What is the quantum theory explanation for transparency and opaqueness?
Considering that atoms are mostly empty space, I don't see it as a problem that something as small as a photon could pass easily though matter if it was in the correct configuration. So long as the molecules are spaced sufficiently far apart.
Are Entropy and Quantum Mechanics related? If so, how?
Of course. Entropy is a very basic idea that plays a vital role in quantum mechanics.
Can you please explain quantum theory to a layman?
regular physics is the study of matter and how it reacts to other matter. Quantum physics tries to explain the behavior of even smaller particles. These particles are things like electrons, protons, and neutrons. Quantum physics even describes the particles which make these particles! That's right; the model of an atom that you were taught in high-school is wrong. The electrons don't orbit like planets; they form blurred clouds of probabilities around the nucleus. Protons and neutrons? They're each made of three quarks, each with its own 'flavor' and one of three 'colors'. Lets not forget the gluons, the even smaller particles that hold this mess together when they collect and form glueballs (not a very original name). The quantum model of the atom is much more complex than the traditional model, so most teachers save that stuff for college. (But this doesn't mean that you can't have a basic understanding) The reason that quantum physics needs complex math to explain the behaviors and properties of small particles is that the world of these subatomic particles is a very bizarre one, filled with quantum probabilities and organized chaos. For example, the exact position and velocity of an electron is very hard to find because attempts to "see" it involve bouncing other particles off of it. By doing this, you've just changed the electron's velocity, so your data is useless. What quantum physics does is give us the statistical probability of the electron's location at any one moment. By learning how these particles act, scientists can better understand the matter which makes up the universe, and the way it behaves (or misbehaves). Quantum physics even plays a part in blackholes, where regular physics is thrown out the window and then some!
Why can't we prove whether String theory or Loop Quantum Gravity are correct or not?
If you have not studied physics at all, I do not think that this question is at all a good one to ask. It was better to look at it in a very abstract sense.I would suggest the following form of the question:Why we cannot decide between theories A and B?As far as you have no idea of what string theory is, neither what is Loop quantum gravity then it is easier to answer a really abstract question.The first thing is to be sure that we are really at a position to decide between two competitive theories. If theories A and B are not at all the only gamers on the ground, then the both of them could be simply experimentally non-verified.Returning to your question, who has told that between the two mentioned hypotheses (and not theories) we are obliged to choose one? The both can be simply refuted by experiment. We are not at all in the position to be obliged to choose one of them.The fact is we know something about the both. Non of them has ever suggested a test which is verified by the experiment. So as far as our knowledge goes today, no matter how mathematically rich they are, they are both mere non-verified hypotheses, (not theories: A scientific theory is a fact, when we say that something a scientific theory we mean that it is a fact). As far as something is not verified experimentally it is a hypothesis, not a theory.
What will happen if String Theory is experimentally proven?
If string theory is proven by relatively good evidence, and we find our vacuum, and we demonstrate the quantum mechanics is exact by building a quantum computer and having it factor a 10,000 or 100,000 digit number, we have reasonable certainty that we are finished with fundamental physics, that we know all that there is to know about the laws of nature at the fundamental level.David Gross said it best, in 1985, after he and collaborators discovered the first realistic string theory: "Let's finish this thing and go home". He meant, let's find the proper vacuum configuration, check it matches standard model data, deduce the consequences for dark-matter/inflation, and then retire from fundamental physics because the project is finished. His program was fine, but he was a little optimistic about the pace of progress. A proper non-perturbative description of heterotic strings wasn't even constructed until 1996, when Horava and Witten figured out how it embeds in M-theory.Knowing the fundamental laws of nature doesn't help at all with any other question, the other questions are about the properties of computations, not about the properties of the fundamental laws. It's precisely because the fundamental laws are not complex, they are not full computers in isolation (they are analogous to the instruction set, not to the behavior at arbitrarily long time), that we can discover them once and for all, and be done, and go home, as Gross puts it.The reason I mention quantum mechanics, is because it is possible that quantum mechanics fails, as 't Hooft sometimes suggests, and that the amount of computation our universe can do is not exponentially larger than classical. This is a reasonable principle, it might be true, it might be false, we have to check it. But if it is false, if quantum mechanics is accurate at the level of computers, it is reasonable to conclude it is exact.