792,458 m/s)

Explanation: As velocity approaches the speed of light, time appears to slow down for the moving observer from the perspective of a stationary observer.

3. Importance of Time Dilation

Details: Time dilation has practical implications for GPS satellite systems, particle accelerators, and understanding astrophysical phenomena. It's a fundamental aspect of modern physics.

4. Using the Calculator

Tips: Enter proper time in seconds and velocity in meters per second. Velocity must be less than the speed of light (299,792,458 m/s).

5. Frequently Asked Questions (FAQ)

Q1: What is proper time?
A: Proper time (Δt₀) is the time measured by a clock at rest relative to the observer.

Q2: How significant is time dilation at everyday speeds?
A: At everyday speeds (e.g., car, plane), the effect is negligible. It becomes noticeable only at significant fractions of light speed (>10% of c).

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

Q4: What happens if v = c?
A: The equation becomes undefined (division by zero). Objects with mass cannot reach the speed of light.

Q5: Does this account for gravitational time dilation?
A: No, this calculator only handles special relativistic (velocity-based) time dilation. General relativity requires additional terms for gravity.