How do Einstein's thought experiments show that time dilation is possible?

As a mass volume is moving in space it would experience a time increase as it travels a particular distance.Thus it can be said that as a mass moves in space time dilates.Hence the greater the distance of travel, the more time dilates. That means no matter how fast you travel time will always follow you. Einstein time experiments were about how clocks measure time. He discovered that no two clocks can measure the same time exactly.If a pendulum clock was located in different gravity fields it would measure time differently. If a mass moving in different gravitational potential levels of space it would experience changes of velocity. Hence light being a micro mass particle moving in different time potential levels of space would fall under the same rules. That means that the way we observe time at large distance is not the same as we observe time in short distances. If an observer on earth viewing a celestial body at astronomical distance it would appear to move very slow as compared to the actual speed its really moving. Hence Einstein relativity is a theory of measurement based on how an observer views it.Hence that means how things appear and not what they really are.

You have asked a very good question! You must have thought long and hard about time dilation in order to come up with it. As you might expect, there is a long answer and a short answer to address the issue you have raised. I’ll give you the short answer here and if it is not enough then you can ask another question and learn what I might have left out. So, here it is: Time dilation is only a part of what happens when an object approaches the speed of light, as an object approaches the speed of light space contracts. Suppose a rocket ship flies past you at 80% of the speed of light and as it passes from your left to your right you notice that a person in the ship is holding a meter stick horizontally. If you measured that meter stick against one that you are holding you would notice that the meter stick in the rocket ship is measurably shorter than your meter stick. If space contracts as time slows down the net change from one inertial from to another is zero. Everyone in each inertial frame measures the same distance per time ratio as Earth revolves around the sun.

Einstein worked with the work of others: Maxwell: The Speed of Light is constant regardless of the motion of the observer Observation by many scientists: Maxwell was correct. Lorentz & Ponicare': Lorentz Transform to convert between moving Inertial Frames of Reference Einstein pulled all the above into a coherent, air tight theory ===> Special Relativity We start with the Train and pitcher thought experiment. You are standing on the ground next to a train track. A train going 100 km/hr is going past. On a flat car is a baseball pitcher that you know can throw 195 km/hr fastballs throwing toward toward you. You have a radar gun so you can measure the speed of the baseballs. What speed would you measure if the train was coming toward you? (100 + 195 = 295 km/hr ) What speed would you measure if the train was going away from you? (195 - 100 = 95km/hr) Now we start Special Relativity: Toward the end of the 1800s scientists measured the speed of light compared with the speed of the earth in orbit. They expected that knowing the speed of the earth going toward the source of light the velocities would add and that when going away from the source of light the velocities would subtract. BUT that is not what happened. It did not matter if they were moving toward the source or away from the source, they got the same value: roughly 3 * 10^8 m/s. VERY STRANGE! They were sure something was wrong. It was not possible, based on their assumption that Time and Space were absolute (unchanging) for that to be true. Einstein's insight: He thought,"What if the speed of light IS absolute and Time and Space could change to make that true? What does that do to everything else? He worked it out for all the physical quantities. It works! What you get is consistent with what we observe in experiments. This site will let you play with what happens at near light speed http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html The only way that the speed of light can be constant for all observers in Inertial Frames of Reference is for time and space to dilate. It cannot work any other way.