වෙනත් සත්භාවවේදයක ක්වොන්ටම් භෞතිකය

මේ ලිපිය 2010 දී
කෝනෙල් විශ්වවිද්යාලයේ සඟරාවක පළවූවකි. අවශ්ය අයකුට එය එහි කියවිය හැකි ය. මෙහි
රූප සටහන් හා ගණිත සංකේත එක්කෝ පළ නොවේ නැත්නම් නිවැරදිව සඳහන් නො වෙ. මුල් ලිපිය
කියවීමෙන් ඒ සියල්ල බලා ගත හැකි ය.

මෙහි කියැවෙන්නේ අංශුවක් දෙතැනක හෝ වැඩි තැනක සිටීම
පිළිබඳ කතාවකි. අංශුවකට එක වර සිදුරු දෙකකින් යා හැකි බවත් එමගින් ද්විත්ව සිදුරු
පරීක්ෂණය තේරුම් ගත හැකි බවත් කියැවෙයි. එහි දී චතුස්කෝටික න්යාය වැදගත් වන
අයුරුද කියැවෙයි.

අද වන විට අංශුවක් දෙතැනක පිහිටීම බටහිර භෞතික විද්යාවේ
පිළිගැනී අවසන් ය. එහෙත් එය ඊනියා යථාර්ථය යැයි මම නොකියමි. එය තවත් කතාවක් පමණකි.

මේ ලිපිය ගැන යමක් කිව යුතු නම් ජාත්යන්තර සඟරාවකට යා හැකි ය. මුහුණු පොතේ තම තම නැණ පමණින් පළ කරන අනම් මනම් නොසලකා හරින බව පමණක් සලකන්න.

arXiv:1006.4712v1 [physics.gen-ph] 24 Jun 2010

Quantum Physics in a different
ontology

Nalin de Silva

Department of Mathematics, University
of Kelaniya, Kelaniya, Sri Lanka

Abstract

It is shown that neither the wave
picture nor the ordinary particle picture offers

a satisfactory explanation of the
double-slit experiment. The Physicists who

have been successful in formulating
theories in the Newtonian Paradigm with

its corresponding ontology find it
difficult to interpret Quantum Physics which

deals with particles that are not
sensory perceptible. A different interpretation

of Quantum Physics based in a different
ontology is presented in what follows.

According to the new interpretation
Quantum particles have different proper-

ties from those of Classical Newtonian
particles. The interference patterns are

explained in terms of particles each of
which passes through both slits.

1 INTRODUCTION

Planck introduced his ideas on quanta
or packets of energy towards the end

of the nineteenth century. In that
sense Quantum Physics is more than one

hundred years old. From the very
beginning Quantum Physics came up with

strange phenomena that made the
Physicists to disbelieve what they themselves

were proposing to understand the new
features that were being observed.

The so-called double-slit experiment1 continues to baffle the Physicists who

are glued to twofold two valued logic
that is behind the Newtonian paradigm. As

it was one of the most fundamental
experiments that they could not understand

in Quantum Physics the Nobel Prize
winning Physicist Richard Feynmann once

declared that no body understood
Quantum Physics! This statement by Feyn-

mann makes one to delve into the
meaning of understanding. In other words

one has to understand what is meant by
understanding. However, it is clear

that if one is confined to an ontology
based in twofold formal logic, and linear

thinking one would be confused by a
statement such as understanding what is

meant by understanding. A decade ago
the intellectuals who were only familiar

with linear thinking and not with cyclic
thinking would have left deliberations

into such statements to whom they call
mystics, as such statements did not

come within the “rational” way of
thinking. However, in this paper we would

not attempt to understand what is meant
by understanding.

The principle of superposition which
was familiar to Classical Physicists as

well, has taken an entirely different
meaning with respect to Quantum Physics.

The essence of the principle can be
explained as follows. If x and y are two

solutions of what is called a linear
differential equation then x + y is also a

solution of the same differential
equation. This is a simpler version of what

is generally known as the principle of
superposition. In Classical Physics two

magnets giving rise to two different
magnetic fields would combine to give one

magnetic field, and a compass that is
brought to the resulting magnetic field

would respond to the resulting field,
and not to the field of any one of the mag-

nets. It has to be emphasised that a
magnet is in only one state, corresponding

to the respective magnetic field and it
is the two fields of the two magnets that

combine to give one field though one
would not find a single magnet that gives

rise to the resultant field. We could
describe this phenomenon as that of two or

more becoming one. However, in the
Quantum world things are different, and

the principle of superposition has an
unusual interpretation.

2 THE WAVE NATURE OF PARTICLES

In order to discuss the new
interpretation of the principle of superposition we

first consider the so called
double-slit experiment where a stream of electrons

(in general, particles or photons) is
made to pass through two slits and then

to strike a screen. If both slits are
open an interference pattern is observed on

the screen. Now in Quantum Physics it
is said that particles such as electrons

posses wave properties and photons
(light) exhibit particle properties in addition

to their respective “normal”
properties. Interference patterns are supposed to

result from wave properties and
according to the Physicists the wave theory

successfully explains the formation of
such patterns in the case of a stream of

particles fired from a source to strike
the screen after passing through the slits.

The Physicists would claim that the
double-slit experiment demonstrates that

particles such as electrons do exhibit
wave properties.

The double-slit experiment has been
carried out with only one electron pass-

ing through the slits one at a time2 (electrons at very low intensities)
instead of a

stream of particles released almost
simultaneously to pass through the two slits.

Even at very low intensities
interference patterns have been observed after suffi-

ciently large number of electrons had
been fired from the source. The Physicists

have been puzzled by this phenomenon.
In the case of several electrons passing

through the slits simultaneously it
could be explained using the wave properties

of the particles, in other words
resorting to the wave picture. Unfortunately in

the case of electrons being shot one at
a time this explanation was not possible

as what was observed on the screen was
not a faint interference pattern corre-

sponding to one electron but an
electron striking the screen at a single point

on the screen. These points in
sufficiently large numbers, corresponding to a

large number of electrons, finally gave
rise to an interference pattern. The wave

nature is only a way of speaking, as
even in the case of large number of particles

what is observed is a collection of
points and not waves interfering with each

other.

The Physicists also believe that an
electron as a particle could pass through

only one of the slits and a related
question that has been asked is whether it was

possible to find out the slit through which
an electron passes on its way to the

screen. Various mechanisms, including “capturing”
the electron using Geiger

counters, have been tried to “detect
the path” of the electron, and it has been

found that if the particular slit
through which the electron passed was detected

then the interference patterns were
washed out. In other words determining the

particle properties of the electron
erased its wave properties. Bohr, who was

instrumental in formulating the Copenhagen
interpretation3, was of the view

that one could observe either the
particle properties or the wave properties

but not both, and the inability to
observe both wave and particle properties

simultaneously came to be referred to
as complementarity. The experiments

that attempted to determine the slit
through which the electron passed were

known as which-way (welcherweg)
experiments as they attempted to find the

way or the path of the particle from
the source to the screen. The outcome

of these experiments made it clear that
the which-way experiments washed out

the interference patterns. It was
believed that at any given time the electrons

exhibited either the particle
properties or wave properties but not both.

However, what the Physicists failed to
recognize was that in the case of one

electron shot at a time there was no
weak interference pattern observed on the

screen for each electron thus
illustrating that a single electron did not exhibit

any wave properties. The electron
strikes the screen at one point, and it is the

collection of a large number of such
points or images on the screen that gave

the interference pattern. In the case
of a stream of electrons fired to strike the

screen each electron would have met the
screen at one point and the collection

of such points or images would have given
rise to an “interference pattern”.

Thus we could say that the interference
patterns are obtained not as a result of

the “wave nature” of electrons but due
to the collectiveness of a large number

of electrons that strike the screen.
The “wave nature” arises out of “particle”

properties and not due to “wave
properties”. Afshar4 comes closer to this
view

when he states “in other words,
evidence for coherent wave-like behavior is not a

single particle property, but an
ensemble or multi-particle property”. We are of

the opinion that in the double-slit
experiments no wave properties are observed

contrary to what is generally believed.
It is the particle properties that are

observed, though not necessarily those
of ordinary classical particles.

As a case in point this does not mean
that a particle in Quantum Physics has

a definite path from the source to the
screen through one of the slits, as could

be expected in the case of classical
particles. For a particle to have a path it

should posses both position and
momentum simultaneously. A path at any point

(assuming that it is a continuous path
without cusps and such other points)

should have a well defined tangent. In
the case of a particle moving, the direction

of the velocity (and the momentum) of
the particle at any given point defines the

unit tangent vector to its path.
Conversely the tangent to the path at any point

defines the direction of the velocity
and the momentum of the particle at that

point. However, according to the
Uncertainty Principle, both the momentum

and the position of a particle cannot
be determined simultaneously, and if the

position is known then the momentum
cannot be determined. Without the

momentum the direction of the velocity
of the particle and hence the tangent

vector cannot be known implying that a
continuous curve is not traced by

a particle in space. On the other hand
if the momentum of the particle is

known then only the direction and
magnitude of the velocity (momentum) and

properties of other non conjugate
observables such as spin of the particle are

known, without the position being
known. Thus the particle can be everywhere,

with variable probabilities of finding
the particle at different points, but at

each point the particle being moving in
parallel directions with the same speed.

However, as will be explained later, this
does not mean that we could observe

the particle everywhere.

In the light of the uncertainty
principle it is futile to design experiments to

find out the path of a particle. The
so-called which-way experiments have been

designed to detect the slit through
which the particle moves, on the assumption

that the particle moves through one
slit only. However, in effect there is no

path that the particle follows and it
is not correct to say that the particle

passes through one of the slits. The
which-way experiment actually stops the

particle from reaching the screen and
hence there is no possibility of obtaining

any “interference pattern”. It is not a
case of observing particle properties

destroying the wave properties of
matter, but an instance of creating a situation

where the particle is either not
allowed to strike the screen or to pass through

only one slit deliberately. In effect
it is the particle properties exhibited at the

screen that are cut off.

What is important is to note that
interference patterns are observed only if

both slits are kept open, and also if
the particles are free to reach the screen. If

one slit is closed or obstacles are set
up in the guise of which-way experiments or

otherwise, so as not to allow the
particles to reach the screen then no interference

patterns are observed. The most
important factor is the opening of the two slits.

In the case of which-way experiments as
well, what is effectively done is to close

one of the slits as particles through
that slit are not allowed to reach the screen.

With only one slit open while the other
slit is effectively closed with the which-

way experiment apparatus, no
interference patterns are observed.

The Physicists are obsessed with the
idea that a particle can be only at one

position at a given time, backed by the
ontology of day to day experience. While

this may be the experience with our
sensory perceptible particles (objects) or

what we may call ordinary Newtonian
classical objects such as billiard balls, it

need not be the case with Quantum
particles. However, from the beginning of

Quantum Physics, it appears that the
Physicists have been of the view that a

particle can be at one position at a
given time whether it is being observed or

not. Hence they seem to have assumed
that on its “journey to the screen from

the source” a particle could pass
through only one of the slits. They have worked

on the assumption that even if both
slits are open the particle passes through

only one of the slits but behaves
differently to create interference patterns as

if the particle is “aware” that both
slits are open. According to the view of

the Physicists if only one slit is open
the particles having “known” that the

other slit is closed pass through the
open slit and “decide” not to form any

interference patterns. It is clear that
the explanation given by the Physicists

for the formation of interference
patterns on the basis of the particle picture is

not satisfactory. We saw earlier that
the explanation given in the wave picture

is also not satisfactory as a single
electron fired from the source does not form a

faint interference pattern on the
screen. If the particles behave like waves then

even a single particle should behave
like a wave and produce a faint interference

pattern, having interfered with itself.
What is emphasised here is that the

final interference pattern is not the
sum of faint interference patterns due to

single particles, but an apparent
pattern formed by a collection of images on

the screen due to the particles. There
is no interference pattern as such but

only a collection of the points where
the particles strike the screen, or of the

images formed by the particles that were
able to reach the screen. The images

finally depend on the probability that
a particle would be at a given position.

Before we proceed further a
clarification has to be made on “seeing” a par-

ticle at a given position at a given
time in respect of the double-slit experiment.

In this experiment we are concerned
with particles released from a source with

a given momentum and given energy. As
such according to the uncertainty

principle, nothing can be said
definitely on the position of these particles, im-

mediately after they leave the source.
It can only be said that there is a certain

probability that the particle would be
found in a certain position. Thus the

particle is “everywhere” “until” it is “caught”
at some position such as a slit or

a screen. Though we have used the word “until”,
time is not defined as far as the

particle is concerned as it has a
definite energy. It can only be said that there is

a certain probability that the particle
could be “seen” at a given place at a given

time, with respect to the observer. The
particle is not only everywhere but also

at “every instant”. Thus it is
meaningless to say the particle is at a given slit at

a given time as neither time nor
position is defined for the particle with respect

to itself. The particle would meet the
screen at some position on the screen at

some time but “before” that it was
everywhere and at every instant. A photon

that is supposed to “move along a
straight line” should not be considered as

such, but being at all points along the
straight line at “all times” “before” it

interacts with a screen or another
particle.

The probability of an electron striking
the screen at a given point with only

one slit open is not the same as that
when both slits are open. Thus when

a large number of particles strike the
screen, the different probabilities give

rise to different “patterns” which are
essentially collection of points where the

particles meet the screen. The “interference
patterns” observed when both slits

are open are replaced by “other
patterns” when one of the slits is closed. The

“interference patterns” as well as the “other
patterns” are the results of particle

properties, the difference being due to
the number of slits that are open. If both

slits are closed there is no pattern at
all as no particle would reach the screen

under such conditions. When one of the
slits is open there is a probability that

the particle can be at the position
where the slit is whereas when both slits are

open there is a probability that the
particle could be at both the slits “before”

reaching the screen. When both slits
are open, the particle is at both slits and

the position is not known while the
momentum of the particle is not changed

and has the original value with which
it was shot. However, when one of the slits

is blocked the particle is at the other
slit implying that the momentum is not

known. These uncertainties of the
momentum would carry different particles

to different places on the screen,
while in the case when both slits are open it

is the uncertainties of position that
make the particle to strike the screen at

different positions. The difference
between the “interference patterns” and the

“other patterns” is
due to this.

3 EXPERIMENTS OF AFSHAR

Afshar5 has claimed that he was able to demonstrate that an electron or a
pho-

ton would exhibit both particle and wave
properties (Figure 1). He allowed

light to pass through two slits and to
interact with a wire grid placed so that

the nodes were at the positions of zero
probability of observing a photon. The

photons were not affected by the wire
grid as the nodes were at the positions of

zero probability and at those positions
there were no photons to interact with

the grid. The photons were then
intercepted by a lens system that was able

to identify the slit through which any
single photon had passed. According to

Afshar the nodes of the grid at the
positions of zero probability indicated that

the wave properties of the photons were
observable while the lens system in de-

tecting the slit through which the
photon had passed demonstrated the particle

properties of the photons. However, in
this experiment, assuming that the lens

Figure 1: The
wire grid and the lens system of Afshra, and the corresponding images

observed. No interference patterns after
the lenses and Afshra claims that the wire grid

demonstrates the wave property while the
images correspond to the particle property.

(Courtesy Afshra)

system detects the slit through which
the photon passed, what is observed is

again the particle properties of the
photons. The wire grid with the nodes at

the position of zero probabilities does
not interact with the photons, as there

are no photons at positions of zero
probability to interact with the grid. No so

called waves are observed, as there is
no screen for the particles to strike. Thus

the wire grid has no effect in this
experiment and with or without such a grid

the lens system would behave the same
way.

Let us consider what would happen if
the wire grid is shifted forwards to-

wards the source, backwards towards the
lens system or laterally. As the nodes

of the wire grid would be shifted from
the positions of zero probability some

photons would strike the grid and they
would not proceed towards the lens sys-

tem. Thus the number of photons that
reach the lens system would be reduced

and there would be a decrease in intensity
of light received at the lens. Though

Afshar claims that wave properties are
observed just by placing a wire grid so

that its nodes are at the positions of
zero probability, it is not so.

The so called wave properties could be
observed only by placing a screen in

between the wire grid and the lens
system. As we have mentioned above, even

then what is observed is a collection
of images at the points where the photons

strike the screen, and not wave
properties as such. In this case as all the photons

would have been absorbed by the screen,
the lens system would not be able to

detect any photons nor the “slit
through which the photons passed”. On the

other hand if the screen is kept beyond
the lens system then there would not be

any photons to strike the screen and
hence no “wave properties”.

4 EXPERIMENTS AT KELANIYA

We at the University of Kelaniya have
given thought to this problem, and one

of my students Suraj Chandana has
carried out a number of experiments, which

may be identified as extensions of the
experiment of Afshar. Chandana and de

Silva6 had predicted that if we were to have a single slit and then a
screen,

instead of the wire grid and the lens
system, “after” the photons have passed

through the two slits, then the photons
would pass through the single slit with

the same probability as that of finding
a photon at the point where the slit was

kept. This implied that if the slit was
kept at a point where the probability of

finding the photon is zero, the photon
would not pass through the slit to strike

the screen, but on the other hand, if
the slit was kept at any other point there was

a non zero probability that the photon
would pass through the slit, and striking

the screen. Thus if a stream of photons
is passed through two slits, and “then”

a single slit, “before” striking the
screen, depending on the position of the single

slit the intensity with which the
photons strike the screen would change. Further

it implies that these intensities
should correspond to the intensities observed in

connection with the “interference
patterns” observed in the case of the standard

double-slit experiment, if the
positions of the slit were varied along a line parallel

(by moving the single slit along a line
parallel to the double-slit and the screen)

to the double-slits and the screen.
Chandana has been successful in obtaining

the results as predicted. In another
experiment Chandana7 had an Aluminium

sheet of very small thickness joining
the points or positions where the probability

of finding a photon is zero (positions
of zero probability), stretching from the

double-slits to the screen as
illustrated in the figure 2. As an obstacle placed at

a position of zero probability would
not affect the photon the Aluminium sheet

had no effect on the visible
interference patterns on the screen. This experiment

was carried out by Chandana with number
of Aluminium sheets placed along

Figure 2: The
figure represents the aluminium sheet joining the positions of zero

probability from a position closer to
the double slit to the screen.

lines joining the positions of zero
probability stretching from the double-slits

to the screen. We were not surprised to
find that the Aluminium sheets did

not interfere with the interference
patterns. However, even if one of the sheets

is slightly displaced the interference
pattern is destroyed as the photons now

interact with the sheets at points
where the probability of finding a photon is

not zero.

These observations are not consistent
with the wave picture as a wave would

not be able to penetrate the Aluminium
sheets without being affected. Even

the pilot waves of Bohm are not known
to go through a material medium undis-

turbed. As we have argued a single
electron emitted from the source would

not exhibit a faint interference
pattern on the screen but a spot or an image

having passed beyond the slits. The
Physicists are interested in the wave pic-

ture to explain the interference
patterns as they find it difficult to believe that

a particle would pass through both
slits simultaneously. Thus they mention of

particle properties when they are
interested in “capturing” particles and of wave

properties in explaining phenomena such
as the interference pattern.

5 PRINCIPLE OF SUPERPOSITION IN QUAN-

TUM PHYSICS

We consider the Quantum entities to be
particles though of a nature different

from that of Classical Newtonian
particles. We have no inhibition in believing

that the Quantum particles unlike the
Newtonian particles could pass through

both slits at the “same time”, as the
logic of different cultures permits us to do

so. Physics and in general Mathematics
and sciences are based on Aristotelian

two valued twofold logic according to
which a proposition and its negation can-

not be true at the same time. Thus if a
particle is at the slit A, the proposition

that the particle is at A is true and its negation that the
particle is not at A

is not true, and vice versa. Therefore if the particle is at
A then it cannot be

anywhere else as well, and hence cannot
be at B. This is based on what may

be called the Aristotelian- Newtonian -
Einsteinian ontology where a particle

can occupy only one position at a given
time in any frame of reference of an

observer. However, in fourfold logic (catuskoti) a proposition and its negation

can be both true, and hence in that
logic it is not a contradiction to say that a

particle is at the slit A and at somewhere else (say at the slit B) at the “same

instant” or “every instant” Thus
according to catuskoti the particle can be at

many places at the same time or at many
instants with respect to the observer.

In the case of the double-slit
experiment, the momentum of a particle is

known, as the particles are fired with
known energy, and hence the position

is not known. In such a situation Heisenberg’s
uncertainty principle demands

that the position of the particle is
not known. The position of the particle is

relieved only after a measurement is
made to determine the position. Before the

measurement, the particle is in a
superposition of states corresponding to the po-

sitions in space the particle could be
found. After the measurement the particle

would be found in a definite position
(state), collapsing from the superposition

of a number of states to that of the
definite state. Before the measurement

what could have been said was that
there was a certain probability of finding

the particle at a given position.
Though the particle is in a superposition of

states before a measurement is made to
find the position, it is in a definite state

with respect to the momentum.

In Quantum Mechanics unlike in
Classical Mechanics, a state of a system,

a particle or an object is represented
by a vector in a Mathematical space

known as the Hilbert space. The
observables such as position, momentum, and

spin are represented by what are known
as Hermitian operators. If a system

is in a state represented by an
eigenstate |_ > of a Hermitian operator A,

belonging to the eigenvalue a, then the system has the value a corresponding

to the observable represented by the
Hermitian operator A. This is expressed

mathematically by A|_ >= a|_ >. If B is the conjugate
operator of A, then the

value corresponding to the observable
represented by B is not known. All
that

can be said, according to the standard
Copenhagen interpretation, is that if the

value corresponding to the observable
represented by B is measured, then
there

is a certain probability of obtaining
an eigenvalue of B as the measurement.

Before the measurement is made nothing
could be said of the value. In plain

language this means that if the value
of a certain observable is known then the

value of the conjugate observable is
not known.

However, the state |_ > can be expressed as a linear combination of the

eigenstates |
> of B in the form |_ >= P|ci i > where ci 2 C, the field of

complex numbers. In other words the
coefficients of | >’s in the expansion

of |_ > are complex
numbers. The Copenhagen interpretation tells us that

when the observable corresponding to B is measured it would result in a state

corresponding to one of the |
>’s with the measurement yielding the
eigenvalue

b to which the
particular | > belongs, the probability of obtaining
the value b

being given by the value of the
relevant |c|2. Before the measurement is made

nothing can be said regarding the
observable corresponding to B. According

to Bohr, it is meaningless to talk of
the state of the system with respect to B

as nothing could be observed. There is
no knowledge regarding the observable

corresponding to B as it has not been observed. The value
or the knowledge

of the observable is “created” by the
observer who sets up an experiment to

measure the value in respect of B. The observed depends on the observer
and

it makes no sense to talk of an
observable unless it has been observed. This

interpretation is rooted in positivism
as opposed to realism in which the entire

corpus of knowledge in Newtonian -
Einsteinian Physics is based. This body of

knowledge is also based in Aristotelian
- Newtonian - Einsteinian ontology.

As a particular case one could refer to
the conjugate Hermitian operators

in respect of position and momentum of
a particle in Quantum Mechanics.

When the position of a particle is
measured then its momentum is not known.

According to the Copenhagen
Interpretation, it can only be said that if an

apparatus is set up to measure the
momentum, the observer would observe one

of the possible values for the momentum
and that there is a certain probability

of observing the particular value.
Before the measurement is made the particle

has no momentum, as such, and it is
meaningless to talk of the momentum of

the particle. The observer by his act
of observation gives or creates a value for

the momentum of the particle, so to
speak of. Once the momentum is measured

the observer has knowledge of the
momentum but not before it. However, after

the momentum is measured, the knowledge
of the position of the particle is

“washed off” and hence it becomes
meaningless to talk of the position of the

particle. The observer could have
knowledge only of either the momentum or

the position, but not of both. A
version of this conclusion is sometimes referred

to as the uncertainty
principle.

What we have been discussing in the
proceeding paragraphs is the principle

of superposition. A particle or a system
with its position known is represented by

a vector |_ >in Hilbert
space, which is an eigenvector of the Hermitian operator

A corresponding to the
position. When the position of the particle or the

system is known, the momentum is not
known. If B is the Hermitian operator

corresponding to the momentum, then |_ > is not an eigenvector of B. However,

|_ > can be expressed as a linear
combination of the eigenvectors | >’s of B

though the momentum is not observed.
The superposition of the | >’s cannot

be observed, and neither can be
resolved into observable constituent parts. This

is different from the principle of
superposition in Classical Physics, where the

resultant can be resolved into its
constituent parts.

For example as we have mentioned in the
introduction the resultant magnetic

field due to two magnets can be
resolved into its two components and can be

observed. One of the magnets can be
taken off leaving only one of the constituent

magnetic fields. The superposition is
there to be observed and if the magnet

that was taken off is brought back to
its original position the resultant magnetic

field reappears. In Quantum Physics the
superposition cannot be observed

without disturbing the system and when
it is disturbed to measure the conjugate

variable, only one of the states in the
superposition could be observed and we

would not have known in advance if that
particular state were to appear as a

result of the disturbance induced by
us.

6 COPENHAGEN INTERPRETATION

In Classical Physics, as we have
already stated, superposition is there to be

observed. However, in Quantum Physics
the superposition cannot be observed,

and further unlike in Classical Physics
interpretations are required to “translate”

the abstract Mathematical apparatus and
concepts into day to day language.

In Classical Physics one knows what is
meant by the position or the momen-

tum of a particle and those concepts
can be observed and understood without

an intermediate interpretation.
However, in Quantum Physics, the state of a

particle or a system is represented by
a vector in Hilbert space and observables

are represented by Hermitian operators
in Hilbert space. An interpretation or

interpretations are needed to express
these and other concepts to build a con-

crete picture out of the abstract
apparatus. Copenhagen interpretation is one

such interpretation and it is the
standard interpretation as far as most of the

Physicists are concerned.

Bohr more than anybody else was
instrumental in formulating the Copen-

hagen interpretation, and he in turn
was influenced by positivism and Chinese

Ying - Yang Philosophy. As a positivist
he believed that only the sensory per-

ceptible phenomena exist and did not
believe in the existence of that could

not be “observed”. When a state of a
particle or system is represented by an

eigenvector of an observable (Hermitian
operator in Hilbert space) the corre-

sponding value of the observable can be
measured and the positivist school had

no problem in accepting the existence
of such state. For example if the mo-

mentum of a particle is known then the
state of the particle is represented by

a certain vector in Hilbert space,
belonging to the particular eigenvalue that

has been measured. However, the problem
arises when the conjugate Hermitian

operator, in this case the position, is
considered, as in positivism the ontology

is connected with observations and
sensory perceptions. We are not considering

logical positivism and there seems to
be no interpretation of Quantum Physics

in a logical positivist ontology.

As we have seen a given eigenstate of a
Hermitian operator that has been

observed can be expressed as a linear
combination of the eigenstates of the

conjugate operator. To a positivist,
though the given eigenstate exists as it is

observed, the eigenstates of the
conjugate operator are not observable and it is

meaningless for him to talk of such
states. Thus if the momentum of a particle

has been measured, the eigenstates
belonging to the eigenvalues of the conjugate

operator, which is the position, are
not observed and the positivist would not

say anything regarding the existence of
such states. As far as the positivist is

concerned, there is only a probability
of finding the particle at some position,

and the particle will be at some
position only after the relevant measurement is

carried out.

In the case of the double-slit
experiment, this means that a positivist would

not say whether the particle passes
through a particular slit as it is not ob-

served. However he assumes that it it
is at one of the slits and not at both as

the Aristotelian - Newtonian -
Einsteinian ontology demands that the particle

should be at one of the slits and not
at both slits. (The positivists share with the

realists the Aristotelian - Newtonian -
Einsteinian ontology. They differ from

the realists when they insist that
nothing could be said of non observables.) If

a measurement is made, that is if an
experiment is carried out to find out the

slit where the particle is, then the
particle would be found at one of the slits

washing out the “interference pattern”.
Then superposition is collapsed and

“decoherance” sets in resulting “chaotic
pattern”.

A realist differs from a positivist in
that the former would want to know the

slit at which the particle is (the slit
through which the “particle passes”) even

without observing it. He would say the
particle would pass through one of the

slits whether one observes it or not,
and that it is an integral property of the

particle independent of the observer.
The Classical Physicists were realists. An

object in Classical Physics has a momentum
whether it is measured or not. The

observer in Classical Physics measures
the momentum that the particle already

possesses. In Quantum Physics the
positivists would say that the particle has

no momentum before it is measured but
acquires a momentum as a result of

the measurement.

We would not go into further details on
the differences between the realist

position and the positivist position.
However, what is relevant to us is that both

the realist and the positivist would
agree that the particle “goes through one

slit”, meaning that at a “given time”
the particle is found only at one of the slits.

They would also agree on the wave
nature of the particles. They have to depend

on the wave nature as they assume that
the particle passes through only one

slit, and as such they would not be
able to explain the “interference patterns”

without the wave properties of the
particles, as particles “passing through” only

one slit would not produce “interference
patterns”.

7 A NEW INTERPRETATION

We differ from the positivists as well
as the realists since we believe that the

particle is found at both slits and
hence “pass through both” in the common

parlance. In general we include the
postulate that the eigenstates | >’s in

|_ >= P|ci i > exist in
addition to |_ > (Postulate 3 below). We have also

introduced the concept of a mode. A
mode of a particle or a system is essentially

a potential observable. A mode has the
potential to be observed though it may

not be observed at a particular
instant. For example, position, momentum, spin

are modes. A particle or a system can
be in both modes corresponding to two

conjugate Hermitian operators, though
only one mode may be observed.

A revised version of the postulates of
the new interpretation formulated by

Chandana and de Silva9 is given below.

1. A state of a Quantum Mechanical
system is represented by a vector (ray) _

in the Hilbert space, where _ can be expressed as different linear
combina-

tions of the eigenvectors in the
Hilbert space, of Hermitian operators, any

operator corresponding to a mode. In
other words a state of a Quantum

Mechanical system can be represented by
different linear combinations of

eigenvectors of different modes, each
linear combination being that of the

eigenvectors of one of the modes. Thus
a state could have a number of

modes, each mode being a potential
observable.

2. If _ is expressed as a linear combination of two or more eigenvectors
of a

Hermitian operator, that is a mode,
then the corresponding mode cannot

be observed (or measured) by a human
observer with or without the aid

of an apparatus. In other words the
particular mode cannot be observed

and a value cannot be given to the
observable, which also means that no

measurement has been made on the
observable.

3. However, the non observation of a
mode does not mean that the mode does

not “exist”. We make a distinction
between the “existence” of a mode, and

the observation of a mode with or
without the aid of an apparatus. A mode

corresponding to a given Hermitian
operator could “exist” without being

observed. The knowledge of the “existence”
of a mode is independent

of its observation or measurement. In
other words the knowledge of the

“existence” of a mode of a Quantum
Mechanical state is different from the

knowledge of the value that the observable
corresponding to the relevant

Hermitian operator would take.

4. If a mode of a Quantum Mechanical
state is represented by a single eigen-

vector, and not by a linear combination
of two or more eigenvectors, of a

Hermitian operator, then the mode could
be observed by a human observer

with or without the aid of an
apparatus, and the value of the correspond-

ing observable (or the measured value)
is given by the eigenvalue which

the eigenvector belongs to. It has to
be emphasised that only those modes

of a Quantum Mechanical state, each
represented by a single eigenvector,

and not by a linear combination of
eigenvectors, of an Hermitian operator

can be observed at a given instant.

5. If a mode of a Quantum Mechanical
state is represented by an eigenvector

of a Hermitian operator then the mode
corresponding to the conjugate

operator cannot be represented by an
eigenvector of the conjugate Her-

mitian operator. It can be expressed as
a linear combination of two or

more of the eigenvectors of the
conjugate operator. This means that the

mode corresponding to the conjugate
operator cannot be observed, or in

other words it cannot be measured.
However, the relevant mode “exists”

though it cannot be observed.

6. It is not necessary that at least
one of the modes corresponding to two

conjugate operators should be
represented by a single eigenvector of the

relevant operator. It is possible that
each mode is represented by linear

combinations of two or more
eigenvectors of the corresponding operator.

In such situations neither of the modes
could be observed.

7. A state of a Quantum Mechanical
system can be altered by making an

operation that changes a mode or modes
of the state. However, not all

operations correspond to measurements
or observations. Only those oper-

ations that would result in a mode
being expressed as a single eigenvector,

and not as a linear combination of the
eigenvectors of an operator would

result in measurements.

8. A particle entangled with one or
more other particles is in general repre-

sented by a linear combination of eigenvectors
of an Hermitian operator

with respect to a mode, while the whole
system of particles is in general

represented by a linear combination of
the Cartesian products of the eigen-

vectors. In the case of two particles
it takes the form Pcij |_i > |_j >. If

one of the particles is in a mode that
is observed, then the particles entan-

gled with it are also in the same mode
as an observable. If a measurement

is made on some other mode then
instantaneously, the corresponding val-

ues in the same mode of the entangled
particles are also determined. In

such case, for two particles the whole
system is represented by vectors of

the form |_i > |_j >. If the number of entangled particles
is less than the

dimension of the space of the
eigenvectors of the Hermitian operator, then

if a measurement is made in the
particular mode, the particle would be

represented by one of the eigenvectors,
while the other particles entangled

with it would be each represented by a
different eigenvector of the Her-

mitian operator. However, if the number
of entangled particles is greater

than the dimension of the space of the
eigenvectors, then in some cases,

more than one particle would be
represented by a given eigenvector.

According to this interpretation if the
momentum of a particle is known then

it has not one position but several
positions. In other words the particle can

be at number of positions in
superposition though we are not able to observe

it at any one of those positions. The
particle could be observed only if it is at

one position. If an experiment is
carried out to determine the position of the

particle the superposition or the wave
function would collapse, and the particle

would be located at one of the
positions where it was before the measurement

was made.

Similarly if the particle is in the
position mode that is observed then it can

have several momenta in superposition
but we would not be able to observe any

one of them. If we perform an
experiment to determine the momentum, that

is if a measurement is made, then the
superposition of momenta would collapse

to one of them, enabling us to
determine the value of the momentum.

With respect to the double-slit
experiment this implies that the particle

is at both slits in superposition without
being observed and if we perform an

experiment to determine the slit “through
which the particle passes” (the slit

where the particle is) then the
superposition collapses and the particle would

be found only at one of the positions.
The positivists while assuming that

the particle “passes through only one
slit” would not say anything on the slit

“through which the particle passes” as
it cannot be observed. For the positivist

it is meaningless to speculate on
something that cannot be observed. The realists

too assume that the particle “passes
through” only one slit but would not be

satisfied with the positivist position,
and claim that a theory that is not able to

determine the slit through which the
particle passes is incomplete.

We make a distinction between being in
existence and being observed. A

particle or a system can exist in a
certain mode without being observed. In this

case the state of the particle or the
state is expressed as a linear combination

or superposition of the eigenstates of
the relevant Hermitian operator and the

particle or the system exists in all
the relevant eigenstates without being ob-

served. The mode is observed only when
the state of the particle or the system

is expressed as a single eigenstate of
the relevant Hermitian operator.

The existence of modes with more than
one eigenstates has been known for

sometime. Monroe10 and his colleagues in 1996 were able to
demonstrate the

existence of two spin states of
Beryllium cation simultaneously however without

observing them. One could say that the
interference obtained by them could

be understood on the basis of the
existence of simultaneous spin states of the

Beryllium cation. Since then similar
experiments have been carried out and the

existence of superposition of
eigenstates cannot be ruled out anymore.

8 A DIFFERENT ONTOLOGY AND LOGIC

In the ontology presented here no
distinction is made of the existence of sensory

perceptible objects and of other
entities. There is no absolute existence as such

and all existences are relative to the
mind. It has been shown by de Silva11 that

even the mind could be considered as a
creation of the mind a phenomenon

not in contradiction with cyclic
thinking. It is the mind that creates concepts

including that of self, and as such
sensory perceptible objects do not have any

preference over the others.

As we have mentioned the positivists
find it difficult to take cognizance of

entities that are not sensory
perceptible and it is this ontology that makes them

not to commit on the existence of unobserved
“objects”. In the present ontology

all existences are only conventional
and not absolute as such. Thus the existence

of simultaneous eigenstates or
superposition of eigenstates is not ruled out in

the present ontology. We have no
inhibition to postulate the existence of such

states and it is not in contradiction
with catuskoti or fourfold logic that may be

identified as the logic of the ontology
presented here.

As Jayatilleke12 has shown in fourfold logic or
sometimes referred to as tetra

lemma, unlike in twofold logic a
proposition and its negation can be both true

and false. (However, we do not agree
with the interpretation of fourfold logic

given by Jayatilleke.). In twofold
logic if a proposition is true then its negation

is false, and if a proposition is false,
then its negation is true. In addition to

these two cases fourfold logic has two
more cases where both the proposition and

its negation can be true or both false.
Thus the proposition that a particle is at

A, and the proposition
that a particle is not at A, can be both
true in fourfold

logic. (According to fourfold logic the
case could arise where the particle may

be neither at A nor not at A.) We may deduce from that a particle
can be

both at A and B (not at A) at the “same time”. In other words a
particle

can be at both slits in respect of the
double-slit experiment, and in general a

mode represented by a superposition of
two or more eigenvectors can exist as

the particle or the system can be at
number of “positions” simultaneously in

fourfold logic.

In twofold Aristotelian logic a
particle has to be either at A or not at A. Thus

the Physicists whether they are
realists or positivists find it difficult to accept

that a particle can “pass through both
slits” simultaneously, and they have to

resort to so called wave nature in
order to explain the interference patterns.

9 DISCUSSION

It is seen that both wave picture and
the ordinary particle picture fail to explain

the interference patterns observed in the
double-slit experiment. The wave

picture fails as a weak intensity
stream of electrons (one electron at a time)

exhibits no interference patterns in
the case of few electrons. The ordinary

particle picture fails as a particle
passing through only one slit would not produce

interference patterns. The Physicists
had to resort to the wave picture as the

logic in either positivism or realism
would not permit a particle to pass through

both slits.

In the case of the experiments
conducted by Chandana then at the Univer-

sity of Kelaniya, Sri Lanka, the wave
picture as well as the classical particle

picture come across more problems as
neither a wave nor an ordinary particle

would be able to penetrate the
aluminium sheets without being affected. These

experiments justify our new
interpretation involving modes of the particle or

the system and the particle picture
presented here where a particle can be at

both slits. In general we postulate
that a particle or system can exist in a mode

where more than one eigenstates are in
a superposition. The position where

a particle is found depends only on the
relevant probability, and the so-called

interference patterns are only
collections of images formed by such particles

striking the screen at different
positions with the relevant probabilities.

The new postulates are consistent with
the ontology where the “existence”

of a particle or an object does not
necessarily mean that it could be observed or

that it is sensory perceptible in
general, and the fourfold logic. It appears that,

unlike Classical Physics with its
twofold logic and realist ontology, Quantum

Physics is rooted not even in a “positivist
ontology” but in a different ontology

and fourfold logic and we should be
able to develop new concepts in Quantum

Physics, especially regarding the
motion of a Quantum particle from a point A

to another point B. It is not known how a particle “moves”
from the double-slit

to the screen in the experiments
carried out by Chandana, nor how a particle

with less energy than the value of a
potential barrier “scales the walls”. In the

latter case all that the Physicists
have done is to come up with concepts such

as “tunnel effect”. It may be that it
is neither the particle that left the point

A nor some other
particle that reaches the point B, if we are to make use of

the fourth case of fourfold logic.
Chandana in his M.Phil. thesis submitted to

the University Kelaniya in September
2008 has described few more experiments

that agree with the present ontology
and fourfold logic.

References

1. Bagget Jim, 1997. The Meaning of
Quantum Theory, Oxford University Press.

2. Afshar, S.S., 2005. Sharp
complementary wave and particle behaviours in the

same welcherweg experiment, Proc. SPIE
5866, 229-244.

3. Bagget Jim, 1997. The Meaning of
Quantum Theory, Oxford University Press.

4. Afshar, S.S., 2005. Sharp
complementary wave and particle behaviours in the

same welcherweg experiment, Proc. SPIE
5866, 229-244.

5. Afshar, S.S., 2005. Sharp
complementary wave and particle behaviours in the

same welcherweg experiment, Proc. SPIE
5866, 229-244.

6. Chandana S. and de Silva Nalin, 2004.
On the double-slit experiment, Annual

Research Symposium, University of
Kelaniya, 57-58.

7. Chandana S. and de Silva Nalin, 2007.
Some experiments involving double-slits,

Annual Research Symposium, University of
Kelaniya,133-134.

8. Bohm D, 1980. Wholeness and the
implicate order, Routledge, London.

9. Chandana S. and de Silva Nalin, 2004.
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Annual Research Symposium, University of
Kelaniya, 59-60.

10. Monroe C., Meekhof D. M., King B.
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Cat” Superposition State of an Atom,
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11. de Silva Nalin, Sinhala Bauddha
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