The short
answer to the question “Is the universe expanding at the speed of light?” is “Yes,
it is!” Or, rather, I think it does and I will,
shortly, explain why. But first have I
have to give you the slightly more involved answer.
The slightly
more involved answer to the question “Is the universe expanding at the speed of
light?” is “No, of course it isn’t!”
If the
universe were uniformly expanding at the speed of light, we could not exist –
everything would be zooming away from everything at the speed of light and that
would make things difficult. Clearly
what we see in our vicinity is not receding at the speed of light – not in the least
because we can see it! We are actually
moving towards our nearest neighbours.
The Canis
Major Dwarf galaxy, is 25,000 light years from us (actually closer to
us than the centre of our own galaxy) – and would be moving away from us at
about 500 m/s – if it wasn’t being “eaten” by our galaxy, which has a notional speed of
between 130 and 600 km/s in the direction of the Hydra constellation. Andromeda, the nearest “proper” galaxy (being
a spiral galaxy rather than a dwarf galaxy or a cloud), is 2,540,000 light
years away and in the direction that we are moving. If it weren’t for the fact that we are due to
collide in about 3.75 billion years,
Andromeda and the Milky Way would be moving apart at about 50,000 m/s – but this
is not enough to overcome whatever is putting us on the collision course.
However, if
we look at more distant galaxies, what we see is that the further away they
are, the faster they are moving away from us.
The relationship between the distance and the speed of recession is
given by the Hubble
Constant. Over the past four
years there have been at least four measurements:
 2011 (Hubble) ~71.5 to ~76 km/s/Mpc
 2012 (Spitzer) ~72 to ~76.5 km/s/Mpc
 2012 (WMAP – after 9 years) 68.5270.12 km/s/Mpc
 2013 (Planck – after four years) 67.03 to 68.57 km/s/Mpc
We can be
reasonably confident, therefore, that the value of the Hubble Constant lies
somewhere between 67.03 and 76.5 km/s/Mpc.
(These are the figures I used for working out how fast our neighbours “should”
be moving away from us.)
The bottom
line is that, if something is sufficiently far away from us, the speed of
recession could be the speed of light – we can’t see things that were receding
at the speed of light (relatively to us) at the time that light was emitted
from it, because that light will never reach us, but we can see the light from distant
galaxies that was emitted billions of years ago and it has been calculated that
these galaxies are currently receding at greater than the speed of light (noting
that there is a simultaneity problem associated with distant moving objects,
the concept of “now” or “currently” gets a little vague when there is no causal
chain to keep us on track).
This is not,
however, what I mean when I say that I think that the universe is expanding at
the speed of light, because we could in one sense be saying that the universe
is expanding faster than the speed of light.
I don’t think that that is the case.
To explain as
simply as possible, I have to work through a hypothetical and hope that the
reader realises at the end that this hypothetical might not actually be that
hypothetical after all. First though, I
do have to briefly explain about Planck units.
Planck units
are natural units based on the properties of free space alone. Their relationship to each other is such that,
in terms of Planck units, the speed of light in a vacuum is 1, the gravitational
constant is 1 and so on. These units are,
however, awkward to use on an everyday basis.
One unit of Planck time is equal to about 5.39106×10^{−44} seconds, while one unit of Planck
length equals about 1.616199×10^{−35} metres. Planck energy units, on the other hand, are relatively
huge: 1.956x10^{9}J.
Let’s say,
hypothetically, that the Planck length and the Planck time represent the
smallest possible division of space and time.
Let’s further say, hypothetically, that the universe is expanding at
precisely the speed of light … in other words, that for every unit of Planck
time, the universe gets one unit of Planck length larger. Putting this in a table:
Age
of the Universe in Planck units

Breadth
of the Universe in Planck Units

1

1

2

2

3

3

4

4

…

…

1,000,000

1,000,000

…

…

8.08x10^{60}

8.08x10^{60}

This isn’t
terribly complicated, I’m just adding one unit to time and one unit to breadth. However, we can look at this in a slightly more
complicated a way.
For every unit
of Planck time, we add 1/n units of Planck time for each unit of Planck length that
exists. I’ll put this in a table to
explain:
#
of Planck Time units

Increment/Planck
Length

#
of Planck Length units

Increment

1

1

1

1

2

1/2

2

1

3

1/3

3

1

4

1/4

4

1

…

…

…

…

1,000,000

1/1,000,000

1,000,000

1

…

…

…

…

8.08x10^{60}

1/8.08x10^{60}

8.08x10^{60}

1

This means,
that for every unit of Planck length (1), we add one unit of Planck length (1),
divided by the number of units of Planck time (N_{pl}). This means that the rate of expansion would
be, at any given time:
H_{o }= 1 / N_{pl }(in units of Planck length, per unit
of Planck time, per unit of Planck length)
Let’s say,
however, that we wanted to know how many units of Planck length would be added
for another unit of length. How about if
we used a megaparsec (Mpc)? There are
1.91x10^{57} units of Planck length in a megaparsec. This would result in:
H_{o }= 1.91x10^{57} / N_{pl }(in units of Planck
length, per unit of Planck time, per megaparsec)
Let’s say
that we wanted to know the rate of expansion at 8.08x10^{60} units of
Planck time into the expansion of the universe:
H_{o }= 1.91x10^{57} / 8.08x10^{60} (in units of
Planck length, per unit of Planck time, per megaparsec)
=
2.36x10^{4} units of Planck length, per unit of Planck time, per megaparsec
This is
interesting, but the units aren’t particularly accessible, so let’s convert the
Planck units to kilometres and seconds:
H_{o }= 2.36x10^{4} * (metres per unit of Planck length)
* (kilometres per metre) / (seconds per unit of Planck time)
=
2.36x10^{4} * 1.616199×10^{−35} * 0.001 / 5.39106×10^{−44}
=
70.75 km/s/Mpc
This might be
a familiar number. This is partly because
8.08x10^{60} is the current age of the universe (13.8 billion
years). In other words, if the universe
is expanding at a rate of one unit of Planck length per unit of Planck time, we
would expect to see a Hubble Constant of … pretty much exactly what we measure
it to be.
Now, I am not
saying that the universe is merely getting broader, because no matter what
direction we look, we see the same rate of expansion for objects at the same
distance. I’m also not saying that some
distant edge of the universe is moving away from us at a rate of one unit of
Planck length for each unit of Planck time.
The added space appears to be evenly distributed throughout the
universe, very much like the whole “fabric of spacetime” were being stretched
which is consistent with the concept that spacetime is expanding as would the
rubber of an inflating balloon.
If my “hypothetical”
is right, then we should be able to determine the age of the universe from the
Hubble constant and/or the Hubble constant from the age of the universe because
they are the reciprocal of each other.
Of course, neither are particularly easy to tie down, so we might just
find that the values are close but not identical. If we find that the Hubble Constant and the reciprocal
of the age of the universe diverge, then naturally my “hypothetical” won’t hold
any water. It would, however, be interesting
to see if it is consistent with other observations.
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