Several points:
1)The sign on gravitational potential energy is backwards from what makes sense to me. When an object is an infinite distance away, its gravitational potential energy is maximized as a negative. Seem bass ackwards to me but that is what they say. This is how the positive energy of the quantum fields in newly created space can be balanced exactly by the negative energy of galaxies moving farther away.
That's an interesting observation, but a convention. As PE is reduced, KE is gained, hence PE gets to zero at the center of the planet. The important point is the change in PE to give you the change in KE. But how much PE is there at the center capable of producing KE.... nada, nothing, zero. No maximum there, IMO.
I prefer to think of PE as being greater when at a higher elevation since it has greater ability to produce more acitve energy, KE. PE has always seemed to me as another one of those terms engineers are handed so they can solve the problems. Just what the heck it really is hasn't seemed to get absorbed in my thick skull, but it is a great tool.
2) Time dilation is not caused by distance travelled per unit time (speedometer) it is causesd by total distance travelled regardless of how fast you got there (odometer).
No. The slower the object, the less the dilation over that same distance. A photon reaches any destination in zero time, regardless of distance.
3) The Twin Paradox in the "zipping by" model, where they don't stop for a meeting, is explained by time dilation and Lorentz contraction. The problem I am having is when they stop for a "sit down" and each one sees the other one as younger. This cannot be. Only in two different reference frames can this be. The explanation supposedly lies in GR.
SR seems to be all that is needed. Scientists had 10 years or so to wirte books about the paradox before GR emerged.
The secrete ingredient, IMO, lies in the timeline differences that can be expressed graphically. The problem is trying to get how that works physically. This is why Einstein likely never got a Nobel Prize for Relativity as it was never obvious, in spite of all the experimental success.
4) Lorentz contraction has been observed in collider experiments where the results could only be explained if the particles were foreshortened. I read this somewhere.
It's time we move on. Oops, I meant
muon.
I saw this, too, years ago. But, I am very confident that time dilation is equally functional to explain its extended life.
But the initial question, notice, is how it could survive the length through the atmosphere. So, if the conversation involves length, we get length contraction.
But notice I used "life" to explain it, which is a cue for the alertnative, but equal, time dilation equation.