# Path Cancellation: Can a Particle Come From Point A?

• StevieTNZ
In summary: But in more realistic situations where there are many particles and interactions, the amplitude will usually have some nonzero value.
StevieTNZ
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?

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.

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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.

## 1. Can a particle really come from point A?

Yes, according to the laws of physics, a particle can come from point A through a process called path cancellation. This occurs when the particle's path is canceled out by the presence of another particle or force, resulting in a new path from point A.

## 2. How does path cancellation work?

Path cancellation involves the concept of superposition, where two or more paths of a particle interfere with each other. If the paths have opposite phases, they can cancel each other out, resulting in a new path from point A.

## 3. Is path cancellation a common phenomenon?

Path cancellation is observed in various physical systems, such as quantum mechanics, electromagnetism, and even acoustics. However, it is a complex phenomenon and is not easily observable in everyday life.

## 4. Can path cancellation be manipulated or controlled?

Yes, path cancellation can be manipulated by adjusting the properties of the particles or forces involved. This is a crucial aspect of various technologies, such as quantum computing and particle accelerators.

## 5. What are the implications of path cancellation in the field of physics?

Path cancellation is a fundamental concept in quantum mechanics and has significant implications in understanding the behavior of particles at the subatomic level. It also has practical applications in various technologies and may lead to further discoveries in the field of physics.

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