1. What is Time Dilation?

Time dilation is a difference in the elapsed time measured by two observers due to a relative velocity between them or to a difference in gravitational potential between their locations. The formula Δt = γΔt₀ shows how time appears to 'slow down' for a moving observer.

2. How Does the Calculator Work?

The calculator uses the time dilation formula:

Where:

• \( \Delta t \) — Dilated time (observed time)
• \( \gamma \) — Lorentz factor (γ ≥ 1)
• \( \Delta t_0 \) — Proper time (time in rest frame)

Explanation: The Lorentz factor γ is calculated from relative velocity as \( \gamma = \frac{1}{\sqrt{1 - v^2/c^2}} \), where v is the relative velocity and c is the speed of light.

3. Importance of Time Dilation

Details: Time dilation has been experimentally confirmed and is crucial for GPS satellite systems, particle physics experiments, and understanding the fundamental nature of spacetime in special relativity.

4. Using the Calculator

Tips: Enter the Lorentz factor (γ) and proper time (Δt₀). Both values must be positive numbers. The calculator will compute the dilated time (Δt) experienced by the moving observer.

5. Frequently Asked Questions (FAQ)

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

Q2: How significant is time dilation at everyday speeds?
A: At everyday speeds (much less than light speed), time dilation effects are negligible. For example, at 1000 km/h, γ ≈ 1.0000000004.

Q3: Has time dilation been experimentally verified?
A: Yes, through experiments with atomic clocks on airplanes and satellites, and observations of fast-moving particles.

Q4: What is gravitational time dilation?
A: Time also runs slower in stronger gravitational fields, described by general relativity (not this calculator's focus).

Q5: What happens when γ approaches infinity?
A: As velocity approaches light speed (v→c), γ→∞, meaning time appears to stop for the moving object from an external observer's perspective.