We observe them *later*, and we see them doing things that they could not have done while observed.
The simplest experiment is to say that if we have two windows for the electron to pass through. We know where it will land if it flies through one window or the other, and if we place a detector in the window then we get exactly the result we’d expect. We detect the electron in that window and then it lands where we’d predict it land if it passed through that window.
But if we don’t put a detector in the window, the electron can land somewhere different – somewhere that it wouldn’t be able to land if it only passed through one window or the other. We’re still detecting it, downrange of the windows, but not *in* the windows where the weirdness happens.
All particles behave differently if they’re being observed vs when they’re not, not just electrons.
The way we know this is by looking at the results when they aren’t observed. Probably the most famous example of this is the double slit experiment, where._not_ measuring which skit a particle goes through results in an interference pattern on the target past the slits.
Simply put, we observe (i.e. measure) them. We must measure the electrons at some end point; however, if we try to observe (measure) them earlier as well, it can significantly change the later measurement in a dramatic way. So in both cases we observe the electrons at the end but by adding an additional observation we can change the outcome. This means observing (measuring) them changed their behavior.
For example, an electron that has 2 paths it can take to the final detector (which can’t tell which path it took) makes an interference pattern that can only be explained by information from both paths. This leading us to believe it must have interacted with (or gone through) both paths. However, when researchers add a way to check which path each electron actually took, the interference pattern is gone and they get a pattern that looks like one would expect from particles that only look one path. In either case, we have to measure them in the end but the act of measuring them earlier changes the very nature of that final measurement.
And in fact, that information doesn’t even need to be collected. Just the fact that the information is out there somewhere, where someone could possibly (no matter how unlikely) use it to figure out which path the electron took, destroys the interference pattern. Interestingly, if you (or something else) somehow physically destroy this path information so it’s irretrievable, you get the interference pattern again. This is called the quantum eraser.
By the way, when physics say “observe” in this context, it’s not the general meaning like from an intelligent being, but rather it’s a measurement that reveals a particular trait of the particle. Such traits (called observables) include location, speed, and direction to name a few. This is to say, particles don’t have some supernatural sense of being watched by people.
You observe the results even if you don’t observe the particle.
For example, I have a living room with a big dog in it. The dog can see me. He behaves well.
I leave the room, come back three hours later. There’s dog hair on the couch, the leftovers disappeared from the table, and there’s a trail of fluff from the destroyed pillow all the way to the corner where the dog is sleeping.
We didn’t observe the destruction, but we roughly know what happened.
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