Quantum entanglement is a phenomenon that, like the two slit and interferometer experiments we looked at previously, makes a mockery of our day-to-day experience of time and space. It brings to mind the vast and unyielding interconnectedness that is Indra’s web.

Let’s say we generate two particles at the same source at the same time from the same material and send them in separate directions. These particles are entangled. What does that mean? It means what I do to one has an immediate effect on the other. They are one system throughout time and space.

Suppose I measure some property of one of the particles of a pair of entangled particles. We can measure the polarization of a photon. Polarization is the orientation of the electromagnetic field of a photon (or en masse of a beam of light). Polarizing filters in glasses block horizontally oriented (polarized) photons that might be reflected off the road or a lake surface, for example, to diminish glare. Both photons in an entangled pair will have the same polarization when measured. Measure the orientation of the polarization of one photon of an entangled pair (say you find it is either horizontal or vertical), when you measure the other photon in the pair it will be in the same orientation.

Or we can measure the spin of an electron or similar subatomic particles. Spin is not really quite spin like say a top or dreidel, as point particles don’t have dimensions like width to be spinning. But certain particles like electrons do have a kind of axis with a direction that can be determined by their interactions with magnetic fields. This spin has momentum of spin, and this angular momentum is conserved, as momentum is energy and energy is conserved; this is an important symmetry. So if one electron of an entangled pair is spin up, the other will be spin down when measured.

Now the most important phrase is “when measured.” This is critical because one of the aspects of entanglement that makes it so mind blowing is that it simply cannot be said what the polarization of either photon or the spin of either electron in the entangled pairs is until a measurement is made. Just like we saw before: there is no what it “really” is. There is no which of the two slits the particle “really” takes or which of the paths in the arms of the interferometer the particle is “really” in. There is superposition. Similarly, there is no spin or polarization until it is measured in one of the particles of the entangled pair. It neither is or isn’t! Such a dualistic, concrete material notion of what is or isn’t doesn’t work!

That should come as a surprise. After all, if I have a pair of shoes, with one shoe here in the room with me and the other shoe in in another room, and the shoe here is a left shoe, the other is going to be a right shoe (much like spin). If one shoe is black, the other will be black, if one is white, you can bet the other is white (like polarization). No great mystery. These are the properties of the shoes! So why can’t it be the same for entangled particles? The properties are inherent, even if sometimes hidden. Surely the property is there, the is or isn’t of it exists, we just don’t know what it is.

But no, there are no hidden properties. There really is no sense in which the particle has that property until it interacts in some way that demands that property, until that is, it is measured. A physicist named Bell suggested a mathematical way to test this and the experiments were later done showing to the satisfaction of almost all physicists that there are no hidden variables in these entangled quantum particles (though, as in so many aspects at the edge of physics there are some who dispute whether the final word is in). The logic for this “Bell’s inequality” is a bit complex so rather than get distracted now I will save it for another post for those interested (a book I recommend if you are interested in that by a world class quantum experimentalist that is written for lay readers and goes into this is “Dance of the Photons” by Anton Zeilinger. Zeilinger is the one who did the experiments showing Bucky balls of 60 carbon atoms have a wave function that will show quantum interference).

One reason I don’t want to get into Bell’s logic now is that there’s more to entanglement and I don’t want to get distracted but the math.

There is nonlocality, spooky action at a distance, as Einstein put it. It doesn’t matter how far away the two entangled particles are when one is measured. Scientists are convinced you could be a million light years away from the scientist measuring the other particle, trillions and trillions of miles and the million years it would take a photon to get from one scientist to the other would collapse into no space and no time separation the instant you measured one of the particles. Information, according to the theory of relativity (say about the spin of a particle), is not supposed to travel faster than the speed of light, but the measurement of one particle of a pair of entangled particles determines the properties of both particles immediately, whether the particles are a tiny fraction of a millimeter apart or they are so far apart that it would take light a million years for information as we understand it and normally experience it to traverse the distance separating them.

Clearly it isn’t a question of sending information across time and space!

And there is more. For that, lets get back to Anton Zeilinger.

Anton Zeilinger, the experimental physicist from Austria, whose book I mentioned above, is an interesting guy. He met with the Dalai Lama and other researchers and Buddhists in one of the Dalai Lama’s science and Buddhism meetings, and his talk is reported in “The New Physics and Cosmology: Dialogues with the Dalai Lama” Edited by Arthur Zajonc, 2004 Oxford University Press.

Zeilinger starts by noting: “in classical physics and everyday life a mountain is there even when I don’t look. In quantum physics, this position no longer works.” Later the Dalai Lama asks him if “nothing can be said about the nature of light independent of the measurement whatsoever?” Zeilinger responds “that’s right.” As we have come to several times thinking about quantum experiments, it is neither there nor not there. It neither is nor isn’t, until it is or isn’t in experience.

Zeilinger goes on to discuss the double slit experiment we have gone over before. When the Dalai Lama asks if particles interact like billiard balls demanding physical contact, Zeilinger makes it very clear that “in quantum physics we have given up such pictures” and “we should not have pictures anymore” as “all pictures fail”. We are misled when we extrapolate our day-to-day experience into this realm, one of the real lessons for Zen students and the rest of us in quantum mechanics. Even science asks that you give up your prejudices, your conditioned perceptual expectations!

He says that all of this “holds not only for small things” [e.g. photons and electrons and Bucky balls] “but also for large things. It’s not a question of size; it’s a question of economy because the larger the things become, the more expensive the experiments get.” It is true that ”physicists now believe that the world is quantum mechanical through and through.”

In discussing entanglement he brings up nonlocality, which is at the heart of what we have seen so far. After all, what I do in Vegas to a photon should stay in Vegas, stay local, unless there is a local to other local to other local transmission of information. A signal propagating through space and time, a photon flying through space from a star to our eyes at the speed of light, or a signal somewhat less quickly moving through a fiber optic cable. Continuous movement, no interruption, here to there, to there, and then to there, through space and time in a predictable and well behaved manner that can be timed and followed. But as we saw, that isn’t what happens in entanglement!

As Zeilinger says “under certain circumstances two particles remain one system even if they are separated by a very large distance. They are not really separated in a deep sense… We can keep going and talk about four or five or six particles. It never ends.”

The Dalai Lama then asks: “Are you implying that the entire universe is internally entangled?”

“Anton Zeilinger: That’s a nice idea, but I would not want to take a position on that because, as an experimentalist, I would not know how to prove it.”

OK, for now we can give him that. He’s trying to be honest and stick to what he knows. It’s his job, he feels responsible to the rules of his physics discipline and to his physics brethren and he won’t speculate. We all should do that to some degree, keep to what we know, though I clearly don’t always; that would not be nearly as much fun. In any case it was pretty cool for him to put himself out there as a physicist and be open. As you can tell, I enjoyed their discussion that also goes on to randomness and causality, but enough for now.

Anton Zeilinger has done very far out entanglement delayed choice experiments. Let’s look at one. If Alice and Bob (they always show up in these things; it is really standard nomenclature in information theory and cryptography to invoke Alice and Bob) each create a pair of entangled particles and send one from each pair to Victor so he now has a pair of particles, one from Alice and one from Bob, and then Victor entangles this pair, then Alice and Bob’s remaining particles will also be found to be entangled, even though they didn’t interact directly! This is called entanglement swapping. If Victor doesn’t entangle his pair of particles, then Alice and Bob’s particles will not be entangled. So you can find out what Victor did by seeing if Alice and Bob’s particles are entangled.

Very clever!

But what if Victor makes his choice AFTER Alice and Bob make the measurements that determine whether their particles are entangled, even if only a tiny time bit after?

You guessed it; what Victor decides and what he does with his particles, even AFTER Alice and Bob measured their particles, will determine what they will have found, whether or not their particles are entangled.

Zeilinger and his colleagues published an article in Nature Physics describing such an experiment (Xiao-sung Ma et al Experimental delayed-choice entanglement swapping, published online 4/12): “This can also be viewed as ‘quantum steering into the past’.”

They end their article saying: “Bohr [a famous founder of quantum mechanics] said that no elementary phenomenon is a phenomenon until it is a registered phenomenon. We would like to extend this by saying that some registered phenomenon do not have meaning unless they are put in relationship with other registered phenomena.”

Like Anton Zeilinger suggests, maybe we should have no pictures, and indulge no speculation beyond the data.

It is enough perhaps to realize that you can’t depend on such pictures, concepts derived from your day-today life at the scale at which you experience the universe with your senses.

But Indra’s web, vast and interconnected beyond imagination, really is a great non-picture picture!