Does energy have mass? by Jim Grozier STS WIP seminar 23.2.12.

Does energy have mass?

by

Jim GrozierSTS WIP seminar 23.2.12

E = mc2

[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 10.12.2011 [3]

Okun [4]

m1 m2

u1 u2

m1 m2

Conservation of Momentum and Kinetic Energy

v1 v2

m1u1 + m2u2 = m1v1 + m2v2

½m1u12

+ ½m2u22 = ½m1v1

2 + ½m2v22

p = mv

E = mc2

p = m0v

E = m0c2

p = (m0)v

E = (m0)c2

p = mv

E = mc2

m = m0“concomitance”

p = mv

E2 = p2c2 + m2c4

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, 19.6.48, in [4]

The end … ?

“If you could do the measurements to one part in a trillion …”

Susskind [5]

m2c2 = (p0)2 – (p1)2

m2c2 = (E/c)2 – p2

m2c2 + p2 = (E/c)2

m2c4 + p2 c2= E2

m2c4 = E2

[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, (27.10.11)

2. Hans C. Ohanion, “Physics”, Norton (1992)

3. New Scientist 10.12.2011, 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, “Einstein’s 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)