Of course the idea that there is an ultimate speed limit seems absurd. While the speed of light is very high by earthly standards, the magnitude is not the point; any kind of speed limit in nature doesn’t make sense. Suppose, for example, that a spaceship is traveling at almost the speed of light. Why can’t you fire the engine again and make it go faster – or if necessary, build another ship with a more powerful engine? Or if a proton is whirling around in a cyclotron at close to the speed of light, why can’t you give it additional energy boosts and make it go faster?
Intuitive explanation. When we think of the spaceship and the proton as made of fields, not as solid objects, the idea is no longer ridiculous. Fields can’t move infinitely fast. Changes in a field propagate in a “laborious” manner, with a change in intensity at one point causing a change at nearby points, in accordance with the field equations. Consider the wave created when you drop a stone in water: The stone generates a disturbance that moves outward as the water level at one point affects the level at another point, and there is nothing we can do to speed it up. Or consider a sound wave traveling through air: The disturbance in air pressure propagates as the pressure at one point affects the pressure at an adjacent point, and we can’t do anything to speed it up. In both cases the speed of travel is determined by properties of he transmitting medium – air and water, and there are mathematical equations that describe those properties.
Fields are also described by mathematical equations, based on the properties of space. It is the constant c in those equations that determines the maximum speed of propagation. If the field has mass, there is also a mass term that slows down the propagation speed further. Since everything is made of fields – including protons and rocketships – it is clear that nothing can go faster than light. As Frank Wilczek wrote,
One of the most basic results of special relativity, that the speed of light is a limiting velocity for the propagation of any physical influence, makes the field concept almost inevitable. – F. Wilczek (“The persistence of Ether”, p. 11, Physics Today, Jan. 1999)
David Bodanis tried to make this point in the following way:
Light will always be a quick leapfrogging of electricity out from magnetism, and then of magnetism leaping out from electricity, all swiftly shooting away from anything trying to catch up to it. That’s why its speed can be an upper limit. – D. Bodanis
However Bodanis only told part of the story. It is only when we recognize that everything, not just light, is made of fields that we can conclude that there is a universal speed limit.
Now let’s take another look at that proton whirling around in an accelerator, using our colored glasses to visualize the fields. We see the proton as a blob of redness “oozing” (I prefer that term to “leapfrogging”) ahead, as the amount of redness at one point affects the redness at a neighboring point. The process is very fast by our usual norms, but it is not instantaneous. The proton can’t move any faster because the field equations put a limit on how fast the redness can ooze.