Proper velocity by Hermann Minkowski's flat-space metric equation . Here a reference map frame of yardsticks and synchronized clocks define map position x and map time "t" respectively, and the "d" preceding a coordinate means infinitesimal change. A bit of manipulation allows one to show that proper velocity where as usual coordinate velocity . Thus finite "w" ensures that "v" is less than lightspeed "c". By grouping "γ" with v in the expression for relativistic momentum p, proper velocity also extends the Newtonian form of momentum as mass times velocity to high speeds without a need for relativistic mass. The proper velocity
Mass spectrometry the time they take to reach the detector. If the particles all have the same charge, the kinetic energies tends to be identical, and their velocities, in this case, will depend only on their masses. Ions with a lower mass will reach the detector first. However, in reality, even particles with the same m/z can arrive at different times at the detector, because they have different initial velocities. The initial velocity is not dependent on the mass of the ion what becomes a problem for the TOF-MS. The difference in initial velocity turns into difference in the final velocity. In