The correctness of the mathematical technique is a nice evidence; not a proof. Everyday people make very precise measurements based on the idea that our space is Euclidean. Well it ain't.
To make a statement as strong as "it went through both slits", you need more than very good evidence.
Why there must be? That's philosophy. The Lorentz transformation shows that there isn't. That's it. But allow me to expand. To talk of a "perspective" is imprecise. What we have are referentials, and time slows down relative to another referential. So to be able to speak of time slowing down, you have to be in a valid referential.
Put another way. One of the most basic consequences of special relativity is that there ain't referentials that are c apart. This is the "you can't travel at c" prohibition. It follows that if anything is at travelling at c, it can't be in a referential. And it can't slow down as well; for that you'd need a Lorentz transformation.
But photons aren't that special. Any massless particle travels at c.
You do integrate through both slits, but that does not mean that every photon has actually gone through them. It's a mathematical technique.
What one proves experimentally is that if the which-path information exists (somewhere), there's no interference pattern. To infer from this that it went through both slits is, at best, non-sequitur, and at worse, philosophy.
Also
But from photon's perspective...
there's no photon's perspective. It makes no sense to try to Lorentz-transform you into a referential that's moving at the speed of light. I understand that you're trying to take a limit somewhere, but you can't, it's not well-defined (mathematically), and leads one to nonsensical conclusions.
Still no, sorry. You have a very romanticized view of quantum mechanics. You don't need photons to "see", that's why I used quotation marks.
In the Stern-Gerlach experiment, a foundational one, there's only a magnetic field and a silver plate. In the double-slit experiment, only two slits (duh) and photographic paper.
The photons do not go through all possible paths, and the thing is not in two places at once. The point is that there's no information about it's location (or the photon path). Even assuming that there exists such information would lead to contradictions.
If you want a simple sentence: it's information that does it.
To calculate the numerical value of the digits I could understand as useless, but there are plenty of properties that are basis-independent, like it's irrationality, transcendence and normality.
Also, there are some quite beautiful representations, look for the continued fractions one.
No, it doesn't. What does have a different value is the ratio of a circumference to it's diameter, that can be grater than pi (hyperbolic surfaces), or smaller (spherical surfaces). But that ain't the definition of pi, 'cos even in a given surface of constant curvature, this value varies.
Nothing. What frame reference independence actually means is that they are encoding a reference frame in the particles themselves, so that you don't have to worry about external alignment. It does nothing about the communication channel, that does not exist through an events horizon.
As someone who works daily with infinite-dimensional vector spaces, I beg you, do not water down the meaning.
You could call it infinite distance, or asymptotic precision, whatever. But it still has only two dimensions, and that's the way it should be. I think it would be a little confusing if you had to be aware of more dimensions to control your windows;p
It explains quite well the heart of the technique. I will, nevertheless, try to explain it quickly. I assume you are familiar with the jpeg compression algorithm. It throws away way more than 5% of the data, and still gives you a nice picture. How? It converts the picture to the wavelet basis, and throws away the high-frequency components. That is, noise and fine-grained details. Depending on the quality of your lens, just noise. Well, this technique makes the measurement directly in the wavelet basis, and never records nor process the components that would be thrown away.
Of course, it is a little more complicated than that, because you have to choose which projectors of the basis you're measuring (answer: a random sample. They recover all the important information with high probability), and you have to make sparsity assumptions (which are true for most images that humans would think of as pictures).
Relevant information: I'm a physicist, and my research group is actively researching quantum state tomography via compressed sensing.
This technique is quite useful also in quantum state tomography. Consider a qubyte. We represent it by an 2^8 x 2^8 matrix of complex numbers. Now we want to measure it. We have to make 2^16 measurements (keep in mind that a quantum measurement is a nontrivial task), and use this data to reconstruct the original matrix, which again is a very intensive task, if done right (there are quick-and-dirty algorithms to do it, but they don't work very well). It is just plain impossible to process so much data, in a day-by-day basis.
But here comes compressed sensing! Normally, we are interested in states that are pure, or quasi-pure. That is, are represented by a sparse matrix, in the correct basis. So, using this technique, we only need to do a quantity of measurements that scale linearly with the dimension of the state (as opposed to the quadratic growth that a full measurement requires), and the amount of processing that we need is also proportional to the amount of measurements.
So, we can shift the limiar of impossibility. Before we needed O(2^(2d)) measurements, now only O(2^d). Still unpleasant, but makes the problem tractable today.
I second that. Many times I've just emailed the paper's authors "SAUCE PLX!!!" and got the code.
Another thing to be aware of is that most code is a piece of shit. Maybe not incorrect, but in a terrible style, unreadable and unmaintainable. Most of the times it is worth to dump someone else's code and start anew, if you have to do modifications.
There are an uncountable number of energy events...
Uncountable? Err... I would think that they are finite. It depends a lot on how you define event, but IMHO it is not possible to get worse than countable infinity.
Yeah, it *is* the same stuff as always, it's only the distance that changed. It was theorized that the particles could *not* remain entangled for nearly that distance -- that makes all the difference.
There was never a theoretical upper bound on the distance within each particles could remain entangled. See the original EPR paper.
What happened recently was an experiment which showed quantum teleportation through a large distance. Which is great, but expected.
You don't flip your particles. You just measure them. You can't determine the outcome. With this in mind, the information you obtained is no more FTL than if each had pre-correlated deck of cards.
What is mysterious in quantum entanglement is that this correlation is kept regardless of which base you measure: this can't be done with a deck of cards.
Just a matter of principle: you can always use math for everything. You can debate it's usefulness.
If you go to a party with the purpose of mating, you probably do some kind of statistic to estimate the percentage of the sex you're fond of that will be present there before you decide to go.
And even more fine-grained, if you go to an electro party there will be less indie people there than in an indie party.
A math as fine-grained as the bloke above, it's hardly useful. But again, it is nigh impossible to have any elaborate thought that does not involve some kind of math.
The fact that people are taking you seriously just proves that the US is a country of uncivilised savages. These things would be unthinkable here in Brasil. I go to the movies weekly, the worst I've faced was a black guy with huge hair sitting in front of me.
Of course, I don't go to films where there will be kids present.
This, my dear, is trolling. It began with Feyerabend, the father of all trolls.
But I actually like the current revisionism, because it makes Galileo a human character that people can relate to, instead of the perfect demigod that lit the torch of science.
The point that he was a prick and played dirty is moot. His life was at stake, ffs.
The point is that it was possible for a parallel government ruin a man's life for what he wrote in a book.
but they are relying on actual physical particles conforming to these rules - which is still under debate
It is not under debate. Quantum mechanics is the most thoroughly tested scientific theory ever.
And it does not rely crucially on that: of course, the particles need to have entanglement so that anything can happen, but it's security (see Ekert's E91) depends only on the validity of the Bell's inequalities, and it's safe even against some magical spy that could violate quantum mechanics.
Of course, no protocol can be safe despite implementation errors. Nevertheless, it's our best shot.
No way. I've never fought Treble directly, but I'm sure that Bass does way more damage. AFAIK it doesn't even have a weapon! If you don't count S-ADAPT.
Slashdot Mirror
The correctness of the mathematical technique is a nice evidence; not a proof. Everyday people make very precise measurements based on the idea that our space is Euclidean. Well it ain't.
To make a statement as strong as "it went through both slits", you need more than very good evidence.
Why there must be? That's philosophy. The Lorentz transformation shows that there isn't. That's it. But allow me to expand. To talk of a "perspective" is imprecise. What we have are referentials, and time slows down relative to another referential. So to be able to speak of time slowing down, you have to be in a valid referential.
Put another way. One of the most basic consequences of special relativity is that there ain't referentials that are c apart. This is the "you can't travel at c" prohibition. It follows that if anything is at travelling at c, it can't be in a referential. And it can't slow down as well; for that you'd need a Lorentz transformation.
But photons aren't that special. Any massless particle travels at c.
You do integrate through both slits, but that does not mean that every photon has actually gone through them. It's a mathematical technique.
What one proves experimentally is that if the which-path information exists (somewhere), there's no interference pattern. To infer from this that it went through both slits is, at best, non-sequitur, and at worse, philosophy.
Also
But from photon's perspective...
there's no photon's perspective. It makes no sense to try to Lorentz-transform you into a referential that's moving at the speed of light. I understand that you're trying to take a limit somewhere, but you can't, it's not well-defined (mathematically), and leads one to nonsensical conclusions.
Still no, sorry. You have a very romanticized view of quantum mechanics. You don't need photons to "see", that's why I used quotation marks.
In the Stern-Gerlach experiment, a foundational one, there's only a magnetic field and a silver plate. In the double-slit experiment, only two slits (duh) and photographic paper.
The photons do not go through all possible paths, and the thing is not in two places at once. The point is that there's no information about it's location (or the photon path). Even assuming that there exists such information would lead to contradictions.
If you want a simple sentence: it's information that does it.
You miss the point. It is not human observation or heat perturbation that collapses the system, it's information obtainment.
The point is, if you can "see" the thing, it will not be in a superposition anymore.
No, they are perfectly deterministic.
To calculate the numerical value of the digits I could understand as useless, but there are plenty of properties that are basis-independent, like it's irrationality, transcendence and normality.
Also, there are some quite beautiful representations, look for the continued fractions one.
No, it doesn't. What does have a different value is the ratio of a circumference to it's diameter, that can be grater than pi (hyperbolic surfaces), or smaller (spherical surfaces). But that ain't the definition of pi, 'cos even in a given surface of constant curvature, this value varies.
Nothing. What frame reference independence actually means is that they are encoding a reference frame in the particles themselves, so that you don't have to worry about external alignment. It does nothing about the communication channel, that does not exist through an events horizon.
As someone who works daily with infinite-dimensional vector spaces, I beg you, do not water down the meaning.
You could call it infinite distance, or asymptotic precision, whatever. But it still has only two dimensions, and that's the way it should be. I think it would be a little confusing if you had to be aware of more dimensions to control your windows ;p
TFA does a terrible job of explaining the technique. No interpolation is involved. You should read this fine article by Terence Tao: http://terrytao.wordpress.com/2007/04/13/compressed-sensing-and-single-pixel-cameras/
It explains quite well the heart of the technique. I will, nevertheless, try to explain it quickly. I assume you are familiar with the jpeg compression algorithm. It throws away way more than 5% of the data, and still gives you a nice picture. How? It converts the picture to the wavelet basis, and throws away the high-frequency components. That is, noise and fine-grained details. Depending on the quality of your lens, just noise. Well, this technique makes the measurement directly in the wavelet basis, and never records nor process the components that would be thrown away.
Of course, it is a little more complicated than that, because you have to choose which projectors of the basis you're measuring (answer: a random sample. They recover all the important information with high probability), and you have to make sparsity assumptions (which are true for most images that humans would think of as pictures).
Relevant information: I'm a physicist, and my research group is actively researching quantum state tomography via compressed sensing.
This technique is quite useful also in quantum state tomography. Consider a qubyte. We represent it by an 2^8 x 2^8 matrix of complex numbers. Now we want to measure it. We have to make 2^16 measurements (keep in mind that a quantum measurement is a nontrivial task), and use this data to reconstruct the original matrix, which again is a very intensive task, if done right (there are quick-and-dirty algorithms to do it, but they don't work very well). It is just plain impossible to process so much data, in a day-by-day basis.
But here comes compressed sensing! Normally, we are interested in states that are pure, or quasi-pure. That is, are represented by a sparse matrix, in the correct basis. So, using this technique, we only need to do a quantity of measurements that scale linearly with the dimension of the state (as opposed to the quadratic growth that a full measurement requires), and the amount of processing that we need is also proportional to the amount of measurements.
So, we can shift the limiar of impossibility. Before we needed O(2^(2d)) measurements, now only O(2^d). Still unpleasant, but makes the problem tractable today.
You know the old Italian proverb: "Si non è vero è ben trovato"
And it was funny.
I second that. Many times I've just emailed the paper's authors "SAUCE PLX!!!" and got the code.
Another thing to be aware of is that most code is a piece of shit. Maybe not incorrect, but in a terrible style, unreadable and unmaintainable. Most of the times it is worth to dump someone else's code and start anew, if you have to do modifications.
59 seconds. So what?
People just don't know how to count.
Nice trolling.
Have you ever heard about basic research? You know, that kind that is very hard to do and takes a long time to become applied?
I have a wild guess that if you forbid basic research in one area you won't get practical results in it.
There are an uncountable number of energy events...
Uncountable? Err... I would think that they are finite. It depends a lot on how you define event, but IMHO it is not possible to get worse than countable infinity.
You just proved that there isn't such a thing as a rigid body. There is this upper limit, imposed by relativity.
You can make some calculations, about the electric pulse propagating through the matter at light speed, but they're trivial and boring.
Yeah, it *is* the same stuff as always, it's only the distance that changed. It was theorized that the particles could *not* remain entangled for nearly that distance -- that makes all the difference.
There was never a theoretical upper bound on the distance within each particles could remain entangled. See the original EPR paper.
What happened recently was an experiment which showed quantum teleportation through a large distance. Which is great, but expected.
Humm... no.
You don't flip your particles. You just measure them. You can't determine the outcome. With this in mind, the information you obtained is no more FTL than if each had pre-correlated deck of cards.
What is mysterious in quantum entanglement is that this correlation is kept regardless of which base you measure: this can't be done with a deck of cards.
I find it amusing that in the math institute I study, there are as much female bathrooms as there are male ones.
The relevant datum is that the female population is ~10% of the total.
Just a matter of principle: you can always use math for everything. You can debate it's usefulness.
If you go to a party with the purpose of mating, you probably do some kind of statistic to estimate the percentage of the sex you're fond of that will be present there before you decide to go.
And even more fine-grained, if you go to an electro party there will be less indie people there than in an indie party.
A math as fine-grained as the bloke above, it's hardly useful. But again, it is nigh impossible to have any elaborate thought that does not involve some kind of math.
The fact that people are taking you seriously just proves that the US is a country of uncivilised savages. These things would be unthinkable here in Brasil. I go to the movies weekly, the worst I've faced was a black guy with huge hair sitting in front of me.
Of course, I don't go to films where there will be kids present.
This, my dear, is trolling. It began with Feyerabend, the father of all trolls.
But I actually like the current revisionism, because it makes Galileo a human character that people can relate to, instead of the perfect demigod that lit the torch of science.
The point that he was a prick and played dirty is moot. His life was at stake, ffs.
The point is that it was possible for a parallel government ruin a man's life for what he wrote in a book.
but they are relying on actual physical particles conforming to these rules - which is still under debate
It is not under debate. Quantum mechanics is the most thoroughly tested scientific theory ever.
And it does not rely crucially on that: of course, the particles need to have entanglement so that anything can happen, but it's security (see Ekert's E91) depends only on the validity of the Bell's inequalities, and it's safe even against some magical spy that could violate quantum mechanics.
Of course, no protocol can be safe despite implementation errors. Nevertheless, it's our best shot.
No way. I've never fought Treble directly, but I'm sure that Bass does way more damage. AFAIK it doesn't even have a weapon! If you don't count S-ADAPT.