Techncially we are all time travelers, sitting at your computer you are moving through time. We are submerged in time and with no effort on our part, we watch the seconds on our clocks tic away. Just as the speed of the river changes slightly from one fish to another, the speed of time changes slightly for us as we accelerate, and thus the laws of physics behave as if we each have our own individual clock. And that our individual clocks vary from one person to another in the precise amount necessary to maintain the speed of light as the universe's constant.
If you flip on your flashlight, the photons escape from the flashlight at the speed of light and one second later those emerging rays of light are exactly 299,792,458 meters away. And, if you were to travel in the direction of that light, even if you were traveling in a spaceship, the light will always be receeding from you at exactly 299,792,458 meters per second. No matter how fast you travel, you could never change that fact. The speed of light is constant in all directions and Newton's model of the universe was flawed.
Einstein first proposed this in 1905, and in the past 100 years there have been a tremendous number of experiments which prove time is relative. These experiements prove that the faster you travel, your clock slows in the precise amount necessary to allow the opportunity for light to travel the distance of 299,792,458 meters in one second as measured by your individual clock. But you should also notice that the constance of light's speed is achieved by slowing your individual clock, hence time is relative to you.
People who disagree don't understand the relativity of time because it defies daily experience. We don't normally travel near the speed of light and we synchronize our lives to the same work, TV or school schedules. But we are time travelers, the universe assigns each of us our own individual clock, and our individual clock is constantly readjusting itself as we move. And this varying of our individual clock maintains the fact that the speed of light as measured from our individual clock is always traveling away from us at 299,792,458 meters per second.
So contrary to what we normally feel about time, time is relative to each of us and the laws of physics behave as if each of us has our own individual clock. And as we move our individual clocks vary from one another in the precise amounts necessary to maintain the speed of light as the universes's constant.