Stability of Electron/Nucleus; Heisenberg Unc.

Enjolras1789

JK423:

What you're saying makes logical sense. It's just a bit different than what I had understood the words to mean. Yours is logical, just different...unless I am missing something.

You describe momentum here as something that is well-defined, just having a higher range of possible measurable values, thus shifting the average of whatever probability distribution function characterizes momentum, and THAT is the meaning of "uncertainty."

I assume when you say dispersion, you mean the same as uncertainty (I just normally associate "dispersion" as meaning a function which gives the frequency dependence of some property and keep using "uncertainty"; please let me know if that is problematic in some other way).

This is different than what I how I had always thought of it. I don't want to mis-represent Fourier or Griffiths...but my understanding of HUP is more akin to my readings of Fourier analysis and Griffiths QM book. To my understanding, Griffiths described HUP as a reflection of the idea that, below a certain scale of size, both of these variables don't have meaning. That makes physical sense to me; at some scale, you can't know the speed and position of a wave/particle, because a wave's "position" is irrelevant unless the packet is extremely localized, etc. This also makes sense to me in terms of Fourier analysis: anything obeying the wave equation, mathematically, obeys the uncertainty principle. This is a statement that these terms are NOT well-defined beyond a certain realm. This is the definition of uncertainty I had walking into this discussion.

Do you view that the purely mathematical expression of the uncertainty principle from Fourier analysis is logically equivalent, no more no less, than the HUP? Do you agree that the Fourier analysis description of the uncertainty principle is about the inability to ascribe clear meaning to these variables? This is also nicely represented by Griffiths in his QM book, in a less mathematical way.

DrChinese

Don't forget that when you have 2 entangled particles, the HUP applies to them. How would you expect that to work using your example? As I see this explanation evolving, you would end up predicting that you could observe their non-commuting observables to unlimited precision. But that is not allowed either.

My point being that the analogy has a limit. And that limit is where you start making incorrect predictions.

Enjolras1789

Dr. Chinese:

I do not understand your point about particle entanglement. Can you please clarify?

Moreover, your comment is about how you expect our conversation to evolve. Perhaps instead of making a prediction of people you don't know (I could be a total moron, remember, and make very stupid arguments), can you say what the fallacy is? I can't respond to a claim about how my thesis is wrong based on the results of the next argument that I haven't yet made.

What do you think about treating this as a purely mathematical notion? In that context, is it a statement of inability to describe both variables meaningfully, or is a statement of higher variance in a probability distribution function?