The number-one question that people ask me when I talk about nonlocality is: how are entangled particles created? I didn’t say much about this in the first edition of my book because the details don’t matter for my overall argument, but since everyone wants to know, I figure I should elaborate. (I’ve also added an appendix to the paperback edition.) I’ve created an animation (below) to convey the essential features of the process.

Courtesy of Enrique Galvez, Colgate University
Courtesy of Enrique Galvez, Colgate University

Quantum optics experiments typically create entangled photons using a crystal of barium borate. This material takes on two different crystalline forms; the one of greater interest is the beta phase. The photo at right shows a sample in a laboratory mount. It looks like a little prism. But unlike the glass in ordinary prisms, the crystalline material is nonlinear: it is not an inert substrate, but its refractive index can be modified by the light that passes through it, enabling all sorts of novel optical effects.

In particular, the crystal allows two light beams to interact, which they wouldn’t otherwise do. The interaction can amplify one of the beams at the expense of the other, as well as create a third beam. In fact, the beam that gets amplified need not be a “beam”: it might simply be random quantum noise in the electromagnetic field. If you set up the crystal properly, the amplification is so powerful that it turns the noise into a proper light beam. A single incoming beam (typically blue or ultraviolet) can thus conjure up two beams (typically red). This process occurs particle by particle: each blue photon splits into two red ones.

Spontaneous parametric downconversion crystal
Courtesy of Centre for Quantum Technologies, National University of Singapore

The splitting, known as spontaneous downconversion, is a low-probability event. Only about one in a billion photons in the incident beam interacts with quantum noise and divides; the rest continue straight through the crystal unaffected. For this reason, you’d never see the beams with the unaided eye. The above image from the Centre for Quantum Technologies in Singapore is a long exposure. The photographer dragged a piece of tissue along the beams to reveal their paths.


By virtue of their common origin inside the crystal, the outgoing red photons can be entangled in any of their properties: energy, momentum, polarization. For simplicity, experimentalists usually concentrate on polarization. The crystal has an optic axis. If the laser light is polarized in the plane defined by that axis, outgoing photons will be polarized perpendicular to the axis. Vertical polarization in, horizontal out; horizontal in, vertical out. Depending on how you arrange the beam and crystal, the outgoing photons can have the same polarization (known as Type I downconversion) or exactly the opposite polarization (Type II). It doesn’t really matter; either way, the photons are perfectly correlated. This correlation reflects the symmetry of the crystal about its optic axis.

Voilà, two photons. But when you want two entangled photons, you need an extra ingredient: the polarization has to be indeterminate. This is really the essence of entanglement, the reason it’s so mysterious. The photons have the same polarization, but that polarization is not horizontal, not vertical, not circular. It’s just plain nothing, a blank that has yet to be filled in, according to the standard interpretation of quantum mechanics.

After all, if the photons did have a specific polarization, there’d be no mystery. You’d create two identical photons and later measure them to be identical, which is no weirder than pairing two socks as soon as they come out of the laundry and later observing that they’re the same color. Entangled photons, in contrast, are like a pair of socks that don’t have any particular color. Each assumes a color only when measured, and both assume the same color. If that boggles your brain, it should. This is what it means to be nonlocal: you can make a statement about the system as a whole—namely, “the parts are the same”—but not about any individual part.

To produce this indeterminacy with the barium borate crystal, you sandwich two thin layers of the material, one oriented vertically, the other horizontally. Then you send in light that is polarized in neither a horizontal nor a vertical direction, but on a diagonal. As long as the layer is thinner than the beam, there’s a quantum uncertainty about which layer the beam will interact with and, therefore, what polarization the outgoing photons will have. Their ambiguity is resolved only when they strike the polarizers and are measured.

Just upstream of the crystal, you can place an optical element known as a waveplate, which can be oriented to ensure the laser photons striking the crystal are diagonally polarized or not. This waveplate therefore decides whether the photons emerging from the crystal are entangled.

What’s nice about the crystal is that it gives you a very controlled way to create entangled photons. I want to emphasize, though, that there’s nothing really special about this crystal. The fact it’s a crystal makes it sound mysterious, but entanglement can be produced in any number of ways. I did a version of the experiment in my basement using a sample of radioactive sodium-22, which gives off entangled gamma rays. Edward Fry of Texas A&M and Richard Holt of the University of Western Ontario used mercury atoms in their pioneering entanglement experiments back in the ’70s. Mercury can emit two photons in rapid succession, and those photons will be entangled. Even the mercury in ordinary fluorescent lights emits entangled photons, Fry says.

The hard part about entanglement isn’t creating it, but creating it in a way that lends itself to measurement. Because the physical implementation isn’t important, it’s perfectly valid to think about it at a higher level of abstraction, such as the coin-flipping metaphor I use in my book. The metaphor is grounded in concrete physics.

entanglement physics quantum entanglement quantum mechanics quantum physics

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  1. No matter how many explanations of aspects of entanglement I read, I still don’t get it.
    My problem is; I can’t see what the problem is.

    If two photons are created which have the same, but unknown, polarisation, and one of them is measured revealing it’s polarisation. Then clearly the other photon’s polarisation is known because it is the same as the first photon.
    What is it that everyone else seems to know that I’m missing completely?

    1. It is indeed tricky. The issue is that, according to our general understanding of quantum mechanics, the polarization is not merely unknown but undefined. A photon gains a polarization only when measured. (If that weren’t the case — if the photon had a polarization that was unknown to us — we would observe different particle statistics.) The polarization it acquires is coordinated with that of its partner, and there is no mechanism to bring about this coordination.

      1. Thanks very much for your reply George.

        What are the statistical differences you mentioned? That is clearly the key to understanding this.

        By using the word “undefined” are you saying photons do not intrinsically have a property called polarisation, and that what we call polarisation is something that becomes apparent to us only as a result of interactions? After the event so to speak.

        1. The statistics are those in the Bell inequality. I discuss one example on pages 101–104 and two others on pages 47–51 of my earlier book on string theory. David Mermin has a series of very helpful articles that give other examples:

          He also has some discussion in his book “Boojums”.

          Regarding polarization, the way it’s usually put is that the photon does not have a determinate polarization; it is in a superposition of polarization states.

  2. How are entangled particles “stored”? That is, how do we physically separate them and determine that they are “entangled”? Is it possible to store them in such a way as to carry them around in a briefcase and then run new tests on them years later? What would that look like?

    1. In the experiments I discuss in the book, the particles aren’t stored. To the contrary, they are prepared and measured as quickly as possible, so as to exclude a classical explanation for the correlations. Likewise, in practical applications such as encrypted communications, speed is of the essence. To separate the particles, we let them fly apart through open space or through an optical fiber. But there is a new class of experiments that do seek to store particles for later readout; see my article at There is also an effort to design quantum computer memory; see

  3. Here is the core problem with “Non-Locality”; the Assumption that both Einstein and Bohr made in their arguments was that because a photon travels at the speed of light it can not change its properties. The Bell Test was essentially designed to disprove that a photon once created “Knows” that it will be entangled however far away and will be created as if it was entangled before the event. That we know for a fact to be false.

    However what if a photon via a small change in its angular momentum can change its properties. The hypothesis would work like this, let us give Bosons a version of the Pauli exclusion principle that exists for Fermions. As two photons approach (or are split apart) their forward motion for a brief time is transferred into angular momentum, in much the same way as a photon changes its direction in the presence of the field of gravity.

    If that is the case… then the Bell Test wouldn’t be able to test for that type of situation. So how would we be able to test for a Boson Exclusion Principle? We know that a spontaneous downconversion using a Barium Borate Crystal, in the right conditions will always create two entangled photons. For the rest of the existence of both of those photons, they should always be entangled. If at any time those two photons become “Un-Entangled” by either entangling with other photons or passing them through a very strong magnetic field, then…

    Photons can change their properties once created and Schrödinger’s Cat is not only DOA, but can be Zombified an indefinite amount of times.

      1. In principle, scattering an electron off a proton could produce an entangled state. This has been done with proton-proton scattering (, but I don’t know of an electron-proton version. The proton and electron in a hydrogen atom are entangled (, but this is not a large effect; one can consider the state of the electron on its own to a high degree of approximation.

  4. Regarding your first question, as the comments you’ve gotten so far, people disagree on what precisely the problem is, let alone what the solution might be. Clearly, though, the correlations can’t be explained by a physical influence that propagates through spacetime, since the propagation would need to be infinitely fast, which violates not only relativity theory but the very definition of “propagation”. On this, I agree with Shuler’s remarks. But we are still left with the question of how we do, in fact, explain the correlations and, more broadly, why we observe determinate outcomes.

    Regarding your second question, I just don’t see how purely information-theoretic interpretations such as QBism can account for the correlations. Information is never disembodied; it is carried by some physical system, and we want to know what that system is.

    Lubos and I, as you have seen, disagree. We disagree even on the source of our disagreement. From my perspective, I think he is using a more restrictive definition of locality — namely, relativistic causality — and is neglecting the full structure of the EPR/Bell argument. From his perspective, he thinks I am simply wrong, even willfully stupid. Maybe so. But then a huge fraction of the physics community, including people Lubos himself respects, is also wrong and stupid. I take this disagreement as an indication that the issues are very subtle and that one should not be so dismissive of positions that one disagrees with or of their proponents.

  5. The article says “the polarization has to be indeterminate….After all, if the photons did have a specific polarization, there’d be no mystery”

    I don’t understand why there’d be no mystery. For ‘normal’ unentangled photons you can do an experiment with 3 polarization filters. If you let the photons stream through two filters, one horizontal, the other vertical, then no photon passes through. If you place a third filter diagonally between the first two filters, then suddenly 50% of photons pass through.

    If you have entangled photons, the experiment should become even more weird: you could repeat the experiment with 3 polarization filters: block all photons of one of the entangled beams with a horizontal and vertical filter and do the spooky distance trick by inserting the diagonal filter in the other entangled beam. Would that work? If no, then what happened to the entanglement? If yes, could one send on/off signals faster than light by inserting/removing the third filter in the other entangled beam? Why not?

    1. Answering my own question. The entanglement is destroyed at the moment one of the entangled photons interacts with the first filter. The second filter can be used to show there is a strong correlation between the interaction of the first filter and the second filter. Any third filter will behave the same as with unentangled photons, because the entanglement was already destroyed by the first filter.

      1. By definition, entanglement is a type of correlation among two or more particles (or other systems). You know they are entangled if you measure them and the results are correlated. Now, there are many subtleties. In measuring these systems, you are apt to destroy the very entanglement you seek. Also, it’s not a given that the correlations will be strong enough to differentiate them from classical correlations. So, in practice, you know that particles are entangled because you prepared them in a proven way. Often you can look for so-called entanglement witnesses, which are large-scale consequences of entanglement.

  6. I understand the idea (Heisenberg) of the observer changing the experiment. which leads me to the question – how do you know that a photon (or anything else, for that matter) is entangled? most of the book depends on entanglement, but, disallowing circular logic, or after the fact experiment or statistics, how do you know that anything was entangled. thanks.

    1. Bell’s Inequalities (1962) allow to distinguish entangled particles. Indeed, Bell realized that Quantum entangled systems would give different statistical result, than envisioned by Einstein Podolsky and Rosen (1935) with their Hidden Variables solution, proposed to preserve Special Relativity premise that every information propagates with v >c.

      1. Just to clarify, Bell’s paper was published in 1964, and I think you meant “v≤c”. But yes, I discuss this at length in chapters 1, 3, and 4 of my book.

        1. Right, year 64 and v < c, sorry. I did'nt read the mentioned chapters! only wanted to help your follower who seemed very concerned about this problem for lack of knowledge of historical development.

  7. Hi, thank you for your nice site and sharing your knowledge.
    I think I will try to replicate your basement experiment with my son.
    I have a question: could you direct me to a paper or a method where I can learn about quantum transmission, please ?
    And do you think It’s possible to do some crude quantum transmission (like POW tap code) with the kind of setup like in your basement experiment ?
    Thank you.

      1. Hi,
        Thank you for your reply.

        It’s not about cryptography, “just” to send a simple message via two entangled particles.
        Our goal would be to send a message via Q-E particles using an on/off syntax like (POW TAP code for exemple).
        Does it sound feasible ? And if so on what distance approximately (with your simple setup) ?

        If you know some papers/abstracts to guide us it would be very nice and appreciated.

        ps: I don’t know if you have heard of it but your project of a cheap & accessible Q-E reminded me of a atomic microscope in the same vein:
        It should interest you.

        Anyway thank you for bridging the gap between the lab’ and the citizen !
        Best wishes,

        1. Quantum entanglement can’t be used to send a message. For that, you still need classical communication. Entanglement provides other functions such as securing the connection or transmitting quantum states. I have it on my to-do list to build an STM. The Prutchis’ wonderful book outlines how to build a transmission electron microscope.

          1. From where come the problem ?
            “storage” of the particles ? i.e: life time not long enough to sustain a transmission ?
            If it is so, may be it could be feasible by using a quick-burst type transmission like for the morse code ?

          2. The limitation is fundamental to what entanglement means. Almost by definition, an entangled link involves no force or other interaction and cannot convey a signal. It must be used in conjunction with classical signaling.

  8. I’m very new to the Quantum Entanglement theory and was wondering: why does having indeterminate polarization cause entanglement? Why doesn’t one photon show one result and the other another once it reaches the detector? And the only answer I can come up with is that they both come from the same source undergoing the same conditions. So is it really because they’re entangled or because the conditions make it so that they will always have the same result? Or perhaps I’m completely misunderstanding the theory?

    1. It’s not that indeterminate polarization “causes” entanglement, but that it makes entanglement peculiar and non-classical. When polarization is determinate, nothing peculiar is going on: each particle is assigned the same polarization at the source and observed later to have the same polarization. But when polarization is indeterminate, there is no mechanism for the particles to maintain their correlation. This is where the coin metaphor is helpful, I think. A coin flip does not have a determinate outcome (at least none that we could ever discern). So, two coin flips should be independent and uncorrelated events.