The effects of time dilation from special relativity can be quite significant, especially at speeds close to the speed of light. The key concept behind time dilation is that time is not absolute but is instead relative to the observer's motion.
According to special relativity, when an object moves relative to an observer at a high velocity, time appears to pass more slowly for that object compared to a stationary observer. This effect becomes more pronounced as the relative velocity approaches the speed of light.
To quantify the time dilation effect, the Lorentz factor is used. The Lorentz factor (γ) is given by the equation:
γ = 1 / √(1 - v²/c²),
where v is the relative velocity between the observer and the moving object, and c is the speed of light.
As the relative velocity increases, the Lorentz factor increases as well, and time dilation becomes more significant. For example, let's consider an observer on Earth (stationary) and a spacecraft traveling at a velocity of 0.99c (99% of the speed of light). Plugging this value into the equation, we get:
γ = 1 / √(1 - (0.99c)²/c²) ≈ 7.09.
This means that from the observer's perspective, time on the spacecraft appears to pass at approximately 1/7th the rate compared to their own time. In other words, for every 7 seconds experienced on Earth, only 1 second would elapse on the moving spacecraft.
However, it's important to note that these effects are not noticeable in everyday situations on Earth. The velocities required for significant time dilation are extremely high, close to the speed of light. The speed of light is about 299,792 kilometers per second, and to see noticeable time dilation effects, velocities that are a significant fraction of the speed of light (such as 0.99c) would need to be attained.
In practical terms, the speeds at which time dilation becomes significant are currently beyond our technological capabilities for manned space travel. Nonetheless, time dilation has been observed and measured in experiments involving high-speed particles in particle accelerators and in observations of cosmic rays.
So, while time dilation is a real and experimentally confirmed effect, it is not something we typically experience or observe in our daily lives on Earth due to the relatively low velocities involved.