# Relative momentum and relative mass

1. Jun 2, 2015

### Amr Elsayed

Hi all,
I feel like I have a misconception about that topic, so I hope I will get an answer for the question:

Momentum should be conserved from the same perspective, but does it have to from different perspectives or frames ? I mean we don't agree about sth's velocity, so we don't agree about momentum. What's wrong with that?
what I know is that mass changes from different frames is because each frame should observe the same momentum.

regards

2. Jun 2, 2015

### Orodruin

Staff Emeritus
Nothing. Both momentum and energy are frame dependent quantities.

3. Jun 2, 2015

### Amr Elsayed

Then why there is a need for mass to change due to special relativity laws ?

4. Jun 2, 2015

### Amr Elsayed

I mean mathematically concerning momentum , Momentum and velocity are relativistic, then why mass is ?

5. Jun 2, 2015

### Janus

Staff Emeritus
It's how the measurement of momentum changes as seen from different frames that distinguishes Newtonian physics and Relativity.

In the former, momentum can be measured as mass times velocity. This is frame dependent because an object's momentum as measured by any frame is dependent on its velocity with respect to that frame.

In Special Relativity, momentum is measured as mass times velocity times the Lorentz factor of $\frac{1}{\sqrt{1-\frac{v}{c^2}}}$

Since the Lorentz factor depends on the velocity, the increase of momentum with an increase of velocity is not linear under Special Relativity like it is under Newtonian physics.

6. Jun 2, 2015

### Amr Elsayed

And why do we multiply it with Lorentz factor ?

7. Jun 2, 2015

### Orodruin

Staff Emeritus
It is not, at least not in the sense most physicists use the term. See our FAQ https://www.physicsforums.com/threads/what-is-relativistic-mass-and-why-it-is-not-used-much.796527/ [Broken]

Last edited by a moderator: May 7, 2017
8. Jun 2, 2015

### Orodruin

Staff Emeritus
If we did not it would violate Lorentz invariance, i.e., the statement that the physics are described by the same equations in all inertial frames.

9. Jun 2, 2015

### Amr Elsayed

Would you please illustrate more ? why?

10. Jun 2, 2015

### Orodruin

Staff Emeritus
Which part of the statement do you have problems with?

In general, depending on your level, it may be more fruitful to think of things in terms of the classical expressions being only approximations to more general ones.

11. Jun 2, 2015

### Amr Elsayed

I need to know what's different about momentum since we discovered time dilation. How this affects mass

12. Jun 2, 2015

### Staff: Mentor

it's not because we discovered time dilation - both time dilation and the relativistic momentum equation come from the Lorentz transformations, which are a consequence of the speed of light being finite and the same for all observers.

And it's not that anything was suddenly "different about momentum" after we discovered the Lorentz transforms. The momentum of a moving object has always been $p=\gamma{m}_0v$ and $p={m}_0v$ has always been just a very good approximation - so good, in fact, that it was several centuries before we figured out that it wasn't exact.

If the speed of light were infinite, then $p={m}_0v$ would be exact.

13. Jun 2, 2015

### Amr Elsayed

Thank you, but I still want to know the mathematical and physical proof of mass change due to special relativity. I mean without mass changing " In my frame" momentum is conserved, and in the frame of any moving object it's conserved too. What is need for mass to change? or it's possible not necessary ?? You can tell me why P= gama*m*v
Sorry for bothering
regards,

14. Jun 2, 2015

### Orodruin

Staff Emeritus
Did you read the FAQ I linked? Mass does not change in relativity.

15. Jun 2, 2015

### Staff: Mentor

The "mass" that changes is relativistic mass, which is just another word for "energy". Do you understand why an object's energy changes when its velocity changes?

16. Jun 2, 2015

### Amr Elsayed

I quickly did, but it was about how physics consider mass. I mean mass that is the resistance of the substance to accelerate.

I don't, sir. Just more kinetic energy is that i know, do you mean sth else ?

17. Jun 2, 2015

### Orodruin

Staff Emeritus
You should read it more carefully. It is about why relativistic mass is not a concept used by physicists. Therefore, we generally only talk about the rest mass. I also suggest you take post #12 to heart and think about it. There is a lot of useful material there.

18. Jun 2, 2015

### Staff: Mentor

Kinetic energy is part of energy, so if kinetic energy increases with velocity, so does energy.

19. Jun 2, 2015

### Staff: Mentor

In other words, you mean inertia (or "inertial mass"). If that's what you're interested in, you shouldn't be looking at just energy and momentum; you should be looking at force, to see how much acceleration a given applied force imparts to an object which is already moving at a given velocity. In other words, you should be looking at the relativistic equivalent of $F = m a$. See, for example, here:

http://en.wikipedia.org/wiki/Four-force

What you will find is that "relativistic mass" is not a useful concept for understanding inertia in general in relativity; it's better to focus on invariant mass (i.e., rest mass, i.e., what relativists mean when they say "mass") and how it appears in the various equations involved.

20. Jun 2, 2015

### Orodruin

Staff Emeritus
Just to add that this ...
... is also covered in the FAQ.

21. Jun 2, 2015

### Amr Elsayed

Thank you but it's not my problem, I wanna learn about relativistic mass, I heard sth like we know it changes because of relativity and conservation of momentum

When an object's in a free fall for example due to gravity it will accelerate but will not reach c, They say because mass increases. I think this relates
Well, I wanna understand what relativistic mass is if i will not waste your time

22. Jun 2, 2015

### Orodruin

Staff Emeritus
It is not our time you would be wasting, it is your own. If you want to learn why resistance to acceleration changes with velocity and is different in different directions, the answer lies in the relativistic expression for momentum - as outlined in the FAQ. It is generally not what is called relativistic mass, which as noted before is just another way of saying "total energy" in relativity.

23. Jun 2, 2015

### Staff: Mentor

This has nothing to do with "relativistic mass". First of all, an object in free fall is not accelerating in any physical sense--its proper acceleration is zero. Its "acceleration" is coordinate acceleration, which is, as the name implies, coordinate-dependent; you can eliminate it by picking appropriate coordinates (those of a local inertial frame). So this is not at all analogous to an object undergoing proper acceleration in flat spacetime, but never reaching c relative to some fixed inertial observer.

24. Jun 2, 2015

### Amr Elsayed

Unfortunately FAQ doesn't contain the proof for the increasing relativistic mass. I need a proof like: C is constant so there is length contraction and time dilation with equations. I think trying to understand sth is not time wasting :)

25. Jun 2, 2015

### Amr Elsayed

I just meant velocity increasing for a fixed frame of reference like the ground. If I fall in a planet that gives enough height and time to reach C ? increasing velocity will continue because of acting force. Why wouldn't it reach C then ?