Lessons from the Particle Waves

The Strange Case of an Isolated Particle in unbound universe

Consider the Free particle Schrodinger Equation for a particle of energy

This give a moving wave. If we stop the time at some instant we will get the following static wave form.

Here we know its energy exactly; but we have no idea where it is and where it came from and which way it is going. It has no defined position. This is due to uncertainty principle which says
Dp Dq ³ h/4p
Since we know the momentum p exactly we have infinite uncertainty in position. Again for a given value of k both +k and -k, give the same energy .

It really doesn't know "if it is coming or going?". Taking the probability interpretation of Born the probability of finding the particle at any one instant is given below

There are many points in the space where it has a probability of 1. The particle is at several places at the same time. In time this distributes and over half the period of the wave it is everywhere. It is an omnipresent particle. This surprising result is because it is an isolated particle and is in unbounded space. An isolated particle with definite energy cannot be localized in an unbound universe!

They have no direction or purpose. They in fact represent the potent (Omni or not), Omnipresent Monad. However when it becomes a composite body it gets meaning and purpose as we show below. I have actually used this argument in order to indicate that God the Absolute (Nirguna Brahman as defined in Indian theology) has no purpose and cannot be known. Because of this Nirguna Brahman do not engage in creation or redemption. Such a God is as good as non-existent.

Effect of Coherent Particle System

Suppose now we have a large number of particles which are coherent – which means each wave is in phase with all the others. Then for all practical purposes we still have a multiple particle which act as one particle - Many in One. Thus a number of personalities that are in coherence, act as one Unit, each enhancing and supporting the other. We still have the same waveform with higher wave amplitude. It is as though we only have one single particle of a larger mass m. They still do not localize and is in no way different from a single particle.

Thus even a totally coherent group of gods do not make a difference because they have no personalities to express.

After all how do we define mass and particle without extensions. They will remain as mathematical imaginations. Indeterminacy is vital to the reality of existence . At least for experiencing the particle we need extensions. A point will remain imaginary unless it is a circle of infinitely small radius. This is also seen in the visibility of line spectra. If the energy levels were discrete and the transitions gave rise to a single discrete frequency in spectra, these will be totally incapable of being seen unless we have a blurring senser. Fortunately each spectral line is given a width due to Lamb Shift so that we can see it.

Effect of Binding the Particle

If we now place this single particle in a bounded box, reflection of the same wave results in what is known as the standing waves. These waves are quantized. This transformation is a transition from the Nirguna Brahman – the God who is unknown and unknowable to Saguna Brahman. The unknowable when restricts himself into a boundary become one with a form. Then this God has properties that are measurable or knowable. Again this is similar to incarnation. The eternal God enters the finite dimensions of human existence brings along with it its own restriction. Thus the incarnate Jesus had limitations with regard to space and time. While he was capable of superceding these restrictions, Jesus as incarnate man never seems to have violated this self imposed restriction. “Having found himself in the form of man, he humbled himself.”

with the probability function as

This is produced by a self-reflection process at the boundaries. Thus it is the boundaries that has produced the properties that we can see. Only those quantized waves will sustain while all the other modes will decay and vanish. This state will remain without decay as long as the system is isolated from the rest of the cosmos. The motion is unabated unless external interference occurs.

Particle in 3D and Degeneracy

When we extend the problem to 3 Dimensions the particle in a 3D box exhibits degeneracy because of its 3 freedoms of motion. Each possible state has a threefold degeneracy.

If we stretch any one axis this degeneracy is broken. Thus in an unbounded space it reduces to omnipresence.

God appears in our finite bounded world as degenerate beings and with specific properties. It is the same Nirguna Brahman appearing as Saguna Brahman by restricting Himself.

Effect of Many non-Coherent Particles

However in the infinite space, if there are several waves that are not in phase or not coherent, these waves interfere with each other and wave packets are formed.

If there are an infinite number of particles of varying energies we have a localized particle.

Look what happens as we add more are more waves with varying phases in the universe which is still considered unbound.

1 Wave 4 waves 16 waves

32waves 128waves

If there are an infinite number of particles of varying energies we have a localized particle. Localization and individual direction of motion develops when large number (ideally infinite number) of non-coherent waves fall on each other.

The Motion is as follows:

Every mathematics students knows how to get these waves given a wave form using Fourier Analysis

Thus it is the lack of coherence within us that gives us the location – the feeling of I – the definition of Ego. In reality we are one with the rest of the cosmos. When the creation is in resonance with the creator we in fact part-take of the divinity with Him. But the entry of sin into the cosmos through the free beings produced a separation – separate beings in the creation each striving and competing with each other resulting in the decaying world. Competition and survival of the fittest really do not produce more efficient systems but a decaying dying system.

The purpose of incarnation was to bring back the coherence and oneness of mind in resonance with the Divine. In other words, it was to bring back Love into the beings. The plan of Jesus in this regard was to start groups of willing beings to come together in oneness of mind. This was his Church on which he places the whole responsibility of redeeming the cosmos as a whole. In fact the whole creation is waiting for the appearance of the “Sons of God” so that through them the redemption can be obtained. Church is essentially is worshipping community.

1Co 10:16 The cup of blessing which we take, does it not give us a part in the blood of Christ? and is not the broken bread a taking part in the body of Christ?

1Co 10:17 Because we, being a number of persons, are one bread, we are one body: for we all take part in the one bread.

1Co 12:12 For as the body is one, and has a number of parts, and all the parts make one body, so is Christ.

1Co 12:13 For through the baptism of the one Spirit we were all formed into one body, Jews or Greeks, servants or free men, and were all made full of the same Spirit.

Eph 4:4 There is one body and one Spirit, even as you have been marked out by God in the one hope of his purpose for you;

Eph 4:5 One Lord, one faith, one baptism,

Eph 4:6 One God and Father of all, who is over all, and through all, and in all.

Author-Work going on to complete

State of a System

”By Their Fruits”

“Actually - so they say - there is intrinsically only awareness, observation, measurement. If through them I have procured at a given moment the best knowledge of the state of the physical object that is possibly attainable in accord with natural laws, then I can turn aside as meaningless any further questioning about the "actual state", inasmuch as I am convinced that no further observation can extend my knowledge of it - at least, not without an equivalent diminution in some other respect.”
The Present Situation in Quantum Mechanics, Erwin Schrödinger, Proceedings of the American Philosophical Society, 124, 323-38

This assumes that behind these observed facts, there is an objective reality that causes these special observable relations that we call the state of existence (State Function or State Vector). This is expressed in Quantum Mechanics as a relation between Wave function (State) and observables. As we associate a property from each reactive relationship, we arrive at the compendium of the state of existence – the State Ket Vector or State Function.

where means represented by

The components of the matrix are the possible states. In all religions, God is defined in terms of his properties. Islam defines Allah with 101 names. All Jewish Patriarchs found and defined God in terms of what he was to them. Thus God is a Provider (Yhvh Jireh), God my healer (Yhvh Rophe) and so on. For a list of Names of God, see http://www.acns.com/~mm9n/names/name.htm

The state of a system is fully described by the wavefunction y(r₁, r₂,...;t). The coordinates of the location of all particles in the system and the time uniquely define the state of the system at any given instant. We must of course include any internal coordinates such as spin, color, charm, truth, beauty, taste or whatever in this definition, but once specified, the system is uniquely defined. Notice that all interactive coordinates of all properties must be defined if the state function is to be complete.

Observables, non-Observables and Hermeticity

For every observable, there is an associated operator which operating on the State function extracts the observable. This extracted value will be one of the possible values of the system.

There is a special class of operators that are called Hermitian operators. They are of particular importance in quantum mechanics because they have the property that all of their eigenvalues are real (and does not contain an imaginary part). This is convenient for the measurement outcome of any experiment must be a real number. There are non-Hermitian operators, but they do not correspond to observable properties. All observable properties are represented by Hermitian operators, but not all Hermitian operators correspond to an observable property. The presence of the imaginary terms will indicate that there are other dimensions involved and we are observing only a projection of the state into the real world. Unless we have the complete picture in all dimensions, our understanding will be only partial.

In soteriology, also the only measurable quantities are the "works". Though Christians would say that the salvation is independent of the "good works", good works are dependent on salvation – or the state function of the person concerned. That is why Paul asserts:

Eph.2: 10 For we are God's workmanship, created in Christ Jesus to do good works, which God prepared in advance for us to do.

James asserts

James 2: 14 What good is it, my brothers, if a man claims to have faith but has no deeds? Can such faith save him?15 Suppose a brother or sister is without clothes and daily food.16If one of you says to him, "Go, I wish you well; keep warm and well fed," but does nothing about his physical needs, what good is it?17 In the same way, faith by itself, if it is not accompanied by action, is dead.18 But someone will say, "You have faith; I have deeds." Show me your faith without deeds, and I will show you my faith by what I do.19 You believe that there is one God. Good! Even the demons believe that--and shudder.20You foolish man, do you want evidence that faith without deeds is useless?

One false argument that is often portrayed is that good works can be the result of a self-motivated sinful nature It may be a ruse for a while. They are then pseudo good works. Nevertheless, taken over a period it simply cannot be true. A bad person cannot bring forth-good fruit. Any such argument will be simply contrary to Jesus’ statements.

Mat. 7: 18 A good tree cannot bear bad fruit, and a bad tree cannot bear good fruit.19 …. 20 Thus, by their fruit you will recognize them.

I had several people asking me "How do we know that someone is saved?" Put it that way it looks impossible to answer. The question is "How do we know the state function of the person?" The answer simply is "by their fruit." John gives the same rule.

1John 3: 10 This is how we know who the children of God are and who the children of the devil are: Anyone who does not do what is right is not a child of God; nor is anyone who does not love his brother.

Again, it is evident from the argument that occasionally an evil person can produce an apparent good work. He can indeed have an ulterior motive. Therefore, a single measurement of the event will not give us the state of the person. On the other hand, his real state betrays the motive and will explain the outcome. In the same way, a saved person will also do evil. However, in the end by repeated measurements over a period of time over a given space the result should be evident. It is not necessarily the mistake of the measuring instrument but it is because the measuring instrument itself is built into our system. Any attempt to present good works, as the result of evil heart is certainly a mistaken -scriptural as well as practically.

Mat: 12: 24 But when the Pharisees heard this, they said, "It is only by Beelzebub, the prince of demons, that this fellow drives out demons."25 Jesus knew their thoughts and said to them, "Every kingdom divided against itself will be ruined, and every city or household divided against itself will not stand.26 If Satan drives out Satan, he is divided against himself. How then can his kingdom stand?27 And if I drive out demons by Beelzebub, by whom do your people drive them out? So then, they will be your judges.28 But if I drive out demons by the Spirit of God, then the kingdom of God has come upon you.

We know that the amount of good works that results from the salvation process varies with individuals. But certainly the saved should show increased good works in their life.

Though we are yet far from writing a Schrödinger equation for the personality we could get much out of the basic Quantum mechanical approach to particles. This is what I am trying to develop in this article. This probably is the first attempt of this kind and therefore I have my limitations. But I believe it contains the germs of a scientific logical approach to several vexing problems in soteriology.

Confronted with apparently difficult situation of relating the unseen and the seen, how Quantum Theory – in which I include all of its variations such as Quantum Mechanics, Wave Mechanics, Matrix Mechanics, Schrödinger Formalism, Quantum Field Theory and all Unified Field theory attempts. – and the scientific community handled the situation is worth following. Understanding the basic difficulties and then accepting what is inevitable had been the result. In contrast in theology we are confronted with a situation of unbelief and disregard for the conflict. There is no point in assuming that there are no conflicts. Saying it louder and in veiled form will not make it disappear. I had often come to doubt even my logical ability when people assert, "Absolute predestination and absolute free will are both consistent and can coexist without conflict. If it does not exist in a fallen creation, it existed in pre-fall Adamic period." I still fail to understand that. Fact is that one precludes another. The first step is to recognize that some of our assumptions are in direct conflict with observations and with the revealed Word of God. We need to learn to accept them as they are and see how they can be reconciled. The scientific world has given us some clue into this mystery.

Even the very existence of God is derived through such observables. Bible is said to be the revelation or unveiling of God. But apart from certain prophetic messages with the indroduction “Thus says the Lord”, and direct messages with the introduction, “ I am the Lord your God”, most of the bible especially the Old Testament is simply the history of the world and eventually the history of the nation of Israel. God appears to Moses as “the God of your fathers”.

Exo 3:6 And he said, "I am the God of your father, the God of Abraham, the God of Isaac, and the God of Jacob."
It is the collective experience of generations that identifies Yhvh.

When Moses asked “What is your name?”, the only answer was “I am that I am” which simply means that he is a state of existence which cannot be fully explained, but can be known by his dealings with people in history. Yhvh proved himself to be God through his action through history. Even the validity of Prophetic messages were subject to validation through history.

Exo 6:7 … you shall know that I am the LORD your God, who has brought you out from under the burdens of the Egyptians.

Mat 7:16 By their fruits ye shall know them.

God is known only through his faithfulness and personal experience of individuals and collective experience. Individual experiences are subservient to the collective experience – because of the Uncertainty Principles, which we will be discussing later. Thus even in knowing God and deducing the existence of God there is an uncertainty. That is why collective experience and national memories are emphasized throughout the bible.

The statistical interpretation of Born (1926)

In Quantum Physics, states are not observables. But there is a direct relation between the observables and the non-observables. Some times the unobservables in relation to observables are referred to as virtual variables. Several interpretations explaining the relation between the two are in existence

Here the wave function is defined as the “Probability Density Amplitude.” The wording is taken following the waves. is and amplitude. So Squaring it will give the Probability Density. Since is a complex function squaring will make

P=^*

Born’s Statistical interpretation maintains that the absolute square of the wave function represents the probability for observation of a certain result, (For example, the probability for finding the electron within a given volume in space.) P is the probability density. It is best explained as P dx will give the probability of finding the particle between x and x+dx.

There is almost complete consensus between physicists with regard to the fact that the predictions, which are obtained from theory applying this rule, match all experiments perfectly. Physicists extend this assumption to other dimensions of properties as well. Hence this should be true even in our multidimensional space, which not only includes human physical level but also the mental and the spiritual dimensions. I have discussed the basis of this assumption in the introduction. Bible abundantly corroborates this assumption.

John 13: 35 By this all men will know that you are my disciples, if you love one another.

John 15: 13 Greater love has no one than this, that he lay down his life for his friends.

So the measurable aspect of Christian faith is to be seen only in the physical expression of love to all mankind. The virtual variable of the "God State" is placed within you. Since God is Love it should manifest itself in love. When the world saw the love of the Christians they deduced that they indeed were special. That changed the world. It was the difference from the norm that showed the unobservable wave function (the guiding potential) that lay behind the expression. If at anytime in history, the church did not produce a statistically significant increase of "good works" within it, we should certainly assume that there is something wrong in the state of the Church. If conversion does not produce a new creature, it is not a rebirth. It should show a fallacy of faith and a falsity in salvation experience. It is not difficult to identify such periods in the history of both the history of Israel and in the history of the Church in various countries. In the history of Israel prophets were not averse to declaring this. However during the church age, we tend to ignore this reality. The best way to check the state of your church is to measure the honesty and goodness of its members and compare it statistically with the general population. Is it significantly higher? If not it is time to rebuild the church on better footing. It is time for a revival. One sad tendency of the evangelical Christians is to play down the "good works", as though they do not matter. This was a necessary reaction to replacing "good works" instead of faith. But we are keeping it beyond the necessary level to the detriment of the basic tenet.

Jam 2:18 But some one will say, "You have faith and I have works." Show me your faith apart from your works, and I by my works will show you my faith.

The world was grappling with the various results and equation of Lorenz, Fitzgerard and Poincare before it could be explained naturally by the formulation of Relativity. The black body radiation behavior and the photoelectric effect led to the quantum theory. This is the normal process of growth. We always go back from observed facts to the reality behind the facts. If we try the other way round it may or may not be correct. This we have seen from the Platonic style of theology starting from the attributes of God. They don’t tally with actual reality or with all revelations of God without tampering. The monism of Origen condemned by the council of Constantinople was also due to such an approach. A strict monistic definition of God certainly required a created trinity. This is also the reason for the Islamic objection for incarnation.

Because the possible internal coordinates are numerous, and since a slight difference in one coordinate can produce a different outcome, a single observation cannot be used to define the state of the system. This is because that observation is only one of the eigenvalues of the equation and not the whole answer. Only when we consider the whole spectrum of eigenvalues (observed facts) we can get a fair idea of the state.

particles and effects

Discovery of Electron
In April 30, 1897, Joseph John Thomson announced that cathode rays were negatively charged particles, which he called 'corpuscles’. Thomson proposed the existence of elementary charged particles, which is now called electrons, as a constituent of all atoms.

Discovery of Neutron
In 1932 Chadwick proposed the existence of Neutron as a result of his studies in alpha particle collisions.

Black Body Radiation
1859 Gustav Kirchhoff’s studies in blackbody radiation showed that the energy radiated by a black body depended on the temperature of the body. Attempts to explain this shape of the energy and the wavelength at which the maximum energy occur continued for several decades

In 1884, Ludwig Boltzmann derived Stefan’s Law theoretically

In 1896, Wilhelm Carl Werner Otto Fritz Franz Wien (1864-1928) Prussia-Germany derived a distribution law of radiation.

In 1900 Max Karl Ernst Ludwig Planck (Germany 1858-1947), who was a colleague based his quantum hypothesis to explain the fact that Wien's law, while valid at high frequencies, broke down completely at low frequencies.

“Moreover, it is necessary to interpret U_N [the total energy of a blackbody radiator] not as a continuous, infinitely divisible quantity, but as a discrete quantity composed of an integral number of finite equal parts”
Planck. On the Law of Distribution of Energy in the Normal Spectrum. Max Planck. Annalen der Physik 4 (1901): 553.

In 1900, Planck devised a theory of blackbody radiation, which gave good agreement for all wavelengths. In this theory the molecules of a body cannot have arbitrary energies but instead are quantized - the energies can only have discrete values. The magnitude of these energies is given by the formula

E = nhf

where n = 0,1,2,... is an integer, f is the frequency of vibration of the molecule, and h is a constant, now called Planck's constant:

h = 6.63 x 10^{- 34} J s

Furthermore, he postulated that when a molecule went from a higher energy state to a lower one it emitted a quanta (packet) of radiation, or photon, which carried away the excess energy.

With this photon picture, Planck was able to successfully explain the blackbody radiation curves, both at long and at short wavelengths. Using statistical mechanics, Planck derived an equation similar to the Rayleigh-Jeans equation, but with the adjustable parameter h. Planck found that h = 6.63 x 10^-34 J·s, fitted the data. As we can see, h is a very very small number. Thus the electromagnetic waves (light) consists not of a continuous wave but discrete tine packets of energy E = hf where f is the frequency of the light.

Photoelectric Effect

1905 when Einstein extended the photon picture to explain, another phenomenon called photoelectric effect. In this effect when light is allowed to fall on a metal and electrons are released. However there is a lower cut off frequency below which every electron stopped. Einstein was able to explain this assuming that photons are particles of energy E=hf.

Hydrogen Spectrum

1913 Niels Bohr (1885-1962) was able to explain the discrete spectrum of hydrogen atom with the assumption that there are possible stable energy levels where electrons can stay without emitting any wave and the light is emitted when it falls from a higher level to a lower level. The frequency of the light so emitted was given by Energy of the difference in levels = hf.

Compton Effect

In 1923, Arthur Compton showed that he could explain the collision of a photon with electrons at rest using the same idea. These phenomena came to be known as Compton Effect

Wave-Particle Duality

Thus, it appears that light could behave like a wave some time (to explain reflection, refraction and polarization, interference) while at other times (Photoelectric effect, Compton effect) it behaved like a particle. The wave-particle duality of electromagnetic wave is a fact of experience and seemed mutually exclusive without compromise.

In 1924 in his doctoral thesis, Prince Louis de Broglie argued that if light waves exhibited the particle properties, particles might exhibit wave properties. The experiment to test was done on a stream of electrons as particles at a double slit and single slit and the pattern exhibited fitted the interference pattern for a wave given by

m= mass v = speed of the electron thus: mv = momentum of the electron

Schrodinger Equation

In 1926, Erwin Schrödinger introduced operators associated with each dynamical variable and the Schrodinger equation, which formed the foundation of modern Quantum Theory. A partial differential equation describes how the wave function of a physical system evolves over time. In the Schrodinger picture differential calculus was used.
The time-independent one-dimensional Schrödinger equation is given by

The solution for the value of E gives us a spectrum of values for the Energy of the system.

Using the spherical coordinates, this equation gives:

And using the separable form of the wavefunction in terms of the radial, angular parts in three dimensions

Using the potential energy as:

it gave the correct energy levels and correct spectral frequencies because of transitions. This indeed was the greatest success of Quantum Theory and which gave it the impetus.

Operators and Quantum Mechanics

In quantum mechanics, physical observables (e.g., energy, momentum, position, etc.) are represented mathematically by operators. For instance, the operator corresponding to energy is the Hamiltonian operator

Where i is an index over all the particles of the system.

Later Dirac developed the Matrix method and is known as Dirac Bracket formalism.

In this mechanism the operators are replaced by matrices and the wave equation then reduce to a matrix equation

Quantum Wave Functions and State Vectors

While operators represent the observables, the operand – the function on which the operators act is known as the wavefunction , which is a function of the position for stationary solutions.

Postulates of Quantum Mechanics were developed later as below:

Postulate 1. The state of a quantum mechanical system is completely specified by a function that depends on the coordinates of the particle(s) and on time. This function, called the wave function or state function, has the important property that is the probability that the particle lies in the volume element located at time t.

Postulate 2. All observables are associated with a hermitian operator. In any measurement of the observable associated with operator , the only values that will ever be observed are the eigenvalues a, which satisfy the eigenvalue equation

The solution to the eigenvalue problem given above will give a spectrum of possible values for a corresponding to a spectrum of eigenfunctions . These eigenfunctions form a set of linearly independent functions. At any point in time, we could assume that the state of the system will be a linear combination of these functions.

Some commonly used operators are given below:

Postulate 3. If a system is in a state described by a normalized wave function , then the average value of the observable corresponding to is given by

Postulate 4. The time evolution of system is given by

The postulates of quantum mechanics, written in the bra-ket notation, are as follows:

1. The state of a quantum-mechanical system is represented by a unit ket vector | ψ>, called a state vector, in a complex separable Hilbert space.

2. An observable is represented by a Hermitian linear operator in that space.

3. When a system is in a state |ψ1>, a measurement of an observable A produces an eigenvalue a :
A| ψ1> = a | ψ1> so that < ψ|A| ψ1> = a < ψ| ψ1> = a since the wavefunctions are orthogonal
The probability of getting this value in any measurement is

|< ψ |ψ1>|²

where | ψ1 > is the eigenvector with eigenvalue a. After the measurement is conducted, the state is | ψ1 >.

4. There is a distinguished observable H, known as the Hamiltonian, corresponding to the energyof the system. The time evolution of the state vector |ψ(t)> is given by the Schrödinger equation:

i (h/2π) d/dt |ψ(t)> = H |ψ(t)>

Heisenberg’s Uncertainty Principle

1927 Heisenberg discovered that there is an inherent uncertainty if we try to measure two conjugate observables. This is known as Heisenberg’s Uncertainty Principle

The simultaneous measurement of two conjugate variables (such as the momentum and position or the energy and time for a moving particle) entails a limitation on the precision (standard deviation) of each measurement. Namely: the more precise the measurement of position, the more imprecise the measurement of momentum, and vice versa. In the extreme case, absolute precision of one variable would entail absolute imprecision regarding the other.

” The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa.”

“I believe that the existence of the classical "path" can be pregnantly formulated as follows: The "path" comes into existence only when we observe it.”

“In the sharp formulation of the law of causality-- "if we know the present exactly, we can calculate the future"-it is not the conclusion that is wrong but the premise. “

--Heisenberg, in uncertainty principle paper, 1927
http://www.aip.org/history/heisenberg/

In 1929, Robertson proved that for all observables (self-adjoint operators) A and B

where [A,B] = AB - BA

In 1928, Dirac introduced his Bracket notation and QT in terms of matrix algebra

In 1932, von Neumann put quantum theory on a firm theoretical basis on operator algebra.

Quantum Non-locality

In 1935 Einstein, with his collaborators Boris Podolsky and Nathan Rosen, published a list of objections to quantum mechanics, which has come to be known as "the EPR paper" One of this was the problem of nonlocality. The EPR paper argued that "no real change" could take place in one system because of a measurement performed on a distant second system, as quantum mechanics requires because it will violate the relativity principles.
Einstein, B. Podolsky, N. Rosen: "Can quantum-mechanical description of physical reality be considered complete?" [i]
For example, consider a neutral-pi meson decaying into electron – positron pair. The spin of Pi meson is zero. Therefore, the total spin of electrons must be zero. Hence one of the electron will have spin (1/2) and the other spin (- ½). If the electron pair moves apart a million light years and we measure the spin of the electron on earth as ½, QM requires that the other should have a spin (-1/2) if someone measures it in his or her galaxy at the same time. How would they know which spin should it be since Relativistically it is impossible to transfer any information with a speed greater than that of light. This is the “spooky action-at-a-distance” paradox of QM

There are two choices.
You can accept the postulates of QM as is without trying to explain it, or you can postulate that QM is not complete, that there was more information available for the description of the two-particle system at the time it was created, and that you just didn't know it because QM does not properly account for it.

So, EPR requires that there are hidden variables in the system, which if known could have accounted for the behavior. QM theory is therefore incomplete, i.e. it does not completely describe the physical reality. In 1952, David Bohm introduced the notion of a "local hidden variable" theory, which tried to explain the indeterminacy in terms of the limitation of our knowledge of the complete system. [ii]

In 1964, John S. Bell, a theoretical physicist working at the CERN laboratory in Geneva proposed certain experimental tests that could distinguish the predictions of quantum mechanics from those of any local hidden-variable theory These involved the use of entangled photons – photons which interacted together at some point before being separated. These photon pair can be represented by one wave function. In 1982, Aspect, Grangier and Roger at the University of Paris experimentally confirmed that the “preposterous” effect of the EPR Paradox, the "spooky action-at-a-distance" is a physical reality. All subsequent experiments established the existence of non-locality as predicted by Quantum Theory.. [iii]

In 1986, John G Cramer of University of Washington presented his Transactional Interpretation for Quantum Mechanics.[iv]

In 1991, Greenberger–Horne–Zeilinger (GHZ) sharpened Bell's result by considering systems of three or more particles and deriving an outright contradiction among EPR's assumptions. They showed a situation involving three particles where after measuring two of the three, the third becomes an actual test contrasting between locality and the quantum picture: a local theory predicts one value is inevitable for the third particle, while quantum mechanics absolutely predicts a different value. Bell-GHZ showed that wave functions "collapse at a distance" as surely as they do locally.[v]

[i] Physical Review 41, 777 (15 May 1935). (The original EPR paper)

[ii] D. Bohm: Quantum Theory, Dover, New York (1957). (Bohm discusses some of his ideas concerning hidden variables.)
D. Bohm, J. Bub: "A proposed solution of the measurement problem in quantum mechanics by a hidden variable theory" Reviews of Modern Physics 38 #3, 453 (July 1966).

[iii] J. Bell: "On the Einstein Podolsky Rosen paradox" Physics 1 #3, 195 (1964).
J. Bell: "On the problem of hidden variables in quantum mechanics" Reviews of Modern Physics 38 #3, 447 (July 1966).
A. Aspect, Dalibard, Roger: "Experimental test of Bell's inequalities using time- varying analyzers" Physical Review Letters 49 #25, 1804 (20 Dec 1982).
A. Aspect, P. Grangier, G. Roger: "Experimental realization of Einstein-Podolsky-Rosen-Bohm gedanken experiment; a new violation of Bell's inequalities" Physical Review Letters 49 #2, 91 (12 July 1982)

[iv] http://mist.npl.washington.edu/ti/

[v] http://www.intercom.net/~tarababe/dissertation.pdf