Interpreting Hubble’s Law
Barbara Ryden
Department of Astronomy
The Ohio State University
All physics & astronomy
majors should take a
cosmology course as a
“capstone” experience.
thermodynamics,
statistical mechanics,
quantum mechanics,
classical dynamics,
general relativity,
nuclear physics,
atomic physics,
particle physics…
For non-science majors, a historical overview of
cosmology emphasizes how new observations lead to
new cosmological models.
Malcolm Longair (1993) QJRAS, 34, 157:
Hubble (1929) PNAS, 15, 168
Lesson: Typos happen.
Hubble (1929) PNAS, 15, 168
What are “VELOCITY”
and “DISTANCE”?
Hubble (1929) PNAS, 15, 168
Humason (1931) ApJ, 74, 35
“VELOCITY” = c z ,
where c = speed of light and
z = percentage shift in wavelength of light.
Observation = redshift (z)
Interpretation = velocity (v)
(Mt. Wilson Observatory, 1931)
Possible interpretations of the observed redshift:
Doppler shift: z = v/c
(Galaxies are moving away from the observer through space.)
Gravitational redshift: z = vesc/c
(More distant galaxies are more luminous, and have deeper
potential wells.)
Cosmological redshift: z = aobservation/aemission - 1
(In the limit of small redshift, z = v/c, where v is the relative
speed of emitter and observer due to expansion of space.)
Tired light: z = Eemission/Eobservation - 1
(Photons lose energy as they move through static space.)
λ observed  λ 0
c
λ0
Hubble (1929) PNAS, 15, 168
Big Problem for Astronomers:
no sense of depth looking at the sky.
Comet Hale-Bopp:
10 light-minutes away
Andromeda Galaxy:
2 million light-years away
Lesson: measuring the distance to an
astronomical object is damnably difficult.
Hubble used the “standard candle” method.
f
L
4 r
2
L assumed
r
4 f observed
Obvious problem with standard candles:
if your assumed luminosity is crap,
your computed distance is crap
Edwin Hubble fell into this trap.
(Beware of “appeal to authority”: even Homer nods.)
0.061
0.050
0.49
0.88
0.77
0.80
7.2
5.0
8.0
3.6
3.2
3.7
10.
5.4
4.7
12.
9.0
14.
7.5
12.
17.
16.
17.
17.
Hubble
(1929)
PNAS,
15, 168
λ observed  λ 0
c
λ0
L wrong
4 π f observed
Hubble (1929) PNAS, 15, 168
Hubble’s law in mathematical form:
v = H0 r
v = “velocity”
r = “distance”
H0 = Hubble constant
Hubble’s value of the Hubble constant ≈ 500 km/s/Mpc
WMAP value = 71.0 ± 2.5 km/s/Mpc
Not-as-obvious problem with standard candles:
our equation assumes Euclidean geometry.
What if Euclid nods on large scales?
Another problem with standard candles:
our equation assumes photon energy is conserved.
Redshifted photons lose energy.
But wait!
These aren’t problems,
they are opportunities!
Deviations of Hubble’s law from
a straight line at large
distance/redshift tells us about the
expansion history of the universe.
One set of observations …
many possible interpretations.
Hubble acknowledged the existence of both
Doppler shifts and cosmological redshifts.