Time is not completely separate from and independent of space as you would ordinarily assume. In his Special Relativity theory, Einstein assumed that the fundamental laws of physics do not depend on your location or motion. Two people, one in a stationary laboratory and another in a laboratory aboard a train or rocket moving in a straight line at uniform speed, should get the same results in any experiment they conduct. In fact, if the laboratory in the train or rocket is soundproof and has no windows, there is no experiment a person could conduct that would show he/she is moving.
The laws of physics include the laws of electromagnetism developed by James Clerk Maxwell (1831 - 1879) and Maxwell found that electromagnetic waves should travel at a speed given by the combination of two universal constants of nature. Since the laws of physics do not depend on your location or motion, Einstein reasoned that the speed of light will be measured to be the same by any two observers regardless of their velocity relative to each other. For example, if one observer is in a rocket moving toward another person at half the speed of light and both observers measure the speed of a beam of light emitted by the rocket, the person at rest will get the same value the person in the rocket ship measures (about 300,000 kilometers/second) instead of 1.5 times the speed of light (= rocket speed + speed of beam of light). This assumption has now been shown to be correct in many experiments. To get the same value of the speed (= distance/time) of light, the two observers moving with respect to each other would not only disagree on the distance the light traveled as Newton said, they would also disagree on the time it took.
Einstein found that what you measure for length, time, and mass depends on your motion relative to a chosen frame of reference. Everything is in motion. As you sit in your seat, you are actually in motion around the center of the Earth because of the rapid rotation of the Earth on its axis. The Earth is in motion around the Sun, the Sun is in orbit around the center of our Galaxy, the Galaxy is moving toward a large group of galaxies, etc. When you say something has a velocity, you are measuring its change of position relative to some reference point which may itself be in motion. All motion is relative to a chosen frame of reference. That is what the word "relativity'' means in Einstein's Relativity theories. The only way observers in motion relative to each other can measure a single light ray to travel the same distance in the same amount of time relative to their own reference frames is if their ``meters'' are different and their ``seconds'' are different! Seconds and meters are relative quantities.
Two consequences of Special Relativity are a stationary observer will find (1) the length of a fast-moving object is less than if the object was at rest, and (2) the passage of time on the fast-moving object is slower than if the object was at rest. However, an observer inside the fast-moving object sees everything inside as their normal length and time passes normally, but all of the lengths in the world outside are shrunk and the outside world's clocks are running slow.
One example of the slowing of time at high speeds that is observed all of the time is what happens when cosmic rays (extremely high-energy particles, mostly protons) strike the Earth's atmosphere. A shower of very fast-moving muon particles are created very high up in the atmosphere. Muons have very short lifetimes – only a couple of millionths of a second. Their short lifetime should allow them to travel at most 600 meters. However they reach the surface after traveling more than 100 kilometers! Because they are moving close to the speed of light, the muons' internal clocks are running much slower than stationary muons. But in their own reference frame, the fast-moving muons' clocks run forward ``normally'' and the muons live only a couple of millionths of a second.
Time and space are relative to the motion of an observer and they are not independent of each other. Time and space are connected to make four-dimensional spacetime (three dimensions for space and one dimension for time). This is not that strange – we often define distances by the time it takes light to travel between two points. For example, one light year is the distance light will travel in a year. To talk about an event, you will usually tell where (in space) and when (in time) it happened. The event happened in spacetime.
Another consequence of Special Relativity is that nothing can travel faster than the speed of light. Any object with mass moving near the speed of light would experience an increase in its mass. That mass would approach infinity as it reached light speed and would, therefore, require an infinite amount of energy to accelerate it to light speed. The fastest possible speed any form of information or force (including gravity) can operate is at the speed of light. Newton's law of gravity seemed to imply that the force of gravity would instantly change between two objects if one was moved – Newton's gravity had infinite speed (a violation of Special Relativity). The three strange effects of Special Relativity (shrinking lengths, slowing time, increasing mass) are only noticeable at speeds that are greater than about ten percent of the speed of light. Numerous experiments using very high-speed objects have shown that Special Relativity is correct.
Special Relativity also predicts that matter can be converted into energy and energy in to matter. By applying Newton's second law of motion to the energy of motion for something moving at high speed (its "kinetic energy''), you will find that energy = mass × (speed of light)2. More concisely, this is Einstein's famous equation, E = mc2. This result also applies to an object at rest in which case, you will refer to its "rest mass'' and its "rest energy'', the energy equivalent of mass. The amount of rest energy in something as small as your astronomy textbook, for example, is tremendous. If all of the matter in your textbook was converted to energy, it would be enough energy to send a million tons to the Moon!