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The Left Hand of the Electron |
2 - THE LEFT HAND OF THE ELECTRON
I received a letter yesterday which criticized my writing style.
It complained, 'you avoid the poetic to the extent that when a cryptic, glowing,
"charged" phrase occurs to you, I'd be willing to bet that you deliberately
put it aside and opt for a clearer but more pedestrian one.'
All I can say to that is that you bet your sweet life I do.
As all who read my volumes of science essays must surely be aware, I have
a dislike for the mystical approach to the universe,
whether in the name of science, philosophy, or religion. I also have a dislike
for the mystical approach to literature.
I dare say it is possible to evoke an emotional reaction through
a 'cryptic, glowing, "charged" phrase' but you show me a cryptic phrase and
I'll show you any number of readers who, not knowing what it means but afraid
to admit their ignorance, will say, 'My, isn't that poetic and emotionally
effective.'
Maybe it is, and maybe it isn't; but a vast number of literary
incompetents get by on the intellectual insecurity of their readers, and
a vast number of hacks write a vast quantity of bad 'poetry' and make a living
at it.
For myself, I manage to retain a certain amount of intellectual
security. When I read a book that is intended (presumably) for the general
public and find that I can make neither head nor tail of it, it never occurs
to me that this is because I am lacking in intelligence. Rather, I reach
the calmly assured opinion that the author is either a poor writer, a confused
thinker, or, most likely, both.
Holding these views, it is not surprising that I 'opt for a
clearer but more pedestrian' style in my own writing. For one thing, my business
and my passion (even in my fiction writing) is to explain. Partly
it is the missionary instinct that makes me yearn to make my readers see
and understand the universe as I see and understand it, so that they may
enjoy it as I do. Partly, also, I do it because the effort to put things
on paper clearly enough to make the reader understand, makes it possible
for me to understand, too.
I try to teach because whether or not I succeed in teaching
others, I invariably succeed in teaching myself.
Yet I must admit that sometimes this self-imposed task of mine is harder
than other times. Continuing the exposition on parity and related topics
begun in Chapter 1 is one of the harder times,
but then no one ever promised me a rose garden, so let's continue.
The conservation laws are the basic
generalizations of physics and of the physics aspects of all other sciences.
In general, a conservation law says that some particular overall measured
property of a closed system (one that
is not interacting with any other part of the universe) remains constant
regardless of any changes taking place within the system. For instance, the
total quantity of energy within a closed system is always the same regardless
of changes within the system and this is called 'the law of conservation
of energy'.
The law of conservation of energy is a great convenience to
physicists and is probably the most important single conservation law, and
therefore the most important single law of any kind in all of science. Yet
it does not seem to carry a note of overwhelming necessity about it.
Why should energy be conserved? Why shouldn't the energy
of a closed system increase now and then, or decrease?
Actually, we can't think of a reason, if we think of energy only. We simply
have to accept the law as fitting observation. The conservation laws, however,
seem to be connected with symmetries in the
universe. It can be shown, for instance, that if one assumes
time to be symmetrical, one must expect energy
to be conserved. That time is symmetrical means that any portion of it is
like any other and that the laws of nature therefore display
'invariance with time' and are the same at any
time.
In a rough and ready way, this has always been assumed by mankind
- for closed systems. If a certain procedure lights a fire or smelts copper
ore or raises bread dough on one day, the same procedure should also work
the next day or the next year under similar conditions. If it doesn't, the
assumption is that you no longer have a closed system. There may be interference
from the outside in the form (mystics would say) of a malicious witch or
an evil spirit, or in the form (rationalists would say) of unexpected moisture
in the wood, impurities in the ore, or coolness in the oven.
If we avoid complications by considering the simplest possible
forms of matter - subatomic particles moving in response to the various fields
produced by themselves and their neighbors - we readily assume that they
will obey the same laws at any moment in time. If a system of subatomic particles
were to be transferred by some time machine to a point in time a century
ago or a million years ago, or a million years in the future, the change
in time could not be detected by studying the behaviour of the subatomic
particles only. And if that is true, the law of conservation of energy
is true.
Of course, invariance with time is just as much an assumption
as the conservation of energy is, and assumptions may not square with
observation. Thus, some theoretical physicists have speculated that the
gravitational interaction may be weakening in intensity very slowly with
time. In that case, you could tell an abrupt change in time by noting (in
theory) an abrupt change in the strength of the gravitational field produced
by the particles being studied. Such a change in gravitational intensity
with time has not yet been actually demonstrated, but if it existed, the
law of conservation of energy would be not quite true.
Putting that possibility to one side, we end with two equivalent
assumptions:
(1) energy is conserved in a closed system, and
(2) the laws of nature are invariant with time.
Either both statements are correct or both are incorrect, but it is the second,
it seems to me, that seems more intuitively necessary to us. We might not
be bothered by having a little energy created or destroyed now and then,
but we would somehow feel very uncomfortable with a universe in which the
laws of nature changed from day to day.
Consider, next, the law of conservation of momentum. The total
momentum (mass times velocity) of a closed system does not vary with changes
within the system. It is the conservation of momentum that allows billiard
sharps to work with mathematical precision. There is also an independent
law of conservation of angular momentum, where circular movement about some
point or line is considered.)
Both conservation laws, that of momentum and that of angular
momentum, depend on the fact that the laws of nature are invariant with position
in space. In other words, if a group of subatomic particles is instantaneously
shifted from here to the neighborhood of Mars, or of a distant galaxy, you
could not tell by observing the subatomic particles alone that such
a shift had taken place. (Actually, the gravitational intensity due to
neighboring masses of matter would very likely be different, but we are dealing
with the ideal situation of fields originating only with the particles within
the closed system, so we ignore outside gravitation.)
Again, the necessity of invariance with space is more easily
accepted than the necessity of the conservation of momentum or of angular
momentum. Most other conservation laws also involve invariances of this sort,
but not of anything that can be reduced to such easily intuitive concepts
as the symmetry of space and time. -Parity is an exception.
In 1927, the Hungarian physicist
Eugene P. Wigner showed that conservation
of parity is equivalent to right-left symmetry.
This means that for parity to be conserved there must be no reason to prefer
the right direction to the left or vice versa in considering the laws of
nature. If one billiard ball hits another to the right of center and bounces
off to the right, it will bounce off to the left in just the same way if
it hits the other ball to the left of center.
If a ball bouncing off to the right is reflected in a mirror
that is held parallel to the original line of travel, the moving ball in
the mirror seems to bounce off to the left. If you were shown diagrams of
the movement of the real ball and of the movement of the mirror-mage ball,
you could not tell from the diagrams alone, which was real and which the
image. Both would be following the laws of nature perfectly well.
If a billiard ball is itself perfectly spherical and unmarked
it would show left-right symmetry. That is, its image would also be perfectly
spherical and unmarked, and if you were shown a photograph of both the ball
itself and the image, you couldn't tell which was which from the appearance
alone. Of course, if the billiard ball had some asymmetric marking on it,
like the number 7, you could tell which was real and which was the image,
because the number 7 would be 'backward' on the image.
The trickiness of the mirror-image business is confused because
we ourselves are asymmetric. Not only are certain inner organs (the liver,
stomach, spleen, and pancreas) to one side or the other of the central plane,
but some perfectly visible parts (the part in the hair, as an example, or
certain skin markings) are also. This means we can easily tell whether a
picture of ourselves (or some other familiar individual) is of us as we are
or of a mirror image by noting that the part in the hair is on the 'wrong
side', for instance.
This gives us the illusion that telling left from right is
an easy thing, when actually it isn't. Suppose you had to identify left
and right to some stranger where the human body could not be used as reference,
to a Martian who couldn't see you, for instance. You might do it by reference
to the Earth itself if the Martian could make out its surface, for the
continental configurations are asymmetric, but what if you were talking with
someone far out near Alpha Centauri.
The situation is more straightforward if we consider sub- atomic
particles and assume them (barring information to the contrary) to be left-right
symmetric, like perfecfly spherical unmarked billiard balls. In that case
if you took a photograph of the particle and of its mirror image, you could
not tell from the appearance alone which was particle and which mirror
image.
If the particle were doing something toward our left, then
the mirror image would be doing the equivalent toward our right. If, however,
both the leftward act and the rightward act were equally possible by the
laws of nature, you still couldn't tell which was particle and which was
mirror image. -And that is precisely the situation that prevails when the
law of conservation of parity holds true.
But what if the law of conservation of parity is not true under
certain conditions. Under those conditions, then, the particle is asymmetric
or is working asymmetrically; that is, doing something leftward which can't
be done rightward, or vice versa. In that case, you can say, 'This is the
particle and this is the image. I can tell because the image is backward
(or because the image is doing something which is impossible).'
This is equivalent to recognizing that a representation of
a friend of ours is actually a mirror image because his hair part is on the
wrong side or because he seems to be writing fluently with his left hand
when you know he is actually right-handed.
When Lee and Yang (see Chapter 1)
suggested that the law of conservation of parity didn't hold in weak nuclear
interactions, that meant one ought to be able to differentiate between a
weak nuclear event and its mirror image.
-And one common weak nuclear event is the emission of an electron by an atomic
nucleus.
The atomic nucleus can be considered as a spinning particle,
which is symmetrical east and west and also north and south just as the Earth
is). If we take the mirror image of the particle (the 'image-particle'),
it seems to be spinning in the 'wrong direction', but are you sure? If you
turn the image-particle upside down, it is then spinning in the right direction
and it still looks just like the particle. You can't differentiate between
the particle and the image-particle by the direction of its spin because
you can't tell whether the particle or the image-particle is right side up
or upside down. As far as spin is concerned, an upside-down image-particle
looks just like a right-side-up particle.
Of course, a spinning particle has two poles, a north pole and
a south pole, and to all appearances we can tell which is which. By lining
the particle up with a strong magnetic field we can compare the direction
of the particle's axis of rotation with that of the Earth and identify the
north and south pole. In that way we could tell whether the particle was
right side up or upside down.
Ah, but we are using the Earth as a reference here and the Earth
is asymmetric thanks to the position and shape of the continents. If we didn't
use the Earth as reference (and we shouldn't because we ought to be able
to work out the behavior of subatomic particles in deep space far from the
Earth) there would be no way of telling north pole from south pole. Whether
we considered spin or poles, we couldn't tell a symmetrical particle from
its mirror image.
But suppose the particle gives off an electron. Such an electron
tends to fly off from one of the poles, but from which? Suppose it could
fly off from either pole with equal ease. In that case, if we were dealing
with a trillion nuclei giving off a trillion electrons, half would fly off
one pole and half off the other. We could not distinguish one pole from the
other and we still couldn't distinguish the particle from the image-particle.
On the other hand, if the electrons tended to come off from
one pole more often than from the other, we would have a marker for one of
the poles. We could say, 'Viewing the particle from a point above the pole
that gives off the electrons, it rotates counter-clockwise. That means that
this other particle is actually an image-particle, because viewed in that
manner it rotates clockwise.'
This is exactly what should be true if the law of conservation
of parity does not hold in the case of electron emission by nuclei.
But is it true? When atomic nuclei (trillions of them) are shooting off
electrons, the electrons come off in every direction equally - but that is
only because the nuclear poles are facing in every direction, in which case
electrons would shoot off in all ways alike whether they were coming from
one pole only or from both poles equally.
In order to check whether the electrons are coming from both
poles or from one pole only, the nuclei must be lined up so that all the
north poles are pointing in the same direction. To do this, the nuclei must
be lined up by a powerful magnetic field and must be cooled to nearly absolute
zero so that they have no energy that will vibrate them out of line.
After Lee and Yang made their suggestion, Madame Chien-Shiung
Wu, a fellow physics professor at Columbia University, performed exactly
this experiment. Cobalt-60 nuclei, lined up appropriately, shot electrons
off the south pole, not the north pole.
In this way, it was proven that the law of conservation of
parity did not hold for weak nuclear interactions. This meant one could
distinguish between left and right in such cases, and the electron, when
involved in weak nuclear interactions, tended to act leftward rather than
rightward, so that it can be said to be 'left-handed'.
The electron, which carries a unit negative electric charge,
has another kind of 'image'. There is a particle exactly like the electron,
but with a unit positive electric charge. It is the 'positron'.
Indeed every charged particle has a twin with an opposite charge, an
'antiparticle'. There is a mathematical
operation which converts the expression that describes a particle into one
that describes the equivalent antiparticle (or vice versa). This operation
is called 'charge conjugation'.
As it happens, if a particle is left-handed, its antiparticle is right-handed,
and vice versa.
Observe then, that if an electron is doing something left-handedly,
its mirror image would seem to be an electron doing it right-handedly, which
is impossible - and the impossibility would serve to distinguish the image
from the particle.
On the other hand, if you employed the charge conjugation operation,
you would change a left-handed electron into a left-handed positron. The
latter is also impossible and this impossibility would serve to distinguish
the image from the particle.
In weak nuclear interactions, then, not only does the law of
conservation of parity break down, but also the law of conservation of charge
conjugation.*
| * Both conservation laws are true in strong nuclear interactions, however. In strong nuclear interactions, not only are leftward and rightward equally natural at all times, but anything a charged particle can do, the oppositely charged antiparticle can also do. |
However, suppose you not only alter the right-left of the electron
by imagining its mirror image, but also imagine that at the same time you
have altered the charge from negative to positive. You have effected both
a parity change and a charge conjugation change. The result of this double
shift would be the conversion of a left-handed electron into a right-handed
positron. Since left-handed electrons and right-handed positrons are both
possible, you cannot tell by simply looking at a diagram of each, which is
the original particle and which the image.
In other words, although neither parity nor charge conjugation
is conserved in weak nuclear interactions, the combination of the two is
conserved. Using abbreviations we say that there is neither P conservation
nor C conservation in weak nuclear interactions, but there is, however, CP
conservation.
It may not be clear to you how it is possible for two items
to be individually not conserved, yet to be conserved together. Or (to
put it in equivalent fashion) you may not see how two objects, each easily
distinguishable from its mirror image, are no longer so distinguishable if
taken together.
Well, then, consider-
The letter b, reflected in the mirror is d. The letter d, reflected in the
mirror is b. Thus, both b and d are easily distinguished from their mirror
images.
On the other hand, if the combination bd is reflected in a mirror, the image
is also bd. Both b and d are individually inverted and the order in which
they occur is inverted, too. All the inversions cancel and the net result
is that although b and d are altered by reflection, the combination bd is
not. (Try it yourself with printed lower-case letters and a mirror.)
Let's point out one more thing about left-right reflection.
Suppose the solar system were reflected in a
mirror. If we observed the image, we would see that all the planets were
circling the Sun the 'wrong way' and that the Moon was circling the Earth
the 'wrong way', and that the Sun and all the planets were rotating on their
axes the 'wrong way'.
If you ignored the asymmetry of the surface structure of the
planets, and just considered each world in the solar system to be a featureless
sphere, then you could not tell the image from the real thing from their
motions alone. The fact that everything was turning the 'wrong way' means
nothing, for if you observe the image while standing on your head, then
everything is turning the 'right way' again, and in outer space there is
no way of distinguishing between standing 'upright' and standing 'on your
head'.
And certainly the gravitational interaction, which is the
predominant factor in the solar system's working, is unaffected by the reversal
of right and left. If all the revolutions and rotations in the solar system
were suddenly reversed, gravitational interactions would account for the
reversed motions as adequately and as neatly as for the originals.
But consider this-
Suppose that we didn't use a mirror at all. Imagine, instead, that the direction
of time reversed itself. The result would be like that of running a movie
film backward. With time reversed, the Earth would seem to be going 'backward'
about the Sun. All the planets would seem to be going 'backward' about the
Sun, and the Moon to be going 'backward' about the Earth. All the bodies
of the solar system would be spinning 'backward' about their axis.
But notice that the 'backward' that takes place on reversing
time, is just the same as the 'wrong way' that takes place in the mirror
image. Reversing the direction of time flow and
mirror-imaging space produce the same effect. And there is no way of telling
from observing the motions of the solar system alone whether time is flowing
forward or backward. This inability to tell the direction of time flow is
also true in the case of subatomic reactions (T conservation).*
| * We can tell the direction of time flow under ordinary conditions easily enough because of entropy-change effects. This produces the equivalent of an asymmetry in time. Where entropy change is zero, however, as in planetary motions and subatomic events, T is conserved. |
Or consider this-
An electron moving through a magnetic field pointing in a particular direction
will veer to the right. The positron, with an opposite charge, would, when
moving in the same direction through the same magnetic field, veer to the
left. The two motions are mirror images, so that in this case the shift from
a charge to its opposite also produces the same effect as a left-right shift.
Or suppose we reverse the direction of time flow. An electron
moving through a magnetic field may veer to its right, but if a picture is
taken of the motion and the film is reversed and projected, the electron
will seem to be moving backward and, in doing so, will veer to its left.
Again, time flow and left-right symmetry are connected.
It would seem then that charge conjugation (C), parity (P),
and time reversal (T) are all rather closely related and all somehow connected
with left-right symmetry. If, then, left- right symmetry breaks down in weak
nuclear interaction with respect to one of these, the symmetry can be restored
with one or both others.
If a particle is doing something leftward, and its image is
doing something rightward, which is impossible (so that the image can be
spotted through a breakdown in P con- servation), you can reverse the charge
on the image-particle and convert the action into a possibility. If the action
is impossible even with the reversed charge (so that the image can be spotted
through a breakdown in CP conservation), you can reverse the direction of
time flow, and then you will find the action is possible. In other words,
there is 'CPT conservation' in the weak nuclear interaction.*
| * Actually, there was some indication in recent years that CPT is not invariably conserved in weak nuclear interactions and physicists have been examining the possible consequences in rather perturbed fashion. However, all the returns don't seem to be in here and we'll have to wait and see. |
The result is that the universe is symmetrical, as it has always
been thought to be, with respect to strong nuclear interactions, electromagnetic
interactions and gravitational interactions.
Only weak nuclear interactions have been in question and there the failure
of the law of conservation of parity seemed to introduce a basic asymmetry
to the universe. The broadening of the concept to CPT conservation restored
the symmetry - but only in theory.
Does CPT conservation actually present us with a symmetrical
universe in practice? As far as P (parity) is concerned, there is an equal
supply of rightness and leftness in the universe. As far as T (time reversal)
is concerned, there is also an equal supply of pastness and futureness. But
where C (charge conjugation) is concerned, symmetry in practice breaks
down.
The most common subatomic particles to be involved in weak
nuclear interactions are the electron and the neutrino. For symmetry to
exist in practice, then, there should be equal supplies of electrons and
positrons and equal supplies of neutrinos and antineutrinos. This, however,
is not so.
Certainly on Earth, almost certainly throughout our
Galaxy, and, for anything we know to the contrary, throughout the entire
universe, there are vast numbers of electrons and neutrinos, and hardly any
positrons and anti- neutrinos.
The universe then - at least our universe - or at the very least
our section of our universe is electronically left-handed and that
may have had an interesting effect on the development of life.
In order to explain that, I must change the subject radically, however, and
make a new start. That I will do in the next chapter.
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The Left Hand of the Electron |