In his book 'Concepts of MODERN PHYSICS', Chapter 1, Section 1.7, page# 22to 24, Arthur Beiser tries to derive an equation for relativistic momentum, which he finally does. But I found the situation considered by him inappropriate so is with the way he deals with it.(adsbygoogle = window.adsbygoogle || []).push({});

Can anyone please tell me if I am wrong in comprehending his method?

I've attached two snaps of the concerned pages containing the full derivation concerned.

There are some specific assumptions that appear quite normal at the first reading. A careful observation of which is what creates doubt.

1-When the author says both the balls were thrown from rest in their respective frames at the same instant, what instant is he talking about? There's no common instant between both the frames apart from the one when they started moving relative to each other which is not the one he’s pointing at.

2-The orientation of S and S' as shown in the diagram on the right is not correct because if the balls are thrown at such an orientation they will never hit each other because B should be at the left of A before collision as B is travelling along X axis towards right.

3-The balls will never collide at y₌Y/2 in any frame because of a simple logic. Consider frame S. Here A was at rest. After it was thrown with a speed of VA for T seconds it travels for a distance yA ₌ VAT . However B’s speed in S is VB which is <V’B. As previously assumed VA₌V’B. Hence even if B travels for the same time T in S, it will cover a distance yB₌VBT < yA. As seen here if the two balls travel for the same time interval in S they will cover unequal distances. Hence they won’t collide midway.

4- Consider any frame (say S). Let’s focus on only Y axis movement. If we consider relativistic effects on velocities for sure and apply formulas from elastic collison.

Assumption 1: Relativistic effect on mass is not considered.

Two balls of equal mass collide with different velocities as VA>VB.Their final velocities will be simply their initial velocities exchanged. Not as the Author says simply reversed.

Assumption 2: Relativistic effect on mass is considered

Two different balls collide with different initial velocities. Their final velocities cannot be their initial velocities simply reversed.

Where do we see that A will bounce back with simply its initial velocity reversed as does B?

Please clarify.

Thanks in advance.

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# The Arthur Beiser Logic

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