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In fact light speed is not the question you should be asking. It should be "when traveling at the universal speed limit, why does time slow down." The answer is that no matter how fast you are traveling the universal speed limit (equal to light speed because it goes max speed) is viewed the same. The theory is that all clocks/measuring devices are morphed in the same way so that when it measures the speed limit it is still the speed of light (universal speed limit)

AKA, all clocks, even biological, are slowed down as it travels faster through space time. So your perception is slowed and your recognition of this perception is slowed, so for you time appears the same. If you travel 95% the speed of light and flick on a light, it wont travel 5% the speed of light away from you, it will travel 100% the speed of light away from you due to your space time warping. This also happens the nearer you are to a large mass. aka a black hole. It also warps the space time around you.

Alternate points of view... Take for example, you are traveling in a car at any speed. You pass cars traveling slower than you are. They appear to travel backwards. This is of course only relative to YOU. They are actually traveling forwards. If you think of yourself in the car as the speed of light, and the other cars as time, that's how it works. Of course, light travels SO fast that it bends TIME only relative to YOU. It's not like the whole world actually stops or slows down. It's only you who feels it. Just like overtaking a car. But that's only a simple explanation.

In laymans terms, traveling at light speed means that you are traveling at a speed greater than the speed of time. Therefore time is at a fixed rate, and the speed that light travels is at a fixed rate also. So to travel light speed actually gives you an advantage over time itself. It has been mathematically determined that the longer you travel at this speed, the more advantage you gain, so it would be possible for a child to travel at this speed for a computed time, and return to see that several generations have passed while he/she would have only aged the number of days / months traveled in spaceship time.

Another layman's view:Traveling at light speed really doesn't negate time. It is just that time is relative, as is velocity. My computer seems motionless to me, but an observer looking down at the solar system would see me and my computer moving quite rapidly. If you could get into a ship and accelerate to very near the speed of light and travel for ten earth years, your personal experience of time will not seem to you to have been any different from when you were on earth. Every moment would have passed normally for you, without anything seeming odd. It's just that at the end of the trip, you will have experienced it as only a fraction of the ten years. It will seem impossible to you that 10 years has gone by on earth. Time will have gone by differently for you than for earth. The same thing would happen even if you could reach the velocity of light. Upon decelerating, you would not report anything unusual regarding your experience of the passage of time; time will have passed for you as normally as ever. But you will notice that you spanned a huge distance instantaneously. You would find it nearly impossible to believe that dozens, hundreds or thousands of earth years had passed by during that instantaneous surge. From your vantage point in that ship, you could as easily ask: How does traveling at light speed accelerate time (for earth)? It doesn't.
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Q: How does traveling at light speed negate time?
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