As if I’m a ten year old, because I kind of am when it comes to this kind of stuff… how in the world could adding up all alternate realities end up with a single reality? How would that work?
The path integral suggests that all of the possible realities are like waves. When these waves are added up, they can interfere with each other in a way that only one of the possible realities can be seen. It's like when you throw two stones into a pond at the same time. The waves created by the stones will interfere with each other and create a single pattern on the surface of the water. In the same way, the path integral suggests that all of the possible realities can interfere with each other and create a single reality.
Alternative realities may have alternative people living in them - will they observe different laws of physics since their reality is not a sum of all realities, as opposed to ours? Or would they have the same conclusion about sum of realities?
A) these realities can't have people - they're not real enough to be called that
B) physics will be different - that would be a great scientific revelation
C) physics will be the same - making the premise meaningless
The problem here is the word "realities" because it doesn't in any way mean an alternate reality where you're there doing something else.
This is from the math model where the resulting path of a particle can be figured out by finding all possible paths. Then what follows is the conjecture that because the math works maybe those particles really do travel by every possible path. There's no proof of this, and it's very hard to test because the result has to be the same.
So maybe our reality is the sum of particles taking every possible path. Or may be it isn't. Wake me up when the article title is "Our reality IS the sum of all possible realities."
If we station ourselves outside of the quantum system, then the answer is that each reality puts a complex number on every outcome, which get summed into a single complex number. Then, the magnitude squared of that sum becomes the probability with which we will observe that outcome.
If we put ourselves inside the system then saying anything about it comes with a lot of implied philosophy about what "we" are.
"Our" reality is not necessarily the only one, or is somehow special: under the many-worlds interpretation, every "quantum event" forks the universe. It should look somehow similar to "updating" a typical immutable data structure (a tree, a list) so that a new copy is created, sharing most data with the old copy.
You wouldn't necessarily end up with a single reality, but if there was some kind of process "sampling" a finite number of realities from the wavefunction (either continuously, e.g. if quantum collapse is ontic, or e.g. at some time in the distant future god takes a look at the state of the wavefunction) where the sample probability was calculated in the normal way (square of the wavefunction magnitude), that would explain how probability "gets into" quantum mechanics. This is kind of an open question, though - you can find plenty of papers (mostly bad) wondering out loud how you get the appearance of "discrete" realities with things like probability when quantum mechanics appears to be continuous.
I don't have a good answer for you, but the best advice I'd say is to read Feynman's book "QED: the Strange Theory of Light and Matter" (it's really just a four part lecture series).
It’s also surprising at first that infinite series can add up to a specific, finite number. If I go halfway to X, halfway again, and so on, where do I end up?
All next realities are weighted based on their probability given the current one. The probabilities are based on our knowledge of the equations of physics. Some realities are more likely than others and adding this all up results in an average outcome. At the smallest scales the average outcome is not actually what happens, but time is a great equalizer.
