Quantum Mechanics

[Mohsen]

Quantum Mechanics

While studying quantum mechanics, there are four points to keep in mind.

First, quantum mechanics is not a theory. More than eighty years of lab experiments proved the principles to be valid. Mathematics of quantum theory precisely predicts and reproduces the results of physical experiments. We are applying the principles in making delicate instruments and building precise computers. Quantum mechanics is science of subatomic arena.

Second, Quantum mechanics is weird. In this arena,certainty of macro world is replaced by uncertainty and super position of states. Casualty and cause and effect can reverse so cause appears before effect(second Feynman diagram). Direction of time can reverse also and future appear before past. Entanglement exists without apparent link. The law of conservation of energy gets pale in many instances. And so forth and so on.

Third , apparently and we can not 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 which is beyond our today's consensus reality.

And the last point, quantum is not something remote which belongs to laboratories and scientists, It is the basic building block of our body and our macro world and the laws of classical physics are constructed and derived by its mechanics. One of the main tasks of this theory is to propose explanations for unexplained findings in quantum theory.

Quantum Mechanics

One of the main tasks of this theory is to propose explanations for unexplained findings in quantum theory. Mathematics of quantum theory precisely predicts and reproduces the results of physical experiments, But it does not explain the strange behavior we are facing with, neither it helps us to understand them. Niels Bohr's approach to Quantum Mechanics was just to observe the observations 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 persistent properties but Quantum Mechanic theory is deficient and cannot reveal the hidden variables, which affect the mechanics of the findings. He believed 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 tries to offer an explanation for it.(35)

Here I am suggesting 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 can be accepted as the Einstein's deeper theory, which explains the results of quantum experiments and brings the deterministic reality back to picture. At the same time, because it has a mind component, it contains some of the interpretations and views of Neils Bohr. Here are some conclusions derived from quantum theory;

In the nucleus there is a "sea of quarks", which continually pop into and out of existence in our Space-time universe due to quantum fluctuations. This violates the causality principle that we so religiously adhere to, unless we expand the series of related events out of our space-time. Above I suggested that energy can penetrate from Planck holes and create the sea of quarks. Also matter can transform to energy and leave our space-time. Can this two-way transformation of energy and matter be an explanation for quantum foam? “Even in flat space, one can find quantum states in which the energy density is negative locally although the total energy is positive.” (Ref 6, p145) Normally the fluctuation and transformation cancel out each other with no effect. In intergalactic space, the sum of the transformation activities can be slightly positive. This can be responsible for accelerating expansion of space-time. In this scenario we do not have to suppose the notion of negative energy.

Quantum fluctuation on the other hand is comparable to mind activities during awakeness. During normal mind activities our consciousness intermittently is in and out of objective world. In another word, our consciousness' constantly fluctuates between two different arenas. We are alternating between sensation and imagination domains. We may say that our mind is constantly popping into and out of the physical world? We can also use sleep dreaming and awakeness as an analogy. While we are awake we are time bonded and local. We also are dealing with objective reality most of the time. While we are sleep we depart from objective world and become non-local and floating out of time limits. Please refer to Quantum Mind By Arnold Mindell on the related topics. (Ref 14) Dr. Mindell very clearly shows the many resemblances between mind activity and quantum behavior. There is no way that I can do any better.

Orbiting electron is present at the same time in a whole region of space and has a whole range of velocities. In the current understanding of the atom, an orbital is not something like the orbit of a planet around the sun. It is a probability distribution in space. And, the electron cannot be said to be really 'moving'. Current physics explanation says that, subatomic particles do not occupy a specific location. Also they do not follow a trajectory in space to reach to new position. This violates the locality rule in space. Experiments reveal that the electron only ever moves radially -- in and out.... But yet it covers the whole angular range. So this way, it defies 'steel ball' or 'classical' interpretations. Alternatively, we can claim that, an electron inside atom orbits, is everywhere and nowhere. If we cannot follow electrons trajectory, we have to come to conclusion that at times it is absent, and does not occupy a spatial location. If it does not follow the space-time rule of locality, may I suggest that electron or its trace travels to singularity and comes back to our space-time in different location?

This interpretation brings the experiments to a more understandable and meaningful event. "The maximum speed through space occurs if all of an object's motion through time is diverted to motion through space...but having used up all of its motion through time, this is the fastest speed through space that one object - any object - can possibly achieve". (Ref 1, p51) Can we say that if an object approaches the speed limit and, trying to pass that, it will exit our space-time universe and join the singularity? Can traveling back and forth to singularity be an explanation for quantum leap?

Heisenberg Uncertainty Principle

According to Heisenberg and his Uncertainty Principle, we cannot simultaneously determine the position and momentum of a particle.

Dx (location) = h (Plank Constant)/Dp (momentum)

Can it be that this hypothesis about the uncertainty of location of particles is produced by our unconscious attempt to apply Newtonian laws to subatomic particles?To justify the uncertainty principle, error in measurement and lack of appropriate tool are brought up. Neither is very convincing. Can we assume that, we cannot detect particles because they loose their mass and leave the space-time? May be they join an entity, which is non-local, and appear again in a location, which fells in the domain of the orbit. Known Physics tell us that we cannot track a subatomic particle by any method whatsoever. Let us add “ in objective world” to the sentence. The problem arises when we are expecting to see the whole picture in just one arena, real number domain. As an analogy, please note that we can not follow and understand a three dimensional motion in its entirely in a two dimensional world.“ … Heisenberg used matrices _ whole array of numbers _to represent the positions and motions of an atomic particle.“ (Ref 8, p56) In his calculation to create the matrix he used the symbol i which stands for square root of –1, an imaginary number. He had to choose a number, which is out of the domain of our real numbers. We cannot ignore the quantity i and call it imaginary. We have to accept that it stands for a kind of reality. Neither we can ignore Hilbert space. Quantum mathematics drags us to a scope “ …that is really an infinity of imaginary worlds.“ (Ref 8, p57)

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 uncertainty principle. The most famous one is the uncertainty between location and momentum of a subatomic particle. Please note that one of the elements is spatial and the other is energy related. We can say as locality gets blurred the energy is more defined.

We can extend the principle to time and energy in a system.

DE Dt = or bigger than h/2p

The exited state of a radioactive atomic Nucleus decays with time. If the lifetime of such a state is Dt, it can be shown that the energy of the exited states is uncertain by

DE = or greater than h/2pDt.” (Ref 11, p59)

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The second diagram of Feynman for Compton Scattering also leads us to above uncertainty. (Ref 26)

Here we have a complementarity 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?“ 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”. (Ref 11, pp100-101)

Reproduced from Ref 11, p101

Their experiment showed, had 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.

Quantum Super-Position of States

The Schrodinger's Cat story illustrates the quantum super position of states

The schrodinger's cat is dead and alive.

Such a sentence does not relay any meaningful concept to us. Or does it?

In the observable world a cat either is dead or alive. The series of events lead to just one of the possibilities. To suppose that different universes accommodate different possible outcomes, will be far from acceptance because possibilities are endless and it means we have to have endless numbers of universes and the number is growing at rate that transcends all concepts of infinitudes. It is also grossly against conservation of energy if we are holding to it, and it is not economical either.Schrodinger's wave equation 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 hidden from us.” (Ref 8, p58)

The Shrodingers's probability formula for position of a particle in space can be written as:

If we believe that the particle is somewhere in space but we can not exactly pin point it, we can normalize the formula and write:

Which means that we 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 change the formula to reflect normal! condition. If we are revisiting the existing concepts we have to also question normalization. Normalization is the base of major parts of quantum mechanics calculations. If we take normalization out of quantum calculations, we tremble the pillars of these calculations. It is similar to questioning the understanding of reality on the basis of space-time properties alone. Bringing the probability of (1) under question 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. If we expand the particle/particle trace field to include singularity, we will come to an imaginable 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? Going back to Schrodinger's cat story, let us question where can we find such a cat, which is in superposition of life and death? We assumed singularity to contain information without objective structure. In such a domain, every possibilities information can exist simultaneously. But to materialize in space-time and become objective, information has to be reduced to one state. Are we accustomed to such phenomena or is it completely strange to us.Superposition of states happens in quantum level. According to concept presented, physical world connects and intermingles with singularity in every miniscule of space. We assumed quantum arena to be the interface between our physical world and singularity. Surprisingly, such a superposition can happen in our mind. We are familiar with this kind of 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. Then we reduce it to one possibility and make it happen in physical world. See how all of these fall together as different piece of the same puzzle. Remember the three circles of reality presented at the beginning.

Singularity as an informational domain, can contain 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.

Mind you, if we take superposition as actual objective phenomena, it turn to be against dearly loved conservation law! Much 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 Everett presented at 1957. To describe it more James Hartle introduced consistent histories formulation. In 1995 Fay Dawker and Adrian Kent elaborated on the concept further. Do we need to extend the superposition and state reduction 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 somehow out of our universe. Let us then take the state reduction as event inside our physical world. This way we are left only with one universe. Then this is the main question: 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 try to include implausible fantasies, like many universes or multiple histories as part of reality? What I am suggesting in here is to find a solution by simply opening out the scope and include a mindlike entity as other 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.
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Revisiting particle wave function

Wave function was introduced as a model to describe the Heizenberg Probability Principle for the location and velocity of particles. Nevertheless we can examine this model for movement of free particles.While looking at the quantum wave function from mathematical point of view, Professor Roger Penrose indicates; “You can not explain the wave like nature of quantum particles in term of probability waves of alternatives. They are complex waves of alternatives!” (Ref 5, p56). Further he explains that complex number is some combination of purely real and purely imaginary numbers.

Argand Diagram (Ref 5, p56)

Please note that in order to show the quantum wave function Physicists cannot use any of other 3 dimensions. Not even the Kaluza-Klein dimension. And not the extra dimensions in string theory. They have to choose a virtual dimension out of our space-time to be able to explain the quantum wave function, an imaginary dimension. Yes, we can imagine the complex numbers in our mind. But quantum wave function 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 part of the complex numbers.

Let us look at it from another angle. Although wave function was introduced as a model to represent Heizenberg Uncertainty Principle, for a wave particle in an electromagnetic wave, we can bring the following argument.

Special Theory of Relativity says that nothing can travel at or above the speed of light in our space-time universe. The reason behind it, is because in special theory of relativity the formula for relation between mass to its speed is:

m=m0/sqrt (1-v2/c2 )

Where m is relativistic mass (mass in motion). m0 is rest mass, v is velocity of the particle relative to observer and c is speed of light. As the velocity of a particle increases its mass increases, at speed of light v2/c2 becomes 1. In this case m0 will be divided by 0. So mass will increase to infinity. (We came back to infinities where most physicists hate. Another road sign to reach to a deeper understanding of reality which we avoid looking at because we are afraid of pass the edge of the cliff.) . Infinity does not exist in space-time universe. Besides, we need an infinite amount of energy to move this infinite mass. This goes beyond explained physics. Known physics does not have any explanation for it.

“In 1960 Einstein found that, in a condition of static equilibrium, as the radius of the cluster approaches Shwarzchild radius. The particle would eventually have to move faster than light.” (Ref 4, p10)

The linear speed of light in vacuum along the X-axis ( line of propagation) is 299,792,458 m/s. But photon is traveling in another direction as well (vertical)

Let us look at a polarized wave particle which posses mass and propagating along X-axis. If we take the propagation speed as fixed then the velocity has to change according to position of the particle along the curve.The actual speed will exceed the propagation speed as the particle leaves the peak of the curve down the slope.

tan a=D y / D x

Dy = Vy ( median) DT------------------------ Vy ( median) is median linear speed along y- axis

Dx = Vx ( median) DT ------------------------Vx ( median) is median linear speed along x- axis

If we take Vx as constant c then Vx = Vx ( median) then

Dx = Vx DT

tan a=Dy / Dx= Vy ( median) DT / Vx ( median) DT = Vy ( median) DT / Vx DT

therefore tan a= Vy ( median) / Vx

then tan a Vx = Vy ( median)

if a =90 then tan a= infinity

infinity* Vx = Vy ( median)

infinity = Vy ( median)

Vy ( median) = Vy 1 + Vy 2 / 2

Vy 1 = V sin0 =0

infinity = Vy ( median) = Vy 1 + Vy 2 / 2

infinity = Vy ( median) = 0 + Vy2 / 2

infinity = Vy 2

then V 2 = sqr ( Vy 2 2 + Vx 2 ) =infinity

ref. 40

Our speed limit in space time is c. So any speed above it surpasses maximum. In space-time physics because infinity can not be defined normally we would say speed equals maximum. but because this model contains singularity where infinity is defined I chose to leave infinity in place. With infinite speed, the particle can not remain in space-time and has to leave it and enter singularity. We are led to this conclusion by the fact that the only place that an object can have infinite speed is a non-local zone.

The space time in this model is discrete, and singularity is readily available to deportees of space-time. But singularity in this model can not contain mass, so we conclude that particle has to convert to energy and carry the information as a trace with it.

The above formula can be applied to wave- particles with much lower speed than speed of light such as alpha or beta ray.

Then the wave changes the direction and gets closer to the lower peak. Here the Y component of movement decreases so does the actual speed. until the particle reaches the speed that it can have in space-time. This is the time for energy to convert to particle again, which can be an explanation for quantum jumping in and out of the existence in our universe. On the other hand for a particle to accelerate towards X-axis we need a gravity like attractive field. The assumed function mimics the bouncing ball in a frictionless gravitational field.

For this to happen the proposed singularity has to possess an attractive force. Because the above interpretation of wave function is speculative, I did not mention the attractive force as a main character for the singularity at the beginning. Further work has to be done on this issue.

In 1926 Max Born suggested that, “An electron wave must be interpreted from stand point of probability. Places where the magnitude of the wave is large are places where the electron most likely to be found. Places where the magnitude is small, are places where the electron less likely to be found.” (Ref 1, p105)

Although the above statement favors the presence of electron in the vicinity of peaks, electron waves normally travel below the speed of light. We can suppose as the velocity increases according to above formula and reaches 299,792,458 m/s,it disappears from space-time.

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There are published articles which report achieving speeds, in experiments beyond light speed, in experiments. I refer the reader to 1993 R. Chiao et all. who found that a photon traveled through their sample 1.7 c. The photon was in visible range. Also in 1995 at a colloquium in Snowbird, Utah Gunter Nimtz from University of Cologne, made the announcement that his research group managed to send a signal through a gap of 11.4 cm with a speed of 4.7 c. 15

According to above, somehow the particles still can be detected where they have a higher velocity than 299,792,458 m/s. One can offer a solution Max Born's suggestion by exploring the probability that actual C (speed limit in space-time ) to be more than the above amount. The above diagram and formula can guide us to such a solution. If the presented explanation for quantum wave is acceptable, then we can explain the Max Born's suggestion very clearly. The peak of the wave is the place to find the particle, because at that magnitude, its speed is reduced, so the particle is permitted to appear in space-time universe.

If we assume the fabric of space is discrete( which is hopefully verifiable within few years by launching Glast Satellite). Then we can use the velocity of light propagation formula in free space (electromagnetic waves propagation velocity in free space) as another evidence of non locality of singularity or any entity adjacent to our universe. propagation in space formula is;

c= 1/sqrt(µ 0 e 0 )

Where c is light velocity in free space (vacuum), µ 0 is a constant called magnetic permeability of free space (vacuum) and e 0 is a constant called electric permittivity of free space.

µ 0 = 4p*10 -7 Tm/A

e 0 =8.854187817*10-12 C 2 / NM 2

We can write the above formula for a media as V= 1/ sqrt(µ e ) Where V is light velocity in the

media; Because e and µ are properties of space, where there is no space, we can take e = 0 and

µ =0 thus

V= 1/ sqrt(µ e) =1/0 = infinity

With the same token, infinite speed requires non local zone. Thus we can conclude that inside the of fabric of space we are facing singularity or a nonlocal entity. This defies multiverse theory which introduce another space-time universe adjacent to ours.

Tachyon

The above view also incorporates and explains the notion of tachyons. A tachyon is a hypothetical particle that travels at superluminal velocity. By definition, tachyon's mass squared is negative. That means to define it we have to use complex number which has an imaginary component on it. or we may say its rest mass is imaginary. We may also re-word the previous sentence by saying; tachyons rest mass belongs to informational domain.

on the above model, where the speed of particle exceeds light speed it converts to tachyon. it losses its mass and enters the imaginary domain. While its real mass is zero, its energy and momentum are real and continue in singularity. surprisingly tachyons, by definition are not time-bond. so they belong to a domain which lacks time. as the speed of tachyon reduces and approaches the speed of light its energy approaches to zero and it converts to particle again with a real mass.

The process of appearing and disappearing particles are explained in M Theory as particles are being absorbed and emitted by p-brane. The only difference is p-brane is a model inside of space, not out of it. P-brane assumption has the advantage to keep us in our comfort zone while providing solutions for our paradoxes. whereas, proposed singularity is a separate entity outside of space-time. It may sound remote but feels right.

The above description of particle wave function is in line with recent experiment of Shahriar S. Afshar from Rowan university in New Jersey which defies the notion that nature never permits us to observe both a particle and wave aspect of it at the same time. This notion may convey that particle is either wave or particle and never both at the same time. Such an interpretation led some theorists to the assumption of presence of multi universes. In above model I described the particle as a real entity which is moving in a wave like motion.

As an analogy, suppose we are sitting in a room watching the peak of the waves. but since our eye line is in line with base of the window, we can not observe the sea itself and the whole movement of the water waves.

Also Lorentz transformation formula for linear motion can be written as:

X = sqrt (1-v2/c2)

In velocities greater than speed of light Lorentz transformation moves us to imaginary domain because (1-v2/c2) turns to a negative number. Formerly we related imaginary domain to proposed singularity. So in this view, any particle, which exceeds the speed of light, will move to singularity.

Also a particle, which travels faster than speed of light, will have an infinite mass because:

m = m0/ sqrt (1-v2/c2)

A finite world cannot embrace an infinite mass. For particle to exit the world of finites, it has to loose its real mass and transform to energy (can we suppose energy to be the imaginary mass?), because mass as we define it, is not allowed out of space-time. Mass is finite. When the mass is lost, there will be no turbulence. There will be no mass in sight to detect.

In order to find a solution for some of the paradoxes.We cannot assume singularity just as an inactive pool of energy. Because particle wave are continuous, with the energy of transformed particle, information also has to enter singularity. This is how the trace of particle can stay in singularity, during its absence from our physical world. Quantum tunneling can be explained by assuming the presence of such activity in singularity. Below zero is not nothingness. There exists a vast computational territory. Territory of negative numbers. Interestingly, these also interact with positive numbers and affect them drastically. Contextuality in Bell-Kochen-Specker theorem can be an evidence for such activities. The theorem simply states that in quantum mechanics the value of different compatible observables are also correlated with each other. Although they are not complementary pairs.

If we have detailed and precise knowledge about the true nature of things, we will come to conclusion that “God does not play dice with the universe.” We will come back to a deterministic world again.

Quantum Tunneling

Quantum tunneling also does not have any explanation with Newtonian Physics. Below I am including one of the reports regarding this phenomena provided by Daniel F. James from University of Innsbruck in Austria, in collaboration with a scientist at Los Alamos National Laboratory, physicist.

“In the experiment described in the scientific journal Nature, the group achieved teleportation using singly-ionized calcium atoms that were confined and cooled to ultra-low temperatures (around 15 millionths of a degree above absolute zero). Using lasers, the internal configurations of the atoms -- their quantum states -- were controlled very precisely, allowing entanglement between two of the atoms to be created. One of these entangled atoms was then further entangled with a third atom -- the input of the teleporter. By performing a simple measurement on this pair, and another series of interactions dependent on the outcome of the measurement, the original input state was then re-created on the remaining (output) atom. The quantum state teleportation experiments were carried out at the University of Innsbruck's Institute for Experimental Physics.”

Quantum tunneling can be described better if we accept that electron transforms into energy and information about it passes through Planck pores and travels to singularity. “The area formula for the entropy- or number of internal states- of a black hole suggests that information about what falls in a black hole may be restored like that on a record, and played back as the black hole vaporates”. (Ref 6, p62)

The above statement is an example of the ability of saving information and playing it back as a particle.In recent research by Dr. Mohammad Mojtahedi , of the University of New Mexico physics dept., pulses has been measured at faster than speed of light in a vacuum. He measured pulses up to 2.38 times the speed of light. Although different conclusions and interpretations can be derived from this experiment, he attributes results to quantum tunneling effect. We supposed that, in tunneling the trace of particle leaves our space-time when light's speed limit is provoked? When it reappears the collective speed is more than light speed in space-time.
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Observer and Quantum State Reduction

Understanding quantum superposition of states is a not easy. It raised lots of efforts and brought up many controversies. People ask, can we apply it to astrophysics and Macrocosm? and how is this possible?One school of thought believes that the world has different histories up to this moment. And in the future these histories will follow different paths. in five minutes from now what we see of the state of the world depend on which path we followed. Another interpretation is, the history and the state of the world depend on our question. We see the answer depending on our questions. 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.” (Ref 27, p48)

We are seeing the same universe from different angles. At the beginning of this paper I was trying to draw an entity with zero dimension were 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 notion of time is not present . May be we don't have to speculate in remote and very strange thoughts and domains. Multiple universes and multiple histories do not sound very logical. Rather we can assume the intimate proximity and relationship between microcosm and singularity. With this assumption, multiple states stay in the arena, which has the capability to accommodate it. And we don't have to mix it up with space-time and macrocosm. If we do it, it leads to confusion and we will be drawn into an in-deterministic physics that nobody knows how to deal with it.The Copenhagen interpretation of quantum mechanics “…says that 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.“ (Ref 8, p95)

Dr. Walker rejects the measurement error interpretation by reasoning that our measuring device is only another sub-atomic entity, which according to Schrodinger's equation 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 position or its energy level. I chose to call that imaginary world, singularity. Copenhagen interpretation suggests that observer is changing the reality. In following sentences, Dr. Even Walker explores state reduction paradox. “The answer would seem to be that something is wrong with quantum mechanics, that its make-up is incomplete, or that something about the act of conscious observation alters the quantum mechanical description of reality- something that plays a special role in quantum theory”. (Ref 8, p99)

Dr. Walker rejects the measurement error interpretation by reasoning that our measuring device is only another sub-atomic entity, which according to Schrodinger's equation 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 position or its energy level. I chose to call that imaginary world, singularity. Copenhagen interpretation suggests that observer is changing the reality. In following sentences, Dr. Even Walker explores state reduction paradox. “The answer would seem to be that something is wrong with quantum mechanics, that its make-up is incomplete, or that something about the act of conscious observation alters the quantum mechanical description of reality- something that plays a special role in quantum theory”. (Ref 8, p99)

This is in line with the psychologic notion that our positive or negative thinking can change the outcome. Or we say "as a man thinks so is he"

Telekinesis shows how mind can move the objects in macroscopic world. Surprisingly, none of the four physical forces could be detected as a reason for the movement. Can we come to the conclusion that:

our consciousness is extension of singularity?
Can we claim that our will is creating the state vector collapse according to its desire?

State Reduction and Dream Elucidation

Copenhagen interpretation of quantum mechanics has gained popularity against the other theories despite its very strange sketch. It talks about how an observer would collapse superposition of particle properties into a one understandable and objective state. Arnold Mindell compares these phenomena with fantasy and consensus reality. He states, ”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.” (Ref 14, p193)

Double Slit Experiment

Feynman's sum over path approach

Double slit experiment has been performed repeatedly and it's strange result observed by many researchers. "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." (Ref 1, p104) In order to explain the electron two-slit paradox 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 change 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.” (Ref 1, p110) Any particle with a given amount of energy can travel so far passing through different fields, which may insert some resistance. For one, the above assumption is against conservation of energy law. Also the above explanation is obviously against the law that nothing can pass the speed of light. 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 physics in space-time. To have an infinite speed, the particle has to perform in a non-local arena.A better explanation can be reached, if we accept 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 out of this experiment, and then the electron can come from everywhere and nowhere. Using the verb come applies to travel in space. It is better use appear and accept that electrons pop in and out of space-time universe.

On Davsson and Germer's interference phenomena of the electron, Feynman tried to explain the paradox by claiming that each electron will follow all possible tracks before it hits the screen. We can claim that here, the electron follows the non-locality characteristic of the proposed singularity. If the electrons “are being fired one by one at the barrier- say at the rate of one every ten seconds- the resulting photographical plate will still look like ordinary interference pattern.” (Ref 1, p101) And here the electron behaves like it is not time-bound. Either non-locality or being not time-bound can explain this effect more logically. Professor Roger Penrose wrote the mathematic formula for two-slit experiment by using complex numbers (square root of –1, as well as the ordinary real numbers) for quantum state. “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.” (Ref 5, p57)

To introduce the formula he has to use imaginary dimension along real dimension. He could not find any other real dimension in our space-time universe, which can help him to mathematically explain the phenomena. 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. Let us suppose that singularity is there to do it for us. “In general, a complex number is some combination of purely real and purely imaginary numbers, such as

2+3(-1 )1/2 = 2+3i “ (Ref 5- p 57)

If complex numbers represent particle functions, then particles themselves have to have an imaginary (out of space-time) state.Professor Penrose uses the Argand diagram 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.” (Ref 5, p57) Because, we have been facing the concrete wall, trying to understand the meaning of complex numbers, we are advised to take refuge in mathematical domain. 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 elements. 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 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 assumption, 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 Newtonian physics.
[BREAK]
Quantum Teleportation

Quantum teleportation is the transferring of tiny units of information, called quantum bits or qubits, about a particle. By transporting the information to another location, we can create a replica of the particle in new location. This procedure was done inside laboratory in short distances. Samuel Braunstein, a professor of informatics at the University of Wales in Bangor, England was part of a team that teleported photons from one end of a table to the next in 1998. And most recently, Austrian researchers have teleported photons across the Danube River in Vienna. They reported their achievement in April 2004. Because of measurement problems created by uncertainty principle, teleportation in above experiments had to be performed by using entanglement principle of quantum theory. Please note that teleportation was performed by just transferring the information, not the actual particle. In another word for entanglement and teleportation, we need an information media. In this model, the proposed singularity acts as such media. Further more, the above experiments defies string theory interpretation of entanglement. Because in them one string particle is not responsible for entanglement and teleportation, rather phase transitions from particle to qubits and back to particle is shown to be the actual phenomena behind the process.

References

1 The Elegant Universe, Brian R. Greene, March 2000, Vintage Books

4-Bangs, Crunches, Whimpers, and Shrieks, John Earman, Oxford University Press 1995

5- The Large, the Small and the Human Mind, Roger Penrose et al, Cambridge University Press, 1955

6- The Universe in a Nutshell, Stephen Hawking, 2001, Bantam Books

8- The Physics of Consciousness, Evan Harris Walker, 2000, Perseus Publishing

11- The Quantum Challenge, George Greenstein, Arthur G. Zajong, Jones and Bartlett Publishers. 2001

14- Quantum Mind, Arnold Mindell, Lao Tse Press, 2000

15- www.nature.com/nsu/031013/031013-10.htm

26- http://www.glenbrook.k12.il.us/gbssc...n/u14l5da.html

27- Quantum Gravity, Lee Smolin, Basic Books, Perseus Books Group. 2001

35- http://plato.stanford.edu/archives/w...tries/qm-bohm/

37- http://news.nationalgeographic.com/n...portation.html

43- http://axion.physics.ubc.ca/rebel.html

Action-at-a-distance

©“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 implying a correlated collapse in object #2 though it be arbitrarily far away. Though no information can be passed using such a method (thus not coming into conflict with special relativity) it does seem to imply some action-at-a-distance that is NOT accounted for by the exchange of force-mediating quanta such as gravitons or photons. This continues to be an unsettling state of affairs and a focus of philosophical and physical research, as it was for Einstein and as it was for the philosophers of Newton's day who were equally troubled by action-at-a-distance.” - Brent Nelson, M.A. Physics, Ph.D. Student, UC Berkeley

“Non-local effects... Occur in quantum mechanics and they can not be understood in terms of one thing being separate from another - some sort of global activity is taking place.” (Ref 5, p133)

Aspect experiment In 1982, Alain Aspect and col. experimentally proved the reality of the above thought experiment, and the non-local actions. The diagram below sketches the experiment for more detail, please refer to http://roxanne.roxanne.org/epr/index.html - table Or other related academic books and sources. (Ref 25)

Finally Aspect designed and performed the above experiment to examine the concept of quantum entanglement. More recently, in July 1997 (cf. Science, vol. 277, pg.481) Nicolas Gisin and col. proved the existence of this non-local Quantico informational instantaneous action in large scale.

Similar experiment has been repeated in different part of the world since then. They all proved the entanglement exists between particles, which are far apart in space.

The hidden variable explanation for the entanglement has been proved wrong by different articles. (25)

Again if by 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 image of a landscape in a two-dimension 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. As previously mentioned in no-dimension all points will fell on top of each other. One may say that the images fall on each other not real objects. That it is, because the above analogy does not represent the whole picture. Underneath, I try to explain it further.Mind you that quarks functions have an imaginary number component.“ Laszlo (1993) adds to this scenario “the postulate according to which the quantum vacuum is the fifth universal field interacting with matter” stating that “the field ( Which I adopted it as Singularity) acts as a holographic medium, registering and conserving the scalar wave-transform of the 3n-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.” (Ref 20, p204)

Water waves are another analogy for the above concept. As the molecules of water rise from the surface we see them as wave. When they fall, they join the sea of water again. And then the cycle repeats itself. What we see are waves at the surface, but in reality the waves are extension of the sea, which adopt a specific shape while in action.Please note that most probably the identity of the molecules of water in subsequent wave is not similar to previous one. This explains the identity question of particles, in quantum fluctuation. The main factors, which are hidden here, are the energy field, which is moving the water molecules and the data, which regulates the energy and the waves motions. The collective action of field and data which are not objective and the water molecules which are objective form the observable waves.If for nothing else, the presented concept deserves attention for this single property, which can explain action-at-a-distance. As far as I know, there is not many theories which offer explanation for quantum entanglement out there.

Summary

While quantum mechanics is very precise to predicts and reproduce the results of experiments, it does not offer any explanation for the strange results obtained in lab. The proposed singularity as non-local media, offers explanations for the above by defining zero, infinity, imaginary and complex numbers. An explanation for Tonomura's two slit interference, quantum entanglement and other sub-atomic phenomena was proposed.

References

5 - The Large, the Small and the Human Mind, Roger Penrose et al, Cambridge University Press, 1955

20 - http://www.merkabaweb.net/holo2.htm

25 - http://roxanne.roxanne.org/epr/index.html - table

Quantum Entanglement

40- Courtesy of N. Sahelgozin, Alzahra University, Tehran, Iran

www.universaltheory.org This is a chapter of Universal Theory which is based on singularity as a separate entity

This is a work in progress. Your input is very needed to identify the flaws and correct them. Please enter your comments in Message board
To read the whole theory please check;
Universal Theory

©2004. All rights reserved.

Para-psychological activities are claimed and demonstrated, but we cannot explain them.

Quantum behavior is repeatedly shown and recorded in enormous number of researches and we are applying it to our advantage but we cannot explain it either.

Consciousness is in us. It is the basis of our awareness, but still we cannot explain it.

Certain basic mathematical functions and facts exist (like negative and complex numbers) but they cannot be related to physical world, as we explained it so far.

Here, we have to explore the presence of a new domain for physical world - a dimension, which goes beyond matter or other known physical properties.

Pascual Jordan, one of the major early contributors to quantum theory says “ ….We compel [the electron] to assume a definite position.” (Ref 8, p136)

Who are we? Where do we stand in the equation?

[mkirkpatrick]

I think that Quantum mechanics is a really great conception,that has arisen in the mind,and thats really the point,it has arisen in the mind,well that is hardly
surprising as that is all there really is."quote Dr Mindell,There are many resemblances between mind activity and quantum behaviour,"unquote.
Also "quote Mosen,Mind poppiing in and out of the physical world"unquote.
Quantum theory goes a long way into explaining the universe us,and it will extend even further very soon,The recent film What the Bleep do we know,poses some very interesting questions,some of which the film tries to answer.the thing with all Mechanics is that you need a Great Engineer to make sure that all things remain in that place appointed to them,and that all remains
perfectly balanced.the reason particles blink in and out of space is because space has no realality to its name.there are no spaces antwhere in this universe or in an infinity of other ones,everything is absolutely full,so much so
you could not squeeze a banknote between it,and what is it full ofwell Mind ofcourse.

kind regards,michael.

[humanbydefault]

In my mind [wich also means personally] I see the science we identified as quantum mechanics these days as the most complex representation of the universal interaction of two aspects of reality: Reductionism and Holism.
When we say: "We can't explain the quantum world using classical physics..." we are referring to a reality that belongs to a holistic set of events that deep in its nature responds directly to a yet deeper reductionistic process that at the same time is responsible for a holistic world of the "micro-things."
Take for example the movement of planets around a sun>>> If you consider the presence of individual planets in a non-connected way among them, you won't be able to find the true reason why they follow thier actual orbits as they do every single day without interrumption. It is a "bunch" of apparently disconected systems that when "attached to each other" [entangled?] BEHAVE in a way we [scientists, physicists and regular people] could consider... weird?
That's why we can't get it! There was an article in the front page of this forum that accounted for some behaviors of a group of pendulums connected together in a common rod. They seemed to acquire an unexplained symmetry that shouldn't be there assuming we see the process in a reductionistic fashion.
I don't see the problem with understanding why quantum mechanics is "so weird." What is weird is that in the year 2006 we still pretend to be able to explain things in a "clasical" way when we act as pure stubborn reductionistic beings and forget that the universe is in some way "interconnected" in all its parts and "pieces."

That's my opinion about the "contradictory confusion" observed in books and opinions every time we attempt to describe the roll of quantum mechanics in our lives...

HUMANBYDEFAULT

[Hamid]

Standard interpretation of Quantum Mechanics is able to reveal the hidden variables. In fact, these variables are traceable in Gaussian normal distribution function (bell curve) and no more hidden.

In case of standard normal distribution, that is to say when the mean value is zero and σ=1, these variables will transform to −3,−2, −1, 0, +1, +2, +3 as long as uncertainty or tolerance of measurement is within the range ±3 and equal to 6 which is called natural tolerance (σ= standard deviation).

The mentioned variables will lead us towards a real wavefunction as a mathematical tool for calculating the probabilities. Because, in a real wavefunction there isn't any need to use complex or imaginary numbers.

Deep understanding of Gaussian normal distribution function and cumulative distribution function will show us in Quantum Mechanics how are the probabilities converted to well-defined outcome and the so called measurement problem is in fact not problem at all.

For more information, please refer to the following articles published in ToeQuest Research Library:
1- How Can the Photons Tolerate Each Other?
2- Double Slit Experiment and Quantum Mechanics

[bfancis]

I think that the i dea of the uncertainity principle is based on the fact that the half of the electric force contains an integral number of wave legths and hence our measurements are not affected by the principle there fore the problem comes straight from the atom.

[gautam]

Dear Mohsen
In that case,I believe that there is a quantum infinity and that merges with the spatial infinity and with that a maas partcle, once devoid of mass, leaves the material universe. Your thought process is fully in consonance with the mest theory of everything.
regards
Gautam