Hi everyone: I just started to learn special relativity but totally being confused about "velocity", "momentum" and "force". 1. The relativistic momentum is defined by "rest mass * ordinary velocity * gamma". There are 2 kind of explanations. The first one is combining "rest mass * gamma" to be "relativistic mass", it is easily to be accepted because high speed motion own high energy and can be treated as large mass. The second one is combining "ordinary velocity * gamma" to be "proper velocity", and I cannot see any physical meaning of this definition. However, some books said "in recent years, researcher have already abandoned the definition of 'relativistic mass' ". Why about this? And what's the physical meaning of "proper velocity"? 2. Considering in the lab's reference system, we (rest observer in lab's RS ) measure the velocity of a particle as "u", not "gamma * u". Why we still use relativistic momentum to construct momentum conservation law? The only explanation is the mass of particle is changed due to relativistic effect. In this story, we can see the "relativistic mass" is reasonable. How to explain this using "proper velocity"? 3. Using the relativistic momentum "p" here, we can define the ordinary force F = dp/dt, where t is measured in lab's system (This one can also be explained by relativistic mass but not in proper velocity, how to do that????). Also, we can define another kind of force K = dp/dτ, where τ is the proper time. Force K can be transformed by Lorentz Transformation directly but F cannot be. Does this imply that, the whole story of special relativity and 4-vector is trying to find the "what can be transferred by Lorentz Transformation"? And what the physically meaning of this 4-force ? Just to define a "force" can be transferred ??