Thank you for reaching out to us scientists at UCSB! My name is Amanda, and I am currently a graduate student in the Materials Science Department. I did my undergraduate degree in Physics, so I have learned a lot about quantum physics.
Quantum physics can be a very interesting and challenging field of study. The rules and laws of physics that we experience in daily life become more complicated as we get down to the very small scales of atoms (or even smaller). Sometimes, those laws appear to break, and that is where quantum physics comes in--to explain phenomena at very small scales. Let's get to your questions!
1. One interesting phenomenon of quantum physics to me is something called "particle-wave duality." Let's take a photon as an example. A photon is a "unit" of light. Not so long ago, scientists thought that photons were particles, little packets of energy that gave us light. Photons do behave a lot like particles; for instance, they bounce off things like a ball would. Your reflection in a mirror is made up of photons bouncing off of the mirror and going into your eye. The assumption that light was made of particles was challenged by an experiment called the double slit experiment. In this experiment, light was shone onto a pair of slits in a piece of paper, with a detector behind the paper. If light is made of particles, we would expect to see the slits reproduced on the detector, like a shadow. When this experiment was conducted, though, the pattern recorded was actually many slits of light! This makes no sense if light is particle-like, but does make sense if the light is wave-like. When two waves collide, we see a pattern of some peaks where the waves add together and some troughs where the waves cancel each other out. In the experiment, if light is a wave, when it passes through the two slits, we get two waves that can then interfere with each other. The interference of the waves produces the image of many slits on the detector. In a way, we can think of a photon of light going through both slits at the same time. This defies our idea of what a particle should do, but a wave can go through both slits just fine.
2. As I alluded to earlier, quantum physics is the physics of very small things, things at the atomic scale or smaller. This includes the parts of the atom, including protons, neutrons, and electrons. Atomic-scale objects don't obey classical physics laws like we expect. For instance, we might expect electrons to orbit around atomic nuclei, much like the planets orbiting the sun. Quantum physics tells us that this isn't true; in fact, electrons exist in a "cloud" around the nucleus. The biggest difference between classical physics and quantum physics is that classical physics describes the world in a deterministic way, meaning events can be calculated and predicted based on past measurements, and quantum physics describes the world in a probabilistic way, meaning that events have certain probabilities of occurring. As we move from atomic scales to larger scales, the probability of an event (such as where a ball will be after I throw it) becomes almost 100%, so we use the simpler classical physics equations to predict what will happen.
3. Quantum technology is very promising for computers. Computers now work with zeroes and ones to compute things, that is, in binary. With quantum technology, we can use the state of electrons in something called a qubit, which has four states. Using qubits instead of binary computation gives us access to double the number of states, which should make computers faster. Time travel may not be possible with quantum physics, but instantaneous communication might. According to quantum physics, two particles can be paired in such a way that they become "quantum entangled," meaning that if we change one, the other one will respond to that change instantaneously. Given our current technology, this is a very hard concept to test and use, but it may become useful in the future for instant communication.
4. There are many things we don't know about quantum physics! One, as I mentioned in 3, is quantum entanglement. Quantum entanglement has been shown in experiment, but we still do not know why this phenomenon should occur. The theory and mathematics say entanglement is possible, and experiment proves it, but we still don't know how particles can interact with each other so fast (faster than the speed of light). Another interesting idea is that it seems to matter if someone observes a quantum event. Remember the two slit experiment? If a scientist sends in photons to the slits one at a time, and watches them as they go through the slits, the pattern produced will only be two slits, as if the light were made of particles. If instead the scientist does the same experiment, but doesn't watch the photons, the pattern produced will be an interference pattern (and look like many slits), as if the light were made of waves. The observer becomes important in quantum mechanics. It seems odd, doesn't it, that watching a process can change the outcome? This problem perplexes physicists. As Richard Feynman, a famous physicist, put it: "I can safely say that nobody understands quantum mechanics.”
5. You should try the double slit experiment for yourself! All you need is a laser pointer, an index card, an exacto knife (or something to cut with), and a dark room. This website has a nice explanation for the experiment.
Essentially, you just cut two small slits in the index card, about 0.5 mm wide each and 0.5 mm apart. Then, you shine the laser at the slits, and look at the pattern made behind it on a wall. Make sure you don't look into the laser, but where the laser hits the wall. Try different numbers of slits and see what happens!
I hope that answers all of your questions satisfactorily. Please let me know if you have more questions.