In 1887,when Photoelectric Effect was first introduced by Heinrich Hertz, the experiment was not able to be explained using

classical principles. However, Q.M. was able to explain that the kinetic energies of the photoelectrons were independent of the light intensity, which implied that the stopping voltage depends only on the frequency

and not on the intensity.

Thus, Quantum Mechanics which was born in the 1900s, marked a revolution in Physics. It is a very counterintuitive theory that continues

to puzzle physicists throughout the world. Its interpretation is still debated and new ways are introduced almost daily.

Challenging the completeness of Q.M., in 1935, Einstein together with Rosen and Podolsky published

their famous article “Can Quantum Mechanical Description be considered complete?”. Here, they

introduced the EPR experiment which demonstrated the deficiencies of Q.M.

The EPR Paradox drew attention to the phenomenon known as Quantum Entanglement.

Definition of Quantum Entanglement: measurements on spatially separated quantum systems can instantaneously influence one another.

Here, it showed how to measure the property of a particle, such as a position without disturbing it. It is the fact that QM treats two particles, which interacted in the past (and so became entangled) and then separated spatially (i.e., 'flew apart'), as one object. When one such particle is changed, the other will change too (instantly). Einstein called this the ‘spooky-action-at-a-distance’, which he could not accept due to the violation of ‘principle of locality’. Therefore, Bohm came up with a further explanation using ‘color experiment’.

Imagine that a single white particle splits into two, one green and one red. In this experiment spin up is replaced with the color red, spin down is replaced with the color green. The white particle is the combination of red + green.

One flies left while the other flies right, and we do not know which is which.

The particle on the left is measured to be red, while the one of the far right is measured to be green. In Q.M., using Heisenberg’s uncertainty principle, the color could be either red or green depending on the time of measurement. However, Bohm stated that through the hidden parameter theory, the potentiality does not exist and that the left particle had always been red (spin up) while the right particle had always been green (spin down). We just could not see it. It was hidden, thus, violating Heisenberg’s uncertainty principle.

Laws violated by Quantum Mechanics

• Principle of locality : changes performed on one physical system should have no immediate effect on another spatially separated system (formulated by Einstein). In other words, an influence cannot travel faster than the speed of light.

• Heisenberg uncertainty principle: one cannot simultaneously know both the position and the momentum of a given object.

In 1964, after investigation, Bell discovered that Bohm’s hidden variables theories are either non-local or have to satisfy Bell’s inequality equation (next slide). In a local reality, influences cannot travel faster than light. Bell's theorem says that in any reality of this sort, information does not get around fast enough to be explained by quantum mechanics: therefore, reality must be non-local.

)()()( caNcbNbaN

)()()( caNcbNbaN

Bell uses logic in his explanation of inequality equation.

Suppose a photon pair is emitted by a source in opposite directions.the following three categories in which all detections are with spin up. a . detectable at 0° and its pair at 45º . b. detectable at 45º and its pair at 90º . c. detectable at 0º and its pair at 90º.

a b c a b c

>

a ab bC cc

=

Inserting values in to equation 1, we get equation 2

which is evaluated as,

0.1464 >= 0.25

0.0732 + 0.0732 >= 0.25

which is not true. Since, it does not satisfy the inequality, it must be non-local.

))2

90(sin(

2

1))

2

45(sin(

2

1))

2

45(sin(

2

1 22

2))2

(sin(2

1

Q.M. predicts that the probability that two particles will be detected at spin up withan angle Φ between the detectors is as follows.

Eq. 1

Eq. 2

Most physicists agree that local hidden variable theories are unacceptable and that the principle of locality does not hold, which applies that there is an influence faster than the speed of light.Therefore, EPR paradox would only be a paradox because our physical intuition does not correspond to physical reality.

Hence, the book is still not closed on this paradox.

Bell's discovery of the necessary non-locality of deep reality is the most important achievement in reality research since the invention of quantum theory. Hence, quantum mechanics is an incomplete theory, in the sense that it cannot represent all elements of reality of a physical entity.

Thus, Einstein, Podolsky and Rosen had touched on a fundamental problem in quantum mechanics, placing us in a world questioning whether quantum mechanics is complete or not.

http://www.mtnmath.com/willbe/whatth/node60.html

http://deoxy.org/irc/bell.htm

Marshall,Ian and Zohar, Danah. Who’s Afraid of Schrodinger’s Cat? New York.

1997 Pg.64-67                                                    

http://www.mtnmath.com/willbe/whatth/node60.html

http://www.upscale.utoronto.ca/GeneralInterest/Harrison/BellsTheorem/BellsTheorem.html

http://en.wikipedia.org/wiki/EPR_paradox 

htpp://www.yub.ac.be/CLEA/aerts/publications/EPR_paradox.html

http://www.henrysturman.com/english/articles/EPR.php#loopholes