Name: B Hope
One of my 11th grade students is having a really tough
time with the concept of mass. Any suggestions? How can I go about
giving her the simplest of explanations and clear it up for her. She
thinks the definitions for Mass and matter are circular. Mass is the
amount of matter in something and matter is anything with mass....
Your student is very perceptive and is to be congratulated for recognizing
the circularity of the terms mass and matter, in most texts and references
the two definitions ARE CIRCULAR. Van Nostrand's Scientific Encyclopedia
defines "mass" as: " The physical measure of the principal inertial property
of a body, i.e., its resistance to change of motion." It continues: " Under
these circumstances [speeds small compared to the speed of light], the
masses M1 and M2 of two bodies may be compared by allowing the two bodies to
interact [whatever that means]. Then M1/M2 = |a1|/|a2| where |a1| and |a2|
are the magnitudes of the respective accelerations of the two bodies as a
result of the interaction." The two citations below are equally useless
[that is a value judgment on my part].
What is glossed over in physics is that there are certain terms in the
theory that cannot be defined within the system itself. "Matter" (or mass)
is one of these. As you see from above there are logical difficulties
because the definition introduces an undefined term "interact". Such
theories are called "effective theories" because we study the "effects" of
these undefined terms. Geometry provides an example. In plane geometry we
study the behavior of points and lines, but these terms are not defined
within the subject itself. They are the "undefined" terms whose relations to
one another is the subject matter of geometry. If we introduce the concept
of real number plane, we can define a point as an ordered pair of real
numbers (X,Y), which gets us out of trouble with the definition of "point"
only to introduce other undefined terms. For example what is the definition
of "number"? Similarly, within the context of real numbers "i", the square
of (-1), is undefined. This only becomes defined when the theory of complex
numbers is introduced.
In my opinion we must grasp that within any description of nature there are
going to be certain fundamental terms that are undefined within the system.
This is also related to Goedel's incompleteness theorem.
They really are not circular, but as you have indicated below, you can
use one to describe the other.
In our macro universe, and I am not going into quantum mechanics here,
Matter is a term used to describe a collection of molecules/atoms which
make up objects. We have either matter or energy (which of course are
interrelated). When we generally speak of matter, that matter has a
property called Mass. Mass is different then weight. Mass is a
constant that remains with that object and has some control over how
that object reacts in the universe.
Mass and matter are completely different concepts. Matter is anything
that can be touched -- that takes up space and is distinguishable from
empty space. Matter is just another word for "stuff". Mass is a
property of matter -- one of many properties, including color, shape,
Mass is the property of matter that defines what force a piece of
matter feels when it's in a gravitational field (i.e., near some other
thing that has mass), and how strong a gravitational field the piece of
matter generates. (Similarly, charge defines what force a piece of
matter feels from an electromagnetic field, and how strong an
electromagnetic field it generates.)
But mass also defines what an object does when any force acts on it.
Exactly the same property tells you two completely different things:
1) what gravitational force there is on a object, and
2) how that object responds to (is accelerated by) forces of any kind.
I don't think anybody understands why, and people have gone nuts
trying to measure any difference between (1) and (2).
B. Hope H.,
Mass is a measurement, a measure of how much matter there is. Volume is
also a measure of how much matter there is, but a different kind of measure.
An example is groceries. Some groceries have volume on the package. Some
groceries have how much mass. Both tell you how much material you are
Matter is a state of existence. Some things in the universe qualify as
matter. Some qualify as waves. When you get down to super-tiny scales,
i.e. quantum physics, matter and waves start to merge. Things begin to have
both matter and wave properties at the same time. On an everyday scale,
matter interacts according to Newtonian physics. Waves interact according
to different laws. Energy of matter is in the mass and speed. Energy of a
wave is in the frequency. Matter is made of particles (quarks and leptons).
Waves are not. A wave can be made of photons, e.g. microwaves. A wave can
be made of the motion of matter, e.g. sound.
Dr. Ken Mellendorf
Illinois Central College
Dear B Hope,
This is a common misconception that many students (and former students) have
trouble with -- mass and matter are different (but related) concepts, and
mass and weight are different (but related) concepts.
So, start with a definition of matter. Matter is anything that takes up
space (has volume) and has mass. So here are some examples of matter: rocks
(solid), water (liquid), air (gas), your desk, your arm, your shoe. Now
students seem convinced that everything (even the air!!) is matter. So,
what are some things that are NOT matter (things that do not take up space
and do not have mass)? Here are some "non-matter" things to get you
started: heat, light, an idea. These are things that are NOT matter.
Because of its definition, matter has four general properties, that is, four
quantities that can always be assigned to something that is matter: mass,
weight, volume, and density. Mass and weight are different, but related
quantities. An object's mass is a measure of its inertia -- the more mass
an object has, the more resistant it is to changes in motion. So a big rock
has more mass than a small rock. The big rock also weighs more than the
little rock in the earth's gravitational field. If you took both rocks way
into the universe, outside of any gravitational field, both rocks would not
have any weight -- but the big rock would still be more resistant to a
change in motion than the little rock -- that is, the big rock still has
more mass than the little rock, even though both rocks are "weightless".
In the metric system, weight and mass are designated with different units.
An object's weight is a measure of the force of gravity acting on the
object, measured in Newtons. An object's mass is a measure of its
resistance to inertia, measured in kilograms. Let us say that an object has
a weight of about 60 Newtons (about 13.5 pounds) on the earth. Its mass
would be about 6 kilograms. If you took that object to the surface of the
moon, where the gravitational is less, its weight would now be about 10
Newtons (about 2.25 pounds), but its mass is still 6 kilograms.
I hope this helps. The key point is that mass is a property of matter; by
definition, anything that is matter has mass and takes up space. The
property of mass is the object's resistance to changes in motion (its
inertia). The greater the quantity of matter, the more inertia (hence, more
mass) it has.
Todd Clark, Office of Science
U.S. Department of Energy
Matter can be held.
Mass is a measure of the amount of matter.
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Update: June 2012