SR Misunderstanding: Mass from E=mc^2?

[Silverious]

I was reading in my textbook today. And it said that if you compress a spring, the mass increases due to E=mc^2. Technically that sounds right, but where does the mass come from?

 

[LURCH]

As you compress the spring, you add energy to it. This energy has mass. It comes from whatever is compressing the spring.

 

[meteor]

Energy and mass are interchangeable. Take like example a photon, it has not mass. But if a photon hits an object and it's absorbed by it, the object will gain mass (the energy of the photon will transform to mass)

 

[OneEye]

...but any such increase will be so minute that it will be immeasurable.

Also, I am not sure that this view is generally accepted any more. Someone on the board posted something to the effect that "relativistic mass" is a passé concept, replaced by a more general notion of "relativistic energy".

Would anyone else care to comment?

 

[turin]

There is an approach to relativistic kinematics that, first of all, claims c as a limiting velocity, and then goes on to explain this kinematical feature as a consequence of increasing relativistic mass (clearly dynamical). Whether this is passe or not, it seems trite to me.

When one considers the issue of gravitation, it is clear that the compressed spring will induce a greater curvature than the same spring in a relaxed state. In fact, it is this idea that partly results in a black hole. Even if there is a continuous distribution of matter, above some critical mass, the matter cannot support itself. At this critical point, any back pressure actually increases the stress energy, thus inducing a spacetime curvature that overcomes the resistance to compress.

 

[DW]

I was reading in my textbook today. And it said that if you compress a spring, the mass increases due to E=mc^2. Technically that sounds right, but where does the mass come from?

Potential energy is an abstract concept one uses when one does not which to account for where the energy actually is, but one may say it is in the increased potential. More precicely accounting for it, when you compress the spring you are changing the electric field line configuration between atoms and molecules. You are changing the energy stored in the electric field or from a quantum perspective increasing the energy associated with the virtual photons mediating the electric force. This is where the center of momentum frame energy called mass is.

 

[Silverious]

Okay, I think I understand. But I have another question, I'm not sure if it applies but: What happens when I stretch the spring past the elastic limit. Does the "mass" increase in some other way relative to how I elongate it?

 

[turin]

If it's reversible, you can still treat it the same way; you just have to realize that, to do a calculation, it isn't linear. If you extend it into the plastic region, as far as I know, all bets are off.