In infinite dimensional cases things are more complicated because there are various subtitles that can arise. But these subtitles are not at the core of the uncertainty principle, merely a technical distraction that needs to be addressed.
I disagree that it's merely a distraction. Yes, when teaching the Uncertainty principle for the first time, it may be a good idea to show it for finite dimensional Hilbert space (in fact, I wish it was done this way, it's so much simpler, like you said!). For your example of a spin-1/2 particle:
delta(s_x)*delta(s_y) >= abs(<[s_x,s_y]>)/2
It's very nice for an introduction, and it can be derived with very simple math, but you can't honestly say it's graduate-level Physics if you can't even do it for position and momentum, and show that the commutator becomes constant, like so:
delta(x)*delta(p) >= abs(<[x,p]>)/2 = hbar/2
Which is the usual statement, and shows that you can't really expect the state to be exactly an eigenstate of either position or momentum, etc. (but by the time you get to this point you already know that, because things get very fishy with the eigenstate being a Dirac delta, and so on. Or maybe that's just the way I learned, but it seemed fishy to me:)).
And I really don't understand this statement:
you need the features of Hilbert spaces that are unlike Euclidean spaces.
All finite dimensional Euclidean spaces, for which we have a reasonable intuition, are Hilbert spaces. In the infinite dimensional case Hilbert spaces are defined to carry over the properties of Euclidean space while eliminating some of the perverse things that can happen in infinite cases (i.e. ensuring Cauchy sequences have limits in the space).
Sure, but not all Hilbert spaces are Euclidean. Some properties can't carry from finite to infinite dimensional, like I've wrote above: in the finite dimensional case, you can't have unbounded operators, you can't have operators A and B for which [A,B] is constant, and a lot more, things that you do need in physics.
Like I said before, I think there's a lot of value in learning things with simple math, using finite dimensional Hilbert spaces, etc. In fact, I'm mostly interested in Quantum Computing, where there's no need for infinite dimensional spaces. But I have no illusions that this is full graduate level Quantum Physics.
So true, I couldn't agree more about the focus on the wrong problems.
I was expecting something like an introduction to really basic quantum stuff, like superposition, entanglement, measurement, etc. This can actually be done the right way with very little math, like this excellent series of lectures from Stanford, where you can learn something that is actually right, not just analogies.
Instead, based on what's in the first lesson, it looks like it will try to talk about a lot of things, explaining none of them really right.
I think it's pretty easy to explain the concept of a Hilbert space with absolutely no knowledge of calculus, because it's just geometry and common sense.
I agree, but to understand why and how a Hilbert space important to QM, you need the features of Hilbert spaces that are unlike Euclidean spaces.
To see why this is relevant, take the Uncertainty Principle. It can actually be stated for systems described by finite-dimensional Hilbert spaces (for which one could have a nice geometric intuition), but it's not that interesting. The real understanding (at least for me, and I suspect for most people) only comes when you learn the position and momentum operators, which operate in infinite-dimensional Hilbert space states, and realize that the commutator between them is constant no matter what the state they're applied to. To really understand that, you need to get your hands dirty with (very little) functional analysis, the geometric interpretation of a Hilbert space will give no insight over that.
Still, I think there's a lot of value in explaining QM with only very basic math -- and there's a lot that can be done really well that way: entanglement, measurement, Schroedinger's cat, etc. But you also have to understand that a lot of the really interesting bits need advanced vector calculus, linear algebra, funcional analysis, etc. to be done right, otherwise you're only teaching with analogies.
It's because of this complete difference in the kind of explanation of the forces that it's so hard to reconcile Quantum Mechanics and Special Relativity.
Oh, crap. It should read "it's so hard to reconcile Quantum Mechanics and General Relativity", of course.
Quantum Mechanics and Special Relativity were unified in the late 1920s (see the Dirac Equation). Special Relativity is what prohibits FTL. So, even in theory, you can not use entanglement to send information FTL.
You're probably confusing Special Relativity (Einstein's E=mc^2 and no FTL signals) with General Relativity (Einstein's Gravity), which is what has not been unified with Quantum Mechanics.
The Standard Model (Quantum Mechanics) says that all forces it explains for sure (electomagnetic, weak and strong) are carried by particles called bosons. This works so well that everyone wants to explain gravity (the force that is not explained by it) by saying it's carried by a particle we have not detected yet, the graviton[1] (it would also be a boson). General Relativity, on the other hand, says that what we feel as gravity is actually just distortion of space-time caused by mass (or energy), and says nothing about the other forces (although I think it works very well with electromagnetism, but I'm not sure).
It's because of this complete difference in the kind of explanation of the forces that it's so hard to reconcile Quantum Mechanics and Special Relativity.
[1] Note: don't confuse the graviton with the Higgs boson, which also has not been detected but is actually needed by the Standard Model in order for it to work the way everyone expects.
Also, regarding the before mentioned quantum mechanics, there is a law, saying the sum of all quantum states is a constant.
I'm not sure what you mean, are you referring to conservation of angular momentum, which states that in the entangled state, whatever polarization one photon has must be opposite to the other one's? If so, it doesn't imply what you say next:
So, if you are able to change/manipulate the state of the first particle, then, theoretically, the state of the other particle must change accordingly. Of course, this is only on theory, but if these guys are really able to do it....imagine the possibilities.
No, not even in theory. If you manipulate the state of one photon to be whatever you like, the entanglement will be broken, and the other photon will simply "choose" a random state. This does not violate conservation of angular momentum, because you're changing the angular momentum of one photon (at the cost of a tiny change the angular momentum of something else).
So, for the umpteenth time: Quantum Mechanics, being compatible with Special Relativity, does not allow you to send information faster than light, even in theory.
The difference is that with entanglement, there's really no (usable) information being transmitted.
Depending on the interpretation of quantum mechanics you use, you must accept that when one entangled particle is measured, the other is affected by the measurement. There are two points, though:
There's no way to control the outcome of the measurement of the first entangled particle -- this means you can't control the effect it will have on the second. So, as I said before, there's no way to transmit information this way with entanglement.
There are some interpretations of quantum mechanics (Many-worlds, for example) in which there's absolutely no effect on the second particle when you measure the first. So, whether this "spooky action" (as Einstein called it) actually exists, no one can tell. You certainly can explain things with it, but you don't need to.
Actually, hidden variables are not ruled out, only local hidden variables. For example, Bohmian mechanics is a valid (non-local, hidden variable) interpretation of quantum mechanics.
I agree that non-local effects do seem "spooky", but other interpretations are also hard to accept (to me, at least). Still, I like Many Worlds better than Bohm's.
It's important to remember one thing, though. As long as these interpretations give the same measurement outcomes for any imaginable experiment (as they seem to, right now), you should use the one that fits your problem better: there's no need to decide which one you'll accept and forget about the others.
When people say that Quantum Mechanics is not compatible with General Relativity, this is one of the problems they have in mind.
Not really. Special Relativity already has this "feature", and Quantum Mechanics is compatible with it since the late 1920s (see the Dirac equation).
Quantum Mechanics (specifically, the Standard Model) is incompatible with General Relativity because GR describes gravity as a distortion of space-time, but in the SM the other forces (electromagnetic, weak and strong) are carried by bosons. These are fundamentally different views of nature, and there seems to be no coherent way of reconciling them.
When particles are entangled, if you move one the other moves with no outside influence - the action is instantaneous and distance doesn't matter.
No -- if you move one particle, the other doesn't move instantly. Entanglement is much more subtle than that; in fact, it's hard to explain what exactly is shared between the particles without using math. One point is important, though: it's not possible to send information faster than light using quantum entanglement. So, all that talk about "instantaneous" reaction is a little misleading.
The hard part right now is keeping them entangled at a distance - the further apart you move the particles the harder it is to keep them from losing their entanglement.
The difficulty in maintaining (quantum) coherence has nothing to do with the distance between the particles. It's just that the particles must be kept completely isolated from everything else -- any interaction with anything else breaks the entanglement.
So long as they are actually entangled, though, distance doesn't introduce any kind of delay in the reaction of one particle to another.
Well, sure, for a suitable definition of "reaction". And remember it's a one time deal: once you interact with one of the particles, the other one suffers the "reaction" and then the entanglement is broken.
If they could get it to work across the world it would be phenomenal, but so far they've only managed a few feet.
Actually, it has been done over a few kilometers, see for example this paper.
From the post in the forum, it seems that only the source tgz in the mirrors was affected. So, anyone who checked the MD5 agains the official (non-mirrored) tgz would realize the difference.
Apparently, no one bothered to check for a long time, though.
Another assumption underlying repeatability is that science should be objective, i.e. not depend on who performs the experiment or observation, or on their specific viewpoints.
I disagree, I don't think this is essential to science. It's just that the universe (in our experience) so obviously works that way (i.e., it doesn't matter who performs the experiment) that it seems unconceivable to even accept doing science any other way. But it's not hard to imagine a world where (for instance) there's predictable difference in outcome when children or adults perform a given experiment. Science, I think, could conceivably study and explain that. If, on the other hand, there's no underlying regularity on the outcome of an experiment, then I don't think there's anything to be known. So, in my view, science would not apply.
Luckily for us, many of the best scientists seem to be driven by irrational passion and faith.
I agree that scientists, being human, are not driven only by reason. But I don't see how this is relevant.
To me, the main difference seems to be that science has chosen better core assumptions.
We'll have to agree to disagree, then:)
In the end, I think our disagreement is on what exactly science is. To me, science is the activity of someone who says "OK, I'll try to understand this thing. What's the best way of doing that?" and so on.
The only "core assumption" of science is that there's something to be known that can be known.
So, for example, the assumptions that "nature is uniform and gravity and the speed of light, etc. have always operated the same way" can be abandoned without leaving science. It's just that there's no compelling reason to, as far as we know. But believe me, if there was good reason to suspect that gravity or the speed of light is different somewhere, you can be sure that scientists would jump at the opportunity to try to understand it and explain it.
But the main point I was trying to make is that it's silly to compare science and religion based on the fact that they are both based on "faith". The point is that science tries to explain things as best as possible. Religion's goals are completely different.
Science and religion only conflict when you try to make one interfere in the domain of the other. For example, Creationism clearly tries to apply "religious knowledge" to explain nature. Conversely, some people seem to want to give scientific reasons for why God exists or doesn't exist, or derive morals and ethics from science.
You seem to assume that "science" gives mankind an escape from presuppositions.
And you seem to assume that all presuppositions are equally valid.
The whole point of science is that anyone can question the assumptions. Refining and even radically changing basic assumptions happen from time to time; it's an important part of how science evolves.
Every religion, on the other hand, has a set of core assumptions that are true. If you want to change them, you have to found a new religion.
Hey, great idea, I wonder how nobody thought of that before!
Except they have. Section 5 of the GPL v2 explicitly notes that, besides the license, "nothing else grants you permission to modify or distribute the Program".
If the GPL is null and void, Apple can't legally distribute the program.
That is not Apple's problem. They didn't develop the application, they didn't breach the licence.
The GPL is a distribution license, so it applies to the distributor too. Here is a relevant quote from section 0 of the GPL v2:
Activities other than copying, distribution and modification are not covered by this License; they are outside its scope.
Most of the following sections specify the terms under which you can modify and distribute the software.
If Apple is distributing the software, they must comply with the license. (The developers may be in breach of the license also, but that does not mean Apple is not.)
It's a fundamental limitation of how nature works.
This is a subject that is really hard to explain without math, because then you have to rely on interpretations that no one agrees upon.
The part about "there is no defined classical state the system is in" is actually an interpretation of what's happening. There's another one, called Bohm interpretation (as someone pointed out above) where there's always a definite state, but then other strange things happen. Still, it's never possible to predict the state, and it's never possible to control the probabilities of getting any result from the measurements.
That's cute, but can we stay focused on the matter of the discussion?
You said a lot of things in you original post, particularly this:
However I can prepare my side of the link such as to ensure that you will measure Zero with exactly 15.37586 percent probability.
I can't see how someone with a PhD in physics can believe that, this is simply false. If it were true, you could also set things up in a way that the other end would measure one of the states with probability zero, and then you would be able to transmit one bit of information faster than light, violating causality. Regardless of the interpretation you subscribe to, at most locality is violated, never causality.
As to the other things I wrote in my first reply, I was not trying to falsify anything; I was trying to explain how entanglement works. I'm sorry if that offended you. It's just that entanglement does not work the way you described it. No matter what you do to one end of the system, you can't change the probability of any measurement on the other end.
That's a great question. That's exactly the question everybody should ask before anything else.
The answer is: no, there's no way Bob can tell if Alice changed her particle in any way. There's no FTL communication. As to why should we care, it's complicated (I'm assuming you're asking for a theoretical "why should we care", not practical reasons).
If Alice and Bob do things in a certain way, and then compare results in the end, they can see that in some sense the two photons made a choice in response to the measurements they made, and once the choice was made by one, the other one instantly "knew" and agreed with it.
How they know that is a little complicated to explain, as it involves a little bit of math. Physicists call this "violation of Bell's inequalities"; Wikipedia has something about it in the article about Bell's Theorem. I can't recommend it, though, as it tries to explain a lot in a very short space, so it's not too clear. If you're interested, here's a lecture note that explain it all from the very beginning (only math knowledge assumed) that ends exactly at the point of explaining this effect: http://www.eecs.berkeley.edu/~vazirani/f04quantum/notes/lecture1.pdf
No, what you say is the current theory. The experimental results are precisely what the grandparent poster described: that you cannot predict which of the two states you will measure.
The experimental results agree completely with the current theory: you cannot predict which of the two states you will get from the measurement. If that was all the grandparent had said, I wouldn't had bothered answering.
The problem is, he seems to think the entangled state is such that you can fix probabilities in one end with a measurement, and then the measurement in the other end would depend on these probabilities. This is complete bunk, regardless what interpretation you subscribe to. No one serious ever believed that, and no one would publish a paper saying they transmitted information that way. (Well, maybe a crackpot.)
And we know it since Goedel that all interesting, non-trivial frameworks of formal logic have an infinite number of questions to which we'll never know the answer (within that framework). The quantum state of particles may be one such phenomenon in our universe.
There's nothing special in QM to suggest that (any more than any other physical theory). And there are no serious doubts that the mathematical formalism of quantum entanglement I mentioned is complete and self-consistent -- there are serious disagreements regarding its interpretation, not the formalism itself. And no one ever suggested that the equivalent of a "Godel sentence" that's undecidable inside it exists: the formalism doesn't have enough in it to do arbitrary arithmetic.
Yes, everyone is pretty sure quantum mechanics doesn't violate special relativity. So, it does not allow sending information faster than light (which would also allow sending information to the past, therefore violating causality).
The EPR paradox was solved a long time ago by experiments concluding that Bell's Inequalities are in fact violated (see Wikipedia for Bell's Theorem). This means that if you want to believe Quantum Mechanics can be explained by "hidden variables" (as Einstein wanted), you must accept there is a "spooky action at a distance" (as Einstein didn't want). This "spooky action" is faster than light, but it can not be used to send information.
Furthermore, you don't have to believe in an interpretation of Quantum Mechanics that has hidden variables. For example, there's the Many-Worlds interpretation (among others). If you believe in any such interpretation, you don't have to believe in the "spooky action".
Notice, though, that you can use entanglement to double the capacity of a classical channel (i.e., send two bits of information with only one bit travelling through the wire) with help of entanglement. This is called superdense coding, and is essentially the inverse of quantum teleportation.
How did this get moderated up? This poster clearly has no idea what he's talking about.
The whole point of quantum entanglement is that prior to the measurement, there's no basis in which the state is definite. This means it's not just that "you cannot predict which of the two [states] you will measure"; the whole point is that there is no defined classical state the system is in. There's no classical analog for that, so it's really hard (maybe impossible?) to explain without math.
If you don't even know the most basic stuff about quantum mechanics (as is clear from the post), please educate yourself before writing about it or even moderating stuff about it.
Slashdot Mirror
In infinite dimensional cases things are more complicated because there are various subtitles that can arise. But these subtitles are not at the core of the uncertainty principle, merely a technical distraction that needs to be addressed.
I disagree that it's merely a distraction. Yes, when teaching the Uncertainty principle for the first time, it may be a good idea to show it for finite dimensional Hilbert space (in fact, I wish it was done this way, it's so much simpler, like you said!). For your example of a spin-1/2 particle:
delta(s_x)*delta(s_y) >= abs(<[s_x,s_y]>)/2
It's very nice for an introduction, and it can be derived with very simple math, but you can't honestly say it's graduate-level Physics if you can't even do it for position and momentum, and show that the commutator becomes constant, like so:
delta(x)*delta(p) >= abs(<[x,p]>)/2 = hbar/2
Which is the usual statement, and shows that you can't really expect the state to be exactly an eigenstate of either position or momentum, etc. (but by the time you get to this point you already know that, because things get very fishy with the eigenstate being a Dirac delta, and so on. Or maybe that's just the way I learned, but it seemed fishy to me :)).
And I really don't understand this statement: you need the features of Hilbert spaces that are unlike Euclidean spaces. All finite dimensional Euclidean spaces, for which we have a reasonable intuition, are Hilbert spaces. In the infinite dimensional case Hilbert spaces are defined to carry over the properties of Euclidean space while eliminating some of the perverse things that can happen in infinite cases (i.e. ensuring Cauchy sequences have limits in the space).
Sure, but not all Hilbert spaces are Euclidean. Some properties can't carry from finite to infinite dimensional, like I've wrote above: in the finite dimensional case, you can't have unbounded operators, you can't have operators A and B for which [A,B] is constant, and a lot more, things that you do need in physics.
Like I said before, I think there's a lot of value in learning things with simple math, using finite dimensional Hilbert spaces, etc. In fact, I'm mostly interested in Quantum Computing, where there's no need for infinite dimensional spaces. But I have no illusions that this is full graduate level Quantum Physics.
So true, I couldn't agree more about the focus on the wrong problems.
I was expecting something like an introduction to really basic quantum stuff, like superposition, entanglement, measurement, etc. This can actually be done the right way with very little math, like this excellent series of lectures from Stanford, where you can learn something that is actually right, not just analogies.
Instead, based on what's in the first lesson, it looks like it will try to talk about a lot of things, explaining none of them really right.
I think it's pretty easy to explain the concept of a Hilbert space with absolutely no knowledge of calculus, because it's just geometry and common sense.
I agree, but to understand why and how a Hilbert space important to QM, you need the features of Hilbert spaces that are unlike Euclidean spaces.
To see why this is relevant, take the Uncertainty Principle. It can actually be stated for systems described by finite-dimensional Hilbert spaces (for which one could have a nice geometric intuition), but it's not that interesting. The real understanding (at least for me, and I suspect for most people) only comes when you learn the position and momentum operators, which operate in infinite-dimensional Hilbert space states, and realize that the commutator between them is constant no matter what the state they're applied to. To really understand that, you need to get your hands dirty with (very little) functional analysis, the geometric interpretation of a Hilbert space will give no insight over that.
Still, I think there's a lot of value in explaining QM with only very basic math -- and there's a lot that can be done really well that way: entanglement, measurement, Schroedinger's cat, etc. But you also have to understand that a lot of the really interesting bits need advanced vector calculus, linear algebra, funcional analysis, etc. to be done right, otherwise you're only teaching with analogies.
It's because of this complete difference in the kind of explanation of the forces that it's so hard to reconcile Quantum Mechanics and Special Relativity.
Oh, crap. It should read "it's so hard to reconcile Quantum Mechanics and General Relativity", of course.
Quantum Mechanics and Special Relativity were unified in the late 1920s (see the Dirac Equation). Special Relativity is what prohibits FTL. So, even in theory, you can not use entanglement to send information FTL.
You're probably confusing Special Relativity (Einstein's E=mc^2 and no FTL signals) with General Relativity (Einstein's Gravity), which is what has not been unified with Quantum Mechanics.
The Standard Model (Quantum Mechanics) says that all forces it explains for sure (electomagnetic, weak and strong) are carried by particles called bosons. This works so well that everyone wants to explain gravity (the force that is not explained by it) by saying it's carried by a particle we have not detected yet, the graviton[1] (it would also be a boson). General Relativity, on the other hand, says that what we feel as gravity is actually just distortion of space-time caused by mass (or energy), and says nothing about the other forces (although I think it works very well with electromagnetism, but I'm not sure).
It's because of this complete difference in the kind of explanation of the forces that it's so hard to reconcile Quantum Mechanics and Special Relativity.
[1] Note: don't confuse the graviton with the Higgs boson, which also has not been detected but is actually needed by the Standard Model in order for it to work the way everyone expects.
Also, regarding the before mentioned quantum mechanics, there is a law, saying the sum of all quantum states is a constant.
I'm not sure what you mean, are you referring to conservation of angular momentum, which states that in the entangled state, whatever polarization one photon has must be opposite to the other one's? If so, it doesn't imply what you say next:
So, if you are able to change/manipulate the state of the first particle, then, theoretically, the state of the other particle must change accordingly. Of course, this is only on theory, but if these guys are really able to do it....imagine the possibilities.
No, not even in theory. If you manipulate the state of one photon to be whatever you like, the entanglement will be broken, and the other photon will simply "choose" a random state. This does not violate conservation of angular momentum, because you're changing the angular momentum of one photon (at the cost of a tiny change the angular momentum of something else).
So, for the umpteenth time: Quantum Mechanics, being compatible with Special Relativity, does not allow you to send information faster than light, even in theory.
The difference is that with entanglement, there's really no (usable) information being transmitted.
Depending on the interpretation of quantum mechanics you use, you must accept that when one entangled particle is measured, the other is affected by the measurement. There are two points, though:
Actually, hidden variables are not ruled out, only local hidden variables. For example, Bohmian mechanics is a valid (non-local, hidden variable) interpretation of quantum mechanics.
I agree that non-local effects do seem "spooky", but other interpretations are also hard to accept (to me, at least). Still, I like Many Worlds better than Bohm's.
It's important to remember one thing, though. As long as these interpretations give the same measurement outcomes for any imaginable experiment (as they seem to, right now), you should use the one that fits your problem better: there's no need to decide which one you'll accept and forget about the others.
When people say that Quantum Mechanics is not compatible with General Relativity, this is one of the problems they have in mind.
Not really. Special Relativity already has this "feature", and Quantum Mechanics is compatible with it since the late 1920s (see the Dirac equation).
Quantum Mechanics (specifically, the Standard Model) is incompatible with General Relativity because GR describes gravity as a distortion of space-time, but in the SM the other forces (electromagnetic, weak and strong) are carried by bosons. These are fundamentally different views of nature, and there seems to be no coherent way of reconciling them.
When particles are entangled, if you move one the other moves with no outside influence - the action is instantaneous and distance doesn't matter.
No -- if you move one particle, the other doesn't move instantly. Entanglement is much more subtle than that; in fact, it's hard to explain what exactly is shared between the particles without using math. One point is important, though: it's not possible to send information faster than light using quantum entanglement. So, all that talk about "instantaneous" reaction is a little misleading.
The hard part right now is keeping them entangled at a distance - the further apart you move the particles the harder it is to keep them from losing their entanglement.
The difficulty in maintaining (quantum) coherence has nothing to do with the distance between the particles. It's just that the particles must be kept completely isolated from everything else -- any interaction with anything else breaks the entanglement.
So long as they are actually entangled, though, distance doesn't introduce any kind of delay in the reaction of one particle to another.
Well, sure, for a suitable definition of "reaction". And remember it's a one time deal: once you interact with one of the particles, the other one suffers the "reaction" and then the entanglement is broken.
If they could get it to work across the world it would be phenomenal, but so far they've only managed a few feet.
Actually, it has been done over a few kilometers, see for example this paper.
From the post in the forum, it seems that only the source tgz in the mirrors was affected. So, anyone who checked the MD5 agains the official (non-mirrored) tgz would realize the difference.
Apparently, no one bothered to check for a long time, though.
Another assumption underlying repeatability is that science should be objective, i.e. not depend on who performs the experiment or observation, or on their specific viewpoints.
I disagree, I don't think this is essential to science. It's just that the universe (in our experience) so obviously works that way (i.e., it doesn't matter who performs the experiment) that it seems unconceivable to even accept doing science any other way. But it's not hard to imagine a world where (for instance) there's predictable difference in outcome when children or adults perform a given experiment. Science, I think, could conceivably study and explain that. If, on the other hand, there's no underlying regularity on the outcome of an experiment, then I don't think there's anything to be known. So, in my view, science would not apply.
Luckily for us, many of the best scientists seem to be driven by irrational passion and faith.
I agree that scientists, being human, are not driven only by reason. But I don't see how this is relevant.
To me, the main difference seems to be that science has chosen better core assumptions.
We'll have to agree to disagree, then :)
In the end, I think our disagreement is on what exactly science is. To me, science is the activity of someone who says "OK, I'll try to understand this thing. What's the best way of doing that?" and so on.
The only "core assumption" of science is that there's something to be known that can be known.
So, for example, the assumptions that "nature is uniform and gravity and the speed of light, etc. have always operated the same way" can be abandoned without leaving science. It's just that there's no compelling reason to, as far as we know. But believe me, if there was good reason to suspect that gravity or the speed of light is different somewhere, you can be sure that scientists would jump at the opportunity to try to understand it and explain it.
But the main point I was trying to make is that it's silly to compare science and religion based on the fact that they are both based on "faith". The point is that science tries to explain things as best as possible. Religion's goals are completely different.
Science and religion only conflict when you try to make one interfere in the domain of the other. For example, Creationism clearly tries to apply "religious knowledge" to explain nature. Conversely, some people seem to want to give scientific reasons for why God exists or doesn't exist, or derive morals and ethics from science.
You seem to assume that "science" gives mankind an escape from presuppositions.
And you seem to assume that all presuppositions are equally valid.
The whole point of science is that anyone can question the assumptions. Refining and even radically changing basic assumptions happen from time to time; it's an important part of how science evolves.
Every religion, on the other hand, has a set of core assumptions that are true. If you want to change them, you have to found a new religion.
I think it's clear they were talking about free speech on Slashdot, not the general constitutional right of free speech.
Slashdot makes a point of never deleting comments and even allowing anonymous free speech.
Hey, great idea, I wonder how nobody thought of that before!
Except they have. Section 5 of the GPL v2 explicitly notes that, besides the license, "nothing else grants you permission to modify or distribute the Program".
If the GPL is null and void, Apple can't legally distribute the program.
That is not Apple's problem. They didn't develop the application, they didn't breach the licence.
The GPL is a distribution license, so it applies to the distributor too. Here is a relevant quote from section 0 of the GPL v2:
Activities other than copying, distribution and modification are not covered by this License; they are outside its scope.
Most of the following sections specify the terms under which you can modify and distribute the software.
If Apple is distributing the software, they must comply with the license. (The developers may be in breach of the license also, but that does not mean Apple is not.)
It's a fundamental limitation of how nature works.
This is a subject that is really hard to explain without math, because then you have to rely on interpretations that no one agrees upon.
The part about "there is no defined classical state the system is in" is actually an interpretation of what's happening. There's another one, called Bohm interpretation (as someone pointed out above) where there's always a definite state, but then other strange things happen. Still, it's never possible to predict the state, and it's never possible to control the probabilities of getting any result from the measurements.
You are a pathetic lying swine.
That's cute, but can we stay focused on the matter of the discussion?
You said a lot of things in you original post, particularly this:
However I can prepare my side of the link such as to ensure that you will measure Zero with exactly 15.37586 percent probability.
I can't see how someone with a PhD in physics can believe that, this is simply false. If it were true, you could also set things up in a way that the other end would measure one of the states with probability zero, and then you would be able to transmit one bit of information faster than light, violating causality. Regardless of the interpretation you subscribe to, at most locality is violated, never causality.
As to the other things I wrote in my first reply, I was not trying to falsify anything; I was trying to explain how entanglement works. I'm sorry if that offended you. It's just that entanglement does not work the way you described it. No matter what you do to one end of the system, you can't change the probability of any measurement on the other end.
That's a great question. That's exactly the question everybody should ask before anything else.
The answer is: no, there's no way Bob can tell if Alice changed her particle in any way. There's no FTL communication. As to why should we care, it's complicated (I'm assuming you're asking for a theoretical "why should we care", not practical reasons).
If Alice and Bob do things in a certain way, and then compare results in the end, they can see that in some sense the two photons made a choice in response to the measurements they made, and once the choice was made by one, the other one instantly "knew" and agreed with it.
How they know that is a little complicated to explain, as it involves a little bit of math. Physicists call this "violation of Bell's inequalities"; Wikipedia has something about it in the article about Bell's Theorem. I can't recommend it, though, as it tries to explain a lot in a very short space, so it's not too clear. If you're interested, here's a lecture note that explain it all from the very beginning (only math knowledge assumed) that ends exactly at the point of explaining this effect: http://www.eecs.berkeley.edu/~vazirani/f04quantum/notes/lecture1.pdf
No, what you say is the current theory. The experimental results are precisely what the grandparent poster described: that you cannot predict which of the two states you will measure.
The experimental results agree completely with the current theory: you cannot predict which of the two states you will get from the measurement. If that was all the grandparent had said, I wouldn't had bothered answering.
The problem is, he seems to think the entangled state is such that you can fix probabilities in one end with a measurement, and then the measurement in the other end would depend on these probabilities. This is complete bunk, regardless what interpretation you subscribe to. No one serious ever believed that, and no one would publish a paper saying they transmitted information that way. (Well, maybe a crackpot.)
And we know it since Goedel that all interesting, non-trivial frameworks of formal logic have an infinite number of questions to which we'll never know the answer (within that framework). The quantum state of particles may be one such phenomenon in our universe.
There's nothing special in QM to suggest that (any more than any other physical theory). And there are no serious doubts that the mathematical formalism of quantum entanglement I mentioned is complete and self-consistent -- there are serious disagreements regarding its interpretation, not the formalism itself. And no one ever suggested that the equivalent of a "Godel sentence" that's undecidable inside it exists: the formalism doesn't have enough in it to do arbitrary arithmetic.
Touche.
But if you know that the Bohm Interpretation preserves realism, you already know the post I responded to is complete hogwash. :)
Yes, everyone is pretty sure quantum mechanics doesn't violate special relativity. So, it does not allow sending information faster than light (which would also allow sending information to the past, therefore violating causality).
The EPR paradox was solved a long time ago by experiments concluding that Bell's Inequalities are in fact violated (see Wikipedia for Bell's Theorem). This means that if you want to believe Quantum Mechanics can be explained by "hidden variables" (as Einstein wanted), you must accept there is a "spooky action at a distance" (as Einstein didn't want). This "spooky action" is faster than light, but it can not be used to send information.
Furthermore, you don't have to believe in an interpretation of Quantum Mechanics that has hidden variables. For example, there's the Many-Worlds interpretation (among others). If you believe in any such interpretation, you don't have to believe in the "spooky action".
Yes, you're right.
Notice, though, that you can use entanglement to double the capacity of a classical channel (i.e., send two bits of information with only one bit travelling through the wire) with help of entanglement. This is called superdense coding, and is essentially the inverse of quantum teleportation.
How did this get moderated up? This poster clearly has no idea what he's talking about.
The whole point of quantum entanglement is that prior to the measurement, there's no basis in which the state is definite. This means it's not just that "you cannot predict which of the two [states] you will measure"; the whole point is that there is no defined classical state the system is in. There's no classical analog for that, so it's really hard (maybe impossible?) to explain without math.
If you don't even know the most basic stuff about quantum mechanics (as is clear from the post), please educate yourself before writing about it or even moderating stuff about it.