What’s going on with the two logs is the classic “Twin Paradox”, about which there is a voluminous literature, both technical and popular.
You can start here:
I will try to understand that again, but it makes my head spin.
I will try that too. “incorrect and naive”, that is me on this subject. Still I will try. Again. Thanks to both of you!
They can and do try to build high-resolution detectors to detect particles with ultra-short lifetimes, but it is still possible for some particles not to exist long enough and need to be detected indirectly, e.g.
https://webhome.phy.duke.edu/~kolena/modern/roesle.html
https://webhome.phy.duke.edu/~kolena/modern/dudley.html
The fact that the original particles smashing into each other were going really fast does not seem to directly help you, except that it allows for greater energy, as @naita explained.
Oh, and you don’t usually smash particles into smaller particles. Usually, you’re trying to smash particles into bigger particles.
Continuing this discussion, however, in the particle detector we absolutely do need to take into account the ultra-relativistic nature of the particles.
To make up an example, suppose that a particle is created somewhere and decays after time \tau. On the other hand, in the laboratory frame the particle travels during this time, so that the decay appears to take “longer”. Relativistic invariance implies that c^2\tau^2 = c^2t^2-v^2t^2, so t=\gamma\tau where \gamma is the “Lorentz factor”. E.g., the particle travels from its initial position at (x,t)=(0,0) to \bigl(\gamma\beta c\tau,\gamma \tau\bigr), where \beta is its speed relative to the speed of light—there is “time dilation” at work.
One needs to reconstruct the momentum (velocity, mass, proper lifetime, and so on) of the particle from its decay products, tracks, and/or other data. But, just to have some numbers, let us say that we know the particle travels an average distance of 7 mm at an energy of 80 GeV and has a nice, long lifetime of 1.52 × 10-12 seconds. The speed here is 99.8% of the speed of light and the point is that it lasts 15× longer in the laboratory frame; certainly that needs to be taken into account when relating the decay length to the proper decay time of the particle.
Can you objectively age a human? I don’t know, maybe there is a test you can perform. But to my uneducated and naïve self, the twin paradox seems fuzzier. I get that one twin would, in a very real sense, age slower with acceleration (the decay rate of their cells, or whatever), but nothing I’ve read about the twin paradox talked about that, or about testing, just ‘the returning twin is still a child while the stay-on-earth twin is an adult’ type language. Although it may be implied, the writings about the twin paradox I’ve read never mentions that one twin will die sooner due to lack of relativistic effects - only that they look older.
Chimpanzees are genetically similar to humans, yet they rarely live for more than 35 years or so. Despite improvements in our lifestyle in the last 200 years, people living in high mortality hunter-forager lifestyles still have twice the life expectancy at birth as wild chimpanzees do. Why? Cell life? Cell life that might be prolonged (from earth’s perspective) by traveling at relativistic speeds? I don’t know.
But people die of all kinds of things at all different ages. Even with the time dilation, the “younger” twin might still die first (of say a brain tumor, or cancer) thus skewing your experiment. So in my (again, uneducated) mind carbon dating just seemed like a more concrete way to nail it all down.
But then again, maybe I posed the question without thinking it through… assuming that was even possible for me! 
You can objectively determine the age of a human. It’s just imprecise, is all, and with different levels of precision at different ages. But then, all measurements in science have limited precision, and you always have to keep track of the limits of your precision.
But regardless of whether you use growth of wisdom teeth or a cesium-fountain atomic clock, time dilation still occurs, because it’s a phenomenon of time itself, not of any method used for measuring time.
A good way to objectively establish the age of a human would be to ask them to wear a stopwatch all their lives. If you have a pair of twins wearing synchronised stop watches, the one that goes to the stars will show a shorter time on their stopwatch when they get back from the stars than the one which stays at home. That shows it is not just a physiological effect, but a real effect on duration.
Maybe “time dilation” is a confusing name for this phenomenon. Nothing ages, or decays, at a different rate. The point is, though, in order to travel from one place to another, you have to give up some motion in the direction of time and instead travel in space; same thing when you come back, so less time has elapsed on your watch than for someone who stayed in place. But you are not aging at a different rate.
This is correct, within your own local frame of reference. But others outside your frame will measure things differently. When the two twins get back together in the same frame after the trip, the one who stayed home will have aged more and, barring accidents and disease, will die of old age sooner than their twin. Maybe a lot sooner depending on the length and speed of the trip.
This reminds me of a sci-fi story I read long ago about a set of twins who get to experience this classic apparent paradox when one of them gets selected for an interstellar mission. But thanks to improving medical technology back on Earth that the star-traveling twin wasn’t able to take advantage of, guess which one looked older when they had their reunion.
Twin Paradox by Robert L Forward