One of the problems of Common Sense, is that it is derived from your lifetime of experience as a (relatively) slow-moving, medium-sized object interacting with other slow-moving, medium-sized objects. Making things somewhat worse, is that the range of speeds is typically very limited, and the human eye percieves less than 1 octave of EM radiation.

Quantum Mechanics is a fundamental theory about the behavior of individual elementary particles, all of which, by human standards are very small. In certain long-time or group averages, these particles act similar to our common sense, but at short time scales or for individual particles, these particles can exhibit weird behaviors, like quantum tunneling or the Heisenberg (sp?) uncertainty principle or the concept of a "ground state" in a bound system. Without quantum tunneling, some intergrated circuit electronic devices would fail to work. Without the uncertainty principle the electron would spiral into the nucleus and all atoms would be unstable (perhaps neutrons, also). These are the consequences of the non-zero value of Planck's constant.

Special Relativity is a fundamental theory about how two particles can relate to each other. The first assumption is that there is no preferred rest frame of the universe that you have to work in to make your physics equations work out right. The second assumption is that there is an upper speed limit to the universe, and that it is equal to c, the speed of light in vacuum in the Maxwell formulation of Electromagnetism. For slow moving objects, the most obvious effect of Special Relativity is the concept of kinetic energy which is approximately: KE = 0.5 m v^2 + 0.375 m v^4/c^2 + .... -- Other effects mean that observers in relative motion have different, but justifiyable, concepts of what "simutaneous" means for events that don't happen at the same spot. The Time-dilation and other conflicts with common sense are all consequences of the non-infinite speed limit to the universe. If you set c = infinity, KE = 1/2 m v^2.

But is a world where we set h = 0 and c = inifinity really a world of common sense? If you run off a cliff does common sense predict that you will move in a straight line until you run out of inertia and then fall vertically? This Wile E. Coyote model of physics was the standard for over one thousand years after Aristole.

Galileo demonstrated by experiment that Aristolean physics is wrong.

If you are going twice as fast in a car, does common sense say you will need twice or four times the breaking distance. I think this is in the California Driver's Manual because common sense says twice the distance while Newton and experiment show that it is much closer to four times the distance.

If humans could exert themselves to the point where running speeds ranged from 2 to 200 miles (or km, doesn't matter for this argument) an hour, perhaps common sense would more intuatively understand KE = 1/2 m v^2 and braking distance. If humans grew up in a vacuum with a much better perception of the 3-D nature of the trajectories of ballistic objects, then perhaps Aristole would have discovered Kepler's observation that gravity cause objects to travel in conic sections. If humans could see more of the EM spectrum, perhaps common sense would not allow for universally transparent substances like water, glass and diamond so the inutionist concept of a material ether would not arise.

Depending on your school of philosophy, you might not easily accept that human common sense is shaped by perception, experience and perhaps evolution, but the scientific evidence is that we are shaped by our environment. Even our language and culture shapes the answer to what seems like such a basic question: How many basic colors are there?