The splitting of intrinsic energy and the origin of mass density in continuum mechanics

We show that the total intrinsic energy of a body must split into the sum of two terms—an internal energy which depends upon ‘state’ and a kinetic energy which is quadratic in the square of the particle speed.We use the non-relativistic group invariance structure of a generalized form of the balance of energy in continuum thermomechanics, together with a fundamental axiomatic requirement. The fundamental concepts of motion, force, power, heating and intrinsic energy are introduced as primitive, and we derive the notion of mass and its balance.

When James Serrin died on August 23, 2012, this work had just been completed. Jim was my close, personal and treasured friend for over 40 years. We collaborated on several works over those years, and we often talked together and socialized on various occasions. I had highest respect for him in all human and professional ways, and there was a definite mutual expression of affection and appreciation. A friendship could not contain more. This paper drew him back to a subject he had worked on years ago, and he was happy to be involved again with a fundamental issue in continuum mechanics. My efforts in this work are dedicated to the memory of James Serrin. He was such a scholar of great breadth and depth—He was wise and witty, and I benefited greatly from his presence.

Roger Fosdick