Look-Back Times
The velocity of light plays a central role is astronomy and in physics because it places
an upper limit on speeds in our Universe.
A Cosmic Speed Limit
According
to the Einstein's Theory of Relativity, nothing in our Universe can exceed
the velocity of light; thus, it is a kind of cosmic speed limit against which
all other velocities may be measured. More generally, light is part of the
electromagnetic spectrum, which includes infrared radiation, radio
waves, gamma rays, X-rays, ultraviolet radiation, and so on.
All of these are
a form of light; they just have energies that differ from the visible light that
our eyes can see. Thus, these forms of electromagnetic radiation all travel at
the speed of light too.
Furthermore, contrary to normal intuition, the theory of relativity tells us
that light always travels at the same speed relative to some observer,
no matter what the relative motion of the observer.
Although this may seem strange, it has been confirmed in many
experiments: it is the way the Universe works.
Looking Back in Time
Because light travels at a large but finite speed, it takes time for light to
cover large distances. Thus, when we see the light of very distant objects in
the Universe, we are actually seeing light emitted from them a long time ago:
we see them literally as they were in the distant past.
For example, when Supernova 1987A
occurred in the "nearby" galaxy called the
Large
Magellanic Cloud (above figure),
its light was observed on Earth in 1987. But the distance to
the Large Magellanic Cloud is about 170,000 light years. Thus, we normally
say that
Supernova 1987A occurred in 1987, but it really happened about 170,000 years
earlier. Only in 1987 did the light of the explosion reach the Earth!
If we
want to know what the Large Magellanic Cloud looks like "now", we will have to
wait 170,000 years.
In comparison, the Sun is only about 8 light-minutes away. So the light we see
from the Sun represents what the Sun looked like 8 minutes ago, and we must
wait another 8 minutes to see what it looks like "now".
Because of this property of light coming from distant objects, astronomers often
define a quantity called the look-back time. The look-back time is just the
time since the light that we see from an object was actually
emitted. The speed of light is so high that for nearby objects the look-back time is
essentially zero, but for Supernova 1987A it was about 170,000 years and
for very distant objects the look-back time could be 10 billion
years or more.
Time Machines
Such look-back times become critical when we look at the largest distances
because they literally allow us to peer into the early Universe. The most distant
objects observed may now allow us to see what the Universe looked like when it was only
about 1/10 of its present age. Large telescopes
are not just devices for gathering faint light. They are time machines!
The above left figure shows how the look-back time varies with redshift for three
different assumptions concerning a parameter Ω0
that measures the
average density of the Universe and that we shall discuss in Chapter 18
(the look-back time
is expressed in the plot as a fraction of the Hubble time for each case).
The following table
gives recessional velocities, distances, and look-back times as a function of redshifts.
|
Redshifts, Distances, and Look-Back Times
|
| Redshift |
v/c |
Distance
(Mpc) |
Distance
(ly) |
Look-Back
Time
(yr)* |
Age of
the
Universe** |
| 0.00 |
0.00 |
0 |
0 |
0 |
100% |
| 0.05 |
0.049 |
222 |
7.26 x 108 |
7.08 x 108
|
93% |
| 0.10 |
0.095 |
430 |
1.40 x 109 |
1.336 x 109
|
87% |
| 0.50 |
0.385 |
1694 |
5.52 x
109 |
4.57 x 109
|
54% |
| 1.0 |
0.600 |
2704 |
8.82 x
109 |
6.48 x 109
|
35% |
| 2.0 |
0.800 |
3901 |
1.27 x
1010 |
8.10 x 109
|
19% |
| 3.0 |
0.882 |
4616 |
1.51 x
1010 |
8.78 x 109
|
12% |
| 4.0 |
0.923 |
5103 |
1.66 x
1010 |
9.13 x 109
|
9% |
| 5.0 |
0.946 |
5462 |
1.78 x
1010 |
9.35 x 109
|
7% |
| 6.0 |
0.960 |
5742 |
1.87 x 1010 |
9.51 x 109 |
6% |
| 10 |
0.984 |
6448 |
2.10 x 1010 |
9.75 x 109 |
3% |
| 100 |
1.00 |
8312 |
2.71 x 1010 |
1.00 x 1010 |
~0% |
| 1000 |
1.00 |
8939 |
2.92 x 1010 |
1.00 x 1010 |
~0% |
| infinity |
1.00 |
9231 |
3.01 x 1010 |
1.00 x 1010 |
0% |
|
|
| *Assuming flat geometry
**
Percentage of age for present Universe when light emitted (flat geometry)
|
|
|
|
|
The look-back time in the above table
is expressed both in years and as a percentage of the present age of the
Universe when the light was emitted. For example, at a redshift of z = 2
we are seeing light that was emitted 8.1 billion
years ago when the Universe was only 19% of its present age.
Here is a Java
calculator that allows you to calculate the recessional velocity, look-back times,
and distances from the redshift for arbitrary values of
the Hubble constant and the deceleration parameter. (The preceding table can be reproduced
with this calculator by setting the Hubble constant to 65/km/s/Mpc and the deceleration
parameter to 0.5, corresponding to a flat Universe with no cosmological constant.)
|
The Hubble Constant and Age
The age of 10 billion years assumed for the Universe in the preceding table
depends on the Hubble parameter, which we chose as 65 km/s/Mpc. If, for example we had
chosen H = 50 km/s/Mpc (as some researchers favor), the Hubble time would have been
19.6 billion years and the age of the Universe 13.1 billion years with our other assumptions.
If instead we had chosen H = 80 km/s/Mpc (as some other researchers favor) the Hubble
time would have been 12.3 billion years and the age of the Universe 8.2 billion years.
As we have noted, a time as short as the latter would be difficult to reconcile with the
minimum age of globular clusters.
|
|
Large Redshift and Look-Back Times
With the assumptions used to
calculate the look-back times in the preceding table,
the Hubble time is 15.1 billion years and the age of the
Universe is 2/3 of that or a little more than
10 billion years (this depends on choice of Hubble constant, as described in the box).
We will explain the factor of 2/3 in Chapter
18, but it is associated with slowing of the expansion by gravity, which makes the
Hubble time an
overestimate of the age for the Universe.
Note that the look-back times are approaching
a constant value of 10 billion years for large redshift. This is because the look-back time
cannot be larger than the age of the Universe, which is 10 billion years for the assumptions
used in the table. For infinite redshift, the look-back time is
exactly the age of the Universe. However, we cannot look back all the way to infinite
redshift because the corresponding photons are redshifted to zero energy and so cannot
interact with our detectors. Furthermore, as we shall see in Chapter 18,
the Universe becomes highly
opaque to light for redshifts larger than about 1000, so it would be difficult to observe higher redshifts
than that.
Distances and Grains of Salt
As noted in the right panel,
relating distances to large redshifts requires assumptions about the nature of the
Universe. The distances in the preceding table would change somewhat if we made a
different set of assumptions in relating them to the redshifts.
We shall often quote a distance in later
discussion of high redshift objects, but one should always take these distances with a small grain
of salt. They are meant to convey a qualitative sense of distance, but the directly
measurable quantity is redshift.