How fast could a Path Optimization Drive travel through Non-Euclidean/Discrete Space?

I have an idea is for an FTL drive based on the theory that our universe is both Non-Euclidean and Discrete at the Planck Scale, but is instead better represented as a series of interconnected nodes. According to this theory, the speed of light is not determined by how far you must travel along a vector to get from point A to point B, but by how many nodes (each representing a planck unit separated by a planck light second) you must cross. In a universe where space is both Non-Euclidean & Discrete, it means that one entity might need to cross 14 nodes to get from A to B whereas another might find a more efficient path jumping only 8 nodes. At the SUPER microscopic scale, this would make the effective speed of light unpredictable, but because of the law of averages, the speed of light just appears as a constant to us. I've seen this theory used before as a possible explanation for the unpredictable nature of how thing can appear to jump to places they do not belong (like quantum tunneling) when observed at the quantum scale while C appears as a constant at the macroscopic scale.

This is where my idea for a Path Optimization Drive comes in. Non-Euclidean/Discrete space theorizes that C appears constant and space appears Euclidean based on averaged out probabilities, and that space appears continuous because we cannot measure what happens at the planck scale. But, if you were able to manipulate your path through space to only take the most efficient routes possible (basically determining the best possible outcome for each quantum action), it seems like you should be able to effectively exceed the speed of light.

Here is a visual representation of what I am talking about:

While I've often read that quantum physicists often observe things in places they do not belong, I do not know by how much. I'm sure scientists have written off many such things as measurement errors, but for purposes of my setting, I would consider such events as evidence of a really efficient random path being taken. So, what I am trying to do is figure out what the most extreme examples of "how did that get there so fast" observations ever made in quantum physics are and how to use that as a baseline for figuring out how fast a ship could go if it could reproduce that phenomenon with every action taken by every particle that makes it up.

As for comments about computational limitations: I know that it would take the computational power of a computer larger than the observable universe to actually do this; so, my thought for the setting is that someone who discovers that the quantum scale is not actually as random as it appears so that he is able to apply a heuristics algorithm to improve his chances of going fast instead of actually calculating the exact best route. This algorithm allows very subtle, finely tuned magnetic fields to gently guide matter in a pattern that typically follows an optimal path.

My thought is that this would not just allow a ship to go faster than light, but do so without needing a world-endly-powerful source of energy.

• This is great, thought provoking, but I'm not sure it's answerable as such. Wait and see. Jan 28, 2021 at 18:26
• So, calculating routes is just trying to solve TSP - Travelling Spaceship Problem?
– VLAZ
Jan 28, 2021 at 20:03
• With this theory, it's difficult to say. It could be that there are paths between this location, and the other side of the universe, and they just blip there. Perhaps the drive isn't perfected, such that while it can find more optimal paths, it rarely finds a perfectly optimal path that allows for instantaneous travel. You could wonder how computationally expensive that might be. Jan 28, 2021 at 20:58
• @VLAZ Yes, it is a sort of TSP problem... like a REALLY NASTY one... Jan 28, 2021 at 22:25
• @Matthew I see what you are saying, and based on the other comments, it it seems to be a general point of confusion about what I am asking. What I am looking for are clues that exist today that might inform how fast such a drive could go. One possible route would be that, most of us have heard that we cannot measure the position and the momentum of a particle with absolute precision... but when you know momentum for example, how closely can you approximate the position, because that should inform at least what a standard deviation looks. Jan 29, 2021 at 14:47

Don't compute!

This is not a complete answer, but I think it might solve one of the problems, and it won't fit in a comment.

I know that it would take the computational power of a computer larger than the observable universe to actually do this...

This is only a problem if the drive works by comprehending a substantial portion of the "planck graph" and then solving the TSP problem over that graph. So don't do it that way.

How else?

Lighting strikes along the path that offers the least resistance between the sky and the ground. It's my understanding that this happens in a million tiny steps, each taking a fraction of a second. Multiple paths are explored in parallel, and ones with unfavorable resistance gradients are abandoned quickly; the path ultimately taken is the one that held up at every step along the way.

Also, if you're lost in a dark cave, one way to find the exit (at least in stories -- I'm a city cat) is to head towards the feeling of wind.

So let's suppose that this drive works on the assumption that the physical system of the universe is already solving for the TSP in continuous time, and that we can piggyback on that solution. The drive operates in tandem with some kind of sensing equipment that examines subatomic particles or EM radiation which is traveling along the graph. Whatever that population is, let's call it "travelers" for now. The sensor tries to gauge which travelers have had a shorter journey, and the engine then heads down that path.

So, what can serve as travelers? It's got to be something that's everywhere, and it has to have properties that are theoretically measurable.

My first thought would be cosmic background radiation. It's everywhere, and I imagine we can make predictions about its current temperature based on its age, and we know what speed it's supposed to be traveling at. So, maybe it's not a reach to say that if a particular packet of CMB is a little warmer than normal, it has traveled along a shorter route, which means we should go in the direction it came from. (Or maybe I have that backwards.)

Or maybe you're comfortable handwaving how the sensor works.