Going back to the double slit experiment post, suppose you run the experiment with a light source letting only one photon through the system at a time. If the light is a particle, there are no other particles in the system for it to interact with. You still get the same interference pattern, though it takes a long time to build up as each photon lands on the screen. Physics World has more details on the experiment but it's more technical.
Suppose you could set up a system that would prove which slit your individual particle went through. Turn on that system, and the interference pattern vanishes. Take it away, and the pattern returns. Werner Heisenberg said, "The path [of the electron] comes into existence only when we observe it." Heisenberg is remembered for the Heisenberg Uncertainty Principle, which limits how accurately we can measure things: "The more precisely
the position is determined, the less precisely the momentum is known in this instant, and vice versa." You can't get both measurements with total accuracy, and Heisenberg found an equation governing how accurate you can be. This doesn't come into play in everyday life because the precision you use when you're looking at subatomic particles is so much greater than precision in knowing where your car is and how fast it's going.
Observing the experiment changes the result. How does the experiment "know" I'm watching it? What if the light came from a star light years away, diffracted around a black hole instead of through a slit. Does determining which side the light came from alter its path in the past? We don't know for sure, and that's why I love quantum mechanics.