# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Cosmic Ray Muons Not GPS Satellites**

**From:**Frank Reed

**Date:**2021 Nov 27, 11:36 -0800

"It offers a possible alternative to GPS satellites"

The article seems to imply that, but I don't see how that's the case. This proposed positioning system works by detecting naturally occurring muons which are generally travelling more-or-less vertically downward at very high "gamma" values which means they are travelling at highly relativistic speeds like 0.9999c (*). If you have a detector with a known location on the surface of the oceam, and you have a second detector at depth, there's a real chance of seeing the same muon at the surface detector and then again at the detector down below. All muons look alike, but stats of the timiings of individual detections should reveal the subset that are the same at both detectors (yes? no?). If both detectors have highly accurate clocks synchronized to the nanosecond (light and any particles travelling at highly relativistic speeds travel just about one foot or 30cm in one nanosecond) then you can determine the distance from the surface detector to the submarine detector. Do that three times with three different positions for the surface detector, and you've got the otherwise unknown position of the detector at depth potentially within a meter or so, *relative to the surface detecter*. But the concept depends on exact, known positions for the surface detectors. And those are determined by GPS or some other positioning technology. It's an interesting and clever way of extending the GPS grid deep underwater, but I can't see any way that it could serve as an ** alternative** to GPS. It also depends on near real-time communication between the surface detector and the submerged detector which would seem to constrain its usefulness for military applications! Of course, the US DOD has deep, deep pockets, and spending (wasting) cash on things that don't work is part of the adventure.

There's an article with some suggested applications and analysis here: *https://www.nature.com/articles/s41598-020-75843-7*.

Frank Reed

* Back of the envelope calculation tip: The "gamma" factor tells us how much time is slowed down for observers travelling at some significant fraction of the speed of light, or, more relevant here, it tells us how a relativistic particle's total energy (kinetic energy + rest mass energy) compares to its normal rest mass energy (its mc^{2}). So if an object has a gamma of 100, then it's almost all kinetic energy. And particles that are almost all kinetic energy generally behave a lot like high energy photons, like gamma rays, which are all kinetic energy with no rest mass energy. To calculate gamma, you work out gamma=1/sqrt(1-beta^{2}) where beta is the particle's speed relative to the speed of light, c. Now for high fractions of the speed of light c, there's a simple rule (the is the promised "tip"): at 99% of c, gamma is just about 7. You can work that out easily from the original equation. For higher fractions of c, every additional pair of nines multiplies gamma by 10. At 0.99c, gamma is 7, at 0.99*99*c, gamma is 70, at 0.99*99***99**c, gamma is 700, and so on. Each additional pair of nines in the fraction of the speed of light multiplies by 10. You can check this easily from the original equation for gamma. This is just a quick way to estimate the numbers. And now for pure sci-fi fun... With that basic rule for gamma, you can work up the numbers for the usual "Twin Paradox". Imagine you leave Earth orbit, aim for alpha Centauri, and in the first hour of your trip, you get your speed up to 99.9999% of the speed of light (how? don't ask me; I'm in marketing). It would be a quick trip. Your gamma factor would be 700, so time aboard ship is slowed down by a factor of 700. You would arrive there in 2.2 days of shipboard time, while 4.3 years elapse back home. You stay for ten days of tourism and then come home. You're two weeks older while the Earth and everything and everyone you left behind is now 8.6 years older. By the way, be sure to wear your seatbelt since accelerating to that speed will certainly cause some physical distress... :)