Problem understanding relativistic momentum

[cristo]

Hey thanks.Actually i am also spellbound by the derivations of things like time dilation and its elegance and simplicity.THanks for the inspiration,but i have my exams coming up.Maybe after them,ill devote more time on this.In my country every1 expects you to learn other things first rather than to be curious and follow ur interests.Thnx nywyz

I think it's admirable for one to be interested in Physics; especially SR, which is very accessible with little new mathematics (although there is the large seemingly non-intuative concept to get your head around).

However, I'd like to stress the importance of using standard notation, at least when learning the subject. There are many occasions in (mathematical) physics where there are various different notational conventions that one could use (the signature of the spacetime metric is one which immediately jumps to mind). You should make sure that you use one convention all the time, to avoid confusion when conducting your own calculations, as well as talking to others. However, in SR, the general convention that the subscript 0 denotes "proper" [time, distance] is used by more or less everyone, and so it would be advisable if you stuck to this; it will help you avoid confusion.

If you get into the habit of using the "correct" notation, and sticking to one form of notation from as early an age as possible, then it will hugely benefit you as a student in years to come!

 

[anantchowdhary]

thanks ill try to do that.Also I am really bad at using LaTex

 

[country boy]

Heres the text quoted:
Consider a particle moving with a constant speed v in the positive x direction.Classically it has momentum=mv=mDx/Dt

in which Dx is the distance it travels in time Dt.To find a relativistic expression for momentum,we start with the new definition

p=mDx/Dt(o)

Here,as before Dx is the distance traveled by a moving particle as viewed by the observer watching that particle.However t(o) is the time required to travel that distance,measured by not the observer watching the moving particle but by an observer moving with the particle.

Using time dilation t/gamma=t(o)

therefore p=mv[gamma]


I didnt understand why distance Dx is same for both observers!

I went back and looked at the quoted text (above). This derivation is simply making the switch to proper time in order to put the momentum in terms of relativistic velocity u. Ordinary velocity v is not a four-vector. It would have been better if the derivation had just stated this and ended up with p=mu. Incidentally, this also avoids other problems, like the concept of relativistic mass.