I understood the derivation of relativistic momentum, but I am uncertain of how to exactly interpret it. One could interpret the arrangement of terms to be relativistic mass times velocity, and this appears to be in agreement with data from particle accelerators (or so I have been led to believe). Alternatively, one could rearrange the terms to describe relativistic momentum as rest mass times proper velocity. In my opinion, parameterizing position with respect to proper time seems much more natural than using coordinate time, much like parameterizing a space curve with respect to length. Proper velocity also retains the properties of classical velocity in that its magnitude ranges from zero to infinity. What is the popular interpretation of relativistic momentum? Which of these two interpretations is correct? Or is there a deeper relationship between the two?