The Arthur Beiser Logic

[bibhu]

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.

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

Thanks in advance.

[Schrödinger's hat]

Could you outline the situation and derivation you are speaking of? It's unlikely that we'll all have that specific book.

I would also think that uploading a photo of the page, or some sections of the pages in question would fall under fair use.

[swansont]

Could you outline the situation and derivation you are speaking of? It's unlikely that we'll all have that specific book.

I would also think that uploading a photo of the page, or some sections of the pages in question would fall under fair use.

 

Or, unless it's some novel method, find the derivation elsewhere on the web.

[Mike-from-the-Bronx]

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.

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

Thanks in advance.

 

Most textbooks use the same examples. In mine the example for derivation of relativistic momentum goes like this.

 

Mary and Frank are moving in opposite directions horizontally with respect to each other.

Mary throws a ball straight down and Frank throws a ball straight up.

The balls are perfectly rigid and perfectly elastic. The distances, speed and mass of the balls are symmetrical so that the balls bounce off each other and back into their hands.

 

To prove that this must happen in Newtonian physics, you need to use the laws of Conservation of Energy and Conservation of Momentum.

If you still want to have a Conservation of Momentum in SR, you can't use the Newtonian definition of p=mv. So what definition will work?

If that's the example you have in your book, I can help.

[DrRocket]

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.

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

Thanks in advance.

 

I own the book.

 

Beiser is not atteptiing to derive an equation for relativistic momentum. He is trying to derive the equation for relativistic mass, and he is using conservation of momentum to do it. Momentum is mass x velocity.

 

I have not idea what you find "inappropriate", but Beiser's analysis is correct.

 

You should be aware that Beiser's book, originally written in the early 1960's teaches the notion of relativistic mass, while many physicists use the term "mass" to mean rest mass. Mass in relativity is a term that is used in different contexts with different meanings, and you need to be sure that you understand what an particular author means when using that term.

 

Rest mass is just what it sounds like -- the mass of a particle in the rest frame of the particle. Relativistic mass of a particle is gamma x rest m ass. Invariant mass is sometimes used to describe a system of particles and is rest mass in a frame of reference in which the net momentum of the system is zero. So invariant mass is what is measured in the laboratory when a macroscopic body is weighed and it includes thermal energy of the constituent molecules.

Edited January 4, 2012 by DrRocket

[Obelix]

It's unlikely that we'll all have that specific book.

 

It's an old book, classical I'd say. I have a copy in english my father bought back in 1971 (McGraw & Hill) and a greek translation I bought in 2004.

 

I'll look the matter up and try to compare it with the same topic in other books. It would be of help if bibhu gave a few indicative details as to what he finds inappropriate in Beiser's derivation.

[bibhu]

Hi all, Thanks for your replies. 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 V_Afor T seconds it travels for a distance y_A ₌ V_AT _. However B’s speed in S is V_B which is <V’_B. As previously assumed V_A₌V’_B. Hence even if B travels for the same time T in S, it will cover a distance y_B₌V_BT < y_A. 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 V_A>V_B.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 again.

Edited January 8, 2012 by bibhu