1. What is Time Dilation?

Definition: Time dilation is a difference in the elapsed time measured by two observers due to a relative velocity between them or a difference in gravitational potential.

Purpose: This calculator demonstrates the relativistic effect where time appears to pass at different rates for observers in different inertial frames.

2. How Does the Calculator Work?

The calculator uses the time dilation formula from special relativity:

Where:

• \( t' \) — Proper time (seconds) experienced by moving observer
• \( t \) — Coordinate time (seconds) in stationary frame
• \( v \) — Relative velocity (meters/second)
• \( c \) — Speed of light (3 × 10⁸ m/s)

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

3. Importance of Time Dilation

Details: Time dilation has practical implications for GPS satellites, particle accelerators, and understanding the fundamental nature of spacetime.

4. Using the Calculator

Tips: Enter the coordinate time (t), relative velocity (v), and speed of light (c). Velocity must be less than speed of light.

5. Frequently Asked Questions (FAQ)

Q1: What happens at the speed of light?
A: The equation becomes undefined as v approaches c, suggesting time would stop for a photon.

Q2: How significant is time dilation at everyday speeds?
A: Negligible - at 1000 m/s (Mach 3), time dilation is only about 5.56 × 10⁻¹² seconds per second.

Q3: What's the speed of light value?
A: Approximately 299,792,458 m/s (3 × 10⁸ m/s is commonly used for calculations).

Q4: Does this account for gravitational time dilation?
A: No, this is only for special relativity. General relativity requires additional terms for gravity.

Q5: What are real-world examples of time dilation?
A: GPS satellites must account for time dilation, gaining about 38 microseconds per day due to their orbital velocity.