Physics can be a weighty subject, full of substance and gravitas. It is therefore perhaps entirely reasonable that a central topic of the discipline is mass. But what is mass, really? What is the origin and nature of this most essential feature of the world around us? And are there any surprises to be had as we dig deeper into that question? In this article, I hope to surprise every reader at least once.
References
1.
In the interests of full disclosure, I’ve taught this misconception myself. For a certain class of students, the problems associated with this approach are outweighed by the benefits.
2.
D.
Morin
, Special Relativity: For the Enthusiastic Beginner
(CreateSpace Independent Publishing Platform
, 2017
).3.
E.
Hecht
, “Einstein never approved of relativistic mass
,” Phys. Teach.
47
, 336
(2009
);L. B.
Okun
, “The concept of mass
,” Phys. Today
42
(6
), 31
(1989
);T. R.
Sandin
, “In defense of relativistic mass
,” Am. J. Phys.
59
, 1032
(1991
);L. B.
Okun
, “Mass versus relativistic mass and rest masses
,” Am. J. Phys.
77
, 430
(2009
).4.
P. J.
Riggs
, “A comparison of kinetic energy and momentum in special relativity and classical mechanics
,” Phys. Teach.
54
, 80
(Feb.
2016
).5.
T.
Damour
, “Testing the equivalence principle: Why and how?
” Classical Quantum Gravity
13
(11A
); http://iopscience.iop.org/article/10.1088/0264-9381/13/11A/005.6.
C.C.
Speake
and C. M.
Will
, “Tests of the weak equivalence principle
,” Classical Quantum Gravity
29
(18
); https://nssdc.gsfc.nasa.gov/planetary/lunar/apollo_15_feather_drop.html.7.
J.
Webb
et al., “Further evidence for cosmological evolution of the fine structure constant
,” Phys. Rev. Lett.
87
(9
), 091301
(2001
);A. P.
Meshik
, “The workings of an ancient nuclear reactor
,” Sci. Am.
293
(5
), 82
(Nov.
2005
).8.
R. V.
Pound
, “Weighing photons, I
,” Phys. Perspect.
2
, 224
(2000
);R. V.
Pound
, “Weighing photons, II
,” Phys. Perspect.
3
, 4
(2001
).9.
J.
Müller
and L.
Biskupek
, “Variations of the gravitational constant from lunar laser ranging data
,” Classical Quantum Gravity
24
(17
), 4533
(2007
).10.
I.
Sample
, Massive: The Missing Particle that Sparked the Greatest Hunt in Science
, revised ed. (Basic Books
, 2013
).11.
D.
Lincoln
, “The Higgs boson: Is the end in sight?
” Phys. Teach.
50
, 332
(Sept.
2012
).12.
The ATLAS and CMS collaborations
, “Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMW analysis of the LHC pp collision data at a √s = 7 and 8 TeV
,” J. High Energy Phys.
08
, 045
(2016
); https://www.youtube.com/watch?v=1AamFQWwh94.13.
This statement neglects the binding energy of atoms, which is of order a few eV to tens of keV. This is contrasted to the GeV to hundreds of GeV mass energy of the atoms.
14.
F.
Wilczek
, Origins of Mass, MIT Physics Annual 2003
; https://arxiv.org/abs/1206.7114; https://www.youtube.com/watch?v=x8grN3zP8cg.15.
Note that the Higgs field is a scalar field, while the electric field is a vector field, and thus the analogy is imperfect. The potential energy of an electric charge in an electric field depends on the distance traveled within it, while the energy of a particle interacting with the Higgs field is independent of position.
16.
D.
Lincoln
, “Dark matter
,” Phys. Teach.
51
, 134
(March
2013
).17.
E.
Hecht
, “On morphing neutrinos and why they must have mass
,” Phys. Teach.
41
, 164
(March
2003
).18.
C.
Patrignani
et al. (Particle Data Group
), 2017 Review of Particle Physics
(2016
) and 2017 update; http://pdg.lbl.gov/2017/listings/contents_listings.html.20.
Matthew R.
Francis
, “Neutrinos on a seesaw
,” Symmetry
(Feb.
2016
), http://www.symmetrymagazine.org/article/neutrinos-on-a-seesaw.© 2017 American Association of Physics Teachers.
2017
American Association of Physics Teachers
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