for the reason why the speed of light is fastest. The reason can be simple. no need any equations.
The reason is, the speed of light is the same for all constant velocity observer. and we use light as a measurement tool.
For simplicity, we can imagine a "magic bullet" that travel at same speed no mater who measure it.
we can use this magic bullet to build a clock. the clock is made by a gun and a target, a standard time can be defined as when the bullet hit the target.
Lets say, John is moving at speed of this bullet compare with Mary. and the clock is on John's hand. we can freely to say John is not moving but Mary, or Mary is not moving but John. 2 arguments are same.
In John, the clock run normally. since we can say john is not moving.
But in Mary, John is moving at the speed of the bullet. and the bullet also moving at the speed of bullet. therefore, the bullet never reach the target. Thus, time stopped.
people may ask this clock is not a good clock. we can build another clock by different principle and give out different result. But remember physical law is same no matter who or how to check it.
Thus, if John is moving in speed of light. The time for he in others people is undefined. as the time begin undefined, the space also. Thus, John is living in crazy time and crazy space (but existing ?) in Mary's eye. Therefore, normal thing cannot move at speed of light.
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For time begin undefined, the space also.
space, length, we can simple use a ruler to measure or define it. However, it is not always.
first, we have to make sure the 2 ends are not moving compare with each other. if one end is moving, any length measurement is fail.
so, How do we make sure the 2 ends are not moving? we are only 1 human, may be we can make sure out hands are not moving. but how about length is many times longer? ask someone to help? How?
we can use light. because its speed depends on nothing.
John can send a light to Mary, who carry a mirror. They are on the 2 ends. John can simple measure the time for the light return back and forth. if the first time is same as second time, we can say the 2 ends are not moving. ( strictly speaking, John only knew at that 2 time intervals, the ends did not move; the ends can move but at the time the light hit the mirror, Mary is on the same point. )
if the clock of John is broken, he never able to define a length.
by the way, undefined does not mean it is not exist.
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A: Why the speed of light depends on nothing?
Q: i mean, it does not depend on observer. in fact, it real depends on something, the permitivity and permeability.
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