They say that quantum mechanics is counter-intuitive because of microscopic phenomena that we do not observe macroscopically. However, it is possible to explain high-level quantum mechanics using macroscopic examples. Once you learn these examples, quantum mechanics should not seem counter-intuitive at all.
Four of the supposedly counter-intuitive principles are wave-particle duality, superposition, entanglement, and tunneling. Below, I will present a macroscopic example of each. No, the examples aren’t perfect. They are merely intended to show that quantum mechanics is really not as weird as it is often purported to be.
If you throw a rock into a pond, you can see waves radiate outward from the impact on the surface of the water. Now imagine that we are in a room with a door to a hallway and no other way to see into the hallway than the doorway.
If I open the door, go out into the hallway, and then close the door, my position behaves like the wave in the pond. At first, I am probably still in the hallway. A short time later, there is still a probability that I am in the hallway, but there is now a probability that I am outside the building. And given a little more time, there is some probability that I am still in the hallway, some probability that I am outside the building, and now a probability that I am drinking #qoffee in a cafe down the street (high probability, actually).
Once you open the door to the hallway and try to observe me, my position can no longer be thought of as a wave, but as a particle. I am definitely somewhere. Microscopically this happens instantaneously, but if I remained in the hallway, this happens instantaneously macroscopically, as well — you will see my exact position as soon as you open the door. And although it might take you a few minutes to observe my exact position macroscopically, that’s only because you should’ve looked for me in the cafe first. Now you know.
If I once again open the door to go out into the hallway, you will see that the hallway light is definitely either off or on. Once I close the door, however, you can no longer definitively know which state the hallway light is in. From your point-of-view, the hallway light is in a superposition, and has both a probability of being off and a probability of being on.
Once we re-open the door, however, the superposition collapses. You once again definitively know which state the hallway light is in. It is definitely either off or on, and definitely not off and on at the same time.
Imagine that two light switches on a wall are connected by some kind of rigid object (not in the image). If you flip one switch off or on, the other switch flips along with it. And no matter how close or far apart these switches are, flipping one switch instantly flips the other.
Microscopically, we obviously don’t see these rigid connections — or correlations — but the notion of something instantly (in regards to human perception, anyway) affecting something else is macroscopically reproducible.
Think back to a time when you tried to make a phone call or access the Internet while you were inside a concrete building, but you either couldn’t get a signal or the signal was too weak. That’s because the frequency of the signal has a very short wavelength, shorter than the thickness of the wall, and thus too short to penetrate the concrete wall.
In contrast, imagine having a neighbor with a subwoofer and an amplifier. The low range sounds have long wavelengths, longer than walls are thick, and thus you hear the “boom boom boom” of the bass but not the voices or the sounds of the other instruments.
At a high-level, tunneling is comparable to low range sound. Despite the presence of a barrier, we can macroscopically observe — unfortunately — waves penetrating barriers.
One of my hobbies is performing magic tricks. If I pull a solid object through another solid object without damaging either, that should seem counter-intuitive to you; your brain should tell you that I can’t really do that. But, if you study just a little bit about magic, you can watch a new trick, not fully understand it, but hopefully have a general understanding of the principles that make it work.
In a similar manner, we can study quantum mechanics and not fully understand entanglement, for example. How can microscopic anything be correlated instantly over vast distances? But, if we look at macroscopic phenomena that are similar, we can accept that even though we don’t fully understand something, it’s really not that weird afterall.