|
Register | Sign In |
|
QuickSearch
Thread ▼ Details |
|
Thread Info
|
|
|
Author | Topic: Quantum test pricks uncertainty | |||||||||||||||||||||||||||||||||||||||||||
GDR Member Posts: 6202 From: Sidney, BC, Canada Joined: Member Rating: 2.1 |
I put this in coffee house as I am no doubt the least qualified person on this board to discuss the subject, but I find it interesting and I believe others will as well.
quote: He has told you, O man, what is good ; And what does the LORD require of you But to do justice, to love kindness, And to walk humbly with your God. Micah 6:8
|
|||||||||||||||||||||||||||||||||||||||||||
RAZD Member (Idle past 1434 days) Posts: 20714 From: the other end of the sidewalk Joined: |
Hi GDR,
I put this in coffee house as I am no doubt the least qualified person on this board to discuss the subject, but I find it interesting and I believe others will as well. I don't count myself as qualified to discuss quantum mechanics either, but off the cuff it seems that this would seem to challenge entanglement rather than uncertainty per se. I also don't know if this is "old hat" in physics that is just being played. Enjoyby our ability to understand Rebel American Zen Deist ... to learn ... to think ... to live ... to laugh ... to share. Join the effort to solve medical problems, AIDS/HIV, Cancer and more with Team EvC! (click)
|
|||||||||||||||||||||||||||||||||||||||||||
cavediver Member (Idle past 3672 days) Posts: 4129 From: UK Joined:
|
This is a cool bit of physics but it in no way changes Quantum Mechanics or the Heisenberg Uncertainty Principle. What it does show is that the rather nebulous explanations of the Uncertainty Principle as arising from physical restrictions on measurement, sadly used in many intro books on QM, are largely erroneous. And this is all for the good.
|
|||||||||||||||||||||||||||||||||||||||||||
cavediver Member (Idle past 3672 days) Posts: 4129 From: UK Joined:
|
...off the cuff it seems that this would seem to challenge entanglement rather than uncertainty per se. No, it doesn't actually have anything to say about entanglement. Entanglementand the HUP are both deep seated consequences of the quantum nature of reality. What they have challenged is the age old explanation of the HUP in terms of the limitations of measurement wthin classical physics.
|
|||||||||||||||||||||||||||||||||||||||||||
Son Goku Inactive Member
|
As cavediver has said, there was an explanation of the uncertainty principle very common in introductions to QM for undergraduate students (although I don't think most textbooks since the 1990s have used it) and common in popular accounts. The explanation being that when you measure the position of a particle you "destroy" or decrease your knowledge about the momentum of the particle, since the equipment disturbs the particle.
However it has been known for a long time that this is probably a poor way to think about/teach the consequences of the uncertainty principle. Especially since the late 1980s when we began to understand much more about quantum mechanics (the increase in understanding coming from measurement theory and quantum computing). The experiment above agrees with the uncertainty principle, but shows older explanations and understandings of its meaning and content to be incorrect. The uncertainty principle "really says" the following: You prepare millions of copies of a particle all in the same state (let's say they're all produced via some identical procedure to ensure they're in the same state). Then let's say you take half of the particles and measure their position (at some fixed point in time after they're released from where they're produced, let's say). Since quantum mechanics is probabilistic, you'll get a spread of values for the location of the particle, as every measurement will produce a different answer. This is unlike classical mechanics where several particles in the exact same state will always produce the same answer. If you compute the average position of the particles, then you can compute the average distance from the average. This number is the position uncertainty, labeled . Then with the other half of the collection of particles, you do the same thing, except with their momentum and work out the momentum uncertainty, labeled . The uncertainty principle says that no matter what state you choose to create the particles in, the product of these two uncertainties always obeys:
So the uncertainties can only be reduced so far, since their product can never be less than . So this is a statement about the uncertainties in results from experiments due to the non-deterministic nature of particles in quantum mechanics. It's not about the experimental equipment interfering with or disturbing the particle, an explanation which is commonly seen. Entanglement, which is separate to this experiment, is on extremely solid ground, especially with the modern versions of Aspects experiments. Edited by Son Goku, : Square!
|
|||||||||||||||||||||||||||||||||||||||||||
RAZD Member (Idle past 1434 days) Posts: 20714 From: the other end of the sidewalk Joined:
|
Thanks Son Goku
Just for clarity, is the Δp number the squared momentum average distance? So these Δ numbers are like standard deviations squared (and you could compute the standard deviations from them if you know the number of particles) yes? Again, for clarity, what's h? I assume it's one of the Heisenberg numbers with units for (momentum x distance)^2? Enjoyby our ability to understand Rebel American Zen Deist ... to learn ... to think ... to live ... to laugh ... to share. Join the effort to solve medical problems, AIDS/HIV, Cancer and more with Team EvC! (click)
|
|||||||||||||||||||||||||||||||||||||||||||
NoNukes Inactive Member |
The uncertainties are the standard deviations (i.e. the square root of the variances)
I don't understand what you are trying to calculate using the number of particles. That number does not show up in the equation. h bar is Planks constant over 2*pi. The units are joule-sec. Edited by NoNukes, : Add unitsUnder a government which imprisons any unjustly, the true place for a just man is also in prison. Thoreau: Civil Disobedience (1846) The apathy of the people is enough to make every statue leap from its pedestal and hasten the resurrection of the dead. William Lloyd Garrison. Choose silence of all virtues, for by it you hear other men's imperfections, and conceal your own. George Bernard Shaw
|
|||||||||||||||||||||||||||||||||||||||||||
RAZD Member (Idle past 1434 days) Posts: 20714 From: the other end of the sidewalk Joined: |
Hi NoNukes
The uncertainties are the standard deviations (i.e. the square root of the variances) That's not what the post said -- one was just squared and the other was or wasn't (ie not clear)
I don't understand what you are trying to calculate using the number of particles. That number does not show up in the equation. Isn't standard deviation = {sum(m=1→n)[ave - datam]^2/n}^1/2 ? (sorry, I haven't learned latex yet) Certainly using the standard deviation makes sense to me, I'm just looking for clarity that this is what is used (or something similar) Enjoy Edited by RAZD, : .by our ability to understand Rebel American Zen Deist ... to learn ... to think ... to live ... to laugh ... to share. Join the effort to solve medical problems, AIDS/HIV, Cancer and more with Team EvC! (click)
|
|||||||||||||||||||||||||||||||||||||||||||
Son Goku Inactive Member
|
Hi RAZD,
Thanks for reading, there's a mistake in the original post. It should read "the average distance from the average", no squaring. The two quantities are just the standard deviations of momentum and position, as you said. In fact the standard deviation is probably a better phrase to use, as uncertainty implies some limitation on the equipment, where as standard deviation emphasises (correctly) the purely statistical nature of the result.
, said "h bar", is a constant with units Joules x Seconds, specifically:
Edited by Son Goku, : No reason given.
|
|||||||||||||||||||||||||||||||||||||||||||
Son Goku Inactive Member
|
The title of this post would probably be a better name for the result. The whole point being that even if you build equipment which doesn't disturb or influence the particles, you still get the product of the standard deviations being larger than a certain number.
It's a statement about the statistics of measurements performed on a large collection (or ensemble, as is said in physics) of identical particles, all produced in the same way. It does not concern how measurement equipment influences or disturbs a single particle when it measures it. Heisenberg had the original idea of equipment disturbing the particle, however it was Earle Kennard (in 1927) who derived the relation in its correct form first and interpreted it correctly. There are similar results for other physical quantities. For example if are the angular momentum around each axis (x, y and z), then the standard deviations obey:
Where,
is the standard deviation for angular momentum around the x-axis.
is the standard deviation for angular momentum around the y-axis.
is the average value of angular momentum around the z-axis and just indicates that you ignore the sign of this value, i.e. If the value is -0.4, you just use 0.4
|
|||||||||||||||||||||||||||||||||||||||||||
NoNukes Inactive Member |
As cavediver has said, there was an explanation of the uncertainty principle very common in introductions to QM for undergraduate students (although I don't think most textbooks since the 1990s have used it) and common in popular accounts. At the risk of dating myself, I seem to recall the "observation principle" explanation being brought up in my undergraduate class. I cannot recall if the explanation actually appeared in the textbooks, and by the time I finished undergrad I had rid myself (mostly) of that erroneous notion. This reminder from Son Goku and cave diver may have finished the job. In defense of those older text books, Heisenberg used the observation principle explanation, and as I recall, forms of the observation principle formed a part some of those thought experiments that Einstein posed to Bohr. So anyone who makes the mistake is at least in good company.Under a government which imprisons any unjustly, the true place for a just man is also in prison. Thoreau: Civil Disobedience (1846) The apathy of the people is enough to make every statue leap from its pedestal and hasten the resurrection of the dead. William Lloyd Garrison. Choose silence of all virtues, for by it you hear other men's imperfections, and conceal your own. George Bernard Shaw
|
|||||||||||||||||||||||||||||||||||||||||||
NoNukes Inactive Member
|
Isn't standard deviation = {sum(m=1→n)[ave - datam]^2/n}^1/2 ? Yes, but n is only helpful as part of the formula for calculating the standard deviations. If you are doing measurements it is only necessary that n be sufficiently large to make the calculation of std deviation meaningful. The experts have already addressed the rest of your question.Under a government which imprisons any unjustly, the true place for a just man is also in prison. Thoreau: Civil Disobedience (1846) The apathy of the people is enough to make every statue leap from its pedestal and hasten the resurrection of the dead. William Lloyd Garrison. Choose silence of all virtues, for by it you hear other men's imperfections, and conceal your own. George Bernard Shaw
|
|
|
Do Nothing Button
Copyright 2001-2023 by EvC Forum, All Rights Reserved
Version 4.2
Innovative software from Qwixotic © 2024