On exceeding the speed of light.... I had to dig this up. It's a copy/paste. Not my original words - but some of mine DID come from this...


People who use Euclidean intuitions to frame their comprehension of physical reality often interpret the physicist’s statement that “nothing can move through space faster than the speed of light” [i] to mean that humans have not yet found a way to boost something beyond this speed. They tend to respond with the suggestion that advanced technology will eventually enable mankind to overcome this restriction, but they have missed the point entirely.

Physicists are not making a claim about human potential. What we are saying is that within the vacuum, there does not exist a definable speed that exceeds the speed of light. The option for going faster than the speed of light entirely disappears, because the meaning of speed itself is maxed out at the speed of light. There is no definable speed beyond that point because Nature is not geometrically Euclidean.

When we learn to comprehend Nature through its true geometric form, this fact becomes no more fantastic than pointing out that you cannot go farther north than the North Pole, and you cannot have a color more red than the exact color defined as red. These statements are true by definition. They are tautologies. For the same reason, by geometric definition, Nature possesses a limiting speed. Let’s explore this in greater detail.

An object’s speed through space is equal to the amount of space that it traverses (from the observer’s point of view) divided by the amount of time experienced by the observer during that interval. This definition critically sets a finite limit for the maximum speed in space.

To explore how, let’s imagine that we deploy a powerful rocket, or a giant intergalactic miracle machine that possesses the ability to constantly accelerate with the force of one g for a period of 10,000 years. During the entire span of the rocket’s journey its speed will be increasing each second by 9.8 meters per second (from the point of view of those on the rocket). Due to the constant thrust of the rocket’s engines, those aboard will feel a uniform constant acceleration. As it accelerates, the rocket’s speed increases. As a consequence, the rocket’s experience of time begins to decrease relative to Earth’s experience of time. The significance of this is that, although everyone aboard the rocket will continue to feel a constant acceleration of one g, observers from Earth will see the acceleration of the rocket diminishing asymptotically toward zero, as the rocket’s speed increases asymptotically toward the speed of light.

This asymptotic speed limit remains exactly the same (approaches the same limiting value) independent of the magnitude of acceleration we choose for our rocket. This tells us that the limiting speed in Nature has something to do with the way time is swapped for space as speed increases. Because this limit represents the point at which the rocket’s clocks have entirely stopped, it possesses an infinite association. If the ship reached the speed of light, it would move through space without experiencing any time. If speed were defined as the distance an object travels, divided by the amount of time the object experiences during that trip, then the speed of light would give us an infinite value (nonzero measure of distance divided by a zero measure of time yields infinity).

This limiting infinite value is one reason that c is nonrelational. Infinity is equidistant from all locations. As we change our reference frame, we change the value of the numerator in this equation, but the denominator remains zero. A positive number divided by zero yields infinity . This means that, in some sense, to reach the speed of light is to touch infinity.

In any reference frame we choose, our description of the speed of an object not experiencing time must be identical. This is why c is the only nonrelational speed. It does not change when we change our perspective for the same reason that infinity remains identically distant when we change position.

If we chose to define speed as a measure of the distance an object travels (compared to the observer) divided by the time experienced by the object during that translation, then infinite speeds would be at least theoretically attainable. But, because we have specifically defined the speed of an object to be the distance it travels (compared to the observer) divided by the time experienced by the observer during that translation, the maximum value allowed for speed is a finite value known as c instead of [ii].