Problem understanding relativistic momentum

  • #26
I am reading ur posts.But X(o) is the distance measured by the body in motion.Why isnt that correct cuz its lesser than x
 
  • #27
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If you're moving with the particle, you'll measure a certain distance between the stones, say L. But this L is equal to \gamma^-1.L_0, where L_0 is the distance between the stones in the stones' rest frame.

For someone in the stones' rest frame, the distance will not be contracted, but your clocks rate is slower relative to his. T = T_0\gamma, where T_0 is the time you took the cross the L_0 as measured by this observer.
 
  • #28
Hootenanny
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I am reading ur posts.But X(o) is the distance measured by the body in motion.
No it isn't! x0 is the proper length. Look up the definition of proper length. The proper length is the length measure between two events (or stones) in their rest frame and the particle definatly isn't in the rest frame of your two stones because its moving past them!

An alternative defintion;
The proper length is the difference between the spatial coordinates of two events (or stones) in a frame of where the two events appear simultaneous.
 
  • #29
im taking x as the proper length.So x0 is lesser than x
 
  • #30
Hootenanny
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im taking x as the proper length.So x0 is lesser than x
:cry: Perhaps its time someone else stepped in to help you...
 
  • #31
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I think you should step back and carefully restate exactly what question you were asking to begin with. Nobody here looks sure what they're arguing about.
 
  • #32
robphy
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It's probably [been] time for a spacetime diagram.
 
  • #33
Sorry for all the truble to Hoot.Maybe im too young and ive not read much of physics.Ill try to understand myself.And thanks anywayz for all the help provided.
 
  • #34
Hootenanny
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Sorry for all the truble to Hoot.Maybe im too young and ive not read much of physics.Ill try to understand myself.And thanks anywayz for all the help provided.
Anant,

It's nothing to do really with your age and you don't have to read much physics do understand SR, it just takes a bit of getting your head round, some things appear counterintuitive until you actually sit down and think about them deeply.

I'm willing to walk you through this derivation, if we at least agree to use standard notation and you agree to think properly about every step we go through. I'm sure robphy will add a space-time diagram at some point (to show off hit latex skills :wink: ) and that will probably help.
 
  • #35
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
 
  • #36
cristo
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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!
 
  • #37
thanks ill try to do that.Also im really bad at using LaTex
 
  • #38
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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 travelled 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.
 

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