An aura of glamorous mystery attaches to the concept of quantum entanglement, and also to the (somehow) related claim that quantum theory requires “many worlds.” Yet in the end those are, or should be, scientific ideas, with down-to-earth meanings and concrete implications. Here I’d like to explain the concepts of entanglement and many worlds as simply and clearly as I know how.

I.

Entanglement is often regarded as a uniquely quantum-mechanical phenomenon, but it is not. In fact, it is enlightening, though somewhat unconventional, to consider a simple non-quantum (or “classical”) version of entanglement first. This enables us to pry the subtlety of entanglement itself apart from the general oddity of quantum theory.

Quantized

A monthly column in which top researchers explore the process of discovery. This month’s columnist, Frank Wilczek, is a Nobel Prize-winning physicist at the Massachusetts Institute of Technology.

Entanglement arises in situations where we have partial knowledge of the state of two systems. For example, our systems can be two objects that we’ll call c-ons. The “c” is meant to suggest “classical,” but if you’d prefer to have something specific and pleasant in mind, you can think of our c-ons as cakes.

Our c-ons come in two shapes, square or circular, which we identify as their possible states. Then the four possible joint states, for two c-ons, are (square, square), (square, circle), (circle, square), (circle, circle). The following tables show two examples of what the probabilities could be for finding the system in each of those four states.

We say that the c-ons are “independent” if knowledge of the state of one of them does not give useful information about the state of the other. Our first table has this property. If the first c-on (or cake) is square, we’re still in the dark about the shape of the second. Similarly, the shape of the second does not reveal anything useful about the shape of the first.

On the other hand, we say our two c-ons are entangled when information about one improves our knowledge of the other. Our second table demonstrates extreme entanglement. In that case, whenever the first c-on is circular, we know the second is circular too. And when the first c-on is square, so is the second. Knowing the shape of one, we can infer the shape of the other with certainty.

The quantum version of entanglement is essentially the same phenomenon — that is, lack of independence. In quantum theory, states are described by mathematical objects called wave functions. The rules connecting wave functions to physical probabilities introduce very interesting complications, as we will discuss, but the central concept of entangled knowledge, which we have seen already for classical probabilities, carries over.

Cakes don’t count as quantum systems, of course, but entanglement between quantum systems arises naturally — for example, in the aftermath of particle collisions. In practice, unentangled (independent) states are rare exceptions, for whenever systems interact, the interaction creates correlations between them.

Consider, for example, molecules. They are composites of subsystems, namely electrons and nuclei. A molecule’s lowest energy state, in which it is most usually found, is a highly entangled state of its electrons and nuclei, for the positions of those constituent particles are by no means independent. As the nuclei move, the electrons move with them.

Returning to our example: If we write Φ_{■}, Φ_{●} for the wave functions describing system 1 in its square or circular states, and ψ_{■}, ψ_{●} for the wave functions describing system 2 in its square or circular states, then in our working example the overall states will be

Independent: Φ_{■} ψ_{■} + Φ_{■} ψ_{●} + Φ_{● }ψ_{■} + Φ_{●} ψ_{●}

Entangled: Φ_{■} ψ_{■} + Φ_{●} ψ_{●}

We can also write the independent version as

(Φ_{■} + Φ_{●})(ψ_{■} + ψ_{●})

Note how in this formulation the parentheses clearly separate systems 1 and 2 into independent units.

There are many ways to create entangled states. One way is to make a measurement of your (composite) system that gives you partial information. We can learn, for example, that the two systems have conspired to have the same shape, without learning exactly what shape they have. This concept will become important later.

The more distinctive consequences of quantum entanglement, such as the Einstein-Podolsky-Rosen (EPR) and Greenberger-Horne-Zeilinger (GHZ) effects, arise through its interplay with another aspect of quantum theory called “complementarity.” To pave the way for discussion of EPR and GHZ, let me now introduce complementarity.

Previously, we imagined that our c-ons could exhibit two shapes (square and circle). Now we imagine that it can also exhibit two colors — red and blue. If we were speaking of classical systems, like cakes, this added property would imply that our c-ons could be in any of four possible states: a red square, a red circle, a blue square or a blue circle.

Yet for a quantum cake — a quake, perhaps, or (with more dignity) a q-on — the situation is profoundly different. The fact that a q-on can exhibit, in different situations, different shapes or different colors does not necessarily mean that it possesses both a shape and a color simultaneously. In fact, that “common sense” inference, which Einstein insisted should be part of any acceptable notion of physical reality, is inconsistent with experimental facts, as we’ll see shortly.

We can measure the shape of our q-on, but in doing so we lose all information about its color. Or we can measure the color of our q-on, but in doing so we lose all information about its shape. What we cannot do, according to quantum theory, is measure both its shape and its color simultaneously. No one view of physical reality captures all its aspects; one must take into account many different, mutually exclusive views, each offering valid but partial insight. This is the heart of complementarity, as Niels Bohr formulated it.

As a consequence, quantum theory forces us to be circumspect in assigning physical reality to individual properties. To avoid contradictions, we must admit that:

- A property that is not measured need not exist.
- Measurement is an active process that alters the system being measured.

II.

Now I will describe two classic — though far from classical! — illustrations of quantum theory’s strangeness. Both have been checked in rigorous experiments. (In the actual experiments, people measure properties like the angular momentum of electrons rather than shapes or colors of cakes.)

Albert Einstein, Boris Podolsky and Nathan Rosen (EPR) described a startling effect that can arise when two quantum systems are entangled. The EPR effect marries a specific, experimentally realizable form of quantum entanglement with complementarity.

An EPR pair consists of two q-ons, each of which can be measured either for its shape or for its color (but not for both). We assume that we have access to many such pairs, all identical, and that we can choose which measurements to make of their components. If we measure the shape of one member of an EPR pair, we find it is equally likely to be square or circular. If we measure the color, we find it is equally likely to be red or blue.

The interesting effects, which EPR considered paradoxical, arise when we make measurements of both members of the pair. When we measure both members for color, or both members for shape, we find that the results always agree. Thus if we find that one is red, and later measure the color of the other, we will discover that it too is red, and so forth. On the other hand, if we measure the shape of one, and then the color of the other, there is no correlation. Thus if the first is square, the second is equally likely to be red or to be blue.

We will, according to quantum theory, get those results even if great distances separate the two systems, and the measurements are performed nearly simultaneously. The choice of measurement in one location appears to be affecting the state of the system in the other location. This “spooky action at a distance,” as Einstein called it, might seem to require transmission of information — in this case, information about what measurement was performed — at a rate faster than the speed of light.

But does it? Until I *know* the result you obtained, I don’t know what to expect. I gain useful information when I learn the result you’ve measured, not at the moment you measure it. And any message revealing the result you measured must be transmitted in some concrete physical way, slower (presumably) than the speed of light.

Upon deeper reflection, the paradox dissolves further. Indeed, let us consider again the state of the second system, given that the first has been measured to be red. If we choose to measure the second q-on’s color, we will surely get red. But as we discussed earlier, when introducing complementarity, if we choose to measure a q-on’s shape, when it is in the “red” state, we will have equal probability to find a square or a circle. Thus, far from introducing a paradox, the EPR outcome is logically forced. It is, in essence, simply a repackaging of complementarity.

Nor is it paradoxical to find that distant events are correlated. After all, if I put each member of a pair of gloves in boxes, and mail them to opposite sides of the earth, I should not be surprised that by looking inside one box I can determine the handedness of the glove in the other. Similarly, in all known cases the correlations between an EPR pair must be imprinted when its members are close together, though of course they can survive subsequent separation, as though they had memories. Again, the peculiarity of EPR is not correlation as such, but its possible embodiment in complementary forms.

III.

Daniel Greenberger, Michael Horne and Anton Zeilinger discovered another brilliantly illuminating example of quantum entanglement. It involves three of our q-ons, prepared in a special, entangled state (the GHZ state). We distribute the three q-ons to three distant experimenters. Each experimenter chooses, independently and at random, whether to measure shape or color, and records the result. The experiment gets repeated many times, always with the three q-ons starting out in the GHZ state.

Each experimenter, separately, finds maximally random results. When she measures a q-on’s shape, she is equally likely to find a square or a circle; when she measures its color, red or blue are equally likely. So far, so mundane.

But later, when the experimenters come together and compare their measurements, a bit of analysis reveals a stunning result. Let us call square shapes and red colors “good,” and circular shapes and blue colors “evil.” The experimenters discover that whenever two of them chose to measure shape but the third measured color, they found that exactly 0 or 2 results were “evil” (that is, circular or blue). But when all three chose to measure color, they found that exactly 1 or 3 measurements were evil. That is what quantum mechanics predicts, and that is what is observed.

So: Is the quantity of evil even or odd? Both possibilities are realized, with certainty, in different sorts of measurements. We are forced to reject the question. It makes no sense to speak of the quantity of evil in our system, independent of how it is measured. Indeed, it leads to contradictions.

The GHZ effect is, in the physicist Sidney Coleman’s words, “quantum mechanics in your face.” It demolishes a deeply embedded prejudice, rooted in everyday experience, that physical systems have definite properties, independent of whether those properties are measured. For if they did, then the balance between good and evil would be unaffected by measurement choices. Once internalized, the message of the GHZ effect is unforgettable and mind-expanding.

IV.

Thus far we have considered how entanglement can make it impossible to assign unique, independent states to several q-ons. Similar considerations apply to the evolution of a single q-on in time.

We say we have “entangled histories” when it is impossible to assign a definite state to our system at each moment in time. Similarly to how we got conventional entanglement by eliminating some possibilities, we can create entangled histories by making measurements that gather partial information about what happened. In the simplest entangled histories, we have just one q-on, which we monitor at two different times. We can imagine situations where we determine that the shape of our q-on was either square at both times or that it was circular at both times, but that our observations leave both alternatives in play. This is a quantum temporal analogue of the simplest entanglement situations illustrated above.

Using a slightly more elaborate protocol we can add the wrinkle of complementarity to this system, and define situations that bring out the “many worlds” aspect of quantum theory. Thus our q-on might be prepared in the red state at an earlier time, and measured to be in the blue state at a subsequent time. As in the simple examples above, we cannot consistently assign our q-on the property of color at intermediate times; nor does it have a determinate shape. Histories of this sort realize, in a limited but controlled and precise way, the intuition that underlies the many worlds picture of quantum mechanics. A definite state can branch into mutually contradictory historical trajectories that later come together.

Erwin Schrödinger, a founder of quantum theory who was deeply skeptical of its correctness, emphasized that the evolution of quantum systems naturally leads to states that might be measured to have grossly different properties. His “Schrödinger cat” states, famously, scale up quantum uncertainty into questions about feline mortality. Prior to measurement, as we’ve seen in our examples, one cannot assign the property of life (or death) to the cat. Both — or neither — coexist within a netherworld of possibility.

Everyday language is ill suited to describe quantum complementarity, in part because everyday experience does not encounter it. Practical cats interact with surrounding air molecules, among other things, in very different ways depending on whether they are alive or dead, so in practice the measurement gets made automatically, and the cat gets on with its life (or death). But entangled histories describe q-ons that are, in a real sense, Schrödinger kittens. Their full description requires, at intermediate times, that we take both of two contradictory property-trajectories into account.

The controlled experimental realization of entangled histories is delicate because it requires we gather *partial* information about our q-on. Conventional quantum measurements generally gather complete information at one time — for example, they determine a definite shape, or a definite color — rather than partial information spanning several times. But it can be done — indeed, without great technical difficulty. In this way we can give definite mathematical and experimental meaning to the proliferation of “many worlds” in quantum theory, and demonstrate its substantiality.

*This article was reprinted on Wired.com.*

When you say partial information spanning several times do you mean the so called "weak measurements"? If not would you give details of the experiments? In your opinion, do these verify many worlds hypothesis?

Here is another way to think about why as this article correctly states "No one view of physical reality captures all its aspects" and that "physical systems [don't] have definite properties independent of whether those properties are measured."

Let's imagine a universe as a whole enclosed system. Somewhere in this universe there is Schrodinger's cat experiment set up. One observer for whom the time is beating at much the same rate as the experiment, will see that as the time passes the poison capsule will eventually break and the cat will unfortunately meet an unhappy end. Another observer who is moving nearly at speed of light relative to the experiment, will never see the poison capsule break as the whole process will appear to be still.

But what would you see happen in such an experiment if you were observing the whole universe from outside? By you being outside, I mean that you are not part of that system and therefore your relative state to anything within that universe cannot be established (there are several ways that this can happen but I will not dwell on this now). You clearly will not see the process run forward in time because you lack identifiable relative state to that experiment. You will not see the time stop either for the very same reason. Point is that in order to see any certain outcome from the experiment, you have to have (or theoretically choose) some relative state to that experiment. Without it you cannot observe any certain outcomes.

Despite of all this, the question still arises – does the poison capsule break or doesn't it? Which interpretation of the experiment is "true"? Looking at the closed system from outside, answer to this question seems to be that it both happens and does not happen, but which version will be observed depends on choosing an arbitrary starting point from which to make an observation. When you select an arbitrary point for observation and then make that observation, what is then observed should not be regarded as the only "truth" which was hidden until now but which thanks to such observation is now revealed – however it should also not be interpreted as the "truth" instantaneously choosing its state and in some mysterious way collapsing into single state from superposition of all possible states just because an "observation" was made. In my view, reality is far more straight forward in that the observed "truth" is always true when observation (or interaction) is being made from that particular chosen point to the specific observed point and wholly depends on the properties of these two points relative to one another. If the observation (or interaction) is made from another arbitrarily chosen point then no doubt the observed "truth" will also be different – neither observation of "truth" has a priority in this respect to being "fundamental reality".

Therefore the observed outcome/property is just one of the range of states that is a permissible solution that can be exhibited, based on the fundamental properties of the matter that makes up that system.

This has wider implications – picking a point in space-time from which a "relative" position is measured within Einstein's theory is made equivalent to making an "observation" that "collapses" the quantum superposition into a certain state (the act of "observation" is actually the act of selecting a point from which a meaningful measurement can be made within the system). Not only are these two theories extensions of one another but in fact they describe the same physical processes from two opposing points of view – one from within the system (Relativity) which gives deterministic outcomes; and the other from outside of the system (Quantum Superposition) which only gives the possible states of freedom for that system and their probabilities based on the properties of the system itself.

Is this a useful analogy?

Lacrosse has specific rules about the number of players permitted on the offensive and defensive sides of the field. Because of fatigue, there are many player substitutions from the bench. It is as though there are 4 worlds – two benches and two sides of the playing field. It seems as though we can only see one world at a time, say, one side of the field. If a defensive player has gone on to the offensive side of the field (the one we are watching) at some point, her team will want to substitute that defensive player for an offensive player (even though the defensive player is technically an offensive player by virtue of being on the offensive side of the field). Perhaps the coach also wants to substitute a fresh defensive player for the first defensive player we are watching on the offensive side. So, at a given moment, we see the first defensive player disappear from our world, say, to the left, into one of the bench worlds which we can't see and an offensive player simultaneously appears, say, at the top, leaving the other side of the field, which we can't see. Also simultaneously, a new defensive player leaves the bench world and enters the other side of the field world, none of which we can see and are therefore are perfectly oblivious to, unless and until the new defensive player may happen into the world we are watching (instantaneously becoming, technically, an offensive player). What we see seems random and defiant of space and time and the players all seem the same yet different. However, there is an underlying rationale, with the perspective of one world only, we just can't see or predict how or when it is applied.

With all due respect, it seems to me that the article sweeps the difficulties under the rug. After a thorough description of classical entanglement, we are swiftly told at the end, that classical entanglement supports the many World Interpretation of Quantum Mechanics. However, classical entanglement (from various conservation laws) has been known since the seventeenth century.

Skeptical founders of Quantum physics (such as Einstein, De Broglie, Schrodinger, Bohm, Bell) knew classical entanglement very well. David Bohm found the Bohm-Aharanov effect, which demonstrated the importance of (nonlocal) potential, John Bell found his inequality which demonstrated, with the help of experiments (Alain Aspect, etc.) that Quantum physics is nonlocal.

The point about the cats is that everybody, even maniacs, ought to know that cats are either dead, or alive. Quantum mechanics make the point they can compute things about cats, from their point of view. OK.

Quantum mechanics, in their busy shops, compute with dead and live cats as possible outcomes. No problem. But then does that mean there is a universe, a "world", with a dead cat, happening, and then one with a live cat, also happening simultaneously?

Any serious philosopher, somebody with endowed with common sense, the nemesis of a Quantum mechanic, will say no: in a philosopher's opinion, a cat is either dead, or alive.

A Quantum mechanic can compute with dead and live cats, but that does not mean she creates worlds, by simply rearranging her computation, this way, or that. Her various dead and live cats arrangements just mean she has partial knowledge and that Quantum measurements, even from an excellent mechanic, are just partial, mechanic-dependent measurements.

For example, if one measures spin, one needs to orient a machine (a Stern Gerlach device). That's just a magnetic field going one way, like a big arrow, a big direction. Thus one measures spin in one direction, not another.

What's more surprising is that, later on, thanks to a nonlocal entanglement, one may be able to determine that, at this point in time, the particle had a spin that could be measured in another direction. So far, so good: this is like classical mechanics.

However, whether or not that measurement at a distance has occurred, roughly simultaneously, and way out of the causality light cone, EFFECTS the first measurement.

This is what the Bell Inequality means.

And this is what the problem with Quantum Entanglement is. It is the fact that wilful action somewhere disturbs a measurement beyond the reach of the five known forces. It brings all sorts of questions of a philosophical nature, and make them into burning physical subjects. For example, does the experimenter at a distance have real free will?

Calling the world otherworldly, or many worldly, does not really help to understand what is going on. Einstein's "Spooky Interaction At A Distance" seems a more faithful, honest rendition of reality than supposing that each and any Quantum mechanics in her shop, creates worlds, willy-nilly, each time she presses a button.

Can "people measure properties like the angular momentum of electrons?" In these EPR type tests, I always see light used. In experiments like the Stern-Gerlach we measure atoms with internal electrons. In this instance where you are trying to express experiment, it reads like the expression of theory.

Also, I found the labeling in your first two drawings confusing. What are those circles and squares doing on the outside of the drawing along with "system 1" and "system 2" ? Thank you.

I'd like to thank the author for trying to explain the entanglement situation to somebody like me, a complete amateur but devoted would-be science understander. But I have to agree with Ayme: from what very little I could follow far enough to be of use, the article is too smart for the average layman. It literally may not be possible for the professionally very advanced to discuss very advanced states in terms we can absorb.

Ayme's own alternative explanation, though still not fully clear to me, seems more logical than what little I can understand of the author's.

Mr. Reiter picked the perfect example: the confusion caused by the very first illustration, even before any explanation started. I doubt the author expected or had reason to expect that something so basic could be unconstruable by some of us, but there it is, and here we are, still confused.

"But does it? Until I know the result you obtained, I don’t know what to expect. I gain useful information when I learn the result you’ve measured, not at the moment you measure it. And any message revealing the result you measured must be transmitted in some concrete physical way, slower (presumably) than the speed of light."

Wilczek suddenly puts in a conscious observer whose reading the information about the correlation makes the correlation real. He does this so the correlation doesn't happen faster than light. It's saying that Schroedinger's cat is both dead and alive until someone opens the box, except that's not true, and can't be true.

"Upon deeper reflection, the paradox dissolves further. Indeed, let us consider again the state of the second system, given that the first has been measured to be red. If we choose to measure the second q-on’s color, we will surely get red. But as we discussed earlier, when introducing complementarity, if we choose to measure a q-on’s shape, when it is in the “red” state, we will have equal probability to find a square or a circle. Thus, far from introducing a paradox, the EPR outcome is logically forced. It is, in essence, simply a repackaging of complementarity."

If I understand it correctly an unentangled particle would have a 50% probability of being a "square" or "circle." When one of an entangled particle is measured for "color," the "shape of the particles is left indeterminate, because complementarity means you can't measure two complementary attributes simultaneously. But this is irrelevant. Einstein's suspicion of a "spooky action at a distance" comes from the correlation between the colors. In this example, the peculiar thing is the way both are "red." Any supposed paradox as I understand it is in superluminality or non-locality apparently being true but contradicting the apparently illusory existence of the world. (I'm a little shaky on how these are physically different…two entangled particles that are still in contact even though it appears they are separated in spacetime would be non-local I think but how is that physically different from a superluminal contact?) I'm sorry but this paragraph appears to be an illogical diversion, not a resolution.

"Nor is it paradoxical to find that distant events are correlated. After all, if I put each member of a pair of gloves in boxes, and mail them to opposite sides of the earth, I should not be surprised that by looking inside one box I can determine the handedness of the glove in the other. Similarly, in all known cases the correlations between an EPR pair must be imprinted when its members are close together, though of course they can survive subsequent separation, as though they had memories. Again, the peculiarity of EPR is not correlation as such, but its possible embodiment in complementary forms."

It seems to me this flagrantly contradicts principle 1 above, that a property that isn't measured need not exist. (At that, I'm afraid I suspect the usual belief is that a property that doesn't exist.) The entangled particles don't have any "shape" or "color" to remember until a measurement made on one of the seemingly far separated entangled particles.

Let us suppose a physicist, call him Prof. Bertlsmann, has some red and blue yarn. They have the fascinating property that when they are knitted into socks or mittens, they lose their color, becoming transparent. Only if he leaves them shapeless does he see the red or blue colors. Bertlsmann wants to mail samples to a couple of friends in other countries. He has only bubble envelopes with the peculiar property that if they are opened top to bottom, you then see either a sock or a mitten. But if you open them from side to side, you see only red yarn or blue yarn. He mails off his two envelopes. Alice in Australia opens from top to bottom, and finds a sock. If Bob opens from top to bottom too, he will find a sock. But if he open from side to side, he will have a fifty/fifty chance of finding blue or red yarn.

I think this is the correct analogy to complementarity. But I don't think Prof. Wilczek has explained how this isn't peculiar. I don't quite understand how this shaky foundation supports the multiverse. Maybe the idea is that if you interpret the other possibilities as virtual particles, the multiverse is all the virtual particles and all their (virtual) interactions. Reality is the whole thing. Any particular universe is defined by the conservation of all properties measurable according to the rules of complementarity. You can't observe measure the entangled particles and find that one is "red" and another "blue," because that violation of the conservation laws means that in this universe, one must be a virtual particle. But maybe that's just misunderstanding on my part.

What you've written here is confusing me because it doesn't say anything about the relationship between color and shape. When you write:

"Thus if we find that one is red, and later measure the color of the other, we will discover that it too is red, and so forth. On the other hand, if we measure the shape of one, and then the color of the other, there is no correlation. Thus if the first is square, the second is equally likely to be red or to be blue."

I am not in any way astonished because going in I had no reason to believe the two different properties were correlated: how is the above distinguishable from the situation in which both properties are entirely independent? You'd *expect* to get a random shape from the measurement of one particle and a random color from the measurement of the other particle, even if there were local hidden variables in each particle describing the color and shape, both set at the moment they were entangled. I'm not seeing where action-at-a-distance enters into the example.

I feel like the discussion of the GHZ effect could be improved. The concept of "good" and "evil" as defined here are intrinsically quantum mechanical notions. The definitions are already implicitly assuming that there is no such thing as a blue square or red circle (as if both attributes could be defined at once), which classical intuitions would suggest are possible.

Instead of assuming a quantum viewpoint, it's maybe more helpful to imagine — as we would naively expect — that the particles start with both characteristics (shape and color as two hidden variables) and then reason through to a contradiction. (Details: We know that half of particles are blue and there are always an odd number of blue particles. Therefore, sometime [a third of the time] all three particles are blue. On the other hand, we know that if a color and two shapes are measured and the color is blue, then we must measure one of each shape [otherwise we'd get at odd number of "evil" particles]. That tells us that if all three particles are blue — which does occur — and we measure a color and two shapes, we will always measure two different shapes. Thus the true state, when all three particles are blue, must have one of one shape and two of the other. But then it would have been possible to measure a blue and two identical shapes, a contradiction.)

Why in heavens name would you think that this explanation of entanglement is simple or understandable to the non-physicist? Physicists have yet to perfect the art of simple explanation.

All of these analogies aren't helping, and I get the distinct impression of a black box between entanglement and Many Worlds.

Alice creates a pair of entangled photons and measures the polarization of one photon. The other end of the apparatus terminates down the hall where Bob measures the polarization of the other photon. It's not surprising that the polarizations are correlated: Bob's measurement matches Alice's.

But where things get "interesting" is that Alice can choose to divert her photon through a polarizer or not, after it has been created and sent on its way, and her doing so apparently affects Bob's measurement, despite there being no local (light speed or below) means by which Alice's choice can be conveyed to the photon speeding toward Bob's apparatus.

These experiments have been done over and over with the same result: the choice Alice makes at her end, after both photons are in flight, affects the measurement Bob makes at his end.

Maybe this is just my layperson's lack of a critical bit of knowledge, but I don't see how "classical entanglement" can produce that result (the metaphorical Alice glove can be switched from Left-handed to Right-handed while it is in the post, causing Bob's glove to switch while it is also in the post), and I don't see how any of it supports MWI as distinct from Copenhagen.

Methinks there have lately been a lot of efforts to find support for MWI, and they entail making statements about entanglement and other observable properties.

Here's another layperson question, and maybe Luysii or someone (BTW, Luysii, I posted another reply to you in the other column) has an answer to this one: If MWI is correct that the universe splits at every wavefunction collapse, where does all the duplicate energy and mass come from? Or have I been misreading MWI all these years?

While I'm asking layperson questions, I may as well add one more to the list: has anyone done experiments with multiple simultaneous streams of entangled particles and error-correction codes?

Clever explanation, maybe but it is outside the box. What is happening inside the box like with entangled photons? To become entangled do they have to be emitted at the same time, do they have to be in close proximity, are the electric and magnetic fields in phase, at 90 deg, are the polarization's the same or what. I saw no physics in the explanation what-so-ever and a knowledge what's happening in reality space. That's what is necessary to make entanglement useful in the real world.

Zane Green

As a layman who has been reading for a few years, here's how I summarize what (I think) I've learned:

* Everything happens, so there are essentially "many versions" of every system.

* There is no "uncertainty" – there are certainly many groups of versions of everything.

* Most versions of systems are identical or only slightly different, and some are very different (this is how probability becomes relevant, although the complexity appears to be high).

* We are made of the same quantum stuff, so there are many versions of us, too (this is what's seldom made clear, as if it's being rejected for no acceptable reason).

* Quantum fields are multiversal.

* We perceive one result/outcome/branch/history in the macroscopic world.

* Measurements are correlated when the results are compared, so scientists perform the correlation when they communicate results, classically (there is nothing spooky about it).

* Pretending nothing is real unless and until we look at it is childish, as is pretending our consciousness affects reality instantly (like bending spoons?).

* The only way our minds affect reality is by creatively growing and applying knowledge.

* Complete multiversal information is always mapped in a quantum field at each particle point.

* Some of this information becomes locally inaccessible whenever interaction takes place among various versions of systems and environments, and that's how we observe classicality ("decoherence" occurs in a single branch or universe/world); again, the totality of information is mapped and present, but we see one outcome locally.

* Measuring an entangled particle does NOT seem to affect anything "non-locally" as long as the correct description of reality is provided (why do physicists insist upon saying entanglement "seems to affect" a particle, while hiding part of the truth?).

* Words like "Complementarity," "non-local," "quantum jump" and probably a few others should not be used or taught by scientists, since they were designed to prevent simple explanations for what we observe at the quantum level, either by protecting established ideas (of Bohr's, for example) or by protecting Mankind as a special type of system.

* The multiverse is real and causal action is local.

* Because of missing information, the best we can do is use the best available explanation for the part of reality we do NOT perceive with our senses: Everett's theory, which rejects the fundamental application of probabilistically collapsing waves.

Congrats Frank Wilczek on a explanation well done. So, what does this all mean for our everyday lives?

"After all, if I put each member of a pair of gloves in boxes, and mail them to opposite sides of the earth, I should not be surprised that by looking inside one box I can determine the handedness of the glove in the other. Similarly, in all known cases the correlations between an EPR pair must be imprinted when its members are close together, though of course they can survive subsequent separation, as though they had memories."

I'm pretty sure this is either very misleading, or flat-out wrong.

The whole idea of it being spooky *action* is that you're not just uncovering aspects of the particles that were 'already there'. Einstein would have had no problem with that. The problem is that those aspects aren't 'fixed' until a measurement is taken, at which point the influence propagates 'immediately' to the entangled particle. [In other words: no local hidden variables.]

Gloves are at best a bad analogy and at worst, incorrect. Yes, it's not a surprise that they end up correlated left/right, but an entangled particle isn't a package that 'either contains a left glove or a right glove' and you just open it up to find out, and then know that the other package has the twin in it. Until opened, the package you're holding contains a superposition of left and right glove – not one or the other. I'm not sure it even makes any sense to say 'imprinted when its members are close together'.

Whether or not the explanation of entanglement is clear to us, I have to applaud the author for attempting to describe and communicate the complexity of entanglement – which is clearly one of the most challenging and important puzzles in physics.

Best insight sometimes comes from rationalising complexity into more straight forward illustrations (even if such illustrations don’t completely describe the problem). This helps our minds form intuitive insights so that we can approach the problem with more creativity. I consider that these kinds of articles are an attempt to communicate and engage wider audiences in the complexity and beauty of the most baffling questions in science. It’s great that we can all have a view on these interesting questions and that these topics aren’t just left to theoretical physicists.

Very, very interesting. Haven't had time yet to read the whole thing but I can tell by what I read that you might be on to something here, the proverbial "action at a distance".

Some of my work is dependant on the potential understanding of entwinement, and I've been looking for the operative "principle" involved. I'm hoping that like all/most physical processes, there is a simple and direct explination for the pheonominon that we observe.

Will return soon to finish the article and hoping to use your idea in some of my thought and other experiments to see if it holds up. Thank you so very much for taking a stab at this as I was thinking it would be quite some time before any real forward movement in this specific area was forthcomming.

Kudos.

OK, questions… this "spooky action at a distance"…is the GHZ situation the simplest experiment in order for the operative priciple, in this case SAD, to be observed? Is there a simpler one?

For example, can we come out with a beam of electroncs that expresses the state domain talked about in the original cake example, where either both of them, when measured "distantly" and simultaneously, are circle or square. Am I talking about a real situation here (I might be misunderstanding the experiment that leads to the most OVERT example where the human brain's first reaction is "Wow, that's SPOOKIE!")?

The way I'm visualizing it is you come out with an oscilating beam of electrons with the particular "entwinment" that leads only to both circle, or both square (insert appropriate quantum attribute for circle/square) that is preserved when measured at a distance. And don't say "No, the probablity is 50/50 that the other one is either circle or square" that's not spookie, thats just random.

If this isn't how it works please enlighten me. Explain to me what the minimum situation that expresses the spookiness, even it it is the GHZ situation. Another thought I had, is that in the GHZ situation, can you express it entirely mathematically (in terms of probability/statistics) divorced from quantum mechnics, in that I am insinuating the possibility that its purely a mathematical anomoly, rather than a physical property (albeit microscopic). Thoughts?

My main questions is the first one however, can you produce a beam of electrons that produces the "entwined" attribute? I'm visualizing a situation similar (or identical) to the Stern-Gerlach apparatus where an oven producing silver atoms can be split into two beams via an inhomogenous magnetic field. Each split beam would be of an identical spin (I'm thinking non-oscillating, in that one of the beams would be constantly of the same spin…correct me if I'm wrong). Can someone post the design of the actual simplest physical apparatus that displays the attribute of "spookiness" and a concise explination of how the spookiness is observed?

Ok, while I'm asking questions, you brought up the "many worlds" interpretation related to the Copenhagen. Can we take Shrodinger's original intent as literal? For example, do you think there is any experimental merit to physiologically inspecting the cat afterward to see if it shows any signs (ie. fatigue, stress, other forms of disease) of being literally in a metastable (?) state of life and death? I mean being literally half-dead for a period of time should be observable by a trained veteranarian.

Here's an interesting one, does the interpretation only apply to sentient observation because in the original thought experiment we are conveniently forgetting that the cat might be the symetry-breaking observer. Or are we closet human/cat elitists when we talk about consciousness?

Or does the dead cat only exist in a parallel universe that we have no possible way of talking to the exerimenter involved, making the point very, very moot?

OK, more questions…

Complimentarity. How do you feel about this idea (and its just an idea)?

What if complimetarity is an artifact not of the particles themselves, but rather more of an artifact of the mathematics involved. I mean it should be possible to calculate both properties at the same time, maybe if a deeper understanding of matter is involved.

I am reminded of the story about the exeutives going to the head computer scientist in charge of a supercomputer and asking him if they could do such-and-such to which the scientist told them that the machine couldn't do it. One of the executives asked for a clarification "Can the machine not do this? Or are you saying that you don't know how to get the machine to do it?"

For example, throw out the whole concept of particles all together and approach the problem from a waveform point of view only. Instead of trying to attribute spin, or angular momentum or postion from the very human-centric point of view to a more-pr-less arbitrary point of maximal amplitude of the wave function (I mean it is of interest but in no way fundamentally differnent from any other point on the wave function), why not calculate, maybe with modern supercomputers, the wave functions themselves computing position (as the statistical center of the 3D vector field) while afterward computing the angular momentum using the very same data set?

Would we not, at least mathematically, know both at the same time it being the very same data set?

Thoughts?

The questions are, what properties does a quantum particle have and when does it have them? … It would seem to have to have *at least* one property 'at all times', otherwise it wouldn't exist at all. Also, it doesn't have a classical property because it is not a classical object.

Saying that it took all possible 'classical' paths is strictly speaking not correct: classical objects do not have amplitudes that sum.

Many-Worlds did not follow *at all* from what Wilczek said earlier in the paper!!!

Let's be frank: We don't have a mechanical model of quantum entanglement, so the model with gloves is not right either. I learned a bit from the article, but haven't got closer to understanding why would the many worlds "model" be plausible or likely.

It rather seems like an easy way out of the question. Similar to those ways out of understanding the world popular in the old times, when things not understood were simply done by an almighty intellect. No proof needed and no proof possible.

It is much harder to admit, we don't know.

(a Laic)

What people (including einstein) startles most with entanglement is the fact that epr hurts either locality, limited speed of light (or causality). When mr. Wilczek states, what we measure is not more astonishing than putting like-handed gloves in parcels, sending them in different directions and afterwards opening them , he seems to make idiots of these peoples. No word about hidden variables. No word about the ultimate aim of the ghz-experiment to show (at once, not statistically) that hidden variable approaches contradict quantum theory.

This is a remarkably clear popular article on entanglement. I cannot imagine a simpler exposition on the topic with lesser distortion – something that necessarily comes with speaking physics non-mathematically. Yet, the various comments makes one wonder whether popular expositions in physics really aid understanding as much as we'd like to believe (I hope this comment will pass through moderation). On the other hand, for some strange reason, popular exposition on mathematics like one finds on Quanta seems to fair much better.

I don't want to claim that entanglement becomes trivial to understand once someone knows the underlying mathematics. In fact, beginning math students are also confused by the fact that not all elements of the tensor product of two spaces (in this case Hilbert spaces) are tensor products of two elements but are linear combinations (entangled states) of these elementary tensors (pure states).

I am a laymen who is fascinated by physics, and whose math is limited to high-school level geometry, algebra and trigonometry. I do not find this article understandable. As someone else mentioned, the simple-looking diagrams are unclear and lead to several questions. The sentences throughout are short and not overly technical, but by and large are not understandable. The fact that a scientist finds the article understandable and presumably thinks it adequate for ordinary intelligent people to understand, shows what a gap there is between professionals and laymen in judging the worth of 'popularization' articles. There are better and worse, and this is worse. See Dennis Overbye of the New York Times for someone who knows how to write about physics effectively for lay people. This article is definitely not that.

@Charles Zigmund: This is indeed a pressing and complicated problem. It is vital to the health of a modern society that non-scientists such as us (I am a mathematician, I have trouble understanding articles in the biological/cognitive/medical sciences) have at least enough understanding of modern science so as to be able to reason with it in our daily lives. While it is naive to expect any degree of competence but I am slowly beginning to believe that even a more rudimentary form of understanding is also difficult. Quanta is probably the magazine with the highest quality of science journalism and yet the comment section is often filled with misunderstandings (judging from articles on the few topics that I feel I understand a little). Let me end by suggesting you two popular-science books on physics that can be understood by anyone who knows high school math, they are written by Leonard Susskind and are called Theoretical Minimum: Classical Mechanics and Quantum Mechanics.

@DS, thank you, I will read those books. I don't think I'm quite as adrift as you may infer. I've been reading and thinking about physics for a good many years and think I understand some things at least generally. But what, for example, I know about quantum mechanics, the uncertainty principle, quantum entanglement and allied subjects I learned from books and articles for the lay person written more skillfully and carefully than the article here we are discussing. I agree with you that this is important, especially if the public is expected to keep being willing to fund basic research.

YOUR NAME FOR THIS DISCUSSION IS NOT QUITE right.

……not "made simple"

it is not.

try "simpler"

OK, ok, I've been thinking about this a bit and reading the comments. Here's the million dollar question. We're all dancing around the real issue here, but there are a few flirting with saying something that might offend Einstein. (Not the least of which being Wilczek himself insinuating the issue might be logical/mathematical, not mechanical.)

Now someone tell me if this is a bad idea to look directly at entwinement. I like don't want to like disappear in a cloud if Higgs Bosons or something.

So what you are saying is that we can take a laser beam, and "entwine" the photons which are all in a "red" state. We then shoot them through a beam splitter, and then shoot the two beams to two distant cities. Then we got a guy there watching (on both ends…apparently it matters…to prevent the physicist from explaining how the question is flawed/moot/naïve…kidding…kidding) and he's got a polarizer. So the beam comes in and he shoots it through the polarizer. Then he OBSERVES the state of the beam. Comes out "blue"…we knew that, the beam was originally red so rotating the polarization results in the symbolic "red" state.

OK, the million dollar question. They have atomic clocks at either end, all calibrated perfectly so they have super-ultimate simultaneous time. The other guy is there watching in the other city. He measures the beam…

The QUESTION: is that beam blue? Is that what we are saying here. Inquiring minds want to know.

Then they check when the beam was polarized, and they check the timestamps on the atomic clocks and it comes back "simultaneous" (like superluminal simultaneous)?

Then the guy in the first city connects a modulator to the polarizer and starts shooting ASCII symbols over it, they transfer the file and then check the clocks and it is indeed instantaneous.

IS that what we are saying, sir? And yet again, please point out where my reasoning breaks down, and offer any quick solutions you can think of. Thank you.

"But when all three chose to measure color, they found that exactly 1 or 3 measurements were evil."

After measuring 3 colors we can't continue with measuring shapes. So how we detect good/evil from colors only?

"In this way we can give definite mathematical and experimental meaning to the proliferation of 'many worlds' in quantum theory, and demonstrate its substantiality."

That might be true if, and only if, the "many worlds" hypothesis is verifiable [properly testable using the evidence-based scientific method] against both its null hypothesis and its alternative hypotheses.

An unverifiable hypothesis is indistinguishable from pseudoscience and anti-science.

It appears that I'm not up-to-date with the verifiability of the "many worlds" hypothesis. I sincerely hope that Frank Wilczek will provide us with irrefutable peer-reviewed evidence that the hypothesis is verifiable in accordance with the scientific method. As I currently understand the hypothesis, it requires opening our minds wide enough to also accept that the tooth fairy and unicorns exist, if not in this world then on one or more of the other many worlds. I'm long past the stage of keeping my mind so wide open that my brain keep falling out.

"But when all three chose to measure color, they found that exactly 1 or 3 measurements were evil."

You lost me there. If the q-ons are entangled, shouldn't all three measure the same color? So it'd be either 0 or 3. If they'd measure different colours, the q-ons wouldn't have been entangled in the first place, would they?

Do you need an IQ above 180 to comprehend all this?? Either way, fascinating.

I've wondered if quantum entanglement would allow you to evade the uncertainty principal. If you measure the spin of unentangled electron it tells you the spin of it's entangled partner. So if you measure the location of one and the spin of the other you can deduce both the spin and location of one.