### Cats, Dogs and Quantum Mechanics

The game of Cats and Dogs works like this: You and your teammate are placed in separate rooms and forbidden to communicate. You are each asked a randomly chosen question: Either “Do you like cats?” or “Do you like dogs?” (Each of your questions is determined by a separate fair coin flip.)

A little reflection should convince you that if you are allowed to meet with your partner and plot strategy before the game, then the best you can do is agree to always agree — say by both always answering “yes”. That way, you win 75% of the time, and there’s no way to do better. In particular, there’s nothing to be gained by randomizing your answers.

That, at least, is true, in a world governed by the laws of classical physics and probability theory. But in a world governed by the laws of quantum mechanics — which is to say, in the world we live in — you can in principle do better. Namely: You each carry with you one of a pair of entangled “quantum coins” (actually elementary particles, but I prefer to think of them as coins, since you’re going to use them as randomizing devices).

Because these coins are very small, you need special apparatus to see whether they’re heads-up or tails-up. Before making your measurement, you can rotate your apparatus through either of two angles — call them C and D. The two coins agree 85% of the time — unless both you and your partner’s apparatus have been rotated through angle C, in which case they disagree 85% of the time.

Now you and your partner can each adopt this strategy: If you get the cat question, rotate your apparatus through angle C; if you get the dog question, rotate through angle D. Then examine your coin, and answer “yes” if it’s heads, or “no” if it’s tails. If you both follow this strategy, you’ll win 85% of the time.

Moral of the story: Quantum technology can improve your performance in strategic situations.

Some time ago, Gordon Dahl and I wrote a paper that explores the implications of quantum mechanics for the cat/dog game and similar (more economically interesting) strategic interactions. Early versions of this paper have floated around for a while, but we’ve just completed a substantial rewrite that I both hope and believe is substantially more readable. We’ll be very glad for feedback from readers who have a taste for this sort of thing. Click here to read it!

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#### 83 Responses to “Cats, Dogs and Quantum Mechanics”

1. 1 1 JimW

I don’t get it. If you are allowed to have a quantum-entangled link to your partner, why aren’t you allowed to have a cell phone link to your partner? It all seems rather arbitrary.

2. 2 2 Harold

It is never easy to get one’s head around the quantum world. One thing I find difficult is the entaglement issue. You say in the paper that if each person were given a coin of the same color, then as soon as player one saw his coin, he would know the color of player two’s coin. There would have been no communication. This is easy. What gets me about entanglement is that the color of both coins is not determined until player one looks at his coin. If the coins could be red or yellow, my understanding is that the coins are in a superposition of red and yellow (orange, perhaps?) until someone looks at them. In the analogy, player one’s coin resolves to be, say, red when he looks at it. At the same instant, player two’s coin must also resolve to be red. It is harder to see there is no communication here. I accept is as part of quantum wierdness, but do not understand it.

3. 3 3 S.V.

Very interesting idea, but if they are allowed to use this mechanism, why not allowing them to use a mobile phone? What the quantum mechanics device does is communication, i.e. transmitting information.

4. 4 4 Dave

If they’re allowed to communicate, why can’t they they just email each other and win 100% of the time?

5. 5 5 Ken B

@Dave: They are not COMMUNICATING. They are using special coins that match more than 75%.

@Steve: You need a new coin for each question don’t you? That is not clear in your note.

6. 6 6 Steve Landsburg

JimW, Dave, SV: A cellphone or an email link is detectible (as is any other form of communication) and can presumably be forbidden. The entangled coins, by contrast, can’t be detected (they look and behave exactly like unentangled coins). Since they can’t be prohibited, it’s interesting to ask what happens when people use them.

7. 7 7 Steve Landsburg

Harold: Your summary is exactly correct, including the part where you say there is no communication. As far as not understanding it, I think you understand it as well as it can possibly be understood — all that’s left is for you to get over the prejudice that you understand the classical world any better! Familiarity is not the same thing as understanding.

8. 8 8 Steve Landsburg

Ken B: Yes, you need a new pair of coins for each question.

9. 9 9 JimW

But the entangled communications link (it IS communication, since information is communicated) CAN be detected. It would be obvious to anyone watching as the partners kept pulling out coins after each question and fiddling with them. The referee would have to be blind not to detect that.

10. 10 10 Steve Landsburg

JimW: It’s certainly not communication. What information do you think is being communicated?

There is no way for an outside observer to distinguish between entangled and non-entangled coins.

11. 11 11 JimW

Of course it is communication. It is a noisy signal that allows them to partially coordinate their answers to increase their probability of winning.

12. 12 12 Ken B

@JimW: Is a conventional coin then communication? It gives 75% success. That beats some strategies (ie A always says Yes, B always says No). If the quantum coin “is a noisy signal that allows them to partially coordinate their answers to increase their probability of winning” then so is the classical coin. Which is a tretty odd notion of communication.

13. 13 13 JimW

No, with a standard coin you cannot improve your winning percentage, so obviously no information is communicated.

14. 14 14 Ken B

@JimW: With a standard coin you can improve your chances versus the strategy I suggested, which is A always says YES and B always says NO. So the classical coin, like the quantum one, can increase success vs some strategies. But it uses no communication.

15. 15 15 Steve Landsburg

Jim W:

Suppose I observe my coin, and then my partner observes his a fraction of a second later — sooner that a light beam originating at my observation could have reached him. Are you saying that there can be faster-than-light communication?

PS: It would be a lot easier to understand you’re claim if you’d tell us precisely what information you think has been communicated.

16. 16 16 JimW

You cannot improve your chances beyond an optimal strategy with a standard coin. You need some sort of communication to improve your chances.

Since information is obviously being communicated, then if that information is transmitted instantaneously, apparently there is faster-than-light communication.

How do you think it is possible to achieve a win rate with quantum entanglement that is higher than that with an optimal strategy (without communication) if there is no communication going on with the entanglement link?

You could simulate the quantum entangled link without quantum effects by having two computers connected together, with a pseudo-random number generator and a simple algorithm. Would you claim that there was no communication in that case?

17. 17 17 Ken B

@JimW: 1. You still don’t identify what is communicated. You merely assert it must exist. This is religion not argument. 2. The quantum coin beats the classical coin strategy, hence the classical coin strategy is NOT optimal.

Your assertion under 1 sounds a lot like: “Houdini cannot escape a locked box without dematerializing. He escaped so he must have dematerialized.” Your major premise is wrong.

Some months ago someone posted a nice puzzle about prsioners escaping by flipping numbered cards. Some posters assumed you needed to have the prisoners communicate, but you didn’t, you just needed a clever trick. The quantum coin is the clever trick. It has a useful probabilistic property that can make it better than a classical coin in some situations.

18. 18 18 JimW

Ken B:

By your absurd reasoning, the optimal strategy is to talk to your partner via cell phone, then you can win 100% of the time. Give me a break.

19. 19 19 Ken B

@WillA: You still out there? I think you’ve been out-non-sequitured! :>

20. 20 20 nobody.really

I don’t get it. If you are allowed to have a quantum-entangled link to your partner, why aren’t you allowed to have a cell phone link to your partner? It all seems rather arbitrary.

Yeah! And while we’re at it, why can’t you and your partner be in a polyamorous relationship? Then, at least, you’d have some reason to stay in communication. Or non-communication.

(Out-non-sequitur THAT!)

21. 21 21 ThomasBayes

I haven’t read Steve’s paper yet, but I will. Before doing so, though, I have an example that should help me learn if I am on the right track, and might help JimW and others see why the two players are not communicating with each other.

Suppose the players have decided to determine their answers by flipping a new fair coin for each question. By doing so, they think their probability of winning will be 1/2. They are unaware, however, that their coins are being supplied by oracles who are observing the questions and providing the coins according to some diabolical scheme.

The oracles have decided to use a collection of coins that are completely unfair: they either show heads or tails with probability 1. The oracle for the first player gives them a ‘head’ or ‘tail’ coin at random (heads half the time, tails half the time). If both players get cat questions, then the oracle for Player 2 gives them a coin that will not match Player 1; otherwise, the oracle gives a matching coin. If the players play 1000 games without being told the results, they will expect to have won about 500 of the games. They will be shocked to learn that they won all of the games, and they will be certain they did not communicate with each other to do so.

The oracles could change their scheme to correspond to Steve’s example, and the players would still be certain they weren’t communicating with each other. (To do so, I think they would need to drop the ‘certainty’ on their unfair coins to about 0.9183.)

22. 22 22 Steve Landsburg

ThomasBayes: It is certainly true in your examples that the players don’t communicate with each other. However, surely some communication must take place, because the oracle for Player Two must somehow learn both players’ questions. Thus, in particular, your scheme would not work if the players flipped their coins near-simultaneously (so that information could not travel to the oracle in time for him to choose the right coin). By contrast, the quantum scheme works no matter how far apart the players are, and no matter how close to simultaneously they flip their coins.

23. 23 23 ThomasBayes

Steve:
It seems that some communication must take place in your example too. What happens, for instance, if one player rotates their coin and flips it before the other player has set their rotation? Doesn’t the rotation of both coins need to be set before either is flipped? (This seems to be the same as the oracles knowing both questions, then giving the players the appropriate coins.)

I can see how this works without the players communicating with each other, but I don’t see how this works without someone or something knowing both of the questions. If one of the players sets their rotation wrong, for instance, won’t this affect the probabilities? And if this is true, then aren’t the players communicating with someone or something?

(I apologize if you addressed this in your paper; I still haven’t had a chance to look it over thoroughly.)

Thanks for sharing this problem.

24. 24 24 Steve Landsburg

Thomas Bayes:

Doesn’t the rotation of both coins need to be set before either is flipped?

No, it most emphaticallly does not.

Coin A is rotated through angle C or angle D. Coin A is observed. Coin B is rotated through angle C or angle D. Coin B is observed. It makes no difference in what order these events occur, and it makes no difference whether or not they occur simultaneously or centuries apart. (In practice, in the centuries-apart case, outside interferences are liable to screw things up, but in principle these interferences can be eliminated.) You get exactly the same correlations no matter what the timing.

(Edit: When I said the order of events makes no difference, that’s of course subject to the condition that Coin A is rotated before it’s observed and likewise for Coin B. There are no other restrictions.)

25. 25 25 ThomasBayes

Steve: Why do you need a new pair of coins for each question?

26. 26 26 Ken B

@Thomas Bayes:
The coins are quantum objects in an entangled state. Electrons polarized in a magnetic field is the standard example. That state however *cannot be known until they are probed*. Once they are probed they are no longer in that state. This is a key fact of quantum theory: measurement destroys the previous state. Hence they cannot be re-used.

27. 27 27 Al V.

I think folks need to understand quantum enganglement before arguing that the quantum coins are communicating. Here’s Wikipedia’s article about “Spooky action at a distance”, as Einstein called it: http://en.wikipedia.org/wiki/Action_at_a_distance_(physics). In summary, Steve is right, there is NO communication. And here is Schrodinger’s cat: http://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat. Personally, I think that there is something missing from the Copenhagen Interpretation, and that the two quantum particles are really manifestations in the observable universe of a single particle, where the rest of the particle(s) is hidden either in other dimensions or in other universes.

28. 28 28 Steve Landsburg

Thomas Bayes: Ken B’s answer to your question about new pairs of coins is exactly right (he clearly understands this stuff).

The coins are initially in an entangled state. Observing them changes them into an unentangled state.

29. 29 29 nobody.really

Some clarifying questions I should have asked earlier:

You are each asked a randomly chosen question: Either “Do you like cats?” or “Do you like dogs?” (Each of your questions is determined by a separate fair coin flip.)

These are NOT the entangled coins, right? You’re just saying that each player has a 50% chance of getting each question.

The two coins agree 85% of the time — unless both you and your partner’s apparatus have been rotated through angle C, in which case they disagree 85% of the time.

This 85% probability reflects something about quantum mechanics – but the strategy to be employed, and the philosophical questions that flow from it, really apply equally to any probability other than 50%, right? (Probabilities below 50% would require inverting the strategy.)

As with others, I’m drawn to the question of whether this strategy involves “communication.” In short, Landsburg is describing a system by which a partner would alter her behavior strategically based upon information known to one, but not both, parties. Does that constitute a form of communication?

Looks like communication to me. The message is, “This is the coin flip I want you to use when implementing the strategy we discussed.” Admittedly, neither party would know whether she was giving the message or receiving it.

How does this scenario compare to the Monty Hall problem? Monty Hall would offer a contestant Options A, B and C, one of which was the winning choice. The contestant would make a choice (say, A). Monty Hall would then remove one of the two rejected choices (say, B) and ask the contestant if she would like to switch her choice to the other one (in this case, C). The choice would seem to be an arbitrary one. But if the contestant realized that Monty Hall would never remove the winning option, the contestant would be able to extract useful information from Monty Hall’s actions.

In both the Cat/Dog scenario and the Monty Hall scenario, the actors are implementing in a mechanistic fashion a strategy devised before the game began. But the inputs to that strategy are determined in the middle of the game. Whether you say those inputs were “communicated” in the middle of the game seems like a matter of semantics.

30. 30 30 maznak

Steve, I guess that I have got your point. Now the challenge is to come up with real life scenarios where this technology might improve the odds. Prisoners dilemma type situations come to mind (your exaple seems to be one of them). Any other ideas?

31. 31 31 Ken B

@nobody.really:
Let’s imagine another scheme. A and B have photopies of a list of YES and NO. They use the answers sequentially (and hence always agree). Communication?
Or they use fuzzy photopies that ahve errors a few times. Communication?

Those arguing for communication seem to be arguing either
1. co-ordination implies communication. I think my lists just discussed refute that.
Or 2. Beating 75% implies communication. But why? It implies something other than a classical coin for sure, but why must that something else be *communication*? Why can it not just be *a surprising probabilistic fact*? Quantum theory gives us lots of surprising facts, like super conductors and electron microscopes. Why can’t this be one of them? Arguing there MUST be communication implies arguing there CANNOT be such probabilistic behaviour. Well, why not? Combining amplitudes gives all sorts of surprising behaviour.

What they don’t do is *show the communication*.

32. 32 32 maznak

It seems that the typical use is by agreeing “if quantum state A, do X, if quantum state B, do Y”. So you instantly know what someone far away has done, possibly sooner than lightspeed communication might bring the news. Somehow I would be tempted to think that information was passed in such case by definition – because my uncertainty about something (what the other person is doing) has decreased. I know that information cannot travel faster than light, so please point my mistake to me, someone. I guess the answer is, the information is not passed from A to B or B to A, but we rather have both learned the same thing (some quantum state) in the same time.

33. 33 33 Steve Landsburg

Maznak:

So you instantly know what someone far away has done, possibly sooner than lightspeed communication might bring the news.

No, this is quite impossible.

but we rather have both learned the same thing (some quantum state) in the same time.

Not at all. You learn the (post-observation) state of your own penny; the other guy learns the state of his. Those are not the same thing.

34. 34 34 maznak

One possible use: you want to start an attack on extensive alien starfleet, from two sides simultaneously, at random moment (so that their commander cannot pump up their energy hungry shields at just the right moment). So you begin both attacks on cue from your entangled randomizers with 85% probability at exactly the same moment – should give you some edge over those evil intergalactic warriors.

35. 35 35 maznak

Steve: sure, by “learned” I meant and should have said “guessed with 85% probability of being right”

36. 36 36 Ken B

@Maznak: it’s not good to reveal our secret military plans. Plus we have a better one: we beam them all of Paul Krugman’s columns and while they are laughing — they are smart enough for interstellar travel after all — we pounce. Tell no-one.

37. 37 37 nobody.really

Let’s imagine another scheme. A and B have photopies of a list of YES and NO. They use the answers sequentially (and hence always agree). Communication?
Or they use fuzzy photopies that ahve errors a few times. Communication?

I’m interested in circumstances in which information known to Joe alters Joe’s behavior in a manner that then alters Sue’s behavior. I’ll call that communication. If Joe knows of some strategy involving photocopies, and shares this strategy with Sue, and Sue alters her behavior as a result, then I’d say communication occurred. It is less clear that any communication is occurring in the process of implementing the strategy; the scenario described does not involve either Joe or Sue gaining new information.

In contrast, both the Cat/Dog scenario and the Monty Hall scenario involve actors receiving new information and acting on the information as part of implementing a strategy. Consequently I distinguish between those scenarios and the photocopy scenario.

38. 38 38 Steve Landsburg

Maznak:

So you begin both attacks on cue from your entangled randomizers with 85% probability at exactly the same moment

We can of course agree in advance on a particular moment at which to launch our attacks. Or, if we somehow want to randomize without agreeing in advance, we could take two coins in a maximally entangled state that agree 100% of the time — no need to settle for 85%. Of course we could accomplish the same thing by generating (say by machine) two ordinary classical coins that are in exactly the same state (heads up or tails up), and carrying them with us, being careful not to flip them. When we examine our coins, they’re sure to match. No quantum effects needed.

39. 39 39 Steve Landsburg

nobody.really:

In contrast, both the Cat/Dog scenario and the Monty Hall scenario involve actors receiving new information and acting on the information as part of implementing a strategy.

Scenario One: You and I each have (perfectly ordinary classical) coins that were prepared by a referee to be in identical states (either heads up or tails up). You know there is a 50/50 chance that your coin is heads up. Now you look at your coin and discover that it’s heads up, from which you infer that mine is also. Is that communication?

Scenario Two: The cat/dog game. You have a coin that you know has a 50/50 chance of being heads up. You look at it and find that it is indeed heads up, from which you infer that if I looked at my coin from a certain angle, it has an 85% chance of being heads up and if I looked from a different angle, it has a 15% chance of being heads up. Is that communication?

If your answers to the first question was yes, then you have a very unorthodox idea of what constitutes communication. If your answer to the second question was no and your answer to the second question was yes, then you’ll have to explain why it counts as “communication” when I learn some probabilities (in Scenario 2) but not when I learn about a 100% probability (in Scenario 1). Good luck with that.

40. 40 40 Ken B

Nobody:”I’m interested in circumstances in which information known to Joe alters Joe’s behavior in a manner that **then** alters Sue’s behavior. I’ll call that communication.” My emphasis, on THEN.
Where do you get the THEN? Sue has no more information about what Joe will do than if they had agreed to always say yes. Joe’s looking at the list has not affected Sue’s behaviour at all. Joe could be dead for all she knows. Her behaviour is ‘altered’ only by the list.

Once again you are making an error I pointed out, confusing co-ordination with communication.

41. 41 41 Ken B

One of the fun things about this blog is what generates the most heated arguments. So far the biggest fight was whether a number smaller than 2 was actually 2. That one took days and spread to other blogs.

42. 42 42 nobody.really

I’m interested in circumstances in which information known to Joe alters Joe’s behavior in a manner that then alters Sue’s behavior. I’ll call that communication.

Scenario One: You and I each have (perfectly ordinary classical) coins that were prepared by a referee to be in identical states (either heads up or tails up). You know there is a 50/50 chance that your coin is heads up. Now you look at your coin and discover that it’s heads up, from which you infer that mine is also. Is that communication?

Scenario Two: The cat/dog game. You have a coin that you know has a 50/50 chance of being heads up. You look at it and find that it is indeed heads up, from which you infer that if I looked at my coin from a certain angle, it has an 85% chance of being heads up and if I looked from a different angle, it has a 15% chance of being heads up. Is that communication?

I find no distinction between Scenario One and Scenario Two regarding communication. I do not see the significance of the 85%/15% distinction to this discussion. I regard any signal other than chance as having the ability to convey information.

When each of two people learn something independently, and also then realize that the other party will (with some likelihood greater than chance) be learning the same thing, does that constitute communication? Or, as George Carlin sagely observed, when two people are in an elevator and one of them farts, they both know who did it; should we regard this as a form of communication? I know I need to improve my communication skills, but honestly, I’m not excited about attending this seminar….

Admittedly, this circumstance differs from the circumstance in which an idea is conveyed from one person’s mind to another. So I concede the difference, regardless of how anyone uses the word “communication.”

But is that all the cat/dog game is about? Here’s what I thought we were talking about:

Scenario Three: Sue hears the question “Do you like cats?” Sue rotates her coin through angle C. Her choice to rotate the coin through angle C alters the probabilities governing the appearance of the coin in Joe’s hands. Joe looks at the coin in his hands and, based on the appearance of that coin, alters the answer he gives to a question posed to him.

Scenario Three involves one person sending a message to another – even if the message contains noise, and even if it is unclear to either party who ultimately was the sender and who was the receiver.

43. 43 43 Steve Landsburg

nobody.really:

Her choice to rotate the coin through angle C alters the probabilities governing the appearance of the coin in Joe’s hands.

No, no, no, no. Joe gets heads/tails with probabilities 50/50 quite independently of her choice of angle.

If her choice could alter Joe’s probabilities, then her influence could travel faster than light. That’s surely impossible.

44. 44 44 nobody.really

The two coins agree 85% of the time — unless both you and your partner’s apparatus have been rotated through angle C, in which case they disagree 85% of the time.
Now you and your partner can each adopt this strategy: If you get the cat question, rotate your apparatus through angle C; if you get the dog question, rotate through angle D. Then examine your coin, and answer “yes” if it’s heads, or “no” if it’s tails.

nobody.really: Her choice to rotate the coin through angle C alters the probabilities governing the appearance of the coin in Joe’s hands.

No, no, no, no. Joe gets heads/tails with probabilities 50/50 quite independently of her choice of angle.

To rephrase, Sue’s choice to rotate the coin through angle C alters the probability that the coin in Joe’s hands would appear with the same face up as the coin in Sue’s hands. Joe looks at the coin in his hands and, based on the appearance of that coin, alters the answer he gives to a question posed to him.

Does this describe the cat/dog game accurately?

45. 45 45 Keshav Srinivasan

Steve, your claim that the entangled particles don’t communicate with each other may or may not be true depending on what interpretation of quantum mechanics is right. There are three basic views you can have on entanglement:

1. Non-realism: The particles are in a superposition of states until one of them is measured. This is the Cophenhagen view.

2. Non-local realism: The particles are able to communicate with each other faster-than-light and change their states depending on what angle the other particle is measured at. This is the de Broglie-Bohm or pilot wave view.

3. Superdeterminism or local realism: the states of the particles are fixed from birth, and the choice of what angle to turn the apparatus is not really a free choice at all, but is predetermined by the laws of universe. This is the view taken by a few people, including Nobel laureate Gerard ‘t Hooft, who are keeping local hidden-variables alive by denying the existence of free will.

No experiment can be performed which distinguishes which of these is correct, unless it also disproves quantum mechanics in the process.

46. 46 46 Steve Landsburg

nobody.really:

Sue’s choice to rotate the coin through angle C alters the probability that the coin in Joe’s hands would appear with the same face up as the coin in Sue’s hands.

Taking Joe’s choice of angle as given, this is correct. Remember, though that Joe does not learn this probability, and does not learn what Sue chooses. Remember also that it makes no difference whether Susan makes her observations before, after, or simultaneously (more precisely in a way that is spacelike-separated from) Joe’s observations.

47. 47 47 Steve Landsburg

Keshav Srinivasan: You are of course completely right. I think, though (and perhaps you want to correct me here) that choices 2 and 3 are fairly far outside the mainstream of physical thought (though perfectly respectable). So it might be more accurate to say this:

1) Under the mainstream interpretation of quantum mechanics, there is no communication.

And more importantly:

2) The correlations in this example certainly do not *require* communication. This, I think, is the inference that some commenters have been drawing, and it is certainly incorrect.

48. 48 48 Robert Ayers

For a conversational-tone discussion of “spooky action at a distance” I recommend the essay “Is the moon really there when nobody looks? Reality and the quantum theory” by David Mermin, Physics Today, April 1985. (If you search for the first sentence of the title, the article is the first hit.)

49. 49 49 Henrico Otto

Keshav,

A fourth possibility is many worlds, ie all the possible entanglement states exist, the question is which branch you occupy. My naive understanding is that this interpretation has trouble accounting for the right probability distribution, but that could be seen as a research issue, rather than fatal to the interpretation.

50. 50 50 Keshav Srinivasan

Steve: Yes, the traditional view is the Copenhagen interpretation, under which the wave function keeps evolving until a measurement occurs, and then there is a wave function collapse. But the most popular position nowadays is the so-called “decoherence” view, which is a kind of variant of the many-worlds interpretation.

In the classic Everett many-worlds interpretation, the entire universe is always in a superposition of states, which NEVER collapse into a given states. But this posed a problem: what causes the *appearance* of collapse? Under the decoherence view, it’s that when you have a really large number of particles, like on the scale of a human, their wave functions can become wildly out of phase, so the interference pattern becomes smeared out and it appears that collapse has occurred.

Anyway, you’re right in both of your points: communication does not occur according to mainstream thought, and it is not required to explain entanglement.

Full Disclosure: I believe in superdeterminism, which is admittedly a fringe position. As I mentioned above, it doesn’t believe in communication either.

51. 51 51 Keshav Srinivasan

Robert: That’s a classic article, but here’s an even simpler explanation of Bell’s theorem along similar lines:

http://quantumtantra.com/bell2.html

I think the polarizer angles used by Herbert, 0-30-60, are the ones Bell himself used when giving lectures to popular audiences.

52. 52 52 Harold

Keshav: has not the collapse of the universal superposition been used as an argument for God? There must be “an observer” outside the universe to cause the superposition to collapse.

53. 53 53 Keshav Srinivasan

Harold: Yes, there are so-called consciousness-causes-collapse interpretations going back to von Neumann. The way quantum mechanics works under Copenhagen is that you have to split the world into two parts:

1. The “observer” or measurement device
2. The “observed” or the particles you’re measuring

The measurement device is assumed to behave classically. The particles in category 2 are in a superposition of states described by a wave function which keeps evolving until it interacts with the classical measurement device. The question is where to draw the line. You could consider a photon to be the observed system and an atom to be the measuring device, but you can also consider the photon-and-atom system as in a superposition of states, and take a Geiger counter to be the measurement device. So there is this von-Neumann chain, going from elementary particles to Geiger counters to human beings, and we have to decide where to cut it off.

Von Neumann proved in his famous Bible of QM that regardless of where you cut the chain, you would get the same experimental results. But he reasoned that wherever you cut the chain you have things made out of particles on each side of the cut, so there’s no principled way to place the cut in the middle. So he decided that you should place the cut between the human mind and the human body, because he believed that the mind is non-physical. That was von Neumann’s interpretation, but later other people decided to place the cut between God and the universe.

Nowadays, as I said before, the mainstream position is that there is no cut, and hence no collapse. It’s just that decoherence creates an illusion that the system has settled on a given state.

54. 54 54 Harold

Keshav: thanks for the very clear explanation – very helpful.

55. 55 55 Jonathan Campbell

Steve – could you not use 100% in place of 85% in your post?

56. 56 56 Steve Landsburg

Jonathan Campbell: The laws of quantum mechanics won’t let you go past 85% (more precisely cos^2(pi/8).) See the paper for more details!

57. 57 57 Jonathan Campbell

oh yes, that make sense.

58. 58 58 Al V.

@Keshav, Thanks! Great discussion.

59. 59 59 Robert Ayers

Keshav Srinivasan:
Thanks for posting the Herbert reference. I appreciated that rotated-polarizer-errors version when I read his book, and was going to mention it along with the Mermin, but I couldn’t find the book in my library-chaos …

60. 60 60 Keshav Srinivasan

Steve, why don’t you write a post explaining Bell’s theorem and it’s philosophical implications? It seems right up your alley, considering that you have elucidated a lot of interesting arguments and proofs in your book and the blog.

61. 61 61 Steve Landsburg

Keshav: Thanks for the suggestion. I will consider it.

62. 62 62 Ken B

Steve needs write such a post as there are already good ones out there. Here is one, which does not require serious math to read http://www.upscale.utoronto.ca/PVB/Harrison/BellsTheorem/Analogy.html

63. 63 63 Ken Arromdee

This question has nothing to do with quantum mechanics and everything to do with trickery with definitions. When we are told “you perform this experiment without communication”, this is normally understood to mean that you perform the experiment without any way for one person to make inferences (at a greater than chance level) about the other person’s state.

If you use some quantum device which lets you do that, then you are, in fact, communicating in the sense implied by the context, even if the technical details of quantum entanglement mean that it is not, strictly speaking. communication.

64. 64 64 Steve Landsburg

Ken Arromdee: So if we each carry one of a pair of matched socks, and I examine my sock, discover it’s blue, and infer that the other guy’s sock is blue, do you consider that “communication in the sense implied by the context”?

65. 65 65 Ken Arromdee

Consider the clause “in a relevant way” to be implied.

If the experiment was such that I could increase my chance of success by deducing the color of the other guy’s sock, then providing a pair of socks that allow me to do so would certainly be communication. Exactly who is doing the communication (is it being done by me or by some third party who provides the socks?), and exactly when the communication is happening (is it before or during the experiment?) would depend on the details of the experiment.

Consider the hypothetical where the experiment is exactly the same, but instead of using quantum-mechanical coins, you use a computer which can watch both individuals and is programmed to turn the coins to heads or tails with the exact same probability that the quantum device would in the same situation. Is that computer communicating any information between them?

66. 66 66 Harold

I think we are stuck with the 3 choices laid out by Keshav Srinivisan: my paraphrase is spooky action at a distance OR faster than light information transfer OR total predetermination. None of them fits well with our notions of how things work. There also seems to be some breaking of the convention in QM that the protagonists are Bob and Alice. I mean, Sue and Joe? That makes no sense.

67. 67 67 Steve Landsburg

Ken Arromdee:

Exactly who is doing the communication (is it being done by me or by some third party who provides the socks?), and exactly when the communication is happening (is it before or during the experiment?) would depend on the details of the experiment.

Communication before the game is played is explicitly allowed. If you want to consider the acquisition of the entangled coins (or the acquisition of a pair of matched socks) a form of communication that’s fine — but note that all the communication takes place in advance. Once the game starts, there’s no further communication.

Consider the hypothetical where the experiment is exactly the same, but instead of using quantum-mechanical coins, you use a computer which can watch both individuals and is programmed to turn the coins to heads or tails with the exact same probability that the quantum device would in the same situation. Is that computer communicating any information between them?

Of course. What you’ve illustrated is that the outcome that is achievable without communication is also achievable with communication. So what?

68. 68 68 Steve Landsburg

Harold: my paraphrase is spooky action at a distance OR faster than light information transfer OR total predetermination.

Harold: Right. Except that “spooky action at a distance” is arguably a prejudicial and misleading characterization of Option 1; I’d rather characterize this option simply as “the correlations are dictated by the laws of quantum mechanics”. And those who opt for choice 2 ought at least to be aware of (a) how far out of the mainstream of physical thought this option is, (b) the reasons why it remains far out of the mainstream, (c) the amount of additional machinery you’ve got to buy into to make this work (pilot waves, etc), and (d) the fact that all is quite unnecessary to explain these phenomena.

69. 69 69 Ken Arromdee

What you’ve illustrated is that the outcome that is achievable without communication is also achievable with communication. So what?

You haven’t analyzed it far enough. *Why* do you consider it to be communication? If you try to analyze why it’s communication, you’d come up with something like “it is communication because after it is over, someone now has information which lets him make a deduction that increases his chance of success and which he could not make previously”. That’s what we mean when we say that the experimental subjects do or do not communicate, and it’s true in both the computer and quantum versions. It’s not relevant that the quantum example is not communication in a technical sense; saying that is like insisting that tomatoes are fruits and therefore should be sold in the fruits section of the supermarket.

70. 70 70 Steve Landsburg

Ken Arromdee:

“it is communication because after it is over, someone now has information which lets him make a deduction that increases his chance of success and which he could not make previously”

Okay, let’s run with that. Here I have a colored chip. I break it in half, give you half in a sealed envelope, and send you to a faraway place. Once you’re there, you are challenged to predict the color of my chip. You open your envelope and receive information which lets you make a deduction that increases your chance of success and which you could not make previously.

1) Are we agreed that there was some communication between us in advance of the play of the game?

2) Are we agreed that there was no communication between us during the play of the game?

3) Are we agreed that similarly, in the quantum case, there was some communication in advance of the game but not during the game?

If your answer to part 3) is “yes”, then we have no disagreements. If your answer to part 3) is “no”, then you still haven’t explained what it is about the quantum case that counts as “communication during the game”.

Note: In all of the above, I mean the word “communication” to be taken in its ordinary everyday sense, not in any special technical sense. It seems to me that in the ordinary everyday sense of the word communication, the answers to 1) and 2) are both clearly yes.

71. 71 71 Ken Arromdee

I’m not convinced that “when does the communication occur” is always well-defined. Consider some other scenarios:
– Same scenario, except that I don’t open the envelope; instead an assistant walks into the room and opens it for me.
– Same scenario as that, except that the envelope wasn’t in my possession; the assistant brought it with him (still sealed).
– Same as that except that the assistant peeked into the envelope.
– Same as that except the assistant doesn’t show me the chip; instead, he tells me the color.
– The chip is broken into three pieces. One fragment is in the assistant’s envelope and one fragment is in my envelope. He hasn’t seen either one. He walks into the room carrying his envelope, mixes up the two envelopes, and randomly picks one, not knowing which one it is. He then shows me the contents.
– Same except he has seen the one in his envelope. Still, neither of us know whether he has shown me the one from his envelope or mine.

And another scenario: Before the start of the experiment, I write out a sentence describing the color of the chip and encrypt it with a one-time pad. The encrypted message and the one-time pad are both mathematically random and provide information only when combined together; however, the one-time pad is preexisting and the encrypted message was just created. I then randomly pick the one-time pad or the encrypted message and give it to you before the experiment, not knowing which one I gave you. The other one I give to you during the experiment. You decode it.

In which of the scenarios is communication happening before the experiment and in which is it happening during? And why? Just about anything you pick here will have very counterintuitive implications.

72. 72 72 Steve Landsburg

Ken Arromdee:

Just about anything you pick here will have very counterintuitive implications.

I’m not convinced that’s true, but rather than pick through your various examples, can we agree that:

1) In some cases, we can say unambigously that there is no communication once the game begins?

2) In the case I described — I put the chip in the sealed bag in my pocket the night before the game, then wait till the game has begun before I open it — there is no communication once the game begins?

3) You have not pointed to any significant difference between 2) above and the quantum case?

If your answer to 1) is no, then your position seems to be not that communication takes place in the quantum case but that the very question is too ambiguous to answer.

If your answer to 1) is yes, we can go on to question 2).

If your answer to question 2) is that opening the bag counts as communication, then I agree that by your definition, ‘communication’ takes place in the quantum case as well. I also contend that I have never met or heard of anyone else who uses the word ‘communication’ the way you do.

If your answer to question 2) is that opening the bag does *not* count as communication, we can go on to question 3).

If your answer to 3) is that you’ve not pointed to any significant difference, then I think we can agree that you’ve given me no reason to believe there’s communication in the quantum case. If your answer to 3) is that you *have* pointed to a significant difference, I’d appreciate your being explict about what that difference is.

73. 73 73 Jim

This is an interesting exercise.

I believe it also demonstrates why the classic view of random selection as the driving force in evolution is not true, and fails even more miserably to explain the evolution of markets, cultures and say, ideas.

Outcomes are driven, and they are at least partly driven by quantum mechanics, not random success. We would not be here if it were (And I am not making a religious statement).

74. 74 74 Ken Arromdee

At first glance the answer seems to be no, but the point of my other examples is that it’s hard to decide exactly what factor would make it “no”. If the assistant walked in and told me the color, he communicated it. What about this makes it communication: the fact that he’s a human with agency, the fact that he entered the room, the fact that the knowledge entered the room, the fact that he knew what he was telling you, the fact that he told you at all, the fact that you ended up with more knowledge?

As for the bag example, I’d say as a first approximation that the information is transmitted before the experiment, but received during the experiment. Whether this counts as “communication during the experiment” is a matter of definition.

(This is only a first approximation, because questions similar to the ones I asked above still arise.)

75. 75 75 Steve Landsburg

Ken Arromdee: communication is usually taken to imply the sending of a message chosen (at least proabilistically) by the sender.

In this case, once I enter the room where the game is played, I learn two things and two things only: I learn what question I’m asked, and I learn whether my coin is heads or tails. Neither of those pieces of information can be sent by my partner, because my partner is entirely ignorant of them.

In any event, do be aware that if you’re going to claim there is communication in the quantum example, it’s going to have to be faster-than-light communication, which in turn implies that the communication can go backwards in time. Are you comfortable with that implication?

76. 76 76 Ken Arromdee

Neither of those pieces of information can be sent by my partner, because my partner is entirely ignorant of them.>/i>

This is part of what my one-time pad question was meant to elicit.

The non-quantum equivalent is that your partner doesn’t know the question (and coin), but he does know the result of encrypting it with a random one-time pad. He doesn’t know the one-time pad, but you do. Your partner transmits his result to you.

In this example, as far as the partner is concerned, what he knows is a sequence of bits that by all statistical tests is purely random. It conveys no information to him whatsoever.

When he transmits it to you and you decode it with the one-time pad, has he communicated any information?

Are you comfortable with that implication?</i<

Yes, because this communication can't produce causality problems. That is, the usual reason why we might want to be worried about faster-than-light communication and time travel doesn't apply.

77. 77 77 Al V.

For anyone still following this thread, Mark Oliver Everett, lead singer of the band eels, is the son of physicist Hugh Everett, proposer of the Many Worlds theory. Here is a Nova clip where Mark discusses his father: http://www.youtube.com/user/OfficialEels?blend=1&ob=4#p/u/41/aIP4Eydwbio .

78. 78 78 nobody.really

In any event, do be aware that if you’re going to claim there is communication in the quantum example, it’s going to have to be faster-than-light communication, which in turn implies that the communication can go backwards in time. Are you comfortable with that implication?

I think I’m more comfortable with the idea that signals can travel faster than light, or that communication can go backwards in time, than I am with the idea that logic flows from the conclusion to the premise. Our conclusions about communication – presumably a factual matter – should not be contingent upon the extent to which we can reconcile that conclusion with our preconceptions. Let’s develop theories to explain outcomes, not vice versa.

Look, the whole premise of Landsburg’s original post is that people can engage in strategic behavior that will influence outcomes remote from themselves. You can call it communication, and ponder the mystery of a signal traveling faster than light. Or you can not call it communication, and STILL ponder the mystery of Sue engaging in conduct that would tend to alter the behavior of Joe faster than light. Thus, it’s unclear to me that the “communication”/”not communication” distinction matters: the mystery abides.

79. 79 79 Al V.

@nobody.really, Remember, as Keshav explained, the idea of quantum enganglement is just one explanation. Another is that the universe is basically a big mechanical system where all interactions are pre-determined. For example, if we view time as just another dimension like the three spacial dimensions, then there is no such thing as cause and effect. Some physicist (I forget who) posited that time is that – just another dimension – and that we only perceive it as moving in a single direction because as living organisms we can only perceive time as moving in the direction of increasing entropy.

80. 80 80 nobody.really

I think I’m more comfortable with the idea that signals can travel faster than light, or that communication can go backwards in time, than I am with the idea that logic flows from the conclusion to the premise.

[T]he idea of quantum entanglement is just one explanation. Another is that the universe is basically a big mechanical system where all interactions are pre-determined.

Funny juxtaposition, this. Permit me to walk back my prior statement a bit.

I get suspicious when people evaluate a premise on the basis of the conclusions that might flow from it. But I acknowledge strategic reasons to make exceptions.

Thus, when looking for a lost object at night along a huge street, I look under the streetlights – not because I know the object to be there, but because I know that this is the only place where my searching efforts could produce any desirable result. That is, I reason from my desired conclusion (I find the object I’m looking for) to the premise that enables me to reach that conclusion (The object is in a findable location). It’s a reasonably good heuristic, assuming I have no other use for my time than to look for the object.

The concept of determinism lends itself to a similar analysis. I don’t deny the possibility of determinism (assuming it even makes sense to speak of possibilities where determinism is concerned). But I can’t conceive of a manner in which I could correctly conclude that determinism obtains – for the simple reason that if determinism obtains, then *I* don’t conclude anything, or do anything; I merely become one more instrument by which things occur. The only circumstance in which my cognitive efforts matter is the circumstance in which determinism does not obtain. Restricting my analysis to the assumption that determinism does not obtain, then, I find it more adaptive to conclude (accurately) that determinism does not obtain than to conclude (inaccurately) that it does. Again, I concede that I’m reasoning from my desired conclusion (My cognitive efforts matter) to the premise that enables that conclusion (Determinism does not obtain).

For what It’s worth, I find little harm in Pascal’s Wager, for similar reasons. That is, I reason from the desired conclusion (Good things happened to me after I die) to the conclusion that enables that outcome (I have the qualities, such as a religious faith, that enable good things to happen to me after I die). Why not secretly adopt a faith upon your deathbed? Seems harmless enough to me. But I suspect that’s a topic for another post.

81. 81 81 Al V.

That’s a great pun: “I don’t deny the possibility of determinism.” Personally, I have no problem with the apparent conflict that determinism exists at the micro level, while I act as if free will exists at the macro level. Sure, in a deterministic universe my actions are preordained, but 99.9% of the time I can “choose” to ignore that. After all, none of us have access to a computer than can predict the outcomes based on the current state of the universe.

82. 82 82 Robert Simmons

I have a much simpler solution that works 100% of the time. I always answer yes, and my partner answers yes to dogs and no to cats.

83. 83 83 Robert Simmons

I withdraw my submission.