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Using Averages To Bend the Uncertainty Principle
summerbreeze writes "Researchers at the University of Toronto have conducted a two-slit experiment, published in Science, that uses 'weak measurement' on photons to push back the boundaries of what can be known about them, given the Heisenberg Uncertainty Principle. Jason Palmer does a great job reporting this experiment to us mere mortals in a BBC article: 'The team allowed the photons to pass through a thin sliver of the mineral calcite which gave each photon a tiny nudge in its path, with the amount of deviation dependent on which slit it passed through. By averaging over a great many photons passing through the apparatus, and only measuring the light patterns on a camera, the team was able to infer what paths the photons had taken. While they were able to easily observe the interference pattern indicative of the wave nature of light, they were able also to see from which slits the photons had come, a sure sign of their particle nature."
Yeah Canada, again!
Canada certainly does punch above it's weight in many areas...
But this is a really interesting experiment! It really does turn the classic double slit experiment on it's ear!
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In the classic experiment, if you try to find out which slit the photons are going through, they stop behaving as waves.
In this experiment, they can know which slit the photons when through, but still get the light to behave as a wave.
The key here is surreptitiousness. The researcher must act uninterested and as if they aren't trying to measure anything in particular and especially not with any fine accuracy. It helps if they whistle and distractedly reorganize bottles on a shelf while glancing fleetingly over at the experiment letting out a bored "Meh" as they do so.
Some of my favourite people are from th US; Vonnegut, Chomsky, Bill Hicks.
You're understanding of the basic assertion of the Uncertainty Principal is correct - in order to know the exact position of a particle at an exact moment, you have to measure the particle which changes it's position. Right on.
However, when speaking of electromagnetic phenomena, it's generally understood that we're speaking of something which can be either a particle or a wave, depending upon the property being observed. Call it a 'wavicle', if you like. It's the act of measuring the behavior that "collapses the wave function" - i.e., I can demonstrate exactly where a photon struck a sensor under a certain set of conditions, but doing so collapses the wave function. OR I can demonstrate the wavelike properties of light, but only by sacrificing any clue to the position of the photons which create that wave structure (oddly enough, collapsing the wave function once again).
Now, this is only my understanding of the condition, and I'm not really that certain I've got it right . . .
The HUP is more fundamental than that. It doesn't just say that we can't know where a particle is because measurement disturbs it; rather it's telling you that the particle actually doesn't have a definite trajectory. In fact, it's so fundamental that it has its own mathematical formalism (commutativity of operators), upon which most of quantum mechanics is constructed.
It's important to realize that in quantum mechanics, the position of a particle is indefinite, and is specified by a diffuse/spread-out "cloud" probability, and only in special cases does this cloud collapse to a single point (which corresponds to the particle being in a definite place).
Note that it is possible (theoretically) to know the position or momentum of a particle, just not at the same time, since measuring one causes the other to become indeterminate.
Averaging over many measurements won't allow you to "defeat" uncertainty principle, as uncertainty principle tells you the width of the distribution (of measurements). If you wanted to get a precise measurement of the center of that distribution, yes, you can take many averages and reduce the error on that (see error of the mean), but the width of the distribution (given by uncertainty principle), remains unchanged.
Reading the paper abstract:
It looks like the goal of experiment is to nail down (or get further in nailing down) what constitutes "measurement". But I'm still trying to figure out how this experiment is different from the standard QND (which doesn't claim not to collapse the wavefunction as all measurements ought to).
That's the idea of quantum physics : particles or waves don't move on any specific path, they move on all possible paths between 2 points. But once anything interacts with them the "potential history" function collapses, and they have taken one specific path, which had only one specific set of events taken place.
So photons only go through both slits in the function that describes their movement, not in reality. It's just that the only way to describe their behavior is to assume they go through both slits, because we can't measure these things without disturbing them.
Why not ? Well imagine you have to determine if it's the national holiday in India (they have a big elephant parade). But you don't actually have any tools smaller than elephants to measure this. So every hour or so you catapult an elephant into the main street of New Delhi, and you see if the elephant hits the detector you've set up at the other end of that street. Obviously any "detected" elephant will not be unaffected, and won't ever get to the place where the parade elephants normally end up, and your interference pattern will be gone. Now s/elephants/photons/ and you have the problem of quantum physics (and yes this is a simplification).
Now what these scientists did is they place an "elephant guide" (say a slide) in front of one of the two slits, which does not really affect the elephants, but it does alter their path a little bit, and this is reflected in the position the elephant hits the plate behind the detector. Now they know (not for certain, but better than 50%) which slit the elephant went through, yet they have managed to avoid totally destroying the normal path the elephants take, so the elephants from both slits are still in a position to interact.
A (very) nice video about this : http://www.youtube.com/watch?v=DfPeprQ7oGc
The fun thing is that you can do this with photons which were gravitational lensed around both sides of a galaxy and *still* collapse the wave function. Your measurement instantly changes something which happened a billion years ago (the lensing).
No sig today...
Quantum mechanics is a statistical theory, valid only in the statistical limit of an infinite number of measurements and looking at the ensemble. It actually places no inherent limits on a single measurement, only on an ensemble of measurements. Hence, you have no violation of the uncertainty principle because you are tracking individual photons or a very small number of them. The Stern-Gerlach experiment back in the day observed individual particle strikes but when viewed as a large average you had the interference pattern characteristic of wave phenomena, while the individual flashes on the phosphor screen indicated a particle nature.
That's absurd. The interference patterns in the two-slit experiment are still created even when the intensity is reduced to the point that there is never more than one photon traversing the slits at a time. The QM rules apply to every wavicle, not just to aggregations.
You are misinterpreting Stern-Gerlach which also shows that each particle has quantized values for angular momentum and hence meets QM predictions.
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Sorry to burst some bubbles, but I believe this analogy is not correct :( In fact it is not really possible to analogize quantum mechanics with anything classical, which is what people are getting at when they say that nobody really understands it.
In the experiment in TFA, they never found out which slit any particular photon went through. They have only collected some data about the average behaviour of the total set of photons. TFA suggests the scientists gathered a statistic somewhat like "X photons went through slit 1 and Y photons went through slit 2". Even here, I do not believe this is correct as I have worded it. I haven't read the paper at the article is based on, however if we follow the explanation of the first paragraph of your post, we will have an interference pattern that looks a bit different to the 50-50 one, where the possible paths between the two points have a greater 'density' of going through one of the particular slits. I would imagine that as you gradually change this ratio from 50-50 through to 0-100 the pattern would morph until it ended up being a one-slit diffusion pattern.
The rest of your post makes the same mistake as early efforts to explain the 'uncertainly principle', which was initially thought to be something like: "The particles have exact positions and momenta, but any attempt to measure them must disturb the system'. It was fairly quickly found that this was wrong, and the particles actually do not have well-defined positions and momenta (this is implicit in Schrodinger's equation and other such equations, the 'uncertainty principle' just describes a fact of the mathematical description of what a wavefunction is).
Certainly, photons behave according to the function that describes their movement. However, what is 'reality' is an open question (this is known as the interpretation of quantum mechanics). Some interpretations say that the photon travels through one slit but we cannot know which; some say that the function describing their movement *is* reality, and some say that 'reality' only consists of the photon's emission and its detection; not the stuff in between.
That's much better than the original explanation. To boil it down even further, quanta are waves when they are going somewhere (propagating) and particles when they get there (interacting). Each photon does actually go through both slits, which isn't a problem because it's a wave. When it hits the screen, it interacts in an all-or nothing, localized fashion, which gives the appearance of a particle.
The interesting thing about this experiment is that it further demonstrates that there is a continuum between particle and wave, interaction and propagation, but that this can only be shown as a statistical effect using many observations.
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that it has its own mathematical formalism (commutativity of operators) It's the commutators that matter. Let u and v be the operators for position and momentum in the same direction (plus or minus). Then the commutator is uv-vu. As the operators do not commute, the difference is not zero. Hence, we get the uncertainty principle.