I just started taking a Quantum Mechanics course at my university (only 3 days into it) and some of the topics got me thinking about stuff. Namely, about "particles". I searched on Physics Forums and found some other posts pertaining to my question, but a lot of the responses referenced topics I haven't learned yet or seemed like intentional obfuscation. So I'm looking for simple and easily understandable explanations. Here's the question: Imagine an empty universe, with only space and time, but nothing within it. Say an electron appears within then universe, and it has a velocity. Define a time t such that t = 0 upon the electron's appearance. Now for each location in the universe, that location will either be affected* by the electron's existence or it will not (i.e. some location trillion's of light years away from the electron will not be immediately affected). So for any location, and for a given t, there are two states possible: either it is affected by the electron, or it is not. Now let's create some 3D plots with axes x, y, and z, and title the plots according to the value of t. For any x, y, or z that is affected by the electron, we make that point black. (We would have, for example, an empty plot for t < 0.) If I were to look at these plots for different values of t, what would they look like? If I looked at the plot for t=0, would there be a single, zero-dimensional black dot? For t > 0, I assume you would have a continuous 3D region of the plot that is black, completely predicted as a function of t and the electron's velocity. Is this correct? I know this may seem like a weird question, but the whole particle-wave nature of the electron confuses me. I hate that in most physics courses, macroscopic analogies are given to topics for which the analogies do not translate well. It forces my mind to try and imagine a small marble or an ocean wave, which I think is counterproductive to understanding how these things work. It's easier for me to think "Here are some mathematical functions. These functions describe how things that exist affect other things that exist, and experiment confirms that they predict reality well". The problem is -- I never really understand to what extent or scale these functions have an effect -- how a particle really affects other particles within space and time. And for me, the easiest way to see that is with a plot. One thing I wonder about the plot is if the "blob" of the electron's effect is solid black and has a well-defined edge. Or are parts of the blob shades of gray (superpositions?) And is it really solid gray, or is it gray like a computer monitor with alternating white and black pixels that makes the whole screen look gray when standing back from it? *By "affected", I mean if there was a test particle at x, y, and z, would it behave differently than if no electron were present at all in the universe? If it would behave differently, then it is "affected". If it wouldn't, then it is "not affected".