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.