Why does this matter? Does anybody seriously question whether the basic math can work? So somebody found a nice parallel between pilot wave theory and another physical phenomenon, but then the parallel wasn't as strong as thought. This experiment is the equivalent of arguing that light isn't a particle because your tennis ball doesn't bounce off the wall the way you thought it would.
When I saw the droplet experiments, I thought "that's cool, but it doesn't prove anything about pilot wave theory because the arguments are over much deeper things than what this is demonstrating". Debunking it is just as meaningless. The people who actually know about this stuff are arguing over determinism and non-locality and what not. I thought oil droplets are just a nice way to introduce people to the concept.
Disclaimer: I don't really know anything about any of this
It matters because the theory in this case wasn’t that both light and tennis balls behave like a particle. It was that light behaves like a tennis ball. As such, demonstrating that tennis balls succeed or fail to display certain light-like behavior is certainly an important result.
So, the most controversial aspect of pilot wave theory is the idea that a classical system can reproduce some phenomena considered only to arise in a quantum one. The 2006 result was important because it appeared to definitively prove a classical system could do just that, and for one of the most famously “weird” quantum results. How accurately it correlated with a hypothetical pilot wave based quantum reality wasn’t really relevant. And if the original result was important, then the failure to reproduce it is also important.
More generally, scientists can argue about theory, mathematics and the “deep” stuff until the cows come home. But what actually advances science is experiment. It may not always be the most glamorous or exciting work (CERN notwithstanding). It can be an expensive, years-log slog to add a single negative data point against an idea a theoretician dreamt up in an afternoon, and which they’ll dismiss as irrelevant, or avoid by tweaking a single equation. But it’s, quite literally, the part of science that gets results.
One excercise that is fun to do: reduce the Schrodinger equation by splitting the real and complex parts, the figure out how to build a damped spring system that can support the wave. My interpretation of quantum mechanics is that everything is springs and dashpots in the end.
This is great, I think I'm going to explain it using your method from now on.
Edit: I love that there's a segment of people in the QM community approaching these "very serious" thought experiments like Schrodinger's Cat (as the classic example), instead using absurdism to produce equivalent but blatantly ridiculous results. Like the Surrealist reactionary art movement but with the often insane results QM produces. Sometimes I think string theorists need a group kind of like this too.
My favorite of these types of bizarro QM communities is that of the "holographic fractal" universe. Nassim Haramein[1] being one of the popular figures of this movement. If you're willing to sift through the mysticism, the r/holofractal subreddit has some interesting ideas to chew on during an otherwise dull lunch break.[2]
Well, I think the opposite result would have been very interesting/surprising. So I think it's a good experiment, and it's good to publish negative results.
The subhead seems a tad sensationalist. If interference had been shown, it would have suggested strongly that this can happen at the smaller scale as well, and that it didn't is probably disappointing for those that hoped to show it in the analogy. Not sure how it "crushes" those theories.
HN users asked for results of experiments that "tried but failed to contradict the null-hypothesis", not "tested something not related to null hypothesis and claimed that it contradicts it". That's what I think the OP meant, don't know much about QM either.
But still, someone had thought this question and experiment, if they published how it was done and the results others that have same question can look at it, decide to redo it but in a different way or not waste the time doing it again.
And we have an answer for a question, I assume if the result was different then the reaction from OP would be different,
So.you are essentially saying that that oil droplet on water analog cannot be treated as an analog computer (in every sense of the word) for pilot wave theory?
> Unsustained by the particle or droplet, the wavefront disperses long before reaching its slit, and there’s no interference pattern. The Danish researchers verified these arguments with computer simulations.
Wait, what? From what I've always understood, the math behind de Broglie-Bohm interpretation results in the same exact results as the Copenhagen interpretation. It shouldn't be possible for any "computer simulation" to disprove it, by definition.
This article feels 1) pointless and 2) like it has an agenda. Oil droplets are a macro-scale approximation of something on the particle level where we already know the math works. This doesn't disprove anything, any more than doing experiments with rubber sheets and basketballs lets you disprove the general theory of relativity.
> crushing a century-old dream that there exists a single, concrete reality.
This is just sensationalist, cheap journalism. I expected far better from Quanta Magazine, and I'm disappointed in them. I've enjoyed many of their articles in the past, but I'm not sure I can trust them editorially any more if they print something so obviously incorrect as this article.
If you read all the way to the end, de Broglie-Bohm is discussed. I think the point is that the simpler, original pilot wave theory, which was never fully nailed down, is disproven.
correct, and the Broglie-Bohm uses an abstract amplitude wave just like copenhagen - the only difference is in copenhagen the result auto-magically appears, in-toto, when it is "measured" (¿), and in Broglie-Bohm the particle really exists the whole time and travels the whole path mapped out by what the abstract amplitude wave specified.
> Wait, what? From what I've always understood, the math behind de Broglie-Bohm interpretation results in the same exact results as the Copenhagen interpretation.
The de Broglie-Bohm interpretation is not the same as the pilot-wave theory, which was never fully fleshed out. de Broglie-Bohm is valid and makes the same predictions as the standard interpretation, but as I understood it, has never been generalized to the relativistic versions of the standard theory. That is, there is no de Broglie-Bohm version of quantum field theory.
This is discussed in the article; the de Broglie-Bohm interpretation relies on a global pilot wave, which has non-locality issues that pilot wave theory hoped to avoid.
> It shouldn't be possible for any "computer simulation" to disprove it, by definition.
Here I believe they are disproving the idea that the oil droplets riding the pilot waves cannot result in the double-slit interference pattern, using standard fluid mechanics (which appears to be Tomas Bohr's area of expertise).
> The de Broglie-Bohm interpretation is not the same as the pilot-wave theory, which was never fully fleshed out.
Most contexts (https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory) define pilot-wave theory and the de Broglie-Bohm interpretation as the same. de Broglie himself also proposed a specific pilot-wave theory that is not valid (see article). When referring to a "pilot-wave" theory it is helpful to state specifically who the author is in order to resolve any likely confusion, which this topic usually seems to involve.
> has never been generalized to the relativistic versions of the standard theory
>This is discussed in the article; the de Broglie-Bohm interpretation relies on a global pilot wave, which has non-locality issues that pilot wave theory hoped to avoid.
Isn't it the other way round? Pilot-Wave theory having issues with non-locality that de Broglie-Bohm hoped to avoid?
Bohm's pilot wave theory is interesting to me not because it is so intuitive or tasteful or something, but because it works without sacrificing realism, and thus demonstrates that the Cophenhagen interpretation (neither local nor real) claims strictly more about the nature of the universe than is required by the evidence we have. Nonlocality is established by experiment, non-realism is not. In my experience, this tends to be underappreciated (or I'm misunderstanding - please teach me if so).
I personally favor epistemological interpretations, in which the wave function models our knowledge, and the universe operates via an as-yet-unknown dynamics. Wave function collapse on measurement isn't weird anymore if the wave function represents your knowledge of the system. Thinking about it this way makes "shut up and calculate" work nicely in my head.
> but because it works without sacrificing realism, and thus demonstrates that the Cophenhagen interpretation (neither local nor real) claims strictly more about the nature of the universe than is required by the evidence we have
Nicely put!
> Wave function collapse on measurement isn't weird anymore if the wave function represents your knowledge of the system.
To me it is intuitive if you consider that the wave function of the small entity is interacting with the much larger (and more specific) wave function of the observing apparatus. I never understood the mystical aspect with which this was treated in the typical explanations of the Copenhagen interpretation. And I would also appreciate the guidance of someone with a better understanding of the physical theories, if my stated perspective is confused.
It has no effect on Bohmian mechanics because it posits a real wave function. PBR rules out most "psi-epistemic" models where the wave function represents only our ignorance of the system, and not some fundamental, real property of the system.
>I personally favor epistemological interpretations, in which the wave function models our knowledge, and the universe operates via an as-yet-unknown dynamics.
Would this not be a 'hidden variable theory' of the type that is ruled out by Bell's theorem?
There is recent research on photons (rather than bouncing oil droplets) that backs up the Bohmian interpretation. "Experimental nonlocal and surreal Bohmian trajectories" http://advances.sciencemag.org/content/2/2/e1501466
I am not sure if the different QM interpretations are only a matter of taste in terms of all predictions. These surreal trajectories are seen as nonsense under the Copenhagen interpretation.
I don't think this is all that surprising to anyone. The "pilot waves" in the oil bath aren't superluminal, so of course they don't correspond with perfectly QM pilot waves, ie. they will only correspond in scenarios where the non-locality doesn't matter.
Edit: the article actually agrees with this, so it's hyperbolic all the way through except this critical passage:
> In a quantum reality driven by local interactions between a particle and a pilot wave, you lose the necessary symmetry to produce double-slit interference and other nonlocal quantum phenomena. An ethereal, nonlocal wave function is needed that can travel unimpeded on both sides of any wall.
1. Theory X hypothesizes Q
2. Phenomenon Y models theory X
3. Phenomenon Y does not demonstrate Q
Surely there would be an insurmountable burden of proof on 2. Similarity does not mean identical. For any Y claiming to be the same as X, why can't it be rebutted with a "No it isn't" Proving that they are the same would be a different thing altogether but if as the article suggests X is not fully defined, it strikes me as impossible to prove. It just ends up in the not-falsifiable bin.
That's a fair observation. Though, I think the thought experiment to about the distance between the two slits as irrelevant to QM more concretely disproves the pilot wave theory.
Most physicists when asked about QM will just say that this is a useful model to predict the outcomes of experiments. In fact the most successful model, ever. The magic that happens in the middle is currently untestable and thus uninteresting beyond philosophy.
The problem with determinism is that it introduces more complexity to the model without improving any accuracy. Moreover, it doesn't help us predict the outcome of any experiments.
Even if this experiment was successful, who cares? Does it change the math or predictions? Science works in a very simple way. We have evidence about how the universe works. We make models to explain that evidence. The models also make predictions about new evidence that we would expect to see. New evidence appears and either confirms or limits the domain of the model. Basically nothing but gravity has limited the domain of QM.
> Though, I think the thought experiment to about the distance between the two slits as irrelevant to QM more concretely disproves the pilot wave theory.
This sort of experiment does not disprove pilot waves.
> Science works in a very simple way. We have evidence about how the universe works. We make models to explain that evidence. The models also make predictions about new evidence that we would expect to see. New evidence appears and either confirms or limits the domain of the model
This is a very anemic view of the scientific process. Scientific theories have predictive and explanatory power. You described the process covering only the former, but the latter is critical for advancing theory.
For instance, without Bohmian mechanics John Bell probably would never have developed Bell's Theorem and all the subsequent no-go theorems which have dramatically improved our understanding of quantum foundations.
Theories that provide a mental framework for thinking about problems guide you in devising new experiments. Theories with no explanatory power provide no meaningful framework within which to devise new experiments.
The whole value of pilot wave theory was that it was an interpretation of QM in terms of things that behaved like ordinary macroscopic particles and waves. Given that ordinary particles and waves don't actually behave like that, there's absolutely no reason to prefer pilot wave theory over simpler, more direct interpretations of QM.
I think your whole characterization of pilot theory's value and its relation to other interpretations is incorrect.
Firstly, it's primary value is that it's an ontological interpretation, meaning it preserves realism where most other interpretations sacrifice realism. The motion of its beables has nothing to do with this.
Secondly, pilot wave theory still requires the fewest number of assumptions, roughly on par with Many-Worlds, which means it's axiomatically simpler than other interpretations.
Whatever you mean by "simpler", its not a form of simplicity that actually matters when gauging plausibility of a theory.
I see many-worlds as a strict subset of pilot wave theory, since the pilot waves behave in exactly the same way as a many-worlds wavefunction. Adding a layer of particles-guided-by-the-waves on top of that is an extra complication that can only be justified (if at all) in terms of the intuitive appeal of their resemblance to macroscopic physics.
(There's an argument of avoiding nonlocality/spooky-action-at-a-distance which I find specious: the particles are indeed localised but they don't actually play any significant role in determining behaviour. The pilot waves are doing all the work in the theory, and they have all the usual entanglement/interference/... behaviour (as they must, in order to be a correct theory of QM)).
> Adding a layer of particles-guided-by-the-waves on top of that is an extra complication that can only be justified (if at all) in terms of the intuitive appeal of their resemblance to macroscopic physics.
This "Bohmian mechanics is Many-Worlds in disguise" is simply false [1]. The axiomatic basis is completely different, and this is apparent because with Bohmian mechanics you can easily derive the Born rule, and as a result, it also makes a new prediction that isn't allowed in typical QM, quantum non-equilibrium [2]. Deriving the Born rule with MWI is a hotly debated open problem.
> This "Bohmian mechanics is Many-Worlds in disguise" is simply false [1].
Saying "clearly" a lot does not convince me, and seems to be all that paper does.
> The axiomatic basis is completely different, and this is apparent because with Bohmian mechanics you can easily derive the Born rule, and as a result, it also makes a new prediction that isn't allowed in typical QM, quantum non-equilibrium [2].
You've contradicted yourself: a quantum non-equilibrium condition would be one that did not follow the Born rule. Excluding quantum non-equilibrium requires an additional rule and looks to be much the same problem as deriving the Born rule under MWI. Were quantum non-equilibrium to be observed, that would be major evidence that our current understanding of QM is wrong; however, by the same token, our non-observation of it must count as evidence against a theory that predicts it.
> pilot wave theory still requires the fewest number of assumptions, roughly on par with Many-Worlds, which means it's axiomatically simpler than other interpretations
Isn't the most common complaint about pilot-wave that the wave corresponds to normal QM and the pilot is a superfluous detail? I would not pick minimalism as one of its strengths.
> I would not pick minimalism as one of its strengths.
Minimalism is one of its strengths. The type of objection you raise is a fundamental misunderstanding of both pilot wave theories, and what "minimalism" actually means when it comes to selecting among competing theories.
only benefit of "Pilot Waves" are that they're intuitive and "humane". This hypothesis doesn't make any falsifiable predictions so far, only has lots and lots of very complex math.
It is mostly popular among people who want their physics to be visual and understandable to our scale intuition.
With this it basically drops only thing which made it attractive.
I'm a bit sad that they couldn't reproduce the double slit interference pattern. I'm still holding out hope that we'll eventually develop a model of reality where the apparent indeterminism of quantum mechanics can be explained by currently unobservable interactions in higher dimensional space (such as the space described here: https://www.quantamagazine.org/physicists-discover-geometry-... )
What you're describing has been desired by many (including Einstein). However, John Bell more or less proved it impossible[0] in a landmark, sweepingly general result. He would have won a Nobel for it if he had lived long enough.
On the other hand, if you are willing to accept superluminal messages and also unobservable mechanics, there is always the pilot wave interpretation[1]. The fluid analogy is disappointing to see go but pilot wave theory lives on.
Thanks for the link to Bell's Theorem (I recalled there being a result like that, but didn't remember the details of it). If the hidden variables really are in a higher dimensional space, then maybe superluminal communication (in our observable dimensions of space) isn't off the table either? But that comes with its own can of worms that would have to be taken care of as well.
If you give me both sides of a superluminal telephone I can use it along with special relativity to set up a time paradox. If I only have one end of the phone, or if I can't have a phone at all (not all apparently superluminal interactions allow signaling) then it's considered an undesirable trait but not paradoxical.
The order of events is fair game to reverse so long as they are far enough away from each other that one couldn't have caused the other. The order of pairs of events like that reverse all the time. It's only a time paradox if you can actually do something paradoxical, like killing your grandfather.
Here is an article that goes in to the detail[0]. In so many words, you can use the superluminal telephone to transmit information to your own past. In essence, there is a certain amount of freedom in the simultaneity of events that is well-known to exist (having been experimentally verified). You can abuse it to create time paradoxes if and only if you can send messages faster than light - without FTL it is a curiosity that seems strange to some but otherwise doesn't upset anything.
> On the other hand, if you are willing to accept superluminal messages and also unobservable mechanics, there is always the pilot wave interpretation[1]
All quantum interpretations have superluminal characteristics, but that's not the same as superluminal messaging/signaling.
I hold out some hope that the Holographic Universe principle will prove true and tractable, and in the holographic isomorphism there will still be some profound sense in which two entangled photons still somehow locally share a quantum qubit prior to disentanglement.
Don't be fooled by "local" in there; all non-locality results in 4D spacetime would remain true, because of course they have to. It would be "local" in an isomorphism that will be extraordinarily counterintuitive and probably never really be something anyone can "visualize".
But, if this did pan out, there would be a reasonable sense in which the Copenhagen interpretation would have something physics-al about it (as in, grounded in physics, not necessarily "physical" in the traditional sense), where it wasn't in fact "action at a distance". I for one have no problem with the universe creating probability distributions and then randomly picking a result, as some seem to. (The Universe May Do As It Damned Well Pleases. It's true that a good sense of aesthetics has given us a lot of power up to this point, but "I don't think that's very aesthetic" is not a very strong argument. I'll give it more than 0, but not much.)
So, pilot wave theory remains a strong intuitive model, by confirming an inability to perfectly predict the future state of a system of quantum events.
I don't understand why non-locality is a problem. Fields are non-local. If particles are point-like, fields are volume-like and permeate all of space. Problems like spooky action at a distance aren't really problems if there is no distance from the field's point of view.
But it's still considered one field, not many individual fields at each point. That's why I called it volume-like. The electric field of the universe doesn't have a position. It has a volume.
I guess I'm arguing it's more a change of the field, not something propagating in it. Faster than light restrictions do not apply to space itself which, e.g. can expand faster than light. The electric field is a property of space. It's strength and properties do not depend on spacial coordinate.
When two particles are entangled, maybe instead the field is 'twisted/warped' at those particles. Entangling particles alters the field, not the particles.
Has anyone done the double slit experiment with the long wall before the slits? I'm not entirely convinced it still works unless it has been demonstrated.
All the paradoxes disappear if we use Quantum Field Theory instead of Quantum Mechanics. I would really like someone with deep knowledge on Quantum Theory to explain if something is wrong with a theory that otherwise makes a lot of sense to me. A good read on the topic is the paper "There are no particles, there are only fields" — https://arxiv.org/pdf/1204.4616.pdf
Surprisingly, physicists are very much aware of the field nature of all "entities" in the world, having invented QFT themselves. Even more surprisingly, popular journalistic explanations simplify things considerably, making it seem that the thoughts of physicists are much less refined than they really are. To complete the trifecta of surprises, in the refined thought process of us physicists, using QFT, many problems and paradoxes of interpretational nature or otherwise remain with quantum theory that need to be resolved.
Regarding "in the refined thought process of us physicists...many problems and paradoxes...remain".
It seems to me that a true paradox in physics must mean a theory provides at least two different incompatible predictions for a given physical situation. Given the success of the Standard Model, that surprises me. Do you have an example?
The use of the word "paradox" in physics usually means any conclusion that is considered unacceptable or unnatural for any reason, even intuitive. In logic there are no paradoxes, only contradictions. As far as we know there aren't any contradictions in the standard model, but there are plenty of suspicious conclusions that we would like to see resolved either with greater understanding or a better theory.
I did not read the whole thing, but I skimmed it. Its not a new-results type of paper. It is just collecting the works of other people and being careful about the language used. I have grappled with some of these issues/formalism/language in my own research as have many other physicists over the decades. The purpose of this paper is to argue that "Textbooks need to reflect that fields, not particles, form our most fundamental description of nature. This can be done easily, not by trying to teach the formalism of QFT in introductory courses, but rather by talking about fields, explaining that there are no particles but only particle - like phenomena caused by field quantization."
Notice that he is talking about teaching/talking/explaining. It is a for-teachers paper, not a for-researchers-working at-the-cutting-edge-of-fundamental-physics paper. And its nothing new. I taught an introductory level course on quantum mechanics recently and I refused to use the words "particle" or "wave" at any point in the course because I think they are confusing. I talked instead in terms of wavefunctions which is just an easier word for fields - at least as far as undergraduates are concerned.
I did condensed matter Physics, where QFT isn't that essential, but from the QFT I did study the "it's all fields" way of looking at it came out quite naturally (well, how natural something as profoundly weird as QM can be, can be discussed..). So I fail to see how this can be considered particularly controversial.
I mean, if you want something controversial and non-mainstream, take the subject of this article, pilot wave theory.
PS: Do you have suggestions on a good introductory QM study materials (textbooks, online stuff,...) that emphasize the fields viewpoint?
You can say that the only thing that exists is the quantum wave function, as what basically this paper says (particles are epiphenomena). That is basically hard-line Everettianism e.g. many worlds. There are still problems. QFT does not explain gravity very well either.
The paper claims "it's neutral on the interpretations" - it is not.
You have the most senior research professor of physics at caltech admitting there are problems still - there are of course physicists that insist they have the correct answer or interpretation - the hard part is convincing enough physicists to agree with them, which they universally do not agree.
> You have the most senior research professor of physics at caltech
What is the ranking of seniority of research professors at Caltech? Are you implying that a research professor is somehow better than a “regular” professor?
I’m trying to understand if “most senior research professor of physics at caltech” is supposed to mean something different from “professor of physics at caltech”.
that's what it claims, but that is the only way to make sense of "particles are epiphenomena" + "Thus the Schroedinger
field is a space-filling physical field whose value at any spatial point is the probability amplitude for an interaction to occur at that point."
it is saying that the only thing that exists is the quantum wave function
the only theory with a hope of credibility/coherence that says the only thing that exists is the quantum wave function is many worlds.
I was thinking about the double-slit problem the other day, and was trying to make connections to any other phenomenon that exists in the natural world and I think I came up with one.
In conditional probability theory, there exists something called the boy or girl paradox. The paradox shows that the likelihood of an event can be drastically affected by how you know even seemingly innocuous information. I think that observation of the atoms passing through the slit is affecting the search space for the other atoms in such a way that we currently do not understand. This observation while seemingly innocuous has a drastic affect on the distribution which would explain why we see such confounding results. It follows the same logic as this other naturally occurring phenomenon so I think its an avenue at least worth exploring.
An example of the paradox would be if I told you that my neighbor has 2 children and at least one of them is a boy. If I asked you what the probability that their other child is a girl, normally the result would be 2 / 3, but if I know one child is a boy because I spot him in front of a tree then the odds his other child is a girl drops to 1 / 2.
I think the problem with QM isn't the fact that the probabilities are confusingly calculated. It's that there's no underlying mechanism.
Imagine I flip a fair coin. The odds of you guessing it correctly are 50%. In your mind, you know it's probabilistic. Simultaneously, you imagine that if you had more information you could get it right more than 50% of the time. Maybe if you new the force or the initial velocity, that'd help. The thing with QM, there's no more information to get. You can't get better than 50%, ever. It's basically magic. The problem with any deterministic model is that it adds more complexity than just assuming magic and we can't test any of the predictions of current deterministic models so why bother.
That's a key point - classical randomness is still causal.
QM effectively seems to be non-causal - or at least, much less causal.
Tidying this away under the heading of "It's probabilistic, let's just do the math and not worry about why" seems to be ignoring some very basic questions.
I can't seriously imagine Newton saying "Well, the Moon stays in the sky instead of falling down - and that's frankly a bit weird, but I'm not going to wonder why because it's just a mystery and anyway, I can predict its orbit with these epicycles."
He didn't let figuring out "how gravity works" hold him back. He just figured out the equations that predict its effects based on observation. The unknowns happened to conveniently coalesce around a single constant G, but that doesn't make them "known".
[IANAP - do we have any convincing popularly accessible models for how gravity works even today?]
Anyway, that's kind of similar to going "oh I don't understand the subatomic mechanism that is causing this interference pattern, but the pattern itself is consistent so lets call that P!".
Unless I completely sped past the point you were trying to make - which is completely possible at this subatomic level of reasoning (-:
Actually, both you and GP got it wrong. There is no need to speculate what Newton was thinking, it was all recorded.
Newton was looking for methods to manipulate (push, pull) objects at a distance without touching them. He had strong ideas about the occult and what we today call black magic, in addition to being an alchemist. He devised that the Earth was manipulating the untouched Moon (capitalized, proper noun) and sought to explain the influence of the Earth on the Moon.
Interestingly, I thought that I could simply point you towards Wikipedia [1] and call it a day. However, obviously Newton's viewpoints were controversial in his day and remain so. The controversy is hinted at in Wikipedia, without details. Even the "History of gravitational theory" [2] article completely eliminates this aspect and the "Newton's law of universal gravitation" concentrates completely on the dispute with Hooke.
Many science-related articles on Wikipedia suffer from good-meaning but over-zealous gatekeeping of religious influences on science. So I'll just recommend to you to read a biography or three on Newton. His entire story is fascinating and we can see how tiny events in his childhood (death of father, influence of priest uncle) have affected the history of physics.
No, that is not what this says. What this says is that there is ambiguity in the description of the situation. Is the question about the probability of a second girl in the set of all families with 2 children and at least one boy, or is the question about the probability of a second girl in the set of all families with 2 children given that we know one of them is a boy.
They are different sets of families. That is the point of this paradox.
Say my wife tells me that the neighbor has 2 kids and one of them is a boy what is the likelihood that their other child is a girl?
Given what I know about the current situation, the probability that their other child is a girl is 66.666%
If I look out the window to that neighbor's yard and see a boy playing outside, the probability that their other child is a girl drops to 50%.
How I know the information about on data point one affected the likelihood of an unrelated one. What seems like identical knowledge on the outside, changes outcomes based on how I accrued that knowledge. If that doesn't mimic the double-slit experiment, I don't know what does.
Probability means this: "in X tries, how likely is it for Y to happen". The ambiguity here is this: what is the set of X? Is the set of all families with two children at least one boy, or the set of all families with 2 children of which you have determined one is a boy.
Those are different sets. It doesn't matter how you discovered the information. The apparent paradox is all grammar and set description.
Think of it this way - you want to test this out and actually run this experiment? Great! What's the experiment? Are you starting with all families with 2 children, or all families which 2 children at least one boy.
>> How I know the information about on data point one affected the likelihood of an unrelated one
It doesn't make sense to me that in order to get the probability of 2/3, you implicitly consider "a boy and a girl" to be different from "a girl and a boy".
Somehow, you're saying that seeing the boy means you have ruled out the possibility of "a girl and a boy". But the ordering is in no way related to some arbitrary observation. It's just lexical.
Here's the math, I will break it down based on Boy/Girl and seen.
For the first case here are the different combinations for two children based on sex (let's say left denotes older and right denotes younger to distinguish the difference between girl and a boy and boy and a girl.)
B B
B G
G B
G G
These outcomes are each equally likely, but since we know that one has to be a boy we can eliminate the (G G) case leaving us with two chances out of three that the other child is a girl.
The other case can be viewed as follows (S) denotes seen.
B(S) B
B B(S)
B(S) G
B G(S)
G(S) B
G B(S)
G(S) G
G G(S)
I can eliminate all cases where I see a girl out the window, leaving me with the following equally likely cases:
The neighbor has two boys and I see the older boy. The neighbor has two boys and I see the younger boy. The neighbor has an older boy whom I saw and younger girl. The neighbor has an older girl and a younger boy whom I saw. The neighbor has a girl in 50% of the remaining possible cases.
If you assume that the siblings can be differentiated (thus ordered), it makes no difference. You can for example order them taking their names alphabetically, or by weight, or by location at a given time, etc...
If differentiation is not possible, then they are the exact same person [1], so the parents have one child and it must be boy then ;)
Ignoring the increased probability that twins are of the same gender, no. Regardless, the chance of having two children of different genders is twice that of having two boys. If you split the set into 'two boys, a boy and a girl, and two girls', you must accept that the 'a boy and a girl' case is twice as likely as the first and last options.
I wrote a program and successfully got the right answers experimentally for each case, so I'm not doubting the answers, but I don't buy the explanation.
While you may argue that one twin is always born first, this is an idealized mathematical problem, so it can't depend on particular details of physical reality in that way. There is nothing logically preventing them from being the same age, so it can't be pivotal to solving the problem.
And in fact, I experimentally got the right result without any reference to ages.
So, you don't actually have to regard BG and GB as separate cases if you don't want to.
People like to write the outcome space as ordered pairs BB, BG, GB, GG (ordered by age or whatever else), because this has the advantage that all four outcomes are equiprobable, so you can calculate probabilities just by counting.
If you prefer to regard the outcome space as unordered pairs {B,B}, {B,G}, {G,G} this is absolutely fine: you just have to bear in mind that the prior probability of {B,G} is 1/2, whereas it's 1/4 for the other pairs, so a tiny bit more calculation might be required.
P({B,G}| not {G, G}) = P({B,G})/(P{B,B} + P{B,G}) = (1/2)/((1/2) + (1/4)) = 2/3 as with the other method.
I'm having a fundamental problem understanding why the paradox is modeled the way it is.
"Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?"
For some reason, it's expanded as a choice from {BB, BG, GB, GG}. But why on Earth does the order of children matter in this question? The way I see it, it should be modeled as {both-boys, boy-and-girl, both-girls}; by telling me that one of the kids is a boy, you eliminated one possibility out of three, leaving us with 1/2 as an answer.
Let's say I flipped two coins. I tell you I did this. You ask me, "Did heads come up at least once?" I answer yes.
What are the odds that the other coin was tails? 2/3, because there are three scenarios (HH, HT, TH) that satisfy my first answer to you.
If you flip a pair of coins a few thousand times, and search the flip pairs for all the ones that had a heads among them, you'll find a tails in those pairs 2/3 of the time, and a pair of heads 1/3 of the time.
Same with the girl-boy problem.
Now if you ask me if the left coin came up heads—and I say yes—that doesn't give you any information whatsoever on the right coin. And if you search through the thousands of pair flips looking for an "H" in the left column, the right column will 50/50 have an H or a T.
> Now if you ask me if the left coin came up heads—and I say yes—that doesn't give you any information whatsoever on the right coin.
Exactly. "At least one" gives information about the whole set, implicitly giving information about the second one whereas "the first one is X" gives no information about the second one.
Because if you select a random family from the set of familes with two children, the 4 permutations (BB,BG,GB,GG) are equally likely, at 25% each, so it's the simplest way to model it. If you model it in your way with 3 possible scenarios you'll find that the probabilities are BB: 25%, one of each: 50%, GG: 25%, and dealing with those differing probabilities is harder than just splitung the one of each scenario into two.
Try it with 2 coins flipped at the same time and you'll see it's the case. You'll get 2 unmatching coins about twice as often as you get either HH or TT.
I read the wikipedia article and then it clicked for me. Here is the intuition I got:
If you know one of the kids is a boy then there is a 2/3 chance of there being a girl kid. I will assume you are happy with the reasoning behind this (3 options BG GB BB, two of which yield a girl).
Now why does spotting one of the boys change the odds? You already knew they had a boy right?
Well the boy being spotted conveys some information!
In particular you DIDN'T see a girl. You could have seen one, it would be possible right... but it didn't happen.
That fact means it is a bit more likely that they have two boys. How much is that bit, well 1/6th to be precise. So 1/3+1/6 = 1/2 chance they have two boys. And 2/3-1/6 = 1/2 chance they have two girls.
That gives me the intuition and makes this no longer a paradox intuitively. Although it was never a paradox logically.
CAREFUL:
The conditions under which the boy was 'revealed' to you matter.
If it was random 50-50 chance of seeing the girl or the boy then the above applies.
If the boy was picked, i.e. you said "ah you have at least 1 boy, show him to me". Then no information has been conveyed.
If something else situational (e.g. girls birthday party and all the girls are inside in the room, and boys are playing soccer outside [sorry for stereotyping but my imagination isn't so good] and so you see him) there may be a non 50-50 and non 100-0 probability then there are some more calculations to do :-).
>The way I see it, it should be modeled as {both-boys, boy-and-girl, both-girls}; by telling me that one of the kids is a boy, you eliminated one possibility out of three, leaving us with 1/2 as an answer.
This would be like saying "When I buy a lottery ticket, the only outcomes are {lose lottery, win lottery}; therefore, I have a 50% chance of winning the lottery."
The difference is that boy-girl is twice as likely to occur of those three choices.
I think the way you stated the first problem is ambiguous; the answer could be 1/2 or 2/3. After all, maybe you only have that information because you've met just one of your neighbour's children who happens to be a boy.
The Wikipedia article does a great job of being explicit in the differences between the 1:2 and 2:3 cases.
Unfortunately articles pop up every now and then claiming 2:3 is the correct answer (since it's counterintuitive and therefore interesting), while losing the conditions necessary for 2:3 in the translation of the problem description from mathematical to plain English.
Information changes the question asked. You don't state the questions. Did you mean: neighbor has 2 children, we don't know the sex, what is the probability one or more is a girl? Next question is: neighbor has 1 child of unknown sex, odds of it being a girl?
This is actually a very interesting musing, and not quite correct.
> observation of the atoms passing through the slit is affecting the search space for the other atoms in such a way that we currently do not understand
Observation is the key word here. Actually, you don't need to observe the atoms to affect the pattern on the screen - though its the easiest way to do so in the double-slit experiment. All you need is the possibility of observing or distinguishing between two events to destroy the interference between them. Note that possibility of observing is a much weaker condition than observation itself. Physicists have, over the years, done many experiments to clarify these issues. Essentially, if you believe that causality only flows forward through time, then what you are saying is not correct.
If it were just a probability paradox, Bell's theorem wouldn't be a thing. You can win certain coordination games more often using quantum correlations than is possible with classical correlations.
That being said, I have complained about specific papers and articles making this exact mistake. For example, explanations of delayed choice eraser experiments are almost always confusing correlation or post-selection for causation ( http://algassert.com/post/1720 ). But Bell tests are not of that form, which is why the first thing you should ask of any proposed interpretation is "How do you deal with Bell tests?".
It's more like seeing one boy actually impacts the gender of the second child, which is why the quantum experiment is so mind boggling. It doesn't seem to have any resemblance with classical physics and only makes sense in quantum physics.
No it doesn't. In the 2/3 case, you're given information about the whole set, not just one member. Instead of "seeing one boy" affecting the gender of the other child, it's "seeing there are more than 0 boys" affecting the gender of one of the children.
Here's another example: If I flipped 100 coins, and told you there were 99 heads, what's the likelihood the other 1 was tails? The answer is 100/101, because there are 100 ways the one tail could happen, while only one way zero tails can happen. But if you're only told that the first 99 are heads, the answer is 1/2. You know the last flip has exactly the same odds as all the other ones -- the trials are independent. The difference is in one all the flips were included in the results (and the question isn't about any one specific flip), while in the other you had no information about the last flip (which the question was about).
Another way of looking at it: In the first example, the question was asking about the sum of 100 trials and you were given information about 99 of those 100 trials. You were given 99/100s of the information you need to answer the question. In the second example, the question was asking about the last trial and you were given information about 99 unrelated trials beforehand. You were given none of the information you need to answer the question.
Is this basically to do with the fact that you know how likely it is to see a boy given any of the combinations? So there's a 33% chance that there are two boys and you see a boy, a 33% chance that there's a boy and girl and you see a boy, and a 33% chance that there's a boy and a girl and you see a girl. Given that you've seen the boy you've eliminated one of the outcomes so the other two outcomes are equally likely?
I'm confused by your comment but I'll try to explain more.
Given one of the children is a boy. The only combinations possible are: GB, BG, & BB. Where G is Girl and B is Boy. The question is about the probability of the other child being a Girl.
When we eliminate one of the B from each combination, we get:
The boy or girl paradox does appear in physics but not like this. Distinguishable particles behave like "older child is a girl", while indistinguishable particles behave like "at least one child is a girl"
It's a paradox only because how question is put. Your wife says that neighbours have children, and she observed a boy. Then she observed boy again. What difference in probability having neighbours having a girl if you seen a boy once or twice.
You have red and black pebbles otherwise identical. Bag has 2 pebbles, you draw a pebble, it's red. You put it back. What's the probability of bag having black and red pebble? Draw again - red again. What's the probability of bag having black and red pebble?
You acquire more data, therefore your estimate changes.
When I saw the droplet experiments, I thought "that's cool, but it doesn't prove anything about pilot wave theory because the arguments are over much deeper things than what this is demonstrating". Debunking it is just as meaningless. The people who actually know about this stuff are arguing over determinism and non-locality and what not. I thought oil droplets are just a nice way to introduce people to the concept.
Disclaimer: I don't really know anything about any of this