Quantum Mechanics Violating Bell’s Inequality | Quantum Science Philippines
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Quantum Mechanics Violating Bell’s Inequality

Lotis R. Racines

Einstein never liked quantum mechanics. He didn’t like the idea that the momentum of a particle, if it’s position was known, was completely unknowable: that is, random [1]. He even said that: “God does not play dice with the universe.” which was referred to Copenhagen Interpretation of quantum mechanics that there exists no objective physical reality other than that which is revealed through measurement and observation.

Einstein wasn’t the only one who didn’t like Quantum Mechanics. In 1935 he got two other physicists, Boris Podolsky and Nathan Rosen, and wrote a famous paper entitled Can Quantum-Mechanical Description of Physical Reality be Considered Complete? We now refer to it as simply the EPR Paradox. EPR Paradox occurs when phenomenon appears disobeying local realism, EPR’s assumption. With this, EPR concluded that since there were “real” properties of the world not even definable in quantum theory, then quantum theory is “incomplete”.

Aside of Einstein, Podolsky and Rosen, there were already several physicists trying to convey quantum mechanics. One of these physicists was David Joseph Bohm, a British quantum physicist who made significant contributions in the fields of theoretical physics, philosophy, neuropsychology and to the Manhattan Project. He published his first book, Quantum Theory, on 1951 but was not satisfied with some he had written in that  book. So he began to develop his own approach, Bohm interpretation, a non-local hidden variable deterministic theory whose predictions agree perfectly with the nondeterministic quantum theory. In 1959, Bohm and his student, Yakir Aharonov, discovered the Aharonov-Bohm effect, which states that a quantum mechanical phenomenon in which an electrically charged particle shows a measurable interaction with an electromagnetic field despite being confined to a region in which both the magnetic field B and electric field E are zero. (In fact this effect was predicted first by Werner Ehrenberg and Raymond Siday in 1949.) He then claimed that either we abandon the locality principle or we are forced to accept the realization that the electromagnetic potential offers a more complete description of electromagnetism than the electric and magnetic fields can [2]. His work and the EPR argument became the major motivation of John Bell deriving the Bell’s theorem.

In 1964, after a year’s leave from CERN that he spent at Stanford University, the University of Wisconsin-Madison and Brandeis University, he wrote a paper entitled “On the Einstein-Podolsky-Rosen Paradox“. Applying the EPR’s assumption, a mathematical relation that was expressed by an inequality shown below, was derived concerning outcome of some measurements of microscopic particles.

[eq] 1 + P(\vec{b},\vec{c}) \ge | P(\vec{a},\vec{b}) – P(\vec{a},\vec{c})| [/eq]

With this, he showed that carrying forward EPR’s analysis permits one to derive the Bell’s inequality. This inequality conflicts with the predictions of quantum theory. That is, Bell’s inequality shows that there are limits that apply to local hidden variable modes of quantum systems, and that quantum mechanics predicts that these limits will be exceeded by measurements performed on entangled pairs of particles.

Now, there are several yet different responses [3] regarding violation of Bell’s inequality.

  1. to  simply assume that quantum mechanics is wrong. However, experiments undergone have supported quantum mechanics!
  2. to abandon the notion of hidden variables and to argue that the wave function does not contain any information about the outcome of the measurement of the values in the particles which leads to the Copenhagen interpretation of quantum mechanics.
  3. to give up locality in favor of the non-locality principle which leads to Bohm’s interpretation of quantum mechanics. However, this type of interpretation is regarded as inelegant, since it requires all particles in the universe to be able to instantaneously exchange information with all other particles in the universe!
  4. to assume counterfactual definiteness. However, in the Everett many-worlds interpretation, the assumption of counterfactual definiteness is abandoned because this interpretation assumes that the universe branches into many different observers each which measures a different observation!

After Bell’s article appear many experiments from all over the world to test Bell’s theorem. But the most interesting experiment was carried out by a physicist at the University of Geneva, Switzerland, Nicolas Gisin in 1997. He was able to measure entangled particles (emanating from a single particle to two particles) about 10 kilometers apart through a detector. This could mean that particles no matter how distant they maybe, could somehow communicate with each other and somehow affect each others’ measurement.

Up to these days, Bell’s inequality with EPR’s assumed principles is still being debated. However, most of the experiments we’re to violate Bell’s Inequality which implies that locality should not be generally assumed, since there are instances that an action of  a particle could affect the behavior of the other particle though remote; hence, pushes quantum theory  as a better candidate to theoretical and applied physics.

This was based from John Bell’s article in 1964 entitled, “On the Einstein-Podolsky-Rosen Paradox” [4] which basically shows that the principle (“local realism”) assumed by Einstein and colleagues contradicts to the statistical predictions of quantum mechanics.


[1] http://library.thinkquest.org/C008537/cool/bellsinequality/bellsinequality.html

[2] http://en.wikipedia.org/wiki/David_Bohm

[3] http://www.starrepublic.org/encyclopedia/wikipedia/b/be/bell_s_theorem.html

[4] J. S. Bell, “On the Einstein Podolsky Rosen Paradox”, Physics Vol. 1, No. 3, 195-200, 1964


If there’s no separation of reality from the observer, could it be that the universe only exists because we are conscious of it? Or perhaps we only exist because someone or something is conscious of us? This is where physics wonderfully melds with philosophy and religion.


A little about the Author:

Lotis R. Racines is an MS Physics Student of Mindanao State University – Iligan Institute of Technology, Iligan City. Hopefully, she’ll take up other fields of Science after her Master’s Degree in MSU-IIT.

One Response to “Quantum Mechanics Violating Bell’s Inequality”

  1. Quantum Mechanics Says:

    Quantum mechanics is the study of the relationship between quanta & elementary particles in physics. Among other relationships the valence shell electrons & photons are quantized.

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