But there is a medium for waves-- in the case of electromagnetic waves, the medium is the photon; in the case of "matter waves" (which actually do exist, although it's more of a "statistical" wave than something that's really moving as a wave) it's the components
of the atom. Quantum mechanics says that everything (both matter and energy) has the property of wave-particle duality, where in some situations it behaves as a particle, while in others, it behaves as a wave-- it's trivial to show both the wave and particle
nature of light in any high school physics lab, while the wave-particle dualtiy of matter is more difficult to show and requires some pretty specialized equipment.
There is not, however, any kind of common, omnipresent medium in which energy and matter waves travel (according to our current understanding of physics)-- that's the concept of the lumniferous aether, which has been thoroughly debunked for about a
century (specifically, relativity doesn't work if you have the aether, and the laws of relativity can be shown to be an accurate description of reality fairly easily-- the doppler effect in light is one example (in that you can measure the relative velocity
between the two objects and calculate the doppler shift of the light without having to know the relative velocity of the medium in which the waves are traveling-- this becomes important when measuring the doppler shifts of objects in space).
If you'd like some more information (in a pretty readable form), I'd recommend
Six Easy Pieces (for quantum mechanics) and
Six Not-So-Easy Pieces (for relativity) by Richard Feynman. I haven't read them myself (yet), but I've heard wonderful things about them, and Feynman is most definitely one of the most talented writers amongst the modern physics community. They're available
from Amazon or should be available from your local library.
it's trivial to show both the wave and particle nature of light in any high school physics lab, while the wave-particle dualtiy of matter is more difficult to show and requires some pretty specialized equipment.
You don't need sophisticated equipment. You can show that light is a particle via the photoelectric effect (E = hf is quantized); you can also show that it's a wave via the diffraction property around gratings (particles
don't diffract). The combination of these two IS the wave-particle duality.
You can derive all sorts of fun from the wave-particle duality - including heisenburg's uncertainty principle (that the product of the std.dev of the particles linear momentum and the std.dev of the particles position is
strictly positive (more than or equal h-bar over 2)) - i.e. that measuring momentum affects position of particles and vice-versa. It's been subsequently shown that the uncertainty is more inherent than even in measurement - the particle itself is undecided
on its exact position and linear momentum.
Photon is the medium for light waves. So, if we have a space without photon, we get a space that light will disappear? Is it possible to create such space? And is such space suitable for human if we apply proper presure,
temperature, air, and everything else. Meaning, is it possible make a space that no light can ever exist, but we can still feel the object inside such space?
You are right to notice that light travels at different speeds through different mediums. The speed of light 'c' - 3x10^8 m/s is the speed of light through a vacuum. Interestingly a vacuum isn't completely empty - particles
are created and annihilated there all the time in so-called "dark energy", but according to statistical laws of quantum mechanics this is unavoidable, and even if it were it would not change the speed of light beyond a tiny fraction of the current value.