One of the axioms of general relativity is that the speed of light is constant in all inertial frames, even ones that are moving at nearly the speed of light. However, in the normal world, if you travel at the speed of something, that something appears to be moving with velocity zero from your perspective. How can it be, then, that light is different than everything else in the universe?
I will tell you how it can be: light travels orthogonal to space. Consider yourself to be holding a radar gun that police use to catch speeders and driving a car approaching a crossroad. Travelling towards you along that crossroad is a race car. You flash your lights, signalling a race, and begin to speed up. The race car, not knowing that he has been challenged, continues at a steady pace.
As you speed up, you expect the difference in speed between you and the racecar to diminish, but, dishearteningly, the race car continues to move in the positive direction, even as you surpass its meager pace.
If the racecar had been travelling in the same direction and along the same road as you, it would have appeared to stop, then travel backwards towards you as you reached its speed and surpassed it.
The difference? Orthogonality. Light always appears to be travelling at 3x10^8 m/s, no matter what, because it is moving perpendicular to three dimensional space.
But how to prove it... One way would be to spontaneously combust hot enough to turn all of your molecules into light and see what happens. Unfortunately, the reverse process is not very predictable, so gathering evidence and showing reproducability would be difficult. Another way is to consider things that behave sometimes like light and sometimes like particles: electrons in the double slit experiment.
Electrons have charge that produce an electromagnetic (EM) potiential and fields. There is an upper limit on their mass, but they could very well be massless. When there is a single slit present, electrons pile up behind the slit in a gaussian distribution, behaving like a particle. When there are two slits present, however, it is believed that they travel through both slits in a wave-like manner, causing an interference pattern behind the slit.
Now change your idea of what an electron is. Think of it as an EM particle living in the EM space that is perpendicular to our 3D space. We already know that EM waves can interact with things in our world. Afterall -- we can see. How they move, however, could very well be a mystery, if there is indeed a 4th dimension.
As an aside, imagine yourself at a campfire in late autumn. You forgot to bring a sweatshirt, so are sticking fairly close to the fire. There is a ring around the fire in which the temperature is comfortable and you feel like you can hang out for the rest of the night. Closer in you start sweating or start to feel burnt, whereas any farther out you get cold and start to shiver. This heat field is like a potential well. It attracts you to the ring around the fire at which you body heat lets you be in comfortably.
Now, consider 3D space to be the campfire and you to be the electron. The electron can be in any ring of 3D space that is an equipotential to its own potential field. It spreads out over that space in a way that is not alltogether clear, it being a 4th dimension and whatnot. The two slits comprise two equipotentials that the electron can pass through without problem. It follows the 3D potentials through the holes to the detector plates and causes an interference patter. Not, however, because it is a wave, but because it is travelling along the 3D equipotentials of space.
If one of the slits is closed, the potential of that particular path is increased by a whopping amount, and the electron can no longer pass through it. It must stick to the single, open slit, behind which the 3D space potential is that of a macroscopic particle.
If you believe me this far, you might be wondering how we can map this 4th dimension. Ponder for a moment, if you will, the orbits of electrons around an atom. They move along EM equipotentials at discrete energy levels. If the EM dimension is perpendicular to 3D space, then these equipotials have to be wrapped around the fabric of space itself. All we have to do is map the electron orbits to see how EM space fits in with our own.
And there you have it. The culmination of my thought experiment. Now to prove it...
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