Can anything 'real' be
We often here the terms 'infinite' and 'infinity', sometimes used in
connection with the size of the universe, such as an infinite universe for
example. The terms more properly belong in the world of mathematics, where
for example we may have an infinitely long string of numbers as the result
of a calculation, such as pi. The terms are very real to mathematics, but
can anything real, not theoretical, be infinite?
An infinite Universe?
Coma galaxy cluster
Naturally in mathematics we can have infinity, numbers go on for ever,
but numbers are not real, they are abstract. I cannot imagine anything 'real'
that we could apply an infinite number to. The only thing I can imagine
that could be really infinite is nothing, the 'nothing' I described earlier
in Where did the universe come from?
and we have no idea if that exists.
The concept of infinity is a puzzling one. For example: imagine a standard
pack of playing cards that consists of just one of each card but two jokers.
Imagine that the packs of playing cards are infinite in number (A thought
exercise only of course). We therefore have more jokers than any other card
in each pack, so do we have more jokers in total? You could reply that as
the packs are infinite in number they can't be counted so it would be impossible
to know. However, as the ratio of jokers to other cards in each pack is
fixed, then at any number of packs there will always
be more jokers. This would appear to indicate, that mathematically, we can
have degrees of infinity. Sounds odd doesn't it? It is a valid mathematical
We have a theory for black holes that describes infinite density. See
Exploding Black Holes? What does it mean,
other than an unresolvable equation that occurs in mathematics? Exactly
what is infinite density? Taking a rather simplistic view it could be argued
that if one black hole has infinite density then nothing else can have ANY
density. Clearly though in this sense we can have lots of infinite density,
so the term obviously carries a meaning in mathematics that does not have
the same meaning outside of it. Is the term used in the theory only because
that is the way the sums work out, regardless as to its significance in
the real world, or is it real?
Strictly speaking, according to Einstein's Theory of Relativity, a singularity
does not contain anything that is actually infinite, only things that MOVE
MATHEMATICALLY TOWARDS infinity. A black hole is formed when large
stars collapse and their mass has been compressed down to a very small size
and the powerful gravitational field so formed prevents anything, even light,
from escaping from it. A black hole therefore forms a singularity at its
centre from the concentrated mass of the collapsed star itself and from
the accumulated mass that is sucked into it. A singularity's mass is therefore
finite, the 'infinity' refers only to the maths.
Can we have an infinite universe for example? The answer is no, the universe
is finite. Stephen Hawking in 'A Brief History of Time' (1989 page 44) describes
the universe as being "finite but unbounded". The simplest answer
is that as the universe is known to be expanding, it cannot possibly be
infinite. To be precise, the dictionary definition of the word universe
is "all that is. The whole system of things." In this sense the
universe is not expanding into anything other than itself, for whatever
it is expanding into is part of the universe, there being nothing else but
the universe. However, for the sake of simplicity, I am referring only
to our Big Bang expanding universe as 'the universe'. (Even if you happen
to disagree with the Big Bang theory, the term 'universe' will still have
the same meaning here, as it refers to 'our' universe only, and does not
include whatever may or may not exist outside of it.) I will try and explain
a finite universe as some people understandably have problems with it.
A good place to start is to understand the very real difference between
infinity and a large number.
For example, imagine an ordinary size diamond, as you would expect to
find set in a typical lady's engagement ring. Now imagine a super-being
armed with super-tweezers, picking out atoms from this diamond one at a
time, one every second, since the creation of the universe, some 13 billion
years ago. How much of the diamond would by now have been removed? The answer
is you couldn't tell without looking through an electron microscope, less
than a millionth of the atoms would have been removed. Try and imagine how
many atoms there are in that diamond. Now try and imagine how many atoms
there are in the entire universe. It is a very large number, but it is finite,
and is 10 followed by 80 zeros, (maybe a few more zeros, maybe a few less),
expressed as 10 to the 80th. If you want to see what it looks like.........
0r written as - One hundred million, billion, billion, billion, billion,
billion, billion. billion, billion
Even this very large number would count as nothing when compared with
infinity, because infinity is NOT A LARGE NUMBER be absolutely clear
on this point, IT IS NOT A LARGE NUMBER, infinity is ALL
THERE IS, it is NOT a number. You could keep counting (or measuring) for
ever, and never reach infinity, it is only a description. Infinity describes
a thing as having no end, no limit, no boundary or edge, it literally goes
on FOREVER, ad infinitum.
Because infinity is not a number, large numbers are no 'nearer' to infinity
than small numbers. Number 1 billion for example is no nearer to infinity
than number 1, because the two, numbers and infinity, are in no way related.
It is then impossible to approach infinity, a thing is either infinite and
immeasurable, or finite and measurable, it cannot be part way towards infinity.
Imagine running up a 'down' escalator, never moving forward. If you run
for a week you are no nearer reaching the end of the escalator than if you
run for a minute, you cannot get any closer to something that has no end.
An infinite universe for example would exist in every direction forever,
there could be nothing else, ONLY the universe. It is then very easy to
understand why our universe cannot be infinite, it is because it is expanding.
It cannot be both infinite and expanding. It could be infinite OR expanding,
but CANNOT possibly be both, that is a contradiction in terms, and we do
know it is expanding. For an explanation of the Big Bang and why we know
the universe is expanding. See The
Big Bang Theory
I understand that many people have a problem with the idea of our universe
being finite, that it has an 'end' to it, a boundary. They ask what this
boundary would be physically like, as though it were some form of partition
that we couldn't get through. However, there is not a particular direction
that we could set off in our warp speed space craft that would lead us to
a boundary, no matter how far or fast we travelled. The explanation for
this seeming impossibility is that space-time is curved, thus you would
be travelling in a circle that only appears to be a straight line. If it
were possible to direct a laser beam from here through the centre of the
universe it would not hit the other side of the universe, it would eventually
hit the back of your head (metaphorically speaking). Einstein demonstrated
how matter in the universe distorts the space-time continuum by accurately
predicting how much our Sun distorted local space. He used a total eclipse
of the Sun (as the only time that stars and the Sun can be seen at the same
time in close proximity) to demonstrate that a star that was behind the
Sun, and therefore not visible from our line of sight, would in fact be
visible (in the darkness of totality) because the Sun warps the space-time
around it and thus curves the light beam around the Sun, enabling us to
see the star. Strictly speaking, the Sun does not actually curve the light
around itself, the entire space-time continuum is curved, the light is still
travelling in a 'straight' line.
Galaxies naturally create even larger distortions, and the total mass
of the universe gives a distortion that results in our 'straight' line of
light curving forever through the universe and never reaching the 'end'.
That's why Hawking's describes it as 'finite but unbounded'. As an aid to
visualization, but not an accurate representation, consider an ant crawling
around a huge beach ball and never coming to the end, it would consider
the beach ball as infinite as it has no boundaries. If you now consider
the ant as only a two dimensional creature and crawling round a three dimensional
beach ball, you could understand why the ant would consider the beach ball
to be infinite, the three dimensional picture, that shows how restricted
its movement really is, is simply not available to it. Thus with the universe,
from our perspective, restricted to our view from within the universe, it
appears to be infinite, but this is just an illusion, we are confined to
the limits of our universe and cannot escape from it. We are bounded within
a finite universe.
The next question that people naturally follow up with is to ask what
it is that our finite universe is expanding into. This is a good question
and one that can never be answered, we will never be able to escape the
confines of our universe to find out. We can only theorise about this, and
there are plenty of theories to choose from. I tend to think that we are
expanding into an infinite nothing, but for a fuller description check out
my page Where did the universe come
from? but the truth will never be known. Your guess is as good as mine,
So what is there within our universe that we can truly apply the term
infinity to? The universe itself is finite. Infinite mass, in black holes
for example, would only appear to be a mathematical description. The age
of the universe is finite, and even the number of particles in it is finite.
What do I think?
I think infinity exists only as a means of description, such as found
in mathematics for example, or any other thing that exists only in the abstract.
I do not believe that it has any real existence in the universe such as
infinite mass or infinite size. The word 'infinity' is a descriptive term
and not a measure of size, and I therefore do not see how it can be applied
to anything 'real', as real things can be measured.
I have come across web sites, and maybe you have also, that claim that
atoms can be subdivided down into infinity, and that they contain tiny universes
within them, and no doubt tiny people as well. Although science has not
yet been able to prove we have reached the ultimate elementary particle
from which all complexity is built, there is very strong theoretical
and experimental evidence to show that quarks could be it. Smaller than
quarks enters the realm of energy, not particles, as in string theory. As
matter has been subdivided down from complex objects, to parts of the whole,
to molecules, to atoms, to particles, to quarks, at each stage we see a
simpler model, each stage is less complex than the previous level. All of
which is in perfect agreement with the Big Bang model that describes how
all matter is built up from simple to more complex elements, stage by stage.
So when breaking down complex objects into smaller parts, it would come
as a bit of a surprise if suddenly an entire universe popped up at even
smaller scales than wave energy. Entire universes tend to be a bit complex!
However, if string theory is shown to be correct, then tiny loops, or
strings, of vibrating wave energy may be the smallest, but they are not
particles anyway, and strictly speaking quarks aren't either, as they can
not exist independently outside of a particle.
Stephen Hawking in his latest book "The Universe in a Nutshell"
(2001. page 176) describes the smallest possible size in our universe, termed
the Planck length after Max Planck, as being in the region of a millimeter
divided by a hundred thousand billion billion billion. If we were able to
probe to even smaller sizes, (which is not feasible as it would require
particles that reside in black holes) we would not find anything smaller,
we would, according to M-theory, see the other 6 or 7 dimensions of the
10 or 11 dimensions that go to make up our universe, only 4 of which are
currently observed by us.(3D + time). These extra dimensions of our universe
are curled up so small that we are unable to detect them, but the mathematics
of theoretical physics have long said they must exist as part of the fabric
of our universe. Please note that they are not 'other dimensions' with other
universes, merely the smallest possible unit of our universe.
I think we can quite safely rule out infinite smallness.
Some claim that our universe is but an atom of another 'mega-universe',
thus giving an infinite expansion in size. If our universe is finite (as
indeed it is believed to be) then anything at all may be postulated as to
what it may be that it exists in and is expanding into. You could for example
propose that our universe is indeed an atom of a 'mega-universe' but equally
you could propose that it as an atom of a mega-donkey's hind leg, but as
neither hypotheses is testable or falsifiable there is little point in proposing
them. That's why this argument regarding infinity is restricted to just
our known universe. However, although the idea that our universe may be
a single atom within a 'mega-universe' may have some appeal, it is rather
fanciful, and our universe bears absolutely no resemblance whatsoever to
the atoms that we observe, or indeed to the particles within those atoms.
Sorry, sounds fun but just doesn't match up with observation.
I do not believe that infinity exists in our universe.
Please take a moment to register your vote on the poll, and to make a
comment if you wish. Thank you.
Is infinity real?
Do you believe our known universe contains any 'real' infinities
other than those found in mathematics?
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