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Nobel Lecture 1965: Richard P. Feynman
The Development of the Space-Time View
of
Quantum Electrodynamics.
We have a habit in writing articles
published
in scientific journals to make the
work as
finished as possible, to cover all
the tracks,
to not worry about the blind alleys
or to
describe how you had the wrong idea
first,
and so on. So there isn't any place
to publish,
in a dignified manner, what you actually
did in order to get to do the work,
although,
there has been in these days, some
interest
in this kind of thing. Since winning
the
prize is a personal thing, I thought
I could
be excused in this particular situation,
if I were to talk personally about
my relationship
to quantum electrodynamics, rather
than to
discuss the subject itself in a refined
and
finished fashion. Furthermore, since
there
are three people who have won the prize
in
physics, if they are all going to be
talking
about quantum electrodynamics itself,
one
might become bored with the subject.
So,
what I would like to tell you about
today
are the sequence of events, really
the sequence
of ideas, which occurred, and by which
I
finally came out the other end with
an unsolved
problem for which I ultimately received
a
prize.
I realize that a truly scientific paper
would
be of greater value, but such a paper
I could
publish in regular journals. So, I
shall
use this Nobel Lecture as an opportunity
to do something of less value, but
which
I cannot do elsewhere. I ask your indulgence
in another manner. I shall include
details
of anecdotes which are of no value
either
scientifically, nor for understanding
the
development of ideas. They are included
only
to make the lecture more entertaining.
I worked on this problem about eight
years
until the final publication in 1947.
The
beginning of the thing was at the Massachusetts
Institute of Technology, when I was
an undergraduate
student reading about the known physics,
learning slowly about all these things
that
people were worrying about, and realizing
ultimately that the fundamental problem
of
the day was that the quantum theory
of electricity
and magnetism was not completely satisfactory.
This I gathered from books like those
of
Heitler and Dirac. I was inspired by
the
remarks in these books; not by the
parts
in which everything was proved and
demonstrated
carefully and calculated, because I
couldn't
understand those very well. At the
young
age what I could understand were the
remarks
about the fact that this doesn't make
any
sense, and the last sentence of the
book
of Dirac I can still remember, "It
seems
that some essentially new physical
ideas
are here needed." So, I had this
as
a challenge and an inspiration. I also
had
a personal feeling, that since they
didn't
get a satisfactory answer to the problem
I wanted to solve, I don't have to
pay a
lot of attention to what they did do.
I did gather from my readings, however,
that
two things were the source of the difficulties
with the quantum electrodynamical theories.
The first was an infinite energy of
interaction
of the electron with itself. And this
difficulty
existed even in the classical theory.
The
other difficulty came from some infinites
which had to do with the infinite numbers
of degrees of freedom in the field.
As I
understood it at the time (as nearly
as I
can remember) this was simply the difficulty
that if you quantized the harmonic
oscillators
of the field (say in a box) each oscillator
has a ground state energy of (?) and
there
is an infinite number of modes in a
box of
every increasing frequency w, and therefore
there is an infinite energy in the
box. I
now realize that that wasn't a completely
correct statement of the central problem;
it can be removed simply by changing
the
zero from which energy is measured.
At any
rate, I believed that the difficulty
arose
somehow from a combination of the electron
acting on itself and the infinite number
of degrees of freedom of the field.
Well, it seemed to me quite evident
that
the idea that a particle acts on itself,
that the electrical force acts on the
same
particle that generates it, is not
a necessary
one - it is a sort of a silly one,
as a matter
of fact. And, so I suggested to myself,
that
electrons cannot act on themselves,
they
can only act on other electrons. That
means
there is no field at all. You see,
if all
charges contribute to making a single
common
field, and if that common field acts
back
on all the charges, then each charge
must
act back on itself. Well, that was
where
the mistake was, there was no field.
It was
just that when you shook one charge,
another
would shake later. There was a direct
interaction
between charges, albeit with a delay.
The
law of force connecting the motion
of one
charge with another would just involve
a
delay. Shake this one, that one shakes
later.
The sun atom shakes; my eye electron
shakes
eight minutes later, because of a direct
interaction across.
Now, this has the attractive feature
that
it solves both problems at once. First,
I
can say immediately, I don't let the
electron
act on itself, I just let this act
on that,
hence, no self-energy! Secondly, there
is
not an infinite number of degrees of
freedom
in the field. There is no field at
all; or
if you insist on thinking in terms
of ideas
like that of a field, this field is
always
completely determined by the action
of the
particles which produce it. You shake
this
particle, it shakes that one, but if
you
want to think in a field way, the field,
if it's there, would be entirely determined
by the matter which generates it, and
therefore,
the field does not have any independent
degrees
of freedom and the infinities from
the degrees
of freedom would then be removed. As
a matter
of fact, when we look out anywhere
and see
light, we can always "see"
some
matter as the source of the light.
We don't
just see light (except recently some
radio
reception has been found with no apparent
material source).
You see then that my general plan was
to
first solve the classical problem,
to get
rid of the infinite self-energies in
the
classical theory, and to hope that
when I
made a quantum theory of it, everything
would
just be fine.
That was the beginning, and the idea
seemed
so obvious to me and so elegant that
I fell
deeply in love with it. And, like falling
in love with a woman, it is only possible
if you do not know much about her,
so you
cannot see her faults. The faults will
become
apparent later, but after the love
is strong
enough to hold you to her. So, I was
held
to this theory, in spite of all difficulties,
by my youthful enthusiasm.
Then I went to graduate school and
somewhere
along the line I learned what was wrong
with
the idea that an electron does not
act on
itself. When you accelerate an electron
it
radiates energy and you have to do
extra
work to account for that energy. The
extra
force against which this work is done
is
called the force of radiation resistance.
The origin of this extra force was
identified
in those days, following Lorentz, as
the
action of the electron itself. The
first
term of this action, of the electron
on itself,
gave a kind of inertia (not quite relativistically
satisfactory). But that inertia-like
term
was infinite for a point-charge. Yet
the
next term in the sequence gave an energy
loss rate, which for a point-charge
agrees
exactly with the rate you get by calculating
how much energy is radiated. So, the
force
of radiation resistance, which is absolutely
necessary for the conservation of energy
would disappear if I said that a charge
could
not act on itself.
So, I learned in the interim when I
went
to graduate school the glaringly obvious
fault of my own theory. But, I was
still
in love with the original theory, and
was
still thinking that with it lay the
solution
to the difficulties of quantum electrodynamics.
So, I continued to try on and off to
save
it somehow. I must have some action
develop
on a given electron when I accelerate
it
to account for radiation resistance.
But,
if I let electrons only act on other
electrons
the only possible source for this action
is another electron in the world. So,
one
day, when I was working for Professor
Wheeler
and could no longer solve the problem
that
he had given me, I thought about this
again
and I calculated the following. Suppose
I
have two charges - I shake the first
charge,
which I think of as a source and this
makes
the second one shake, but the second
one
shaking produces an effect back on
the source.
And so, I calculated how much that
effect
back on the first charge was, hoping
it might
add up the force of radiation resistance.
It didn't come out right, of course,
but
I went to Professor Wheeler and told
him
my ideas. He said, - yes, but the answer
you get for the problem with the two
charges
that you just mentioned will, unfortunately,
depend upon the charge and the mass
of the
second charge and will vary inversely
as
the square of the distance R, between
the
charges, while the force of radiation
resistance
depends on none of these things. I
thought,
surely, he had computed it himself,
but now
having become a professor, I know that
one
can be wise enough to see immediately
what
some graduate student takes several
weeks
to develop. He also pointed out something
that also bothered me, that if we had
a situation
with many charges all around the original
source at roughly uniform density and
if
we added the effect of all the surrounding
charges the inverse R square would
be compensated
by the R2 in the volume element and
we would
get a result proportional to the thickness
of the layer, which would go to infinity.
That is, one would have an infinite
total
effect back at the source. And, finally
he
said to me, and you forgot something
else,
when you accelerate the first charge,
the
second acts later, and then the reaction
back here at the source would be still
later.
In other words, the action occurs at
the
wrong time. I suddenly realized what
a stupid
fellow I am, for what I had described
and
calculated was just ordinary reflected
light,
not radiation reaction.
But, as I was stupid, so was Professor
Wheeler
that much more clever. For he then
went on
to give a lecture as though he had
worked
this all out before and was completely
prepared,
but he had not, he worked it out as
he went
along. First, he said, let us suppose
that
the return action by the charges in
the absorber
reaches the source by advanced waves
as well
as by the ordinary retarded waves of
reflected
light; so that the law of interaction
acts
backward in time, as well as forward
in time.
I was enough of a physicist at that
time
not to say, "Oh, no, how could
that
be?" For today all physicists
know from
studying Einstein and Bohr, that sometimes
an idea which looks completely paradoxical
at first, if analyzed to completion
in all
detail and in experimental situations,
may,
in fact, not be paradoxical. So, it
did not
bother me any more than it bothered
Professor
Wheeler to use advance waves for the
back
reaction - a solution of Maxwell's
equations,
which previously had not been physically
used.
Professor Wheeler used advanced waves
to
get the reaction back at the right
time and
then he suggested this: If there were
lots
of electrons in the absorber, there
would
be an index of refraction n, so, the
retarded
waves coming from the source would
have their
wave lengths slightly modified in going
through
the absorber. Now, if we shall assume
that
the advanced waves come back from the
absorber
without an index - why? I don't know,
let's
assume they come back without an index
-
then, there will be a gradual shifting
in
phase between the return and the original
signal so that we would only have to
figure
that the contributions act as if they
come
from only a finite thickness, that
of the
first wave zone. (More specifically,
up to
that depth where the phase in the medium
is shifted appreciably from what it
would
be in vacuum, a thickness proportional
to
l/(n-1). ) Now, the less the number
of electrons
in here, the less each contributes,
but the
thicker will be the layer that effectively
contributes because with less electrons,
the index differs less from 1. The
higher
the charges of these electrons, the
more
each contribute, but the thinner the
effective
layer, because the index would be higher.
And when we estimated it, (calculated
without
being careful to keep the correct numerical
factor) sure enough, it came out that
the
action back at the source was completely
independent of the properties of the
charges
that were in the surrounding absorber.
Further,
it was of just the right character
to represent
radiation resistance, but we were unable
to see if it was just exactly the right
size.
He sent me home with orders to figure
out
exactly how much advanced and how much
retarded
wave we need to get the thing to come
out
numerically right, and after that,
figure
out what happens to the advanced effects
that you would expect if you put a
test charge
here close to the source? For if all
charges
generate advanced, as well as retarded
effects,
why would that test not be affected
by the
advanced waves from the source?
I found that you get the right answer
if
you use half-advanced and half-retarded
as
the field generated by each charge.
That
is, one is to use the solution of Maxwell's
equation which is symmetrical in time
and
that the reason we got no advanced
effects
at a point close to the source in spite
of
the fact that the source was producing
an
advanced field is this. Suppose the
source
s surrounded by a spherical absorbing
wall
ten light seconds away, and that the
test
charge is one second to the right of
the
source. Then the source is as much
as eleven
seconds away from some parts of the
wall
and only nine seconds away from other
parts.
The source acting at time t=0 induces
motions
in the wall at time +10. Advanced effects
from this can act on the test charge
as early
as eleven seconds earlier, or at t=
-1. This
is just at the time that the direct
advanced
waves from the source should reach
the test
charge, and it turns out the two effects
are exactly equal and opposite and
cancel
out! At the later time +1 effects on
the
test charge from the source and from
the
walls are again equal, but this time
are
of the same sign and add to convert
the half-retarded
wave of the source to full retarded
strength.
Thus, it became clear that there was
the
possibility that if we assume all actions
are via half-advanced and half-retarded
solutions
of Maxwell's equations and assume that
all
sources are surrounded by material
absorbing
all the the light which is emitted,
then
we could account for radiation resistance
as a direct action of the charges of
the
absorber acting back by advanced waves
on
the source.
Many months were devoted to checking
all
these points. I worked to show that
everything
is independent of the shape of the
container,
and so on, that the laws are exactly
right,
and that the advanced effects really
cancel
in every case. We always tried to increase
the efficiency of our demonstrations,
and
to see with more and more clarity why
it
works. I won't bore you by going through
the details of this. Because of our
using
advanced waves, we also had many apparent
paradoxes, which we gradually reduced
one
by one, and saw that there was in fact
no
logical difficulty with the theory.
It was
perfectly satisfactory.
We also found that we could reformulate
this
thing in another way, and that is by
a principle
of least action. Since my original
plan was
to describe everything directly in
terms
of particle motions, it was my desire
to
represent this new theory without saying
anything about fields. It turned out
that
we found a form for an action directly
involving
the motions of the charges only, which
upon
variation would give the equations
of motion
of these charges. The expression for
this
action A is
where
where is the four-vector position of
the
ith particle as a function of some
parameter
. The first term is the integral of
proper
time, the ordinary action of relativistic
mechanics of free particles of mass
mi. (We
sum in the usual way on the repeated
index
m.) The second term represents the
electrical
interaction of the charges. It is summed
over each pair of charges (the factor
? is
to count each pair once, the term i=j
is
omitted to avoid self-action) .The
interaction
is a double integral over a delta function
of the square of space-time interval
I2 between
two points on the paths. Thus, interaction
occurs only when this interval vanishes,
that is, along light cones.
The fact that the interaction is exactly
one-half advanced and half-retarded
meant
that we could write such a principle
of least
action, whereas interaction via retarded
waves alone cannot be written in such
a way.
So, all of classical electrodynamics
was
contained in this very simple form.
It looked
good, and therefore, it was undoubtedly
true,
at least to the beginner. It automatically
gave half-advanced and half-retarded
effects
and it was without fields. By omitting
the
term in the sum when i=j, I omit self-interaction
and no longer have any infinite self-energy.
This then was the hoped-for solution
to the
problem of ridding classical electrodynamics
of the infinities.
It turns out, of course, that you can
reinstate
fields if you wish to, but you have
to keep
track of the field produced by each
particle
separately. This is because to find
the right
field to act on a given particle, you
must
exclude the field that it creates itself.
A single universal field to which all
contribute
will not do. This idea had been suggested
earlier by Frenkel and so we called
these
Frenkel fields. This theory which allowed
only particles to act on each other
was equivalent
to Frenkel's fields using half-advanced
and
half-retarded solutions.
There were several suggestions for
interesting
modifications of electrodynamics. We
discussed
lots of them, but I shall report on
only
one. It was to replace this delta function
in the interaction by another function,
say,
f(I2ij), which is not infinitely sharp.
Instead
of having the action occur only when
the
interval between the two charges is
exactly
zero, we would replace the delta function
of I2 by a narrow peaked thing. Let's
say
that f(Z) is large only near Z=0 width
of
order a2. Interactions will now occur
when
T2-R2 is of order a2 roughly where
T is the
time difference and R is the separation
of
the charges. This might look like it
disagrees
with experience, but if a is some small
distance,
like 10-13 cm, it says that the time
delay
T in action is roughly or approximately,
- if R is much larger than a, T=R?
a2/2R.
This means that the deviation of time
T from
the ideal theoretical time R of Maxwell,
gets smaller and smaller, the further
the
pieces are apart. Therefore, all theories
involving in analyzing generators,
motors,
etc., in fact, all of the tests of
electrodynamics
that were available in Maxwell's time,
would
be adequately satisfied if were 10-13
cm.
If R is of the order of a centimeter
this
deviation in T is only 10-26 parts.
So, it
was possible, also, to change the theory
in a simple manner and to still agree
with
all observations of classical electrodynamics.
You have no clue of precisely what
function
to put in for f, but it was an interesting
possibility to keep in mind when developing
quantum electrodynamics.
It also occurred to us that if we did
that
(replace d by f) we could not reinstate
the
term i=j in the sum because this would
now
represent in a relativistically invariant
fashion a finite action of a charge
on itself.
In fact, it was possible to prove that
if
we did do such a thing, the main effect
of
the self-action (for not too rapid
accelerations)
would be to produce a modification
of the
mass. In fact, there need be no mass
mi,
term, all the mechanical mass could
be electromagnetic
self-action. So, if you would like,
we could
also have another theory with a still
simpler
expression for the action A. In expression
(1) only the second term is kept, the
sum
extended over all i and j, and some
function
replaces d. Such a simple form could
represent
all of classical electrodynamics, which
aside
from gravitation is essentially all
of classical
physics.
Although it may sound confusing, I
am describing
several different alternative theories
at
once. The important thing to note is
that
at this time we had all these in mind
as
different possibilities. There were
several
possible solutions of the difficulty
of classical
electrodynamics, any one of which might
serve
as a good starting point to the solution
of the difficulties of quantum electrodynamics.
I would also like to emphasize that
by this
time I was becoming used to a physical
point
of view different from the more customary
point of view. In the customary view,
things
are discussed as a function of time
in very
great detail. For example, you have
the field
at this moment, a differential equation
gives
you the field at the next moment and
so on;
a method, which I shall call the Hamilton
method, the time differential method.
We
have, instead (in (1) say) a thing
that describes
the character of the path throughout
all
of space and time. The behavior of
nature
is determined by saying her whole spacetime
path has a certain character. For an
action
like (1) the equations obtained by
variation
(of Xim (ai)) are no longer at all
easy to
get back into Hamiltonian form. If
you wish
to use as variables only the coordinates
of particles, then you can talk about
the
property of the paths - but the path
of one
particle at a given time is affected
by the
path of another at a different time.
If you
try to describe, therefore, things
differentially,
telling what the present conditions
of the
particles are, and how these present
conditions
will affect the future you see, it
is impossible
with particles alone, because something
the
particle did in the past is going to
affect
the future.
Therefore, you need a lot of bookkeeping
variables to keep track of what the
particle
did in the past. These are called field
variables.
You will, also, have to tell what the
field
is at this present moment, if you are
to
be able to see later what is going
to happen.
From the overall space-time view of
the least
action principle, the field disappears
as
nothing but bookkeeping variables insisted
on by the Hamiltonian method.
As a by-product of this same view,
I received
a telephone call one day at the graduate
college at Princeton from Professor
Wheeler,
in which he said, "Feynman, I
know why
all electrons have the same charge
and the
same mass" "Why?" "Because,
they are all the same electron!"
And,
then he explained on the telephone,
"suppose
that the world lines which we were
ordinarily
considering before in time and space
- instead
of only going up in time were a tremendous
knot, and then, when we cut through
the knot,
by the plane corresponding to a fixed
time,
we would see many, many world lines
and that
would represent many electrons, except
for
one thing. If in one section this is
an ordinary
electron world line, in the section
in which
it reversed itself and is coming back
from
the future we have the wrong sign to
the
proper time - to the proper four velocities
- and that's equivalent to changing
the sign
of the charge, and, therefore, that
part
of a path would act like a positron."
"But, Professor", I said,
"there
aren't as many positrons as electrons."
"Well, maybe they are hidden in
the
protons or something", he said.
I did
not take the idea that all the electrons
were the same one from him as seriously
as
I took the observation that positrons
could
simply be represented as electrons
going
from the future to the past in a back
section
of their world lines. That, I stole!
To summarize, when I was done with
this,
as a physicist I had gained two things.
One,
I knew many different ways of formulating
classical electrodynamics, with many
different
mathematical forms. I got to know how
to
express the subject every which way.
Second,
I had a point of view - the overall
space-time
point of view - and a disrespect for
the
Hamiltonian method of describing physics.
I would like to interrupt here to make
a
remark. The fact that electrodynamics
can
be written in so many ways - the differential
equations of Maxwell, various minimum
principles
with fields, minimum principles without
fields,
all different kinds of ways, was something
I knew, but I have never understood.
It always
seems odd to me that the fundamental
laws
of physics, when discovered, can appear
in
so many different forms that are not
apparently
identical at first, but, with a little
mathematical
fiddling you can show the relationship.
An
example of that is the Schr? dinger
equation
and the Heisenberg formulation of quantum
mechanics. I don't know why this is
- it
remains a mystery, but it was something
I
learned from experience. There is always
another way to say the same thing that
doesn't
look at all like the way you said it
before.
I don't know what the reason for this
is.
I think it is somehow a representation
of
the simplicity of nature. A thing like
the
inverse square law is just right to
be represented
by the solution of Poisson's equation,
which,
therefore, is a very different way
to say
the same thing that doesn't look at
all like
the way you said it before. I don't
know
what it means, that nature chooses
these
curious forms, but maybe that is a
way of
defining simplicity. Perhaps a thing
is simple
if you can describe it fully in several
different
ways without immediately knowing that
you
are describing the same thing.
I was now convinced that since we had
solved
the problem of classical electrodynamics
(and completely in accordance with
my program
from M. I. T., only direct interaction
between
particles, in a way that made fields
unnecessary)
that everything was definitely going
to be
all right. I was convinced that all
I had
to do was make a quantum theory analogous
to the classical one and everything
would
be solved.
So, the problem is only to make a quantum
theory, which has as its classical
analog,
this expression (1). Now, there is
no unique
way to make a quantum theory from classical
mechanics, although all the textbooks
make
believe there is. What they would tell
you
to do, was find the momentum variables
and
replace them by , but I couldn't find
a momentum
variable, as there wasn't any.
The character of quantum mechanics
of the
day was to write things in the famous
Hamiltonian
way - in the form of a differential
equation,
which described how the wave function
changes
from instant to instant, and in terms
of
an operator, H. If the classical physics
could be reduced to a Hamiltonian form,
everything
was all right. Now, least action does
not
imply a Hamiltonian form if the action
is
a function of anything more than positions
and velocities at the same moment.
If the
action is of the form of the integral
of
a function, (usually called the Lagrangian)
of the velocities and positions at
the same
time
then you can start with the Lagrangian
and
then create a Hamiltonian and work
out the
quantum mechanics, more or less uniquely.
But this thing (1) involves the key
variables,
positions, at two different times and
therefore,
it was not obvious what to do to make
the
quantum-mechanical analogue.
I tried - I would struggle in various
ways.
One of them was this; if I had harmonic
oscillators
interacting with a delay in time, I
could
work out what the normal modes were
and guess
that the quantum theory of the normal
modes
was the same as for simple oscillators
and
kind of work my way back in terms of
the
original variables. I succeeded in
doing
that, but I hoped then to generalize
to other
than a harmonic oscillator, but I learned
to my regret something, which many
people
have learned. The harmonic oscillator
is
too simple; very often you can work
out what
it should do in quantum theory without
getting
much of a clue as to how to generalize
your
results to other systems.
So that didn't help me very much, but
when
I was struggling with this problem,
I went
to a beer party in the Nassau Tavern
in Princeton.
There was a gentleman, newly arrived
from
Europe (Herbert Jehle) who came and
sat next
to me. Europeans are much more serious
than
we are in America because they think
that
a good place to discuss intellectual
matters
is a beer party. So, he sat by me and
asked,
"what are you doing" and
so on,
and I said, "I'm drinking beer."
Then I realized that he wanted to know
what
work I was doing and I told him I was
struggling
with this problem, and I simply turned
to
him and said, "listen, do you
know any
way of doing quantum mechanics, starting
with action - where the action integral
comes
into the quantum mechanics?" "No",
he said, "but Dirac has a paper
in which
the Lagrangian, at least, comes into
quantum
mechanics. I will show it to you tomorrow."
Next day we went to the Princeton Library,
they have little rooms on the side
to discuss
things, and he showed me this paper.
What
Dirac said was the following: There
is in
quantum mechanics a very important
quantity
which carries the wave function from
one
time to another, besides the differential
equation but equivalent to it, a kind
of
a kernal, which we might call K(x',
x), which
carries the wave function j(x) known
at time
t, to the wave function j(x') at time,
t+e
Dirac points out that this function
K was
analogous to the quantity in classical
mechanics
that you would calculate if you took
the
exponential of ie, multiplied by the
Lagrangian
imagining that these two positions
x, x'
corresponded t and t+e. In other words,
Professor Jehle showed me this, I read
it,
he explained it to me, and I said,
"what
does he mean, they are analogous; what
does
that mean, analogous? What is the use
of
that?" He said, "you Americans!
You always want to find a use for everything!"
I said, that I thought that Dirac must
mean
that they were equal. "No",
he
explained, "he doesn't mean they
are
equal." "Well", I said,
"let's
see what happens if we make them equal."
So I simply put them equal, taking
the simplest
example where the Lagrangian is ?Mx2
- V(x)
but soon found I had to put a constant
of
proportionality A in, suitably adjusted.
When I substituted for K to get
and just calculated things out by Taylor
series expansion, out came the Schr?
dinger
equation. So, I turned to Professor
Jehle,
not really understanding, and said,
"well,
you see Professor Dirac meant that
they were
proportional." Professor Jehle's
eyes
were bugging out - he had taken out
a little
notebook and was rapidly copying it
down
from the blackboard, and said, "no,
no, this is an important discovery.
You Americans
are always trying to find out how something
can be used. That's a good way to discover
things!" So, I thought I was finding
out what Dirac meant, but, as a matter
of
fact, had made the discovery that what
Dirac
thought was analogous, was, in fact,
equal.
I had then, at least, the connection
between
the Lagrangian and quantum mechanics,
but
still with wave functions and infinitesimal
times.
It must have been a day or so later
when
I was lying in bed thinking about these
things,
that I imagined what would happen if
I wanted
to calculate the wave function at a
finite
interval later.
I would put one of these factors eieL
in
here, and that would give me the wave
functions
the next moment, t+e and then I could
substitute
that back into (3) to get another factor
of eieL and give me the wave function
the
next moment, t+2e and so on and so
on. In
that way I found myself thinking of
a large
number of integrals, one after the
other
in sequence. In the integrand was the
product
of the exponentials, which, of course,
was
the exponential of the sum of terms
like
eL. Now, L is the Lagrangian and e
is like
the time interval dt, so that if you
took
a sum of such terms, that's exactly
like
an integral. That's like Riemann's
formula
for the integral Ldt, you just take
the value
at each point and add them together.
We are
to take the limit as e-0, of course.
Therefore,
the connection between the wave function
of one instant and the wave function
of another
instant a finite time later could be
obtained
by an infinite number of integrals,
(because
e goes to zero, of course) of exponential
where S is the action expression (2).
At
last, I had succeeded in representing
quantum
mechanics directly in terms of the
action
S.
This led later on to the idea of the
amplitude
for a path; that for each possible
way that
the particle can go from one point
to another
in space-time, there's an amplitude.
That
amplitude is e to the times the action
for
the path. Amplitudes from various paths
superpose
by addition. This then is another,
a third
way, of describing quantum mechanics,
which
looks quite different than that of
Schr?
dinger or Heisenberg, but which is
equivalent
to them.
Now immediately after making a few
checks
on this thing, what I wanted to do,
of course,
was to substitute the action (1) for
the
other (2). The first trouble was that
I could
not get the thing to work with the
relativistic
case of spin one-half. However, although
I could deal with the matter only nonrelativistically,
I could deal with the light or the
photon
interactions perfectly well by just
putting
the interaction terms of (1) into any
action,
replacing the mass terms by the non-relativistic
(Mx2/2)dt. When the action has a delay,
as
it now had, and involved more than
one time,
I had to lose the idea of a wave function.
That is, I could no longer describe
the program
as; given the amplitude for all positions
at a certain time to compute the amplitude
at another time. However, that didn't
cause
very much trouble. It just meant developing
a new idea. Instead of wave functions
we
could talk about this; that if a source
of
a certain kind emits a particle, and
a detector
is there to receive it, we can give
the amplitude
that the source will emit and the detector
receive. We do this without specifying
the
exact instant that the source emits
or the
exact instant that any detector receives,
without trying to specify the state
of anything
at any particular time in between,
but by
just finding the amplitude for the
complete
experiment. And, then we could discuss
how
that amplitude would change if you
had a
scattering sample in between, as you
rotated
and changed angles, and so on, without
really
having any wave functions.
It was also possible to discover what
the
old concepts of energy and momentum
would
mean with this generalized action.
And, so
I believed that I had a quantum theory
of
classical electrodynamics - or rather
of
this new classical electrodynamics
described
by action (1). I made a number of checks.
If I took the Frenkel field point of
view,
which you remember was more differential,
I could convert it directly to quantum
mechanics
in a more conventional way. The only
problem
was how to specify in quantum mechanics
the
classical boundary conditions to use
only
half-advanced and half-retarded solutions.
By some ingenuity in defining what
that meant,
I found that the quantum mechanics
with Frenkel
fields, plus a special boundary condition,
gave me back this action, (1) in the
new
form of quantum mechanics with a delay.
So,
various things indicated that there
wasn't
any doubt I had everything straightened
out.
It was also easy to guess how to modify
the
electrodynamics, if anybody ever wanted
to
modify it. I just changed the delta
to an
f, just as I would for the classical
case.
So, it was very easy, a simple thing.
To
describe the old retarded theory without
explicit mention of fields I would
have to
write probabilities, not just amplitudes.
I would have to square my amplitudes
and
that would involve double path integrals
in which there are two S's and so forth.
Yet, as I worked out many of these
things
and studied different forms and different
boundary conditions. I got a kind of
funny
feeling that things weren't exactly
right.
I could not clearly identify the difficulty
and in one of the short periods during
which
I imagined I had laid it to rest, I
published
a thesis and received my Ph. D.
During the war, I didn't have time
to work
on these things very extensively, but
wandered
about on buses and so forth, with little
pieces of paper, and struggled to work
on
it and discovered indeed that there
was something
wrong, something terribly wrong. I
found
that if one generalized the action
from the
nice Langrangian forms (2) to these
forms
(1) then the quantities which I defined
as
energy, and so on, would be complex.
The
energy values of stationary states
wouldn't
be real and probabilities of events
wouldn't
add up to 100%. That is, if you took
the
probability that this would happen
and that
would happen - everything you could
think
of would happen, it would not add up
to one.
Another problem on which I struggled
very
hard, was to represent relativistic
electrons
with this new quantum mechanics. I
wanted
to do a unique and different way -
and not
just by copying the operators of Dirac
into
some kind of an expression and using
some
kind of Dirac algebra instead of ordinary
complex numbers. I was very much encouraged
by the fact that in one space dimension,
I did find a way of giving an amplitude
to
every path by limiting myself to paths,
which
only went back and forth at the speed
of
light. The amplitude was simple (ie)
to a
power equal to the number of velocity
reversals
where I have divided the time into
steps
and I am allowed to reverse velocity
only
at such a time. This gives (as approaches
zero) Dirac's equation in two dimensions
- one dimension of space and one of
time
.
Dirac's wave function has four components
in four dimensions, but in this case,
it
has only two components and this rule
for
the amplitude of a path automatically
generates
the need for two components. Because
if this
is the formula for the amplitudes of
path,
it will not do you any good to know
the total
amplitude of all paths, which come
into a
given point to find the amplitude to
reach
the next point. This is because for
the next
time, if it came in from the right,
there
is no new factor ie if it goes out
to the
right, whereas, if it came in from
the left
there was a new factor ie. So, to continue
this same information forward to the
next
moment, it was not sufficient information
to know the total amplitude to arrive,
but
you had to know the amplitude to arrive
from
the right and the amplitude to arrive
to
the left, independently. If you did,
however,
you could then compute both of those
again
independently and thus you had to carry
two
amplitudes to form a differential equation
(first order in time).
And, so I dreamed that if I were clever,
I would find a formula for the amplitude
of a path that was beautiful and simple
for
three dimensions of space and one of
time,
which would be equivalent to the Dirac
equation,
and for which the four components,
matrices,
and all those other mathematical funny
things
would come out as a simple consequence
-
I have never succeeded in that either.
But,
I did want to mention some of the unsuccessful
things on which I spent almost as much
effort,
as on the things that did work.
To summarize the situation a few years
after
the way, I would say, I had much experience
with quantum electrodynamics, at least
in
the knowledge of many different ways
of formulating
it, in terms of path integrals of actions
and in other forms. One of the important
by-products, for example, of much experience
in these simple forms, was that it
was easy
to see how to combine together what
was in
those days called the longitudinal
and transverse
fields, and in general, to see clearly
the
relativistic invariance of the theory.
Because
of the need to do things differentially
there
had been, in the standard quantum electrodynamics,
a complete split of the field into
two parts,
one of which is called the longitudinal
part
and the other mediated by the photons,
or
transverse waves. The longitudinal
part was
described by a Coulomb potential acting
instantaneously
in the Schr? dinger equation, while
the transverse
part had entirely different description
in
terms of quantization of the transverse
waves.
This separation depended upon the relativistic
tilt of your axes in spacetime. People
moving
at different velocities would separate
the
same field into longitudinal and transverse
fields in a different way. Furthermore,
the
entire formulation of quantum mechanics
insisting,
as it did, on the wave function at
a given
time, was hard to analyze relativistically.
Somebody else in a different coordinate
system
would calculate the succession of events
in terms of wave functions on differently
cut slices of space-time, and with
a different
separation of longitudinal and transverse
parts. The Hamiltonian theory did not
look
relativistically invariant, although,
of
course, it was. One of the great advantages
of the overall point of view, was that
you
could see the relativistic invariance
right
away - or as Schwinger would say -
the covariance
was manifest. I had the advantage,
therefore,
of having a manifestedly covariant
form for
quantum electrodynamics with suggestions
for modifications and so on. I had
the disadvantage
that if I took it too seriously - I
mean,
if I took it seriously at all in this
form,
- I got into trouble with these complex
energies
and the failure of adding probabilities
to
one and so on. I was unsuccessfully
struggling
with that.
Then Lamb did his experiment, measuring
the
separation of the 2S? and 2P? levels
of hydrogen,
finding it to be about 1000 megacycles
of
frequency difference. Professor Bethe,
with
whom I was then associated at Cornell,
is
a man who has this characteristic:
If there's
a good experimental number you've got
to
figure it out from theory. So, he forced
the quantum electrodynamics of the
day to
give him an answer to the separation
of these
two levels. He pointed out that the
self-energy
of an electron itself is infinite,
so that
the calculated energy of a bound electron
should also come out infinite. But,
when
you calculated the separation of the
two
energy levels in terms of the corrected
mass
instead of the old mass, it would turn
out,
he thought, that the theory would give
convergent
finite answers. He made an estimate
of the
splitting that way and found out that
it
was still divergent, but he guessed
that
was probably due to the fact that he
used
an unrelativistic theory of the matter.
Assuming
it would be convergent if relativistically
treated, he estimated he would get
about
a thousand megacycles for the Lamb-shift,
and thus, made the most important discovery
in the history of the theory of quantum
electrodynamics.
He worked this out on the train from
Ithaca,
New York to Schenectady and telephoned
me
excitedly from Schenectady to tell
me the
result, which I don't remember fully
appreciating
at the time.
Returning to Cornell, he gave a lecture
on
the subject, which I attended. He explained
that it gets very confusing to figure
out
exactly which infinite term corresponds
to
what in trying to make the correction
for
the infinite change in mass. If there
were
any modifications whatever, he said,
even
though not physically correct, (that
is not
necessarily the way nature actually
works)
but any modification whatever at high
frequencies,
which would make this correction finite,
then there would be no problem at all
to
figuring out how to keep track of everything.
You just calculate the finite mass
correction
Dm to the electron mass mo, substitute
the
numerical values of mo+Dm for m in
the results
for any other problem and all these
ambiguities
would be resolved. If, in addition,
this
method were relativistically invariant,
then
we would be absolutely sure how to
do it
without destroying relativistically
invariant.
After the lecture, I went up to him
and told
him, "I can do that for you, I'll
bring
it in for you tomorrow." I guess
I knew
every way to modify quantum electrodynamics
known to man, at the time. So, I went
in
next day, and explained what would
correspond
to the modification of the delta-function
to f and asked him to explain to me
how you
calculate the self-energy of an electron,
for instance, so we can figure out
if it's
finite.
I want you to see an interesting point.
I
did not take the advice of Professor
Jehle
to find out how it was useful. I never
used
all that machinery which I had cooked
up
to solve a single relativistic problem.
I
hadn't even calculated the self-energy
of
an electron up to that moment, and
was studying
the difficulties with the conservation
of
probability, and so on, without actually
doing anything, except discussing the
general
properties of the theory.
But now I went to Professor Bethe,
who explained
to me on the blackboard, as we worked
together,
how to calculate the self-energy of
an electron.
Up to that time when you did the integrals
they had been logarithmically divergent.
I told him how to make the relativistically
invariant modifications that I thought
would
make everything all right. We set up
the
integral which then diverged at the
sixth
power of the frequency instead of logarithmically!
So, I went back to my room and worried
about
this thing and went around in circles
trying
to figure out what was wrong because
I was
sure physically everything had to come
out
finite, I couldn't understand how it
came
out infinite. I became more and more
interested
and finally realized I had to learn
how to
make a calculation. So, ultimately,
I taught
myself how to calculate the self-energy
of
an electron working my patient way
through
the terrible confusion of those days
of negative
energy states and holes and longitudinal
contributions and so on. When I finally
found
out how to do it and did it with the
modifications
I wanted to suggest, it turned out
that it
was nicely convergent and finite, just
as
I had expected. Professor Bethe and
I have
never been able to discover what we
did wrong
on that blackboard two months before,
but
apparently we just went off somewhere
and
we have never been able to figure out
where.
It turned out, that what I had proposed,
if we had carried it out without making
a
mistake would have been all right and
would
have given a finite correction. Anyway,
it
forced me to go back over all this
and to
convince myself physically that nothing
can
go wrong. At any rate, the correction
to
mass was now finite, proportional to
where
a is the width of that function f which
was
substituted for d. If you wanted an
unmodified
electrodynamics, you would have to
take a
equal to zero, getting an infinite
mass correction.
But, that wasn't the point. Keeping
a finite,
I simply followed the program outlined
by
Professor Bethe and showed how to calculate
all the various things, the scatterings
of
electrons from atoms without radiation,
the
shifts of levels and so forth, calculating
everything in terms of the experimental
mass,
and noting that the results as Bethe
suggested,
were not sensitive to a in this form
and
even had a definite limit as ag0.
The rest of my work was simply to improve
the techniques then available for calculations,
making diagrams to help analyze perturbation
theory quicker. Most of this was first
worked
out by guessing - you see, I didn't
have
the relativistic theory of matter.
For example,
it seemed to me obvious that the velocities
in non-relativistic formulas have to
be replaced
by Dirac's matrix a or in the more
relativistic
forms by the operators . I just took
my guesses
from the forms that I had worked out
using
path integrals for nonrelativistic
matter,
but relativistic light. It was easy
to develop
rules of what to substitute to get
the relativistic
case. I was very surprised to discover
that
it was not known at that time, that
every
one of the formulas that had been worked
out so patiently by separating longitudinal
and transverse waves could be obtained
from
the formula for the transverse waves
alone,
if instead of summing over only the
two perpendicular
polarization directions you would sum
over
all four possible directions of polarization.
It was so obvious from the action (1)
that
I thought it was general knowledge
and would
do it all the time. I would get into
arguments
with people, because I didn't realize
they
didn't know that; but, it turned out
that
all their patient work with the longitudinal
waves was always equivalent to just
extending
the sum on the two transverse directions
of polarization over all four directions.
This was one of the amusing advantages
of
the method. In addition, I included
diagrams
for the various terms of the perturbation
series, improved notations to be used,
worked
out easy ways to evaluate integrals,
which
occurred in these problems, and so
on, and
made a kind of handbook on how to do
quantum
electrodynamics.
But one step of importance that was
physically
new was involved with the negative
energy
sea of Dirac, which caused me so much
logical
difficulty. I got so confused that
I remembered
Wheeler's old idea about the positron
being,
maybe, the electron going backward
in time.
Therefore, in the time dependent perturbation
theory that was usual for getting self-energy,
I simply supposed that for a while
we could
go backward in the time, and looked
at what
terms I got by running the time variables
backward. They were the same as the
terms
that other people got when they did
the problem
a more complicated way, using holes
in the
sea, except, possibly, for some signs.
These,
I, at first, determined empirically
by inventing
and trying some rules.
I have tried to explain that all the
improvements
of relativistic theory were at first
more
or less straightforward, semi-empirical
shenanigans.
Each time I would discover something,
however,
I would go back and I would check it
so many
ways, compare it to every problem that
had
been done previously in electrodynamics
(and
later, in weak coupling meson theory)
to
see if it would always agree, and so
on,
until I was absolutely convinced of
the truth
of the various rules and regulations
which
I concocted to simplify all the work.
During this time, people had been developing
meson theory, a subject I had not studied
in any detail. I became interested
in the
possible application of my methods
to perturbation
calculations in meson theory. But,
what was
meson theory? All I knew was that meson
theory
was something analogous to electrodynamics,
except that particles corresponding
to the
photon had a mass. It was easy to guess
the
d-function in (1), which was a solution
of
d'Alembertian equals zero, was to be
changed
to the corresponding solution of d'Alembertian
equals m2. Next, there were different
kind
of mesons - the one in closest analogy
to
photons, coupled via , are called vector
mesons - there were also scalar mesons.
Well,
maybe that corresponds to putting unity
in
place of the , I would here then speak
of
"pseudo vector coupling"
and I
would guess what that probably was.
I didn't
have the knowledge to understand the
way
these were defined in the conventional
papers
because they were expressed at that
time
in terms of creation and annihilation
operators,
and so on, which, I had not successfully
learned. I remember that when someone
had
started to teach me about creation
and annihilation
operators, that this operator creates
an
electron, I said, "how do you
create
an electron? It disagrees with the
conservation
of charge", and in that way, I
blocked
my mind from learning a very practical
scheme
of calculation. Therefore, I had to
find
as many opportunities as possible to
test
whether I guessed right as to what
the various
theories were.
One day a dispute arose at a Physical
Society
meeting as to the correctness of a
calculation
by Slotnick of the interaction of an
electron
with a neutron using pseudo scalar
theory
with pseudo vector coupling and also,
pseudo
scalar theory with pseudo scalar coupling.
He had found that the answers were
not the
same, in fact, by one theory, the result
was divergent, although convergent
with the
other. Some people believed that the
two
theories must give the same answer
for the
problem. This was a welcome opportunity
to
test my guesses as to whether I really
did
understand what these two couplings
were.
So, I went home, and during the evening
I
worked out the electron neutron scattering
for the pseudo scalar and pseudo vector
coupling,
saw they were not equal and subtracted
them,
and worked out the difference in detail.
The next day at the meeting, I saw
Slotnick
and said, "Slotnick, I worked
it out
last night, I wanted to see if I got
the
same answers you do. I got a different
answer
for each coupling - but, I would like
to
check in detail with you because I
want to
make sure of my methods." And,
he said,
"what do you mean you worked it
out
last night, it took me six months!"
And, when we compared the answers he
looked
at mine and he asked, "what is
that
Q in there, that variable Q?"
(I had
expressions like (tan -1Q) /Q etc.).
I said,
"that's the momentum transferred
by
the electron, the electron deflected
by different
angles." "Oh", he said,
"no,
I only have the limiting value as Q
approaches
zero; the forward scattering."
Well,
it was easy enough to just substitute
Q equals
zero in my form and I then got the
same answers
as he did. But, it took him six months
to
do the case of zero momentum transfer,
whereas,
during one evening I had done the finite
and arbitrary momentum transfer. That
was
a thrilling moment for me, like receiving
the Nobel Prize, because that convinced
me,
at last, I did have some kind of method
and
technique and understood how to do
something
that other people did not know how
to do.
That was my moment of triumph in which
I
realized I really had succeeded in
working
out something worthwhile.
At this stage, I was urged to publish
this
because everybody said it looks like
an easy
way to make calculations, and wanted
to know
how to do it. I had to publish it,
missing
two things; one was proof of every
statement
in a mathematically conventional sense.
Often,
even in a physicist's sense, I did
not have
a demonstration of how to get all of
these
rules and equations from conventional
electrodynamics.
But, I did know from experience, from
fooling
around, that everything was, in fact,
equivalent
to the regular electrodynamics and
had partial
proofs of many pieces, although, I
never
really sat down, like Euclid did for
the
geometers of Greece, and made sure
that you
could get it all from a single simple
set
of axioms. As a result, the work was
criticized,
I don't know whether favorably or unfavorably,
and the "method" was called
the
"intuitive method". For those
who
do not realize it, however, I should
like
to emphasize that there is a lot of
work
involved in using this "intuitive
method"
successfully. Because no simple clear
proof
of the formula or idea presents itself,
it
is necessary to do an unusually great
amount
of checking and rechecking for consistency
and correctness in terms of what is
known,
by comparing to other analogous examples,
limiting cases, etc. In the face of
the lack
of direct mathematical demonstration,
one
must be careful and thorough to make
sure
of the point, and one should make a
perpetual
attempt to demonstrate as much of the
formula
as possible. Nevertheless, a very great
deal
more truth can become known than can
be proven.
It must be clearly understood that
in all
this work, I was representing the conventional
electrodynamics with retarded interaction,
and not my half-advanced and half-retarded
theory corresponding to (1). I merely
use
(1) to guess at forms. And, one of
the forms
I guessed at corresponded to changing
d to
a function f of width a2, so that I
could
calculate finite results for all of
the problems.
This brings me to the second thing
that was
missing when I published the paper,
an unresolved
difficulty. With d replaced by f the
calculations
would give results which were not "unitary",
that is, for which the sum of the probabilities
of all alternatives was not unity.
The deviation
from unity was very small, in practice,
if
a was very small. In the limit that
I took
a very tiny, it might not make any
difference.
And, so the process of the renormalization
could be made, you could calculate
everything
in terms of the experimental mass and
then
take the limit and the apparent difficulty
that the unitary is violated temporarily
seems to disappear. I was unable to
demonstrate
that, as a matter of fact, it does.
It is lucky that I did not wait to
straighten
out that point, for as far as I know,
nobody
has yet been able to resolve this question.
Experience with meson theories with
stronger
couplings and with strongly coupled
vector
photons, although not proving anything,
convinces
me that if the coupling were stronger,
or
if you went to a higher order (137th
order
of perturbation theory for electrodynamics),
this difficulty would remain in the
limit
and there would be real trouble. That
is,
I believe there is really no satisfactory
quantum electrodynamics, but I'm not
sure.
And, I believe, that one of the reasons
for
the slowness of present-day progress
in understanding
the strong interactions is that there
isn't
any relativistic theoretical model,
from
which you can really calculate everything.
Although, it is usually said, that
the difficulty
lies in the fact that strong interactions
are too hard to calculate, I believe,
it
is really because strong interactions
in
field theory have no solution, have
no sense
they're either infinite, or, if you
try to
modify them, the modification destroys
the
unitarity. I don't think we have a
completely
satisfactory relativistic quantum-mechanical
model, even one that doesn't agree
with nature,
but, at least, agrees with the logic
that
the sum of probability of all alternatives
has to be 100%. Therefore, I think
that the
renormalization theory is simply a
way to
sweep the difficulties of the divergences
of electrodynamics under the rug. I
am, of
course, not sure of that.
This completes the story of the development
of the space-time view of quantum electrodynamics.
I wonder if anything can be learned
from
it. I doubt it. It is most striking
that
most of the ideas developed in the
course
of this research were not ultimately
used
in the final result. For example, the
half-advanced
and half-retarded potential was not
finally
used, the action expression (1) was
not used,
the idea that charges do not act on
themselves
was abandoned. The path-integral formulation
of quantum mechanics was useful for
guessing
at final expressions and at formulating
the
general theory of electrodynamics in
new
ways - although, strictly it was not
absolutely
necessary. The same goes for the idea
of
the positron being a backward moving
electron,
it was very convenient, but not strictly
necessary for the theory because it
is exactly
equivalent to the negative energy sea
point
of view.
We are struck by the very large number
of
different physical viewpoints and widely
different mathematical formulations
that
are all equivalent to one another.
The method
used here, of reasoning in physical
terms,
therefore, appears to be extremely
inefficient.
On looking back over the work, I can
only
feel a kind of regret for the enormous
amount
of physical reasoning and mathematically
re-expression which ends by merely
re-expressing
what was previously known, although
in a
form which is much more efficient for
the
calculation of specific problems. Would
it
not have been much easier to simply
work
entirely in the mathematical framework
to
elaborate a more efficient expression?
This
would certainly seem to be the case,
but
it must be remarked that although the
problem
actually solved was only such a reformulation,
the problem originally tackled was
the (possibly
still unsolved) problem of avoidance
of the
infinities of the usual theory. Therefore,
a new theory was sought, not just a
modification
of the old. Although the quest was
unsuccessful,
we should look at the question of the
value
of physical ideas in developing a new
theory.
Many different physical ideas can describe
the same physical reality. Thus, classical
electrodynamics can be described by
a field
view, or an action at a distance view,
etc.
Originally, Maxwell filled space with
idler
wheels, and Faraday with fields lines,
but
somehow the Maxwell equations themselves
are pristine and independent of the
elaboration
of words attempting a physical description.
The only true physical description
is that
describing the experimental meaning
of the
quantities in the equation - or better,
the
way the equations are to be used in
describing
experimental observations. This being
the
case perhaps the best way to proceed
is to
try to guess equations, and disregard
physical
models or descriptions. For example,
McCullough
guessed the correct equations for light
propagation
in a crystal long before his colleagues
using
elastic models could make head or tail
of
the phenomena, or again, Dirac obtained
his
equation for the description of the
electron
by an almost purely mathematical proposition.
A simple physical view by which all
the contents
of this equation can be seen is still
lacking.
Therefore, I think equation guessing
might
be the best method to proceed to obtain
the
laws for the part of physics which
is presently
unknown. Yet, when I was much younger,
I
tried this equation guessing and I
have seen
many students try this, but it is very
easy
to go off in wildly incorrect and impossible
directions. I think the problem is
not to
find the best or most efficient method
to
proceed to a discovery, but to find
any method
at all. Physical reasoning does help
some
people to generate suggestions as to
how
the unknown may be related to the known.
Theories of the known, which are described
by different physical ideas may be
equivalent
in all their predictions and are hence
scientifically
indistinguishable. However, they are
not
psychologically identical when trying
to
move from that base into the unknown.
For
different views suggest different kinds
of
modifications which might be made and
hence
are not equivalent in the hypotheses
one
generates from them in ones attempt
to understand
what is not yet understood. I, therefore,
think that a good theoretical physicist
today
might find it useful to have a wide
range
of physical viewpoints and mathematical
expressions
of the same theory (for example, of
quantum
electrodynamics) available to him.
This may
be asking too much of one man. Then
new students
should as a class have this. If every
individual
student follows the same current fashion
in expressing and thinking about electrodynamics
or field theory, then the variety of
hypotheses
being generated to understand strong
interactions,
say, is limited. Perhaps rightly so,
for
possibly the chance is high that the
truth
lies in the fashionable direction.
But, on
the off-chance that it is in another
direction
- a direction obvious from an unfashionable
view of field theory - who will find
it?
Only someone who has sacrificed himself
by
teaching himself quantum electrodynamics
from a peculiar and unusual point of
view;
one that he may have to invent for
himself.
I say sacrificed himself because he
most
likely will get nothing from it, because
the truth may lie in another direction,
perhaps
even the fashionable one.
But, if my own experience is any guide,
the
sacrifice is really not great because
if
the peculiar viewpoint taken is truly
experimentally
equivalent to the usual in the realm
of the
known there is always a range of applications
and problems in this realm for which
the
special viewpoint gives one a special
power
and clarity of thought, which is valuable
in itself. Furthermore, in the search
for
new laws, you always have the psychological
excitement of feeling that possible
nobody
has yet thought of the crazy possibility
you are looking at right now.
So what happened to the old theory
that I
fell in love with as a youth? Well,
I would
say it's become an old lady, that has
very
little attractive left in her and the
young
today will not have their hearts pound
anymore
when they look at her. But, we can
say the
best we can for any old woman, that
she has
been a very good mother and she has
given
birth to some very good children. And,
I
thank the Swedish Academy of Sciences
for
complimenting one of them. Thank you.
Source: http://nobelprize.org/nobel_prizes/physics/laureates/1965
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