PHYSICS 230 – PROBLEM SET 2
1. UNITS
Theoretical physicists often work in units where ¯
h
=
c
= 1. What does
this mean? From the equation
x
=
ct
we see that if
c
= 1 then [
length
]
and [
time
] are the same units. From the equation
E
= ¯
hω
we see that
[
energy
] and [
time
]

1
are the same units. Using similar relations show
that all cgs units can be expressed relative to one basic unit. Often
this is taken to be [energy], say electron Volts. Express the size of a
typical room, say 10 meters, in eV.
Show in this system that [
G
N
] = [
mass
]

2
, where
G
N
is Newton’s
gravitational constant. Express
G
N
in GeV. This mass,
m
P
is called
the “Planck Mass.” Express the Planck Mass
m
P
as 1
/l
P
where
l
P
is
a length, the Planck Length. Express
l
P
in centimeters. This mass
and this length are where we expect quantum gravity eﬀects to become
important. Compare this mass to the mass of a minimum size raindrop,
taken to be of radius 500 microns. Express the characteristic energy
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 Spring '09
 R
 Quantum Gravity, 10 meters, 500 microns, dimensional hilbert space, Planck Length

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