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While, you're right, it is minimalistic, Einstein's Statistical Ensemble Interpretation is an incomplete theory. It doesn't tell you which possible future you'

While, you're right, it is minimalistic, Einstein's Statistical Ensemble Interpretation is an incomplete theory. It doesn't tell you which possible future you'll end up in. And if you try to patch the theory by saying there's some deeper element of reality that we just haven't found yet that's deciding the outcome of experiments, then the violation of the Bell Inequalities renders that whole line of thinking moot. If, instead, you try to patch it the other way and say that everything in the ensemble is real, then you've just reinvented Many Worlds by a different name. I'm unclear why you're bringing up Hitach's experiment and what you think it shows. Maybe you could elaborate? My understanding is that the raison d'être of the experiment is to show that multiple particles are not necessary for quantum interference to occur, and that a single particle is perfectly capable of destructively interfering with itself. This is pretty direct evidence for superposition, because you're getting measurable effects from the superposition. And if anything, it's evidence against the Ensemble Interpretation. Also, quantum computers are real and here today. Any successful theory of physics must explain how 15 was factored using Shor's Algorithm. (http://arxiv.org/abs/quant-ph/0112176 http://arxiv.org/abs/quant-ph/0112176)

deleted 13y ago
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VladRussian2 13y ago
>Einstein's Statistical Ensemble Interpretation is an incomplete theory. It doesn't tell you which possible future you'll end up in. not sure that we're talking about the same. My understanding here is that one calculates probabilities the same way. It is the interpretation different. In Copenhagen the particle is supposed to carry all probabilities which magically "collapse" on the measurement, while in statistical a given particle is in "collapsed" state to start with (there is a distribution of the states over the ensemble), and the probabilistic model describes the evolution of these states and distribution of final states - there is no collapse on measurement, we just measure specific state. >I'm unclear why you're bringing up Hitach's experiment and what you think it shows. Maybe you could elaborate? My understanding is that the raison d'être of the experiment is to show that multiple particles are not necessary for quantum interference to occur, and that a single particle is perfectly capable of destructively interfering with itself. in Hitachi experiment it is shown explicitly clear that quantum interference is emerging only for multiple particles. It is basically a visualization of underlying probability distribution, like it happens in any statistical experiment when enough samples are taken. During the Hitachi experiment nothing happened that looks like or requires an explanation by a single particle supposedly interferencing with itself. If you don't see this in Hitachi experiment, lets run the following experiment. Imagine 2 doors in a wall, and imagine another, parallel, wall at several meters distance from the doors. Imagine that frogs jump out, one at a time, from either door pretty randomly. The frogs jump in general direction of the wall opposite the doors. The precise direction of each frog is varying a bit. It takes a frog several jumps to reach the wall. The probability density of the places where the frog's legs touch the ground is square of cos(pi*x/A) (correctly scaled to be a probability density) where x is the distance from the door the frog jumped out, and A is the avg. frog jump length. A frog only exist (i.e. can interact with anything else) when it touches the ground, and doesn't exist when it is flying during the jump. Whenever a frog lands near the wall, say not farther than a body distance from the wall, it touches the wall and leaves a wet spot. It is easy to see that after a big enough bunch of frogs, there would be an "interference pattern" of dry and really wet areas on the wall - i.e. some places have low probability of a frog landing near it while some have high, and that probability distribution looks like an "interference pattern". No superposition, no destructive interference of a frog with itself is necessary to observe the effect. This is what Hitachi experiment shows. >This is pretty direct evidence for superposition, yes, an interference of a particle with itself would be such evidence. I'm yet to learn about an experiment which can only be explained by such interference. > Any successful theory of physics must explain how 15 was factored using Shor's Algorithm. agree. While 15 seems too small a number to exclusively lock a superposition explanation, i don't have another ready. I'd like to have quantum computers and other quantum miracles too :) I just want them to be a bona fide miracles, not figments of our interpretation :)
- chrislipa 13y ago
  The way you're describing the theory sure seems like the Ensemble Interpretation to me, but to be honest, I have never heard of the "Statistical Aggregate Interpretation". Just to be sure I know what we're discussing, could you provide a reference to the Statistical Aggregate Interpretation? What you're suggesting -- that the information is there, but we just don't know which one -- sounds a lot like a hidden variables theory. Unfortunately, all theories with local realism (which includes hidden variables theories) are ruled out experimentally by Bell's theorem. [1] I like your classical frog example because it's a thought experiment that illustrates how classical particles behave, and we can compare the distribution of the classical frogs to the distribution of whatever we're measuring (like electrons), and if the distributions we get are different, then we'll learn that whatever we're measuring is behaving non-classically. However, the probability density you gave for the frogs in the classical case, cos^2(pi*X/A), is incorrect. The probability distribution for the classical case the way you set it up will, in fact, be almost Gaussian (but not precisely for reasons that aren't relevant or worth discussing here)[2]. The combined probability distributions for frogs coming from the two doors will be the sum of two individual Gaussians, so it will be a "two-humped" distribution. As a point of fact, if you run your frog experiment, there will be two wet spots. It will not look like an interference pattern precisely because there is no superposition and no destructive interference. The fact that electrons in Hitachi's experiment display a "many-humped" distribution is good evidence that the electrons are not following the same rules as the frogs, and hence that the electrons are behaving non-classically. > in Hitachi experiment it is shown explicitly clear that quantum interference is emerging only for multiple particles. This is the exact opposite of what the Hitachi experiment shows. The experiment is interesting and surprising precisely because particles are sent one at a time but still show an interference pattern. The experiment shows a single particle interfering with itself. [1] http://en.wikipedia.org/wiki/Bell%27s_theorem http://en.wikipedia.org/wiki/Bell%27s_theorem [2] It's easy enough to show the general idea with a Monte-Carlo simulation.
  - VladRussian2 13y ago
    >The way you're describing the theory sure seems like the Ensemble Interpretation to me, but to be honest, I have never heard of the "Statistical Aggregate Interpretation". yes, my mistype, it is basically Ensemble Interpretation. > However, the probability density you gave for the frogs in the classical case, cos^2(pi*X/A), is incorrect. it isn't resulting probability distribution on the wall. It is probability distribution of the frog legs touching the ground on a radial line from door to the wall, i.e. peaks at 0, A, 2A, 3A,.... It is about the same as position operator for electron would produce on a radial line from slit to the screen. Also note that the frog doesn't interact with the wall if the frog is "airborne" (i.e. one can imagine that it just goes through the wall without leaving a wet spot or even better - the wall is too low, say 0.1m , so airborne, mid-flight, frogs would fly over it). If you look at this image http://micro.magnet.fsu.edu/primer/java/interference/doubleslit/doubleslitjavafigure1.jpg http://micro.magnet.fsu.edu/primer/java/interference/doubles... the red concentric lines is where a frog most probably touches the ground and the greenish-yellow - where a frog is most probably mid-jump airborne (flying at the height enough to fly over the wall). Where 2 yellow-greenish lines intersect right near the wall - it is the place with minimal probability of a frog landing near the wall, ie. dry place. While intersection of 2 reds - correspondingly a very wet place. >The fact that electrons in Hitachi's experiment display a "many-humped" distribution is good evidence that the electrons are not following the same rules as the frogs, and hence that the electrons are behaving non-classically. this non-classical behavior is the quantization of position, ie. position probability density looks like concentric waves starting at a slit. I.e. cut along the radial line, the profile of that density is a correctly scaled cos(x), with x - distance from the slit. The superposition isn't necessary for the observed effect. >> in Hitachi experiment it is shown explicitly clear that quantum interference is emerging only for multiple particles. >This is the exact opposite of what the Hitachi experiment shows. The experiment is interesting and surprising precisely because particles are sent one at a time but still show an interference pattern. The experiment shows a single particle interfering with itself. i'm trying to understand where do you see the interference of a particle with itself. Lets say the experiment was run only until there is only 1 (i.e. 2 sec into the clip), or say 3 particles hit the screen (4 seconds into the clip). What would be an indication of the interference in such a case?

deleted 13y ago

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VladRussian2 13y ago

>Einstein's Statistical Ensemble Interpretation is an incomplete theory. It doesn't tell you which possible future you'll end up in. not sure that we're talking about the same. My understanding here is that one calculates probabilities the same way. It is the interpretation different. In Copenhagen the particle is supposed to carry all probabilities which magically "collapse" on the measurement, while in statistical a given particle is in "collapsed" state to start with (there is a distribution of the states over the ensemble), and the probabilistic model describes the evolution of these states and distribution of final states - there is no collapse on measurement, we just measure specific state. >I'm unclear why you're bringing up Hitach's experiment and what you think it shows. Maybe you could elaborate? My understanding is that the raison d'être of the experiment is to show that multiple particles are not necessary for quantum interference to occur, and that a single particle is perfectly capable of destructively interfering with itself. in Hitachi experiment it is shown explicitly clear that quantum interference is emerging only for multiple particles. It is basically a visualization of underlying probability distribution, like it happens in any statistical experiment when enough samples are taken. During the Hitachi experiment nothing happened that looks like or requires an explanation by a single particle supposedly interferencing with itself. If you don't see this in Hitachi experiment, lets run the following experiment. Imagine 2 doors in a wall, and imagine another, parallel, wall at several meters distance from the doors. Imagine that frogs jump out, one at a time, from either door pretty randomly. The frogs jump in general direction of the wall opposite the doors. The precise direction of each frog is varying a bit. It takes a frog several jumps to reach the wall. The probability density of the places where the frog's legs touch the ground is square of cos(pi*x/A) (correctly scaled to be a probability density) where x is the distance from the door the frog jumped out, and A is the avg. frog jump length. A frog only exist (i.e. can interact with anything else) when it touches the ground, and doesn't exist when it is flying during the jump. Whenever a frog lands near the wall, say not farther than a body distance from the wall, it touches the wall and leaves a wet spot. It is easy to see that after a big enough bunch of frogs, there would be an "interference pattern" of dry and really wet areas on the wall - i.e. some places have low probability of a frog landing near it while some have high, and that probability distribution looks like an "interference pattern". No superposition, no destructive interference of a frog with itself is necessary to observe the effect. This is what Hitachi experiment shows. >This is pretty direct evidence for superposition, yes, an interference of a particle with itself would be such evidence. I'm yet to learn about an experiment which can only be explained by such interference. > Any successful theory of physics must explain how 15 was factored using Shor's Algorithm. agree. While 15 seems too small a number to exclusively lock a superposition explanation, i don't have another ready. I'd like to have quantum computers and other quantum miracles too :) I just want them to be a bona fide miracles, not figments of our interpretation :)

chrislipa 13y ago
The way you're describing the theory sure seems like the Ensemble Interpretation to me, but to be honest, I have never heard of the "Statistical Aggregate Interpretation". Just to be sure I know what we're discussing, could you provide a reference to the Statistical Aggregate Interpretation? What you're suggesting -- that the information is there, but we just don't know which one -- sounds a lot like a hidden variables theory. Unfortunately, all theories with local realism (which includes hidden variables theories) are ruled out experimentally by Bell's theorem. [1] I like your classical frog example because it's a thought experiment that illustrates how classical particles behave, and we can compare the distribution of the classical frogs to the distribution of whatever we're measuring (like electrons), and if the distributions we get are different, then we'll learn that whatever we're measuring is behaving non-classically. However, the probability density you gave for the frogs in the classical case, cos^2(pi*X/A), is incorrect. The probability distribution for the classical case the way you set it up will, in fact, be almost Gaussian (but not precisely for reasons that aren't relevant or worth discussing here)[2]. The combined probability distributions for frogs coming from the two doors will be the sum of two individual Gaussians, so it will be a "two-humped" distribution. As a point of fact, if you run your frog experiment, there will be two wet spots. It will not look like an interference pattern precisely because there is no superposition and no destructive interference. The fact that electrons in Hitachi's experiment display a "many-humped" distribution is good evidence that the electrons are not following the same rules as the frogs, and hence that the electrons are behaving non-classically. > in Hitachi experiment it is shown explicitly clear that quantum interference is emerging only for multiple particles. This is the exact opposite of what the Hitachi experiment shows. The experiment is interesting and surprising precisely because particles are sent one at a time but still show an interference pattern. The experiment shows a single particle interfering with itself. [1] http://en.wikipedia.org/wiki/Bell%27s_theorem http://en.wikipedia.org/wiki/Bell%27s_theorem [2] It's easy enough to show the general idea with a Monte-Carlo simulation.
- VladRussian2 13y ago
  >The way you're describing the theory sure seems like the Ensemble Interpretation to me, but to be honest, I have never heard of the "Statistical Aggregate Interpretation". yes, my mistype, it is basically Ensemble Interpretation. > However, the probability density you gave for the frogs in the classical case, cos^2(pi*X/A), is incorrect. it isn't resulting probability distribution on the wall. It is probability distribution of the frog legs touching the ground on a radial line from door to the wall, i.e. peaks at 0, A, 2A, 3A,.... It is about the same as position operator for electron would produce on a radial line from slit to the screen. Also note that the frog doesn't interact with the wall if the frog is "airborne" (i.e. one can imagine that it just goes through the wall without leaving a wet spot or even better - the wall is too low, say 0.1m , so airborne, mid-flight, frogs would fly over it). If you look at this image http://micro.magnet.fsu.edu/primer/java/interference/doubleslit/doubleslitjavafigure1.jpg http://micro.magnet.fsu.edu/primer/java/interference/doubles... the red concentric lines is where a frog most probably touches the ground and the greenish-yellow - where a frog is most probably mid-jump airborne (flying at the height enough to fly over the wall). Where 2 yellow-greenish lines intersect right near the wall - it is the place with minimal probability of a frog landing near the wall, ie. dry place. While intersection of 2 reds - correspondingly a very wet place. >The fact that electrons in Hitachi's experiment display a "many-humped" distribution is good evidence that the electrons are not following the same rules as the frogs, and hence that the electrons are behaving non-classically. this non-classical behavior is the quantization of position, ie. position probability density looks like concentric waves starting at a slit. I.e. cut along the radial line, the profile of that density is a correctly scaled cos(x), with x - distance from the slit. The superposition isn't necessary for the observed effect. >> in Hitachi experiment it is shown explicitly clear that quantum interference is emerging only for multiple particles. >This is the exact opposite of what the Hitachi experiment shows. The experiment is interesting and surprising precisely because particles are sent one at a time but still show an interference pattern. The experiment shows a single particle interfering with itself. i'm trying to understand where do you see the interference of a particle with itself. Lets say the experiment was run only until there is only 1 (i.e. 2 sec into the clip), or say 3 particles hit the screen (4 seconds into the clip). What would be an indication of the interference in such a case?