Einstein told us that the speed of light must always, not only appear, but BE the same in every frame of reference no matter how fast we are moving towards or away from it. So even if you are moving at half the speed of light towards a light beam, the entire universe must conspire to either "speed up" or slow down your "time" to account for this difference.
If that makes sense to you, you are no longer sane. You cannot create scenarios of two mutually exclusive events at the same time and call that reality. This is fundamental to reason.
To show this contradiction, consider you are running away from a light beam and towards another at the same time. You move at half the speed of light. Of course in real life you will encounter the light you are moving towards first, but in Einstein's universe both beams MUST (in your world) hit you at the same time. However, in Einstein's universe, someone else will see them hit you at different times because they also MUST see light travel at a certain speed. This is just plain fucking stupid.
At best you can have an illusory effect, but to confuse that with a real difference in simultaneity is to truly give up on reason itself.
Just never forget that everything you see, you see with a delay proportional to the distance from you to the object you observe. If oblect you observe moves with speed close to the speed of light, light from different parts of object (head and tail of your train, f.e.) need additional time to reach your eyes.
Meanwhile, there is funny thought experiment that always make relativists hang indefinitely.
They often talk about time dilation effect. However, you could make a clock using speed of light as a source of time intervals. Pulse a LED into a sensor through mirror at a distance (or fiber) and use delay as a clock sync. Use delayed pulse from sensor to pulse LED again. You will get a simple clock base frequency generator. Since there is constant speed of light dogma in relativity, then this clock just can't have any dilation effect, regardless of any relative movements and inertial frames. :) Whoever observe this clock, he will have to see exactly same tick-tock in all cases. :) Even more - all such clocks in a universe will be syncronized by definition. And gravity also could not dilate that clock - speed of light is always the same, and clock using speed of light as a frequency source just can't run faster or slower. :) It's their own dogma. :)