I laughed out loud at the n lg n ^ (1 - 2^{-182}). It is so funny.
No way this is the correct upper bound, and I imagine it'll get refined fairly quickly. IIRC, the GapCVP results were released with a 1/n^400 complexity term, but people quickly got it down to 1/n^8 by more careful accounting.
sqrt(n) now https://github.com/Mira-acc/cvp
This also reaffirms my (wishful) thinking that if there’s a way to do FTL communication it’ll be something with an absurdly tiny factor like 2^-182 with a slight asymmetry in a probability somewhere.
Then you’re not violating FTL, just gaining a very slight chance that you might know something FTL – probably.
From that angle, beating light speed by some absurdly tiny factor would probably correspond to a means of predicting the future at some almost absurdly tiny factor better than random guessing.
Edit: Actually...it doesn't make sense to call this FTL communication, it's just predicting the future state of a system given some previous state. FTL comms would have to be predicting the future state of a system without information about the previous state.
Practically speaking predictive modeling would be a means of compensating for light speed comms, kind of like branch prediction in processors or speculative decoding in LLMs, but that wouldn't actually be FTL comms.
It’d likely involve exponentially more energy as well. It’d be a good sci-if plot point if FTL communications required machines the size of Jupyter to get a few milliseconds of prescience.
If you know what will happen in one minute, write down the message you see yourself writing down in one minute. In a minute, do the same thing. Now you can pass messages back two minutes.
Wouldn't faster than FTL mean that that's the speed of causality? If I send a message from a light year away telling you to "jump up and down" and you receive it in 6 months doesn't and you jump up and down, then doesn't that mean that the speed of causality in that cause was actually 2*C?
So, yes, we could've measured c wrong. We just would have no idea if we did.
Source: Veritasium did a very fascinating video explaining this problem.
We know we've got it pretty well close to accurate, for the bulk of the observable universe.
If c changes, then chemistry changes, and stuff like hydrogen absorption lines shift. This is how scientists have looked for changes in c in the early universe.
We even use the Lorentz transform, developed for post-Michelson aether theories, precisely because you cannot tell whether you’re in a varying aether or a varying geometry.
We define distance and time relative to c, so we cannot measure it in the usual sense.
... Sarcasm, if you couldn't tell.
Causality is conceptually out of time, so it's not traveling. Instead we except causality to operate everywhere anytime uniformly, and all physical dimensions to be bound by causality.