Journal Examples
Apparatus to measure relativistic mass increase, John W. Luetzelschwab, Am. J. Phys. 71(9), 878, Sept. (2003).
Relativistic mass increase at slow speeds, Gerald Gabrielse, Am. J. Phys. 63(6), 568 (1995).
In defense of relativistic mass, T. R. Sandin, Am. J. Phys. 59(11) 1032 (1991).
A simple relativistic paradox about electrostatic energy, Wolfgang Rindler and Jack Denur, Am. J. Phys. 56(9), Sept. (1988).
An elementary development of mass-energy equivalence, Daniel J. Steck, Frank Rioux, Am. J. Phys. 51(5), May (1983).
Observed Relativistic Mass Increase for 0.3 eV Electron, G. Gabrielse and H. Dehmelt, Bull., Am. Phys. Soc. 25, 1149 (1980).
Mass & Energy - by Q. ter Spill, Institute of Physics Education
Specific Instances - Not Used Throughout Text
Gravitation, Misner, Thorne and Wheeler, W.H. Freeman & Co., (1973), page 141. Proof that stress-energy tensor is symmetric
Calculate in a specific Lorentz frame. Consider first the momentum density (components Tj0) and the energy flux (components T 0j). They must be equal because energy = mass ("E = Mc2 = M")
T j0 = (energy flux)
= (energy density) x (mean velocity of energy flow )j
= (mass density) x (mean velocity of mass flow )j
= (momentum density) = T 0j
Cosmological Principles, Peacock, Cambridge Univ. Press, (1999).
From page 18
When dealing with mechanics, however, we have not one conserved quantity, but four: energy and vector momentum. So, although Jm is a perfectly good 4-vector mathematically it is not physically relevant for describing conservation laws involving mass. For example, conservation laws involving Jm predict that density will change under Lorentz transformations as r --> gr, whereas the correct law is clearly g2 (one power of for change in number density, one for relativistic mass increase.
From page 17-18
The only ingredient now missing from a classical theory of relativistic gravitation is a field equation: the presence of mass
must determine the gravitational field. [...] Now, if this equation is to be covariant, Tmn must be a tensor and is known as the energy-momentum tensor (or sometimes as the stress-energy tensor). The meanings of its components in words are T00 = c2x(mass density) = energy density, T12 = x-component of current of y-momentum etc. From these definitions the tensor is readily seen to be symmetric. Both momentum density and energy flux density are the product of a mass density and a net velocity, so T0m = Tm0.
A First Course in General Relativity, Schutz, Cambridge Univ. Press, (1990). Page 94
One final note: it is clear that
(4.6) N*N = n2, n = (-N*N)-1/2
Thus, n, is a scalar. In the same way that 'rest mass' (a.k.a. proper mass) is a scalar, even though energy and 'inertial mass' are frame dependant, here we have that n is a scalar, the 'rest density,' even though number density is frame dependant.
A Short Course in General Relativity, Foster & Nightingale, Springer Verlag, (1994). Discussing light climbing out of a gravitational field
Then in traveling from the emitter to the receiver a photon suffers a loss in "intrinsic" energy equal to its gain in gravitational potential energy. The loss in intrinsic energy is h(nE - nR), while the gain in gravitational potential energy is
on assigning the mass hnE /c 2 to the photon. Equating these leads to the fractional-shift formula (4.17). This formula assumes that the photon's energy has both inertial mass and gravitational mass, and depends in an essential way on the equivalence principle.
The Evolution of Physics, Einstein & Infeld, Touchstone Pub., (1966). Commenting on the observation made by an observer inside an accelerating elevator that light is ‘weightless’ Einstein
But there is, fortunately, a grave fault in the reasoning of the inside observer, which saves our previous conclusion. He said: “A beam of light is weightless and, therefore, it will not be affected by the gravitational field.” This cannot be right! A beam of light carries energy and energy has mass.
University Lecture Notes - Online Examples
From Second INTERNATIONAL GIREP Seminar on Quality Development in Teacher Education and Training, 1 - 6 September 2003 University of Udine, Italy. -- Ambiguities in Teaching Physics: The case of weight and Energy-Mass
We think that, all three opinions are equivalent with one another, except in the cases where their supporters pretend to prove the priority of one opinion upon another, or, in the worst cases, to proclaim other opinion/s as wrong, even when these opinions are formulated or stated by Einstein, Heisenberg, Feynmann or Hawking.
Syracuse University: Special Relativity - Lecture 16 , Lecture 17
The Special Theory of Relativity - J D Cresser, Department of Physics, Macquarie University
Washington State University - Einstein and Relativity
Michael Fowler - University of Virginia
Keith E. Holbert - Relativity notes - Arizona State University
Relativity - University of Chicago
Relativistic mass and dynamics - Royal Holloway, University of London
Special Theory of Relativity - Florida State University
Physics 110 - Astronomy Dept. U. Washington - &quoot;But the most honest answer to your question is yes--light has mass."
Particle Accelerator Labs
The real limiting factor is the basic design – all particles must orbit at the same frequency, whatever their speed. As particles approach the speed of light, however, they behave as if their mass is increasing. Accelerating them becomes more difficult and they start to lag behind the oscillating electric field. As cyclotrons approached 20 MeV they began to reach their limits and a new design had to be produced.
Lawrence Berkeley National Laboratory
University of Wisconsin-Madison
Other
Dr. Greg Snow - University of Nebraska
Physics Today - Concepts of Mass in Contemporary Physics and Philosophy - Mass Jammer
Statistical Physics - Kip Thorne - Inertial mass per unit volume
What is mass? - by R. I. Khrapko, Physics - Uspekhi, 43 (12), 1267 (2000)