Completely Dense, Volume?
Name: Andrea P.
How can I answer a student who asks, "If something is
completely dense, does it have volume?"
I do not know of anything that is "completely" dense. Even "black holes"
have mass and volume -- very dense, Yes, but not "infinitely dense".
There are two answers I can think of:
1) If you squeeze anything as hard as we are capable of squeezing it-- or
as hard as we are likely to be able to squeeze it in the foreseeable
future--it will still have a measurable volume.
2) If you were to squeeze something to the point that it's the size of,
say, a fundamental particle, such as a proton or neutron, then the ideas
about matter that we are comfortable with from everyday experience stop
being good approximations to reality. Everyday ideas no longer describe
what we actually observe, where very small volumes are concerned. For
very small volumes, you have to use ideas from quantum mechanics.
In this case, density becomes a complicated topic, because nature seems to
(or perhaps actually does) impose constraints on the information we can
have about matter restricted to a very small volume. For example, if we
know the location of a particle well enough to say that it is in some very
small volume, then we can't at the same time know with good accuracy its
speed. (There is an equation that tells us how uncertain we must be about
a particle's speed, and the uncertainty gets larger when the volume within
which the particle is known to be gets smaller.)
But if we do not know its speed very well, we have to accept the
possibility that its speed is large enough that it will not remain
within that small volume for very long. As you squeeze down to an
infinitesimal volume, the speed uncertainty approaches infinity, so the
length of time for which that volume will actually contain the particle
In other words, volume, mass, energy, and time all have to be considered
at once--they are not as separable as our everyday experience would
(I am really glad you are the teacher and not me, because I would have a
lot of trouble getting this across to a kid.)
If the student understands that "density" is a measure of the compactness
of matter and is expressed mathematically as the ratio of matter's mass to
its volume ==> D = M/V, then it's appropriate to ask him/her what does
he/she mean by "completely dense?" Indeed infinite density happens when a
sample of matter has a volume of zero because d = m/0 and that (entirely
hypothetical) result is equal to infinity. However, if it has a mass and
its volume is zero, where did the sample go? Put another way, how might
one compress a sample of matter until its volume became zero? So,
squeezing a sample of matter to ever decreasing volumes will raise its
density. However, the density cannot become infinite so long as the sample
has any volume at all.
I would ask what he or she means by "completely dense?"
What the student may have in mind could be a state of matter in which the
spaces between electrons and nuclei are eliminated and the nuclei are as
closely packed as possible. In this case, there is a volume: neutrons and
protons have volumes too.
If we think of "dense" to mean a substance having high density -density
being mass divided by volume - then it goes without saying that volume has
to be finite for "dense" to have any meaning at all. So, in my mind, dense
implies the existence of a volume.
Hope this helps.
Ali Khounsary, Ph.D.
Argonne National Laboratory
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Update: June 2012