Logically it makes sense why they act like particles when observed and waves when not observed. Quantum physics is common sense to anyone who understands the statistics of 2 coin flips and how those statistics are affected by observing the coins. I will explain why the double-slit experiment is the same experiment as something you can do with 2 coins.
In the double-slit experiment, an electron (or other particle/wave) has 2 holes it can go through and then is detected hitting somewhere on the back wall. If it goes through the left hole, statistically it will paint a pattern on the back wall. If it goes through the right hole, it paints a different pattern. It goes through each hole equally often as the other. Most peoples' common sense tells them that statistically it doesnt matter if you know which hole it went through because you can simply average the 2 patterns to get the pattern on the back wall for when it could go through either hole. But its a very different pattern from the average of the left-hole-pattern and right-hole-pattern. Its the same pattern as waves interfering with each other.
Sometimes electrons act like particles and sometimes like waves, but why? I'm going to explain why that happens using common sense instead of equations. The problem is most people don't have all the parts of common sense that they think they have. If you understand the following about 2 coin flips, and you see the patterns created in the double-slit experiments, then you can put them together and understand why electrons (and other particles/waves) sometimes act like particles and sometimes act like waves. Logically, without considering the specific equations of physics, we can know there has to be something like that in physics somewhere. Here's the 2 coin question:
If I flipped 2 coins and at least 1 coin landed heads, then whats the chance both landed heads?
Its 1/3, not 1/4 or 1/2 like most people think, because there are 4 ways 2 coins can land and I only excluded "both tails" when I said "at least 1 coin landed heads" so that leaves 3 possibilities and I asked what is the chance of 1 of those 3 things which happen equally often. Its 1/3. If you still don't believe it, flip 2 coins many times and only ask the question when at least 1 of them lands heads and you will see that 1/3 of the time you ask the question they both land heads. The flaw in Human minds is the need to choose 1 of the coins and say it certainly landed heads, but I did not tell you any specific coin landed heads, and it does change the answer if you take that shortcut.
Most peoples' common sense tells them that since its a symmetric question (between the 2 coins), it can't matter if they start with 1 of the 1-or-2 coins that landed heads, and they think it will get the same answer as not knowing if a specific coin is heads or not. How could it matter? We know at least 1 of the 2 coins landed heads, so I'll just define a variable called coinX=heads and figure out if coinY=heads or coinY=tails. Since coinY was randomly flipped and coins have a 1/2 chance of heads, then the chance both are heads must be 1/2. But then they think about the extra information I told them: at least 1 coin landed heads. That has to change something, so how could coinY be 1/2 chance of heads by itself and with coinX? CoinX and coinY are symmetric. You can trade them in this question and not change the answer. So whatever is true of coinY has to also be true of coinX on average. So maybe the chance both are heads is 1/4. Most people go back and forth between 1/2 and 1/4, but the answer is 1/3 as I explained above.
How is the 2-coin experiment related to the double-slit experiment?
The patterns of the 2 coins (how often they land heads) individually can not always be averaged to get the pattern of both coins together. If at least 1 coin landed heads and you observe a specific coin being heads, then the chance they are both heads is 1/2. If at least 1 coin landed heads but you don't observe any coin, then the chance both are heads is 1/3.
Logically, observing a specific case of something you know has to be true in general, about the 2 coins, produces a different outcome than only knowing its true in general.
The analogy to quantum physics is that when you observe a heads or tails, you collapse the wavefunction (including the other coin you didn't observe) to a particle and the other becomes a different wavefunction, but if you do not observe any heads or tails then its a symmetric wavefunction between the 2 coins.
I can say the same thing about the 2 holes in the double-slit experiment. If I put an electron detector past the left hole, and shoot an electron that could go through either hole, and the detector observes or does not observe an electron, then I get a different pattern (statistically on the back wall of where the electrons hit) than if the detector was not observing the space between the left hole and the back wall. If any part of the possible paths are observed (as containing or not containing an electron), then the other possible paths are affected even though they were not observed. The electron could have gone through both slits or neither or left or right, but still the path on the right is affected by observing the path on the left.
Most quantum physics scientists explain it as the electron going through the left hole, the right hole, both holes simultaneously, or bouncing off the thing containing the 2 holes without going through either hole. If the electron does not go through either hole, they do not count that in any of the patterns on the back wall.
In the 2-coin experiment and double-slit experiment, there are 4 possibilities, and 1 is excluded. I need to label the 2 coins for this, like the left and right holes/slits are labeled "left" and "right". One coin is a nickel and the other is a dime. This is not the only way to pair the 4 possibilities. Its just a way to explain that they are the same problem:
(1) Nickel heads. Dime tails. Electron left slit. Electron not right slit.
(2) Nickel tails. Dime heads. Electron not left slit. Electron right slit.
(3) Both coins heads. Electron goes through both slits.
(4) Both coins tails. Electron bounces off the thing containing the slits and does not go through either. It is not true that "at least 1 coin landed heads" so I don't ask the question or keep statistics of it. The electron didn't hit the back wall so its not part of the statistical patterns.
In the design of both experiments (2-coin and double-slit), cases (3) and (4) are opposites and cases (1) and (2) are symmetric. Exactly 1 of (3) and (4) is not counted in the statistics, but the chance is equally balanced between (1) and (2). It works the same way if you swap the left and right slits or swap the nickel and dime or swap heads and tails or swap going through a slit with not going through a slit. Its practical to test it going through the slit but not practical to test it after it bounces because bouncing is an observation by the thing it bounced on.
Quantum physics is a kind of statistics. So is the 2-coin experiment. In the double-slit experiment and the 2-coin experiment, observing any part changes the outcome statistically. I'm not saying the math of the double-slit experiment is exactly the math of a bayesian-network (which is the kind of statistics used for the 2-coin experiment), but I explained enough similarities that quantum physics scientists should take this seriously.
The double-slit experiment is a variation of the 2-coin experiment that uses continuous angles instead of only heads/tails.
That is why observing things changes the outcome and why electrons/photons/etc act like particles when observed and act like waves when not observed.
If I flipped 2 coins and at least 1 coin landed heads, then whats the chance both landed heads? The most important thing to remember is the question is symmetric between the 2 coins, but observing either of those coins changes the outcome, like observing what goes through either slit changes the outcome.
Quantum physics is common sense to anyone who understands the statistics of 2 coin flips.
