But can't an electron have a definite variable position? A moving target, if you will, can still be determined where it'll appear down the road.
I know once you measure or pinpoint, it changes the thing being measured.
But what if there's a way around it? Look at my questions to Severian for an idea of this, below.
1. Ok, by "dies off rapidly" and having infinite extent, can I describe the wave as follows?
You have the one part where all its energy is bunched up, the "particle" aspect of it. From that particle area, the rest of the wave quickly diminishes in magnitude/concentration, like so: by 1/2, then 1/2, again 1/2, until infinity (an oversimplified and mathematically inaccurate example, but I'm just looking for the gist of it).
2. If that's how it works, does the wave stretch in two directions only (as usually portrayed)? Or infinite directions (like a blast radius going in all directions?)
3. Now, if the wave's magnitude indeed tapers off quickly, why not attempt to measure it a good distance from its "particle" area? There it might be weak enough that if one measured a good distance away from the concentration of energy -- on both sides of it -- the results might be used to deduce the position/momentum of the energy between without disturbing the particle area.
4. So everything is a wave. Then, can I accurately illustrate the whole Earth as a bunched collection of those "particle areas" held close by gravity, and waves taper off infinitely from each particle (it'd resemble an image of Earth and wisps stretch and taper off from the planet). I'd like to try drawing an oversimplified example.
5. And on waves tapering off endlessly...isn't there a rule in Physics to avoid infinities (like a singularity)?
So a wave is really a collection of smaller waves. A wave of waves, so to speak.
And regardless if the wave's main thrust is going in one direction, the individual plain waves are going in their own directions within it.
Or so I gather.
So are gauge bosons waves? Or a form of energy? Or both/neither?
Since you're so good at explaining the other stuff, what is a point-like particle, exactly? Couldn't quite grasp it from Wikipedia and online sources.
Does that mean (using the example by Severian of plain waves going in various directions), the larger wave crest or "particle" -- once measured-- would then (consequently) newly adopt the position and momentum of one of its underlying plain waves?
(Others can answer too )
Fields is another term I couldn't really grasp. But after this discussion, I might have a better idea.
If wrong, please correct me.
A field would be every part of a wave? From its particle area to everything tapering off from it? So if one traced the wave's shape, the result is the field.
If so, I visualize it as having a bulky middle, and progressively getting thinner.
A shape maybe a bit like the side view of a galaxy (if waves move in two directions only)
Would a field be shaped like that galaxy above (yet more infinitely stretched)?
Second that.
The same reason it helped me understand. If really complicated or not intuitive, gotta be able to visualize it, then I'll grasp it a lot better.
Would position eigenstate be analogous to coordinates (for example, GPS)?