Let’s assume two observers.
Observer A is on the spaceship
Observer B is ouside watching the spaceship
Let’s also assume the spaceship has an infinite amount of massless fuel (just go with me on this).
Also, through the magic of hypotheticals assume Observer B can clearly see the spaceship and Observer A throughout this whole process without violating any physics or ‘moving’ himself.
Ok…
Observer A, throughout his entire trip (even if it is forever), will never notice anthing change. His watch ticks like it always has, he’s still 6 feet tall, the ship is accelerating at a constant 0.0064 mi/sec/sec and he measures the speed of light at 186,000 miles per second. He will observe all of this to be true from day 1 of the trip till the end of his life 70 years from now. To help you buy this imagine Observer A has no windows in his spaceship. Indeed, if we want to say he was born there then as far as he knows the inside of the ship is the entire universe. As far as he is concerned he is standing still in a gravity well (acceleration and the effects of gravity are indistinguishable from each other…this is called the Equivalence Principle).
Now, Observer B knows different. He put the baby on the ship and has watched it race away. Observer A gets closer and closer to light speed but never quite reaches it. Observer B also notices that while the spaceship is spewing out the same amount of fuel it always has it is accelerating slower and slower. Instead of 0.0064 mi/sec/sec we’ll say it’s now down to 0.000064 mi/sec/sec. Again through the magic of examples Observer A measures the spaceship and Observer A’s mass as increasing. No wonder it’s slowing down.
Question: Why does Observer A notice no difference? Why doesn’t he notice a slowing of acceleration?
Because time is slower AND distance is smaller…his rulers are shortening compared to Observer B’s rulers.
So, he is now only accelerating at 0.000064 mi/sec/sec but since his ruler has shortened one mile to Observer A seems like 1/1000[sup]th[/sup] (or whatever it really is…I’m not up to the math) of a mile to Observer B. Since time also slows down when Observer A starts his stopwatch it will run slower than Observer B’s stopwatch. When measuring the speed of light Observer A’s photon has less distance to travel from Observer B’s perspective and Observer A’s watch will slow (compared to Observer B) in a combined manner to give him exactly the same measurment for the speed of light as Observer B.
Finally, another way to look at what would happen to you if you reached the speed of light –
An infinite mass may be hard to swallow so take it from another angle. Distance shortens for you as you approach light speed. This will have the effect of making the universe appear smaller (to you). At light speed the universe will be the size of a point to you. You are now effectively (from your perspective) everywhere in the universe at once. Neat huh! Unfortunately, from your perspective, if you decided to hit light speed for just the briefest moment, say as fast as you could hit the button to start and then stop (i.e. hitting a button twice), the universe would come to an end before you could turn your engines off. Not so neat…