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Quantum Entanglement

It is possible for a particle to interact with another particle in such a way that the quantum states of the two particles form a single entangled state. The definition of an entangled state is that it is not entirely independent of other states: its state is dependent on another state in some way. Because of this dependency it is a mistake to consider either state in isolation from the other. Rather we should combine the states and treat the result as a single, entangled state.

For example, a light beam is a composed of a stream of photons. The direction of light's electric field is its direction of polarization. The polarization direction of a photon can be at any particular angle, for example "vertical" or "horizontal". It is possible to generate a pair of entangled photons if, for example, a laser is shone at a crystal. In that case, a single photon can split to become two photons. Each photon produced in this way will always have a polarization orthogonal to the other photon (see this Physics World article or this Laser Focus World article). For example, if one photon has vertical polarization then the other photon must have horizontal polarization (this is due to the law of the conservation of angular momentum: angular momentum of the system before the split must equal the angular momentum of the system after the split).

So if two people each receive one of the entangled photons and performs a measurement, they will find that the other person's photon has orthogonal polarization. There is an apparent connection between the particles, no matter how far apart they are taken.

"I cannot seriously believe in quantum theory because it cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance." - Albert Einstein

The EPR Paradox

Einstein was never happy with the implications of quantum theory and at the legendary 1927 Solvay conference (and throughout the late 1920s) he proposed several thought experiments which he believed revealed flaws in the theory. However, all of these objections were successfully refuted by Niels Bohr, and a humbled Einstein went home to lick his wounds. However, in 1935 Einstein and two colleagues, Boris Podolsky and Nathan Rosen (EPR) described a thought experiment commonly referred-to as the EPR paradox, the implications of which shook quantum theory to its core.

Einstein's great objection to quantum theory came from its denial of physical reality before observation (quantum theory says that only after we measure a property value of a particle does that property gain physical reality - before we measure it we must consider it to be in a superposition state). We often quote Einstein's rejection of quantum indeterminacy: "God does not play dice", but his less-quoted objection to quantum theory's denial of physical reality reveals his more serious concern: "I like to think the moon is there even if I am not looking at it."

In order to dispute quantum theory on this basis, the EPR paper contained - for the first time in the history of science - an operational definition of physical reality:

"If, without in any way disturbing a system, we can predict with certainty the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity."
- Definition of physical reality from the EPR paper.

Let's say the same thing in other words: If a physical property of an object can be known without it being observed, then that property could not have been created by observation. If it wasn't created by observation, it must have existed as a physical reality before its observation.

Einstein believed that quantum entanglement could be used to reveal a flaw in quantum theory, because he thought that quantum entanglement could determine physical reality before observation - at odds with the principles of quantum theory. Consider two entangled photons, one of which is sent to observer Alice, and the other is sent to observer Bob (see the diagram below). The two observers could be a considerable distance apart. Now remember from the discussion at the top of this page that two entangled photons must have orthogonal polarizations. So when Alice measures the polarization of her photon and finds it to be, say, vertically polarized we instantly know that Bob's photon will have horizontal polarization - even though Bob has not yet measured it!

When Alice measures her photon polarization, we instantly know what value Bob will get when he performs his measurement. (Based on a diagram from the book Quantum Enigma)

But quantum theory says that before Bob measures his photon it can have no defined value for its polarization property - it is in a superposition state. Only when Bob measures it does its value become physically real. How then can we know the result Bob will obtain before Bob measures it? The solution according to quantum theory is that it is the measurement of Alice which collapses the wavefunction of both Alice's and Bob's photons. It is the observation of the polarization of one of the photons as being, say, vertical that instantaneously collapses both photons, resulting in Bob's photon having horizontal polarization.

However, Einstein realised that such instantaneous communication of polarization value between the two photons was forbidden by his own theory of Special Relativity (nothing travels faster than light). Hence, Einstein believed that the model of quantum mechanics was incomplete: it did not describe the physical reality of Bob's photon before observation.

Einstein believed the correct way out of this paradox was to assume that Bob's photon (and all particles) possessed some sort of fixed properties which were hidden from our view (generally referred-to as hidden variables). No faster-than-light communication is then required: the particle properties were set when the particles were created. Crucially, though, this would mean the particles possessing more information than quantum theory said they should have. If particles had these hidden variables then quantum theory was wrong.

An associate of Bohr tells that "this onslaught came down upon us like a bolt from the blue. Its effect on Bohr was remarkable ... as soon as Bohr heard my report of Einstein's argument, everything else was abandoned."

Bell's Inequality

In 1964, John Bell devised an ingenious test for the existence of hidden variables. Bell's theorem (which is commonly called Bell's Inequality) has been called "the most profound discovery of science" (see here).

Bell showed that for a group of objects with fixed properties A, B and C, the number of objects which have property A but not property B plus the number of objects which have property B but not property C is greater than or equal to the number of objects which have property A but not property C.

This can be written more compactly as:

Number(A, not B) + Number(B, not C) >= Number(A, not C)

An easy-to-understand version of this inequality is provided by David M. Harrison of the University of Toronto (see here). Let's consider our collection of objects with fixed properties to be a collection of people. And let their fixed properties be the following:

  • A: Sex ("Male" or "Female")
  • B: Height (over 5' 6" ("Tall") or under 5' 6" ("Short" - don't be offended!))
  • C: Eye colour ("Blue" or "Green")

Then, no matter which group of people you are dealing with, you are always able to issue the following statement (inequality): "The number of short males plus the number of tall people, male and female, with green eyes will always be greater than or equal to the number of males with green eyes. I absolutely guarantee that for any collection of people this will turn out to be true."

That's always true. Isn't that amazing? That's a bit of quantum mechanics you can try out at your next party!

It's relatively simple to prove this. Note that every person can be classified into one of the following eight groups:

Referring to this diagram, Bell's Inequality is saying that:

(Group 1 + Group 2) + (Group 4 + Group 8) >= (Group 2 + Group 4)

Which, if you study it, is clearly always going to be true.

So Bell's Inequality will always hold true for normal, everyday objects with fixed properties. But now let's analyse the situation for quantum particles. Let's consider the polarization (more commonly called "spin") of a photon as the property to be measured. We now find we have a limitation imposed by quantum mechanics: the Heisenberg Uncertainty Principle says we cannot obtain the correct value for the spin in two different directions, for example, we cannot know the spin of a particle in both the 90° direction ("up") and the 45° direction at the same time. So how can we perform a test of Bell's Inequality on a particle? This is where quantum entanglement appears to come to our rescue, suggesting we can find the values of two properties if we have two entangled particles. Let's treat "spin up" as our Property A, and "spin 45°" as our Property B. If we measure one entangled particle for Property A then it would appear we can test the other still-unmeasured second particle for Property B (note: this would imply we have somehow "beaten" the Uncertainty Principle).

Referring back to our original statement of Bell's Inequality:

Number(A, not B) + Number(B, not C) >= Number(A, not C)

We will have to divide our quantum particles into three groups (called ensembles), and extract entangled pairs of particles from each group:

Because we cannot measure all three of the properties of each particle (i.e., we cannot measure A, B, and C for each particle - we can only measure the values of two of the properties), we cannot conclusively say if the inequality is broken or not. The best we can do is run the test on an ensemble of many thousands of particles and consider the statistics of the results. The first published experiment was by Clauser, Horne, Shimony and Holt in 1969 using photon pairs (with the different properties corresponding to polarization angles of 0, 45°, 22.5° and 67.5° - see here) and it was found that the statistics strongly suggested that the inequality was, indeed, violated.

What does this mean? Well, taking our example given earlier of a collection of people, considering the right-hand side of that inequality, in order for the inequality to be violated a person would have to be more likely to have green eyes if the other (entangled) person had been found to be a male. In other words, the property measurement was dependent on the type of observation performed on the other entangled particle: there is an instantaneous connectedness between the particles. What happens to one particle can instantaneously affect the other (as a result, it shows that we failed to "beat" the Uncertainty Principle - we cannot get a true measurement of two property values: when we measure one property, we "poison" the other reading - see here).


To sum up, Einstein believed the following:

  1. There was no "spooky action-at-a-distance" which apparently violated Special Relativity (i.e., there was locality).
  2. Objects had definite reality, properties independent of observation.

However, the violation of Bell's Inequality reveals that the reverse is true:

  1. There is a strange connection between particles which instantaneously informs the undisturbed particle of the type of measurement just carried out on its partner (however Special Relativity is not violated because no information can be transmitted using this method).

In his book "Quantum Reality, Nick Herbert considers the fact that our bodies form a connected part of that single entity, the universe: "Physicists have discovered that the very atoms of our bodies are woven out of a common superluminal fabric". He then proceeds to quote Einstein who realised the social implications of the illusion of separateness: "A human being is part of the whole, called by us 'Universe'; a part limited in time and space. He experiences himself, his thoughts and feelings as someone separated from the rest - a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest us. Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty."

Photo of a board washed up on a beach.
We are all one.


The secret for analysing entangled systems is that you can no longer talk of the wavefunction for just a single localised particle, you have to to talk of one single wavefunction for the entire system.

It's quite useful at this point to introduce another useful piece of common notation. In the previous page on The Quantum Casino we were introduced to the common "bra-ket" notation, with a state being denoted by . If we have two states, and , then the joint state is the tensor product of the two states (see back to the explanation of the tensor product in The Quantum Casino). The resultant, single state is then:

For an example, consider a particle which, after measurement, can be in one of two states: or (a particle such as this is known as a qubit and is used in the exciting new field of quantum computing). The orthonormal basis of the Hilbert state space should therefore have two vectors representing the and states (a two-dimensional Hilbert space is denoted by H2 - see back to the page on The Quantum Casino for an explanation of Hilbert spaces and the orthonormal basis):

A Qubit must be in state 0 or 1

Before measurement, and "wavefunction collapse", the qubit's state could be any mix (superposition) of these two states. But after measurement, the qubit's state is always found to be in state or (the superpositions apparently disappear).

What happens if our qubit is a photon and has an entangled partner photon (as explained earlier)? You might think each photon has its own state, and hence each photon would have its own separate Hilbert state space:

Two Qubits

That's wrong.

Remember that the states of two entangled photons are dependent on each other. For our entangled qubits, let's say that if the first qubit is in state then the second qubit is constrained to be in state as well, and if the first qubit is in state then the second entangled qubit is constrained to be in state as well. Now instead of having two separate state spaces for the two qubits we have one entangled state space, and instead of one wavefunction for each qubit we now have one wavefunction for the entire system (composed of two qubits).

In order to construct the entangled space, we first see that each of the two vector spaces is spanned by similar sets of two basis vectors:

The resultant single, joint state space can be constructed by taking the tensor product of the two sets of basis vectors of the two original state spaces (the tensor product of two vectors is a matrix - see back to the discussion of bra-ket notation in The Quantum Casino). This is achieved by performing a matrix multiplication of the two sets of basis vectors:

We can see that the original two-dimensional state spaces combine to produce a single four-dimensional state space:

So the resultant set of four basis vectors for the new entangled space is:

Note that with just one entanglement the Hilbert space has rapidly increased from two dimensions to four dimensions. This rapid increase in complexity due to entanglement - and the huge number of entanglements in the environment - will be shown to be key to what really happens during "wavefunction collapse". This will be explained in the next page on Quantum Decoherence.

For more on qubits and this method, see this PowerPoint presentation.

Separable and Entangled Systems

After receiving the comments of AKP below, I decided it would be useful to clarify the distinction between separable and entangled systems.

Let's consider eye colour (which can be either blue or green) of two non-related people. The two people could be treated as a single system, in which case the resultant combined system (I see Wikipedia call it a composite system here) could have four possible states for eye colour (essentially, each person is like a qubit, and we are dealing with a two-qubit system):

It is possible to decompose the system because there was no dependence between the eye colour of person 1 and the eye colour of person 2: they were completely independent systems. However, if we now consider the situation of identical twins we find there is now a dependence: the eye colour of person 1 depends on the eye colour of person 2 - they are identical.

It is now not possible to decompose this system into two separate systems (people) because of that dependence between the two twins. For example, you are no longer free to select blue eyes for person 1 and green eyes for person 2 - that combined state is forbidden. For this reason, this combined system with the two twins is non-separable: it is an entangled state. So this is the reason why an entangled two-qubit system cannot be decomposed into two independent one-qubit systems.

For a mathematical description of this, see the PowerPoint presentation, especially pages 16-20 on "Two Qubits". On page 20, "Two Qubits, Entangled", you could think of the entangled state as representing the situation when both identical twins have blue eyes, and the entangled state as representing the situation when they both have green eyes.

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Comments are now closed on this page.

Many thanks for this site. I have been looking for something like this for ages. I want to understand QM, but getting past the basic concepts and jargon on for example wikipedia was proving too laborious. These pages you have created a real blessing. - Frank, 25th February 2007
Thank you so much, Frank. That's appreciated. I tried to make it as readable as possible. - Andrew Thomas, 25th February 2007
nice page! i'll be sure to come back to read more. a few questions/comments to possibly consider:

maybe you could expand the heisenberg uncertainty comments into a paragraph. i think its important to talk about the difference between two conjugate measurements on one particle and these measurements being performed on separate particles from the same ensemble. and being a statement about standard deviations in measurements on two different groups of particles, the principle is not telling us how one measurement will "disturb" the results of a second conjugate measurement.

regarding particle spin measurements, if i have an ensemble of x-spin-up particles and i measure y-spin and z-spin each on a half of the ensemble, dont i get 1/2, 1/2 in each case? isnt this perfectly precise? what is lower bounded here is the product of the std devs of these two probability distributions. again being measurements on different particles.

i really liked the clarity of the bell inequality discussion. it would be cool to see a picture like the green eyes, etc. with the quantum tests inserted.

jmahoneyatphysicsdotucdavisdotedu - john, 29th March 2007
Hi John, thanks for your comments. I've actually just added a section on the Heisenberg Uncertainty Principle to my page "Quantum Mechanics: An Introduction":

Regarding your comments about particle spin, I'm really referring to what might be called a "generalized Uncertainty Principle" - not the same as the complementary pair idea (see ). This just states that you can't measure all spin values simultaneously: taking a measurement along one axis destroys the information in the other axes. - Andrew Thomas, 30th March 2007
This is an excellent resource for those who only want to understand instead of being bombarded with intense mathematics and obscure terminology. If only more scientists would write like the author of this page. Very much appreciated. - Gibran Shah, 9th May 2007
Thanks very much, Gibran. I'm trying to strike a happy medium by making the articles accessible to the general reader, but also providing more advanced technical information and mathematics for those who want to dig a bit deeper. - Andrew Thomas, 9th May 2007
Hi Andy, Excellent site! I think it's fantastic that you're presenting QM fundamentals in such an easy to understand manner. I do have a question about your phrasing, though. In my experience, two particles are said to be "entangled" iff their joint state is not decomposable as a tensor product of two individual states. So it's a bit confusing to read your explanation here:

"then the entangled state is the tensor product of the two states (see back to the explanation of the tensor product in The Wavefunction). The resultant, single entangled state is then..."

Perhaps you mean "the composite state" or similar instead of "entangled state"? Keep up the good work! - AKP, 16th June 2007
Hi AKP, thanks for your comments. I've added an entirely new section to the main text - "Separable and Entangled Systems" - because of your comments to clarify the situation. You're right, two systems are said to be "entangled" if their joint state is not decomposable as a tensor product of two individual states - this would be the example I give of the eye colour of two identical twins. You can't decompose the system into two independent people because of the dependency. It's an entangled system.

But you're right - I shouldn't have described the entangled state space as resulting from the tensor product of the two state spaces. I've changed the wording to "joint state space" instead of "entangled state space". Thanks. - Andrew Thomas, 18th June 2007
Above you have:-
Number(A, not B) + Number(B, not C) >= Number(A, not C)
with C:Eye colour ("Blue" or "Green") but "not C" is "not Blue" rather than "Green" as you have it later. Blue and green are not the only eye colours.

B: Height (over 5' 6" ("Tall") or under 5' 6" ("Short")) is OK since it covers everyone

A: Sex ("Male" or "Female") could also be dubious. - John Middlemas, 22nd July 2007
I suppose you have a point about the eyes - but surely everyone falls into one of the two sex categories! - Andrew Thomas, 22nd July 2007
Nice but..... what is actually entangling these particles? How are they actually linked. Maybe the superposition is forced to randomly collapse in a way that however maintains the conservation of energy, so that it sums up to zero.... is that enough to explain it? Or do you need communication for the particles to know how to maintain the conservation of energy? And if so... HOW! - Morn, 12th September 2007
Well, nobody knows the answer to that. If you know, please tell us!! David Bohm tried to explain it by his "Implicate Order" idea which proposed the universe had a hidden holistic connectedness.

Here's my take on it: Imagine two entangled photons are emitted from a source. As time progresses, they move apart in space, so we view them as separate. However, if we view the entire spacetime block (as opposed to a single moment in time) then we find the two photons form a single object made up of the worldlines of the two photons. Hence, the impression that they are actually separate point particles in space is really a false impression. A particle is really a line in spacetime. And two particles are really two lines in spacetime, which can be joined. Hence, separation is an illusion.

I might write on this in the main article sometime. - Andrew Thomas, 12th September 2007
Hi Andrew, it is interesting that uncertainty relation arises between two orthogonal components of the angular momentum (not between two orthogonal components of the momentum); the momentum acts like an unitary observable, but the angular momentum acts like three separate observables! - Marian, 29th September 2007
Hi Marian, yes, that's very interesting. It's another example of how we have to be careful not to confuse intuitive classical concepts in physics with quantum mechanical concepts. (For the technically minded, Wikipedia shows how the components of angular momentum do not commute, i.e., the result we get when we measure two components depends on the order in which we measure them - hence the Heisenberg Uncertainty Principle kicks in: ) - Andrew Thomas, 29th September 2007
I was confused by your statement "Bell showed that for a group of objects with fixed properties A, B and C, the number of objects which have property A but not property B....." and wondered if you could clarify. Surely all objects must always have properties A, B, or C. It is the values of these properties which can vary? So having property A and not B, what does that mean in terms of the values? - Brett Wilson, 30th September 2007
Yes, I was a bit casual in the use of "properties" and "values". The way it is written is such that instead of property A being "Sex" with two possible values - "male" or "female" - I'm in fact defining property A as "maleness" with two possible boolean values: "true" or "false". Similarly, instead of property B being "height" with two possible values - "tall" or "short" - I'm in fact defining property B to be "tallness" with the same two possible boolean values: "true" or "false".

So if property A is "true" we're actually saying it's a male, and if property A is "false" then it's a female. And when I say "The number of objects which have property A (i.e., property A is true) but not property B" I mean the number of short males.

If instead we consider the "The number of objects which do NOT have property A but DO have property B" it would be the number of tall women. I hope that's clarified what I meant in the text (or maybe not!). - Andrew Thomas, 30th September 2007
Hi. This is the best site I have come across which explains complex ideas in everyday language. If you are not a professor, then you sure should be. A shortcut to this one will be on my desktop, you can bet! - Bruce Penney, 25th October 2007
Oh, you're too kind! - Andrew Thomas, 25th October 2007
This is the MOST LUCID site I have found on QM intro principles, great work !
One thing I don't understand is the association of the 3 Bell properties ( e.g. A,B,C) with the photon polarization ( 0,45, and 90 ), particularly 45 degrees, as both articles which talk about photon entanglement generation reference vertical/horizontal polarization pairs that are 90 degrees related. How do we get the 45 degree polarized photons, and how are they related to the entanglement state ? - Dan, Philadelphia Pa. USA, 19th February 2008
Thanks, Dan. I've just added a fair bit of new text to the section on Bell's Inequality to clarify the principle of 90 degree and 45 degree photon polarization, and the implications for entanglement. - Andrew Thomas, 20th February 2008
Great explanations! I have a bachelor of science in physics, but I think I've learned more from your page than I did at University. - Tony LaMonica, 29th February 2008
Thanks for that, Tony. There's a review of Roger Penrose's book "The Road to Reality" on which seems to sum it up: "People who have done a degree, even in physics at a prestigious university often come out not really knowing what's going on. Courses almost exclusively focus on examineable material and so the beauty of the whole thing is lost in routine calculations and derivations." - Andrew Thomas, 29th February 2008
Hi Andrew,

First of all - thanks for such a wonderful set of articles on QM for the layman.

I had a question on entanglement: is it possible to determine experimentally whether a particle is part of an entangled pair or not, if you have no idea of the history of that particle?

Gopi - Gopi, 5th May 2008
Hi Gopi, no, because we don't understand the principle behind the entanglement we can't test for it. If we have two particles, we have no way of telling if they are entangled or not. However, if we had a **collection** of many entangled particles, and we ran the Bell's Inequality experiment and found the inequality was violated, we could say there was some spooky connection there. - Andrew Thomas, 5th May 2008
Ok, You lost me at the part where the photons violate the inequalities... i dont understand how that works....any other way you could explain it? - Sean, 15th May 2008
It's possible to ignore all the complicated maths and explain it quite simply. Imagine you have a series of objects (say, billiard balls) and they all have fixed properties which never alter (e.g., their colour). Because we know they have fixed properties we might then be able to make a statement such as "the number of blue balls will always be greater than the number of red balls" (this is a similar statement to Bell's Inequality). If we then perform an experiment which measures the colour of the balls and we find that the number of red balls is, in fact, greater than the number of blue balls then the inequality has been violated (broken). We then know that some of the blue balls have changed their colour and become red balls, i.e., their colour property was not fixed after all. Hence, if the inequality is broken we know they do not have fixed properties.

In quantum mechanical terms, it means that the value we get when we take a measurement can depend on the type of measurement we perform, and can even depend on the value we obtain when we measure its entangled twin ... many thousands of miles away! - Andrew Thomas, 15th May 2008
Another simple but comprhensive view of Entanglement can be found at
A few ideas... By presupposing that blind chance established the universe, scientism denies that there is rationality behind nature. Reason cannot possibly comprehend a non-rational universe. To assume that you have already reached the limits of knowledge is either 'weak conceit' or 'ill-applied moderation'. (Francis Bacon) The universe is neither eternal nor infinite, yet it is real and good. This is a necessary presupposition of science. - Addamstaft, 9th June 2008
Consider an elephant who walked upon a frozen lake. Two of its legs broke down through the ice. A fish below the ice sees the two legs as being independent things. It nips at one of the legs and the other leg jerks. The fish wonders if this is quantum entanglement? How is it that these two separate entities react to each other without being connected? In reality, there are not two things but one, one elephant. From the limited point of view of the fish, the one elephant appeared as two entities. If the fish could somehow rise above the ice, it could see that in reality there is only one entity. I wonder if the same thing applies to quantum entanglement? It seems to me that we space-time observers can only see four of the theoretical eleven dimensions which M Theory postulates exists. Perhaps, for instance, two entangled photons are really only one photon in a fifth dimension, which manifests as two photons in our 4D space-time. If, for instance, a hypercube would appear as a simple cube in our 4D space-time, its other dimensions hidden from us or a hyper-sphere would appear as a normal sphere in 4D, then the appearance of a 5D photon would seem to be a 4D photon, until we do something to it. "Doing something to it" (in other words observing or measuring it) involves a space-time change in its coordinates and as such, the extra-dimensionality of the hyper-photon is revealed. In the same way, if we could move a hypercube, it would be obvious to us that this was no ordinary cube because parts of its hidden dimensions would be revealed when its space-time coordinates were tampered with. All hyperdimensional objects can only reveal themselves to us as regular 4D objects. Thus, if we went into the realm of religion, a hyper-dimensional God would appear to us 4D creatures as a 4D being of some kind. It's unity would be separated or appear as three distinct separate manifestations, as if three legs of the elephant broke through the ice. This could be (from a religious standpoint) an argument for the Trinity, which could be thought of as a collapse of the wavefunction of ultimate (bulk or full dimensional) Reality. Or not. - Kalai Strode, 11th June 2008
That's a great comment! Thanks a lot, Kalai. - Andrew Thomas, 11th June 2008
I don't understand the big deal about Schroedinger's quantum entanglement.
Suppose you had a pair of socks ('entangled particles') and sent one off on a spaceship to Andromeda. If the Andromedan found it was a right sock, why should it imply "spukhafte Fernwirkung" when we (obviously, I would have thought) immediately find the earthbound sock to be left? - John Marks, Gisborne, Newzealand, 3rd July 2008
Hi John, yes, if we're dealing with large ("macroscopic") objects like socks then we can consider them to have fixed properties (left sock/right sock). This is because quantum effects are not visible with macroscopic objects. But if we start dealing with microscopic objects, such as particles, then quantum effects become evident.

Imagine we shine a light beam through a beam splitter so that half goes to one planet, and the other half of the beam goes to another planet many light years away. Now we turn down the intensity of the light so that only one photon is emitted at a time and passes through the beam splitter. If we have two experimenters - one on each planet - and they try to detect the photon then only one experimenter will detect the photon, i.e., the photon has taken just one path to one of the planets. This is as you would expect. But now imagine if the experimenters do not try to detect the photon but instead both experimeters reflect their received light beams onto a third planet (i.e., both beams go to the same third planet). Then it would be possible to create an interference pattern on that third planet like in the double-slit experiment - even though we are only dealing with a single photon. In other words, the photon has apparently travelled both paths to both planets! That's the only way an interference pattern could be produced.

This shows that before we measure a particle we should consider it to be in a quantum superposition of all possible states - both left sock and right sock at the same time! - Andrew Thomas, 3rd July 2008
Dear Andrew,
Thanks for your amazingly speedy reply. I appreciate and understand what you're saying, in particular the weirdness of the double-slit experiment with a single photon producing interference patterns.
Instead of socks, let a pair of 'gewirrt' (entangled) photons, such as might be created from the annihilation of an electron, be the two travellers, one staying here (reflected round a bathtub, say) and the other going off to Andromeda. As I understand it, each photon will have an opposite spin, let us call them 'right' and 'left', though we would not know which has which.
Then Schroedinger's phenomenon (of entanglement) seems to say that, if I measure the earth-bound photon to have a left-hand spin, the Andromedan must find his to have a right-hand spin. And, analogous to the socks, there would be nothing mysterious about this and no need to invoke Einstein's 'spukhafte Fernwirkung'.
Certainly, as beautifully described by Feynmann and others, the double-slit experiment encapsulates the mystery of wave-particle duality. But there is nothing there about spukhafte Fernwirkung and I don't understand why this problem is raised. In the example you give of the single photon interfering with itself, you basically describe the double-slit experiment. What puzzles me is the invocation of Einstein and Schroedinger's spukhafte Fernwirkung: it seems to me unnecessary but I assume I haven't understood the problem posed by Einstein et al. and Schroedinger back in 1935. How is the problem that Aspect tested different in principle from the double-slit experiment? Why is there the concern over faster than light communication when the problem is conceptually no different from a pair of socks? - even though they may be quantum socks! - John Marks, 3rd July 2008
Hi John, yes, I answer quickly so I don't forget to answer. You said: "The phenomenon (of entanglement) seems to say that, if I measure the earth-bound photon to have a left-hand spin, the Andromedan must find his to have a right-hand spin." That's correct. But quantum mechanics (according to the Copenhagen interpretation) also says that the spin does not have an assigned value at all before it is measured - that's the key. That's very different to a pair of socks. I know this is a difficult concept to understand, but before we measure the particle, it's spin value is "undetermined" according to quantum mechanics. We cannot say it has any value at all. This is not due to lack of our knowledge - it's not that the particle has a spin value which we don't know. No, that's not the situation at all. The particle's spin value is **fundamentally undetermined** before measurement.

But when we measure one entangled particle it has to take a determined (fixed) value. Which implies that the other particle instantaneously also has to take the opposite value. So Einstein suggested there had to be instantaneous communication between the two. - Andrew Thomas, 3rd July 2008
I believe that I share John Marks's opinion in that when one states that a particle does not have a value before measurement, one must have conclusive evidence to support this.

I realize that Andrew is trying to say that experiments such as double slit conclusively indicate that particles "must" be in superposition, because supposedly there is no other way to explain the interference pattern. But I do not agree with the logic of this assertion.

Simply stated, because the notion of superposition (an unobserved proposition) may provide an explanation on a piece of paper, what's to say that there is not some other unrealized intrinsic property to matter light which manifests as the double slit effect? - Stefan Hostetler, 8th August 2008
Stefan, yes, that's certainly a possibility for the position of photons in the double-slit experiment. But other particle properties (such as particle spin) also seem to be subject to the quantum superposition. It's not just about position, and it's not just about light. - Andrew Thomas, 8th August 2008
Hey there, been a while since a post on here, and I am really hoping I am the dim wit to to re-ignite this. Absolutely well laid out piece by the way, I came across Schroedinger's cat thought experiment sometime ago reading Terry Pratchett and never really got it until a couple of days ago!! From what I get of it all so far, we are saying that an object (yes a very small object) is in an in-determined state until we observe it? Is it the observed or the observer that it is deciding what state it is in when we look? or are we just catching it in a moment of time when it is in a different state (either going through the slot or bouncing of the panel) after all, these things could be moving at faster than the speed of light. Also if we are the ones that are somehow making the decision for the "observed" doesn't this have some implications for madness or at least give hallucinations some grounding in reality? Like I said I am new to this, but have this feeling that your everyday average Joe's (please don't take offence dudes) like the guys in here are going to be the ones that ask the questions that are stupid enough to just maybe open some more doors (obviously to a whole lot more questions!! lol (sorry for telling you that that was funny!!))(but it was!) - Peter Wawoczny, 11th October 2008
Sorry just read back through that above post and just want to let you all know that I am well and truly included in the average Joe (or certainly below) bracket!! yee gods, I answer a bloody phone all day. And by the way Andrew keep this stuff going and ignore the dudes that want to get all precise in this, as far as I can tell you are wanting to get people in general engaged in this discussion, and you won't get that by putting Degree level formulas all over the gaff, well done I say. Combine the minds of a world and you will always get (G+F) where (G) = Geeks and (F) = f%$K Wits, which=a greater mass of brainpower, energy and ideas than (G) or (F) as a singular observed form!!! LOL. Good Site (and yes before you all jump on board and point it out I am an (F)) - Peter Wawoczny, 11th October 2008
Hi Peter, the whole Schodinger's cat idea is loved by fiction writers and writers of popular science books, but it is actually now considered rather outdated - see this article by Tony Leggett. Before I write further about your other queries, I would instead suggest that you read further on this website, particularly the next page on Quantum Decoherence.

I put some mathematical formulae on the site for people who want to dig deeper. This is an inclusive site for everyone - I'm not just aiming it at f%$K Wits! You're right, I want to "Combine the minds of a world". Nice line.

Heck, I've had some great comments on this site recently! - Andrew Thomas, 11th October 2008
Hi Andrew (agian),
I will inquire once agian on something soon enough, but first i shall give you some praise (as others have been) on such an awesome site! i have read some other things on it (even did some research on a lower level of this dastardly stuff) and on those a lot of the time its put out in a lot more complicated manor which takes a little longer to get my head wrapped around it, but here its well laid out and in a mixed level between avr. joes and smarty pants. which is awesome!

Ok, now for my point to raise. i think Einstien was on a correct path. Becuase these experiments havent proven that the protons don't gain their spin at the begining of the experiment and retain that same value throghout? i know that this interfers with particle uncertainty but the whole theory is based off of the theory that particles change thier actions based on observation. Doesnt this mean that if someone finds a way to prove that one observation isn't what chooses how a particle will act that the whole quantrum physics theory will crumble? i also realise this is extremely hard to figure out a way to do this, but the whole reason the theory stands is becuase apparently if we observe a particle it changes the action that it was going to perform. - Austin Cunningham, California, 19th October 2008
Austin, yes, you're right. But experiments to test Bell's Inequality have been performed (as described in the article) and these show particles do not have fixed properties.

Imagine if we have a group of people (instead of particles). Imagine if we measure their hair colour and their height (two different properties). Let's say after we measure their hair colour we measure their height and we find they are all short people. Now we do the same experiment again. This time we measure their height FIRST instead of second. This time we find that have a lot of tall people. So statistically speaking, it would appear that our measurement of the people's hair colour has affected the height measurement in some way! The height value was not a fixed property! Very strange, but this is what we find with quantum particles.- Andrew Thomas, 19th October 2008
I approched your site looking for a layman explanation of quantum computing. Found a lot of good stuff, but not exactly what I looked for. Whers shall I go next? Perhaps you will add a chapter?

- Nils of Sweden, 20th October 2008
Nils, this paper by John Boccio contains a useful explanation of quantum computing:

An introduction to quantum computation can be found in "A Shortcut Through Time: The Path to a Quantum Computer" by George Johnson, while the standard textbook on quantum computing is "Quantum Computation and Quantum Information" by Michael A. Nielsen and Isaac L. Chuang

I don't think there's anything particularly special about a quantum computer - it's just like running several classical computers in parallel. They can only tackle problems which are amenable to parallelization, such as factoring and searching.

I haven't included a section on quantum computation as that is really an **application** of quantum mechanics, whereas this website deals with **fundamentals**. - Andrew Thomas, 20th October 2008
Just refering to entanglment and the EPR paradox
if bob and alice's photons are no entirely independent of each other, then why wouldnt measuring alice's photon be exactly the same as measuring bob's photon. Therefor by measuring alice's photon, we are actually measuring bob's, hence the photon changes from its superpositioned state, to a defined value.
Probably a silly question but thanks anyway, this site is really helpful and easy to follow along - corey, 5th November 2008
Hi Corey, it's certainly not a silly question, but the answer is very difficult to get one's head around. Yes, measuring Alice's photon is the same as measuring Bob's photon, but before we measure either photon they are both in a superposition state (and could show this is the case by getting a strange pattern off both photons in the double-slit experiment: ). But when we measure Alice's photon we get a *particular* value, and that means Bob's photon is instantaneously forced out of its superposition state to take a particular value as well. So what you actually said was perfectly correct, but that implies an instantaneous connection between the photons. - Andrew Thomas, 5th November 2008
hum very intresting well being it is 1.50 in the morning in the u.k and i desided to look at Quantum Entanglement is suprizeing for myself being that i am only 16 but i have been studying QM for some time and some of the wording is over welming for me to say the least but papers like this make it alot simpler do you no of any outher sites such as this one with other theories like this. the slit theorie i still can not really see how some one can say that 1 if you not looking and dont no the results any result could happen even if you no there a 50% chance a certain even will happen and you know 100% a sertain even will not happen i should really re-read theorie when im more awake do u no of any more sites like this that make well science easy :D i feel a little erm thick commenting on this page due to the fact that 1 every 1 els has many degrees 2 has probables written there own theorie and 3 much older than me but any help would well help

sorr if i make you page look bad - caine, 19th December 2008
caine, not only do you NOT make this site look bad, you give us all great hope for the future that a 16-yr-old has a deep interest in this stuff. Keep going! Working on your grammar would help though. Punctuation is good too.

Andrew, major props, bro. I have been struggling with this stuff for decades, and this one page makes the subject vastly more understandable! Props, man. A good teacher makes up for all the crappy ones, which is most of them. You rule.

As a aside, have you read Louise Gilder's "The Age of Entanglement?" I'm almost finished with her book and that has helped greatly as well. What are your thoughts on the book? I had no idea who John Clauser was prior to reading it, and find it a shame he has no Wikipedia entry.

Viva la John Stewart Bell, laddies! And Albert Einstein too. Even his mistakes were amazing!

Finally, you tackle the subject of 5D v 4D amazingly well. Lisa Randall also does a great job in her book: "Warped Passages" Ciao. - Greg Sivco, January 14, 2009, 14th January 2009
Hi, thanks for all that enthusiasm, Greg, and thanks for the book recommendations. - Andrew Thomas, 14th January 2009
No problem, mate, but I'd like to make one point on entanglement:

In theory, 2 particles can be entangled if they are light years apart. In PRACTICE however, Entanglement seems to break down on the order of kilometers. Why is that?

I don't know why, but he's where being an Engineer helps, because we have all sorts of experience in things NOT working as predicted, when they should.

I submit, and this is just an idea I had last month or so, that the problem may be virtual particles, i.e. the STRANGE fact (or is it just theory? ... consult your local particle Physicist for an exact answer) that particle-antiparticle pairs can be instantaneously created in a vacuum, then almost immediately annihilate each other.

If so, what happens if one of the 2 entangled particles runs into such a pair (or one of the pair) post-Creation but pre-Destruction? Well, a mess happens, that's what. In any event, one of the entangled particles is messed with, but not the other, and so the entanglement breaks down.

Just a thought. - Greg Sivco, 28th February 2009
Hi Greg, yes, I think you're absolutely correct: "Other particles and fields degrade the connection" but that doesn't explain Entanglement Sudden Death! - Andrew Thomas, 28th February 2009
But it should explain it thanks to Uncertainty.

I thought below the level of electron outer orbitals (Chemistry), that randomness takes over. That's what I read from Uncertainty and the Wavefunction (good old Schrodinger).

Randomness reigns.

Or is it England reigns?

Well OK, both. - Greg Sivco, 1st March 2009
Hi Greg, yes, as you suggest, at the quantum level everything is random so effectively *anything* can happen. However, the more significant the effect, the less likely it is to happen. So a sudden complete loss of entanglement should be unlikely - possible, but unlikely.

I haven't read their original paper, but I think this explains it quite well: "Decoherence is the term used to describe loss of entanglement, and in very simplified terms, we showed that ambient 'noise' leads to decoherence that can attack entanglement in an unexpected way. In particular, it can cause entanglement to disappear non-smoothly, in a sense, abruptly. This non-smooth behavior is at variance with virtually all prior results."

I consider the progressive nature of decoherence on the "Quantum Decoherence" page: "Decoherence, then, is not a sudden 'jumping' effect. Rather, the interference terms disappear due to the progressive influence of billions of particles (and associated entanglements) as a particle passes through our measuring apparatus. So there is a progressive filtering (of the interference terms) and amplification (of the eventual measurement." - Andrew Thomas, 2nd March 2009
I have the original paper of "Sudden Death of Entanglement", as well as its "Supporting Online Material". Of the later, in the 3rd section "Entanglement vs. decoherence", they said "The word 'decoherence' is commonly used as shorthand for loss of, or lack of, correlation in many contexts - quantum and classical. Entanglement is a purely quantum form of correlation, and is applicable by definition only to multi-part quantities. It is important to keep in mind that loss of entanglement doesn't require complete loss of coherence. A single electron exhibits a form of coherence, for example, when its spin processes in a regular predictable way. Weak environmental influences will slowly disturb the regularity of the precession and thus reduce the coherence, i.e., lead to decoherence, whether the electron is entangled with another or not. It is easy to see that ESD is a form of decoherence..."

In their paper the entanglement is measured with the value "concurrence", which is defined as max[0, Q(t)], where Q(t) is defined on the eigenvalues of an auxilliary matrix. Entanglement can reach 0 before coherence is gone. I think what implied is ESD does not mean progressive decoherence is invalid. - Shengchao Li, 2nd March 2009
Thank you very much for your comment. So it looks like ESD is a form of decoherence. So it's not really "Entanglement Sudden Death", it's really "Entanglement Progressive Death". Very interesting. - Andrew Thomas, 2nd March 2009
According to the paper, ESD means early-stage disentanglement, and Entanglement Sudden Death is just a recent, more dramatic name. It does not mean a sudden disentanglement before forms of decoherence. It merely means a progressive decoherence leads to a death of entanglement before infinite time, instead of a diminishing, always live entanglement.

This might shed more light on the transition from quantum to classical.

I am amateur too. Thank you for your website. - Shengchao Li, 2nd March 2009
Thanks for shedding light on that. Brilliant! - Andrew Thomas, 2nd March 2009
I just picked up the latest issue of Scientific American in the American News stands, and lo and behold it is about Quantum entanglement, or as one sage calls it: Quantanglement. Here is the link to the magazine article on the internet:

Frankly I feel Andrew explains the subject much better on this page. - Greg Sivco, 12th March 2009
First of all kudos for the website.. it is brilliant.

I still don't see what exactly of entanglement in QM violates the non-locality. I agree I am being vague, but in my defense it is because this concept hasn't been fully understood by me :D

I am looking more for say EPR predicts either QM violates locality or is incomplete and needs a hidden variable theory. Violation of Bell's inequalities prove hidden variable theory is not true but what about locality, how does entanglement work around that ??

Thanks again for the wonderful site..

Arun - Arun, Switzerland, 12th March 2009
"I am looking more for say EPR predicts either QM violates locality or is incomplete and needs a hidden variable theory"

Almost right. I believe what EPR says is that QM is incomplete and needs a hidden variables theory, otherwise the Universe is non-local and niether Einstein, Podolsky, or Rosen accepted that.

But they were wrong, according to results by Clauser, Aspect, etc.

Bohr's response was to come up The Copenhagen Interpretation: don't worry about it, doesn't matter.

Also wrong. Given the knowledge of their day however, all are to be be forgiven IMO.

"Violation of Bell's inequalities prove hidden variable theory is not true but what about locality, how does entanglement work around that ??"

Entanglement works around it by saying locality is wrong. It doesn't ask "Why?" QM is very much about the "How?", like Socrates, rather than the "Why?" like Plato and Aristotle. Plato and Aristotle asked the more important question, but they needed Socrates to ask his first.

This page is probably the crux of this whole website. The first 2 pages lead to this, and starting on the next page re Quantum Decoherence, and moving forward, the implications of all this get really exciting.

The first wall in QM that people hit (and which turns so many away) is Heisenberg's Uncertainty Principle. If you can grasp that, then Quantum Tunneling is weird and the next significant wall. Get past that and you will hit all manner of weirdness, but Entanglement is the weirdest of them all. - Greg Sivco, 12th March 2009
Hi Andrew, I have a question as I am trying to understand better and not to fall too deep into mystical:).
What exactly is the "observation", the action that determines the property of the particle? I'm in the middle of "The elegany Universe" and from there I understood that through observation we actually intervene in the system, for instance we shine light on the electron. The frequncy of the light beam will change either the position or the velocity of the electron. Is this correct? What I did not get was: is this physical "intervention" that collapses the vawefunction of the observed particle?
Thank you!
- Monica Garliceanu, Winnipeg, MB, Canada, 19th March 2009
Well, it seems that I got my answer on the very next page. I'm reading now. - Monica Garliceanu, Winnipeg, MB, Canada, 19th March 2009
OK, Monica. - Andrew Thomas, 19th March 2009
I'm still unsure of what is meant by "observation" or its associate, "measurement."
The reason I raise this point is that it seems to me that however we analyse or describe the 'entanglement' of two particles, our knowledge of the state of the 'unobserved' particle is dependent upon the fact that we have 'observed' the other.

Two related questions arise in my mind.

(1) Before either particle has been 'observed', are the states of both intdeterminate (as suggested by the Copenhagen Interpretation)?

(2) Does 'observation' additionally imply 'by a conscious entity'?

- Martin Woodhouse, 21st May 2009
My apologies: you have covered the matter of 'observation' in your section [6] on Quantum Reality.

I still think you have left something out of your overall survey -- which, by the way, I find to be both well-structured in concept and, more to the point, understandable in content; I congratulate you.

Consider the following three facts:

(1) Action at a distance: the 'transmission' of 'something' (whatever it may be) 'instantaneously' (in some sense) through (some medium):

(2) That there has not, during the entire history of scientific endeavour, been the slightest inkling of an idea of the way in which conscious experience is produced. There's a pretty strong suggestion that it arises -- or is at least affected -- as a result of neural activity, but not the faintest suggestion of how this might happen:

(3) The fact, known ever since Descartes or earlier, but which has been shoved as a result of our enthusiam for physics into an intellectual siding somewhere, that the only 'thing' we can ever observe is the content of our own, singular, consciousness. Everything else, including the whole of physics, exists in the form of inference from what we have thus observed. Or, rather: from an unverifiable -- though not necessarily invalid -- correspondence between what you observe, what I observe, and what Charlie or Charlene over there observe and which we report, more or less reliably, to one another.


Do these three facts suggest anything to you?

They do, to me. It is that there exists a parallel world connected (everywhere, though in a so far undefined fashion) with the material world of physics, and that this world is (a) primary and (b) immaterial.

Since it's immaterial, there's no reason why instantaneous transmission cannot take place in or across it.

Since it's immaterial, it's an excellent location for 'qualia' -- the observations made by way of conscious experience -- and it's hardly surprising that we can't identify any causal link between what we experience on the one hand and particles popping around (in a quantum-indeterminate fashion) inside a neural network, on the other.

And, since it's in a very real sense the primary world, any conclusions we may reach concerning the existence of matter and its properties are, in the end, inferences drawn from qualia (which we may think of, perhaps, as being the 'particles' of the world of conscious experience) and deductions -- which may be quite valid -- drawn from agreed collections of those inferences.

I believe that the structure I suggest above should inform the next area of study into our conclusions of The Way Things Actually Are.

My own site, may perhaps show where I'm coming from. - Martin Woodhouse, 21st May 2009
Hi Martin, as I have actually now deleted my Quantum Reality page, I thought I should repeat what I said about "observation" on that page:

Firstly, we have to define what we mean by "observation". Do we limit this to mean "conscious human observation"? Surely not. For example, a radioactive uranium nucleus buried in rock on a distant planet will decay to emit an alpha particle. It does not matter if a human observer looks at the rock or not. As Carver Mead agrees in this excellent American Spectator article: "That is probably the biggest misconception that has come out of the Copenhagen view. The idea that the (human) observation of some event makes it somehow more 'real' became entrenched in the philosophy of quantum mechanics. Even the slightest reflection will show how silly it is. An observer is an assembly of atoms. What is different about the observer's atoms from those of any other object? What if the data are taken by computer? Do the events not happen until the scientist gets home from vacation and looks at the printout? It is ludicrous!".

"I like to think that the moon is there even when I am not looking at it." - Albert Einstein.

Clearly, "measurements" must somehow be taking place all the time and do not require conscious observers. Instead, let us describe a "measurement" or "observation" as the process which produces a single property value from a state which was previously in quantum superposition, i.e., we now define a measurement to be the process of quantum decoherence which reduces the superposition state. In this case, any connection with the environment could produce a measurement. However, for all interference terms to disappear, i.e., for decoherence to be complete with the object no longer in a superposition state, the particle must make some macroscopic effect. This is described in the book Quantum Enigma: "Whenever any property of a microscopic object affects a macroscopic object, that property is 'observed' and becomes a physical reality". For example, if we use a macroscopic photon detector to detect the photon in the double slit experiment then that will destroy the interference pattern. So as long as there is a macroscopic effect from a quantum entity, that object can be considered to be "observed" or "measured" - no need for a conscious human observer. - Andrew Thomas, 21st May 2009
Andrew, thanks for this site but I have a question. I almost understand this stuff but not quite.

Say I destroy one of an entangled pair. Is the other one also destroyed? - Sam, 11th June 2009
Sam, no, basically they are just two particles in space. It just so happens that some of their characteristics (e.g., particle spin) must have related values. - Andrew Thomas, 11th June 2009
Thanks, Andrew! That was fast! OK, I understand much better now. So what you're saying is we know something about the other particle no matter how far away it is, but the (now) orphan particle lives on, possibly to be entangled with something else? Although how can that be if particles are only entangled at creation?

Your answer really helps, but just like everything else an answered question leads to another, like those (to confirm I understand) and my next one.

So the orphan particle, can it ever entangle again with another particle? I'm almost there, but based on your answer (I was confused because I thought entangled particles shared the same wavefunction so I was thinking they were the same super-particle), I'm thinking no the other particle will always be an orphan.

That would mean that "the universe is entangled with itself" is not completely true, because we have orphans. Is that true?

Before you answer I know particles fates are to change or give off bosons like photons, weak particles, etc. like an electron changing direction when it gives off a photon. So I know a particle has other fates other than "re-entanglement" if as I'm asking that's possible at all. - Sam, 11th June 2009
Hi Sam, basically until we measure a particle and force the "collapse of the wavefunction" then particles' wavefunctions can become entangled when they interact and we must then treat them as a single entangled system.

As far as the entanglement of the universe is concerned, I would say that the universe has been entangled as a single system right from the Big Bang. As Michio Kaku says: "When the universe was born, it was smaller than an electron, which is a quantum object that can exist simultaneously in many states. So the universe must also be a quantum object and exist in many states."
- Andrew Thomas, 11th June 2009
I am not a trained physicist and yet I believe I may have understood nearly all of the content of this article, entirely because of its very accessible style and lack of unnecessary jargonese. I have read several other explanations of the EPR paradox and Bells Inequality Theory, and I feel that your article has been the most effective in allowing me an understanding of these ideas (and with far less uncertainty than I usually experience as a novice). I am most grateful for your excellent portrayal of this subject. 25/09/09 - sahill, 25th September 2009
Univerity of California, Santa Barbara scientists report Quantum Entanglement in the macroscopic world. Click on the following link to see it:
- Greg Sivco, 26th September 2009
Fantastic site - many thanks (I am about to sit a QM exam!).

My question is, does entanglement give us a way to escape the Uncertainty principle? Suppose two of us meet at the same point (where the entangled particles are created) and synchronise our clocks. Then we separate and travel alongside each particle. At a predetermined clock time one of us measures the position of his particle and the other measures the momentum of her particle. Wouldn't this give us a simultaneous measurement of position and momentum of each particle, in violation of the uncertainty principle?
- Leslie Moss, 12th October 2009
Thanks Leslie. No, there's no way to beat the uncertainty principle. I considered this in the section on Bell's Inequality in the main text. This is what it says: "it shows that we failed to beat the Uncertainty Principle - we cannot get a true measurement of two property values: when we measure one property, we "poison" the other reading."

In other words, there has to be an instantaneous connection (Einstein's "spooky action at a distance") which has the effect of spoiling the other measurement. - Andrew Thomas, 12th October 2009
Joy Christian has presented what he considers a disproof of Bell's Theorem. His paper is at Do you have any comments on whether or not Dr. Christian's ideas change what Bell developed and changes your analysis above? Thank you very much. - Newt Leroy, 31st October 2009
Hi Newt, thanks very much for the link. I also found a more-readable New Scientist story on this:

I see he takes the time to reply to all criticism:

Several physicists have tried to find loopholes in the Bells Inequality experiment. I've only looked at this work briefly but I get the strong impression that Christian has done a good job here. I haven't found any convincing refutations of his work yet. I'll have to take my time and look into it in more detail.

If Christian turns out to be correct then it means a lot of work for me to rewrite this page! It would essentially put the ideas of Einstein back into the frame again (not the first time that has happened). It would show that it might still be possible for particles to have hidden variables (fixed property values), with no need for "spooky action at a distance" (as Einstein called it).

Christian's work has the feel of the real deal. Thanks a lot, Newt. - Andrew Thomas, 31st October 2009
Then what of the experimental work done by Clauser, Aspect, Zeilinger, etc.? - Steven Colyer, 2nd November 2009
Hi Steven, I've had another closer look at Christian's work and it does appear to be an extraordinary complete refutation of Bell's theorem. Which is amazing. It's not often that happens - a lot of books are going to have to be rewritten (which is an advantage of writing a website!).

The basis of Christian's argument is that Bell made a completely unjustified assumption by saying that the "spin" of a particle is simply either "up" or "down". Christian makes the point that the spin is more likely to be around a single point on a sphere, in which case Bell's model of spin was too simplistic. As Christian says: "The correlations between the EPR elements of reality are correlations between the respective points of two 2-spheres. They have nothing whatsoever to do with the correlations between the points of two 0-spheres as Bell unjustifiably assumed."

There's a particularly damning few sentences on page 6 of Christian's paper: "Comparing the left and right hand sides of the above expression is like comparing correlations between cars in one narrow lane of a highway with correlations between cars on the surface of the planet. The absurdity of the comparison is breathtaking. Regardless of locality, realism, quantum mechanics, or classical mechanics, the two sides of the above expression cannot possibly be the same, for they describe correlations between the points of two entirely different topological spaces. Even the dimensions of these two spaces do not match!"

However, as careless as Bell might have been, quantum computers (based on entanglement and non-locality) have been built and they work. So I suspect the argument has moved-on since Bell's theorem. - Andrew Thomas, 3rd November 2009
Interesting. So are you saying the theory is wrong but its predictions are correct? That blows my mind, if so. On the other hand, we have no idea what "electric charge" is let along "spin." 0-dimensional point particles are difficult to explain in terms of "an intrinsic internal property" which is how "spin" is most often "defined."

Man, I wish Wolfgang Pauli were still alive to comment on this. No, he'd probably just say "It's not even wrong!" :-)

Well, what then does Seth Lloyd think of this? He's at the forefront of quantum computing at M.I.T., yes? - Steven Colyer, 3rd November 2009
Well, yes, there's people like Seth Lloyd who are using quantum computers who probably don't really care anymore about Bell's theorem. I sent an email to Joy Christian to clarify if all he has really done is show that Bell was careless in his original paper.

It looks like Bell made an error, and the Bell's inequality experiment was not 100% valid as a result, but the error was not serious enough to prevent the experiment providing the correct conclusion about entanglement and non-locality. - Andrew Thomas, 3rd November 2009
Joy Christian just got back to me with a nice email (he seems like a very nice bloke). Firstly, he doesn't think we even have quantum computers. He said: "I am not sure what you mean by we *have* quantum computers. For none of the experts in quantum computers I know are claiming that they already have them." Now, that doesn't sound quite right to me. I've heard of many quantum computers being made with several qubits, and my understanding is that we couldn't have quantum computers without nonlocality. So that's a bit of a strange thing for Christian to say.

He then continues in more general terms: "My concerns are far deeper than quantum computers, or indeed any other application of quantum mechanics. My papers do not claim to invalidate “quantum” correlations that we do see in the laboratory, but rather provide an entirely local and realistic explanation for them." Yes, fair enough. I believe he can reveal the errors in Bell's theorem using his method (and I hope the physics community gives him the credit for that). But I don't think he can explain quantum computing using his method. So I stand by my previous comment that it looks like Bell made an error, and the Bell's inequality experiment was not 100% valid as a result, but the error was not serious enough to prevent the experiment providing the correct conclusion about entanglement and non-locality. - Andrew Thomas, 3rd November 2009
We have quantum computers. What we don't have are very stable ones. For the longest time we couldn't make them with more than 7 q.c. bits, called "qubits", which are fundamental particles. Lately I think they've gone as high as 15, so they're not very powerful. Heck, a hundred and then some years ago they tried to build Babbage's mechanical computer and failed miserably. I think Queen Victoria spent quite a bit on that unsuccessful effort.

The instability as far as I can tell comes from the small size of these qubits thus keeping them protected from the environment in which case decoherence would destroy them. They've kept a positron isolated for as long as three weeks I recall. Not sure that's the current world record, probably not. The coolest thing though is they could make the positron jump and do tricks. They even named it!

QC is very important to governments, because they excel at factoring large numbers, which would make it tough to have an unbreakable cryptographic code ... although since it's the government I suspect they wish to use them to break the codes of others.

Thanks Andrew and a big thanks to Joy Christian for getting back to you. I also believe indeterminacy and randomness on the subatomic scale has deterministic sources at a much smaller scale, but I would never have thought to investigate the previously-unassailable John Stewart Bell! What a cool and creative bunch they have at The Perimeter Institute in Canada. Amazing stuff, well done.

Bloke. ;-) - Steve Colyer, 3rd November 2009
Indeed. I sent an email back to him congratulating him. - Andrew Thomas, 3rd November 2009
Andrew, if you change this page you may have to change the "Quantum Reality" page as well. Do you have plans to do that? If so I'd request you save the original versions.

Thanks to your website (as well as the book by Hay and Walters* ) I feel I understand the “How” of Quantum Physics, if not the “Why?” of it, particularly the “Why?” of Quantum Entanglement. Bohr once famously said: “If you think you understand quantum mechanics then you don't understand quantum mechanics.” My fear is that if Christian is correct then I'll understand QM and Bohr will thus rise from his grave and beat me senseless with an object which is both wave and particle simultaneously. J

Obviously I do not understand the maths sufficiently to comment on the truth or falsehood of Christian's paper or his rebuttal, but you seem to know, yet that is not the issue. The issue is that of course we should expect Christian, good bloke that he is, to defend his own work, but what does the greater Mathematical Physics community think of it?

How wonderful if true though. John von Neumann made a mistake re Entanglement in his famous 1932 textbook, which was recognized right away by a young female grad student (who informed Pauli and Heisenberg … neither of whom backed her up professionally as at that time a woman's point of view was considered as dirt, Marie Curie being a notable exception). It would not be until 1964 when John Stewart Bell recognized the same mistake.

Now we have Joy Christian saying Bell made a mistake. Is von Neumann then validated? He was rarely wrong. - Greg Sivco, 4th November 2009
Hi Greg, I'm not planning on changing the text of any of the pages. I think this discussion in the comments is enough.

At the end of the day, as clever as Joy Christian's work is, I think the argument has now moved on from Bell's theorem and most physicists accept quantum non-locality as fact. Like I said, I don't think the likes of Seth Lloyd busy making working quantum computers are that bothered about Bell's theorem anymore. - Andrew Thomas, 4th November 2009