Quantum Mechanics
Flourishing fountains fanfare out of
a still pond
Quantum
Mechanics is the science that studies the sub-atomic particles and deals with
the behavior of objects within their
While studying quantum mechanics,
there are five points to keep in mind.
First, more than eighty years of lab
experiments proved that the principles of quantum mechanics are real and valid.
Mathematics of quantum theory precisely predicts and
reproduces the results of physical experiments. We are applying these
principles in making delicate instruments and building precise computers.
Therefore, Quantum Mechanics is an actual science.
Second, Quantum mechanics is weird.
In this arena, certainty of classic physics is replaced by the uncertainty and definite
state observed in macro-world turns to chaotic world of super-position of
states. Casualty (cause and effect) may reverse so that cause appears before
effect (second Feynman diagram). Direction of time can reverse also and future
arrives before the past. Entanglement between distant particles exists without
apparent link. The law of conservation of energy gets pale in many instances.
And so forth and so on.
Third, apparently we cannot utilize
the logic of classical physics to interpret the weirdness of quantum mechanical
phenomena. We have to develop a new logic to accommodate a reality that is beyond
our today's consensus reality.
Fourth, quantum physics is not an
abstract science that belongs to laboratories and scientists, it is the basic science
which describes the building blocks of our body and our macro-world and it is the
infra-structure of laws of classical physics.
And fifth, Quantum mechanics laws are
applied equally to micro and macro-world.
Good news is quantum mechanics are set to explain the
unexplained. Therefore the mysteries can be explained by scientists through
scientific methodology not mystics approach with the usual misconceptions and
delusions.
Hypothesis
Quantum physics realm is the twilight
zone between space-time and
The proposed non-local
energy-information mind-like singularity.
One of the main tasks of this model
is to propose explanations for unexplained findings in quantum theory. We cannot
explain the Schrodinger's cat (explained in
coming pages) being alive and dead at the same time, with our conventional
logic. Surprisingly though, we can imagine such a superposition in our mind.
Not only our imagination can accommodate such a dual and antagonistic state but
our mind activity is frequently utilizes superposition in its different
functions.
Niels Bohr is the founder of quantum
mechanics. His approach to the strange quantum realm was just to observe the experiments results
and not trying to find causality for their presence or explain the reality and
history behind them. Albert Einstein on the other hand believed that universe
is made of real objects with real and definite properties. He believed that
Quantum Mechanic theory is deficient and cannot reveal the hidden variables
that create strange findings in sub-atomic arena. He further believed that
these variables do exist. Einstein believed a deeper theory would find these
variables, which are hidden in our experiments. Most physicists have not
favored hidden variable theories. Experiments and calculation results
contradict these theories. Although Bohemian mechanics (refer to David Bohem)
tries to offer an explanation for it.35
Here I am introducing a non-local
media, which is connecting different points of space together. Let's see if
this model can offer reasonable explanations for different quantum mechanical paradoxes.
I hope this model prove to be the Einstein's deeper theory, which explains the
quantum mechanical experiments and offers a comprehensible reality.
Furthermore, because this model has a mind component, it contains some of the
interpretations and views of Neils Bohr as well.
Quantum Mechanic Domain
A particle generally behaves quantum
mechanically when observed at distances shorter than its
The
l = h / m c, where h is
the Planck Constant, m is the mass of particle and c is the speed
of light.
What is the mystery within the
Momentum
In classical physics, momentum is
defined as the product of mass (m) and velocity (v) of an object.
P = mv
Simply speaking, momentum is the
impact felt by a boxer receiving the opponent’s tossed feast.
The relation between the momentums of
an object in regards to its spatial position (x) are obtained by:
Pa = a / axa
Where a is a constant. If our object is a subatomic particle
then we need to add imaginary number (i)
and Dirac constant (ħ) to the equation,
Pa = iħ
a / axa
The Dirac constant is a reduced
Planck Constant (h/2p).
The presence of i indicates that the momentum of a subatomic particle is governed
by a complex function. Therefore, the momentum of subatomic particles is
periodic (see the complex number chapter). Therefore, the Assertion C2
specifies that the value of the momentum has to hit zero at each period.
The presence of ħ also points
out that momentum is directly related to Planck constant. In wave-function
chapter, we have assumed that the particle itself disappears and reappears in
space-time in each
Moreover, in the Mass & Gravity chapter we have assumed that the Planck Constant
is the amount of kinetic energy carried by the particle upon its arrival into
the space-time.
In following paragraphs, we will
review the quantum mechanical phenomena while keeping the above conjectures in
mind.
Heisenberg
Uncertainty Principle
According to Werner K. Heisenberg,
the famous German physicist, we cannot simultaneously determine the position
and momentum of a particle at ultra short distances. This kind of correlation
between two properties is called a complimentarity relation. The equation
is written as,
DE Dt
≥ h/ 2p
In Heisenberg’s famous uncertainty relation for position and
momentum, when the position uncertainty changes in position (Dx) is less than the Compton wavelength, the momentum
uncertainty changes in momentum (Dp) is
greater than h/ 2p. Since
momentum carries energy, the uncertainty in energy is greater than, h/ 2p. This implies that if we pin
point a particle’s location, its momentum can vary widely and therefore we can
not be certain about its momentum.
To justify the uncertainty principle,
error in measurement and lack of appropriate tool are brought up. Neither is very convincing.
Therefore, quantum theory tells us
that we cannot track a subatomic particle by any method whatsoever. Can we
assume that, we cannot detect particles because they loose their mass and leave
the space-time? Maybe we have to change the sentence as "we cannot track a
subatomic particle by any method whatsoever in objective world. The
problem arises when we are expecting to see the whole picture in just one
arena, (the real number arena). As an analogy, please note that we cannot
follow and understand a three dimensional motion in it’s entirely in a two dimensional
world. Evan Walker says: “… Heisenberg used matrices (whole array of numbers) to
represent the positions and motions of an atomic particle.8
In his calculation to create the
matrix he used the symbol i which stands for square root of –1, the so
called, imaginary number. He had to choose a number, which is out of the domain
of our real number system. We cannot ignore the quantity i and call it
imaginary. We have to accept that it
stands for a kind of reality. According to Dr. Walker quantum mathematics drags
us to a scope “that is really an infinity of imaginary worlds.”8
Therefore, we have to expand the
science domain to include worlds other than familiar space-time. If mathematics
so precisely is predicting the mystery world of quantum behavior, we have to
value its elements. We have to accept that its unexplained or inapplicable
measures to our physical world have an actual meaning.
Let us revisit the location /momentum
uncertainty. Please note that one of the elements is spatial and the other is
energy related. We can interpret the principle as; when locality gets blurred
the energy is more defined. This was explained in the Boundaries Chapter. We
also can extend the Heisenberg principle to time and energy in a system.
DE Dt ≥ h/ 2p
For example a radioactive atomic nucleus decays with time. If
the lifetime of such a state is Dt, then the energy of the exited states is uncertain by:
DE ≥ ħ/2p Dt
The second diagram of Feynman for Compton Scattering also leads us to above uncertainty. Here again
while t is a spatial element, the other element is energy. As time gets
hazy energy gets more distinct and vise versa.
Spectral/Spatial Complemetarity
We can also extend the uncertainty
principle to information carried in a beam of light after it passes a lens.
Depending on the location of a screen behind the lens, we can either have a
sharp image of the object in experiment, or we may come up with a fuzzy image
or no image at all. On a proper location every portion of image data has a
defined spatial location. Whereas in no image locations the information is
carried by light rays are at spectral version and they do not exist in spatial
location. Interestingly, in spectral form the data are non local. Which means
every small portion of space carries all of the information about our object in
hand.
Here we have a complimentarity
relation between spectral and spatial features. As we come close to focal point
we depart from spectral phase and come to locality. With the same token when we
leave focal point we enter spectral phase again and the non-locality prevails.
Isn't this a good example for understanding the relation between a spatial
local world and non-spatial non-local energy-informatics domain? In our model
this paradigm is the proposed singularity.
Information/ Interference Compementarity
George Greenstein and Arthur Zajong
mention another very interesting complimentarity relation in their book “The
Quantum Challenge”. They explained the complimentarity between information and
interference pattern in double slit
experiment (see the explanation under the same subtitle in this
chapter). Referring to moveable slit modification of the experiment, they wrote:
“Wootters and Zorek have
returned to Einstein's modification of the classic double-slit interference
experiment, and analyzed it from the stand point of partial information…The
slits are free to move. After particle has past through, we measure the slit's
momentum… if the slits are moving downward, the particle must have past through
slit 2…
Wootters and Zorek noted
that the above conclusion is not in fact entirely certain. The same motion of
the slits would also be observed had the particle passed the wrong slit --if
the initial slit momentum had been large and downward…
They evaluated the
probability of the initial slit momentum being large enough to yield such an
erroneous conclusion, and so obtained an expression of the probability that we had obtained path
information. Using the same wave function, they also calculated the
resulting pattern of arrival at the final screen. It turned out to be a partially smeared-out interference pattern”11
Reproduced from Reference #11
Their experiment showed that if they
had certain knowledge about the slit that particle passed through, there where
no interference on screen. But as the uncertainty about the slit increased a
better interference were developed.
Looking at different complimentary
pairs, the elements for each uncertainty relation are different in that, one of
them is either spatial or mass type, and the other is either energy type or
informational type. The two characteristic that we hypothesized for proposed
singularity. The fuzzy states of fundamental elements in boundaries of
space-time were discussed in Boundaries Chapter.
Schrodinger's
Cat: Quantum Super
Position of States
For details check the
link: http://www.upscale.utoronto.ca/
GeneralInterest/Harrison/SchrodCat/SchrodCat.html
Objects in classical physics terms
are in a well defined state, whereas in quantum mechanics the objects are not
in a definite state. For example, in classic physics an object will rotate
either clockwise or counterclockwise. It was shown that in microcosm, a
particle is spinning simultaneously in both directions. In other words, a
particle concurrently exists in any probable state that is possible. Erwin
Schrödinger who first explained the super-position of states offered the analogy
of a cat being dead and alive at the same time after the probability of being
poisoned is famous and is named after him.
In classical physics terms either the
poison is released and cat dies or the poison is contained and cat would be
alive. But in quantum mechanics arena, the both outcomes exist simultaneously. This
is of course before we open the box. As soon as we open the door we just see
one outcome (either a dead or a live cat).
The Schrödinger’s cat is
simultaneously dead and alive. Such a
sentence does not relay any meaningful concept to us. Or does it?
In the observable world a cat is
either dead or alive. The series of events lead to just one of the
possibilities.
How are we going to explain this
quantum mechanical effect.. Multi universe theories claim that there are
different universes that accommodate different possible outcomes, of each
action. This is hard to accept. There are countless actions in each miniscule
of time in the universe and far more possibilities as well. Possibilities are
endless. It means we have to have endless numbers of universes and the number
is growing every second at a rate that transcends all concepts of infinitudes.
It is also grossly against conservation of energy law if we choose to hold it.
This concept is not economical either.
On the other hand, Schrodinger's wave
equation which represent the super-position of states, also contains the
imaginary factor i. Thus quantum state “will always turn out to contain
terms that are imaginary…The complex character of the wave function in
Schrodinger's wave equation means that what is there in a sense is hidden from
us.”8 In other words, Somehow in quantum arena we are exposed to out
of space-time realm.
Renormalization in
Schrödinger’s Equation
The Schrödinger’s probability
equation for the position of a particle during its wave function can be written
as:
Ψ*
Ψ = Probability
If we believe that the particle is
somewhere in space but we cannot exactly pin point it, we can normalize the
formula and write:
∫ Ψ* Ψ cr = 1
Which means that we have altered the formula in a way that
would show the probability of the particle being somewhere in space is %100. We
do this because we believe that everything is confined inside the space-time.
So, it is natural to assume that the particle is in space somewhere. Therefore,
we write a formula to reflect a normal situation by our space-time logic. If we
are revisiting the existing concepts then we are allowed to question
normalization as well. Normalization is a major parts of quantum mechanical calculations.
If we take normalization out of quantum calculations, we tremble the pillars of
its existing mathematics.
Questioning the normalization is similar
to questioning the attempts to understand the reality on the basis of
space-time properties alone. This is a courageous action. But haven't we been
very bold so far? As a matter of fact, solving these great mysteries need
enormous amount of daring. At the same time revisiting the calculations can
confirm or reject the validity of the singularity concept presented above. It
seems that if we redefine the particle wave function to include singularity (a
mind like informational domain), we will come to a logical explanation for the
phenomena that we are facing. I do not see why we shouldn't let our imagination
explore that possibility. Aren't we defining the location of each particle with
a complex number, which contains imaginary part as inseparable feature?
Decoherence
Decoherence – the blossom of just one state in
macrocosm out of infinite quantum superposition states in micro scale.
We see the
world in one definite state. A universe in superposition of states would be an
in-deterministic and chaotic world that nobody could stand it. Nothing would
remain to rely on or build into it. Even we ourselves would be a total mess. As
mixed up as the state that our mind normally is. The proponents of the Decoherence
Principle explain why we do not observe superposition of state in our everyday
experience. Decoherence principle simply points to the fact that each particle
normally exist in an environment. This environment is always bombarded with
other particles and photons. The interaction of particles with each other takes
them out of super position of state and leaves them in a definite state. That
is how the world comes out of confusion and we see one definite state around
us. This is a world where we can live
and be able to rely on.
State reduction at the margin of the
wavelength
Perhaps a
better explanation can be obtained by paying attention to the fact that quantum
behavior is demonstrated inside the wavelength of each object.
The
wavelengths of smaller particles are big enough for us to experimentally
observe their superposition of states. The bigger objects on the other hand
have a very small and almost undistinguishable wavelength. In this view, the
superposition of states takes place within the wavelength of bigger objects.
Singularity, Super Position Domain
If we cannot normally observe the superposition, then
where is the most probable place to comprehend it? Where can we find such a
cat, which is in superposition of life and death? We assumed singularity to
contain information of an object but lacking matter itself. In such a domain,
information about any possibility can exist simultaneously. In particle-wave
model, I assumed the alternative position of objects in singularity and
space-time domain. We can leave superposition of states to singularity and the
definite state to space-time. This is how we can avoid the super position
conflict with the conservation law.
According to the concept presented, the
physical world connects and intermingles with singularity in every miniscule of
space. In addition, we have assumed quantum arena (the realm within the
wavelength) the interface between our physical world and singularity.
Mind a model for
superposition of states
Are we accustomed to superposition of
states or is it completely strange to us? Surprisingly, superposition can
happen in our mind as well. We are very familiar with superposition of states.
In different mind activities such as predicting upcoming events, we imagine
different states of proceedings in order to compare and evaluate. When we are
planning to make a decision, we picture different mode of possibilities. When
we make our decision materializes and the outcome will be just one state.
As a matter of fact, the
Singularity as an informational domain can contain a superposition
of states just like our consciousness, which can hold such a superposition. When
the particle enters the objective space-time, it is reduced to one state and
becomes observable.
Defying the Conservation Law
As mentioned before, if we take
superposition as actual objective phenomena, it turns out to be against the dearly
loved conservation of energy/matter
law. Many discussions and arguments are brought forward by trying to expand
super position of states to macroscopic world. One of the main arguments is the
many worlds of
In the Consistent History approach to
quantum mechanics by
More in the super –position domain
The other dilemma is when and where
and in what level this transformation to reduced state is happening. Please
note that mathematics of superposition is continuous where as reduction
represents a discontinuity and change in state vector.56
So the coarse grain (superposition)
has to be in a continuous media where as the projected reduced state has to be
in a discrete background. In proposed model space-time is discrete and elements
in proposed singularity have a continuous nature. So again in my
interpretation, the course grain state (superposition) happens in singularity
and exists at informational level. The refined and reduced state is projected
and materialized to our space-time. So boundaries of space time are where
transformation actually happens. This is in line with the Copenhagen
Interpretation of Quantum Mechanics as originally suggested by Neils Bohr. He
believed superposition takes place at the mind of observer in informational
state. Reduction occurs when we refine the information.
Do we need to extend the
superposition to macroscopic world and then fall into the doldrums of infinite
number universes, which are growing enormously by instant? Even thinking about it makes one insane. My
humble suggestion is to consider the super position presence somehow out of our
universe. Let us then take the state reduction as an event inside our physical
world. This way we are left only with one universe. This is in line with our
observation.
Here are the main questions: Are we
going to take the every moment experience with mind behavior as a main portion
of reality and accepting it as model to clarify the obscure portions of
physical world?
Or do we keep trying to include
implausible fantasies, like many universes or multiple histories (the idea that
every event that could happen in the past actually happened) as part of
reality? What I am suggesting in here is to find a solution by simply opening
out the scope and include a mind like entity as a contributing domain. Just
like mathematicians who when they could not solve problems in existing domain,
opened out their scope and added negative numbers or imaginary number domains
and opened the gridlock.
Observer and Quantum State Reduction
Experiments show that the act of
measurement by the experimenter will reduce the super position of state to one
definite state. If we open the door in Schrödinger box we find the cat either
dead or alive and never both. Is it the
measuring or measurer who changes the overlapped different states to one single
one?
Evan Walker believes,
“…the system undergoes
state vector collapse because of our mind. This effort to obtain an entirely
practical interpretation of quantum mechanics … lead us to the incredible
conclusion that mind, or consciousness, affects matter.”8
State reduction is not the only place
where the measurer and the act of measuring influence the quantum mechanics. The
observer also affects quantum entanglement. In entanglement two or more
subatomic particles are connected to each other even if they are worlds apart.
If the observer reduces the spin of one of them to a definite state, the spin
of the other particles changes accordingly and immediately. Considering the
history of particles in the world logically each particle should have countless
entanglements with countless particles which it encountered in its past
history.
Surprisingly, when a physicist begins
the entanglement experiment between a pair of particles any preexisting
entanglement is eliminated and just the entanglement between two particles
under experiment is observed. So we as experimenters are changing the world
even at the quantum level.
Understanding how human can affect
quantum mechanics is not easy. It has created many controversies. One wonders,
if the principle can be applied in everyday life. Can we change the world at our will? Many new
school of thoughts are advocating the idea.
One of them believes that the history
and the state of the world depend on our question. We see the answers, which
are in line with what we are looking for.
Others like Lee Smolin believe there is “one universe seen by many
observers, rather than many universes, seen by one mythical observer outside
the universe.”27
State Reduction and Dream Elucidation
“Another
method of marginalizing experience occurs when you start thinking about the
meaning of the fantasy, while in the midst of the fantasizing. Thinking about
it stops the fantasy.”14 and we are back to one state world that we
call reality.
Bohr interpretation of state
reduction
Neils Bohr,
the founder of quantum mechanics expresses his opinion about state reduction
as,
“We customarily think of the outside world as
separate from ourselves, and the boundary between the two is the surface of our
skin. However, think of a blind person who gets around with the assistance of a
cane. In time that person will probably treat the cane as part of his or her
body, and will think of the outside world as beginning just at the tip of the
cane. Now imagine the blind man's sense of touch extending out of the tip of
the cane and into the roadway itself. Imagine it extending further, down the
block, into the countryside, to the whole world. There is no point where the
blind man ends and the world begins. Similarly, we can not say which is the
system and which is us observing it.”
Therefore,
he believed that our body is physically extended through out the universe and
we actually are the universe. According to him there is no boundary and we are
the whole system. That is why we can affect the world and induce state
reduction.
However, we
do feel this isolation of the systems (like our body) inside space-time.
Actually, the physical laws inside space-time are all evidences that systems
are individually interacting with each other. The whole body interpretation ignores the physics of
space-time.
Singularity and State Reduction
At the beginning of this book I have
assumed the presence of an entity with zero dimension where the image of all of
the points in our world can drop in it and stay superimposed. Some place where
different events can happen simultaneously because the in this entity the notion
of time is not present. I have assumed that space-time and this entity are like
two sides of the same coin.The coin being our universe.
Singularity can be the side of the
coin where Bohr sees the wholeness. That is where we can not differentiate the
system from the observer.
May be we don't have to speculate in remote
and strange thought domains. Multiple
universes and multiple histories do not sound very logical. Rather we can
assume an intimate proximity and relationship between macrocosm and
singularity. With this assumption, multiple states stay in one realm
(singularity), which has the capability to accommodate them. This way we do not
mix it up with actual activities, which are allowable in space-time and
macrocosm. Otherwise, it leads to confusion and we will be dragged into an in-deterministic
physics that nobody knows how to deal with it.
Dr. Walker rejects the measurement
error interpretation by reasoning that our measuring device is only another
sub-atomic particle, which according to Schrödinger’s equation entangles with
the particles under observation. This should add to complexity of
superposition, not state reduction. At the beginning we explored the
similarities between mind and proposed singularity. The necessity to utilize
complex numbers in order to explain quantum behavior suggests that elements in
imaginary world participate in determining quantum physics. Previously, I took
the imaginary portion, to represent the effect of the proposed singularity.
My conjecture is that the physical
world is made of separate and discrete parts and bodies. But the duality nature
of the existence connects and interacts each part through the universal
consciousness. The universal
consciousness is extended through our bodies as well and this is how we are
connected and mingled with the whole.
Tonomura Double Slit Experiment:
Feynman's Sum over Paths Approach
In Thomas
Young’s double-slit experiment a beam of light is directed towards a barrier
with two slits that diffract the beam. A screen is installed behind the barrier
that shows light and dark rows or the so-called interference pattern. This is the basic experiment, which shows
the wave property of light. In 1920,
Albert Einstein received the Nobel Prize for introducing the photon as a packet
of light energy. Thereafter, light has been considered as a particle wave
function. Photon is the particle portion of light.
Tonomura Double slit experiment is almost a similar
experiment but with a very strange result. In this experiment, electrons are
fired one by one in time intervals of ten seconds. Interestingly, the
interference pattern appears in the screen similar to the one when a bunch of
electrons is fired towards both slits simultaneously. The experiment has been
repeated by many researchers. Brian Greene explains how the strange results
were first observed:
“In 1920 Davisson and Germer ... were studying how a beam of electron bounces
off a chunk of nickel. The nickel crystals in such an experiment act very much
like the two slits in the double slits experiment of Thomas Young... Their
experiment therefore showed that electrons exhibit interference phenomena...
even if the beam of fired electrons was thinned so that, for instance, only one
electron was emitted every ten second, the individual electron still built up
the bright and dark bands.”1
In order to explain the electron
two-slit paradox the Late Physicist Richard Feynman proclaimed:
“Each electron that
makes it through to the phosphorescent screen actually goes through both slits.
Feynman argued in traveling from the source to a given point on the
phosphorescent screen each individual electron actually traverse every possible
trajectory simultaneously…It goes in a nice orderly way through the left slit.
It simultaneously also goes in a nice orderly way through the right slit. It
heads toward the left slit, but suddenly changes courses and heads through the
right. It meanders back and forth, finally passing through the left slit. It
goes on a long journey to Andromeda galaxy before turning back and passing
through the left slit on its way to the screen. And on it goes- the electron,
according to Feynman, simultaneously sniffs out every possible path connecting
its starting location with its final destination.”1
Of course, this is not his personal
opinion. Different experiments suggest the above conclusion. The so-called
Diffraction Grating Mirror works with the same principle.
Broken Mirror
The reflection angles do not match.
However, a detector placed out of range can still register a signal.52
In addition, the above explanation is
obviously against the Special Relativity that limits the velocity to light
speed. If the electron is going back and forth in different ways, it should
have infinite fold time speed of light, which is contradicting the known
space-time physics.
Singularity and Tonomura Double Slit Experiment
To have an infinite speed, the particle
has to perform in a non-local arena. A better explanation can be reached, if we
assume that the electrons are acting in a field with no time dimension. In this
situation, speed conflict is solved but the paradox is still not completely
resolved. One has to delete the notion of space and distance out of this
experiment as well. This way the electron can come from everywhere and nowhere.
Using the verb come applies to travel
in space. It is better to use appear
and accept that in this experiment electrons pop in and out of space-time
universe.
On above interference experiment,
Feynman tried to explain the paradox by claiming that each electron will follow
all possible trajectories before it hits the screen. We can claim that here,
the electron follows the non-locality characteristic of the proposed
singularity. Either non-locality or
being not time-bound can explain this effect more logically than assuming that
electron traveled along all possible trajectories before hitting the screen.
Roger Penrose offers the mathematic equation for two-slit experiment by using
complex numbers for quantum state. Roger Penrose writes:
“They can be represented
on a two-dimensional plot with the purely real numbers running along the
x-axis, and the purely imaginary numbers running up the y-axis, the imaginary
axis.”5
To introduce the mathematics Roger
Penrose has to use imaginary dimension along real dimension. He could not find
any real dimension in our space-time universe, which can help him to
mathematically explain the phenomenon. Again, we can imagine the complex
numbers in our mind. But quantum two-slit behavior is happening all over the
world in every moment, even if, our mind is not with it. There should be
another being out there to accept the image, to be able to accommodate the
imaginary dimension of complex numbers.
Can we suppose that singularity is there to do it for us?
One can assume that if complex
numbers represent particle functions, then particles themselves have to have an
imaginary (out of space-time) phase.
Abstract World of Mathematics
Roger Penrose uses the Argand Diagram
(presented in the Complex Number chapter) to discuss the complex numbers
behavior.
“The fact that these numbers are
built into the foundation of quantum theory often makes people feel that theory
is a rather abstract and unknowable kind of thing, but once you get used to
complex numbers, particularly after playing around with them on the Argand
diagram, they become very concrete objects and you do not worry so much about
them.”5
Therefore, Professor Penrose is
suggesting staying in the abstract world of mathematics and viewing the
imaginary number as a component of Argand diagram which is drawn in front of
us.
If we try to understand the meaning
of complex numbers with our space-time knowledge, we will face a concrete wall.
Therefore, we choose to take refuge in mathematical domain. We tend to take
imaginary number as a mathematical entity and give ourselves comfort. From school times we have learned how to use
numbers as abstract entities. We are used to perform mathematical calculations
and ignore their relation with objective reality. We cannot stay in this refuge
for long. Our father Adam didn't. We cannot do it either. We have to explore,
find and assign a tangible and deterministic reality to imaginary and notion of
complex numbers. On the other hand because mathematics are so precise in
calculating the Newtonian physics, electromagnetism, GTR and quantum mechanics,
if in some parts it does not match our perception of reality, one could suspect
that our perception might be wrong or incomplete.
In our model, because, there is no
dimension in singularity an electron can move radially -- in and out of
space-time universe, but yet cover the whole angular range, because singularity
is everywhere and nowhere. An electron being at the same time in singularity,
can defy 'steel ball' or ‘Classical’ interpretations of stationary orbital as
perpetual motion in our space-time universe. In this explanation an electron
does not need to follow the laws of classical physics.
Quantum Entanglement
Different Quantum Mechanical
experiments have proved that pair of particles, which traveling back to back in
opposite direction even if they are worlds apart, are entangled. Any change
implicated to any of them will instantly change the other particle accordingly.
It is interesting that the change occurs instantly.
This is one of the discrepancies
between the Special Theory of Relativity and Quantum Mechanics. According to Special Relativity,
nothing can travel faster than light. Instant connection between two spatially
separate objects observed in Quantum Mechanics, is in contrast with the
principles of the Special Relativity.
Professor Roger Penrose describes the
entanglement as:
“Modern preoccupation
with action-at-a-distance (to which Einstein objected) revolves around a purely
quantum phenomenon. This is the celebrated thought experiment in which an
'entangled' system of two objects is created. The wave function of object # 1
is correlated with the wave function of object # 2. By the axioms of quantum
mechanics a measurement of the properties of object #1 forces its wave function
to collapse, instantly implies a correlated collapse in object #2 though it be
arbitrarily far away.”5
Brent Nelson, M.A. Physics, Ph.D.
Student, UC Berkeley writes: “Non-local effects...occur in quantum mechanics
and they cannot be understood in terms of one thing being separate from another
- some sort of global activity is taking place.”
Scientists have been puzzled by this
strange phenomenon. Action at the distance without any apparent link also
exists in electromagnetic field or gravity field. In case of quantum
entanglement, no logical explanation, which can be agreeable by all, has been offered
so far.
Aspect’s Experiment
Alain Aspect and colleagues in 1982
experimentally proved the reality of Quantum Entanglement, and the non-local
actions. The diagram below sketches the
experiment for more detail, please refer to http://roxanne.roxanne.org/epr/index.html
or other related academic books and resources.
Aspect’s experiment for quantum
entanglement25
Alain
Aspect designed and performed the above experiment to examine the concept of
quantum entanglement.
A similar
experiment has been repeated in different parts of the world since then. They
all proved the entanglement exists between pair of particles that are far apart
in space. Albert Einstein struggling to stick to a deterministic world
suggested that there are contributing variables at work that produces this
effect. He believed these variables are hidden from us because of our limited
knowledge. However, the hidden variable explanation for the entanglement has
been proved wrong by
Quantum
physics tells us that two particles are not different. Rather, the two
particles are entangled together and express a seamless unity. Here, the notion
of identity and locality no longer applies.
Telepathy
Telepathy is a common experience. People
who are spatially apart from each other show different signs of connectedness
without an apparent space-time link. This connection is also common between
humans and their pets. 71
Quantum
entanglement provides the scientific basis for this phenomenon. The unexplained
is getting explanations through science and specifically through quantum
mechanics.
No more need
for witches, psychics or priests. Their insights are limited and normally mixed
with misconceptions and delusion.
Science is
revealing the secrets.
Bohr’s
interpretation of Entanglement
Neils Bohr,
the founder of quantum mechanics offers the whole body interpretation to
elucidate the entanglement. Remember the blind man analogy,
“We customarily think of the outside world as
separate from ourselves, and the boundary between the two is the surface of our
skin. However, think of a blind person who gets around with the assistance of a
cane. In time that person will probably treat the cane as part of his or her
body, and will think of the outside world as beginning just at the tip of the
cane. Now imagine the blind man's sense of touch extending out of the tip of
the cane and into the roadway itself. Imagine it extending further, down the
block, into the countryside, to the whole world. There is no point where the
blind man ends and the world begins.”
The
space-time experiments clearly show that communications inside this body (the
space-time universe) will obey light speed limitation. Therefore, quantum
entanglement can not have instantaneous space-time link.
Singularity: The Media for Quantum Entanglement
The Singularity as the other side of
the coin can provide the wholeness and the arena for instant communication.
George Greenstein and Arthur G.
Zajong write “Hidden
behind the discrete and independent objects of the sense world is an entangled
realm.”11
We are looking for a realm where entanglement
and unity of distant objects can take place. If by our assumption, singularity
collects remote distances of our universe in one spot (singularity itself)
action at a distance can be simply described.
Look at an analogy of a landscape
image in a two-dimensional mirror. The images of the objects, which are far
apart in three-dimensional world, but are in a line perpendicular to surface of
the mirror, are superimposed and in contact with each other in two-dimentiality
of a mirror. As previously mentioned in
no-dimension, all points will fall on top of each other. One may argue that the
images fall on each other not real objects. The above statement is true, but
image is carrying the information. Information is not separate from object itself. In one
view, the object is information in its totality.
Please note that, originally we have
assumed that the world has a dual and complimentary nature, an objective nature
and a subjective imaginary nature. These two aspects of the reality intermingle
and create the world. Therefore, in this
view the image is just another expression of the object.
In the Wave-function Chapter, I have
assumed that objects enter informational domain (singularity) during each
wavelength. The particles can exchange information instantly in this realm.
Remember, there is no time element in the proposed singularity.
Ervin László, the famous Hungarian philosopher of science, postulated a similar scenario. He assumed
quantum vacuum as a universal field that interact with matter. He asserts that the field:
“…acts as a holographic
medium, registering and conserving the scalar wave-transform of the
3-dimensional configuration spaces assumed by matter in space. This universal
fifth field is not inferred from space-time interactions like gravitational,
electromagnetic, the strong and weak nuclear forces. In this new type of field,
space and time become implicate, enfolded, as described mathematically by Bohm.
The fifth field is spectrally (holographically) organized, and is made of the
energy present in the interference patterns of the waveforms. The
transformations from space-time order to this spectrum dimension are described
by holographic mathematical formulations.”20
The idea of space-time being embedded
in a sea of something is nothing new. Paul Dirac also speculated that
space-time is embedded in a sea of photon. He later on postulated that universe
is embedded in a sea of negative electrons. However, such a sea has to have
zero dimensions to be able to incorporate quantum entanglement. Singularity/Space-time
duality with proposed description for wave particle function presented in this
book provides such a zero size media where quantum entanglement can
materialize.
The description of entanglement in
this model is compatible with the Special Relativity because it infers that
although a pair of particles may be far apart in space-time, in singularity
domain they are related. Therefore, information does not actually travel beyond
speed of light in space-time to reach the other particle.
This is another indication that the
presented concept deserves attention. The
explanation for action-at-a-distance is embedded in this model. As far as I
know, there is not many theories out there that offers an explanation for
quantum entanglement phenomenon.
Quantum
Tunneling
Cassimir Effect
Courtesy of Nahid Sahel Gozin
During its wave function, if a particle encounters a barrier
where it cannot occupy an energy state (can not be present in the space-time),
it tunnels and appears on the other side of the barrier. Quantum tunneling also does not have any
explanation with Newtonian Physics. An explanation can be offered for the
phenomenon that is similar the one that I offered for wave particle function.
In quantum tunneling if condition does not allow, the trace of particle will
not resurface and stays in singularity and shows up again when the obstacle in
space-time is bypassed.
Super-Luminal Speed
Quantum entanglement and quantum teleportation ar