# Conservation of Momentum

1. Jun 28, 2006

### actionintegral

These forums help me practice my communication skills, thank you to those who helped me reword the following little document.
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I am going to try and deduce as much as I can about the nature of matter from symmetry and the galilean

transformation alone.

Suppose two identical objects approach each other with equal and opposite velocity v.

They meet in front of me.

What will happen next?

Whatever happens, we would expect the same thing to happen to both objects, since they are identical.

Let's imagine that the two objects stop dead.

Now witness this same event from the point of view of an observer moving along with one of the objects.

This observer will see one object at rest, and the other object approaching at -2v.

After the two objects meet, this observer sees them both move away together at -v.

This might be called "conservation of momentum".

Now, I argue that this phenomenon, where the two combined objects appear to move away more slowly is a result

of the galilean transformation and the change in velocity alone. To see this, replace the moving objects with
pixels on a computer screen, dots of light on the wall, or any objects that move toward each other. The only

important thing is that they stop dead upon meeting. The reason for their stopping is immaterial.

Now witness this same event from the point of view of an observer moving along with one of the objects. This

observer will see one object at rest, and the other object approach at -2v.

After the two objects meet, this observer sees them move away together at -v!

You and I know the secret, that the objects really don't have any momentum, and their "collision" is

contrived.

But this observer, not knowing differently, might call that phenomenon "conservation of momentum".

He would claim that the combined object has a mass of 2m, and therefore is moving away at -v in order that
momentum might be conserved.

It is possible to conclude that "conservation of momentum" is really an artifact of the changes in velocity

and the galilean transformation. Of course can be extended to the Lorentz transformation.

2. Jun 29, 2006

### pmb_phy

3. Jun 29, 2006

### nrqed

The problem I have with this is that it is a far too restrictive example. Your discussion can not be used to conclude that momentum is conserved in the way it is usually formulated (for arbitrary masses).
Try to prove that $m_1 {\vec v_1} + m_2 {\vec v_2}$ is conserved for arbitrary masses this way! The only way to do it is to start from Newton's laws and work within a certain approximation.

4. Jul 11, 2006

### actionintegral

Thanks for sharing that link, Pete. Actually, it was a book on special relativity that gave me the idea. It was talking about how "relativistic mass" can be derived from symmetry and the transformation of velocities alone. "Relativistic mass" arises as a useful fiction.

5. Jul 11, 2006

### Quaoar

Hate to be nit-picky but the paragraph breaks make the original post very difficult to read... :)

6. Jul 12, 2006

### actionintegral

I appreciate the feedback. I did a lazy cut and paste from notepad.

7. Jul 12, 2006