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and the higher the speed, the more wrong we are.
Finally, and most interesting, ph?losophácallu tue are cormnpletclg trong with
the approximate law. Our entire picture of the world has to be altered even
though the mass changes only by a little bít. This is a very peculiar thing about
the philosophy, or the ideas, behind the laws. Even a very small efect sometimes
requires profound changes In our ideas.
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Now, what should we teach first? Should we teach the correc£ but unfamiliar
law with its strange and difficult conceptual ideas, for example the theory of
relativity, four-dimensional space-time, and so on? Ôr should we first teach the
simple “constant-mass” law, which is only approximate, but does not involve such
diffcult ideas? “The first is more exciting, more wonderful, and more fun, but
the second is easier to get at first, and is a first step to a real understanding of
the fñrst idea. This point arises again and again in teaching physics. At diferent
times we shall have to resolve 1% in diferent ways, but at each stage it is worth
learning what is now known, how accurate It is, how it fits into everything else,
and how it may be changed when we learn more.
Let us now proceed with our outline, or general map, of our understanding of
science today (in particular, physics, but also of other sciences on the periphery),
so that when we later concentrate on some particular point we will have some
idea. of the background, why that particular point is interesting, and how it fts
Into the big structure. So, what 7s our over-all picture of the world?
1-2 Matter is made of atoms
T, in some cataclysm, all of scientifie knowledge were to be destroyed, and
onÌy one sentence passed on to the next generations of creatures, what statement
would contain the most information in the fewest words? I believe i% is the
atomäc hụpothesis (or the atomic ƒfact, or whatever you wish to call it) that ail
thứngs are mmade oƒ atormns—lifle particles that moue around ?ín perpetual motion,
ttracting cach other t”hen theU are a litie distance apart, Du repelling tupon
being squeczcd ¡no one another. In that one sentence, you wilÏ see, there is an
€norrmmous amount of information about the world, 1 Just a little imagination and
thinking are applied.
To illustrate the power of the atomic idea, suppose that we have a drop
of water a quarter of an ¡inch on the side. If we look at it very closely we see
nothing but water—smooth, continuous water. Even iŸ we magnify it with the
best optical microscope available—roughly ©wo thousand times—then the water
drop will be roughly forty feet across, about as big as a large room, and if we
looked rather closely, we would s#ji see relatively smooth water——but here and
there small football-shaped things swimming back and forth. Very interesting.
These are paramecia. You may stop at this point and get so curious about the
paramecia with their wiggling cilia and twisting bodies that you go no further,
except perhaps to magnify the paramecia still more and see inside. 'This, of
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WATER MAGNIFIED ONE BILLION TIMES
Figure 1-1
course, is a subject for biology, but for the present we pass on and look still
more closely at the water material itself, magnifying it two thousand times again.
Now the drop of water extends about fñfteen miles across, and if we look very
closely at i we see a kind of teeming, something which no longer has a smooth
appearance——it looks something like a crowd at a football game as seen from a
very great distance. In order to see what this teeming is about, we will magnify
it another two hundred and ffty times and we will see something similar to what
is shown in Fig. I-I. This is a picbure of water magnified a billion times, but
1dealized in several ways. In the first place, the particles are drawn in a simple
manner with sharp edges, which is inaccurate. Secondly, for simplicity, they are
sketched almost schematically in a ©wo-dimensional arrangement, but oŸ course
they are moving around in three dimensions. Notice that there are two kinds of
“blobs” or circles to represent the aboms of oxygen (black) and hydrogen (white),
and that each oxygen has two hydrogens tied to it. (Each little group oŸ an
oxygen with its two hydrogens is called a molecule.) The picture is idealized
further in that the real particles in nature are continually jiggling and bouncing,
turning and twisting around one another. You will have to imagine this as a
dynamic rather than a static picture. Another thing that cannot be illustrated in
a drawing is the fact that the particles are “stuck together”—that they attract
cach other, this one pulled by that one, etc. The whole group is “glued together,”
so to speak. Ôn the other hand, the particles do not squeeze through each other.
T you try to squeeze two of them too close together, they repel.
The atoms are 1 or 2 x 10” em in radius. NÑow 10~Š em is called an angstrom
(just as another name), so we say they are 1 or 2 angstroms (Ä) in radius. Another
way to remember theïr size is this: if an apple is magnified to the size of the earth,
then the atoms in the apple are approximately the size of the original apple.
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Now imagine this great drop of water with all of these jiggling particles stuck
together and tagging along with each other. 'Phe water keeps its volume; it does
not fall apart, because of the attraction of the molecules for each other. Tf the
drop is on a sÌope, where it can move from one place to another, the water will
fow, but it does not just disappear—things do not just ñy apart——because of the
molecular attraction. Now the jiggling motion is what we represent as heaf#: when
we increase the temperature, we increase the motion. lf we heat the water, the
Jiggling increases and the volume between the atoms increases, and if the heating
continues there comes a time when the pull bebween the molecules is not enough
to hold them together and they đo ñy apart and become separated from one
another. OŸ course, this is how we manufacture steam out of water——by increasing
the temperature; the particles ñy apart because of the increased motion.
STEAM
Figure 1-2
In Eig. I-2 we have a picture of steam. 'Phis picture of steam fails in one
respect: at ordinary atmospheric pressure there certainly would not be as many
as three water molecules in this fgure. Most squares this size would contain
none—but we accidentally have two and a half or three in the picture (just
so it would not be completely blank). Now in the case of sieam we see the
characteristic molecules more clearly than in the case of water. For simplicity, the
molecules are drawn so that there is a 120° angle between the hydrogen atoms. In
actual fact the angle is 1053”, and the distance between the center of a hydrogen
and the center of the oxygen is 0.957 Ä, so we know this molecule very well.