I meant that P_{i}=P_{x} and P_{f}=\sqrt{P^{2}_{x}+P^{2}_{y}} so P_{f}>P_{i}. I was talking about magnitudes after all the vector operations. Momentum not conserved? How QM deals with simple diffraction, I mean — professors of physics demonstrate the HUP with laser diffraction. So what is the...
O.K. but then there's a problem:
p_{i} initial momentum magnitude
p_{f} final momentum magnitude
Initial state: p_x, p_y=0 , so p_{i} = p_x
At slit: p_x, p_y, and p_{f} is a composition of p_x, p_y
So, p_{f} > p_{i}
Explanation?
The lecture I talked about:
Heisenberg's Uncertainty Principle by Walter Lewin
link: http://www.youtube.com/watch?v=IcOJHJJpd0w&feature=player_embedded
time: about 33:00
He speaks about uncertainty in location and momentum- BUT NOT AROUND A SPECIFIED AXIS. Is it wrong to say that? because...
So basically the notion of explaining diffraction with the uncertainty principle is an approximation of physics-classes, to show that narrowing the slit increases diffraction efficiency, but really you can't understand it like that. I'm talking about Lewin's lectures from MIT.
And I'll take...
Ok, but optics is a classical approximation, how does it sit with the uncertainty principle?
I think I have an explanation:
The wave-function interacts with the slit, it places some boundaries on the probability-wave, so it might be that y-momentum increases but x-momentum decreases so that...
Just thought about something more.
Say an electron moves towards the slits with 100% momentum in the x direction, meaning 0 uncertainty on y-momentum. After it passes the slits the y-location is localized so there is uncertainty in y-momentum, which gives is a total momentum which is a...
I know, the energy-time relation for particle decays - it explains the short life-span of heavy particles.
But I talk about general time-indeterminacy, like in the double slit experiment where you can't know how long it takes for the particle to travel from gun to screen, or the time it take...
I understand, the different approaches and levels make it very complicated.
Is it safe to say though that time-location-momentum-energy uncertainties are inherent in QM and always there in every experiment? Which will manifest in not knowing the time-travel of a particle in the double-slit...
Please, this is a really frustrating technical part of QM I face. From a different thread I understood that time-uncertainty is implied in the double-slit experiment as well as other uncertainties - so this is a decent question.
I'll appreciate any attempt to reply. Thank you.
Sure, but what points are the critical ones? You leave a lot of room for questions with your answers, sorry if this is frustrating for you.
And what do you mean by context?
From the wikipedia page on http://en.wikipedia.org/wiki/Complementarity_(physics)" :
As I recently noticed in the double-slit experiment there is a lot of time-uncertainty, not only position-momentum uncertainty. That is shown in the fact that the probability wave does not reach the screen...
And of course, in the entangled particles experiments - the delayed quantum erasers, you could wait well after one was "detected", according to wiki. Is this so, in the "delayed choice quantum eraser"? I don't understand it fully, but it's something like that right?
I found this under Complementarity in Wiki:
So time and energy are also intertwined in the quantum-uncertainty. You don't know when the "wave" reaches the screen, so for all we know, it reached averagely at the same time at every point on the screen, and therefore the probability is like a...