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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
How does this differ from the classic two-slit experiment?
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.
> So, as I understand it...
You don't. Please read up on it.
Warning: this article may contain humor, sarcasm, parody, and perhaps even irony. Read at your own risk.
But where does the interference come from, if the individual photon does not extend through both holes? They are using single photons.
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.
https://rapidshare.com/#!download|639tl|2460541193|Science-2011-Kocsis-1170-3.pdf|662|R~0
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).
What?
So this is what I don't understand.
Sorry, but this is not the only point you don't understand. None of the points you make in your post show any basic understanding of the issue you are trying to discuss.
...I'm hunting wavicles! Wehehehehehe!
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
Oh boy... a photograph? Of a subatomic 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.
I don't even...
thus knocking the original particle out of its path
This is the only part that made any sense.
If you're detecting a particle, you have to use another particle to do it, 'cause otherwise... how would you? So it's like finding out information about a car by blindly throwing other cars at it and measuring the collision: you're gonna affect the thing you're measuring by the act of measuring it.
You can't take the sky from me...
> 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!
"I think I can safely say that nobody understands quantum mechanics."
- Richard Feynman
So it's like finding out information about a car by blindly throwing other cars at it and measuring the collision: you're gonna affect the thing you're measuring by the act of measuring it.
The point was that you could detect the position of the car by using much lighter objects (or objects with less energy), e.g. ping pong balls, and by deducing the position of the car from the interference pattern.
If Pandora's box is destined to be opened, *I* want to be the one to open it.
Easier if you ask me...
The point was that you could detect the position of the car by using much lighter objects (or objects with less energy), e.g. ping pong balls
Ok, re-substitute "car" back to photon. Your ping-pong ball is a substitution for what, and how are you measuring that?
You can't take the sky from me...
And how would you do that when the particle you're trying to measure IS the size of the smallest thing you can reliably throw at your target?
When measuring the path of a photon, you only have other... photons to throw at it. though there's some that have the idea that they can reverse proton smash to get smaller resolutions, (ie, smash a particle that you reliably know how it should explode, and measure the interactions of those sub-atomic particles with the particle in question) it's a LONG stretch to get there currently.
the car analogy only works if you keep in mind that the car is the smallest unit of matter in that universe. there is no smaller bits that you can pick up and toss around. a better analogy would be pool balls (where they're all the same size/weight) and you can not put anything onto the table. you have to (without looking) determine the vector's momentum and direction with nothing but other pool balls. try getting someone to shoot a ball across the table, and determine it's direction AND momentum using nothing but another pool ball (while blindfolded)
But it IS possible to understand the math behind the uncertainty principle, even though the OP obviously doesn't.
The goal of measurement is to find both the position and momentum of a photon so that they can plot a trajectory in order to predict the future speeds and positions. The uncertainty principle precludes exact measurement of both, but in this experiment they utilize a 'weak' type of measurement and by repeating the experiment they get averages of trajectories. This does not violate the uncertainty principle but does start to give average trajectories in contrasts to single dimensional data (ie position or momentum). It's not as sexy as saying that the uncertainty principle has been circumvented, but weak measurement can be used to give these averages which is a step up from the current techniques for some applications.
Here, robust statistics might be bad. Normally, I would say, robust statistics is superior to the crap called "parametric statistics, based on the junk "arithmetic mean", etc.
Yet, I would guess that the few outliers of interest here would have been missed by the Buick version of statistics - the median. Hence, the AMC Pacer would win hands downs as it would steer away for any folly in its way.
...to see the results themselves, and blow the whole experiment.
I already read about an experiment, where they managed to find the slit a photon went through, without doing a measurement on the photon itself, preserving its wave nature.
It was really ingenious (sorry, can't remember 100% of it):
They entangled the input photon with another one, which went on a parallel course outside the experiment.
Now the two slits had one of the two polarizations. So if the photon went through one slit, it got its polarization. And so did its entangled partner.
Then the photon ended up in the sensor. Which showed a nice wave distribution when the experiment was repeated often enough. Obviously, since no measurement happened.
BUT: Now that the photon had given us the result, its partner could *still* be measured! And thatâ(TM)s what they did. ;)
This allowed them, to find out which slit the first photon went through, by only measuring it after it was too late to get all particle-ey.
To me this is sheer genius. So simple. And so elegant.
P.S.: Measurement is already defined in the most exact way possible. It is the transfer of a structural property (=information) from one particle to another one. Which, if it doesn't happen via entanglement, has to happen trough the exchange of force particles. (Unless I'm misinformed, and entanglement also uses some force.) ;) And unless we have to throw away the standard model (which can, of course, never be guaranteed, since it's only a theory), thereâ(TM)s no way around it.
I specifically said "one". Referring to one quantum.
There's nothing to nail down there. It's already fused to the ground.
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
tl;dr
A: why is this so non-intuitive???
B: Quantum mechanics! *winks knowingly*
A: ohhhhh
But the "beam" can be so weak that there is never more than one particle in transit at a time.
Warning: this article may contain humor, sarcasm, parody, and perhaps even irony. Read at your own risk.
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
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)
Sorry I should have been clear. All I meant was that we wouldnt "see" the interference pattern with just a single electron since it just excites a single atom (talking about wavefunction collapse when it hits the screen). But thats exactly right the electron still interferes with itself and the probability distribution of where we see it is the same as the interference pattern.
The wavelength of the light is a lower bound on the error of detecting the particle's position. Higher frequencies of light correspond to longer wavelengths, which yield higher lower bounds of error.
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.
Higher frequencies of light correspond to shorter wavelengths. The only way to lower the fuzziness is to use higher frequencies, which has a greater effect on changing the momentum.
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.
I'm conducting a government-funded zero-slit experiment.
Still waiting for results.
Will continue the experiment until government (taxpayer) money runs out.
Not to be pedantic (and I'm not a physicist) but you don't "sacrifice any clue to the position" you only sacrifice a precise clue. You still have a pretty darn good clue where the particle is via the quantum wave functions. It's much more likely to be near where it was emitted than far away from that spot for example - you have a statistical clue as to it's position in other words.
I'm not saying you don't know this, just wanted to clarify the language for other readers.
I'm not a physicist but I'm pretty sure this is wrong. It is true that macroscopic objects are predicted to have wave functions, and some macroscopic objects have had quantum properties measured (in pretty esoteric experimental setups), but planet sized objects don't follow orbits around the sun based on their wave functions at all. I'm not even sure if you're suggesting that, but I wanted to clarify in case someone thought you were.
Strictly speaking this would apply only if the Earth was a single particle. You can calculate a de Broglie wavelength for everything, but everything is not a single wave, but a composite object.
What do you want? The result a theory that is correct on average at best?
As Richard Feynman pointed out in 1979.
It may require some time to follow these lectures, but they are awesomely interesting:
http://vega.org.uk/video/subseries/8
Yeah neither do you, which is why your reply is two words long. Either that or you're just an a-hole. Be helpful or be quiet.
The original questioner may have to "read up on it" but methinks he'll see you at the study table right next to him.
have conducted a two-slit experiment
So from reading this, I've gathered that Canada has bridged the basic gap of understanding fundamental physics, which up to this point were merely hypothetical theories based on quantum axioms and differential speculations, pertaining primarily to a photons path based on a set origin and designated destination - thus allowing them to fold time and space using a particles ascertained trajectory. Finally the copious amounts of spice (Frank H reference) they've been hording will come in handy!
(all in good fun, great thread)
just because we understand it does not obligate us to educate every moron spewing complete drivel.
take some initiative and educate yourself. and shut up until you do.
I thought the photons went through both slits.
Ditto.
And (as I read the summary - having not read and understood the paper) it looks like they modified the amplitude, phase, and/or polarization of the wave function/photon path through one of the slits, and measured the resulting changes of the diffraction pattern.
If I've characterized the experiment correctly it does not, IMHO, constitute getting any additional measurement on "which slit each photon passed through".
Bantam Dominique roosters crow a four-note song. Once you've heard it as "Happy BIRTHday" you can't NOT hear it that way
I can't remember where I heard it exactly but I think it was something similar to this or this. I do not know where I picked up the specific idea that earth's possible orbits were influenced by it's wave-particle function. The idea was the if a planet has a wave function as predicted then that wave function would influence it's orbit. I'm not a physicist though so I'm not going to defend the idea, it's just something I remember hearing in relation to electron orbits.
That first article seems pretty theoretical (meaning they are postulating something), and they aren't making a case that the earth's quantum wave function impacts its orbit, they are arguing that the same *math* that can be used for calculating quantum wave functions can also be used *analogously* for describing orbits of captured satellites in star systems.
There's a notion in quantum physics (remember I am not a physicist) that the bigger an object is the smaller it's quantum wave "vibration" or function. So the argument is that a lump of lead will have a teeny wave function (let alone a planet). And I think many physicists believe that above a certain size, the macroworld forces (heat exchange, etc) swamps the wave function. Nevertheless physicists have continued to postulate the upper-limit of where the wave function will be swamped and other physicists continue to push that limit upwards. But still, that upper-limit size is still really really small compared to a planet.
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.
This is not demonstratively true. Welcome to the deBroglie-Bohm theory:http://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory. You might want to read up on it.
Hm. I'm not sure how that works, exactly. If two photons were entangled, measurement on one constitutes measurement on the other (this is the basis of EPR paradox, the seemingly superluminal signal-sending).
If the claim is that a measurement is made on one without disturbing the state of the other entangled photon (i.e. measuring its position, or, in the experiment you described, its polarization is supposed to collapse the polarization state of the entangled photon to that determined by condition of entanglement), then it's a different kind of measurement than what I learned.