The Entanglement Illusion
A Case of Mistaken Topology
by Daniel Sabsay — February 2010

I have long been concerned that the widespread success of the mathematical framework known as quantum mechanics has lumbered physics with a corollary notion known as "entanglement".  Entanglement is the idea that previously-associated sub-atomic particles somehow stay synchronized, not just correlated even when separated by long physical distances.  I am very disappointed that contemporary physicists have come to regard entanglement as an actual physical property of nature, not just a mathematical concept.  The interpretation of entanglement as a real property of nature is absurd on its face, and worse, has provided a popular justification for the belief in telepathy, precognition and other non-existant "psychic" abilities. 

In the early days of quantum mechanics, Einstein expressed his conviction that quantum mechanics was not a complete characterization of reality because of its probablistic description of the sub-atomic world, saying: "I don't believe that God plays dice with the universe" and calling entanglement a "spooky action at a distance"[1].  But in 1964, a physicist named John Bell published a paper with a formula he said could settle the controversy by determining whether or not entanglement was really an innate property of the physical world or merely a convenient mathematical construct.  Subsequent experiments by other physicists — whose findings were interpreted according to Bell's formula — lent increasing creedence to entanglement as a real property of nature.  So for the last 45 years, entanglement has gained virtually universal acceptance, and the popular culture has increasingly relied on entanglement to legitimize its belief in paranormal psuedo-science. 

Also, in the last 10 years or so, a fresh crop of entrepreneurial physicists has figured out that entanglement (if physically real) could be used as the basis for a new type of computer, called a quantum computer.  This type of computer could be very significant, since it would have enough power and speed to crack the encryption codes securing all our online e-commerce.  In fact, most people in the physics and computer communities have come to believe that quantum computers are just around the corner, or already at work in a secret lab somewhere.  However, these last 10 years have sped by, as team after team of quantum-computer builders have proclaimed imminent success, only to have the headlines fade a week or so later.

Maybe the Emperor Has No Clothes

A recent scientific paper may have changed everything.  It makes a strong case that there is a serious flaw in the logic and mathematics of Bell’s 1964 scientific masterwork.  So, even though starting around 1970, many “confirming” experiments have have persuaded most physicists to accept entanglement as a physical fact, this new discovery could negate the meaning of these experiments.

What is Quantum Mechanics?

To explain the recent development, I will start with a short history of Bell’s Theorem, the idea of entanglement, and the theorem's influence on the field of physics.  I will then explain how the discovery of this alleged flaw in Bell's logic has the potential to return entanglement to the esoteric mathematical closet where it belongs. 

The story begins in the 1920s, when physicists codified a set of scientific principles (and an accompanying mathematical framework) called Quantum Mechanics (QM) to describe the behavior of energy and matter at the atomic scale.  Since sub-atomic objects are so small and so light, any attempt to measure their position or motion perturbs them enough that their future course or position cannot be predicted.  Physicists have learned however, that these trajectories do have predictable statistics in the same way that rolling a pair of fair dice can give us a predictable range of results.  So, although we know the outcome of a single roll of dice must be a value between 2 and 12, we cannot predict the result of any particular roll, even though we can confidently predict the aggregate statistics of rolling these dice many times.

So, unlike the deterministic character of classical mechanics, QM is not able to predict the exact state of any single sub-atomic particle.  It is only able to calculate the probability of a range of outcomes of certain events, but it is able to do this with great accuracy.

Tiny Particles, A Huge Question

From the very begining, a fundamental question about QM quickly separated physicists into two opposing camps, one (which included Einstein) argued that QM was incomplete, since it was only probabilistic.  The other camp, believing sub-atomic particles to be intrinsically random in their very essence, maintained that QM was complete because it described everything that could possibly be known about quantum objects.  In his 1964 paper, physicist John S. Bell published an equation, now known as Bell’s Inequality, which he claimed could be used to settle this fundamental question by evaluating results collected from a particular type of experiment (known as an EPR experiment, originally suggested by Einstein, Podolsky & Rosen).  This experiment would measure the state of certain pairs of particles (generated by a single event) which remain correlated as they fly apart in opposite directions, manifesting complementary properties required by conservation laws.

On its face, the complementary properties manifested by these particle pairs are neither surprising, nor unexpected, but it makes no sense if the widely-separated quantum particles really have a non-deterministc (random) internal state.  Physicist Schroedinger coined the term entanglement to describe this non-intuitive condition.

Over the years, beginning in about 1972, many experiments were carried out to investigate this question. When the results of these experiments were interpreted according to Bell’s statistics, they all have confirmed the assertion that the internal state of atomic particles is intrinsically random (i.e. non-deterministic), and therefore would seem to vindicate the view that QM is entirely complete.

Buckle your Philosophical Seat Belt

Thus, it is a PROFOUND paradox (in fact it's known as the EPR Paradox) that pairs of particles, miles apart, remain correlated even though the state of the individual particles is (asserted to be) completely random.

So, if you accept that Bell-inspired experiments have “proved” that particles have truly random “hearts”, then you are forced to conclude that these paired particles somehow maintain a connection with each other by some external mechanism, perhaps even signaling each other at the moment of measurement.  Even weirder, when the distance between the two measurements is increased beyond the reach of a signal carried at the speed of light, the correlation still persists.  To explain this, some theorists have even gone so far as to postulate that space itself must be a kind of holographic illusion, and that entangled particles are really the same particle viewed from different perspectives!  It is this alleged instantaneous connection that has so inspired the imagination of the paranormal crowd [2].

Bell’s 1964 paper has been so influential, and the subsequent experiments so “successful” that several generations of physics students have now been indoctrinated into the received wisdom that sub-atomic particles are inherently random, and yet somehow can stay connected by some “spooky action at a distance”(—Einstein).  But let’s review:

  1. Particle-pair correlations – ARE A FACT
  2. Experimental support of Bell’s statistics – IS A FACT, however...
  3. Entanglement – IS NOT A FACT, it’s a conclusion justified ONLY IF Bell’s Inequality is mathematically correct, which apparently it isn't.

Entanglement: A Vacuous Word

And now friends, we have finally reached the destination of our little journey: An Oxford physicist with the unlikely name of Joy Christian has recently published a paper titled “Disproof of Bell’s Theorem and the Illusion of Entanglement” that may discredit Bell’s Theorem.  Without the validation of Bell’s theorem, and the consequent conclusion that quantum particles have random hearts, entanglement is just a vacuous substitute for the word correlation.  Dr. Christian’s paper is online in Cornell University's open-access science journal at: arxiv.org/abs/0904.4259.  While the math in this document is daunting, the paper has a few paragraphs in layman's terms [3] that explain the issue fairly well.

According to Dr. Christian, John Bell did not appropriately incorporate the topology of ordinary 3-dimensional space into the equation predicting the probability of various orientations of the particles measured at both ends of their outward flight.  When the math is adjusted for the 3-dimensional topology, and the experimental data is cranked back through the revised formula, the "spooky" conclusion DISAPPEARS.

It’s still early days in this debate, and there is as yet no new consensus among physicists, but if Christian's argument prevails, there will no longer be any support for the belief that quantum particles can be linked by an instantaneous communication connection, and physicists will now be free to pursue fresh investigations into the heart of the quantum world.  Let’s just say I have a premonition that Dr. Christian’s new topological perspective will win the day.

And I leave you with these 3 little quotes:

[1] "I cannot seriously believe in [quantum mechanics] because the theory cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance."

— Physicist Albert Einstein

[2] "One of the most surprising discoveries of modern physics is that objects aren't as separate as they may seem.  When you drill down into the core of even the most solid-looking material, separateness dissolves.  All that remains, like the smile of the Cheshire Cat from Alice in Wonderland, are relationships extending curiously throughout space and time.  These connections were predicted by quantum theory and were called "spooky action at a distance" by Albert Einstein.  One of the founders of quantum theory, Erwin Schroedinger, dubbed this peculiarity entanglement, saying ‘I would not call that one, but rather the characteristic trait of quantum mechanics.’"

— The irrepressible & irreproducable Dean Radin, pushing his new book: Entangled Minds

[3] "An elementary topological error in Bell’s representation of the EPR elements of reality is identified.  Once recognized, it leads to a topologically correct local-realistic framework that provides exact, deterministic, and local underpinning of at least the Bell [...] states.  The correlations exhibited by these states are shown to be exactly the classical correlations among the points of a 3 or 7-sphere, both of which are closed under multiplication, and hence preserve the locality condition of Bell.  The alleged non-localities of these states are thus shown to result from misidentified topologies of the EPR elements of reality.  When topologies are correctly identified, local-realistic completion of any arbitrary entangled state is always guaranteed in our framework.  This vindicates EPR, and entails that quantum entanglement is best understood as an illusion [emphasis added]."

— Physicist Joy Christian, from the introduction to his paper [PDF]


Disproof of Bell's Theorem

45 years of being misled are finally over

Videos from Professor Sanctuary's Blog [length in minutes]

linked from:

Professor Sanctuary's Foundation of Quantum Mechanics Blog

Bryan Sanctuary is Professor of Chemistry at McGill University (Montreal, Canada)

[updated December 2011]