Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Nizzle on 09/12/2011 12:37:48
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So, I'm aware that Heisenberg's uncertainty principle implies that it is impossible to simultaneously measure the present position while also determining the future motion of a particle.
But does the particle have both qualities simultaneously, and is it just our inability that prevents us from measuring both simultaneously?
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A particle cannot have a well defined position and momentum - it is not merely a measurement thing. If your theory leads to an exact position or an exact momentum for a quantum mechanical particle then the theory is flawed. There is a similar uncertainty with energy and time - this uncertainty is the basis for the zero-point energy of the quantum mechanical vacuum
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It has to do with the fact that particles on a quantum level behave like waves. If you try to squeeze a wave down to a point (specifying its position very precisely), the wave coming out of that point is going to spread out over a wide range of directions. Since the momentum of the particle behaves like this wave, it is smeared out over a bunch of directions coming out of that point, so it doesn't have a precise value. Similarly, if you know the direction of the outgoing wave, it has to be very wide. Then the position of the particle is smeared out over this wide wave, so it doesn't have a precisely defined value.
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So, in fact, all matter is just a collection of "waves" if only you zoom in close enough?
Like for example, a Hydrogen (the protium isotope) atom is a wave circling three other waves (electron circling three quarks) when looking at planck scale distances?
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Basically, yes, but distances have to be larger than Planck scale. (Planck scale is where our current theories break down, and we don't have powerful enough tools to look at that scale yet.)
In QM, they're waves of probability, telling you the probability of finding the particle at a particular place in space. But its not a matter of the particle actually being somewhere and the wave just expresses that we don't know exactly where it is. It is actually somehow smeared out over that whole wave (and this has been tested and verified by many quantum experiments).
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Would it be correct to say that the particle is not there until it is "observed", and the wave is not there after the particle is observed?
I bet it's not as simple as that. [:-\]
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Sometimes I wonder if the theorems should be quantified with a phrase like: "With our current technology".
For example, not too many years ago, there were discussions about the minimum resolution of light microscopes. And, still the principle remains, but all one has to do is redefine the light input, and one can go well beyond the absolute limits of a few decades ago.
One of the problems is that our methods to view particles always interact with the particles, whether it is shooting photons or electrons at them, or shooting the particles into some kind of a detector.
I'm not sure I buy the idea that an electron orbiting an atom is everywhere at the same time.
It is like saying that if you are viewing a CRT (do they still have those anymore?). Anyway, when viewing the CRT, you are viewing a single pixel created by an electron beam on a discrete spot on the screen. But, saying the electron orbiting the atomic nucleus is everywhere at the same time is like saying that pixel on the CRT is everywhere on the CRT at the same time. Which, of course, isn't the case, otherwise you would see a monochromatic view.
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Would it be correct to say that the particle is not there until it is "observed", and the wave is not there after the particle is observed?
I bet it's not as simple as that. [:-\]
You're right. It's not that simple. It's a wave in between observations, but when you look for it and find it at a point, it becomes a special kind of wave: it's entirely localized at the observation point. The act of observing changes the shape of the wave.
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Sometimes I wonder if the theorems should be quantified with a phrase like: "With our current technology".
For example, not too many years ago, there were discussions about the minimum resolution of light microscopes. And, still the principle remains, but all one has to do is redefine the light input, and one can go well beyond the absolute limits of a few decades ago.
There are two kinds of limits: the limits in place because of the technology being used and the theoretical limits. The resolution limit in a traditional microscope is a technological limit of taking measurement in a certain way (by shining a stationary light through the microscope and looking at the smallest spot you can form). By using clever techniques, the theory says you can do better. It wasn't until recently that people figured out how to do it practically, for example by capturing the near field or by taking multiple images while using fancy illumination schemes and computational image processing.
One of the problems is that our methods to view particles always interact with the particles, whether it is shooting photons or electrons at them, or shooting the particles into some kind of a detector.
This is a hard theoretical limit. We can't get around this unless our theories are wrong.
I'm not sure I buy the idea that an electron orbiting an atom is everywhere at the same time.
The theory works well, even though its odd. There are other interpretations of QM that don't interpret things this way, but they all use the same mathematical framework and they're all very weird.
It is like saying that if you are viewing a CRT (do they still have those anymore?). Anyway, when viewing the CRT, you are viewing a single pixel created by an electron beam on a discrete spot on the screen. But, saying the electron orbiting the atomic nucleus is everywhere at the same time is like saying that pixel on the CRT is everywhere on the CRT at the same time. Which, of course, isn't the case, otherwise you would see a monochromatic view.
Well, the single pixel is huge compared to the size of an electron's wave function and huge compared to an atom. The electron striking it is actually described as smeared out over a wave, but the pixel's so huge this doesn't have a noticeable effect. If the pixels were tiny, you could see the wave nature of the electrons more clearly.
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Well, the single pixel is huge compared to the size of an electron's wave function and huge compared to an atom. The electron striking it is actually described as smeared out over a wave, but the pixel's so huge this doesn't have a noticeable effect. If the pixels were tiny, you could see the wave nature of the electrons more clearly.
Pixels?
CRTs (at least the really old-fangled monochrome ones) just have a continuous phosphor coating, and the electrons are smashing into it while the beam position is being altered. Would you be able to discern the waves if the phosphor granularity was very fine and the beam was scanning very fast?
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The point is that when you look at a CRT, all you ever see is a single dot which is smaller than 1mm2
There is a bit of a decay time, but it really is just one dot that you are looking at... moving from one place to another side to side, top to bottom, 60 times a second (or so). If you took a very fast photo of the TV (1/18,432,000 second) exposure time for a VGA screen at 60 hz), you should see a dot, or perhaps a few dots as the phosphor decayed.
Like an electron orbiting an atom... the single pixel moves around the screen so that it eventually covers the whole screen.
But..
Your computer knows exactly where it is at any given instant, and thus can feed it the proper brightness and color to display.
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Sometimes I wonder if the theorems should be quantified with a phrase like: "With our current technology".
For example, not too many years ago, there were discussions about the minimum resolution of light microscopes. And, still the principle remains, but all one has to do is redefine the light input, and one can go well beyond the absolute limits of a few decades ago.
There are two kinds of limits: the limits in place because of the technology being used and the theoretical limits. The resolution limit in a traditional microscope is a technological limit of taking measurement in a certain way (by shining a stationary light through the microscope and looking at the smallest spot you can form). By using clever techniques, the theory says you can do better. It wasn't until recently that people figured out how to do it practically, for example by capturing the near field or by taking multiple images while using fancy illumination schemes and computational image processing.
When I was in school, there was a theoretical minimum limit placed on the resolution of light microscopy which was some multiple of the wavelength of light, presumably red light. Or, perhaps the actual wavelength, or about 700nm.
The problem is that if you then look at it with violet, you can see stuff that is half as big as what you can see with red which drops you down to 380nm.
But, light, being a wave, one can polarize it, to essentially project a single wave pattern of whatever width one wants to project. And, suddenly the wave and wavelength no longer is a limitation of the resolution. And, the resolution becomes only limited by the technology that one has to project and detect the wave.
And, as mentioned, one might also be able to use an interpolation scheme to capture an image with multiple frames, and also higher resolution.
So, the previous theories about the minimum resolution of a light microscope only applied to standard optical microscopes with broad spectrum light, not ALL light microscopes.
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A photon has some kind of wave/particle duality. But... consider this.
We can describe the time when it was released.
We can describe the wave that it is traveling in.
And, we can detect when it arrives at an arbitrary place.
In many senses, we can describe most of the properties of that photon.
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The point is that when you look at a CRT, all you ever see is a single dot which is smaller than 1mm2
I was thinking of the type of CRTs used in oscilloscopes, although the main difference between them and the ones found in TVs is the deflection method. There really is no "dot". It's more of a line, and its width is a function of the beam focus. If I remember rightly (which is highly unlikely) that's a function of the potential difference between the CRT face and the electron gun.
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Sometimes I wonder if the theorems should be quantified with a phrase like: "With our current technology".
For example, not too many years ago, there were discussions about the minimum resolution of light microscopes. And, still the principle remains, but all one has to do is redefine the light input, and one can go well beyond the absolute limits of a few decades ago.
There are two kinds of limits: the limits in place because of the technology being used and the theoretical limits. The resolution limit in a traditional microscope is a technological limit of taking measurement in a certain way (by shining a stationary light through the microscope and looking at the smallest spot you can form). By using clever techniques, the theory says you can do better. It wasn't until recently that people figured out how to do it practically, for example by capturing the near field or by taking multiple images while using fancy illumination schemes and computational image processing.
When I was in school, there was a theoretical minimum limit placed on the resolution of light microscopy which was some multiple of the wavelength of light, presumably red light. Or, perhaps the actual wavelength, or about 700nm.
The problem is that if you then look at it with violet, you can see stuff that is half as big as what you can see with red which drops you down to 380nm.
Using words like "see" is very tricky here, since technical terms are important. There is no way I know of around the diffraction limited spot produced by a single image, no matter how you massage your light. However, if you take multiple images using clever illumination schemes, you can process them (with the help of computers) to form a computed image with finer details than a single image.
But, light, being a wave, one can polarize it, to essentially project a single wave pattern of whatever width one wants to project. And, suddenly the wave and wavelength no longer is a limitation of the resolution. And, the resolution becomes only limited by the technology that one has to project and detect the wave.
I'm not sure what technique you're talking about there, but as far as I know you can't simply polarize light to beat the diffraction limit. In most experiments these days, we use polarized laser light to design optical setups and we're always limited by the diffraction limit.
So, the previous theories about the minimum resolution of a light microscope only applied to standard optical microscopes with broad spectrum light, not ALL light microscopes.
No. The previous theory is about the minimum spot size for a single image, and it always holds. All the ways around it are basically using some clever technique to get finer structure of a sample out of single images which are each limited by that spot size. (Or using near field imaging, which was never diffraction limited to begin with.)
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The take home point of all if this is that the diffraction limited spot size is a hard theoretical limit for a single image, just like the the HUP is a hard limit on a single particle measurement. By cleverly combining images, you can image finer structure than that spot size would indicate. By using "weak measurements" on many particles, you can get more information than the HUP would indicate: http://www.nature.com/news/2011/110602/full/news.2011.344.html
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A new advanced imaging scheme—with a resolution ten times better than that of its counterparts to date—can resolve objects as small as atoms (optical) (http://www.physorg.com/news/2011-12-sharpening-focus-microscopes.html)
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Ok, but...
Led by Kenji Tamasaku of RIKEN, the researchers used a non-linear optical effect to achieve atomic resolution in diamond. Their process is based on the intrinsic interaction between the electrons of the material’s crystal atoms and UV light that splits an incoming x-ray beam into a UV beam and a lower energy x-ray beam. The combined energy of these scattered beams is the same as that of the incoming beam. This process depends strongly on the activation of the UV beam, which occurs only in the vicinity of the electrons in the atoms, and only if the optical response of the electrons is a match to the incoming x-ray beam, Tamasaku explains.
Analyzing the scattered beams allowed a precise reconstruction of the motion of the electrons under UV illumination. Using a diamond crystal as an imaging object, the researchers demonstrated a resolution of 0.054 nanometers (Fig. 1). Because Tamasaku and colleagues used a non-linear optical effect, they obtained new information not only about how electrons move but also about atomic position.
It's computational imaging based on knowing how the object scatters light and reconstructing the object by capturing the scattered light and applying a physical model. It's not forming a diffraction limited image smaller than the diffraction limit.
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Yeah, it's analyzing the waves reflected. Wasn't there another older scheme in where you could use waves too big for the 'hole' they needed to pass too see beyond the 'hole'. I know I wrote about it here some year ago.
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There are various schemes about fitting waves through sub-wavelength holes. They rely on surface effects. You get electrons on the surface to move and support a wave running along the surface of the metal, then these electrons can emit a wave on the other side of the holes.
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Maybe that was it? I'm not sure JP. I remember SoulSurfer commenting on what I wrote though. It would be really cool with a updated search function that worked for TNS. As it is Google will get me more relevant answers than searching 'internally' on TNS search function, well, at least for me :) But, only if I remember the thing I wrote, at least some specific details of my wording. Then Google is your 'man'.
Then you have this idea too.
Although it's not what I was talking about above.
"in 2000 John Pendry of Imperial College London found a way to beat this "diffraction limit". He understood that, in addition to the light captured by normal lenses, an object always emits "near field" light that decays rapidly with distance. Near-field light conveys all an object's details, even those smaller than a wavelength, but no-one knew how to capture it.
Pendry's answer was negative refraction, a phenomenon that bends light in the opposite direction to a normal substance like glass. If someone could make such a negative-index material, he said, it would be able to reign in an object's near-field light, producing a perfect image."
The battle to find Maxwell's perfect image. (http://physicsworld.com/cws/article/news/45348) Don't know what came of it since then though.
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"in 2000 John Pendry of Imperial College London found a way to beat this "diffraction limit". He understood that, in addition to the light captured by normal lenses, an object always emits "near field" light that decays rapidly with distance. Near-field light conveys all an object's details, even those smaller than a wavelength, but no-one knew how to capture it.
Pendry's answer was negative refraction, a phenomenon that bends light in the opposite direction to a normal substance like glass. If someone could make such a negative-index material, he said, it would be able to reign in an object's near-field light, producing a perfect image."
It's still tricky to manufacture these materials, especially for light. This process also works by capturing the near-field evanescent waves, which have no size limit when forming an image. But they decay rapidly and are only useful within a few wavelengths of the object. There are other techniques that put a sensor within a few wavelengths of the object in order to capture the near field: http://en.wikipedia.org/wiki/Near-field_scanning_optical_microscope
The battle to find Maxwell's perfect image. (http://physicsworld.com/cws/article/news/45348) Don't know what came of it since then though.
This is an extremely controversial bit of work, and most physicists I know (including Pendry) think that it isn't really forming an image. What Leonhard has done is show that if you put a point source at one end of this "perfect lens" and a perfect point sink at the other, you get all the energy to go into the sink. The problem is that this isn't imaging. The sink itself is a source running in reverse, so its designed to match and capture the source field perfectly. If you used this lens for actual imaging, you'd see a diffraction limited spot.
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By the way, there is a nice relationship between the uncertainty principle and the diffraction limited spot size in a microscope.
The uncertainty principle basically says that to get good resolution of a particle's position, it must have a lot of uncertainty in momentum. In wave terms, this means that you have to have a wide wave function in momentum to get a narrow wave function in position. For particles, you can vary momentum by varying the direction and the speed of the particle. If you want to keep making a spot smaller, you an use higher and higher speeds to extend the range of momenta in the wave function.
This idea that you have to have a wide wave in momentum to get a narrow wave in position holds for classical light waves in optics. But you can't change the speed of light, so you can vary the width in momentum by varying its frequency (color) or its direction. If you're using a single frequency of light, you can only vary the direction. If you want to make a small spot, you want to use more and more directions. Of course, there are only a finite number of directions available, so when you use them all up, you're at the smallest spot size possible. This is the diffraction limited spot.
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For particles, you can vary momentum by varying the direction and the speed of the particle. If you want to keep making a spot smaller, you an use higher and higher speeds to extend the range of momenta in the wave function.
Does this have anything to do with the oscilliscope thing I was twittering on about?
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I'm not an expert on electron beams, but I believe that there's a (magnetic) lens in electron guns, and that the physics is extremely similar to an optical beam. Because you're using a lens to spread the electrons over a range of angles, its mostly an angular issue. Of course, spot size is roughly proportional to angular spread, but also to wavelength. The electron wavelength is so tiny that the spot size is going to be orders of magnitude smaller than an optical microscope.
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The electron wavelength is so tiny that the spot size is going to be orders of magnitude smaller than an optical microscope.
Hey! Why don't we convert an oscilloscope into a microscope thingy? I'll bet the resolution would be really good. All we need to do is figure out how to get the sample inside the oscilloscope tube so that we can, sort of, scan it with the e-beam.
Where did I put my patent notebook?
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By the way, there is a nice relationship between the uncertainty principle and the diffraction limited spot size in a microscope.
The uncertainty principle basically says that to get good resolution of a particle's position, it must have a lot of uncertainty in momentum. In wave terms, this means that you have to have a wide wave function in momentum to get a narrow wave function in position. For particles, you can vary momentum by varying the direction and the speed of the particle. If you want to keep making a spot smaller, you an use higher and higher speeds to extend the range of momenta in the wave function.
This idea that you have to have a wide wave in momentum to get a narrow wave in position holds for classical light waves in optics. But you can't change the speed of light, so you can vary the width in momentum by varying its frequency (color) or its direction. If you're using a single frequency of light, you can only vary the direction. If you want to make a small spot, you want to use more and more directions. Of course, there are only a finite number of directions available, so when you use them all up, you're at the smallest spot size possible. This is the diffraction limited spot.
Very nice JP.
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Geezer you are describing what became the field emission microscope something like 30 or 40 years ago it was the first to show "images" of individual atoms.
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I'm not sure about modern electron microscopy, but in the past, I thought it always required some kind of a contrast medium to be added, or having the object actually plated with some kind of a metal.
Anyway, if one can say describe the position of 1 million particles, and describe the momentum of 1 million particles... eventually one could use a probability function to combine the position and the momentum functions.
But, in the future... perhaps that won't be necessary.
Consider billiard balls.
If you roll a billiard ball on a table.
And, one shoots a pingpong ball to hit it.
Based on the resulting vector of the pingpong ball, one should be able to gather a lot of information about the original billiard ball. Certainly the point on the billiard ball that the pingpong ball hits is also important, but at least with a number of similar impacts, one would get a good description of what the billiard ball was doing.
The problem is finding the right pingpong balls!!!
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Geezer you are describing what became the field emission microscope something like 30 or 40 years ago it was the first to show "images" of individual atoms.
Rats! And I was just about to file the patent [;D]
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The problem is finding the right pingpong balls!!!
Not really no. HUP is not about measuring accuracy - within the realm of qm it is not possible to know both the position and momentum of a particle to arbitrarily small levels of accuracy. if a theory predicts that a particle must have an exact momentum and an exact position then the theory is wrong. it is possible we will find in the future a deeper understanding and get around this - but that is when qm starts being replaced. at the moment qm is one of the best tested and most accurate models ever devised - and part of the maths of that model is the non-commutative nature of certain physical variables, the practical upshot of this is that there must be an uncertainty. heisenburgs microscope is a great heuristic but it is not the reason for this effect, it is merely a useful explanation - it isn't that we cannot be precise enough in, even theoretical, measurement; it is an underlying part of the theory.
Anyway, if one can say describe the position of 1 million particles, and describe the momentum of 1 million particles... eventually one could use a probability function to combine the position and the momentum functions.
There is weak measurement, averaging, constrained variables etc. but nothing gets around the HUP to any extent