When physicists say that time is relative to the observer, they are referring to a key concept in Einstein's theory of special relativity called time dilation.
According to special relativity, the flow of time can appear to be different for different observers depending on their relative motion. The faster an object moves, the slower time appears to pass for that object compared to a stationary observer. This phenomenon is known as time dilation.
To understand this, let's consider a thought experiment. Imagine two observers, one stationary and the other traveling in a high-speed spaceship. From the perspective of the stationary observer, time would appear to be passing normally. However, from the perspective of the observer inside the spaceship, time would seem to be passing more slowly.
This means that if the observer in the spaceship were to measure a certain time interval for an event, the stationary observer would measure a longer time interval for the same event. In other words, time is relative to the observer's motion.
The effect of time dilation becomes more significant as the speed of the object approaches the speed of light. At speeds close to the speed of light, time dilation becomes quite pronounced. For example, a hypothetical observer traveling at 99% of the speed of light would experience time passing much more slowly compared to a stationary observer.
Experimental evidence has confirmed the existence of time dilation. For instance, high-speed particles called muons, created in the upper atmosphere by cosmic rays, have a short lifetime at rest. However, due to their high speeds, they can travel significant distances before decaying, as observed from Earth. This is only possible because time is dilated for the muons as they move close to the speed of light.
It's important to note that time dilation is a relative effect. From the perspective of each observer, their own clocks always tick normally. It is only when comparing the measurements of two observers in relative motion that the differences in the flow of time become apparent.
In summary, when physicists say that time is relative to the observer, they mean that the flow of time can appear different for different observers depending on their relative motion. This effect is known as time dilation and is a consequence of Einstein's theory of special relativity.