That is correct. As soon as one party attempts to force their outcome to be heads or tails, the particles become distentangled, and the second party measures an entirely separate coin flip.
Choice does appear to be the distinguishing factor. In a paper by Weaver on “The Recent Contributions to The Mathematical Theory of Communications” he writes:
After searching for a half hour, that’s one of the two sources (both in obscure places) I can find that define information that way. In other sources I see information described as “the minimum number of bits necessary to describe the state of a system.”. The first definition would preclude the coin toss as information, while the second one doesn’t. In any case it’s strange how hard it is to find the definition of information in the context we’re discussing here.
Even the Wikipedia entry on No-Communication Theory doesn’t make it clear. They define the issue as “the theorem states that, given some initial state, prepared in some way, there is no action that Alice can take that would be detectable by Bob.” Thats an awfully specific use of the term “information.”. Anyway, I guess I can accept it now, though I will be holding a grudge for some time against physicists for not making clear their precise definition (at least in their explanations to lay persons on the internet.). 
Note that this jibe was not directed at those answering here. It’s to the ten or so physicists who wrote articles I’ve read about this issue.
If you are a light year apart there is no objective now or synchronized clocks at all. The illusion of a universal clock only holds if you are local…but let’s go back to the idealized thought experiment.
A way to think of the OP is that you don’t know if you were the first to look and just randomly got a result or if the other side forced your particle into that state. It’s only after you compare notes that you know that the two particles were entangled and that the measurement of one depended on the other. Without that communication you cannot tell if either side was dealing with an already-set particle.
Comparing notes is the transfer of information and is not FTL.
I can’t tell if this question has now been clearly answered (Half Man Half Wit has the answer).
The thing is, this scenario does not involve anything strange dealing with quantum mechanics or FTL or paradoxes. You are using particle measurements in the same way as the playing-cards-in-sealed-envelopes example mentioned in this thread. Nothing strange is happening here. The generals get perfect anticorrelation just like they get perfectly different playing cards in that example.
If you try to change the scenario such that “strangeness” was actually happening it would be completely obvious that no information is being passed.
I think the clearest explanation is the wavy graph in the “Overview” section on the Wiki about Bell’s Theorem
That is, the generals would have to measure their particles in slightly different directions, preferably 45 degrees, to get the strangest discrepancy.
(The following percentages are rough illustrations, too lazy to calculate these correctly right now)
So, their results would be only partially correlated. They would attack the same target in 20% of cases (70% anticorrelation), if they repeated this experiment many many times (conquering one planet after another).
So after a quarter century of this, attacking a new planet every month, they’d retire and reminisce about how they messed up in 20% of their conquests.
THEN they’d realize that something strange was going on. They should’ve messed up in 25% of cases (50% anticorrelation)! How is it possible that they only went wrong in 20% of conquests?? How strange! But quantum mechanics has the explanation!
This makes it clear that you only notice the strangeness afterwards!!
Anybody feel free to calculate the correct percentages!
That’s a bit simplified BTW, I could complicate the scenario a bit further to make it “perfectly strange”
The issue isn’t so much whether QM can be exploited in some way to send a specific bit, but rather why the result of a coin flip communicated via distant entangled particles isn’t information. As I explained in a previous post, the playing cards and two entangled particles are qualitatively different. The explanation lies, I think, in my last post that defines information as requiring a choice on the part of the sender.
I assume you are referring to this?
It is true entangled particles are qualitatively different from playing cards. It is NOT TRUE that they are qualitatively different in the specific way you use entangled particles in your example.
You are using entangled particles to send information entirely classically and normally.
(In fact I am still doing the same in my scenario, remember I simplified that a bit too much, maybe I should fix it to show how entangled particles are REALLY qualitatively different.)
It just seems to me that it should matter HOW entangled particles are qualitatively different, I’m not seeing where that (accurately/clearly) enters into your question.
Why can’t you have synchronized clocks if you are a light year apart?
The choice there is, I think, among the number of possible messages still consistent with a signal. Suppose you have some fixed number of possible messages you could send, such as ‘the British attack by land’ and ‘the British attack by sea’. As long as you haven’t received any signal, you have no information about the attack; as soon as you get one bit of information, say by counting the number of lamps hung in some bell-tower, you know exactly what the message is—that is, that information reduced your uncertainty to zero.
But there are cases where a given signal only partially reveals the message; then, each element of the signal—think of something like a series of light pulses, or a stream of letters, or what have you—will further reduce the number of possible messages you could be receiving, thus decreasing your uncertainty about what message is being sent to you, and reducing the amount of choice between possible messages consistent with the signal. A highly unlikely, thus unexpected signal-element will then serve to constrain the message more, reduce your uncertainty about the message by a greater quantity, and highly limit your choice—and thus, carry lots of information. (This is often called the ‘surprisal’ of the signal.)
The information content of the whole message is then the number of bits to specify it fully, to completely eliminate choice, and thus, the freedom of choice you had before. In the case of the British attack, you had a choice between two alternatives, and hence, the message has one bit of information.
As for the information transfer in your scenario, perhaps it helps to think about it in the many-worlds scenario: there, the creation of the entangled pair creates two ‘worlds’, one in which A has spin up, and B has spin down, and the other in which things are the other way around. Upon making a measurement, each general then just learns in which universe they are; thus, no information is exchanged between them, and all information that is transmitted is transmitted from the source of the particles.
Sorry, not buying it. There is (or can be) as much a concept of “now” between two individuals separated by arm’s width as two individuals separated by a mile, the diameter of the Earth, the distance from Earth to the moon, a light-year, and beyond. Being local has nothing to do with it. How accurate you can be about that shared moment of “now” may have something to do with how local you are, but even at a light-year or more an understanding of the physics involved with how you got there can allow you to account for things like time dilation and delays in communication. Two people can synchronize watches, move apart, and take whatever means necessary to be reasonably confident (as confident as they need to be, to within whatever margin of error they deem acceptable for the experiment) that their watches remain synchronized, and then be “reading” the clocks at the same time, coming up with the same time (each having access to the same information) but without being able to communicate. That’s the point I’m getting at. It’s an analogy. If you get hung up on how certain they could be of a shared moment of “now,” it could just as easily be the measurement of time with respect to the orbit of a planet around a star placed exactly midway between them instead of a watch as the “synchronizer.” It’s not meant to be a perfect analogy, only an example of how two people without the ability to communicate can nevertheless have access to the same information at the same moment in time and then make a decision off of it at the same instant—could even know what decision the other will make based off previous communication—but still not be “communicating” at faster than the speed of light, much less instantaneously.
ASL, I’m not sure I’m following you, but are you arguing that two events can be said to be simultaneous for two arbitrary inertial observers? That statement contradicts Special Relativity if the observers are moving with respect to each other. Here is Wikipedia’s explanation.
I don’t think so. Take points A, B, and, C. Put B midway between A and C. Flip a light on at B. A and C both receive news that the light has turned on at B at the same time—or merely “about the same time” if you prefer. Either way, A and C both can make a pre-planned decision on what to do when the light turns on—and “know” that the other will also make a decision, and what that decision will be—and both A and C “know” what decision the other will make (assuming they go off what was previously agreed upon) just based off the light from B. Nothing has been communicated from A to C, and yet both A and C “know,” merely in the time it takes for light to travel half the distance between them what the other will do.
And of course when I use “know” here, I mean to extent that we can predict/anticipate what anyone will do based off a previous agreement (a previous communication, if you will), not in the sense of metaphysical certainty. Because, again, they can’t communicate FTL, they can however receive information from an intermediate source at “about the same time” and make a pre-planned decision off it.
Does that break physics?
ETA: And if it does break physics, than how does two people being "local"to one another (at arm’s reach) break physics any less?
Do you want these events to be exactly simultaneous with each other, or merely ‘about the same time’? The second option is achievable, but the first one is not.
The second will suffice, just so long as A and C can infer each other’s decisions faster than if C were to wait for a signal from A or vice versa.
And, yes, I know how trivial that all is. At least I hope it’s trivial. The idea was to give an example of making a decision under circumstances similar to the OP that seemingly involves faster than light information sharing, but really is just one party inferring what the other will do based off a pre-arranged signal with no means of transmitting new information FTL.
This is just the Einstein’s Train thought experiment. Some observers will see A and C receive the signal at the same time and some won’t. It’s described in the wikipedia article.
Yes you broke physics. Please put it back together before you leave.
Local observers have the same issue but the amount of discrepancy is vanishingly small if the observers are not at cosmological distances.
So it seems like you’re equating, at least in some sense, a reduction in certainty with “choice.” And while a conscious choice between two alternatives reduces uncertainty, so does the result of a coin flip. The information entropy of a coin flip and a conscious choice of heads or tails are both 1 bit. We know Alice receives one bit of data upon measuring her particle’s spin and that her uncertainty drops from .5 to 0. That is definitely information, which leaves the only other possible alternative - which is that it didn’t transfer FTL.
I can begrudgingly accept that since the particles required colocation to be entangled, the ability to communicate information over that distance didn’t happen FTL. One of the reasons I didn’t accept it at first is partly because other posters maintained that information wasn’t transferred, rather than that it wasn’t transferred FTL. When physicists, at least internet popularizers of physics, make the argument for why information can’t transfer FTL, they never mention the colocation issue - they only mention the disentanglement issue. Please correct me if I’m wrong on any of the above.
This is not the train thought experiment. I don’t care at what time observers D/E/F or even A and C see someone receive the signal. I guess, in a sense, you could think of this as a single observer at B sending a signal to A and C at the same time (whatever A might think of C and C might think of A), not personally observing the arrival at either, and yet nodding with satisfaction at the knowledge that both A and C will act on the signal according to pre-arranged plans. A and C both act off a signal from B in a way that suggests communication between A and C, but does not actually involve transfer of information from A to C, only the illusion of it due to the pre-arranged plan (which did require communication between A and C at some point, but was not done faster than light).
Okay, so I don’t get accused of just going “nuh uh!” in response to criticism (and I wouldn’t blame you if that’s what you were thinking), I’ve got my definitive scenario to try and distinguish what I’ve been driving at about apparent (but not actual) “simultaneous” or FTL communication, and why, in spite of the (apparently) deficient explanations I’ve offered so far, it’s not a violation of special relativity:
Scenario: Johnny Rocket will be the first man on Mars. Three women have already been to Mars before him (and returned, to great acclaim), but that’s beside the point. Anyway, prior to leaving for Mars, he got together with his buddy, Jane Newscaster, and his other buddy, Shannon Physicist. The three of them have determined that on the date and time Johnny is to land on Mars, it will take five minutes for light to travel from Earth to Mars. Based on a pre-arranged script, they have worked out the following sequence of events and communication, with t representing the time in minutes.
t=-270000 Johnny, Jane, and Shannon come up with a script and ensure Johnny has a copy of the script packed along with all the other stuff for his EVA
t=-259200 Johnny blasts off in a rocket bound for Mars
t=-1000 Jane and Shannon, in anticipation of Johnny’s landing, start a timer on their watches. It’s a count up timer.
t=-995 Jane and Shannon hit pause on their timers (so it’s paused at five minutes)
t=0 Johnny lands on Mars, rattles off his motivational speech, and starts his count up timer at the conclusion of the phrase “And a Happy New Year!”
t=1.5 Johnny pulls out the script (with time annotations) he was given prior to his departure and says “Yes, like a billion dollars landing in my bank account.”
t=2.5 Johnny continues reading from the script, “I’m going to Disney World!”
t=5 Jane learns Johnny lands on Mars and hears the phrase “And a Happy New Year!” and resumes her count up timer. Being a newscaster, she has of course inserted her script on the teleprompter.
t=5.5 Jane says “Wow, Johnny, we’re all so glad you made it. Now please standby for our science advisor, Doctor Shannon Physicist.”
t=6 Doctor Physicist (who, being a Physicist has memorized the full script) says, “Johnny, is the ansible that we worked on and patented together with Jane working?”
t=6.5 You, sitting in the studio and listening with Jane, Shannon, and half the world hear Johnny say “Yes, like a billion dollars landing in my bank account.”
t=7 Jane says “That’s great, Johnny, what are you going to do next?”
t=7.5 As if that weren’t enough, you, above the uproarious cheers of the studio, hear Johnny say “I’m going to Disney World!”
t=8 The CEO of Disney puts in a call to his or her on-call corporate lawyer to determine whether they should sue for trademark infringement, or just let it slip and think of it as free advertising. “Why not both?” the lawyer replies.
t=10.5 Johnny hears “Wow, Johnny, we’re all so glad you made it. Now please standby for our science advisor, Doctor Shannon Physicist.”
t=11 Johnny hears “Johnny, is the ansible that we worked on and patented together with Jane working?”
t=12 Johnny hears “That’s great, Johnny, what are you going to do next?”
t=12.1 Johnny jumps for joy in the diminished Martian gravity, though weighed down by his suit.
t=? After a long, drawn out legal battle, Johnny is broken and penniless as Disney has taken all his assets and it still isn’t enough to feed the Mouse. Back on Earth, looking up at Mars through his child’s telescope, just before dawn and waiting for the corner pawnshop to open, he wonders, was it worth it?
/Scenario
Did Johnny Rocket and Doctor Physicist just communicate at faster than the speed of light? No, of course not. Does the above scenario contradict special relativity? No, though it helps that you, sitting in the studio, heard Johnny respond to Jane and Shannon at almost the same time they did, the precise simultaneity of the event is not important. Obviously you heard it some fraction of a second after they did, even ignoring relativistic effects, just due to the speed of sound being less than infinity. Even if you weren’t in the studio, but you were in a colony on the Moon and heard it some seconds after they did (and heard them going out some time later too) it wouldn’t matter. The point is, Jane, Shannon, and Johnny, through prior communication at equal to or less than the speed of light, created the illusion of faster than light communication (not even the illusion of simultaneous communication, just faster than light) based on following a pre-arranged script. It didn’t have to be watches or time pieces or Johnny’s initial radio communication that set the script in motion, it could have been the orbit of the four largest moons of Jupiter or myriad other (relatively) mutually observable phenomena that set the plan in motion, and they didn’t even have to see those phenomena occur at the same time, they could have just done the math and accounted for the delay in light traveling from Jupiter to the Earth vs Jupiter to Mars and it still would have worked, just been a little trickier.
And if all that strikes you as trivial, albeit contrived and more than a little convoluted… QED
I’m not saying anything about ‘conscious’ choice or the like. Think of it more in terms of options: before receiving any information, say you have four options—
[ol]
[li]The British attack by land, at night[/li][li]The British attack by land, during the day[/li][li]The British attack by sea, at night[/li][li]The British attack by sea, during the day[/li][/ol]
You have four options—four choices. To single out one of them requires log[sub]2/sub = 2 bits of information. Hence, the choices you have determine the information content of the message.
Before you receive any bit of information, you’re maximally uncertain about the message (your uncertainty is, in this sense, equal to two bits). If you receive the first bit of the message, your uncertainty is reduced—say, you know that the British attack by land, but not when. You still have a choice between two options, so still an uncertainty of one bit, so a message needs to carry one bit of information to eliminate any residual uncertainty.
This is exactly the sense in which your scenario is equivalent to that with the two cards in sealed envelopes—there exists a story according to which the information was just present from the beginning, i. e. from the creation of the entangled particle pair, and there’s no way to operationally distinguish whether that’s the true story without resorting to classical communication at sub-light speeds, which makes the point moot.
It should be noted that two particles need never be in the same place in order to entangle them, since you can swap entanglement between different particles. I. e. you might create an entangled pair of photons, then perform an operation on one of the photons and, say, an atom, which leaves the atom and the other photon entangled, but disentangles the first photon. But of course, this can only be done with particles in the forward light cont of the photon creation event (which only means that photons can only be transported at the speed of light).
It’s not, but it also doesn’t really do what you want it to do (if I understand you correctly). The scenario only works out that way in a specific reference frame. It’s not a problem to synchronize clocks within one reference frame, but once you get to relatively moving frames, synchronization won’t be given anymore.
Take this animation: each row of clocks are synchronized with respect to a co-moving observer; but, viewed from the frame of the ‘bottom’ clocks, the clocks of the ‘moving’ reference frame won’t be synchronized. The scenario is symmetrical: from the point of view of the ‘moving’ reference frame, i. e. from that of a co-moving observer, the clocks of the ‘stationary’ (with respect to you) reference frame will fail to be synchronized.
If that doesn’t help, I think it would be more effective if you opened up a new thread to discuss these issues.