CHAPTER 9
COSMIC NOISE
I am embarked on a program to show that
there are no general laws that govern (or describe) the physical universe. The laws that we have are either (1)
man-made, as I believe that the conservation laws are, or (2) like Newton's laws
of motion, they are not fundamental and can be derived from other more
fundamental laws, or (3) they are descriptions of the way that specific things,
like electrons and protons, behave.
The laws of electromagnetism I believe, fall into this last
category. The other laws Ð
Newton's laws of motion and the conservation laws Ð can be derived from the
laws of electromagnetism. The fact that all these laws can be unified provided
scientists like Einstein with encouragement to work for a complete unification of
all of our scientific information. But no one has yet been successful in this
enterprise. In my analysis I have said that general laws imply design. The fact
that laws, like Maxwell's laws, summarize the information contained in a number
of other laws does not make them general laws. But I do have an outstanding
problem that requires explanation if I am to claim that there is no discernible
design in the universe: Why are the laws of electromagnetism as mathematically
simple as they are? I have never
written down these laws for you either in the form of Maxwell's equations or in
the form of the interaction between two charges because, although I say they
are mathematically simple, they are far more complicated than Newton's laws of
motion. They are often not even presented in their full form in the first
university course in Physics taken by Physics majors. In the simple case of two interacting stationary electric
charges, the accelerations depend on the inverse square of the distance between
the charges. It is this kind of
simplicity that I think must be explained or it will seem that a designer has
been at work.
The order that we find in the physical
world, as I see it, stems from the natural recurrences of the three fundamental
particles: electrons, protons and neutrons. Why there are natural recurrences needs explanation but it
is not unreasonable that, if we can explain, by a theory of evolution, natural
recurrences of plants and animals, the explanation of recurrences of
fundamental particles should also be possible.
So far I have ignored gravitational
interaction and I will continue to ignore it for a while. I have ignored nuclear interaction Ð
the interaction between protons and neutrons in the nucleus of an atom. We do not yet have a really clear
description of this interaction
except to realize that when nucleons (protons and neutrons) are close enough
together there is some mechanism which holds them together. The electromagnetic repulsion between
protons continues to exist but a different mechanism, superimposed on the
repulsion, causes them to be attracted at short-range. This nuclear attraction is the same
between proton and proton, neutron and neutron, or proton and neutron. We say it is
"charge-independent" meaning that it exists whether the nucleon is
electrically charged or not. This
seems to indicate that it is a distinct nuclear mechanism which coexists with
the electromagnetic interaction. Whatever the nuclear interaction is, the
"law of nuclear interaction" will be of the same type as the
"law of electromagnetic interaction" and will be explainable, in the
same sort of way, as a description of the behavior of fundamental objects that
recur naturally.
Another whole set of facts that I am
ignoring, because they seem tentative, are the investigations going on about
fundamental particles. This means
that I am ignoring all the observed spectrum of particles: the leptons,
hadrons, and baryons, as well as the more fanciful quarks, gluons, and
so-ons. It is not that I do not
think this particle research is extremely important but I do not believe that
we have really settled on any laws.
Even if we had, they would again fall into my category of descriptions
of specific objects that recur naturally.
The simplicities would require explanation, but that is what many of the
attempts to systematize the spectrum of observed particles are concerned with.
All sorts of concepts are introduced like "color" and
"charm" to try to make it easier to analyze particle physics but, of
course, these are man-made.
Perhaps it would be a good idea to record
a list of all the laws of physics that I must come to grips with in this
exploration of mine. F.W. Constant
wrote a textbook in l963 called Fundamenta Laws of Physics. Here is his list (Some of the laws have
not yet been mentioned):
I. Newton's
law of motion (second).
II. Newton's
law of action and reaction (third).
III. Newton's
law of gravitation.
IV. The
conservation of energy principle.
V. The
degradation of energy principle (or second law of thermodynamics).
VI. Huygens'
principle of wave propagation.
VII. Coulomb's
law of electrostatic force.
VIII. Ampere's
law of magnetic force.
IX. Faraday's
law of electromagnetic induction.
X. Maxwell's
law of magnetoelectric induction.
XI. The
relativity principle.
XII. The
quantum principle.
XIII. Pauli's
exclusion principle.
XIV. Conservation
of matter principle.
XV. The
law(s) of nuclear force. [1]
First of all I must point out again that, to
Constant, a fundamental law means something very specific:
The great laws of physics are those that express
principles or relations which are independent of the specific properties of
certain materials or objects.
These laws will therefore be called our fundamental laws; they must be distinguished from those restricted
laws which apply only to certain
materials and only under a limited range of conditions. By their nature, fundamental laws are
not derivable from anything else; they are our starting points in the various
branches of physics. [2]
I have been putting forward the thesis that there are
no "principles or relations which are independent of the specific
properties of certain objects".
My fundamental laws are in fact the description of the behavior of
objects Ð objects that are fundamental in the sense that the whole universe is
composed of these objects.
I will refer in turn now to the different
laws in Constant's list of fundamental laws. I have said that Newton's laws (if we ignore the law of
gravitation) can be explained by referring to the more fundamental laws, the
laws of electromagnetism, which Constant separates into the four laws: VII to
X. These four are summarized in
Maxwell's laws of electromagnetism, or the laws of interaction between two
electric charges. Law IV, the conservation
of energy, I have indicated to be only an alternative formulation of other
laws. The relativity principle (XI) is partly contained in Newton's first law
of motion which was extended by Einstein to relate to the laws of
electromagnetism. I will be
writing in detail about this in
the chapter called "Trapped Inside". The "inside" referred to is inside the
universe. We can only observe the
behavior of objects inside the universe and, as I indicated in the chapter on
"The Impossibility of Isolation", the universe is more than a background
for observing behavior. In the
present chapter, which I have given the science-fiction style title
"Cosmic Noise", I want to explore a second facet of the influence of
the universe (cosmos) on the fundamental objects.
This investigation will deal first with
what Constant calls the "degradation of energy principle (or second law of
thermodynamics)" and here the influence of the immediate surroundings on
systems of objects (atoms or molecules) is described. Then I will look at the influence of the universe as a whole
on the particles, as individuals, and will be coming to terms with part of the
information contained in what Constant calls the "quantum principle".
Number XIII, "Pauli's exclusion principle", will have to wait until
after the next chapter when I discuss "The Stochastic Atom".
Just to complete the examination of
Constant's list of fundamental laws, I will mention the others. The one he calls "Huygens'
principle of wave propagation" will be discussed in the chapter on
"The Two-Slit Mystery".
There I will show that it is information contained in Maxwell's
laws. That leaves the
"Conservation of matter principle". Again this is not a general law really but a description of
the universe: that the numbers of electrons, protons, and neutrons do not seem
to change with time. They are
extremely durable. I have already
hinted at the possibility that this durability may not be a static situation,
where a particle just continues to exist in perpetuity, but perhaps a dynamic
situation, in which the particle is constantly decaying (disintegrating) and
constantly being renewed (rebuilt).
In this chapter I will concentrate then
on "the law of degradation of energy" and "the quantum
principle". For both of these
I will invoke the influence of the environment on a particle or a system of
particles. By environment, I mean
the rest of the universe, excluding the system of particles itself. It is not usual to pay very much
attention to the rest of the universe as far as environment is concerned. Resnick and Halliday say this:
The motion of a given particle is determined by the
nature, and arrangement of the other bodies that form its environment. In
general, only nearby objects need to be included in the environment, the
effects of more distant objects usually being negligible. [3]
This clearly states the position that the
effect of distant objects is usually ignored. What Resnick and Halliday call the environment is what we
think of as the interacting objects.
The effect of any one interacting object decreases as its distance from
the particle, whose environment it creates, increases. Since the effect of any one object
becomes negligible it is not unreasonable to assume that the effect of the
totality of all the objects out there, that form the rest of the universe, is
negligible. What I will argue in
this chapter is that the effect of all those objects, which of course are made
of electrons, protons, and neutrons, is not negligible but is taken into
account in four different ways.
None of the ways in which the objects "out there" affect a
particular object is directly attributed to those objects by most scientists. I
have already discussed the fact that it is those objects that create inertial
frames of reference. In this
chapter, I will attribute to those objects what is called the degradation of
energy principle and the quantum principle; in a later chapter I will indicate
that, if the effect of the objects out there is interfered with by some sizable
nearby object, the result is an attraction to that nearby object. The nearby massive object casts a
shadow, if you will, on the particular object under study and makes the effect
of the rest of the objects of the universe asymmetric. That is how I will explain gravity.
Before I launch into a discussion of
these different effects I want to tell you of an incident that happened in
l96l. Dr. Donald Ivey and I were
asked by the Physical Science Study Committee to make a film called
"Universal Gravitation".
We wanted in it to show the motion of a planet around a sun graphically,
by animation. We were told that
this would be possible by using an analog computer at the Lincoln Laboratory of
the Massachusetts Institute of Technology. One afternoon we went to the
laboratory and were given a demonstration. One spot on the screen of a cathode ray tube was stationary
while a second spot was moved about it to represent a planet moving around the
sun (or a satellite moving around a planet). The position of the moving spot was calculated, according to
Newton's law of gravitation, using the analog computer. Analog computers were,
at that time, much faster machines for making this kind of calculation than
digital computers. They could move
the spot along reasonably quickly and give a lively display. But analog computers are not as
accurate as digital computers in that they effectively work only to an accuracy
of 2 or 3 significant digits; digital computers can operate with six or more
significant figures. This meant
that the planet's orbit on the screen of the cathode ray tube did not behave as it ought to
behave according to Newton's laws of motion and law of gravitation. It should have moved in an elliptic
orbit with the sun at one focus and repeated this orbit time after time. What always happened was that the orbit
changed its orientation all the time; it precessed. If the same thing had been done using a modern digital
computer the effect would not have been as noticeable but it would still have
been there.
All calculations that we can do on real
numbers have, in the end, a limit to their precision and, as time goes on, the
orbit would get "out of whack". This demonstration made an indelible
impression on me. Why doesn't a
real planet get "out of whack"?
Is there no limit to the accuracy with which "nature"
operates?
The limited precision with which any
computer represents real numbers introduces a random element into the results
of its calculation. This random
element can be made smaller and smaller by using greater precision but it cannot be eliminated.
It occurred to me that this must also be the case with the way the
universe operates. There must be
an end, a limit to the precision of the operation of laws and, in this limit,
there must be a random element operating.
Real planets do not behave as our graphical planets did. Why not?
There are two places in physics where
random elements are admitted to be present and where the future is not
precisely predictable, but is
instead probabalistically predictable.
These two places are in the second law of thermodynamics and in the
quantum principle. But where does
the randomness arise? The laws
that we have looked at so far have no such element in them; they are
deterministic. If a known
situation exists, what happens next is precisely predictable. We say there is a causal connection between the present state and a future
state. A law will let you
calculate the future state precisely, if you know the present state
precisely. And, in fact, the law
will tell you precisely what the past states were. Danto and Morgenbesser wrote in their book on the Philosophy
of Science:
The initial state is sometimes spoken of as determining every other state of a physical system (it being
arbitrary which state we chose as initial) Ð assuming the system to be
isolated. The concept of
"isolated system" is difficult to explicate, and many argue that the
only instance of an isolated system is the universe itself. [4]
The implication of this is that any departure from
deterministic behavior might be attributed to the fact that isolation is
impossible. But we have happily
assumed that systems that we were
studying, whether they be two particles colliding, many particles colliding,
many particles in a cluster breaking up, or two particles in an atom, were able
to be isolated or maintained in an environment with which there was no net
exchange of energy. Mach indicated that it was essential for progress to focus
on part of the whole universe, not on everything at once:
It is certainly fortunate for us, that we can, from
time to time, turn aside our eyes from the overpowering unity of the All, and
allow them to rest on individual details.
But we should not omit, ultimately to complete and correct our views by
a thorough consideration of the things which for the time being we left out of
account. [5]
Surely it is time to consider "the things which
for the time being we left out of account".
We seem to be getting along very well
without taking the environment into account. But to get along we must attribute a probabalistic (random)
element to the system under study.
David Bohm, in his book Causality and Chance in Modern Physics, suggests that the random influences (contingencies)
might better be related to all the rest of the universe:
Every real causal relationship, which necessarily
operates in a finite context, has been found to be subject to contingencies
arising outside the context in question... For example, in the motion of the
planets, contingencies are still quite unimportant for all practical
purposes... Now here it may be
objected that if one took into account everything in the universe, then the
category of contingency would disappear, and all that happens would be seen to
follow necessarily and inevitably.
[6]
Bohm explains that we resort to
probabalistic calculations and speak of randomness and chance because we do not
have enough information about all the details of the interaction with the rest
of the universe. The events do not really happen by chance; we use chance as a
cover for our own ignorance.
In this book I am trying to maintain that
the question of whether the present state of the universe is the result of
chance or design (or a combination of chance and design) is an unanswerable
question. Most of my effort so far has been spent in trying to show that the
evidence for design, through the existence of general laws, is illusory.
Now, in this chapter, the general laws
have in them the element of chance. I must show both how the general laws arise
and that the element of chance in them is due to ignorance on our part and not
due to something in the universe that is inherently random. In this way they
can neither be construed as evidence for design nor for (radical) chance.
I am going to look first at the
degradation of energy principle. This is often called the second law of
thermodynamics because it appears in the study of heat, which is one of the
forms of energy. The law can be stated many different ways but it is always the
same information. Before I say
what the law is I must explain the idea of a closed system. I have shown that if you define
different kinds of energy: potential, kinetic, heat, etc., in the right way,
energy in an isolated system (sometimes called a closed system) is always
conserved. If you calculate the
energy at any time by adding up the energy of all the components of the system,
you get exactly the same number, no matter how the components of the system
interact with each other.
Suppose that the closed system is a large
number of atoms of a gas, say helium atoms. To contain such a system we must enclose the atoms in a box
(or container). The box must be
maintained at a constant temperature, that is so the atoms in the box will have
a constant average energy. The
temperature of the box must be arranged so that the average energy of the atoms
of the gas is the same as the average energy of the atoms of the box, so that
there will be no net interchange of energy between the box and the gas
contained in it. Then we say the
gas in the box is a closed system.
Its energy will remain constant with time. The first law of thermodynamics is that in a closed system,
energy will remain constant. But
more needs to be said about the behavior in a closed system; energy is not
enough to describe what happens. The second law of thermodynamics indicates
that there is a direction in which
a closed system will change as time goes on; it will not, of itself, change in
the opposite direction. We say the
process of change is irreversible Ð it cannot run backward in time.
As far as a single interaction between two isolated particles is
concerned, everything is reversible.
If you saw a movie of two colliding particles run backward, you would
not say that it was at all unusual, provided there was no change of mechanical
energy into heat. If there is such
a change, running the film backwards would look impossible to you. For instance, suppose you took a movie of a ball bouncing on a
table where the bounce gradually dies out. Energy is conserved here (first law of thermodynamics) but
gradually mechanical energy of the ball (potential and kinetic) changes into
heat energy (the ball and the table are warmer). A bouncing ball shows the second law of thermodynamics in
action. It is why we believe that
macroscopic perpetual motion is impossible. If no energy is fed into the system, all macroscopic mechanical
energy gradually is transformed into heat energy.
But what about a system with no
macroscopic mechanical energy, like our gas in a box? What goes on there?
The energy is heat energy and stays as heat energy. Is there any direction to processes
there? The answer is yes, there
is. Suppose you arranged the atoms
in the box so that all the faster moving ones were in the left side of the box
and all the slower ones in the right side and then photographed the action (if
you could). It would not be very
long before the atoms were all mixed together with no separation between fast
and slow. Showing this movie backward
would look ridiculous.
In the actual process the order, namely
separation by velocity (faster atoms at one end, slower at the other), would
disappear; disorder would be the final result. This idea can be written many ways. One way is to say that in any natural process order tends to
disorder. Another way to record
the facts is to notice that if the left end of the box contains faster moving
atoms, that end must be at a higher temperature than the right end of the
box. After a time the whole box is
at the same temperature. We say
heat energy flows from the hotter to the colder end. Or put another way, heat does not of itself flow uphill from
a colder to a hotter part.
The usual way to justify the second law
of thermodynamics is to say that a system that is isolated tends to the state
that is most probable (or has the highest probability). Suppose you were playing a game called
"locate the atom in a box" by running some wheel of fortune to decide
randomly where it should be located and you had atoms, some of which were fast
moving and some were slow moving.
At each spin, you would place one atom in the box and carry on spinning
until all atoms were located. The
number of different ways of doing this is enormous, just as the number of
different bridge hands that can be dealt is. Many of the ways look the same, sort of jumbled up,
disorderly. Only a small number of
arrangements would have fast atoms at one end and slow at the other. It is like finding bridge hands with
two all red hands and two all black hands. It is very improbable compared to a mixture of black and red
in each hand.
So scientists have come to accept the
fact that all processes tend to anarrangement that is more probable; and in the
end to the one of greatest probability.
It is possible, on the basis of probability calculations alone, to
predict the actual distribution of velocities of atoms in a gas at equilibrium. The distribution is predictable even
though it results from random events.
All probability calculations imply randomness, that is, unpredictability
which, when you deal with large numbers of things or events, yields virtual
predictability. The predictability is not precise predictability but, as the number
of individual objects making up the system increases, it might as well, for all
the difference it makes, be precise predictability.
So the second law of thermodynamics
indicates that there is a randomizing influence on the behavior of systems like
gas in a box. Why do we call the
law the "principle of degradation of energy". I have indicated that mechanical energy
tends to "disappear" and heat energy "appears". The second law of thermodynamics tells us
also that you cannot transform heat energy back 100% into mechanical energy,
although it is perfectly possible to get some mechanical energy from heat. Think of the steam engine running a
train. Just as macroscopic
perpetual motion is impossible so too is the perfectly efficient conversion
from heat to mechanical energy.
You always have some heat left, and this is often just wasted in an
engine's exhaust for instance, or given off by a radiator to the air. We think of mechanical energy as first
class energy and heat as second class energy. So the principle of degradation of energy is that all first
class energy naturally degrades into second class energy. We never lose energy
but it becomes less useful to us.
What people mean when they tell you to conserve energy is to conserve
first class energy, since, of course, energy is automatically conserved always. It is defined that way. The energy crisis people talk about, is
that we are depleting our sources of first class energy.
To "explain" the principle of
degradation of energy (the second law of thermodynamics) we must either say
that there is absolutely no information in it, beyond the laws of interaction
of objects (Newton and Maxwell) or to account for the random influences on a
system of objects by pointing to the apparently innocent bystander - the box in
which the system is contained.
Since the box is connected with the rest of the universe its influence
contains the random influences of all the particles in the whole universe. If we could deal with the whole universe
we might not have to worry about these apparently random influences. But if we try to do this, Bohm says:
Of course, by broadening the context, we may see that
what were chance contingencies in the narrower context present the aspect of
being the results of necessary causal connections in the broader context. But,
then, these necessary causal connections are subject to still newer
contingencies, coming from still broader contexts. [7]
We cannot expect to know what it would be like to get
outside the universe but what we must do is build up information about what it
is like inside.
To me the second law of thermodynamics
can be summed up by saying that, although a system can be kept in such a way,
relative to the rest of the universe, that there is no gain or loss of energy of
the system on the average, it cannot be isolated from the microscopic random influences
of the rest of the universe. This
means as well that there must
always, microscopically, be a give and take of energy between the individual
elements of the system and the environment even for what we call an isolated
system. The net overall result of this give and take is zero energy flow one
way or another; energy is conserved macroscopically. Here is a summary of this
in the Physics text that D.G. Ivey and I wrote:
In thinking about gas molecules bouncing around in a
container, we know that individually they make collisions with the walls in
which they gain or lose energy. However, for a system in thermal equilibrium we
assume that on the average there is no net gain or loss, and the total energy
of the gas is constant. Therefore we can think of the collisions with the walls
as being perfectly elastic (or think of the walls as being perfectly
reflecting) and speak of the gas as isolated, exchanging no energy with its
surroundings. It is, however, because the system is not really isolated that
the concept of thermal equilibrium exists. [8]
I would say then that microscopic energy conservation
is impossible. And this is what I
mean by "cosmic noise".
I call it cosmic because the effect is an interaction with the cosmos
(the rest of the universe). I call
it noise because it appears to the system as a random influence. As Sir Fred
Hoyle says:
... by taking account of an influence of the universe
it is possible to avoid the assumption that the local laws of physics are lopsided
with respect to time. [9]
We explain the irreversible part of thermodynamics by
noting that the effect of the rest of the universe on the system appears to the
system as a random influence. I
quoted Bridgman as agreeing with this point of view:
What prevents the following out through all future
time of a definite sequence is the walls, the atoms of which are supposed to be
in such a complex state of motion because they are in connection with the
entire outer universe ... [10]
The last film that Donald Ivey and I were
to make for the PSSC group we called "Energy is not enough". It was to be a film about the second
law of thermodynamics from a microscopic point of view. This view is usually called the
statistical mechanics point of view.
This is because ideas of probability, or statistics, are applied to the
distributions of position, velocity, and energy of atoms or molecules. In the script for the film we had
suggested that the random influence that resulted in the unpredictability of
the behavior of individual atoms or molecules had its root in the walls of the
container. In the conference with
a group of scientists that always preceded the making of any PSSC film, it
became clear that no two of those scientists agreed about the basis of
statistical mechanics. In the end
the film was never made. I had not
before really encountered a situation where it became so obvious that beneath
the formulas in science there were so many interpretations. It seems that there is superficial
agreement about what we (scientists) all should believe but I found that
underneath this is not the case.
Kuhn says:
Though there still is a paradigm few practitioners
prove to be entirely agreed about what it is. [11]
That brings me to the second fundamental
law that I want to talk about in this chapter, what Constant calls the
"quantum principle". I am going to divide this quantum principle into
two parts. The whole principle
attests to the dual, wave-particle nature of matter and radiation. I will address only the dual nature of
matter in this chapter.
Radiation's dual nature I question, and for this reason put it off until
the chapter on "The Two-Slit Mystery".
Perhaps I should begin by saying where
the word quantum comes from. It means "a certain amount". Originally
it was applied to electromagnetic radiation. It was decided that the energy in electromagnetic radiation came in
certain amounts as a sort of package (a quantum). The amount of energy in a radiation quantum was determined to
be proportional to the frequency of the electromagnetic waves. This development
took place at the beginning of this century. It
was due to the work of Planck and Einstein.
When, in the early 1920's, there appeared
to be indications that the idea of a dual, wave-particle nature could be
ascribed to particles of matter, like electrons, protons, and neutrons, the
theory that included this property
was called quantum mechanics.
Just as the second law of thermodynamics
can be stated in several ways, there are several ways of describing what I have
called the wave-particle duality of matter. One way was originated in 1923 by Louis de Broglie. He said that there was a wavelength
associated with every particle of matter that is moving. This wavelength L was inversely proportional to the momentum m*v of the particle. Thus
L = h / ( m * v )
The constant h in this formula was Planck's constant. It had appeared earlier when
Planck and Einstein had said that the energy E in a quantum of electromagnetic radiation (a photon)
was proportional to the frequency f
of the electromagnetic wave
E = h * f
This is perhaps the most striking evidence of design
in the universe: that the constant h, Planck's constant, should appear in both these formulas and that they
both should be so simple. I will
have a lot of explaining to do to eliminate proof of a Designer here.
Then, in 1924, the same constant turned
up again. This time Werner Heisenberg
used it in his uncertainty principle.
This principle stated that there was a limit to the accuracy with which
the position and velocity of a particle could be measured simultaneously. For a
particle constrained to move along a line, the uncertainty in the measurement of
position x we call U(x), the uncertainty in velocity v we call U(v). The Heisenberg uncertainty relationship for a particle of mass m is
U ( x ) * U ( v ) > = h' / ( 2 * m )
This is a more complicated relationship (or law) than
de Broglie's formula for wavelength.
The constant h' in the
formula is not Planck's constant but is Planck's constant h divided by 2 times pi. (Remember pi?
The area of a circle is pi multiplied by the radius squared.) The
uncertainty relation says that the product of the uncertainty in position and
the uncertainty in velocity is greater than (>) or equal to (=) h' divided by two times the mass of the particle.
It can be shown that, although de
Broglie's and Heisenberg's relations are stated quite differently, they contain
the same constant and they really have the same information content. One can be derived from the other. Actually it is easy (but not really
easy) to derive both Heisenberg's and de Broglie's relations from a third
statement of the same information.
If you want to see this done, and are mathematically ready, take a look
at Chapter 18 of my textbook Physics (John Wiley and Sons). The actual statement of the relation from which
the others can be derived is that the amplitude of the probability density of
position
for a steady state of a system of particles and the
amplitude of the probability density of momentum for that same steady state is
that of a Fourier pair (x, k)
provided that the momentum is related to k by the relation
m * v = h' * k
where h'
is, as before, Planck's constant h
divided by 2 times pi.
So there is no need to
"explain" all three of these relations (Heisenberg, de Broglie, and
the Fourier pair relation). If you explain one, you explain them all.
I am going to suggest that the
uncertainty that exists in measuring the position and velocity (or momentum) of
a particle (which is really why we say it has a dual nature of wave and
particle) is because the motion of a particle has a jitter to it which is the
result of the random (uneliminable) influences on it from the rest of the universe. Heisenberg's relationship has often
been presented in terms of the uncertainty in our knowledge of the state
(position and velocity) of a particle.
Heisenberg has this to say:
Certainly quantum theory does not contain genuine
subjective features, it does not introduce the mind of the physicist as part of
the atomic event. But it starts
from the division of the world into the "object" and the rest of the
world, and from the fact that at least for the rest of the world we use the
classical concepts in our description.
This division is arbitrary... [12]
Heisenberg is saying that we want to
treat the rest of the universe as classical (deterministically) and this leads
us arbitrarily, to assign to the particle itself this uncertainty or dual
nature. We say that its behavior
can only be calculated probabalistically.
But if we say that there are random influences from outside, the
particle is in fact behaving classically (deterministically). Because we can never know all the
influences in detail we are compelled to make probabalistic (or statistical)
calculations. Heisenberg speaks
about the random influences on the nucleus of an atom which cause it to disintegrate
and emit an alpha-particle, apparently at random:
We know the forces in the atomic nucleus that are
responsible for the emission of the alpha-particle. But this knowledge contains the uncertainty which is brought
about by the interaction between the nucleus and the rest of the world. If we wanted to know why the alpha-particle
was emitted at that particular time we would have to know the microscopic
structure of the whole world including ourselves, and that is impossible. [13]
The mechanics that we use to predict what will happen
in the nucleus of the atom or in the atom is called quantum mechanics. It is called this because it
incorporates the element of uncertainty in the behavior of the particles that
constitute the atom. The
predictions that can be made using quantum mechanics are probabalistic in
nature. There is absolutely no possibility that they can be other than this. Most
scientists would say that this is because of the uncertainty principle or
because of the dual nature (wave-particle) of all the constituents of the
atom. Since I cannot accept the
idea of a general law governing (or describing) the behavior of all objects, and
that is what either of these implies, without looking for an explanation, I
must go further.
I believe that the effect of the universe
on each particle is what produces the result that we are noticing here. I believe that the laws of
electromagnetism describe accurately how charges would interact if they could
be isolated from the random fluctuating influences of the microscopic structure
of the universe. Of course, the
laws of electromagnetism do in themselves already incorporate the steady part
of the influence of the rest of the universe in producing the inertial
environment. As Heisenberg says,
the division we have now is arbitrary.
We assign the randomness to the particles and claim it is part of their
nature.
I am going to claim that the behavior of
particles is very similar to the behavior of particles of pollen suspended in water
which were observed under a microscope in 1827 by the botanist Robert
Brown. It was first thought that
the random jumpy motions of the pollen particles was due to the fact that they
were "alive". Then it was observed that all tiny particles showed
this same kind of motion.
It might have been possible for
scientists at the time to say that the particles of pollen, or whatever, had a
dual nature or that their behavior
was described by an uncertainty principle. But instead scientists began to attribute their zigzag
motion to the influence of their environment. Even though they could not see what was going on, they
imagined that the environment was made up of other much smaller particles,
moving about in a similar zigzag fashion, bumping into each other and into the
pollen particles. The smaller particles
were called atoms. Here are
Resnick and Halliday:
The earliest and most direct experimental evidence
for the reality of atoms was the proof of the atomic kinetic theory provided by
the quantitative studies of Brownian motion. [14]
The "atomic kinetic theory" was that atoms
in a gas were moving about randomly and bumping into each other and the walls
of their container. In doing this
they caused the suspended particles to move about as well. As Resnick and Halliday continue:
The suspended particles are extremely large compared
to the molecules of the fluid and are being continually bombarded on all sides
by them. If the particles are sufficiently large and the number of molecules is
sufficiently great, equal numbers of molecules strike the particle on all sides
at each instant. For smaller
particles and fewer molecules the number of molecules striking various sides of
the particle at any instant, being merely a matter of chance, may not be equal;
that is, fluctuations occur. Hence
the particle at each instant suffers an unbalanced force causing it to move
this way or that. [15]
For Brownian motion it has been shown that a
relationship of exactly the same form as Heisenberg's uncertainty relation
exists for all Brownian particles.
From the Brownian motion we concluded
that atoms were present. Bohm says:
Thus, in the case of the Brownian motion, the
postulate was made that the visible irregular motions of spore particles originated
in a deeper but as yet invisible level of atomic motion. [16]
Now we know that an uncertainty relation describes
the motion of particles like electrons and protons, which we cannot see. Are we wrong to imagine another
invisible level (say of messengers) bombarding the fundamental particles from
all sides giving them a Brownian-like motion?
So I turn to cosmic noise to explain
the behavior both of systems of
particles and now of individual particles.
SUMMARY
1. The
natural recurrences of the fundamental particles might be explained by a theory
of evolution in much the same way as we explain the natural recurrences of
plants and animals.
2. The
randomizing influence on a system of particles that is evidenced by the second
law of thermodynamics is due to the effect of the atoms in the walls of the
container and the entire rest of the universe. The system cannot be isolated
from the environment.
3. Microscopic
energy conservation is a physical impossibility because isolation of the system
is impossible.
4. The
bahehavior of a particle that is described by the uncertainty principle
is similar to Brownian motion and is due to the fluctuating influence of the
rest of the universe. The fluctuations are describable as random but the chance
element is just an ignorance cover, not radical chance. The randomness cannot,
however, be eliminated.
5. Particles have a wave nature only in that their motion, as particles, has a jitter due to the fluctuating effect of the rest of the universe.
Copyright © 1983 J.N.P. Hume All rights in this book reserved