Mass-Energy

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Discussion

relatavistic momentum

p =	mv					= γmv
	√	⎛ ⎜ ⎝	1 −	v2	⎞ ⎟ ⎠
				c2

relativistic energy

E =	mc2					= γmc2
	√	⎛ ⎜ ⎝	1 −	v2	⎞ ⎟ ⎠
				c2

binomial expansion (or taylor series)

E = mc2

⎛ ⎜ ⎝

1 +

1

v2

+

3

v4

+

5

v6

+ …

⎞ ⎟ ⎠

2

c2

8

c4

16

c6

the first term is the rest energy

E = mc²

the second term is the classical formula for kinetic energy

K = m	1	v2
	2

relativistic mass

m' =	m
	√	⎛ ⎜ ⎝	1 −	v2	⎞ ⎟ ⎠
				c2

for massed particles

E² = p²c² + (mc²)²

for massless particles

E = pc

Summary

• bullet

Problems

practice

1. Write something.
   • Answer it.
2. Write something.
   • Answer it.
3. Write something.
   • Answer it.
4. Write something completely different.
   • Answer it.

numerical

1. The luminosity of the sun is 3.85 × 10²⁶ W.
   1. Determine the mass of the sun converted to energy in one second.
   2. How many elephants is this?
2. Fermi National Accelerator Laboratory (a.k.a. Fermilab) in Batavia, Illinois is a US Department of Energy National Laboratory and home of the world's most powerful particle accelerator, the Tevatron, which accelerates beams of protons and antiprotons to ultra-high energy and brings them into head-on collision. Protons in the Tevatron's accelerator ring acquire energies on the order of 10¹² elevtronvolts — a teraelectron volt (TeV).
   1. From the Tevatron's energy …
      1. determine the speed of a proton in the accelerator
      2. and then verify (or contradict) the laboratory's claim that protons "circle the four-mile [6.4 km] ring 57,000 times each second."
   2. Determine the mass increase of a proton in the Tevatron in …
      1. atomic mass units and
      2. multiples of the proton's rest mass

Resources

• general
  • Numerical Relativity Exhibitions, University of Illinois at Urbana-Champaign
  • Usenet Relativity FAQ
  • The Mechanical Universe and Beyond (video on demand, login required)
    • Mass, Momentum, Energy, The new meaning of space and time make it necessary to formulate a new mechanics.
• original publications
  • Does the Inertia of a Body Depend upon its Energy-Content? Albert Einstein, 27 September 1905 (English translation of "Ist die Trägheit eines Körpers von seinem Energiegehalt abhängig?" Annalen der Physik. 18:639, 1905)
  • Einstein, Albert. "Brief Outline of the Development of the Theory of Relativity." Nature 106 (1921): 782–784.
  • Relativity : the Special and General Theory by Albert Einstein, Project Gutenberg
  • Year of Physics: Relativity Revisited, Nature, 2005

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