Does energy have mass? by Jim Grozier STS WIP seminar

E = mc 2 [1]

[2]

This formula suggests that tiny amounts of mass can be converted into huge amounts of energy …matter and energy are really different forms of the same thing. Any mass has an associated energy and vice versa

New Scientist [3]

Okun [4]

m1m1 m2m2 u1u1 u2u2 m1m1 m2m2 Conservation of Momentum and Kinetic Energy v1v1 v2v2 m 1 u 1 + m 2 u 2 = m 1 v 1 + m 2 v 2 ½m 1 u ½m 2 u 2 2 = ½m 1 v ½m 2 v 2 2

p = mv E = mc 2 p = m 0 v E = m 0 c 2 p = (m 0 )v E = (m 0 ) c 2 p = mv E = mc 2 m = m 0 concomitance p = mv E 2 = p 2 c 2 + m 2 c 4 p = mv interconvertibility

It is not good to introduce the concept of [relativistic mass] of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the `rest mass Einstein, letter to Lincoln Barnett, , in [4]

The end … ?

If you could do the measurements to one part in a trillion … Susskind [5]

m 2 c 2 = (p 0 ) 2 – (p 1 ) 2 m 2 c 2 = (E/c) 2 – p 2 m 2 c 2 + p 2 = (E/c) 2 m 2 c 4 + p 2 c 2 = E 2 m 2 c 4 = E 2 [6]

strictly speaking measuring rods and clocks would have to be represented as solutions of the basic equations (objects consisting of moving atomic configurations), not, as it were, as theoretically self-sufficient entities Einstein, Autobiographical Notes, in [7]

[8]

As science finds a very well-defined, narrow focus on certain problems, it has to neglect other problems – forget about certain questions, even certain facts, certain ways of looking at nature. My personal view about the mission of the history and philosophy of science is that we ought to be in the business of picking up all those things science drops as it goes on its triumphal march. – Hasok Chang, January 2012

References: 1.Ian Sample, Kindle makes for heavy reading, Guardian 2, ( ) 2.Hans C. Ohanion, Physics, Norton (1992) 3.New Scientist , page 44 4.Lev B Okun The Concept of Mass, Physics Today, (1989) 5.Leonard Susskind The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics, Little Brown & Co (2008) 6.Space, Time & Cosmology, Unit 7, Open University (1997) 7.Harvey Brown, Einsteins Misgivings about his 1905 formulation of special relativity, European Journal of Physics 26 (2005), S85-S90 8.Advancing Physics, Institute of Physics (2000) 9.Max Jammer, Concepts of Mass in Contemporary Physics & Philosophy, Princeton (2000)