How Does Quantum Indeterminacy Relate to the Uncertainty Principle?

[bryan.picc]

I am an entering college freshman and i have a few questions about the uncertainty principle and hope my misunderstanding can be cleared up. Below is my horrible understanding thus far since my technical abilities are much below necessary for understanding qm, although it is too interesting a problem for me to wait. Correct my misconceptions:

Due to the fact that subatomic scale is near the lower limit for size of particles in the universe, no particle X can reveal information about another particle Y without making a nonnegligible disturbance on the particle Y. Using a high energy photon to observe, an electron's momentum is obfuscated, and using a low energy photon, the momentum is known but not the position. This is quantified in the Heisenberg uncertainty principle that neither can be determined with accuracy simultaneously. This (to me) says, the amount of information particle X can reveal about particle Y will always be probabilistic, therefore making the information impossible to deduct.

I don't understand how you get from this idea to the idea that an electron is inherently a smudge of positions. Obviously, I am wrong, but i don't understand where this notion of inherent non-determinism comes in from a problem that seems to be a problem of information one particle can reveal of another. I can't fully grasp this.

 

[Drakkith]

The problem is that the only successful models of QM involve describing particles as a wavefunction. It is inherent that these wavefunctions can either show momentum OR position accurately but not both at the same time. This applies to wavefunctions in QM AND outside of QM. Outside of QM momentum and position are instead replaced by other applicable properties, but the results are the same.

As an example, imagine I am transmitting a radio signal to you. The wavefunction describing this signal can be A: A single tone (frequency) of infinite length. B: A "pulse" of finite length but the frequency now varies depending on the length of the pulse. The shorter the pulse the more frequencies add together to produce the wavefunction, so one can never determine the exact frequency AND determine an exact length of the tone. (Frequency is analogous to momentum and length of the pulse is analogous to position in QM)

 

[DrChinese]

...Due to the fact that subatomic scale is near the lower limit for size of particles in the universe, no particle X can reveal information about another particle Y without making a nonnegligible disturbance on the particle Y. Using a high energy photon to observe, an electron's momentum is obfuscated, and using a low energy photon, the momentum is known but not the position. This is quantified in the Heisenberg uncertainty principle that neither can be determined with accuracy simultaneously. This (to me) says, the amount of information particle X can reveal about particle Y will always be probabilistic, therefore making the information impossible to deduct.

I don't understand how you get from this idea to the idea that an electron is inherently a smudge of positions. Obviously, I am wrong, but i don't understand where this notion of inherent non-determinism comes in from a problem that seems to be a problem of information one particle can reveal of another. I can't fully grasp this.

Welcome to PhysicsForums, bryan.picc!

The first problem is that your understanding of the Uncertainty Principle is outdated. That explanation has been thrown around over the years, but has been soundly discredited.

It is more accurate to say that a particle does not have simultaneously well-defined values for non-commuting observables. See for example Bell's Theorem, which shows that such values cannot exist if the predictions of QM are accurate (which they have been shown to be).

Please note that the Uncertainty Principle applies only to pairs of non-commuting observables. If your understanding were correct, it should apply to all observable pairs.