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February 1970
Volume 222
Number 2
AMERICAN
ARTICLES
13
THE ASSESSMENT OF TECHNOLOGY, by Harvey Brooks and Raymond
Bowers
How can technology be fostered while avoiding undesirable effects?
22
LARGE-SCALE INTEGRATION IN ELECTRONICS, by F. G. Heath
Thousands of circuit elements can now be simultaneously made on a single "chip."
32
THE AFAR TRIANGLE, by Haroun Tazieff
A fantastic landscape beside the Red Sea appears to be an ocean in the making.
52
THE PHYSIOLOGY OF HIGH ALTITUDE, by Raymond J. Hock
How do men and other animals adapt to permanent residence above 6,000 feet?
.. 68
PARTICLES THAT GO FASTER THAN LIGIIT, by Gerald Feinberg
They have not been discovered, but there are reasons to believe they may exist.
82
PHOSPHENES, by Gerald Oster
The patterns we see when we close our eyes are clues to how the eye works.
88
THE RANCELANDS OF THE WESTERN U.S., by R. Merton Love
These vast tracts normally reserved for grazing can have other humane uses.
98
CELL SURGERY BY LASER, by Michael W. Berns and Donald E. Rounds
A tiny, intense spot of light is used to probe the physiology of the living cell.
DEPARTMENTS
6
LETTERS
9
50 AND 100 YEARS AGO
10
THE AUTHORS
42
SCIENCE AND THE CITIZEN
112
MATHEMATICAL GAMES
116
THE AMATEUR SCIENTIST
122
BOOKS
126
BIBLIOGRAPHY
BOARD OF EDITORS
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PRODUCTION DEPARTMENT
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T
.
Efforts to detect such particles, named tachyons, have yielded
only negative results. Contrary to common belief, however, their
existence would not be inconsistent with the theory of relativity
by Gerald Feinberg
S
Yince the formulation of the special
theory of relativity by Einstein in
1905 and its subsequent verifica-
tion by innumerable experiments, physi-
cists have generally believed that the
speed of light in a vacuum (about 300,-
000 kilometers per second) is the maxi-
mum speed at which energy or informa-
tion can travel through space. Indeed,
Einstein's first article on relativity con-
tains the statement that "velocities great-
er than that of light ... have no possibil-
ity of existence."
The basis of Einstein's conclusion was
his discovery that the equations of rela-
tivity implied that the mass of an object
increases as its speed increases, becom-
ing infinite at the speed of light (which
is usually denoted c). Since the mass
of a body measures its resistance to
a change of speed, when the mass be-
comes infinite the body cannot be made
to go any faster. Stated somewhat differ-
ently, the relation between energy and
speed implied by relativity is such that
as the speed of a body approaches c its
energy becomes infinite. Since this ener-
gy must be supplied by whatever is ac-
celerating the body, an infinite source of
energy would be needed to speed up a
body to the speed of light from any low-
er speed. No such infinite energy source
is available, and so it is impossible to
make a body go from less than c to c.
Furthermore, if a body could some-
how be made to go from a speed less
than c to one greater than c, the same
relativity equations imply that its energy
and momentum would become imagi-
nary numbers, that is, numbers contain-
ing a square root of a negative number.
This situation does not seem to have any
physical meaning. Objects with imagi-
nary energy clearly cannot exchange
energy with objects having real energy
and hence cannot affect them. Accord-
ingly, such objects could not be detected
by real instruments, and can be said not
to exist. Within the context in which
Einstein worked, where the properties
of objects varied continuously and where
the creation of new objects was not con-
sidered, it therefore seemed a logical
conclusion that no form of energy, and
hence no matter, could travel faster than
light.
With the development of subatom-
ic physics, however, the context has
changed considerably. We now know
that the subatomic particles can easily
be created or destroyed, and that in their
mutual interactions their energies and
other properties change discontinuously,
rather than in the smooth way envi-
sioned in classical physics. Therefore one
can imagine the creation of particles al-
ready traveling faster than light, and so
avoid the need for accelerating them
through the "light barrier" with the at-
tendant expenditure of infinite energy.
-
In addition, one can consistently re-
quire that such particles always travel at
speeds greater than c, which obviously
cannot be the case for known particles.
If one assumes these conditions, there
is no problem in satisfying the require-
ment that the particles carry real en-
ergy and momentum. This can be done
mathematically by allowing a certain
constant that appears in the relation be-
tween energy and speed to be an imagi-
nary number, rather than a real number
as it is for ordinary particles [ see top il-
lustration on next two pages]. This con-
stant is usually known as the rest mass,
because for ordinary objects, which can
be slowed to rest, it gives the value of
the object's mass when at rest.
For the hypothetical faster-than-light
particles, which can never be brought to
7
K-
SEARCH FOR TACHYONS led the author and his colleagues at Columbia University to
scrutinize thousands of bubble-chamber photographs such as the one on the opposite page
for indirect evidence of the occurrence of neutral tachyons among the by-products of cer-
tain subatomic interactions. The photographs, which were originally made at the Brook-
haven National Laboratory for another experiment, were analyzed by means of the "miss-
ing mass" method. In this approach the energy and momentum of the charged particles in
the reaction are measured directly from the configuration of the tracks they make in the
bubble chamber. Although neutral particles are usually not observed directly, it is possible
to tell from the values measured for the charged particles whether or not any neutral par-
ticles have been produced, and also what the missing mass of these particles is. In this case
a negative K meson (K-) was allowed to come to rest and be captured by a proton in the
hydrogen bubble chamber (see diagram at left). One neutral particle, a lambda hyperon
(4º), was produced and was detected through its decay into two charged particles, a nega-
tive pion (=") and a proton (p+ ). In order to conserve energy and momentum, another
neutral particle (x0) had to be produced in this reaction, but the experimenters were able
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a
E
mc2
/1-(v2)(2)
b
E = mc2
C
E=
μc2
(v2)(2)-1
EQUATIONS OF RELATIVITY pertinent to a discussion of the
possible existence of tachyons are shown on these two pages. The
relation between energy and speed that must be satisfied by any
object obeying the special theory of relativity is given by equation
a, where E is the energy of the object, v is its speed and c is the
speed of light. The quantity m is known as the rest mass of the ob-
ject and is related to the energy Eo that the object has at rest by
equation b. For a body traveling faster than light v2/c2 is greater
than one; consequently the quantity under the square-root sign in
equation a is negative, and the denominator of the quantity that is
equal to E in the same equation is an imaginary number (that is, a.
number containing a square root of a negative number). In order
to make E a real number one must choose mn to be an imaginary
number, say m = p\-1. As long as the object always travels at
more than the speed of light, its energy, which can be written in the
form shown in equation c, will then be real, because (12/c2) - 1
rest, this constant is not directly measur-
able, and there is no need for it to be
real. The square of the rest mass, how-
ever, can be expressed in terms of the
measurable energy and momentum of an
object and hence can be directly mea-
sured. For ordinary objects the rest mass
squared is found to be a positive real
number. For faster-than-light particles
it would be a negative number; indeed,
this fact is the basis of one attempt to de-
tect such particles. It should be men-
tioned that there is a third class of parti-
cles, including photons (light quanta)
and neutrinos, for which the rest mass is
zero and which always travel at c.
The possibility therefore seems to
exist that there is a new kind of natural
object: one that always travels faster
than light. The latter statement is in-
variant, in the sense that if a body trav-
els faster than light with respect to one
observer, it will do so with respect to any
other observer himself traveling in rela-
tion to the first at less than the speed of
light. These are the only observers of
which we have any knowledge. It must
be stressed that all the considerations
given here and below are consistent with
the special theory of relativity, and as-
sume the validity of its equations for de-
scribing particles, even if the particles
travel faster than light.
In anticipation of the possible discovery
of faster-than-light particles, I named
them tachyons, from the Greek word
tachys, meaning swift. In order to show
how physicists have gone about search-
ing for tachyons, I shall describe some
of the properties that would distinguish
them from ordinary particles.
One such property follows directly
from the relation between energy and
speed given in the equations of relativ-
ity. We have seen that for ordinary par-
ticles, as their speed increases, their en-
trast, an increase in speed results in a
decrease in energy. Hence a tachyon
that was losing energy by interacting
with matter or by radiating light would
speed up, whereas a tachyon that was
gaining energy from some outside source
would slow down, and its speed would
approach c from above rather than be-
low. Thus c acts as a limiting speed for
tachyons also, but the limit is a lower
limit, rather than the upper limit that
it is for ordinary objects.
In the limiting case of a tachyon mov-
ing at infinite speed its total energy
would be zero, although its momentum
would remain finite. It should be empha-
sized that for a tachyon at infinite speed
it is the total energy that is zero and not
just the kinetic energy. For an ordinary
particle with nonzero rest mass the total
energy can never vanish.
The condition of infinite speed is,
however, not invariant but depends on
the observer. If a tachyon were moving
at infinite speed as seen by one observer,
its speed as measured by another ob-
server in motion with respect to the first
would not be infinite but rather some
finite value between c and infinity. This
is another way of phrasing Einstein's
discovery that simultaneity for events at
different points in space has only a rela-
tive and not an absolute meaning.
A second property of tachyons that
substantially distinguishes them from or-
dinary particles comes about from the
way measurements of energy and time
change with the relative motion of ob-
servers. For ordinary particles the ener-
gy is a number whose value will change
from observer to observer but that will
always be positive. A tachyon whose en-
ergy is positive for one observer, how-
ever, might appear to be negative to oth-
er observers in motion with respect to
the first. This can occur for tachyons be-
cause of the equation of relativity that
ways less than its momentum multiplied
by c; this ambivalence does not apply
to ordinary particles. if negative-energy
tachyons were emitted by the unexcited
atoms of ordinary matter, this would
cause the emitting atoms to be unstable,
and hence the existence of such tachyons
would contradict the known stability of
ordinary matter.
"The change in the sign of the energy
of a tachyon from observer to ob-
server is connected to another peculiar
property of tachyons. If an ordinary par-
ticle is seen by one observer to be emit-
ted (say by an atom A) at one time and
absorbed elsewhere (by atom B) at a
later time, then any other observer in
relative motion will see this process in
the same way-as emission by atom A
followed at a later time by absorption by
atom B-although the time interval will
vary from observer to observer. Tachy-
ons, however, because they would travel
faster than light, would move between
points in "space time" whose time-order-
ing can vary from observer to observer.
Therefore if one observer saw a tachyon
emitted by atom A at one time t1 and
absorbed by atom B at a later time to,
another observer could find that the time
t1' that he measures corresponding to t1
is later than the time to' that he measures
corresponding to to. If this occurs, the
latter observer would naturally want to
interpret what happens in the following
way: The tachyon is emitted by atom B
at the earlier time to' and absorbed by
atom A at the later time t1'.
It can be seen that this interchange of
emission and absorption also removes
the problem of negative-energy tachy-
ons, since the reversal between observers
of the sign of the energy occurs if and
only if the reversal in time-ordering oc-
curs. Since the emission of a negative-
energy particle ;
ud the absorption of a
er Approved For Release 2000/08/10 CIA-RDP96-90787R000100030001 traveling in the

d
p ="
1-(v2/C2)
e
Approved For Release 2000/08/10 : CIA-RDP96-00787R000100030001-9
E2 - p2℃2 = m2℃4
C
E
will in this case be a positive quantity. The momentum p of any
body obeying the special theory of relativity can be expressed in
terms of its speed by means of equation d, in which mn is indepen-
dent of v. It follows from a combination of this equation and equa-
tion a that the quantity represented by equation e does not depend
on v and hence is the same for all observers. The quantity m2
(called the rest mass squared) is then a constant for each object,
even for bodies such as photons (light quanta) or tachyons, which
are never at rest. One can also deduce from these relations equation
f, which implies that if v/c is less than one (as it is for ordinary
objects), then pc/E is less than one, E- - p2c2 is greater than zero
and hence m2 is positive. On the other hand, for objects that go
faster than light v/c is greater than one, E? .- p2c- is less than zero
and hence m2 is negative. In either case the rest mass squared
should always have the same value for a given object and can be
measured by measuring the energy and momentum for the object.
opposite direction produce the same ef-
fect on the energy of a system, it is al-
ways possible for any observer to insist
that all tachyons have positive energy,
and that emission and absorption take
place in the familiar time-ordering, thus
removing the instability problems that
negative-energy tachyons would present.
This interpretation of the negative-ener-
gy states of the tachyon was first pro-
posed in 1962 by O. M. P. Bilaniuk,
E. C. G. Sudarshan and V. K. Deshpande
of the University of Rochester.
The description given above is in
agreement with the principle of relativ-
ity requiring that any process that can
be seen by one observer must also be a
possible process for any other observer.
The principle does not require, however,
that different observers agree on the in-
terpretation of any individual process.
Hence there is no contradiction of the
principle of relativity involved in the
fact that one observer views as absorp-
tion what another views as emission,
since both absorption and emission can
be witnessed by either observer under
suitable conditions. The novelty of tachy-
ons is that emission and absorption must
be converted into each other by a change
in the observer's velocity, and this im-
plies a closer connection between the
two processes than exists for ordinary
particles.
It also implies that the number of
tachyons in some region of space must
vary from observer to observer. Suppose
one observer views the process of emis-
sion of a tachyon by an atom, with the
subsequent escape of the tachyon to in-
finity. A second observer may view the
same process as the tachyon's coming
in from outer space and being absorbed
by the atom. Hence the two observers
will disagree on the number of tachyons
present in the past and in the future.
Again this situation differs from that for
ordinary particles, where the number of
particles present at any time is inde-
pendent of the observer. A detailed theo-
ry of the interaction of tachyons with
ATOM A
ATOM B
TIME
ATOM A
ATOM B
TIME
0
to
0
0
-
---
0
>
t2
0
-- >
> ti
PECULIAR PROPERTY OF TACHYONS arises from the fact
that the time-ordering of points in "space time" between which a
faster than-light particle would move could vary from observer to
observer. Thus a process that appears to one observer as emission
of a tachyon by one atom followed by absorption of the tachyon by
another atom could be reversed for another observer moving with
respect to the first. In this schematic representation of such a
phenomenon the first observer (left) sees atom A at rest in its
ground state and atom B at rest in an excited state at time to. At #1
atom B emits a tachyon (color), dropping to its ground state and
recoiling (broken arrow). At to this tachyon is absorbed by atom A,
which jumps to an excited state and also recoils. In this situation
the time-ordering would be to, 11, to. To another observer (right),
for whom emission and absorption have been exchanged, the same
process would appear as follows: Atom A is now moving at time
to' but is still in its ground state. It emits a tachyon at to' and jumps
to an excited state, losing some of its translational energy. Atom B,
which is moving and in an excited state at to', absorbs the tachyon
at ty', dropping to the ground state and gaining translational
energy. For this observer the time sequence would be to, 19 4'-
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71
0
to
A
tı

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TIMĘ
TIME
to
0
to
V
- tı
tı
POPULATION OF TACHYONS in a region of space at any given time would also vary
from observer to observer. One observer (left) would view the emission of a tachyon by
an atom at rest, with the subsequent recoil to the atom and the escape of the tachyon to
infinity. A second observer (right) would view the tachyon coming in from outer space
and being absorbed by a moving atom, causing the atom to lose translational energy.
matter, which has not yet been worked
out, would have to take these features
into account.
J-Taving convinced ourselves that the
existence of faster-than-light parti-
cles does not imply any contradiction
of relativity, we must nevertheless leave
the determination of whether such ob-
jects really happen in nature to the ex-
perimental physicist. In the present state
of theoretical physics there are few cir-
cumstances in which theories flatly pre-
` dict that certain objects must exist. In-
stead these theories generally enable us
to describe various hypothetical objects,
and we must determine by experiment
which objects exist in reality. For exam-
ple, present theories allow for the de-
scription of particles with an electric
charge equal to half the electron's charge
and a mass six times the electron's mass,
but we are fairly confident from experi-
ments that no such objects are to be
found in nature. We do not, however,
know why this is so, and we may not
know until we have more fundamental
theories than we have now.
The situation with tachyons is similar;
to settle the issue of their existence one
turns to the experimentalist. This is not
to say, however, that he must hope to
stumble on them somewhere in the uni-
verse. One feature of all particle theories
based on relativity is that they imply that
if particles of some type exist at all, it
must be possible to create them from
other particles, provided that enough
energy is available. For tachyons this
condition of having enough energy is
particularly easy to satisfy, because fast
tachyons have very low energy. It is
therefore easy to set
experimental
condApproved For Release
be produced from other particles if
tachyons indeed exist. The only un-
known factor, apart from their existence,
is the rate at which they would be pro-
duced. Among known particles the pro-
duction rate varies by many orders of
magnitude. Pions, for instance, are pro-
duced quite readily, whereas neutrinos
are very difficult to produce. Therefore
whereas an experiment with a positive
result could establish the existence of
tachyons, a negative result could at best
establish an upper limit for the rate at
which tachyons are produced from the
particles involved. Only the demonstra-
tion that this rate, in all reactions stud-
ied, is much less than the rate of produc-
tion of any other particles would lead
to the conclusion that tachyons probably
do not exist at all.
Two kinds of experimental attempt to
produce and detect tachyons have
been made so far. These experiments are
sensitive to different types of tachyon
and use very different methods, and so
they will be discussed separately. The
first experiment, which was done two
years ago at Princeton University by
Torsten Alväger and Michael N. Kreisler,
was a search for electrically charged
tachyons. It has been known for 35 years
that electrically charged particles can be
produced in pairs by the passage of high-
energy gamma rays (photons) through
matter. Many of the known types of
charged elementary particle have been
made in this way. It follows that if elec-
trically charged tachyons exist, it should
be possible to produce them from pho-
tons. As indicated above, the fact that
tachyons can occur with zero total en-
ergy means that a pair of them can be
energy greater than twice the individ-
ual particle's rest energy.
Assuming that charged tachyons are
produced, how can they be detected and
distinguished from other charged parti-
cles that may be produced in the same
way, such as an electron-positron pair?
A convenient way to do this is to make
use of the fact that charged tachyons
would continuously radiate photons even
when passing through empty space. This
phenomenon, known as Cerenkov radia-
tion after the Russian physicist who first
observed it from electrons in 1937, oc-
curs whenever a charged object moves
through a substance at a speed higher
than the speed of light in the substance.
Thus an electron moving through glass
· at a speed greater than about .7 c will
emit Cerenkov radiation, since the speed
of light in glass is about .7 times its val-
ue in free space. Since the speed of a
tachyon is greater than that of light in
free space, one would expect the tachyon
to emit Cerenkov radiation even in a
vacuum, and a calculation confirms the
expectation: The light would be emitted
at a characteristic angle depending only
on the speed of the tachyon [ see illustra-
tion on opposite page]. Calculation also
shows that a tachyon with the same
charge as an electron would lose energy
so quickly through Cerenkov radiation
that even if it is produced with a very
high energy, its energy will drop below
one electron volt before it has traveled
one millimeter. When this happens, the
Cerenkov radiation will no longer in-
clude visible light, whose photons have
energies of more than two electron volts.
Instead the radiation will consist of infra-
red and longer wavelengths, which are a
good deal harder to detect. In order to
avoid this problem the Princeton experi-
menters used the ingenious scheme of al-
lowing any tachyons produced to move
through a region empty of matter but
containing an electric field. The electric
field would transfer energy to charged
particles, but it would not cause ordinary
particles to radiate detectable amounts
of light. A tachyon passing through the
region, on the other hand, would reach
an equilibrium between gaining energy
from the field and losing energy through
radiation, and would therefore continue
to radiate photons of about the equilibri-
um energy. By fixing the value of the
field, the experimenters were able to
make this equilibrium energy correspond
to photons of visible light, thus making
the radiation easy to detect.
2000/08/10* CIA RDP96-00787R00010003000719 väger and Kreis-
Viercas a pair of ordinary particles can
only be produced by a photon with an
ler used gamma rays from a radioactive
cesium source. These high-energy pho-

--
tons hit a lead shield that prevented clos; it is called the missing-mass meth-
will have the same value in each event,
them from reachingdoved di" Release 2000/08/10 : CIA-RDP96-00787R00010003000119is pro-
ly. Beyond the shield was a high-vacuum
region containing two parallel plates
with an electric field between them [sce
illustration on next page]. Pairs of
charged tachyons could be produced by
the photons in passing through the lead,
and some of these would escape (since
they speed up while losing energy) into
the region between the plates. A photo-
multiplier tube was used to detect any
photons radiated by the tachyons passing
through the region.
No positive indication of Cerenkov
radiation, and hence no evidence for
tachyon production, was found in this
experiment. More precisely, the rate of
production of tachyon pairs was found
to be less than one ten-thousandth of the
known rate for producing electron-posi-
tron pairs by photons of slightly higher
energy. The mass-energy relation satis-
fied by tachyons makes it highly unlikely
that this rate can depend very sensitively
on either the photon energy or the
tachyon mass. Therefore it seems, with
one qualification to be discussed below,
that tachyons with a charge approxi-
mately equal to the electron's charge
simply do not exist. Tachyons with a
charge differing from the electron's
charge by more than a factor of two in
the upward direction or .1 in the down-
ward direction would probably not have
been seen in the experiment. Of course,
uncharged tachyons, which would not
emit Cerenkov radiation, would not have
been detected either.
The qualification that must be made to
these conclusions is that it is uncer-
tain whether or not tachyons might lose
energy through processes other than
Cerenkov radiation. One such possibility
is that a single tachyon could decay into
several tachyons, each of lower energy.
If there were such other energy-loss
mechanisms, the amount of Cerenkov
radiation actually emitted might be
smaller than the anticipated amount,
and the value of the upper limit for the
number of tachyons produced would be
too low. For this reason, and because we
are in general ignorant about possible
interactions of tachyons with matter, it
was thought desirable to search for
tachyons in a manner independent of
how they interact after being produced.
Such an experiment was performed
recently by a group at Columbia Uni-
versity consisting of Charles Baltay,
Ralph Linsker, Noel K. Yeh and myself.
The method used was a well-known one
for searching for new elementary parti-
reactions among elementary particles are
examined in a detecting apparatus (in
our case a bubble chamber) in which the
momentum and energy of the charged
particles in the reaction can be mea-
sured. In some fraction of the reactions
a number of neutral particles will be pro-
duced in addition to the charged parti-
cles observed. These neutral particles are
usually not observed directly, and it is
often not even known how many of
them are produced. By applying the
laws of the conservation of energy and
momentum, however, it is possible to
tell from the values measured for the
charged particles whether or not any
neutral particles have been produced,
and also what the momentum and en-
ergy carried away by these particles are.
The latter quantities, defined as the dif-
ference between the energy or momen-
tum of the particles observed going into
the reaction and the energy or momen-
tum of the particles observed emerging
from the reaction, are known as the miss-
ing energy and momentum. If there are
no missing energy and momentum in a
given event, it suggests that no other
particles have been produced.
From the missing energy and momen-
tum in a specific event one can calculate
a "missing mass squared" for the event.
If exactly one missing neutral particle
has been produced, the missing mass
squared is the actual mass of the parti-
cle squared. A number of elementary
particles, such as the neutral cta meson,
have been detected in this way. The ob-
vious advantage of the method is that
nothing need be assumed about what the
missing particle does after being pro-
duced. Its presence is indicated simply
by the mass it represents, which is in-
ferred from measurements made on
known particles.
If a single neutral particle of a spe-
cific kind is produced, the missing mass
duced, the missing mass will not have a
unique value but will vary from event to
event, depending on the angle between
the directions of the two neutral parti-
cles, among other things. Hence those
events containing several neutral parti-
cles will in general show a distribution
in the missing mass squared over a range
of values. Since there is no way of know-
ing a priori whether a given event con-
tains one or many neutral particles, the
experimenter must combine all events to
obtain an overall distribution of missing
mass squared [see illustration on page
77]. The production of single particles
will usually stand out as a peak at a
specific value in the distribution of miss-
ing mass. If there is no such peak, it usu-
ally means that the production of a single
neutral particle is improbable compared
with the production of several neutral
particles.
In using the missing-mass method to
search for neutral tachyons, we note that
if a single neutral tachyon is produced,
the missing mass squared is a negative
number. Furthermore, if two or more
neutral tachyons are produced, the miss-
ing mass squared can be either positive
or negative depending on the configura-
tion. If the missing mass squared is ob-
served to be negative for any events,
then necessarily at least one tachyon
must have been produced among the
neutral particles. In other words, a col-
lection of ordinary particles cannot have
a negative mass squared. Hence in order
to investigate neutral-tachyon produc-
tion by means of specific incident parti-
cles, one makes a plot of the missing
mass squared for all events and looks for
any events with a negative missing mass
squared. The production of single tachy-
ons would give a peak in the missing-
mass-squared distribution at some nega-
tive value, whereas the production of
two neutral tachyons would give a broad
0
CERENKOV RADIATION would be emitted continuously by an electrically charged tachy-
on moving in a vacuum. The characteristic angle (0) at which the photons (black) would
be emitted would depend only on the speed of the tachyon: the faster the tachyon, the great-
er the angle. Ordinary charged particles, such as the electron, emit Cerenkov radiation
only when they move through a substance faster than the speed of light in the substance.
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73
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. ... .
. .. . .

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distribution of the total missing mass
squared, over both positive and negative
values, without any sharp peaks.
In our experiment two reactions were
studied. In one, negative K mesons
were allowed to come to rest and be cap-
tured by protons in a hydrogen bubble
chamber. One neutral particle, a lambda
hyperon, was produced and was detect-
ed through its decay in the bubble cham-
ber into two charged particles. (The mo-
mentum and energy of the lambda par-
ticle can then be inferred from the mea-
sured values for the charged particles.)
In order to conserve energy and momen-
tum other neutral particles had to be
produced. These were usually a single
neutral pion, or sometimes a neutral pion
and a photon. The events had all been
analyzed previously for other purposes,
so that the momentum and energy of the
charges were already measured. A plot
of the missing mass squared was made
for some 6,000 events involving the cap-
ture of a negative K meson. It should
be realized that in this case the missing
energy and momentum are defined as
the difference between the sum of the
initial values for the K meson and the
proton, and the values for the emerging
lambda particle, which, as indicated
above, can be inferred from its decay
products, even though it is neutral. In
our first set of measurements a number
of events were found with a negative
missing mass squared, which suggested
tachyon production. Caution, however,
suggested that various tests be made be-
fore this conclusion could be accepted.
One test involved making sure that
the K mesons were really at rest when
captured. If this were not the case, the
missing mass squared would be incor-
rectly calculated for a given event, since
in the calculation it was always assumed
that the meson was at rest when cap-
tured. If the direction of the lambda par-
ticle were nearly the same as the actual
direction of a K meson captured in flight,
then the missing mass squared could be
measured as negative when it was really
positive. Accordingly all events in which
the angle between the K meson and the
lambda particle was less than 60 degrees
were removed from the sample. For true
tachyon-production events this should
only reduce the number by the ratio of
remaining events to total events, where-
as it should eliminate all spurious nega-
tive-mass-squared events due to capture
in flight. When this test was carried out,
the number of events with negative miss-
ing mass squared was reduced to 23
from an original total of 101, indicat-
ing that most of the supposed tachyon
events were actually captures in flight,
producing ordinary particles.
The remaining events were carefully
remeasured to ensure that the missing
mass squared had been correctly mea-
sured. It was found in each case that the
true missing mass squared was positive
or zero, within the precision of the mca-
surements. Hence what was originally a
substantial number of tachyon-candidate
events was reduced, after careful study,
to none at all. By comparing the limit on
tachyon production (less than one) with
the total number of events seen, most of
which had a missing mass squared rep-
resented by a neutral pion, it can be in-
ferred that the rate of tachyon produc-
tion is less than one part in 400 of the
PHOTOMULTIPLIER
GAMMA RAY
SOURCE
Y
++
LEAD SHIELDING
VACUUM
EXPERIMENT designed to detect charged tachyons by means of
their Cerenkov radiation was carried out two years ago by Torsteni
Alväger and Michael N. Kreisler at Princeton University. They
used a radioactive cesium source to provide high-energy gamma
rays (y), which were allowed to hit a lead shield that prevented
them from reaching the detection apparatus directly. Pairs of
charged tachyons could be produced by the gamma ray photons in
high-vacuum region, which contained two parallel plates with an
electric field between them. The purpose of the electric field was to
transfer just enough energy to the tachyons to compensate for the
energy they lost through radiation, thus enabling them to continue
to radiate photons of visible light. A photomultiplier tube was used
to detect any photons radiated by the tachyons passing through
this region. No positive indication of Cerenkoy radiation (and
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a strong production process. Of course,
the tachyon production rate was also
consistent with zero.
A similar search by the same group,
carried out on the annihilation of anti-
protons with protons, gave no examples
of tachyon production and a similarly
low limit for the rate of tachyon produc-
tion in that reaction. In each of the ex-
periments single tachyons could be pro-
duced only if their mass squared was
within a specific range of values, and
hence the experiment tested single-
tachyon production only for particles in
that mass range. There are reasons to
believe, however, that single-tachyon
production is forbidden anyway, just
as single production of electrons with-
out other similar particles is forbidden.
Nonetheless, production of two tachy-
ons, or of tachyon-antitachyon pairs, is
not so forbidden. Such two-particle pro-
duction could occur in either experiment
no matter what the squared mass of the
individual tachyons was, and so the ex-
periments actually put rather sharp lim-
its on the production of tachyons of any
mass, except for values so near zero that
they are within the experimental error of
being positive.
Both of the direct experimental search-
es for tachyons that have been car-
ried out have therefore yielded negative
results. Indirect arguments have also
tended to restrict still further the pos-
sible interactions of tachyons. According
to one of these arguments, if charged
tachyons exist, the photon would not be
a stable object but instead would decay
within some time period into a pair of
charged tachyons. We know that pho-
tons can travel for billions of years across
intergalactic space without so decaying.
This implies that if charged tachyons
exist at all, then either their charge is
many orders of magnitude smaller than
that of the electron, which means that
they interact very weakly with photons,
or else their mass squared is very close
to zero, which makes them difficult to
distinguish from ordinary particles. Sim-
ilar conclusions can be drawn from in-
direct arguments about the very small
interactions of neutral tachyons.
The possibility that tachyons exist but
do not interact at all with ordinary par-
ticles need not concern us, because if
they do not interact with the objects that
compose our measuring instruments, we
have no possible way to detect them, and
or our purposes it is the same as if they
do not exist at all.
If we plausibly interpret the above
150
NUMBER OF EVENTS PER .002 BILLION ELECTRON VOLTS SQUARED
100
50
0
-. 15
-. 1
-. 05
0
.05
.1
MISSING MASS SQUARED (BILLIONS OF ELECTRON VOLTS SQUARED)
20
15
10
5
0
--. 15
-. 1
-. 05
0
.05
.1
MISSING MASS SQUARED (BILLIONS OF ELECTRON VOLTS SQUARED)
RESULTS of the analysis by the author and his colleagues at Columbia of some 6,000
bubble-chamber events involving the capture of a negative K meson are presented here in
the form of two curves representing the overall distribution of missing mass squared for all
events in terms of its energy equivalent in billions of electron volts squared. The highest
peak in each case corresponds to the production of single neutral pions. The production of
single neutral tachyons would result in a similar peak at some negative value of missing
mass squared, whereas the production of two neutral tachyons would give a broad distribu-
tion of the total missing mass squared over both positive and negative values without any
sharp peaks. In an early set of measurements (top) a number of events were found with a
negative missing mass squared, which suggested tachyon production. In a subsequent test
. (bottom), which involved rechecking some of the measurements, the number of events
with negative missing mass squared was reduced to essentially zero, indicating that most
of the supposed tachyon events were actually errors in the first set of measurements.
results to conclude that tachyons cannot
be produced at all from ordinary parti-
cles, we seem to be left with two possi-
bilities. One remote possibility is that
tachyons do interact with ordinary par-
ticles and can exchange energy with
them but cannot be produced from them.
This situation would strongly contradict
all our experience with relativistic quan-
tum theories of particles, and so it is im-
probable but perhaps not impossible.
The hypothesis could be tested by
searching for tachyons in natural phe-
nomena, such as cosmic rays. A difficulty
in carrying out such a search is that
tachyons should lose energy rapidly and
become hard to detect. The second pos-
sibility is that tachyons simply do not
exist, and that nature has not filled the
niche that is allowed by the theory of
relativity. If this is- the case, as now
seems probable, we may not understand
why it should be so until we reach a
much deeper understanding of the na-
ture of elementary particles than now
exists.
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