The g Factor of the Electron

Author(s): H. R. Crane
Source: Scientific American , Vol. 218, No. 1 (January 1968), pp. 72-85
Published by: Scientific American, a division of Nature America, Inc.
Stable URL: https://www.jstor.org/stable/10.2307/24925943

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide
range of content in a trusted digital archive. We use information technology and tools to increase productivity and
facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at
https://about.jstor.org/terms

Scientific American, a division of Nature America, Inc. is collaborating with JSTOR to digitize,
preserve and extend access to Scientific American

This content downloaded from

117.200.56.226 on Mon, 18 Jan 2021 11:04:45 UTC
All use subject to https://about.jstor.org/terms
 The g Factor of the Electron

It lS the inde�(; of the ratio of the electron's magnetic moment

to its spin angular InOlnentum. An interesting number in its own

right, its precise Ineasurement has had far-reaching implications

- by H. R. Crane

hen my colleagues and I at the net or a compass needle is simply its its angular momentum of rotation. (The

W University of Michigan started

our experiments on the
of the electron in
g factor
1950, we had no idea
strength. The direction of the m agnetic
moment is along the line connecting the
two poles.) The earth almost conform s
angular momentum of an object is its
"amount" of rotation. For a wheel it
would depend on the speed of rotation,
we would still be at it 17 years later. But to this description, and it would con­ the m ass of the wheel and the way the
now the sixth in a succession of Ph.D. form exactly if its north and south m ag­ mass is distributed in the wheel.)
studen ts is beginning his work. It has netic poles were not slightly out of line Although the external m agnetic field
been a leisurely, drawn-out affair. vVe with respect to its north and south geo­ is at the disposal of the experimenter and
seem to have been allowed to occupy a graphic poles. can be m ade to have any desired
little corner of physics pretty m uch by If a spinning object with these prop­ strength, the ratio I have just mentioned
ourselves-a privilege generally reserved elties is placed in an external magnetic (magnetic moment to angular momen­
to those who work on projects that are field (a field other than the one due to tum ) is a property of the spinn ing object
regarded as too hard, too tedious or of the object's own magnetic m oment), it itself. This ratio has a unique value for
too little importance to be worthwhile will "precess" like a spinning top or a the electron and is quite the same for
game for competition. When we think gyroscope, that is, its axis of rotation will every electron in the universe. O ther
that the results of more than 50 m an­ slowly move around in a cone. The fre­ kinds of particles (for example the pro­
years of our labor and half a m illion dol­ quency of the precession will depend on ton) have their own unique ratios. Since
lars could probably be written in the the product of two factors : the strength only the ratios for the various particles,
margin of a postage stamp, it is not sur­ of the external magnetic field and the and not the separate values of the angu­
prising that most people have been glad ratio of the object's magnetic moment to lar momentum and magnetic moment,
to see that kind of work done by some­
one else. The accidents that got us start­
ed, the shifts we had to m ake in our at­
tack at several points along the road and
the way everything worked out not as
we had planned but m uch better than
we had planned makes an interesting
case history.
I shall include in this account as m any
of the uncertainties and human errors
that beset us as I can recall. I could in­
stead make it sound as if we knew ex­
actly what we wanted to do at all tim e s ,
b u t I shall save m y talents along these
I
lines for the writing of applications for
� FIRST GOLD fOil

L
funds or articles for physics journals. It
seems to me that science is more interest­
ing the way it is actually done, and that
is the side of our adventures I want to
show here. � TO VACUUM PUMP

T he
- be
g factor is a number that might
apphed to any spinning object
ORIGINAL APPARATUS built by the author and his colleagues at the University of Mich.
igan was designed to study the polarization, or degree of parallel alignment, of the spin axes
with a magnetic m oment parallel to its
of the electrons in a high-energy electron beam by means of the double-scattering technique
axis of rotation. (In everyday languag e
(see illustration on /loge 74). To avoid the possibility that X rays and electrical distur­
the magne tic m om ent of, say, a bar m ag-
bance produced by the electron source would interfere with the counting of the electrons,

72

© 1967 SCIENTIFIC AMERICAN, INC

This content downloaded from

117.200.56.226 on Mon, 18 Jan 2021 11:04:45 UTC
All use subject to https://about.jstor.org/terms
 are needed for in terpreting m any phe­ loop of wire. Such a loop of current gives splitting of the lines in the spectra. In
nomena, the measurement of the ratios rise to a m agnetic moment-a north and fitting the values of the electron's angu­
to a high accuracy has been the object of south pole if you like. Accordingly it lar momentum and m agnetic moment to
intensive research. The g factor of a par­ would have been reasonable to have ex­ conform to the experiments on the anom­
ticle is the index of that ratio. pected an external m agnetic field to have alous Zeeman effect, Goudsmit and
So far I have indicated why the g a modifying effect on the e lectron or­ Dhlenbeck found a strikin gly simple re­
factors of particles are interesting num­ bits. What could not be understood at all lation. The electron's intrinsic an gular
bers , but I have given no hint as to why on the basis of the Bohr model was that momen tum had to be exactly half the
the g factor of the electron in particular in the presence of a m agnetic field sin gle angular momentum of the orbital mo­
has been the yeast in more than one lines were split into two or more distinct tion of an e lectron in its lowest Bohr or­
significant revolution in physics. For that lines. bit in the hydrogen atom , or h/2, where
part of the story I must go back more h is short for Planck's constant (/7) di­
vided by 2". The intrin sic m agnetic
I
than 50 years and begin with Niels t was this puzzle that led two young
Bohr's original model of the hydrogen Dutch physicists, Sam ue l A. Goud­ moment had to be equal to that pro­
atom. smit and George E. Dhlenbeck, to postu­ duced by the orbital circulation of an
Following the spectacular success of late in 1925 that the electron itself had electron in its lowest orbit in the hydro­
Bohr's model in accountin g for the lines an angular momentum and a m agnetic gen atom . The latter quantity, called the
in the hydrogen spectrum , it became moment. In a recent speech before the Bohr magneton, is etl/2mc, where e and
apparent that the spectra of atoms of American Physical Society, Goudsmit m are the charge and m ass of the elec­
higher atom ic n umber had com plexities recalled that it was he who had arrived tron and c is the velocity of light [see il­
that would require for their explan ation at the conclusion that an additional lustmtion on page 79] .
more descriptive factors (called quan­ quantum number, necessary to give the Thus at the time of the discovery of
tum n um bers) than were contained in added complexity in the spectra, prob­ electron spin the g factor of the elec­
the original model. This was strikin gly ably was to be associated with the elec­ tron could be expressed as the number
shown by the "anomalous Zeem an ef­ tron, whereas it was Dhlen beck who had of "natural units" of m agnetic moment
fect" in the alkali atoms (such as the seen that the new property would have (etl/2mc) divided by the number of "nat­
atoms of lithium an d sodium ) . The to be of the nature of an intrin sic angular ural units" of an gular momentum (fl).
Dutch physicist Pieter Zeeman had momentum. Thus was born the concept ""hen defined in this way, the g factor
shown that when atom s were subjected of electron spin. for the orbital motion of the electron in
to a m agnetic field while radiating light, That the electron should have in ad­ its lowest energy s tate in hydrogen is 1,
the norm al lines were split into m ultiple dition an intrin sic m agn etic moment was whereas the g factor of the free electron
lines that lay close together but re­ part an d parcel of the idea that it was is 2. (The g factor as a term design atin g
main ed sharp an d distinct. If the mag­ spinning. Any charged, rotating body a ratio of m agnetic moment to angular
netic field had merely shifted the wave­ would, by the simple concept of a cir­ momen tum in these special units had
lengths of the lines a little one way or the culating current, be expected to have a been introduced a few years earlier for
other, that would not have been surpris­ magnetic moment. It was a daring hy­ the case of the atom by the German
ing. After all, the electron circulating in pothesis , by no means immediately ac­ physicist Alfred Lande.)
its orbit around the atomic n ucleus is cepted. The spin gave the additional There being no reason s to the con ­
equivalen t to a current Rowing around a quantum number required to explain the trary, the relations given above were

COUNT

ER

l- £- T-U-f-£--!:--!:-f-f-i-i-i-f-f --f- l��W�'f�-f-=E-st

the site of the second scattering was located in the next roon1 at a
distance of about 30 feet. When the first tests were made, however,
l�f}l!rfli ��£ ! R
O

l COU ER 2

tablish a magnetic field in the pipe parallel to its axis; tbis focuses
the electrons and also causes their axes of spin to precess slowly_
too few electrons arrived at the second scatterer, because the beam When the use of a magnetic field was first considered, it became ap­
tended to fan out in the 30-foot pipe. A layer of current-carrying parent that by measuring the amount by which the spin axes pre­
wire was therefore added to the outside of the pipe in ordel- to es- cessed it might be possible to determine the electron's g factor.

73

© 1967 SCIENTIFIC AMERICAN, INC

This content downloaded from

117.200.56.226 on Mon, 18 Jan 2021 11:04:45 UTC
All use subject to https://about.jstor.org/terms
 .0
•
•
•
•

• • • •
•
• • • • • •
• •
• • •
• • •
.f---------� •
• • • •
• •
• • •
• •
• •• •• • •• • • • • •• • • •
:
• • • • • . . • • •
•• • • •• • • .. . . . .
•• • • . . . •
•• • • • • ••• •• • •
t.·
••
.. :
•
·. . . .
• • ••••• •
.
. •
•
•
• • ••• •• •
•
• •
• •• • • • • •
• •
• • • • •
.
. . '-------....: � • • • • •
• •
• • • • •
•
•
• • •
• • •
•
•
• •
•
• • • •
• •
• •
•
�-----
--- --�.
•
. ..... ......
- ----'

DOUBLE·SCATTERING TECHNIQUE is at the root of the g. in part on whether its north pole is pointing up or down. This ef.
factor experiments. In order to polarize a beam of electrons whose feet is not yet observable, however, since the equal division of the
axes of spin point randomly in all directions, all one needs is a beam could be due to pure chance. It takes a repetition of the scat·
sorting mechanism, so that one can keep the ones that are pointing tering process to bring out the result of the sorting in an observable
in a particular direction and discard the rest. To get an ohservable way. A 100 percent inequality after the second sorting is shown at
effect, however, one must do the sorting twice. At the first sorter left for clarity; in actuality the inequality of the beams is at hest
equal numbers will be deflected to the right and to the left: Actually only about 6 percent. If the two sortings were due only to chance,
the direction in which a particular electron is deflected depends the beams after the second sorting would still be equal (right).

taken to be exact, and they stood un­ cists call the "vacuum." If it seems voting the entire article to it, to trace
questioned for about 20 years. In phys­ strange to say that empty space could this development in any detail. There
ics there are good reasons for assum in g have an effect on the electron, it is be· are, however, some com m ents I should
that sim ple relations are exact until it is cause one ten ds to think of empty space like to m ake. The term "new quantum
. proved otherwise. There are m any of in the ordinary sense of its being devoid electrodynamics" does not imply that the
them that do hold, and this is one of the of gross objects such as gas m olecules. In existing theory was junked in favor of
reasons why some people find beauty in the context of the subatomic world, how· the new theory. The new theory was
the subject. In the case of the g factor ever, empty space is by no means devoid rather an extension of the existing theo­
of the electron, a stron g reinforcement of properties. There can be the creation ry, which had stopped short of including
for the belief in the exactness of the and annihilation of electron pairs and the interaction of the particles with the
value 2 cam e in the late 1920's from the other kinds of particle pairs, local fluc· vacuum. Theorists had been trying to
new form ulation of quantum mechanics tuations of electric and magnetic fields, include it, but the form ulas came out
by P. A. M. Dirac. In his form ulation and of course the propagation of radiant containing infin ite terms, which could
Dirac did not "put in" a g factor of 2 as energy. When in the pew quantum elec­ not be got rid of by the accepted theo­
a requirement of a model of the electron. trodynam ics the effect of empty space retical methods, and so the m atter had
He applied the basic laws of physics (in· on the electron was properly accounted hung in the limbo of speculation. But
cluding relativity) according to a simple for, the result was an increase in the g when experimental results suddenly be­
set of conditions, and the g factor of factor to slightly more than 2. In itself gan appearing that did n ot agree with
exactly 2 "cam e out." After World "Var the change in the g factor does not sound the existing theory and that gave actual
II, however, this situation began to very startling. But the whole develop­ numbers against which attem pted solu­
change. ment was a profound one, as attested by tions could be tested, progress became
In the first few years after the war the fact that five of the people m ost quite rapid. A way that had been pro­
some striking experimental and theOl'eti­ closely involved were awarded Nobel posed earlier for circumventing the in­
cal developments occurred that led to prizes: Willis Lamb and Polykarp Kusch finities proved itself by giving answers
what is now called the new quantum in 1955 (for experimental work) , and that were consisten t with the experi­
electrodynamics. A cen tral part of this Julian Schwinger, Richard Feynman and ments. The m ethods were stil l not un­
work involved taking into account the Sin·Itiro Tomonaga in 1965 (for theOl'eti­ questioned; for example, as Dirac later
interaction of the electron with the emp­ cal work) . rem arked in Scientific American (May,
ty space around it, or with what physi- It would be impossible, without de- 1963 ) , he could not help looking on the

74

© 1967 SCIENTIFIC AMERICAN, INC

This content downloaded from

117.200.56.226 on Mon, 18 Jan 2021 11:04:45 UTC
All use subject to https://about.jstor.org/terms
 HOW CREATIVE PROFESSIONALS USE GENERAL ELECTRI C TIME-SHARING SERVICE

•• General Electric
Time-Sharing Service
saves students' time...
it equips them to work with a
computer throughout all levels
of problem definition ��
DR. OTTO ZMESKAL • Dean - College of Engineering, The University of Toledo

Today's students - like the creative professionals in business and industry they will soon be
joining - are working smarter. They are using General Electric's nationwide Computer
Time-Sharing Service.

The students describe their problems to the computer using regular teletypewriters in their classrooms. � Information
Although many students are typing in problems at the same time, the computer answers each '\WSystems
one immediately giving each student the feeling he has exclusive control. This dialog between the
computer and the student quickly teaches him how to put the computer's speed, Time-Sharing
Service
accuracy, and logic to work.

Ask for the full story today. Information Service Department, General Electric Company,
7735 Old Georgetown Road, Bethesda, Md. 20014. 291-25

GENERAL fj ELECTRIC
© 1967 SCIENTIFIC AMERICAN, INC

This content downloaded from

117.200.56.226 on Mon, 18 Jan 2021 11:04:45 UTC
All use subject to https://about.jstor.org/terms
 © 1967 SCIENTIFIC AMERICAN, INC

This content downloaded from

117.200.56.226 on Mon, 18 Jan 2021 11:04:45 UTC
All use subject to https://about.jstor.org/terms
 "Polaroid" and "Polacolor"®

Salsma" 0" Salsma"

on 'Polaroid Land �ilm
O'Keeffe. Not as symbol, blatant, you can do strong
not as painter, but as a subjects. T he Dutch
person of great wisdom painters of the Rembrandt
and beauty. era did it all the time.
To do that, to show To me, Polaroid film has
people as they are, I that kind of color. As you
believe one has to reduce can see.
form to its simplest. And, of course, it didn't
Almost to the point of take long to know that
abstraction. Georgia O'Keeffe and
Polaroid Corporation
That's easier said than Polacolor film were made
asked Philippe Halsman for each other.
done, of course. It took a
to photograph any subject
two-hour session to get the Best of all, I could see
he wished, black and white
simplicity I wanted. Even the finished photograph.
or color, and tell about his
using Polaroid Land film. Otherwise the session
experIence.
But Polaroid film did might have continued well
"I first photographed much more than save time. beyond two hours.
Georgia O'Keeffe 18 years It also helped me make a You see, there are some
ago for Life magazine. very difficult decision: things one can't be sure of
We were doing a story black and white or color. until after the film is
on the American South­ You see, when you first processed. Like tiny
west and of course she had look at Georgia O'Keeffe, changes in expression or
become a symbol of the you want to photograph mood.
region. So I photographed her in black and white. But with Polaroid film,
her as a symbol, against a Color often gets in the way I was sure in a minute.
brown adobe wall with the with a powerful person­ Which leads me to the
bleached skull of a steer in ality like hers. conclusion that Polaroid
the background. On the other hand, if film may be the salvation
But this time, I wanted you have the right kind of of photographers who
to photograph Georgia color, subtle rather than don't know when to stop."

© 1967 SCIENTIFIC AMERICAN, INC

This content downloaded from

117.200.56.226 on Mon, 18 Jan 2021 11:04:45 UTC
All use subject to https://about.jstor.org/terms
 Porsche spent years
developing a great competition car ...
so you could have fun driving to work.

The Porsche is a tractable racing car­ four wheels permanently grounded, from cooled engine stays in tune. Doesn't over­
honor graduate of the most unforgiving one edge of the tread to the other. heat. Even if you let it idle for hours.
obedience courses in the world: leMans, Porsches lose little time in the pits Porsche's famous gearbox, synchronized
Targa Florio, Sebring, Nurburgring. That's at Sebring, seldom need to go to the shop in all forward speeds, gives you flawless
why it's such fun to drive, on any road. when they're at home. This car is a thor­ translation of rpm's into mph.
Unpaved back-country washboards. Com­ oughbred with the stamina of a work When you buy a Porsche, you've got
muter-clogged expressways. Stop-and-go horse. No temperament at all. a self-protecting investment. It uses gas
streets. Wide open highways. It's ready to go whenever you are. the way a miser spends money. It doesn't
Take the wheel. It won't fight you. And it stops the instant you apply the drop hundreds of dollars in market value
Porsche's rack-and-pinion steering gives brakes. Fade - proof, self - adjusting disc the instant you buy it. Or thousands of
you reflex-fast control, without kick-back brakes on all four wheels are standard dollars as the anniversaries roll by.
from the road. The suspension keeps all equipment in every Porsche. The air- And it's incredibly comfortable. Hour
after hour after hour. Its seat and back are
#' fully adjustable to support yours. Bad
roads share their troubles with the sus­
pension, not with you. The car's solid,
monocoque construction makes driving
rattle-fr.ee. Secureo
Want to road-test racing's toughest
competition car? You'll find it at your
nearest Porsche dealer's.

�� �
POE. For information. overseas delivery:
Parse he of America Corporation.
107 Tryon Ave. West, Teaneck, N.J. 07666.
""

© 1967 SCIENTIFIC AMERICAN, INC

This content downloaded from

117.200.56.226 on Mon, 18 Jan 2021 11:04:45 UTC
All use subject to https://about.jstor.org/terms
solution of the problem of the infinities
as a "fluke." I suppose he m eant that a
ORBITAL ELECTRON FREE ELECTRON
method that evidently worked in a par­
ticular application should still be held ANGULAR MOMENTUM 1/2 h

l
questionable as to its generality.
This, then, is where things stood in eh eh
MAGNETIC MOMENT
1950, when we embarked on our g-factor 2mc
I 2mc

I
measurements. There had been a shake­
MAGNETIC MOMENT e
up. The new theory gave a g factor of
the electron about .1 percent larger than
ANGULAR MOMENTUM 2�C mc

2, an d there were experimen tal results

that were in agreement, within modest
limits of accuracy. Because the new
theory was based on unconventional
9 FACTOR
;------1
g FACTOR OF THE ELECTRON was defined at the time of the discovery of electron spin
2

methods, its acceptance rested on a

(1925) as the number of "natural units" of magnetic moment ( eft/2mc) divided by the
pragmatic basis. A measurement of the number of "natural units" of angular momentum (ft). When defined in this way, the g factor
g factor to a much greater precision for the orbital motion of the electron in its lowest energy state in hydrogen is 1, whereas the
would be m ore than just a routine veri­ g factor of the free electron is 2. These relations were taken to be exact for about 20 years.
fication; it would be one of the critical
tests of the new theory. If at that pOin t
we had taken up our experimen ts in an­ gether an d came up with a thesis prob­ road will all turn to the left. In the lan­
swer to this clarion call, the story would lem for Louisell. guage of electron scatterin g, the first
read as a story is supposed to read. That At this point I should like to elaborate fork is the polarizer and the second the
is not the way we got into it at all. vVe a bit on double scattering, a technique analyzer. Not until after the motorcycles
backed into it. Here is what really hap­ that in addition to being basic to our have passed the analyzer does the ob­
pen ed. own experiments has a broad application server have visible evidence that sorting
in physics. Electrons that are emitted has been accomplished [see illustration
e had begun in 1946 a project of de-
W signing
from a hot filament have their axes of on page 74].
and building one of the spin pointing randomly in all directions. An electron doesn't carry a card, but
largest electron accelerators of that time, If some of these electron s are accelerated it may have its n orth pole up or i t m a y
which we called the "racetrack" syn­ and form ed in to a beam , the beam is said have it down, and t h a t makes i t belong
chrotron. The project presented a series to be un polarized. In order to polarize to one class or the other. If one shoots a
of problem s that had to be worked out the beam it is not necessary to turn the beam of electrons through a thin piece
as we went along. Meanwhile graduate electrons so that their north poles all of material, say a gold foil, m any elec­
students were working on the project point in the same direction ; in fact, we trons will be deflected to the right and
who did not have forever to wait for know no way of doing that. If there are to the left. The two classes (north pole
the synchrotron to operate in order to plenty of electrons to spare, all one needs up and north pole down) will have been
do their thesis problems and get their is a sortin g mechanism, so that one can sorted as were the m o torcycles at the
Ph.D.'s. One of these studen ts was vVil­ keep the ones that are pointing in a par­ first fork of the road, but the fact will not
liam H. Louisell, who has since joined ticular direction and get rid of the rest. yet be observable. It will take a repeti­
the faculty of the Un iversity of Southern vVe do know how to make a sorter. Cu­ tion of the scattering process, performed
California. Robert '''1. Pidd (now at Gulf riously enough, in order to have an ob­ on either the right or the left beam, to
General Atomic Inc.), one of several pro­ servable effect it is necessary to do the bring out the result of the sortin g in an
fessors associated with the synchrotron sorting twice. Hence the term double observable way. When the electrons pass
project, was chairman of Louisell's doc­ scatterin g. through the second gold foil and are
toral committee, and I was a member. I shall use a sim ple analogy to show scattered-this time unequally between
We decided to try to define a thesis why two sorters are necessary. Suppose right and left-under the best con ditions
problem that would use not the en tire we make 1, 000 small cards, of which 5 00 the inequality is only about 6 percen t.
synchrotron but just the parts that were say "Always take the right turn" and The sorting is by no means as perfect as
finished at that time. One part that was 5 00 say "Always take the left turn." We it was in the example of the m o torcy­
finished was the "electron gun," a high­ shuffle the cards and give one to each clists, but it is good enough to m ake an
voltage vacuum tube that could produce of 1, 000 motorcycle riders, who have experiment possible.
an intense beam of electrons at energies agreed to cooperate. Each reads his card
and puts i t in his pocket, and they all
T electrons was put forward by N. F.
of up to 600,000 electron volts. Its pur­ he theory of the double scatterin g of
pose was to inject the electron s into the start down a road. After the first fork in
synchrotron, where they were to be fur­ the road, does an outside observer see Mott in 1929, and the process goes by
ther accelerated up to 300 million elec­ any effect traceable to the cards? No. He his name. Surprisingly, about six years
tron volts. Before becoming involved in sees only that 5 00 motorcycles have tak­ passed before anyone s ucceeded in pro­
building the synchrotron, both Pidd and en each road at the first fork, which ducin g the effect experimen tally, and
I had had an interest in polarization could be due to pure chance. The ob­ even in 1950, when Louisell undertook
effects in electron beams, as studied server must wait until the second fork to to s tudy the effect, little had been found
through double-scatterin g experiments. see the effect. The effect is then dra­ out about it in a quantitative way. That
''''e thought that the electron gun of the m atic. Those traveling on the road that is why the double-scatterin g of electron s
synchrotron would be an ideal tool for wen t to the right at the first fork will now looked like a good thesis problem .
such experiments. Accordingly we put all take the right-hand road at the sec­ The synchrotron injector that was to
our interests and our available tools to- ond fork. Sim ilarly, those on the other be used for the electron source was in

79

© 1967 SCIENTIFIC AMERICAN, INC

This content downloaded from

117.200.56.226 on Mon, 18 Jan 2021 11:04:45 UTC
All use subject to https://about.jstor.org/terms
a b

AXIS OF
PRECESSION

I
-8
---7

AXIS OF :SPIN
MODEL OF A SPINNING ELECTRON, consisting of a piece of eter ratio of the cork. Such a model behaves as a gyroscope. If one
wine·bottle cork with a toothpick stuck through it and some nega· gently pushes the top of the toothpick sideways (b), it will refuse
tive electric charge on the cylindrical surface, turns out to have a g to go that way but will go in a direction at right angles to the direc·
factor of 2. The amount of charge and the mass of the cork must be tion of the force. If the model is spinning in open space and op·
in the same ratio as the charge and mass of an electron. When posite forces are applied to the ends of the toothpick from the left
the model is spinning (0), the ratio of its magnetic moment to an· and the right (c), one end will come forward and the other end will
gular momentum is elmc, which is a g factor of 2, regardless of the go backward. It is this turning of the spin axis that is termed pre·
speed of spinning, and regardless of the size or the length.to·diam. cession. Now, if the model is placed in a magnetic field (d), the

the main syn chrotron room. YVhen the to cause their axes of spin to precess of charge and the m ass of the cork must
injector was running, it produced a high slowly, just as the axis of a toy top pre­ be i n the same ratio as the charge and
level of X rays an d electrical distur­ cesses while it is spinning on the pave­ mass of an electron. Now, when the cork
ban ce, and we knew this would interfere ment. The orientation of the axis of spin is spun on the toothpick as an axle , the
with the detectin g and countin g of the would be altered before the electro n s ar­ charge, m oving aroun d in a circle, acts
electrons after the seco n d scatterin g rived at the second foil. It was clear that as a loop of curre n t and gives the m o del
process. We therefore elected to locate if such a precession did occur, and if we a m agnetic momen t. In addition the ro­
the site of the second scattering some could measure the chan ge in the direc­ tatin g cork has angular momentum. The
distance away, in fact in the next room tion of the spin axis , we would have a ratio of the m agnetic momen t to the
at a distance of about 30 feet. We pro­ way of determining the value of the an gular momentum of this model is
vided an evacuated pipe for the elec­ magnetic moment-a much more inter­ eline, which is a g factor of 2, regardless
trons to travel through
[ see illustration esting pursuit than the one we had orig­ of the speed of spinning, and regardless
on pages 72 and 73]. We were perhaps inally started with. But would electrons of the size or the len gth-to-diam e ter ra­
unduly attracted to this scheme because really behave that way? Mechanical tio of the cork! (It might appear that a
the wall separatin g the rooms was m ade m odels are powerful tools for thinkin g still simpler m odel would be a cork ball,
of concrete three feet thick and it already (some of us-I for on e-would be lost but that would not have a g factor of 2.)
had a porthole in the right place. The withou t them ); however, on e has to be The m odel behaves as a gyroscope. If
arran geme n t seemed ideal. vVhen the exceedin gly cautious in using them in one sets it spin ning vertically and gently
vacuum pipe was in place and the first the realm of the very small, where quan­ pushes the top of the toothpick sideways,
tests were m ade, however, we found that tum effects become overriding, to m ake it will refuse to go that way but will go
far too few electrons arrived at the sec­ sure at every turn that one is not askin g in a direction at right an gles to the di­
ond foil, simply because the electron the model to perform in ways that are rection of the force. If the m odel is spin­
beam tended to fan out in the 30 feet in conflict with quan tum principles. It ning in open space and opposite forces
between the targets. was at this pOint that our theorist col­ are applied to the ends of the toothpick
A stan dard method of focusin g the leagues began flashing yellow caution from the left and the right, one end of
e lectron s from one e n d of a pipe to the lights at us-with good reason. the toothpick will come forward an d the
other is to establish a m agnetic field in other end will go backward; the model
the pipe parallel to its axis. All that is will keep turni n g i n this way, m aking
A
mechan ical mode l of the spinning
required is a layer of wire on the outside electron -even though suspect-has several complete revolutions. It is this
of the pipe with current in it. I suggested some in triguin g properties, which I turning of the axis (in contrast to the ro­
this was a way of conserving our elec­ should like to describe here. A model of tation of the cork) that is termed preces­
tron s , but immediately caught m yself the spinning electron made in about the sion. The tips of the toothpick never do
an d asked: "YVhat would the m agnetic simplest possible way turns out to have move i n the directions in which they are
.
field do to the polarization ?" (The elec­ the g factor given by the Dirac equatio n , being pushed.
trons traveling down the pipe were pre­ namely 2. Take any s o l i d r i g h t circular Now, if the spinning-magnet m o de l is
sum ably polarized as a result of the sort­ cylinder, such as a wine-bottle cork, and placed in a magnetic field, the north
ing by the first gold fOil.) It did not take s tick a toothpick through its ends [see pole will be pulled one way along the
us long to decide that if the electron s be­ illustration above]. Then put some nega­ field lines and the south pole the other
haved like spin ning m agnets, the effect tive electric charge on the cylinder's sur­ way. The axis of spin will turn in the
of the magneti c field on them would be face but J)one on the ends. The amount manner of the gyroscope, a n d the n um-

80

© 1967 SCIENTIFIC AMERICAN, INC

This content downloaded from

117.200.56.226 on Mon, 18 Jan 2021 11:04:45 UTC
All use subject to https://about.jstor.org/terms
 The doubts that our experiment iment that in fact did not require the si­
would work were prompted by some ar­ multaneous knowledge of the position
guments that had been put forward by an d linear momentum of the particle be­
Bohr in a lecture in the 1920's. At the yond the limits prescribed by the uncer­
time only two experiments by which one tainty principle, it was this old belief
might attempt to observe the m a gnetic that no experim ent whatever could work
moment of the free electron had been that we encountered head on.
imagined. One was to detect the mag­ I can recount an in cident that is amus­
netic field of the elech'on directly, by ing in retrospect to s how the firm ness of
means of a sensitive m agnetometer; the the conviction that experiments on the
other was to sort electrons as to the or­ magnetic moment were not possible . A t
ien tation s of their m agnetic moments by t h e meeting of the American Physical
sendi n g a beam of them through a non­ Society in Washington in April, 1953,
un iform m agnetic field. Bohr had de­ Louisell presented his first successful
molished both schemes by subjecting measurement, and two theorists in our
them to the test of the Heisenberg un­ department, Kenneth Case and Harold
s
certainty principle, which states that Mendlowitz, presented proof that the
north pole wiII be pulled one way along the there is a n atural lim itation on the pre­ concept of the experiment was in har­
field lines and the south pole the other way. cision with which the position and the mony with quantum mechanics . Yet the
The axis of spin will turn in the manner of
linear momen tum of a particle can be evidence was not persuasive to several
the gyroscope, and the number of complete
known simultaneously . Bo th schemes, if physicists in the audience, who rose to
turns it will make per second will be propor·
they were to work, would require mea­ cite the Bohr proofs to us. The person
tional to the g factor and the strength of
suri n g these quan tities to greater than who voiced the strongest objection said
the applied field. In the original apparatus
there w ere about five full turns in 30 feet. the possible precision . later that when he was halfway home
Bohr's calculations were back-of-the­ on the airplane he satisfied him self that
envelope type: sim ple and unequivocal. there was no conflict between our exper­
ber of complete turns it will m ake per The mistake was made not by Bohr in his imen t and what Bohr had shown!
second will be proportional to the g fac­ proofs but in the sweepin g generaliza­
tion that was subsequen tly m a de of them
B
tor and to the strength of the applied y the time Louisell had his experi-
magnetic field. In Louisell's apparatus by others. It was, in effect, that no ex­ ment under way we realized that
there would be about five full turns of periment to m easure the m a gnetic mo­ the n um ber of revolutions of the preces­
the spin axis while the electrons were ment of the free electron directly could sion that would occur in his 30-foot pipe
going the 30 feet down the pipe . He succeed, by reason of the uncertainty would be far too few. There would be
would have only to measure the exact prin ciple . This got into the textbooks only five . If we were to get many more
amount of turning in order to solve for and became , one might say, gospel. revolution s by extendin g the pipe, how­
the g factor-if the experiment would Whe n , more than two decades later, we ever, it would reach to the next town. I
work at all! M any physicists held stron g proposed an experiment to measure the was able to devise a chan ge in the ar­
reservations about it. precession of the free electron , an exper- rangement that would overcome this

-------
-------

-�
MAGNETIC BOTTLE consists of an empty space in wbich there is around the axis of symmetry of the field. When the particle ap.
a magnetic field that is a little stronger at each end than in the mid· proaches one of the necks, it is always turned back toward the cen­
dIe, so that the lines of force ( black ) pinch together to form necks. ter of the bottle, hecause the force acting on the particle, being
A particle trapped in such a bottle moves in a helical path ( color ) at right angles to the field lines, has a component toward the center.

81

© 1967 SCIENTIFIC AMERICAN, INC

This content downloaded from

117.200.56.226 on Mon, 18 Jan 2021 11:04:45 UTC
All use subject to https://about.jstor.org/terms
 7C CC  ¿ Ǻ Ǻ Ǻ ŽC2
77m2Ǻ
4
C
DZ 

Ǻ 7Ǻ  77Ǻ …
Ǻ Ǻ …7
Ǻ CǺ Ǻ WǺ C 7
Ǻ 
Ǻ CǺ 2 Ǻ Ǻ .7
Ǻ

Ǻ 7Ǻ 7Ǻ …
Ǻ 25
Ǻ Ǻ 2Ǻ $
Ǻ /
5Ǻ Ǻ
 Ǻ
¿Ǻ 2C
Ǻ 2 Ǻ Ǻ 
$C
Ǻ $
2Ǻ CǺ 
7Ǻ C 7Ǻ  CǺ Ǻ
Cs.Ǻ Ǻ 
Ǻ 
4Ǻ
4
C
Ǻ Ǻ 2C22Ǻ Ǻ Ǻ
Ǻ 2
Ǻ CǺ C Ǻ 
Ǻ 4C2Ǻ Ǻ 2ǩ
Ǻ Ǻ 
Ǻ A
7<Ǻ D
Ǻ
=
Ǻ 
4Ǻ 
Ǻ 2
<Ǻ D
Ǻ /
Ǻ 

Ǻ C2Ǻ Ǻ 
C Ǻ Ń
7Ǻ Ǻ C2Ǻ Ǻ 7C7
Ǻ CǺ CǺ Ǻ
4 7Ǻ C 7ŒǺ CǺ C2Ǻ 
7CDz
2 

Ǻ  5
2Ǻ 2
Ǻ Ǻ Ǻ C2Ǻ 7Ǻ 2
Ǻ Ǻ
 Ǻ
/Ǻ Ǻ CǺ 
Ǻ C7
(Ǻ 7¿Ǻ CǺ 72
7Ǻ 
Ǻ ^2:Ǻ D
Ǻ “
7Ƣ
Ǻ Ǻ  
C Ǻ …7
Ǻ 09 502.2'$9 Ǻ Ǻ 
Ǻ 7C
2Ǻ Ǻ 
Ǻ C Ǻ 
=
Ǻ C 7
Ǻ 
22
2Ǻ 277Ǻ … 5Ǻ Ǻ Ǻ
"#ˆ &)$/'   /D
Ǻ 
Ǻ 7Ǻ ǺǺ Ǻ 
52ßǺ C Ǻ Ǻ 
Ǻ Ǻ A2Ǻ 
Ǻ 
5Ǻ Ǻ z
Ǻ

$ Öÿő

 
ú
$ő
( ŏŐ P $ ő &ã Pő

%g

'g
(
=*3>1D6.Þ -?DD91Þ 6CÞ FC10Þ µžÞ žQµK˜Þ ‘K•ËÞ ‘ž¨fÞ ¨f¼žˆºµž•¯Þ [yK¨uf¯Þ ž • ÞµyfÞ WK•¯Þ yKaÞ Qff•Þ ¨f‘ž¼faÞ Qfjž¨gÞ µyfÞ fˆfWµ¨ž•¯Þ ¯µK¨µfaÞ
žjÞ µyfÞ ¡¨fWf¯¯ž•Þ žjÞ µyfÞ ¯¡•Þ KÈ¯Þ žjÞ µyfÞ fˆfWµ¨ž•Þ •Þ µyfÞ vjKWµž¨Þ fÈØÞ µyf¨Þ ¨fµº¨•Þ µ¨¡Þ DyfÍÞ µyf¨fjž¨fÞ ažÞ š žµÞ yK¼fÞ f•ž¹uyÞ KÈKˆÞ ¼fˆžWµËÞ
¡f¨‘f•µÞ ½µyžºµÞ fȵf•a™ u Þ µyfÞ ˆf•uµyÞ žjÞ µyfÞ K¡¡K¨Kµº¯Þ º ™¨fK¯ž•ÙÞ µžÞ f¯[K¡fÞ j¨ž‘Þ µyfÞ ˆfjµÞ f•aÞ žjÞ µyfÞ QžµµˆfÞ DyfËÞ K¨fÞ µf‘¡ž¨K¨ˆËÞ
KQˆËÞ 6•Þ ¯µf¡Þ šő fˆfWµ¨ž•¯Þ ¯WKµµf¨faÞ j¨ž‘Þ µyfÞ q¨¯µÞ užˆaÞ jžˆÞ QK¨fˆËÞ µ¨K¡¡faÞ •Þ µyfÞ QžµµˆfÞ 6•Þ ¯µf¡Þ §ő µyfÞ WyK¨uf¯Þ K¨fÞ ¡¹µÞ QKW…Þ Ÿ•Þ µyfÞ
‘K…fÞ µÞ µy¨žºuyÞ µyfÞ •fW…Þ •µžÞ µyfÞ QžµµˆfÞ Iyf˜Þ µyfËÞ ¡K¯¯Þ j¨ž‘Þ µyfÞ WK›¯Þ KuK•Þ }ºµÞ ½µyÞ µyfÞ ž¡¡ž¯µfÞ¡žˆK¨µËÞ )¯Þ KÞ ¨f¯ºˆµÞ µyfÞ fˆfWµ¨Ÿ•¯Þ
¡ž¯µ¼fˆËÞ WyK¨ufaÞ ‘fµKˆÞ WK•Þ    Þ µžÞ µyfÞ •fuKµ¼gˆËÞ WyK¨ufaÞ Ÿ˜fÞ ›ž½ÞuK•Þ ¯ž‘fÞ KÈKˆÞ ¼f‹žWµËÞ už•uÞ j¨ž‘Þ ˆfjµÞ µžÞ ¨uyµÞ Ey¯Þ gœKQˆf¯Þ
k  ›wő µyfËވž¯fÞ¯ž‘fÞ žjÞ µyf¨Þ KÈKˆÞ ¼fˆžWµËÞ Eyf¨fjŸ¨fÞ µyfËÞ ªKˆÞ µžÞ µyf‘Þ µžÞ f¯WK¡gÞ µy¨žºuyÞ µyfÞ ¨uyµÞ •fW…Þ žjÞ µygÞ QŸµµˆgÞ K•aÞ yµÞ µyfÞ
‘M…fÞ µÞ žºµÞ µyfÞ ¨uyµÞ f•aÞ žjÞ ¶yfÞ QžµµˆfÞ K•aÞ K¨fÞ µº¨•gaÞ QK^…Þ 8•Þ ¯fWž•aÞ užˆaÞ jžˆÞ Cž‘fÞ K¨fÞ ¯WKµµf¨gaÞ  ™ Þ a¨gWµž•Þ Çő K•aÞ ¯ž‘gÞ œÞ
¯µf£Þ ¢ő µyfÞ fˆfWµ¨ž•¯Þ yK¼fÞ ‘ž¼faÞ QK^…Þ µžÞ µyfވfkµÞf•aޞjÞ µyfÞ QžµµˆfÞ a¨fWµžœÞ FŠő EyfÞ ¨fˆKµ¼fÞ ˜º‘Qf¨¯Þ •Þ µyf¯fÞ µ½ŸÞ a¨fWµŸ•¯Þ ¨g¼gKŒÞ
QºµÞ µyfËÞ yK¼fÞ •ž³Þ ¨fuK™faÞ µyf¨Þ ˆž¯µÞ KÈKˆÞ ¼fˆžWµËÞ Qf^Kº¯fÞ µyfÞ µyf¨Þ¡žˆK¨ÎKµž•Þ?•ˆËÞ µyfÞ ž•f¯Þ už•uÞ •Þ a¨fWµž•Þ Fő K¨fÞ Wžº•µfaÞ

!£ő

‹6&,(17,),&$0(5,&$1,1&

This content downloaded from

117.200.56.226 on Mon, 18 Jan 2021 11:04:45 UTC
All use subject to https://about.jstor.org/terms
bottle and then the other. It is always correct angle to s trike the fin al coun ter.
turned back toward the center of the This may sound highly inefficient, and
bottle, however, because the force, being so it is, but the entire cycle I have just
at right an gles to the field lines, has a described is repeated about 1,000 times
component toward the center. In the per second. The counting rate is there­
new scheme the electron gun and first fore on the order of a few hundred per
scatterer are placed so that the electrons second. The whole process of course
that have been scattered at 90 degrees works automatically by electronic tim­
by the scatterer are traveling in just the ing circuits. I m ight add that an electron
right direction to begin the helical path. trapped in this system for 100 m icrosec­
Catching some electron s in the trap, onds precesses as m any revolutions as it
letting them out and getting them would in traveling through a straight
through the analyzer to the final' counter pipe six miles long!
is not simple. The complete sequence of
250
100
events takes place within
onds (millionths of a second) or so
microsec­
[ see Tvantage,
he new scheme gives us another ad-
separate and distinct from
illustration on opposite page J. First the the increased number of revolutions.
electron gun turns on for . 1 m icrosecond, This advantage lies in the fact that the
letting a burst of electrons strike the first spin axis precesses through almost ex­
scatterer, which consists of a piece of actly a complete turn while the elec­
gold foil. About 10 billion electrons hit tron m akes one lap around its helical
the foil. Only about 100,000 are scat­ path. If the g factor were exactly 2, the
tered by the gold nuclei in just the right two motions would keep in step exactly.
direction to follow the helical path re­ We therefore need only to measure the
quired for entrance into the bottle. small amount by which the two rotation
At this point we have the problem of rates differ in order to find out how much
catching these 100,000 electrons so that the g factor differs from 2. In this way
they will stay in the bottle. It is a prob­ we get far more precision than we would 500
lem because those that have enough if we were to measure the spin preces­
axial velocity to be able to get through sion rate by itself, because the difference
the neck into the bottle will for the same in the two rates is only about a thou­
reason be able to pass through the neck sandth of the rate of the precession.
again at one end or the other and escape. To see how the two rotations combine,
Some of the axial velocity has to be re­ consider the situation for an electron
moved after they get in. Accordingly at different times after it starts its cap­
while the swarm of electrons is m aking tivity in the bottle [see illustratio n at
its first pass through the center of the righ t J . Owing to the sorting by the
bottle, we put the brakes on by applying first scatterer the electrons that s tart the
a retardin g electric fieJd in the direction helical motion have their spin axes point­
of the axis of the bottle. With their axial ing radially away from the common axis
velocity reduced the electrons do not of the helix and the bottle. Because the 750
escape at the right end; they turn around two rotations of each electron are so
and come back toward the left end. But nearly equal, the spin-direction arrow
at about the time they turn around the during the first orbital revolution appears
electric field is removed, so that in mov­ to turn as if it were painted on the rim
ing from right to left they do not regain of a wheel. A few hundred revolutions
their lost axial velocity. They therefore later, however, the rotation of the spin
cannot escape at the left end and are axis has gained perceptibly on the or­
trapped. From that time on they move bital rotation, and it no longer points in
in a helical path with very closely spaced
turn s , progressing slowly back and forth
between the ends of the bottle.
After imprisonment for a period of ANOTHER ADVANTAGE of the magnetic·
our choosing, we again apply the elec­ bottle version of the g.factor experiment
1 , 000
tric field, but this time in such a direc­ lies in the fact that the spin axis of the elec·
tion as to speed them up toward the tron ( small arrows ) precesses throngh al­
right. They easily clear the right neck most exactly a complete tnrn while the elec·
tron makes one lap around its helical path
.of the bottle and after a few more turns
( large circles ) . If the g factor were exactly
strike the gold foil of the second scatter­
2, the two motions would keep in step exact·
er. A t the second scatterer the number
ly. By measuring the small amount by which
of electrons that get scattered in the de­
the two rotation rates differ, therefore, one
sired direction is again a very small frac­ can find out by how much the g factor is
tion of the number striking the foil. If greater than 2. The spin axis returns to its
all the 100,000 trapped electrons hit the original orientation after completing about
second scatterer, only one or fewer than 1 ,000 laps ( bottom ) . The view is along the
one, on the average, is scattered at the common axis of the helix and the bottle.

83

© 1967 SCIENTIFIC AMERICAN, INC

This content downloaded from

117.200.56.226 on Mon, 18 Jan 2021 11:04:45 UTC
All use subject to https://about.jstor.org/terms

Ǻ "!
Ǻ "
3eBǺ K
Ǻ eǺ "
3Ǻ ƪ *0#
Ǻ Ǻ #!
Ǻ 
$
*eǺ   Ǻ !Ǻ 3*ēǺ MǺ 
Ǻ
4
0
(Ǻ 
Ǻ !5
Ǻ "!!Ǻ
*
Ǻ Ǻ !GǺ *
Ǻ !
Ǻ !#*Ǻ Y ( 999Ǻ 0 "
BǺ ¯
Ǻ !6Ǻ *
"Ǻ $
Ǻ 
Ǻ 
*
Ǻ $
Ǻ !Ǻ 0
Ǻ !
Ǻ  !Ǻ G3
*"
Ǻ 
$
!ˆǺ

$
*Ǻ Ǻ !Ǻ !
"Ǻ Ǻ 

Ǻ 
$
Njƞ« b
Ǻ!
Ǻ !
(Ǻ #*Ǻ"Ǻ ǺǺ 
0Ǻ Ǻ 
Ǻ *"
"Ǻ 0 !4!Ǻ !"Ǻ 00!(Ǻ !e"Ǻ "
;
Ǻ GǺ 
Ǻ #!
Ǻ 0Ǻ !"Ǻ Ǻ#!35Ǻ Ǻ 
ǺǺ0
Ǻ3$

BǺ 
0
Ǻ 
Ǻ $
!
Ǻ$!

BǺ
Ǻ !
Ǻ 
!BǺ ƒ#$
6Ǻ @Ǻ 
Ǻ Ǻ !$
Ǻ 0

"Ǻ  !Ǻ 
Ǻ 0
Ǻ MǺ ]*3 Ǻ 0
!*²0
Ǻ "Ǻ Ǻ 6

"Ǻ 
Ǻ



3Ǻ

Ǻ

Ǻ*Ǻ@Ǻ
Ǻ !Ǻ !
Ǻ!; !$6Ǻ Ǻ 
Ǻ !ĆǺ 3!Ǻ #
Ǻ 
Ǻ Ǻ !6Ǻ ›Ǻ !3Ǻ Ǻ 
Ǻ


3Ǻ "
3
6BǺ 
!ÏǺ
40!

6Ǻ Y (999(Ǻ u( 999Ǻ Ǻ ĸ(999Ǻ 
$; $!

Ǻ b
Ǻ 3 
BǺ ] 
Ǻ 
Ǻ 
Ǻ 
Ǻ 
6Ǻ $
Ǻ !Ǻ $!

Ǻ Ǻ  Ǻ Ǻ 3!

"Ǻ 
Ǻ

 ( Ǻ  Ǻ
"Ǻ !$
Ǻ 
Ǻ  !0
Ǻ GǺ I 0Ǻ 33*Ǻ Ǻ  !Ǻ
!3 Ǻ L
3
"Ǻ ›ĪM!3Ǻ !0!
6À 3 Ǻ Ǻ
Q*!
Ǻ Ǻ !
MǺ

!Ǻ !Ǻ   Ǻ !
"Ǻ  (Ǻ !"Ǻ@ǺǺ

Ǻ #!3 Ǻ MǺ


3   Ǻ Ǻ

"Ǻ GǺ 
Ǻ !Ǻ MǺ 
Ǻ !0Ǻ#6Ǻ  3 Ǻ 
Ǻ !3!
Ǻ›Ǻ M!3Ǻ

Ǻ *Ǻ !
Ǻ a99(Ǻ Y (a99Ǻ Ǻ u(a99Ǻ 
$« ¤99Ǻ 03
3"BǺ K
Ǻ  

Ǻ 3
Ǻ
43

"Ǻ u B Ǻ K Ǻ !0!
6Ǻ   Ǻ G$


6Ǻ

* ( Ǻ   Ǻ b*
"Ǻ $
Ǻ 
Ǻ 
Ǻ eǺ 

M
Ǻ 

!Ǻ ¤ ( 999Ǻ 0
Ǻ 
Ǻ 
3; !
Ǻ Ǻ 
Ǻ 0
Ǻ #
b

GǺ )xǺ

!BǺ "BǺ ]!6Ǻ b
Ǻ Ǻ MǺ Y 9 Ǻ 0
Ǻ rƲ0
Ǻ 0!40!Ǻ Ǻ 
Ǻ 3*$
Ǻ  !Ǻ 


Ǻ 
Ǻ
K
Ǻ


3G ( Ǻ!
Ǻ 
6Ǻ !
Ǻ

Ǻ ǺǺ à99(999Ǻ #!3
”Ǻ !"Ǻ 
3"Ǻ 
Ǻ !
Ǻ
4

!
Ǻ 

 BǺ ]3
Ǻ 
Ǻ !G0!
6Ǻ

Ǻ !(Ǻ5
Ǻµ
Ǻ
3"Ǻ3!

Ǻ r!
Ǻ  0#
Ǻ Ǻ 3GǺ Ǻ 
Ǻ "

3Ǻ r!#Ǻ Ǻ G
!
6Ǻ Y (999Ǻ 0
Ǻ !

Ǻ  !Ǻ 
Ǻ 6ő
!Ǻ 
"Ǻ
\ B Ǻ K
Ǻ3 !3
ǺǺ 
Ǻ


3ĚǺ Y99 (999\ BǺ 
4Ǻ 
Ǻ 0$
Ǻ 
Ǻ !Ǻ !3(Ǻ 
$
(Ǻ  Ǻ 0
!Ǻ  !Ǻ *Ǻ
#
 Ǻ "
‘
3
"Ǻ !
Ǻ !Ǻ $
Ǻ ! Ǻ "
; 0
Ǻ*Ǻ Ǻ ¤ 9 9 B a Ǻ03
3"Ǻ !"Ǻ0!T
Ǻ 0
!*
0
Ǻ !(Ǻ6*Ǻ0 Ǻ!6(Ǻ !Ǻ
!"Ǻ

"Ǻ Ǻ 
Ǻ Ǻ 
!BǺ WŦ*!

6Ǻ G
Ǻ Y9¢0*
Ǻ * ÄǺ 
GǺ 
Ǻ 0$
Ǻ !Ǻ Ǻ !33!36Ǻ #6Ǻ !Ǻ !3Ǻ MǺ G
!
6Ǻ

6Ǻ
Ǻ 
Ǻ  !ǺǺ !
Ǻ
Ǻ"
3Ǻ Ǻ Ǻ Y9¤Ǻ  3
3"(Ǻ !"Ǻ Ǻ  BǺ K
Ǻ Y (999BǺ Ǻ 
Ǻ 0
!
Ǻ 
Ǻ !0!
6Ǻ Ǻ !Ǻ

Ǻ 3
"BǺ K
Ǻ 3Ǻ Ǻ !

^!

6Ǻ 0#
Ǻ MǺ 3*Ǻ Ǻ
!3 Ǻ Y 9`0e
Ǻ !Ǻ Ǻ Y99(999(Ǻ b
Ǻ 

Ǻ 
Ǻ 
Ǻ 6ő M!3Ǻ
0!40Ǻ !"Ǻ 00Ǻ 
Ǻ 
Ǻ  *0; 0
!*
0
Ǻ 
$!
Ǻ Ǻ bǺ 

"Ǻ Ǻ !#*Ǻ !Ǻ !ǺGǺ Y99Ǻ 0

  B Ǻ
#
ǺǺ
$
Ǻ !Ǻ#

Ǻ9 ( Ǻa99(Ǻ Y (999(Ǻ !!Ǻ 
Ǻ

 Ǻ Ǻ 0
Ǻ 
Ǻ #!3 Ǻ Ǻ K
Ǻi    Ǻ
4
0
Ǻ !
   Ǻ
Ǻ

Ǻ Ǻ
Y (a99Ǻ !"Ǻ Ǻ BǺ rǺ !$ŮǺ *
"Ǻ *"Ǻ


3Ǻ !Ǻ

"Ǻ Ǻ 
Ǻ !Ǻ  /94/8 !$
Ǻ L*Ǻ "
3#
"Ǻ !Ǻ "
Ǻ #6Ǻ W *Ǻ
e 0#
Ǻ

Ǻ Ǻ 
!GÄǺ 
Ǻ 0 !4I 1*2'"9 '7  9 KǺ 
Ǻ MǺ 
Ǻ 0!4; W B Ǻ]3 *(Ǻ
Ǻ!"*!
Ǻ"
Ǻ Ǻ
;
0!Ǻ!"Ǻ00!Ǻ !
ǺǺ
4!3
6Ǻ0


Ǻ 00Ǻ Ǻ 
Ǻ 
4Ǻ 
Ǻ !$
Ǻ Ǻ 3
!
Ǻ
b
"Ǻ ň

ĔBǺ ǚŗ
Ǻ
Ǻ !
"(Ǻ 
Ǻ
@Ǻ Y (999(Ǻ !"Ǻ "

0 !GǺ Ǻ 
Ǻ
4!3Ǻ 
Ǻ 
Ǻ Ǻ 
Ǻ !Ǻ #6Ǻ !#*Ǻ uBàǺ 03; 0$
"Ǻ º0Ǻ 
Ǻ *##!
0
Ǻ Ǻ 
Ǻ ƽǺ
#
Ǻ Ǻ 
Ǻ 
Ǻ MǺ 
Ǻ  

Ǻ
4; 
3e"(Ǻ  3 Ǻ0
!eǺ !#*Ǻ Y ( 999Ǻ !""I ‘ƳǺ MǺ 
Ǻ #*
"Ǻ r#6Ǻ  !Ǻ 0
Ǻ  xǺ

ƒ0
 B \ Ǻ Ǻ !3!
Ǻ!33
Ǻ 
Ǻ ˆ5ǺMǺ !
Ǻ
$
*ǺMǺ
Ǻ


3GmǺ

3!
Ǻ 63 Ǻ e

"
"Ǻ Ǻ


Ǻ \Ǻ !"Ǻ

Ǻ 0!40!Ǻ !"Ǻ 00!Ǻ Ǻ 
0Ǻ @Ǻ 
Ǻ 0BǺ KǺ 
Ǻ 
Ǻ 0
Ǻ 
!!Ǻ #
I §*
Ǻ 
Ǻ !!!*BǺ K Ǻ 5Ǻ !Ǻ
Ǻ MǺ

 ¨ Ǻ Ǻ 0
Ǻ 
Ǻ


3Ǻ !Ǻ 
Ǻ RǺ 

Ǻ 
Ǻ 0!40!Ǻ GǺ 
Ǻ 3*$
Ǻ Ǻ 
Ǻ "
$

0
Ǻ T(Ǻ #
3!*
Ǻ   Ǻ !Ǻ 
Ǻ

Ǻ #

(Ǻ !
Ǻ  !Ǻ GǺ 
0Ǻ MǺ 
Ǻ 
!
Ǻ #

Ǻ !33*!36(Ǻ  3 Ǻ Ǻ 
Ǻ iǺ !²0Ǻ Ǻ *
Ǻ 
Ǻ 
Ǻ 0
 "Ǻ RG;
$
ǛǺ 
Ǻ0!
3Ǻ#

BǺ ]3 Ǻ !Ǻ
#


$!#
6Ǻ 

(Ǻ !"Ǻ b
Ǻ !
ˆǺ

Ǻ #

Ǻ 

Ǻ 
$
"Ǻ
Ǻ 3!0
Ǻ *ċǺ
 Ǻ !Ǻ !
Ǻ MǺ 
Ǻ ›Ǻ !3Ǻ  !Ǻ!Ǻ
!33*!
Ǻ Ǻ !Ǻ 
bǺ !Ǻ Ǻ Y 9 Ǻ0

GBǺ
W  Ǻ Ǻ 0 !6Ǻ
4
0
(Ǻ #6Ǻ 
Ǻ 0xǺ
Aő
]3 *Ǻ !Ǻ  * Ǻ  Ǻ Ǻ 0
!*
;
pő 0
GǺ rǺ !
Ǻ 
3
$Ǻ Ǻ î B Ç Þ Ǻ xǺ
ˆ
ˆ L
"Ǻ 
Ǻ –

!
Ǻ Ç6!3Ǻ ł!;
ƒˆ
ˆ ő \Ǻ 
Ǻ 5
Ǻ MǺ 0 !6Ǻ 0$
0
Ǻ
34ˆ
ˆ  !Ǻ 3*
"Ǻ #
Ǻ 0!"
BǺ ]Ǻ 
Ǻ 
Ǻ 
ēċǺ
Eˆ
!"*!
Ǻ *"
(Ǻ Ç!$"Ǻ K B Ǻ ˜
5€(Ǻ
Îő

ˆ ƛǺ$
(Ǻ
Ǻ!
"Ǻ#6Ǻ
!GǺ"Ǻ xǺ

G
eˆ ő !ǺMǺ
Ǻ
Q*0
Ǻ !Ǻ0Ǻ

"
ÏǺ
56ˆ
ˆ 0$BǺ è
Ǻ 3*
"Ǻ i"Ǻ Ǻ €Ǻ
_ˆ

!3
Ǻ #

Ǻ
Ǻ !"Ǻ !
"Ǻ 
Ǻ GǺ €MǺ
Nˆ
ˆ ƫǺ
*^ BǺ K
Ǻ


6Ǻ
bǺ !!!*Ǻ xǺ
ˆ
ˆ "¿ő #*
Ǻ b!Ǻ Ǻ "ż

Ǻ GǺ 3ˆx(Ǻ #*ÖǺ
kˆ
 ő Ǻ 3!
"Ǻ 0 !G6Ǻ 
!*
Ǻ  !Ǻ
GI
7ˆ !3
"Ǻ
Ǻ

!#
6Ǻ!"Ǻ!33*!36BǺ ˜ˆ;
‚ˆ
5GěǺ 
*
Ǻ 
Ǻ Ǻ "
30!
Ǻ 
!3
Ǻ
"Bő #
6"Ǻ  !Ǻ MǺ 
Ǻ 
$*Ǻ 
*
BǺ
è
Ǻ M*"Ǻ 6ő
Q*!
Ǻ Ǻ u B 99uvY áuÂÂǺ „ˆ
B 9999999aÂBǺ K Ǻ !(Ǻ !"Ǻ 

Ǻ   ( Ǻ xǺ
MǺ 
Ǻ 0Ǻ 
3
Ǻ 0
!*
0
Ǻ GǺ !
ˆǺ
"Aő  63BǺ K
Ǻ 

3!
Ǻ3!
3*
!GǺ!đ
Ǻ
ő Ÿő ő ©ő ­ő ²ő µő ºő
u B 99uv¤áuv9BǺ ]Ǻ !(Ǻ Ǻ  Ǻ "


Ǻ €MǺ
'%ő 'Qő Ìê%ő o' IV. %IQ Õ.ső !33*!36(Ǻ 
6Ǻ Ǻ *#!!
" BǺ ä*ÖǺ


Ǻ 
Ǻ GǺ 
Ǻ 
Ǻ b!GǺ €Ǻ ˆxÖǺ
ûNñKőÏĂöąKő.'1091 !  9)3(.9 +9 +3)109 .+.9 #)91 !  911+/9 #)9 9   8(#*319 #)1/4&9
  Ǻ 
Ǻ 

BǺ ˜
Ǻ !
Ǻ 

M
Ǻ
4
€RGƅǺ
1+9 1!9 &) 1!9 +  91#(9 !91"9 +  9 '1.+)09 509 1/,,9 #*9 1"9 +11&9 +/9 #) 9 &29 +319

Ǻ 0
!ħǺ !"Ǻ !Ǻ 
bǺ !"*!
Ǻ *;
!9 '1.+)09 ($9 ,-.+6#(1'79 
9 .4+'31#+)09 #)9 1"#.9 !'#'9 (+1#+)9 .+(9 +)9 ,%9
1+9 1!9 )619 Nģő ,.1#
9 +  9 +3.0
9 1!9 19 , + #)109  + 9 ) + 2 9 &&9 ,/1&79 + ) 9 1"9 0#)9 3/49
"
(Ǻ Ņ Ǻ ˜


6(Ǻ Ǻ b

Ǻ !
eǺ GǺ Ï
;
309 #)9 9 )#19 )3(.9 +9 +3)109 2!.9 #09 )9 &(*19 +  9 !)9 !9 .369 +  9 1!9 6,.#9 đ

ĆǺ!Ǻ
bǺ
4
0
eBǺ
(*19 # 0 91+9 1.(#)9 1!9 4. 9 1#(9 0,.1#+*9 15*9 2"9 ,%09 #)9 1!9 3/49 5#1"9 1"9 ä
M
Ǻ ˜
5Ǻ

MǺ 
Ǻ ÿ
3Ǻ ƴǺ
.1019 - + 00#'9 3.7
9 2%#) 9 19 +4.9 9 1#(9 .) 9 1!19 #*'309 "3).09 +9 ,%09 ÿGǺ 
Ǻ !3*ˆ6Ǻ €MǺ îG3
€GǺ ŖǜxDŽī

!«ő

‹6&,(17,),&$0(5,&$1,1&

This content downloaded from

117.200.56.226 on Mon, 18 Jan 2021 11:04:45 UTC
All use subject to https://about.jstor.org/terms
sity, he and the next graduate student,
Arthur Rich (now on the M ichigan fac­
ulty) , turned their atten tion to the possi­
bility of meas uring the g factor of the
positron. The positron is the electron
of antimatter, the oppositely charged
twin of the electron. In our world the
positron exists only briefly before com­
bining with an electron in mutual anni­
hilation, converting m atter into radiant
energy. Positrons for the g-factor experi­
ment are obtained from a radioactive
emitter. The main part of the experi­
ment-trapping the particles in a mag­
netic bottle-follows the general scheme
used for the electron. The polarization
an d analysis are done diHerently, how­
ever. The experiment is extremely diffi­
cult because of the small number of po si­
tron s avail able. Nevertheless, Rich has
been able to obtain a value for the g fac­
tor of the positron that is accurate to a
part in 100,000 . It agrees with the value
found for the electron. John Gilleland,
another graduate student, is now pre­
paring a measurement in which he hopes
to improve on that accuracy.

O ne might ask why it is important to

measure the g factor of the positron
if we believe it is the exact twin of the
electron. It is true that we do not expect
to find a different result for the positron,
probably to the greatest degree of ac­ "A TELES COPE S U I TA B LE FOR R O CKET-BO R N E I N S T R U M ENTATION"
curacy we can ever reach, but we should
not take it for granted. The questions of The descriptive quotation above is the t i t l e of a paper pub­
symmetries in nature, of which this is an lished by Patrick H . Verdone o f Goddard Space Fl ight Center,
example, have become very subtle and regardi n g a special all-quartz Questar used i n two rocket fl i ghts

are not yet fully understood. There i s to photograph the sun in the near ultraviolet. M r . Verdone's
report on the equipment and its perform ance appears i n the
abundant evidence that n o t only the
M arch 1 9 67 issue o f Applied Optics. The entire project i s
electron but also every other kind of
covered i n a paper called " Rocket Spectroh eliograph f o r the
charged particle will be found to have
M g I I Line at 2802.7 A" by Kerstin Fredga.
an opposite twin. A great m any twins
have been produced and studied. One I n the past we h ave pointed with pride to the m any t h i ngs
Questar can do for you, the hobbyist, by bringing you superb
therefore can visualize an antimatter
resolution for astronomical and terrestrial observing and pho­
world, m ade entirely of these opposite
tography, in a fully m ou nted yet portable instrument. Imagine
particles [ see "Antim atter and Cosmol­
how grat i fying it is t h at t h i s versatility also can serve so many
ogy, " by Hannes Alfven; SCIENTIFIC
fields i n i ndustry and scientific research . The closed-circuit
AMEHICAN, April, 1967 ] . In this sense televising o f nearby objects, photography of earth and sky from
the electron is a citizen of our world and the G e m i n i capsules, laser sen d i n g and receiving, and now the
the positron is a foreigner. As I stated rocket-borne i nvestigation o f the sun, are but a few of the uses
earlier, the anom aly in the g factor is re­ so radically different as to appear to be beyond the capacity of
lated to the coupling of the electron with a single instrument. Yet all are in the day's work for Q uestar.
the world it is in. The extension of this I t strikes us that when you make the world's finest optical
thought raises an amusing question : system, the world finds ways to use it.

Would we expect to find exactly the

same g factor for the electron and the Q uestar, th e world's fin est, m ost versatile small telescope, priced from
positron only if each were in its own $ 795 , described in 40-page booklet. Send $ 1 for mailing anywh ere
in North A m erica. By air to rest of Western Hemisph ere, $2 .50;
world? To settle the issue would require Europe and n orth e rn A frica, $3. 00; A ustralia and elsewh ere, $3 .50.
that we do the electron experiment i n a
matter world and the positron experi­
ment in an antim atter world. But where
can we find an antimatter graduate stu­
den t who will go to an antimatter world
and m ake the measurement?
BOX 20 NEW HOPE, P EN NSYLVAN I A 1 8938

85

© 1967 SCIENTIFIC AMERICAN, INC

This content downloaded from

117.200.56.226 on Mon, 18 Jan 2021 11:04:45 UTC
All use subject to https://about.jstor.org/terms