5.1
The Uncertainty Principle of Heisenberg
(1927).
Heisenberg
Uncertainty Principle states that no two
conjugate properties of a particle (like
position and momentum, Energy and time
etc.) can be measured with accuracy
greater than value of Planck’s constant.
This Principle has been shown to be a
built in reality of the Quantum Model.
If we try to pin point the position, the
momentum of the particle will be heavily
uncertain. This is because they are
correlated. The reason for this
uncertainty is that the state of the
particle is so changed during the
process of the measurement, that we will
have changed its conjugate element in
that process. The implication of this
statement is that in the phase space of
displacement and momentum minimum size
of the pixel is of the order of h. Thus
anything within that range cannot be
defined properly. The same goes to
energy and time.
Dp
Dq
³
h/4p
DE
Dt
³
h/4p
Cartoon by John Richardson for
Physics World, March 1998
http://www.aip.org/history/heisenberg/p08c.htm
The full
expression for any two observables A and
B is given by
![\Delta A\,\Delta B \ge \frac{1}{2} \left|\left\langle\left[\hat{A},\hat{B}\right]\right\rangle_\psi\right|](qt5_files/image003.gif)
A
and B are two observables,
and 
their
corresponding operators,
![[\hat{A}, \hat{B}]](qt5_files/image006.gif)
denotes
the
commutator of and = -
denotes
averaging for the state 
and
ΔX is the
Standard Deviation of X given
by 
.
5.2
Conjugate Observables
In general
not all the classical physical
observables of a system can be
simultaneously known with unlimited
precision, even in principle. There
are several pairs of observables, which
give different, but nonetheless maximal
possible descriptions of the system.
These sets are sets are known as
"maximal sets of commuting
observables." Observables from
different sets are "noncommuting
observables". These pairs can be
normally known with precision and will
depend only on our measuring tool.
In
classical physics the errors of the
observation are still there. As a result
one would get a probability distribution
for the initial values of the conjugate
variables and something very similar to
the probability function in quantum
mechanics is still obtained.
The disturbing factor is that the
state of the system does not have a
specific value until a measurement is
made. Does it mean that physical world
has no independent existence apart from
the observer? If so the two grand
foundations of science are at stake –
realism and determinism. Realism is the
statement that the external world exist
independent of whether someone is there
to see or not. Determinism is the
statement that there is a law – whether
we know it or not - that links cause to
effect in the physical world. If this is
known we can predict the future from the
present.
This led
to the development of what is known as
the Hidden Variable Theory. It assumes
that if we had known the whole truth we
could retain both realism and
predictability. What is lacking in
quantum theory is that we have only a
part of the information. It is the
hidden variable in our knowledge that
causes the crunch. John von Neuman
apparently proved through a slight twist
in the mathematical formalism that no
such theories could be developed. (This
was later proved to be a false alarm
based on a mathematical error by Bell)
So Bohr
put forward his complementarity
principle, which led to the Copenhagen
interpretation of quantum theory.
5.3 The complementarity concept of Bohr
This proposes that the state of the
system is the complete only with the
microscopic system plus the macroscopic
measurement apparatus. Then the
complementary nature of wave-particle
duality, and the character of the
uncertainty principle are an intrinsic
property of the nature and not a
peculiarity of the measurement process.
In Bohr's
Copenhagen interpretation, it does not
make any sense to speak about
characteristics of the quantum system in
itself explicitly without the rest of
the wider system including the measuring
devices. It is therefore even more
senseless to assign to a quantum system
simultaneously complementary attributes
like position or momentum, since the
apparatuses, which are needed to measure
them, are mutually exclusive. For
example, it is impossible to build an
apparatus, which simultaneously measures
both position and momentum to arbitrary
precision. So any question related to
them cannot be asked intelligently.
This interpretation received its crucial
test at the Solvay Conference in 1927
in Brussels. Especially Einstein again
and again discussed those experiments,
which had always led to the worst
paradoxes, in all details. New mental
experiments were invented to trace any
possible inconsistency of the theory. It
was then seen that the theory was
consistent as far as we can think of and
seemed to fit all the experiments known
so far.
[See
Physics and Philosophy,
Werner
Heisenberg, 1958; Published
by George Allen and Unwin
Edition, 1959.]
5.4
Heisenberg identifies the state vector
with the "knowledge of the system".
The two
Einsteinian concepts of locality and
seperability are quantum mechanically
untenable. Locality principle states
that measurements which are made far
apart (at spacelike distances) cannot
affect each other. Separability
principle states that even when two
systems, which have previously
interacted, are separated , the
measurements on any one of them should
not make a difference in the other.
Quantum Mechanically the system by
definition should include itself and
also the rest of the cosmos, which
interact with it. You cannot isolate a
system nor separate it. This concept is
then used to explain the collapse of the
state vector to eliminate simple
nonlocality problems. Thus we do not
have an isolated particle or isolated
person or even an isolated God. While
there is a difference in terms of space
and time and quality, all form together
into a complete unity. This leads us to
the concept of God in the Eastern
Churches. While beings in existence are
different from God himself, beings have
their being within Him.
Act 17:28
for in him we live, and move, and have
our being; as certain even of your own
poets have said, For we are also his
offspring.
5.5
The Minimal Interpretation
In quantum
mechanics a system is supposed to be
described by its quantum state,
sometimes also called as its state
vector. Given the state vector, one can
derive probability distributions for all
the physical quantities pertaining to
the system such as its position,
momentum, angular momentum, energy, etc.
using their corresponding operators and
evaluating
or <
|
A|>
The
operational meaning of these probability
distributions is that they correspond to
the distribution of the values obtained
for these quantities in a long series of
repetitions of the measurement. If we
make large number of measurements for
any A on similar systems, the result
will be portrayed by the probability
distribution. This is true of any
observable. Thus the explanation do not
assume simultaneous measurements at
all. Thus the uncertainty relations
are simply statements about the spreads
of the probability distributions of the
several physical quantities arising from
the same state. Thus in the minimal
interpretation the uncertainty as
limits on the simultaneous measurements
as proposed by Heisenberg or Bohr, need
not be supposed. In this case the
uncertainty of measurement is inherent
in all measurements. We cannot know
anything with certainty as long as these
properties are interrelated in the
state. This brings to Bohr’s warned that
the principle of complementarity not
only "set a limit to the extent of the
information obtainable by measurement,
but also set a limit to the meaning
which we may attribute to such
information."
5.6 Distinct yet forms Part.
The whole
creation is part of God. It is the
assertion that we are distinct and
isolated that leads to selfishness and
egocentric sin. We cannot know an
individual without knowing his
circumstances, his relation with God and
God’s relation with him. Redemption is
when we partake of the divine nature and
be in the likeness of His Son. This
theology leads to the concepts of
theosis or divinization. The simple
statement of this is, that since
creation and beings are created by God
and since apart from God nothing existed
nor can exist, it implies that creation
is simply a part of God – not as an
identity but as a part. Just as hands
and feet and eyes are part of human
body, we form a part of the body of
God. Hence in order to know God or man
we need to know the whole. It is a union
with God in his Energies or union by
grace making us partake of his divine
nature, without our essence becoming one
with the essence of God.
In this
sense the rest of the cosmos and its
relation to the particle creates the
particle or the state of the particle.
The very concept of the state of the
system is defined only in this way.
While the state contains all information
related to the system, we could get the
particular information by applying
particular operators. Thus in order to
know how God deals with man, we need to
look into history. Each event in
history provides a part of his character
with all the uncertainties that are
attached to the event.
5.7 Time
Evolution
“In the sharp formulation of the law of
causality-- "if we know the present
exactly, we can calculate the future"-it
is not the conclusion that is wrong but
the premise.”
--Heisenberg, in uncertainty principle
paper, 1927
In the
Copenhagen interpretation, the wave
function is only our way of representing
that part of our knowledge about the
history of a system, which is needed for
calculating future probabilities for
specific measurement results. . To give
an example - in the case of the
double-slit-experiment, the wave
function makes it possible for us to
calculate both the probability of
finding the electron passing through a
given slit, and the probability where it
will strike on the screen. So it is
especially impossible in principle to
predict with certainty both through
which slit the electron will go and
where it will fall on the screen.
The notion
of randomness is a perennial problem. To
what extent can we predict the future?
Is out limitation of knowledge that
determines our inability to predict
future? In the early 19th century
Physics known today as Classical Physics
was based on deterministic laws of Isaac
Newton. Thus knowing the present state
of the Universe, one could predict the
future exactly. This is because the
laws of nature are immutable and
eternal. Predictability is fundamental
to Science. We do use Statistics where
such randomness is assumed as inherent
in the system to predict the evolution
in time. We have done well in that
direction. Within limits of errors
statisticians were doing very well.
Then
quantum mechanics came along and it
changed our view. Quantum Mechanics
introduced probability and randomness at
the basic root level of Physical laws.
It is so disturbing that even Albert
Einstein considered it as basically
untenable and that it will destroy the
foundations of Science. The modern
study of nonlinear dynamics - The
Theory of Chaos - revealed that
randomness and unpredictability are
indeed fundamental even in the Classical
Physics. Things got even worse when it
turned up even in Mathematics. G. J.
Chaitin of IBM shows that there are
theorems connected with number theory
that cannot be proved because when we
ask the appropriate questions, we obtain
results that are equivalent to the
random toss of a coin.
“God
not only plays dice in physics but also
in pure mathematics. Mathematical truth
is sometimes nothing more than a perfect
coin toss. “
Gregory Chaitin A Random Walk in
Arithmetic
New
Scientist 125, No. 1709 (24 March 1990),
pp. 44-46 http://www.cs.auckland.ac.nz/CDMTCS/chaitin/ns.html
In
"classical physics,” the future motion
of a particle could be exactly
predicted, or "determined
precisely,” from a knowledge of its
present position and momentum and all of
the forces acting upon it. Stated thus
it is the basis of the law of Karma. It
is perfectly logical. The problem is
that one cannot know the precise
position and momentum of a particle at a
given instant. Therefore its future
cannot be determined exactly. Since
there is always indeterminacy in the
measurement of the particle in the
initial state we can only have a range
of possibilities for the future motion
of the particle.
The
implications of this principle in
soteriology are direct. We have a lot of
conjugate measurements in the field. A
few of them are: Sovereignty and Decrees
of God; Freedom of Will of Man and
Foreknowledge of God (Predestination);
Inability and Responsibility etc. It is
evident that if we insist on absolute
measurement in one element the certainty
of the conjugate element will
correspondingly vanish. Hence there must
be a phase space where there is
uncertainty. We should conclude
therefore that we would never be able to
observe exactly both the conjugate
elements simultaneously. However we
should mention that these are not
directly measurable observable
quantities and the problem arise only
when we look into the history (in the
Bible) to see the actual working of
these elements.
5.8
Sovereignty of God and Free Will of Man
Thus it
seems that even God is bound by the
Uncertainty Principle, and cannot know
both the position, and the speed, of a
particle. So God does play dice with the
universe. All the evidence points to him
being an inveterate gambler, who throws
the dice on every possible occasion.
Does God Play Dice? Stephen Hawking
If we make
a note of any Sovereign act of God in
terms of the Freedom of will of man
involved, we will certainly see an
uncertainty. It is in this sense only
that we could say both exist
simultaneously. God in his sovereignty
permits freedom of will within bounds
thus limiting his own sovereign
imposition. Man in his Freedom of will
creates his own constraints and limits
his own bounds and limits. The decrees
of God are not independent of the
behavior of Man or the behavior of Man
independent of the decrees and laws of
God. It also applies to the purposes of
God and direction of history in terms of
human freedom. God predestines in terms
of his foreknowledge. This foreknowledge
includes the freedom of will of man.
Similarly God assigns and demands
responsibility in terms of human
ability. Within the phase space of these
conjugate elements, there is a volume of
uncertain space. This uncertainty says
that we will never know the decrees of
God absolutely; we will never know the
predestined destinations absolutely. Put
it in another way, God does not decree
absolutely nor man’s free will is
absolute. The latter is clearly evident,
but we are reluctant to admit the
former. At least in terms of the visible
observable areas this is certainly true.
I was in fact surprised when I came
across a book called “God always has a
Plan B”
5.9 Time
Evolution, Determinism and Prophecy
The
soteriological application to this
approach will simply be that though the
path taken by individual persons are not
predictable and is totally dependant on
the free will of the person; groups, the
church, and mankind as a whole will be
guided by the wavefunction directing the
course of history to its predetermined
culmination. So there is perfect freedom
of will for each individual under
constraints - which are bound to
socio-psychic and genetic conditions.
Yet history is perfectly guided to its
predestined end. To put it directly,
each individual is free totally within
constraints, but God guides the path of
mankind as a whole so that all
eventually reach the predestined end
according to the will of God for
Mankind. This argument leads to the
conclusions of Origen where all mankind
will be eventually (not necessarily in
this age or in the immediate ages to
come. I certainly do not believe in
reincarnation, which defeats the
purpose. I believe in continuation of
life and personality through
resurrection) saved, but each one has
the perfect freedom to take their own
trajectory. They can even move back
against God’s direction. It is the
constraint that directs the envelope.
God’s direction is like a carrier wave.
1 Tim 2: 3
This is good, and pleases God our
Savior,4 who wants all men to be saved
and to come to a knowledge of the truth.
2 Peter 3:9
The Lord is not slack concerning his
promise, as some men count slackness;
but is longsuffering to us-ward, not
willing that any should perish, but that
all should come to repentance.
John 1:9 That
was the true Light, which lighteth every
man that cometh into the world.
Most
evangelicals find a threat to the gospel
in such an interpretation. But is it
there? We should be aware that the
gospel of salvation to mankind, which we
preach today, is limited to this age. We
are not given any revelation regarding
the ages to come, though we are
positively guaranteed that they do
exist. There indeed will be a separation
of the sheep and the goats, the right
and the left, one that goes to eternal
heaven and others to eternal punishment.
Eternal is an undefined mathematical
concept indicating ignorance. But heaven
and punishment are clearly defined. The
message is clear that the time of
salvation is now and the result of
rejection is unimaginable.
While a
particle is localized in a particular
volume, its electron still has a finite
though infinitesimal chance of being at
the other end of the galaxy. What holds
together the particle in place is the
reality that it is only for an
infinitesimal period of time? This
permits a lot of opportunity for freedom
of movement for the electron without
losing the property of the particle as a
whole. Human thinking and the freedom of
man are similarly unbounded. What
defines the person is the time average
(of conduct), which determines the
properties (character) of the person.
The choices form a continuous chain of
events. It is in the direction of these
ongoing choices that we see as the
personality of a person. This is no new
teaching or experience. Even the very
best of men err and even the worst of
men do well occasionally.
While
determinism is totally ousted, there is
a probabilistic evolutionary concept.
Can we predict future exactly?
The
interesting thing about it is that
though the trajectories of individual
particles are not predictable the
probabilities of each motion, and the
distribution of many particles following
these motions, could be calculated
exactly from Schrödinger wave equation.
How does this translate into soteriology?
Even though we cannot predict the action
path of each individual, it is still
possible to predict the path of a group,
a community, a church, or a nation with
almost certainty. For an individual
person we can still predict a
probability distribution, which
inherently defines uncertainty of
exactness.
While the
enveloping guiding wave moves history
towards a predetermined end, the history
of nations and communities and families
and ultimately of individuals are not
that clearly defined. This will allow
predestinations in spite of freedom of
will. There is always indeterminacy but
it becomes smaller and smaller as the
sample gets larger and larger.
Let me
take a historical situation of Nineveh.
Even though the prophet declared
unequivocally without a condition that
God was going to destroy Nineveh in
forty days. God changed his mind.
Because of the free will of the people
of Nineveh, the prophecy did not come to
pass. The impossible happened: the
people of Nineveh believed God, the
greatest of them to the least of them.
Jon 3:4 Jonah
began to go into the city, going a day's
journey. And he cried; "Yet forty days,
and Nineveh shall be overthrown!"
Jon 3:5 And
the people of Nineveh believed God; they
proclaimed a fast, and put on sackcloth,
from the greatest of them to the least
of them.
Jon 3:10
When God saw what they did, how they
turned from their evil way, God repented
of the evil which he had said he would
do to them; and he did not do it.
In most
religious traditions God experience is
always emphasized as a personal
experience. While it is certainly a
personal experience the indeterminacy
principle makes each experience only a
possible observable among many. The
certainty can be attained only in
collective experience or repeated
experience. This is obviously the
scientific approach. Thus while the God
experience is intensely personal, the
validity of the experience is tested
only through collective consensus. Thus
the reality of Yhvh is based not on
Prophetic utterances or on individual
experience but on Israel’s experience of
the Crossing of the Red Sea, The
appearance of Yhvh in Mount Sinai and in
the Covenant Dinner when the 72 elders
saw the God of Israel.
Exo 24:9
Then Moses and Aaron, Nadir, and Abi'hu,
and seventy of the elders of Israel went
up,
Exo 24:10
and they saw the God of Israel; and
there was under his feet as it were a
pavement of sapphire stone, like the
very heaven for clearness.
Exo 24:11 And he did not
lay his hand on the chief men of the
people of Israel; they beheld God, and
ate and drank.
All the
rest of the revelations got their
validity from the Mosaic revelation for
which over a million witnesses were
there to vouch. The same is true of the
Christian experience. Christ experience
is not only based on individual
transformation experience of the
believer, but is based essentially and
validated by the historical revelation
of the resurrected Jesus for which we
have massive witness and massive
evidence.
1Co 15:17
If Christ has not been raised, your
faith is futile.
Einstein
never accepted Quantum Mechanics. His
first objection was the probabilistic
aspect of the time evolution operator.
This seems to imply that the future is
random. Einstein repeatedly said, "God
does not play dice with the universe,”
Bohr’s response was: "Quit telling God
what to do!" In other words we cannot
define God and use it as an axiom for
further logical derivation. It should
be the other way round. Our
understanding of God is limited by how
God reveals himself to us through
history.
Personally
I believe that the fact that we are left
with a probabilistic aspect for any
given observable is indicative of the
reality that we are not really dealing
with a materialistic world alone. This
cosmos itself is only a subset of a
wider set and our space-time is only a
small part of the infinite dimensions of
the reality. We can never describe the
state with the observables within the
real world because there is an unseen
world beyond and the state vector exists
in this multi-dimension.
This
multidimensional aspect was even present
in the elementary Bohr Theory of
Hydrogen where the vector model was
successfully employed. Angular momentum
quantum numbers and the spin quantum
numbers were obtained by projection of a
vector along the magnetic field of
reference.
