The Kantian Revolution
Long before modern science knew anything about the processes of perception or the structure of matter, the eighteenth-century German philosopher Immanuel Kant had drawn a clear distinction between our perception of reality and the actual object of perception. He argued that all we ever know is how reality appears to us—what he referred to as the phenomenon of our experience, "that which appears to be". The underlying reality he called the noumenon, meaning "that which is apprehended", the thing perceived.
At the time, Kant's arguments were a watershed in Western thinking. They were, as Kant himself saw, the equivalent of a Copernican Revolution in philosophy. Whereas Copernicus had effectively turned the physical universe inside out, showing that the movements of the stars are determined by the movement of the earth, Kant had turned the epistemological world inside out, putting the self firmly back at the center of things. We are not passive experiencers of the world; we are the creators of the world we experience.
Because all we ever know is the product of the mind operating on the raw sensory data, Kant reasoned that our experience is as much a reflection of the nature of the mind as it is of the physical world. This led him to one of his boldest and, at the time, most astonishing, conclusions of all. Time and space, he argued, are not inherent qualities of the physical world; they are a reflection of the way the mind operates. They are part of the perceptual framework within which our experience of the world is constructed.
It seems absolutely obvious to us that time and space are real and fundamental qualities of the physical world, entirely independent of my or your consciousness—as obvious as it seemed to people five hundred years ago that the sun moves round the earth. This, said Kant, is only because we cannot see the world any other way. The human mind is so constituted that it is forced to impose the framework of space and time on the raw sensory data in order to make any sense of it all.
Strange as Kant’s proposal may have seemed then, and strange as it may still seem to many of us today, contemporary science is proving him right.

Spacetime
The first significant scientific challenge to the assumption that space and time are absolutes came in 1905 with Einstein's Special Theory of Relativity. He showed that what we observe as space and what we observe as time are but two aspects of a more fundamental reality, which he called "the spacetime continuum". How much of this continuum manifests as space, and how much manifests as time varies from one observer to another, depending on their motion. Space and time may appear to us to be fixed qualities, but that is because we are not traveling at speeds close to that of light. If we did, things would look very different.
Just what the spacetime continuum itself is like we never know. Einstein agreed with Kant; all we ever know of the underlying reality are the ways in which it appears as the two very different qualities of space and time.
Although observers moving at different speeds may disagree on the amounts of time and space separating two events, they do agree, no matter how fast they may be moving, on the amount of spacetime separating them—what Einstein called the "interval". It is a little like cutting a string in two; cutting it in different places will give pieces of differing lengths, but the total length of string will always be the same. Similarly, any observation divides the spacetime interval into a certain amount of time and a corresponding amount of space, the exact proportions depending on the motion of the observer. (With the difference that the mathematical formula for the combination of space and time is not simple addition; it is more like "space squared minus time squared.")

The "Speed" of Light
In proposing his theory Einstein postulated that the speed of light was a universal constant. However fast you may be traveling, you will always measure the speed of light relative to you to be the same—186,000 miles per second. You can never catch up with light. Even if you were traveling at 185,990 miles per second, light would still pass you by at 186,000 miles per second.
Why should this be so? It seems totally counter-intuitive that the speed of light never varies. But this perplexing behavior takes on a rather different character when we distinguish our image of reality from the underlying reality. Space and time, and hence speed, are aspects of the phenomenal world; they have no meaning, it turns out, for light itself.
According to the equations of Special Relativity, as an observer's speed increases, time slows down, and length (in the direction of motion) contracts. At the speed of light, time has slowed to a standstill and length contracted to zero. Although no object with mass can ever attain the speed of light (the equations predict that it would then have an infinite mass), light itself does (by definition) travel at the speed of light. From light's point of view—and this after all must be the most appropriate perspective from which to consider the nature of light, not our matter-bound mode of experience—it travels no distance and takes no time to do so.
This reflects a unique property of light. In the spacetime continuum, the interval between the two ends of a light ray is always zero. How can we interpret this? We probably should not even try to interpret it. Any attempt to do so would make the mistake of applying concepts derived from our image of reality to the underlying reality. All we need to recognize is that, from light's perspective, this zero interval manifests as zero space and a corresponding amount of zero time.
However, when we in the world of sub-light speeds perceive light, we see a different manifestation of the zero interval. We observe a finite amount of space along with an "equal" amount of time. In our world, the light does travel through space and time. Since the total interval must be zero, the distance covered must exactly balance the time taken—that is, we must always observe 186,000 miles of space for every second of time. This we interpret as the speed of light. But this "speed" is not an intrinsic property of light itself; traveling no distance in no time, light has no need of speed. What we interpret as the speed of light is actually the ratio in which space and time manifest in our perception of reality. It is this ratio that is constant. And this is why all our measurements of the apparent speed of light are constant.

Wave-Particle Duality
The fact that light itself knows no space or time resolves another difficult conundrum. In our image of reality we observe light traveling across space and time and so observe energy traveling from the point of emission of the light ray to its point of absorption. Naturally, we ask how the energy travels. Is it a wave, or is it a particle?
The answer, it seems, is both. In some situations light behaves as a continuous wave spreading out in space—but, curiously, a wave without a medium. In other situations it behaves as a particle traveling through space—but, equally curiously, a particle without mass. Physicists have accommodated these two strange and seemingly paradoxical conclusions by deciding that light is a "wave-particle." In certain circumstances it appears as a wave; in others as a particle.
But if we look at things from light’s point of view, the reality is very different. Since it did not travel through space and time, it needed no vehicle or mechanism of travel. Light itself has no need to be either a wave or a particle. From its own frame of reference—which is probably the most appropriate frame of reference from which to consider light—there is no duality, and no paradox.
The physicist’s conundrum appears only when we mistake our image of reality with the "thing in itself", and try to visualize light in concepts and terms appropriate to our image of reality—that is, waves and particles.