Energy, Gen’rl Rel., &
Space-time diagrams,
Class 4: (ThT Q)
Does Kinetic Energy still
have a meaning in
relativity?
What is rest energy?
What does E= mc2 mean?
How does the equation
come into being?
Did you complete at
least 70% of Chapter
1: 8-10 & Appendix 2
and view the assigned
MU 44: 9’15” to 14’ 30” ?
A.Yes
B.No
Energy
(moving particle)
E = γ mc2
Rest Energy: E0 = mc2
Kinetic Energy: K = mc2 (γ -1)
Rest Energy
Electron: mc2 = 0.511 MeV
Proton: mc2 = 938 MeV
Consider an electron and a
proton, each with a kinetic
energy of 1 MeV. Which
particle is moving at
relativistic speeds? (pp)
A. electron
B. proton
Let’s do the work
Electron
K = 1MeV
• Classical K = ½ mv2  v≈ 2c
• Relativity K = mc2 (γ -1)
 γ = k/mc2 +1 =
1MeV/[0.511MeV+1] = 2.95
• γ = 1/√[1-v2/c2] 
• v = c√[1-1/γ2] = 0.94c
Proton
K = 1MeV
• Classical: K = ½ mv2 v =0.046c
• Relativity:
• γ = 1MeV/938MeV +1 = 1.001066
• V = c√[1-1/γ2] = 0.046c
What do you know!!
Neutron: as cosmic ray
• K = 50 J ≈ 3 x 1020 eV
• γ = K/mc2 + 1 = 6 x 1014
• v = c√[1-1/γ 2]; γ -2 is as close to 0 as you
are likely to get, so do binomial expansion.
• ≈ c[1-½ (1/γ2)]; keeping only 1st term
• 0.9999999999999999999999999
99985c
What is the lifetime for the
speedy neutron in lab frame?
• Basic facts: neutrons which are
not in a nucleus are unstable
decaying to a proton, an
electron and an antineutrino.
The mean half life is 886 s.
• γ*886s = 5 x 1017s = 1.5 x 1010
years, life of the Universe.
Suppose that the distance
between stars is about 4light years.
• What is distance between stars
in the frame of this relativistic
particle?
• L = 4 x1016m/γ = 4
x1016m/6x1014
• = 67 m.
• Can you imagine stars that
close?
What happens to the
Energy when the particle
hits an atom in the earth’s
atmosphere?
• What does this have to do with
E = mc2?
Converting Mass to
Energy
• Fusion and fission.
1. (a) What is the total energy
of a particle with rest mass of
one gram moving at half the
speed of light?
(b) A 20-megaton hydrogen bomb
explodes and releases the same
energy as 20 million tons of TNT.
Given the equivalence that 1 ton of
TNT equals 4.18 × 109J, how
much mass was used up in the
explosion?
2. (2 pts) (a) A particle with a rest
energy of 2400 MeV has an energy
of 15 GeV. Find the time (in Earth's
frame of reference) necessary for
this particle to travel from Earth to a
star four light-years distant.
(See the front of your text book for the
definition of 1 eV.)
(b) How much work (in MeV) must be
done to increase the speed of an
electron from 1.2x108m/s to
2.4x108m/s?
• 3. (2 points) Twins Bill and Abby
separate. Abby travels at a
uniform speed (except for a
brief turn-around period) to a
star 4.2 light-years away, and
upon returning, finds she is 5.2
years younger than Bill.
(a) How fast was Abby traveling?
(b) By how much has Bill aged
during the period Abby was
traveling?
• 4. (2 pts) Rocket A moves with a
speed of 0.75c in a northerly
direction relative to the origin.
Rocket B moves to the west
relative to the origin with speed
0.4c. How fast and in what
direction does the pilot of
Rocket A observe rocket B to be
traveling?
5. (2 pts) An observer detects
two explosions that occur at
the same time, one near her
and another 100 km away.
Another observer finds that
the two explosions occur 160
km apart. What time interval
separates the two explosions
according to the second
observer?
6. (2 pts) Consider the births and deaths of
three people as seen from two different
inertial frames S and S0. S0 moves along
the x-axis at a speed of 0.98c with respect
to S. At t = t0 = 0, observers in S record
the simultaneous births of three people:
Jack, born at the origin; Astrid, born at x =
+10 ly; and Jill, born at the origin. Both
Jack and Astrid are always at rest with
respect to S throughout their 70-year
lifespan. Jill is born and remains on a
spaceship, which is at rest with respect to
S0. With respect to S0, Jill also lives 70
years. According to observers in S, how
long does Jill live?
General Relativity
(includes gravity)
• Equivalence Principle:
Object in free fall in equivalent
to an inertial frame of reference
without gravity.
• Acceleration is the same as
gravity.
Consider a box in free-fall. A
laser in the box shoots a
beam from one side of the
box to the other. In the ref.
frame of the box, the laser
beam will be: (pp)
A.curved upward
B.curved
downward
C.not curved
Consider the space shuttle
in orbit around the Earth. Is
the shuttle in an inertial
frame of reference? (pp)
A. yes
B. no
Gravity disappears
• Space tells matter how
to move.
• Matter tells space how
to curve.
•John Wheeler.
• Question:
•Can the other Forces
disappear?
EXTRA CREDIT (2 pts) SIM:
Relativistic Movies
• Watch the simulations of relativistic
effects at
http://www.anu.edu.au/physics/Savage/
TEE/gallery.html
• Write a paragraph about what you
observed or learned about
relativistic effects while watching
these movies. You can select a
single movie to discuss or use
example from multiple movies to
describe what you observed.
1
1
v2
c2
Relativity
• F = dp/dt
• p = γmv = relativistic momentum
conserved in collisions
• γ = 1/√[1-v2/c2]
• v«c  γ ≈ 1  p = mv
•vcγ∞p∞