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Violation of Heisenberg's Uncertainty Principle
mbone writes "A very interesting paper (PDF) has just hit the streets (or, at least, Physics Review Letters) about the Heisenberg uncertainty relationship as it was originally formulated about measurements. The researchers find that they can exceed the uncertainty limit in measurements (although the uncertainty limit in quantum states is still followed, so the foundations of quantum mechanics still appear to be sound.) This is really an attack on quantum entanglement (the correlations imposed between two related particles), and so may have immediate applications in cracking quantum cryptography systems. It may also be easier to read quantum communications without being detected than people originally thought."
Let's just get all the Walter White jokes out of the way...
I learned about it on the factual science TV show (currently honored on Google.com), Star Trek. They need a Heisenberg compensator.
"Microsoft issues yet another patch to its quantum communications system to prevent hackers from eavesdropping on encrypted signals. The updates will be issued on Tuesday, but they might not be..."
Sorry, but gray text on gray background is making my eyes bleed.
"...so the foundations of quantum mechanics still appear to be sound..."
Are they sure about that? I think they fe-line to us.
I've calculated my velocity with such exquisite precision that I have no idea where I am.
This is exactly how I feel when it comes to quantum-anything. Especially quantum-computing, which leaves me looking at papers on it the way my cat looks at me when I ask him to do my taxes. It's one of the best examples I've encountered of anything sufficiently advanced enough being indistinguishable from magic.
that Walt Jr. can have BOTH pancakes AND cereal for breakfast?
I like microcars
Quantum "encryption" was never that. It is only quantum "modulation" and its "security" is pure conjecture, not anything actually provable in the mathematical sense as you get with real encryption. That does not hinder a log of gullible fools to hail it as the new thing. (It does have a lot of other fundamental and unsolved problems, even if it should be secure.)
Most ACs are not even worth the keystrokes to insult them. Be generically insulted by this and ignored otherwise.
Actually, it's the equivalent of finding socks in the dark. If two photons are produced by an interaction of spin zero then the two photons will have spin up and spin down, although you can't know which is which without measuring one. What you DO know is that they have opposite spin, so by measuring one you instantly receive information about the other, however far away it is. There are several "pairs" of information which each particle/photon can have, such as momentum/location, the more accurately you measure one the less accurately you know the other, what these guys are proposing (as far as I can tell, it's at the limit of my understanding) is that they can use entanglement properties to discover information beyond Heisenberg's original limit.
Please consider this account deleted, I just can't be bothered with the spam anymore.
Back in the day we didn't have Quantum Computers, but we did have Quantum hard drives. You were never certain when they were going to fail
The uncertainty on my understanding of this article is very large, that mean the uncertainty on someone else's understanding is very small. That person needs to explain it.
Q: "So, how do your Heisenberg compensators work?"
The researchers: "They work just fine, thank you."
Ezekiel 23:20
that they checked heir cables before publishing this.
Most people won't consider quantum physics magic simply because it involves things that aren't experienced in everyday life. If I see a chair float in the air, I'd say it's magic because a chair suddenly floating up is contrary to my everyday experience of chairs. Familiar things behaving in unfamiliar ways, that's magic. A person being cut up and put back together is a magic trick. A medieval person might consider the Amazon Kindle magic because it resembles a book or at least a biblical tablet and yet contains the contents of thousands of books.
I'd consider quantum states magical only in so far as they produce macroscopic effects, a real-life cat that's both alive and dead. Quantum entanglement would be magical if it would allow us to develop instantaneous communication devices or, even more magical, Star Trek-style teleportation.
Shouldn't be hard, just dont focus on his speed.
Besides, if guns kill people, then meth will ruin your teeth... no... ehhhh... never mind...
Just dont focus on his speed ok!?!
rm -rf --no-preserve-root /
This article is horrible.
"The Heisenberg uncertainty principle is in part an embodiment of the idea that in the quantum world, the mere act of observing an event changes it."
That's not the Heisenberg uncertainty principle. That's just the observer effect, and it's not something peculiar to quantum mechanics. You want to measure the temperature of a system, so you stick a thermometer in there. Okay, the mercury in the thermometer absorbs a bit of heat from the system, providing you with a temperature measurement at the same time it changes the temperature of the system. If you want to measure the parameters of a particle, you stick a bubble chamber in the way, and as the particle flies through the chamber it smacks into hydrogen molecules, showing you what it's doing but also taking a different path than it would have if none of those hydrogen molecules were in the way. Big fat hairy deal.
The HUP doesn't just say that you can't simultaneously measure the position and momentum of a particle, it says that a particle *does not simultaneously possess* a well-defined position and momentum. If the particle's doing something in a system and is interacting in such a way that you can define its position to arbitrary precision, then it *does not have* a well-defined momentum for you to measure, and vice versa. Position and momentum are what are called quantum conjugate variables, and the HUP says that when you have a pair of those variables, then the product of their uncertainties is greater than or equal to a constant. There is *no state* in which that particle is even *allowed* to exist in which it possesses both a well-defined position and well-defined momentum.
A signal processing analogy, for any analog people. A particle's wavefunction carries information about its position and its momentum. Where the wave exists is where the particle actually is, and the wavelength is the particle's momentum. Take a particle whose momentum you know to the utmost precision, and graph that. Range of momentums on the x axis, probability of the particle having that momentum on the y axis. You'll get a graph that looks like a Dirac function, a value of 0 everywhere except for a single spike corresponding to the particle momentum, area under the curve of 1.
Now switch domains, change from the momentum to the position domain, this is mathmatically the same thing as changing from a time domain to a frequency domain, which means you can use your old friend the Fourier Transform.
What do you get when you do an FT of a Dirac function? You get a constant value everywhere, from -infinity to +infinity. If you know exactly where that particle is, you have no idea *where* it is, and it's not because you disturbed it in measuring it, it's because *it* has no idea where it is, a well-defined position does not exist; since the uncertainty in the momentum measurement approaches zero than the uncertainty in the position measurement has to approach infinity so that the product of those uncertainties remains greater than a constant.
The "you change the system by measuring it" is an analogy, and it's one that Heisenberg himself used to explain the HUP, but *that is not what it says*. The HUP is not a statement about the process of measuring things, it is a statement about the nature of the universe, and finding a way to improve a measuring system to reduce the disturbance it creates in the system it's measuring has nothing to do with the HUP.
So the paper says we are not sure about the uncertainty principle?
Bearing in mind that it's generally an error to try to summarise anything about quantum mechanics in a paragraph or two:
Actually, it's the equivalent of finding socks in the dark. If two photons are produced by an interaction of spin zero then the two photons will have spin up and spin down, although you can't know which is which without measuring one. .
I'm sorry,. but the way you write that makes it seem that they have spin up and spin down, and then you measure them to find out which is which. If that's indeed what you meant, I'm afraid that's fundamentally incorrect.
The whole point about the weirdness of quantum entanglement is that the quanta are NOT in a state where one is up and one is down prior to the measurement. Only when you make the measurement does this happen. Prior to the measurement, quantum mechanics says that they are both in a state that is BOTH up and down at the same time.
In other words, quanta are not like socks. We can be reasonably sure that socks' measurable properties are fixed before we actually look at them. Not so with quanta.
You can think of this in this way: when you make a measurement on one of the quanta, it flips a coin that tells it whether to be up or down. Its twin quantum is then bound to give the opposite result. But prior to the coin toss, neither quantum knows how it will respond to a measurement. The most that can be said is that whatever the result of measuring one, the other will give the opposite result.
This has been tested experimentally. http://en.wikipedia.org/wiki/Bell_test_experiments
In soviet russia the government regulates the companies.
I'm waiting for the undead cat.
Mind the frickin' laser...
Yes, sorry, I over-simplified. What I should have said is that the two photons have a combined spin of zero, both have an indeterminate state so that indeterminate state A + indeterminate state B = spin zero. When one particle or the other is measured the two wavefunctions collapse (Copenhagen) or we find out which of the possible universes we are in (Everett).
Does this experiment have any bearing on Bell's Inequality? (And on that thread, would Bell's Theorem be satisfied by an infinite number of hidden variables?)
Please consider this account deleted, I just can't be bothered with the spam anymore.
To prove Bell's Theorem you simply assume a single other hidden variable exists, perhaps signifying if the particle is actually spin up or spin down before you measure it. This assumption contradicts quantum mechanics and therefore cannot be true, so there is nothing else you can know about the system if quantum mechanics is the correct description.
If simply one more variable produced this result, I do not see how adding infinitely many more variables would help, or be of any practical use as a theory of nature.
That is a good description of classical entanglement - what, in this context, would be called a hidden variable theory (the cards have a certain face value, even if you can't see them).
Let's see if I can expand this analogy. Suppose you had two decks of cards, each with only two cards - say the king of hearts and the king of spades. Off-stage, I shuffle them, so that there is either one deck of 2 hearts, and one of two spades, or one deck of both, and another of both. Say that the chances of either shuffle are the same.
Now, repeat your experiment, except you and your friend only get to pull 1 card each, each from your own deck. Classically, the chances are
- 50%, you pull from 1 spade and 1 heart
- 25%, you pull from 2 spades
- 25%, you pull from 2 hearts.
And, of course, ditto for your friend.
Now, if you pull a spade, then the classical chances are
2/3 the other card is a heart
1/3 the other card is a spade
and the classical chances for your friend are thus
2/3 he has a spade and a heart
1/3 he has 2 hearts
so his (classical) chances on his card are
2/3 he pulls a heart
1/3 he pulls a spade.
(If you pull a spade, you CANNOT have two hearts, while he can.)
So, if you pull a Spade, you can tell your friend he is likely to have a heart. Do this a lot of times, and you should be correct 2/3 of the time. The cards are indeed entangled, but classically. Experimental error (maybe you can't always see your cards well) will lower this, but (for a long enough term average) cannot raise this.
In Quantum Mechanics, however, you can get correlations that you cannot get in classical physics, i.e., greater than 2/3 in this case. That is the essence of Bell's Theorem - you have correlations that you just can't "get there from here," classically. This is a consequence of having a complex amplitude. Again, it's not just having a correlation, it's that you can get correlations you just can't classically.
I saw a lecture from Dick Feynman once where he showed that you could explain all of this by allowing for negative probabilities for intermediate results, and that this was mathematically the same as the normal (i.e., complex) formulation of QM. (Since you cannot actually measure the intermediate results, you never actually measure a negative probability.) In some ways, I find that helps to grasp the weirdness. YMMV.
I have a lemon 20MB Quantum hard drive in an ancient box. It's a lemon because it still reads and writes!
There are a huge number of yeast infections in this county. Probably because we're downriver from the bread factory.
Feynman's path integrals are over all space, or all paths, but are of the wave function. Bell's proof showed that any hidden variables would produce different results when measurements are taken, or Feynman's path integrals calculated. So no, hidden variables do not exist. Thinking about whether the particle is actually spin up or spin down before measurements are taken is meaningless, as quantum mechanics only give probabilities of the outcome of a measurement using the wave function to calculate these probabilities. It actually says nothing at all about the particle before measurements are taken.
But could it have been hearts? No, it was actually a spades card the whole time, you just didn't know. It had the property of being a spades the entire time (a hidden variable). Could you spin flip his card to a hearts and have yours change to a spade faster than light? No. Quantum mechanics however works this way, although you still cannot transfer information faster than light, and there is no property (hidden variable) that tells you what it was before the measurement was made. Measuring the spin on a different axis will also give you non classical results in these entangled states.
Prior to measurement by whom or what? - You, me, some physical process somewhere that no-one is aware of? Surely it's just a status of lack of knowledge - not an actual physical status.
This has been troubling philosophers for the last 100 years or so, but the majority viewpoint now is that when something "measures" a system, what's happening is that the measurer interacts with the system, and they become entangled together. The result of this entanglement turns out to be that "me-seeing-down + it-being-down" and "me-seeing-up + it-being-up" dominate the possible outcomes.
Look up 'interpretation of quantum mechanics' on wikipedia for much more detailed info
The 'lack of knowledge' theory is fairly easily debunked (see Bell inequailities). There's no way you can explain the results of the experiment in terms of there being a concrete physical status that we just don't know about yet.
I have a lemon 20MB Quantum hard drive in an ancient box. It's a lemon because it still reads and writes!
You won't know whether it still works unless you open the box.
Wait...
If it weren't for deadlines, nothing would be late.
There's no way to measure whether a measurement has been performed. However there's a way to determine whether the measurement result has been predetermined by the state before the measurement. The most striking one is the Mermin paradox: There you measure a certain state (called GHZ state), and get a complete contradiction to predetermined values, no probabilities involved!
Here's how it goes:
You have a system composed of three subsystems, and prepared in a certain way (namely the way which gives that GHZ state). On each of the subsystems you can do one of two measurements, named X and Y, each of which can give either +1 or -1 as result. Now consider the following: We measure X on the first subsystem, and Y on the second and third, and multiply the results together (for brevity, denote that specific measurement as XYY). If we do that on the GHZ state, we find -1 every single time. The same is true for YXY and YYX (which jus thave the X measurements on another subsystem).
Now let's assume that for each single preparation, the measurement result was predetermined. That is, even before measuring e.g. X on subsystem 1, it is either determined that the result will be x1=+1, or x1=-1. Of course for the next preparation, the value of x1 may already be different. However, in each single instance, we would have six pre-determined values, x1, y1, x2, y2, x3 and y3, each one being either -1 or +1.
Now our experiments showed us that our preparation procedure always produces states where measuring XYY gives -1. Now under the assumption that all measurement results are predetermined, the measurement XYY of course gives the result x1*y2*y3. In other words, our preparation procedure obviously generates only systems with x1*y2*y3=-1. Also, the fact that all measurements of YXY give -1 leads to the condition that y1*x2*y3=-1. Finally, since we get always -1 for the YYX measurement, we also have y1*y2*x3=-1. Now, let's multiply all three equations together, to get x1*y2*y3*y1*x2*y3*y1*y2*x3=-1*-1*-1=-1. Note that each of y1, y2 and y3 occurs twice in the product. But since each of them can only be either +1 or -1, those cancel out and you are left with x1*x2*x3=-1 (note that this is pure mathematics; no physical assumptions go into that calculation). So you'd conclude that if you measure XXX, you shoul get, unconditionally, the value -1.
Now let's get back to our laboratory, and do that measurement. What do we get? We get +1, unconditionally. So where in the above have we been wrong? Well, the only assumption we've put in the above calculation is that the values are predetermined by the system's state (that is, the values x1, x2, x3, y1, y2, y3 actually exist). All the rest is either pure mathematics (and quite elementary mathematics, at that), or something you can measure (and which have been measured; and while in real live you'll always have some noise, it's not hard to see that for sufficiently low noise, you still get a contradiction). So the only way where our argumentation can be wrong is the assumption that the values are predetermined by the system we prepared.
The Tao of math: The numbers you can count are not the real numbers.
Well, the pdf link goes to arXiv, which is accessible by anyone. For quantitative results, see esp. figure 4.
The Tao of math: The numbers you can count are not the real numbers.
There's no way to measure whether a measurement has been performed. However there's a way to determine whether the measurement result has been predetermined by the state before the measurement.
But aren't those the same thing? Say you have two physicists. One does his little quantum teleportation experiment and writes down the states of the photons. Then he hands of the photons to another physicist, but doesn't tell him that the photons come from a teleportation experiment. The second guy now does all those fancy other experiments to check if they have a predefined state. So how can the second guy come out negative, but the first guy can have all the states written down on a piece of paper?
No, those are not the same thing. Maybe I should clarify that first sentence, because if interpreted in a too broad way, it's actually wrong; for example, if we know that we prepared the spin of a set of spin-1/2-particles in positive x direction, and someone might have measured them in z direction, then of course we can find out whether that happened by measuring the spins: Just measure them in x direction again, and if the z measurement had been performed, and only then, half of them will be found to have the spin in negative x direction.
However what we cannot determine is when we do a measurement, whether the same measurement has been performed before (that is, we cannot exclude for sure whether some specific result was predetermined. However we can create states where we can rule out that all possible measurement values had been predetermined (of which I gave an example).
Now for your teleportation scenario, it won't work. The point is that if you look closer, the very mechanism which allows you to to do quantum teleportation at all disables you to draw any conclusions from measurements of your part of the state alone (note that for the Mermin paradox, which proves that you can't have all measurement results predetermined, you also need to access to the measurement results on all subsystems; if you only have access to one or two of them, you cannot make any conclusions, and indeed the measurement results look completely random). Unfortunately I don't know an easy way to explain that without going through the actual maths.
The Tao of math: The numbers you can count are not the real numbers.