I would not recommend the site listed above. It perpetuates the misconception of the HUP that I have written about, that it is the uncertainty in a single measurement. I have seen this mistake repeated several times within the past week on here.Dr.Brain said:
Who is this "we"?matness said:time is also an observable so why do we always take Δt= 0 while
Δx*Δp >= hbar/2 ?
What are "solid proofs"? Would the statment that says "IT WORKS" be considered as "solid proof"? How about if I point to you your modern electronics? Would that be considered as "solid proof"?Nomy-the wanderer said:I've a simple answer, hope u won't consider it naive...
Most of the working theories right now weren't based on solid proofs but because we needed them, and some observations needed explanations...Theorists make theories, without confitmations, but we assume they r correct untill they r proven wrong, technology gives us the chance to make sure that we r on the right track, we can't yet find the electron and the uncertainty principle is what really works right now...
See u when they find out something strong that would give us the opportunity to observe electrons..
I don't understand. You want a "sketch of proof" for the HUP? What is this?matness said:"i" was thinking these as you said , until i see the word 'simultaneous' for measurements in the defn of HUP. if we say nearly simultaneous then i think there will be no problem(i hope so...)
Also there are different explanations for HUP, and maybe this the problem about understanding it. at first i was thinking i get it , but it didnt take a long time for me to confuse (because i am a beginner only)
Zz 's article is very helpful but if anyone can send a sketch of proof for HUP it will be more clear
The second part answers to the first part of your post.mrfeathers said:I dont understand why it is so hard to find the exact position and velocity of orbiting electron. And also, why would we want to know it, if it is always moving? im not trying to disprove it or anything, so dont make fun of me, i am an uneducated peon
my (rather naive) understanding of it is that in a classical system:seratend said:The second part answers to the first part of your post.
In QM, we may define the position of a particle. We may also define the momentum of a particle. However momentum is not the velocity of the particle. Many people in this forum always mix the momentum with the velocity (due to their equality for average values: i.e. Erhenfest Theorem) and tend to make incorrect deductions.
QM tells one thing: we cannot associate a classical path to a particle, hence we cannot define a couple (position, velocity) to the particle.
The HUP property applied to the (position, momentum) observables just highligh this fact: we cannot find a particle where both position and momentum have "defined" values equal to their mean values (i.e. through the Erhenfest Theorem, they have a classical path if is the case).
No, that's not correct. The HUP doesn't says something about only one simultaneoulsy measurment. It says something about a serie of simultaneously measurements (always the same conditions). You see?so that measuring the position and then measuring the momentum, is not the same as measuring the momentum and then measuring the position. infact, they will always differ by
Umm, how can momentum be equal to velocity ? Ehrenfest theorem is about equality of average QM momentum, which is defined as [tex]-i \hbar \vec \nabla[/tex] and classical momentum [tex]m \vec v[/tex]. Or generally it shows that average values of QM operators are equal to corresponding quantities in classical mechanics (I guess that's what you had in mind).seratend said:Many people in this forum always mix the momentum with the velocity (due to their equality for average values: i.e. Erhenfest Theorem) and tend to make incorrect deductions.
Ok, let's explain the "due to their equality for average values" in my previous post.Igor_S said:Umm, how can momentum be equal to velocity ? Ehrenfest theorem is about equality of average QM momentum, which is defined as [tex]-i \hbar \vec \nabla[/tex] and classical momentum [tex]m \vec v[/tex].