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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!
CAN-CON 2019 - Ottawa's only book oriented Science Fiction Convention! October 18-20, Sheraton Hotel, Ottawa, Canada h
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.
So, as I understand it, the uncertainty principle tells us that in order to determine the position of a particle, we'd have to make a photograph of it using a sufficiently high frequency of light, otherwise we'd get a severe interference pattern. However, this high frequency of photons is coupled to high energy, thus knocking the original particle out of its path (in other words changing its momentum). So far so good.
However, assume that the particle is perfectly symmetric, e.g. a sphere. Then the interference pattern will also be symmetric. The image we'd get by making a photograph would look like a bunch of concentric circles. Where is the original particle? Well, at the center of those cirlces of course!
So this is what I don't understand. We can actually deduce the position of the particle precisely from the interference pattern. So where is all the fuzz coming from?
If Pandora's box is destined to be opened, *I* want to be the one to open it.
I thought the photons went through both slits.
(and also took a detour around the Horsehead Nebula along the way...)
No sig today...
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.
Longtime since I thought about this, but isn't everything a wave-particle? I remember reading somewhere that even the earth has properties of wave such that it has specific orbits around the sun. As I recall the orbits only differ by millimeters (something to do with the way the wave function lines up in orbits around the sun similar to why electrons exist in certain orbits but not in between) but nonetheless the earth has wave properties too.
In this experiment, they can know which slit the photons when through
They infer through a study of averages.
You can't take the sky from me...
obviously particles because of the impressions they made on the photo-sensitive paper
No, that's got nothing to do with being a particle or not. The fun of this experiment is that it shows light to be a wave (because of the interference pattern) unless you measure photons going through the slits, in which case there is no interference pattern. Also works with electrons, btw.
You can't take the sky from me...
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
...I'm hunting wavicles! Wehehehehehe!
> 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).
You just described quantum physics... with elephants.
Excellent.
-- IANAL, this isn't legal advice, and definitely isn't legal advice for you. Also, Squee!
Eh, hard to explain what I mean without drawing graphs of wavefunctions, but I'll try (and I may be wrong anyway, someone who's done QM past two 400 level classes four years ago would have to weigh in there).
The interference pattern isn't the result of the photons going through both slits per se (that's a really awkward, but accessible way of explaining the math, and I don't think it works very well), but a result of the wavefunctions of the photons from each slit overlapping and interfering with each other. When you measure which slit the photons travel through the position wavefuction (x-hat Psi) collapses to a Dirac Delta function (basically an infinite probability spike at x=x_0, where x_0 is the position of the slit). Because of this the wavefunctions from the photons going through different slits no longer overlap, so they no longer interfere with each other. The summary's use of the term 'weak measurement' suggests to me that they measure particle position in a way which did not collapse the wavefunctions to a dirac delta entirely, but only enough so that the probability that a photon went through one slit and not the other is large (I'd have to read the actual article to be more specific than that). It is then conceivable that the wavefunctions would still overlap and interfere with each other.
Essentially, they aren't measuring which slit the photons go through exactly, they're taking a measurement which of slit the particles very, very likely went through. For each photon they're saying something like "there's a 99% chance it went through the left [or right] slit," and that measurement apparently doesn't destroy the interference pattern.
Or I could be entirely misreading the summary, or the summary could be fubar.
The point is that if you measure whether or not the photon went through slit 1, you "force it to take a stand", and choose which slit to go through. Thus, the wave function collapses and you no longer get the interference pattern, but just two blops of photons on the back wall.
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.
Only people who do not understand quantum mechanics (and they are legion) forget that it is a statistical theory and go off on tangents about Schrodinger's Cat (a severe criticism of an interpretation of QM that was once fashionable) and the like any more.
The interest of this experiment is that they succeeded in finding an apparatus which was capable of going below the Heisenberg limit--recall that Heisenberg posed many measurement examples where there would be perturbations of the measurement process at least as large as the limits imposed by the (statistical) uncertainty principle. In this sense, it is a sort of confirmation that QM is a statistical theory and describes the outcomes of measurements, and need not describe nature directly (in the same sense that you do not need to understand the mechanics of dice in order to predict the probabilities for the next throw).
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.
Intron: the portion of DNA which expresses nothing useful.
Richard Feynman, in The Character of Physical Law (1965)
That said, I think I can attempt to clarify some of your misunderstandings from my own understanding. In fact someone set me straight if I have any issues of my own :)
The entire notion of a point particle is essentially a classical approximation (as far as geometry goes). In fact, all the spatial information that can be known (ie not completely transparent to the rest of the universe) about a particle is completely contained in its wave function, complex valued defined at every point in space. But the wave function in time must satisfy the Schrödinger equation, and it has been shown by people smarter than I that wave function solutions *must* satisfy the uncertainty principle.
Its easiest to consider what this means in one dimension. Solutions of the Schrödinger Equation are linear combinations of sinusoidal functions of all wavelengths and velocities (with the solution for a particular particle determined like with any differential equation by the spatial and temporal boundary conditions). This is immediately consistent with the wave description of light and matter, as a sinusoidal function has a definite velocity but its position is not defined at all (it looks like a wave :P). So how then
can we get a localized particle, like those we apparently observe enough
to create an entire classical theory around? Well it turns out that taking
linear combinations of waves of differing velocities causes local areas of
destructive and constructive interference, and one can mathematically construct
what's known as a wave
packet. Btw, the time evolution of the wave packet in the picture
on wikipedia is incorrect for solutions to the Schrödinger Equation: particle
wave packets necessarily disperse over time depending on the represented wave
velocities (don't quote me on that). This means the range of represented wave
velocities actually has physical significance. Anyway there's a limit to how
localized a wave packet can get, called a Gaussian wave packet. To achieve
this limit, one has to sum over essentially every possible wave velocity.
So solutions of the Schrödinger Equation can be something with no localization at all and a perfectly well defined velocity, like a sinusoidal function, or with a very acute (but not perfect) localization achieved by an almost infinite range of velocities of component waves. In fact there is a very simple inequality expressing the relationship between the smallness of the localization to the range of velocities (momenta, actually)...
So all that's not that bad. The real strangeness of QM comes with what observation does to the wave function of a particle. Somehow, the act of observation (something I am not knowledgeable enough to define, but examples of which are hitting it with a photon or having it excite the screen in the double slit experiment, or even covering up a slit thus knowing it must go through the other) "collapses" the wave function of a particle back into its most localized form. The probability distribution of the center of the new localized form is given by the product of the wave function with its complex conjugate just before the observation.
The interference pattern corresponds to the probability distribution of particles when they reach the screen behind the double slit. If I fired only one particle through the double slit, it would cause a single photon (probably) to be emitted from the screen, with its location determined by the probability distribution. We can see an interference pattern because we are firing a beam of particles, not just one at a time. The kicker from the experiment is if we observe the interference pattern (say b
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.
I think you misunderstand the post you're replying to. For each photon fired in the two-slit experiment, the photon can register at ANY point on the detector -- that's a fact. It is only once we have fired many photons that we find fewer photons registered in certain areas and more photons registered in other areas, which cannot be explained in classical terms.
The single photon wouldn't necessarily end the superposition, it would just entangle the tree with the environment (which it already was anyway).
Obviously it's absurd to suggest that humans cause collapse, but nobody has yet suggested a convincing enough explanation of what does cause collapse (or if collapse even happens at all), so I don't think the tree is dead just yet :)
The same attitude is needed to look at Higg's Wife's bosom without getting punched.
My first Journal Entry ever, in 8 years! http://slashdot.org/journal/365947/aphelion-scifi-fantasy-horror-poetry-webzine
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.
"Is life so dear, or peace so sweet, as to be purchased at the price of chains and slavery?" - Patrick Henry
That they can reliably measure cats.
I think you have that backwards. QM places strict limits on the information obtainable from individual measurements, but much less strict limits on measurements of ensembles. Any individual interaction can only yield so much information, many interactions can yield more information - but each interaction is separate and doesn't technically say anything about any of the other individual interactions, but rather about the process producing the interactions. The Heisenberg uncertainty principle (specifically the time-energy form) applies even to classical waves - I've seen it myself in testing tunable-Q filters - no need for particles at all. Also, ensembles are not needed for a rigorous statistical theory - the Bayesians deride those who think that ensembles are the basis of statistics as "frequentists", and instead say that probability is really a measure of observers' information, and has different values depending on the degree of information each observer has. The "statistical distribution" of the frequentists is not an objective thing, but depends on the degree of information the observer has, and changes as more data comes in. The Bayesian approach meshes much better with information theory and QM and easily explains apparent paradoxes such as the Monty Hall problem.
"Is life so dear, or peace so sweet, as to be purchased at the price of chains and slavery?" - Patrick Henry
"...the falling tree would have to avoid hitting anything at all (even a single photon hitting it would end it's superposition)"
No, , (assuming the timing of the fall of the tree has some uncertainty, which it must) the tree would just entangle whatever it interacted with into that superposition between fallen and not-fallen and as those things in turn interacted with other things there would be an outward spreading wave of entanglement that would quickly become effectively irreversible (decoherent). In one set of paths the environment (including humans) would be indirectly entangled with a standing tree, in the other with a fallen tree. Decoherence is a matter of degree - for slight degrees it can be reversed, the "observation" undone - see the "quantum eraser" experiments.
"Is life so dear, or peace so sweet, as to be purchased at the price of chains and slavery?" - Patrick Henry
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."
Just like over-inflating a balloon...
"I like to lick butts!" by MobileTatsu-NJG (#32700246) (Score:5, Informative)
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.
>>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).
Even weirder? You can undo the wavefunction collapse, so the photon that you were about to measure appears instead two billion light years away.
http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser
I don't get it How does this differ from the classic two-slit experiment?
Well, the explanation might be a bit long, but try to bare with us.
You see, the main difference is
#include <article.h>
See? Simple as can be!
Sorry if that post got too long winded...
So What? We are the average of the various quantum states of our constituent particles, at least in THIS universe.
Keep Doing Good.
After getting up from laughing so hard, I will say this: "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." What in reality you will actually get is: a: Dead elephants. B: crushed people, cars, wholes in buildings, blood and carcass everywhere. You will never get whether its an national holiday. You will get very angry animal rights people and eternal hatred. And you will hit the detector only once.
your understanding of the HUP is not correct. It isn't that measuring the elephants disturbs them, it's that quantum elephants have trajectory and position, and the more you know of one the less you can possibly know about the other. When you measure one variable, the more exactly you measure it, the less you know about the second variable. It's not that the instrument disturbing the particle that creates uncertainty. For a better explanation, involving dogs and rabbits, I recommend "How to Teach Quantum Physics to Your Dog" by Chad Orzel. Even relatively simply put, there will be parts of the experiments discussed that most people will have to read more than once to at all get even a basic, dog-like understanding.