Path Cancellation: Can a Particle Come From Point A?

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Discussion Overview

The discussion revolves around the concept of path cancellation in quantum mechanics, specifically addressing whether a particle can originate from a point (point A) if all paths to another point (point B) cancel each other out. The conversation explores implications of path amplitudes, probabilities, and the nature of quantum states in relation to particle detection.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions if a particle can come from point A to point B if all paths cancel each other out, suggesting that cancellation implies zero probability of reaching point B.
  • Another participant clarifies that if all amplitudes from A to B cancel, the total amplitude is zero, leading to zero probability of detection at B, but notes that zero probability does not equate to impossibility.
  • A later reply acknowledges the explanation and expresses gratitude for the clarification.
  • One participant relates the discussion to the double slit experiment, noting that some areas on the screen receive hits from electrons despite predictions of zero hits, and introduces a mathematical perspective on assigning probabilities to outcomes.
  • Another participant counters that if electrons are hitting a specific area, they must have a nonzero probability of doing so, emphasizing that perfect amplitude cancellation is rare in practice.
  • A further contribution raises the question of whether everything has a finite probability of being anywhere in the universe, with a response affirming that real-world probabilities are typically nonzero due to numerous interactions affecting amplitudes.
  • One participant mentions that in simplified scenarios, such as a spherically symmetric potential, there can be regions where particles have zero probability of appearing.

Areas of Agreement / Disagreement

Participants express differing views on the implications of path cancellation and the nature of probabilities in quantum mechanics. There is no consensus on the interpretation of zero probability and its implications for particle origins.

Contextual Notes

Participants discuss the complexities of probability in quantum mechanics, including the effects of infinite outcomes and the nature of amplitude cancellation. The conversation highlights the nuanced understanding required to navigate these concepts.

StevieTNZ
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If, at one particular spot a particle can from (point A), all the paths from that spot to point B cancel each other out, does that mean the particle cannot come from point A?

Or likewise, if only some paths from point A to point B cancel out, and paths from point C to point B cancel the rest of the paths from point A to B, the particle can't come from point A?
 
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Your question is a bit unclear, but this may help: if the amplitudes for all the paths going from A to B cancel each other out, then the total amplitude to go from A to B is zero, and thus there is zero probability that the particle will go to B if it starts out at A. (By the way, zero probability doesn't mean it will never happen, at least for continuous states; it means it will almost surely not happen.)

And one thing you should understand is that you can't just talk about the amplitude that the particle will be measured in point B. In quantum mechanics, you need both an initial state and a final state, and the question asked is "Given a particle in this initial state, what is the amplitude for it to be detected in that final state.'
 
Yup - that answers my question. Thanks!
 
I guess that explains why even though certain areas on the double slit screen are hit with electrons even when there it is predicted they don't hit there

EDIT: from a Maths lecturer at my university "This is all inevitable. If you have an infinite number of possible disjoint outcomes and only a total probability of one to share around, then plenty of possible events must receive probability zero. It may seem counterintuitive, but the mathematics of infinity often is."
But can't you just assign each outcome a probability such 0.00000001 (of course with a lot of more zeros). 0.0000001 isn't 0.
 
Last edited:
StevieTNZ said:
I guess that explains why even though certain areas on the double slit screen are hit with electrons even when there it is predicted they don't hit there
I'm not sure what you're talking about, but if you're talking about a situation where electrons are systematically hitting some place, then definitionally they have some nonzero probability of hitting there. If you had zero probability, then it would literally occur infinitely rarely. Of course, in the real world the amplitudes almost never cancel out perfectly, so you almost never get zero probabilities for anything.
 
lugita15 said:
I'm not sure what you're talking about, but if you're talking about a situation where electrons are systematically hitting some place, then definitionally they have some nonzero probability of hitting there. If you had zero probability, then it would literally occur infinitely rarely. Of course, in the real world the amplitudes almost never cancel out perfectly, so you almost never get zero probabilities for anything.

Yeah, I was wondering about the perfect cancellation, as doesn't everything have a finite (but not a zero probability) of being anywhere in the universe?
 
StevieTNZ said:
Yeah, I was wondering about the perfect cancellation, as doesn't everything have a finite (but not a zero probability) of being anywhere in the universe?
Yes, in the real world probabilities all tend to be nonzero, just because there are so many interactions that are affecting the amplitude. But in simple example like a spherically symmetric potential we can get lots of regions where particles of zero probability of appearing.
 

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