# Inertia of Stress

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#### Pmb

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##### Inertia of Stress
« on: 09/07/2012 00:25:40 »
Hi Everyone! I'm back!

A while back we discussed relativistic mass (RM), m. RM is defined as the m in p = mv. I keep seeing people support their anti-RM position in several ways. One of those was is by saying that relativistic mass m is just another name for energy since E = mc2, I the paper I wrote I give a simple example of where that notion doesn't hold true. The paper is at http://arxiv.org/abs/0709.0687

In cases where stress contributes to inertia you will find that this assertion isn't true. There are few aricles on the subject in the American Journal of Physics. One of the articles is

The inertia of stress, Rodrigo Medina, Am. J. Phys. 74(11), November 2006
Quote
Abstract - We present a simple example in which the importance of the inertial effects is evident. The system is an insulating solid narrow disk whose faces are uniformly charged with equal charges of equal magnitude and opposite signs. The motion of the system in two different directions is considered. It is shown how the contribution of energy and momentum of the stress that develops inside the solid to balance the electromagnetic forces have to be added to the electromagnetic contributions to obtain the results predicted by the relativistic equivalence of mass and energy.
This means that if you have a rod lying on the x-axis which is under stress but for which the forces on the body are in equalibrium the relation E = mc2 does not hold.

This was someting Einstein knew too so this isn't new by any stretch of the inagination. In 1907 Einstein wrote a paper called On the Inertia of Energy Required by the Relativity Principle Annalen der Physik 23 (1907). Section 1 is called On the kinetic energy of a rigid body in uniform translation subject to external forces. This kind of thing is rarely, if ever, mentioned in modern relativity texts. Its implicit in the stress-energy-momentum tensor but you have to know what to look for. I found it because I did a deep search into Einstein's papers. This idea can be used to show that E = mc2 doesn't hold for stressed bodies. The artilcle on the inertial properties of stress notes this and states that for E = mc2 to hold for the energy stored in the capacitor the stress in the capacitor must be taken into account.

I raised that notion in my article because it seems that nobody else who wrote articles on the subject knows about it. In the article Einstein starts out by saying
Quote
We consider a rigid body that is moving in uniform tranlation (velocity v) in the direcction of increasing x-coordinate of a coordinate system (x, y, z) that is assumed to be at rest. If external forces do not act upon it, then, according to the theory of relaivity, its kinetic energy is given by the equation

$K_0 = \muV^2[\frac{1}{\sqrt(1 - (v/V)^2)} - 1]$

where $\mu$ denotes mass (in the conventional sense) and V the velocity of light in vacuum. We now want to show that according to the theory of relativity thi expression does not hold any longer if the body is acted upon by external forces that balance each other.[
I then use this same scenario to show that relativistc mass isn't just another name for energy since the normal relationship E = mc2 does hold under these circumstances. That's a very important point that has been over looked in this debate on relativistic mass vs rest mass.

#### Geezer

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##### Re: Inertia of Stress
« Reply #1 on: 09/07/2012 00:45:55 »

Hi Everyone! I'm back!

Wait a minute! Didn't you promise never to darken our doorstep ever again?  [] []
There ain'ta no sanity clause, and there ain'ta no centrifugal force æther.

#### Pmb

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##### Re: Inertia of Stress
« Reply #2 on: 09/07/2012 04:26:41 »
I had a change of heart. Why? Do you want me to leave?

#### Geezer

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##### Re: Inertia of Stress
« Reply #3 on: 09/07/2012 04:40:02 »
I had a change of heart. Why? Do you want me to leave?

Certainly not!

I was just yanking your chain. A rather low form of humor, I admit.
There ain'ta no sanity clause, and there ain'ta no centrifugal force æther.

#### simplified

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##### Re: Inertia of Stress
« Reply #4 on: 09/07/2012 07:42:15 »
If development of physics uses relativistic mass then relativistic mass is useful.We would like to see such development.

#### Pmb

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##### Re: Inertia of Stress
« Reply #5 on: 09/07/2012 12:30:48 »
If development of physics uses relativistic mass then relativistic mass is useful.We would like to see such development.
From what I've seen there is a slight trend on looking at the inertia of stress. I've seen two articles on the subject in the American Journal of Physics. I myself have been addressing the issue too. I'm dressing up my work for an attempt to be piblished in another journal so if I'm luck enough to have it published then that will be a third time touching on it. There was a paper by David Griffith on mass renormalization where he addresses the inertia of stress to.

#### Pmb

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##### Re: Inertia of Stress
« Reply #6 on: 09/07/2012 13:25:34 »

Certainly not!

I was just yanking your chain. A rather low form of humor, I admit.
Yeah. I understand. I'm touchy nowadays. Too many people around me in forums who keep exagerating things out of proportion has made me jumpy I guess.