# PARTICLES THAT GO FASTER THAN LIGHT - SCIENTIFIC AMERICAN, FEBRUARY, 1970

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Fstablisled 18-17
AN February 1.970 Volume 222 Number 2
ARTICLES
13, THE ASSESSMENT OF TECHNOLOGY, by Ilarvey Brooks and Raymond
Bowers How can technology be fostered while avoiding undesirable effects?
22 LARGE-SCALE INTEGRATION IN ELECTRONICS, by F. C. Heath
Thousands Of circuit elements can now be simultaneously made onasingle "chip."
32 THE AFAR TRIANGLE, by Maroon Tazieff
A fantastic landscape beside the Red Sea appears to be an ocean in the making.
52 TIIE PHYSIOLOGY OF IIICII 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 LIGHT, by Gerald Feinberg
They have not been discovered, but there are reasons to believe they may exist.
82 PIIOSPIIENES, by Gerald Oster
The patterns eve see when we close our eyes are clues to how the eye works.
88 THE RANGELANDS OF THE WESTERN U.S., by R. Alerton 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.
9
10
42
112,
116
122
126
LETTERS
50 AND 100 YEARS AGO
THE AUTHORS
SCIENCE AND TIIE CITIZEN
MATHEMATICAL GAMES
TIIE AMATEUR SCIENTIST
BOOKS
BIBLIOGRAPHY
? OF EDITORS Gerard PICT (Publisher), Dennis Flanagan (Editor), Francis Bello (Associate Editor),
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Efforts to etect such particles, named tucllyo s, have yielded
only 71e~;atice results. C07111'(11) '"[0 conrrno71 belief. however, their
existence would not be inconsistent with the theory of relativity
by Gerald Feinberg
unce the formulation of the special
Stheory 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-
nium 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.
Furthennore, 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
SEARCH FOR TACIIYONS 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 parr
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
(Al), was produced and was detected through its decay into two charged particles, a nega-
tive pion (--') and a proton tp+). In order to conserve energy and momentum, another
neutral particle (xa) had to be produced in this reaction, but the experimenters were able
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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 in is known as the rest mass of the ob-
ject and is related to the energy E0 that the object has at rest by
equation b. For a body traveling faster than light v-'/c" 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 in to be an imaginary
number, say m= 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 (v'/c) - I
rest, this constant is not directly measur- trast, an increase in speed results in a
able, and there is no need for it to be decrease in energy. Hence a tachyon
real. The square of the rest mass, how- that was losing energy by interacting
ever, can be expressed in terms of the with matter or by radiating light would
measurable energy and momentum of an speed up, whereas a tachyon that was
object and hence can be directly mea- gaining energy from some outside source
sured. For ordinary objects the rest mass would slow down, and its speed would
squared is found to be a positive real approach c from above rather than be-
number. For faster-than-light particles low. Thus c acts as a limiting speed for
it would be a negative number; indeed, tachyons also, but the limit is a lower
this fact is the basis of one attempt to de- limit, rather than the upper limit that
tect such particles. It should be men- it is for ordinary objects.
tioned that there is a third class of parti- In the limiting case of a tachyon mov-
cles, including photons (light quanta) ing at infinite speed its total energy
and neutrinos, for which the rest mass is would be zero, although its momentum
zero and which always travel at c. would remain finite. It should be empha-
The possibility therefore seems to sized that for a tachyon at infinite speed
exist that there is a new kind of natural it is the total energy that is zero and not
object: one that always travels faster just the kinetic energy. For an ordinary
than light. The latter statement is in- particle with nonzero rest mass the total
variant, in the sense that if a body tray- energy can never vanish.
els faster than light with respect to one The condition of infinite speed is,
observer, it will do so with respect to any however, not invariant but depends on
other observer himself traveling in rela- the observer. If a tachyon were moving
tion to the first at less than the speed of at infinite speed as seen by one observer,
light. These are the only observers of its speed as measured by another ob-
which we have any knowledge. It must server in motion with respect to the first
be stressed that all the considerations would not be infinite but rather some
given here and below are consistent with finite value between c and infinity. This
the special theory of relativity, and as- is another way of phrasing Einstein's
sume the validity of its equations for de- discovery that simultaneity for events at
scribing particles, even if the particles different points in space has only a rela-
travel faster than light. tive and not an absolute nicaning.
~n 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 theirspeed increases, their en- cause of the ce nation of relativity that n r r~ rf ~s!~~1~t"j n the absorption of a
er~}pprey. F+Qfl Re*ap a 2QDWAWA, ; tT~E' ^ "Y'PC`t!4,497, ~I n{1~c6 ii 7i 00 G~i
l f. - tCR4'?'11'l`T .n
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 slumber 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-
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 Imown 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) atone time and
absorbed elsewhere (by atom 13) 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 $t and
absorbed by atom B at a later time t?,,
another observer could find that the time
t1' that he measures corresponding to tl
is later than the time t4' that he pleasures
corresponding to t_ If this occurs, the
latter observer would naturally want to
interpret what happens in the following
way: The tachyon is emitted by atom 13
at the earlier time t,' and absorbed by
atom A at the later time tt'.
It can be seen that this interchange of
emission and absorption also removes
the problem of negative-energy tachy-
ons, since the reversal betwccti 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-
~41eetwt 2000/08/10: CIA-RD4
E2 - p2c2 = m2c4
-0078ZRC~010Q9 001-9
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 in is indepen-
dent of v. It follows from a combination of this equation and equa-
tion a that the quant.ity represented by equation e does not depend
on v and hence is the same for all observers. The quantity ni'
(called the rest crass squared) is then a constant for each object,
even for bodies such .as photons (light quanta) or tachyons, which
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 0. M. Y. 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
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, E2 - psc- 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, E2 - p'c2 is less than zero
and hence nis 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.
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.
TIME - I
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 taehyon 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 all excited state at time te. At ti
atom B emits a taehyon (color), dropping to its ground state and
recoiling (broken arrow). At t_ this tachyou is absorbed by atom .4,
which jumps to all excited state and also recoils. In this sit.nation
the tine-ordering would be tar, tt, t.,. 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 t.,' and jumps
to an excited state, losing some of its translational energy. Atom 11,
which is moving and in an excited Mate at to', absorbs the taehyon
at tt', dropping to the ground state and gaining translational
energy. For this observer the time sequence would be to', t..', tn'.
Approved For Release 2000/08/10 : CIA-RDP96-00787R000100030001-9
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 taehyon by an atom, with the
subsequent escape of the tacltyon 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
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CO)
TIME
to
POPULATION OF TACHHYONS 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 coining 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.
Having 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 he 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.. eneirgy. Itt is
coed 1e~~NcYe~ ltic~r ~~
~t