Okay, thought experiment: somewhere in deep space are N satellites, arranged on a plane, like locations in a TSP problem. Each is configured with N lasers, each pointing at different satellite, and N laser receivers, each to receive signals from each different satellite. They are a long way apart, like several light minutes average.

The process starts when the first satellite sends out a signal, simultaneously, through all its lasers. Encoded in the laser signal via an n-bit number is every satellite the signal has been to so far. so the first signal is an n-bit number with all zeros, with a one somewhere. (Each bit position in this number corresponds to a different satellite.) Maybe also some information about the path it has traveled so far is included.

The time it takes to transmit this signal (to encode that information in light) we'll call b. Maybe its a millisecond, a microsecond, I don't know. its a time interval b.

When each satellite receives a signal through one of its laser receivers, it does the following, very quickly via something like FPGA:

1) Changes the bit position corresponding to itself from 0 to 1.

2) Adds it to a FIFO queue, which is capable of being as long as we need.

The laser transmitters are busy meanwhile transmitting the signals in the queue. They transmit each signal to each satellite that corresponds to a zero bit position (so no satellite ever gets its own signal back). When the signal that is all 1's is found, the satellite broadcasts the halt signal: The shortest path between all satellites has been found, and the path can be reconstructed from whatever data about that is included.

So point is: even for hundreds of satellites, if b is infinitesimally small, than the time it takes to find the solution should be measured in hours, while it would take the biggest computers on earth millions of years. So in this case, God/The universe can find a solution to the TSP that we can't with our algorithms.

But b is not infinitesimally small. Because of this, it may very probably be the case that some transmission that was part of the actual shortest path arrived later than it should, because it got trapped in a queue somewhere behind a bunch of other signals that arrived at more or less the same time at some satellite, and thus got sent out late. (Calculating the probability of these distortions would be an interesting, and I think doable, problem.)

So the question is, if my satellites model can't solve it, is there any physical model that can? Can the universe solve the TSP of a large size, or are there fundamental physical laws which prevent it?