Time dilation is a fascinating effect predicted by special relativity, which states that time can appear to pass differently for observers moving relative to each other. The effects of time dilation become noticeable when objects or observers are moving at speeds close to the speed of light, which is approximately 299,792 kilometers per second (or about 186,282 miles per second) in a vacuum.
The formula for time dilation in special relativity is given by:
Δt' = Δt / √(1 - v²/c²)
Where: Δt' is the time interval measured by an observer in relative motion. Δt is the time interval measured by an observer at rest (or in a different frame of reference). v is the relative velocity between the two observers. c is the speed of light in a vacuum.
As the relative velocity (v) approaches the speed of light (c), the denominator of the equation approaches zero, resulting in a larger value for time dilation. This means that as an object or observer approaches the speed of light, time appears to slow down for them relative to a stationary observer.
To make the effects of time dilation noticeable on Earth, where the relative velocities are typically much lower than the speed of light, extremely high speeds would be required. For practical purposes, the effects of time dilation are negligible at everyday speeds. However, time dilation becomes significant in experiments involving high-energy particles or when dealing with extremely fast-moving objects, such as spacecraft traveling at a substantial fraction of the speed of light.
For example, in the context of space travel, if a spacecraft were to travel at 99% of the speed of light (0.99c), significant time dilation effects would occur. Time would appear to pass much slower for astronauts on the spacecraft compared to an observer on Earth. This means that the astronauts' onboard clocks would appear to tick slower, and they would experience a slower passage of time relative to people on Earth. This effect is often depicted in science fiction as "time dilation" or "time travel."
In summary, while time dilation is a real and observable phenomenon, noticeable effects require velocities approaching the speed of light, which are not achievable in everyday situations on Earth.