The parent isn't just picking nits here. A lot of responses say something along the lines of "yes, but in our frame of reference, with x=0,t=0 being Earth and Now, this explosion happens at t0" -- and this is perfectly correct. It's not the case, though, that we're stuck with that frame of reference. 1000 years -- the length of time it will take the explosion's light to reach us -- is a really long time. In 400 years, maybe someone will build a spacecraft that could accelerate fast enough to reach 99.9% of the speed of light (relative to Earth's velocity) -- not an entirely ridiculous proposition.
Looking back at the fast-receding Earth, and the fast-receding Pillars of Creation, our intrepid astronaut could reasonably say "Oh -- those pillars will be destroyed in just a few thousand years, and then the light will take a few thousand more to reach me." And that's not just a technicality -- that's honestly what would be true in the astronaut's frame of reference, even if he were the same fellow who wrote today's article.
The pillars' perspective when? Presumably you mean "now, as defined in my reference frame" in which case yes, they have been destroyed. A traveller moving past us at high speed could say that "now, as defined in my reference frame, from the pillars' perspective, they're still intact."
He'd be correct too -- it isn't a matter of what things look like when you're moving fast, it's a matter of how things are. This fellow would say "well, I'm standing still, and those pillars are 6000 light years away; but the light from the explosion will take more than 6000 years to reach me, so it hasn't happened yet." Only he'd say it in some alien language, 'cause presumably he isn't human.
*As far as he's concerned, of course, he's standing still and we're whizzing past him. **Because he's moving so fast in that direction, he doesn't see the distance as being 6000 light years; adjust the numbers appropriately, but the point still holds.
Right, except that for photons, m=0. This equation basically says that no massive particle may ever move at the speed of light (according to current physical theory, of course) because it would take an infinite amount of energy to get it there. The fact that v==c gives us a singularity is another way of saying "all those 9s matter": there's no such thing as "really close" to the speed of light. Because no matter how close you are, get a little closer and you have *way* more energy.
For anyone who's interested, the actual velocity of the electrons is about 0.999999869 times the speed of light -- which is why talking about GeV is more instructive than talking about how fast the particle goes. The math follows, if you're interested.
1GeV = energy = gamma * m * c^2 (gamma = 1/sqrt(1-v^2/c^2)) 1 GeV / c^2 / m = gamma 1957 = gamma = 1/sqrt(1-v^2/c^2) v/c = 0.999999869... or you can type sqrt(1-1/(1GeV / electron mass / c^2)^2) into Google Calculator.
Interesting fact: we usually hear about E = mc^2. That's the direct matter->energy conversion when the matter is at rest: if the matter is moving, we add on a factor of "gamma" -- which, at small velocities, is about 1 + 1/2 * v^2/c^2 (giving E = mc^2 + 1/2 mv^2, or rest mass + classical kinetic energy!)
...while it mostly wouldn't make a difference, Feynman (in his Lectures) once went on a tiff about the difference between matter and antimatter. He said that if you were in voice communication with a far-distant planet, there would be no way to determine whether those people were made of matter or anti-matter. The only way in which the two can not be switched is chirality; basically, an electron in a magnetic field revolves one way, and a positron revolves the other way. The problem is that this is a difference between left and right, and those two concepts are down to vocabulary. Feynman said that you might not know the difference until you held out your right hand to shake, and the other guy held out his left... at which point it would be time to run away very fast.
It's not so much that he's a fraud. My understanding is that D-Wave is really working on this stuff, but they're known for somewhat optimistic press releases. Realistically it doesn't seem very likely that this approach is going to have us factoring like mad any time soon (much less getting quadratic speedups on more mundane problems).
The contest has changed a lot over the years. I would agree that the tasks of many moons ago are quite simple algorithmically: on this year's contest I suspect you would have a great deal more trouble. For an example of recent World Finals problems, please see The live archive. I think you'll find them much more interesting.
A correction: I just followed the paper trail back and discovered that it isn't talking about cloning as I discussed above: it's talking about cloning as one would normally imagine it (actual copies), but with limited fidelity. If you want to get above the ceiling on fidelity, you have to start entangling your states as per my discussion of cloning above. Please save me some embarrassment by not modding the parent up.:-)
Let me see if I can explain this in English, with minimal math. (ed: not without taking a page)
First, I should make it clear that this isn't a dramatic new idea or a new "take" on quantum physics. That being said, it's pretty neat. Like quantum teleportation or quantum computing, it's the sort of thing that you know is theoretically possible, but is still very exciting when somebody does it.
Let's talk about three things: quantum teleportation, quantum cloning, and quantum telecloning.
I'm going to talk about everything in the context of "qubits," quantum bits. As anyone reading this probably already knows, a normal bit can have the states 0 and 1; so can a qubit, though we call them |0> and |1>. Unlike a bit, a qubit can also have intermediate states, like (|0> + |1>). [*] As you also may know, whatever the qubit's state is -- |0> + |1>, |0> - |1>, 1/2 |0> + sqrt(3)/2 |1>, or whatever -- if you measure the qubit, you'll get either |0> or |1>, and no indication of what state it was in previously.
That's why we need QUANTUM TELEPORTATION. Suppose I have a qubit in state A = a|0> + b|1>, and I want to send it to you on the other side of the world. Even supposing that I knew what my state was -- and if I don't, I can't find out -- it would take a long time to transmit a and b, since they're arbitrary real numbers. Quantum teleportation is the transmission of an exact copy of A from me to you. We need to start off with some entangled qubits that we made last time we met, but for the moment we'll assume that we have those.
So what is QUANTUM CLONING, and why isn't teleportation it? Well, teleportation has the unfortunate feature that if I want you to have a copy of A, I have to destroy my copy of it in the process. Ideally, what quantum cloning would do is give you and me each a copy of A. Unfortunately, you can't do that: there's something called the No Cloning Theorem [**] that expressly forbids doing that. The best you can do with quantum cloning is make a copy that isn't only a copy; it's entangled with the original. What that means is if I measure my copy of A and get |0> or |1>, your copy is stuck with the same result: if I got |0>, you'll get |0>. Mathematically, we start with a|0>|0> + b|1>|1>, and measuring with result |1> will change that to |1>|1>. So it's a clone, but the clones' destinies are intertwined.
There's another post where someone asks about Heisenberg's Uncertainty Principle: could I use this to make two copies of A, and measure the position of one and the momentum of the other? Well, you could, but it would be exactly equivalent to just taking A and measuring its position and then its momentum. By measuring, you change the state of both copies.
So now we bring all this together, with QUANTUM TELECLONING. We're going to do quantum teleportation just like before: you and I already shared some entangled qubits ahead of time, and we want to teleport. But this time, instead of just a pair of entangled qubits, we have a triplet: I got one of the qubits, and you and my MSc supervisor Bill each got one. Now when I send A to you both, you get a copy and Bill gets a copy (and I lose mine), just like in quantum teleportation. But the copies you have are clones as I discussed above: if either of you ever makes a measurement, it will affect the other's state.
The application of this to quantum communication is that I can throw a wiretap into your communication line, and through this technique I can clone a copy of your qubit for myself -- and also let you have an exact copy of the original go through unimpeded. So what does this do to quantum cryptography? To be honest I'm not sure, but it's clearly not quite like you're just another receiver. I'm going to a lecture on this either tomorrow or Tuesday, so I'll post a followup then. You can also contact me at slashdotphysicist at geemail if you're interested in more.
- merge with semantic web work to be able to search on higher level concepts (e.g. if I type "bubble sort" it returns all bubble sorting code even if it doesn't explicitly say "bubble sort" anywhere)
And after that, you could search for "given the initial input, code that terminates"! That would be awesome.
All right; I've read the abstract and skimmed the article. The number 2^16 never shows up either in that form or as 65,536. I have no idea where the reporters got that number, nor can I find anything in my knowledge of quantum computing to justify it. There's no '4' in single qubits, and no reason to square the number of states you have available. Just like 8 bits, 8 qubits allow for 256 entangled states.
A qubit has an uncountably infinite number of states: choose any two complex numbers A and B such that |A|^2 + |B|^2 = 1, and they define an allowed qubit. On the other hand, when you measure a qubit's state, you can get one of two results: 0 (with probability |A|^2) or 1 (with probability |B|^2).
I can't find the original article, so I don't know where this 2^16 business is coming from, but I assure you that a qubit does not have four states -- the only useful numbers for counting a qubit's number of states are infinity (quantum states) and two (possible measurement results).
If someone can link the paper this comes from, I'd be interested in reading it: I'm doing a MSc in quantum computing right now, so I might be able to decipher the source of this 2^16 stuff.
Slashdot Mirror
The parent isn't just picking nits here. A lot of responses say something along the lines of "yes, but in our frame of reference, with x=0,t=0 being Earth and Now, this explosion happens at t0" -- and this is perfectly correct. It's not the case, though, that we're stuck with that frame of reference. 1000 years -- the length of time it will take the explosion's light to reach us -- is a really long time. In 400 years, maybe someone will build a spacecraft that could accelerate fast enough to reach 99.9% of the speed of light (relative to Earth's velocity) -- not an entirely ridiculous proposition.
Looking back at the fast-receding Earth, and the fast-receding Pillars of Creation, our intrepid astronaut could reasonably say "Oh -- those pillars will be destroyed in just a few thousand years, and then the light will take a few thousand more to reach me." And that's not just a technicality -- that's honestly what would be true in the astronaut's frame of reference, even if he were the same fellow who wrote today's article.
The pillars' perspective when? Presumably you mean "now, as defined in my reference frame" in which case yes, they have been destroyed. A traveller moving past us at high speed could say that "now, as defined in my reference frame, from the pillars' perspective, they're still intact."
He'd be correct too -- it isn't a matter of what things look like when you're moving fast, it's a matter of how things are. This fellow would say "well, I'm standing still, and those pillars are 6000 light years away; but the light from the explosion will take more than 6000 years to reach me, so it hasn't happened yet." Only he'd say it in some alien language, 'cause presumably he isn't human.
*As far as he's concerned, of course, he's standing still and we're whizzing past him.
**Because he's moving so fast in that direction, he doesn't see the distance as being 6000 light years; adjust the numbers appropriately, but the point still holds.
Right, except that for photons, m=0. This equation basically says that no massive particle may ever move at the speed of light (according to current physical theory, of course) because it would take an infinite amount of energy to get it there. The fact that v==c gives us a singularity is another way of saying "all those 9s matter": there's no such thing as "really close" to the speed of light. Because no matter how close you are, get a little closer and you have *way* more energy.
For anyone who's interested, the actual velocity of the electrons is about 0.999999869 times the speed of light -- which is why talking about GeV is more instructive than talking about how fast the particle goes. The math follows, if you're interested.
... or you can type sqrt(1-1/(1GeV / electron mass / c^2)^2) into Google Calculator.
1GeV = energy = gamma * m * c^2 (gamma = 1/sqrt(1-v^2/c^2))
1 GeV / c^2 / m = gamma
1957 = gamma = 1/sqrt(1-v^2/c^2)
v/c = 0.999999869
Interesting fact: we usually hear about E = mc^2. That's the direct matter->energy conversion when the matter is at rest: if the matter is moving, we add on a factor of "gamma" -- which, at small velocities, is about 1 + 1/2 * v^2/c^2 (giving E = mc^2 + 1/2 mv^2, or rest mass + classical kinetic energy!)
...while it mostly wouldn't make a difference, Feynman (in his Lectures) once went on a tiff about the difference between matter and antimatter. He said that if you were in voice communication with a far-distant planet, there would be no way to determine whether those people were made of matter or anti-matter. The only way in which the two can not be switched is chirality; basically, an electron in a magnetic field revolves one way, and a positron revolves the other way. The problem is that this is a difference between left and right, and those two concepts are down to vocabulary. Feynman said that you might not know the difference until you held out your right hand to shake, and the other guy held out his left... at which point it would be time to run away very fast.
It's not so much that he's a fraud. My understanding is that D-Wave is really working on this stuff, but they're known for somewhat optimistic press releases. Realistically it doesn't seem very likely that this approach is going to have us factoring like mad any time soon (much less getting quadratic speedups on more mundane problems).
BAHAHAHAHAHAHAHA. Awesome.
The contest has changed a lot over the years. I would agree that the tasks of many moons ago are quite simple algorithmically: on this year's contest I suspect you would have a great deal more trouble. For an example of recent World Finals problems, please see The live archive. I think you'll find them much more interesting.
New tags: terrifying, horrifying
A correction: I just followed the paper trail back and discovered that it isn't talking about cloning as I discussed above: it's talking about cloning as one would normally imagine it (actual copies), but with limited fidelity. If you want to get above the ceiling on fidelity, you have to start entangling your states as per my discussion of cloning above. Please save me some embarrassment by not modding the parent up. :-)
b 01.pdf )
(The paper in question: http://www-users.cs.york.ac.uk/~schmuel/papers/LB
Let me see if I can explain this in English, with minimal math. (ed: not without taking a page)
First, I should make it clear that this isn't a dramatic new idea or a new "take" on quantum physics. That being said, it's pretty neat. Like quantum teleportation or quantum computing, it's the sort of thing that you know is theoretically possible, but is still very exciting when somebody does it.
Let's talk about three things: quantum teleportation, quantum cloning, and quantum telecloning.
I'm going to talk about everything in the context of "qubits," quantum bits. As anyone reading this probably already knows, a normal bit can have the states 0 and 1; so can a qubit, though we call them |0> and |1>. Unlike a bit, a qubit can also have intermediate states, like (|0> + |1>). [*] As you also may know, whatever the qubit's state is -- |0> + |1>, |0> - |1>, 1/2 |0> + sqrt(3)/2 |1>, or whatever -- if you measure the qubit, you'll get either |0> or |1>, and no indication of what state it was in previously.
That's why we need QUANTUM TELEPORTATION. Suppose I have a qubit in state A = a|0> + b|1>, and I want to send it to you on the other side of the world. Even supposing that I knew what my state was -- and if I don't, I can't find out -- it would take a long time to transmit a and b, since they're arbitrary real numbers. Quantum teleportation is the transmission of an exact copy of A from me to you. We need to start off with some entangled qubits that we made last time we met, but for the moment we'll assume that we have those.
So what is QUANTUM CLONING, and why isn't teleportation it? Well, teleportation has the unfortunate feature that if I want you to have a copy of A, I have to destroy my copy of it in the process. Ideally, what quantum cloning would do is give you and me each a copy of A. Unfortunately, you can't do that: there's something called the No Cloning Theorem [**] that expressly forbids doing that. The best you can do with quantum cloning is make a copy that isn't only a copy; it's entangled with the original. What that means is if I measure my copy of A and get |0> or |1>, your copy is stuck with the same result: if I got |0>, you'll get |0>. Mathematically, we start with a|0>|0> + b|1>|1>, and measuring with result |1> will change that to |1>|1>. So it's a clone, but the clones' destinies are intertwined.
There's another post where someone asks about Heisenberg's Uncertainty Principle: could I use this to make two copies of A, and measure the position of one and the momentum of the other? Well, you could, but it would be exactly equivalent to just taking A and measuring its position and then its momentum. By measuring, you change the state of both copies.
So now we bring all this together, with QUANTUM TELECLONING. We're going to do quantum teleportation just like before: you and I already shared some entangled qubits ahead of time, and we want to teleport. But this time, instead of just a pair of entangled qubits, we have a triplet: I got one of the qubits, and you and my MSc supervisor Bill each got one. Now when I send A to you both, you get a copy and Bill gets a copy (and I lose mine), just like in quantum teleportation. But the copies you have are clones as I discussed above: if either of you ever makes a measurement, it will affect the other's state.
The application of this to quantum communication is that I can throw a wiretap into your communication line, and through this technique I can clone a copy of your qubit for myself -- and also let you have an exact copy of the original go through unimpeded. So what does this do to quantum cryptography? To be honest I'm not sure, but it's clearly not quite like you're just another receiver. I'm going to a lecture on this either tomorrow or Tuesday, so I'll post a followup then. You can also contact me at slashdotphysicist at geemail if you're interested in more.
[*] There should be a
All right; I've read the abstract and skimmed the article. The number 2^16 never shows up either in that form or as 65,536. I have no idea where the reporters got that number, nor can I find anything in my knowledge of quantum computing to justify it. There's no '4' in single qubits, and no reason to square the number of states you have available. Just like 8 bits, 8 qubits allow for 256 entangled states.
A qubit has an uncountably infinite number of states: choose any two complex numbers A and B such that |A|^2 + |B|^2 = 1, and they define an allowed qubit. On the other hand, when you measure a qubit's state, you can get one of two results: 0 (with probability |A|^2) or 1 (with probability |B|^2).
I can't find the original article, so I don't know where this 2^16 business is coming from, but I assure you that a qubit does not have four states -- the only useful numbers for counting a qubit's number of states are infinity (quantum states) and two (possible measurement results).
If someone can link the paper this comes from, I'd be interested in reading it: I'm doing a MSc in quantum computing right now, so I might be able to decipher the source of this 2^16 stuff.