A question on the Aharonov-Bohm effect

In summary, the Aharonov-Bohm effect, which is explained by quantum theory, occurs when the solenoid is enclosed by the two paths in a two-slit experiment. However, if the solenoid is moved far away from the paths, the effect disappears due to the lack of magnetic flux through the enclosed surface. Quantum mechanics does not consider the distance between the solenoid and the paths, but rather focuses on the contribution of the two straight paths and their close neighbors to the interference pattern. Some QM books, such as Gottfried and Yan's Quantum Mechanics Fundamentals, mention this.
  • #1
Younghun park
20
0
We know that Aharonov-Bohm effect is explained by quantum theory.

But, I imagine the situation that the solenoid is very far from two-slit.
In this case, does Aharonov-Bohm effect happen?

Current quantum theory doesn't consider the distance between two-slit and the solenoid.
When the distance two-slit and the solenoid becomes larger, Aharonov-Bohm effect disappears or continues?
 
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  • #2
The solenoid must be enclosed by the 2 paths in order for there to be an effect. If the 2 paths does not enclose the solenoid, then no such effect would be present, even quantum mechanically.
 
  • #3
MatterWave
I think that the solenoid is enclosed by the 2 paths even if that is far from two-slit.
Quantum mechanics doesn't say that the solenoid is not enclosed although solenoid is far from two-slit.
What kind of QM books or quantum theorists say like your opinion?
I want to know what your opinion is based on.
 
  • #4
The Ahronov-Bohm effect says that for a 2 slit experiment, if the particle "travels" on 2 possible paths to the end point, then there is a relative shift in phase between the 2 even if the path lengths are the same because of this solenoid. This relative phase shift is proportional to the flux of the magnetic field going through the surface which is enclosed by the 2 paths. If you move your solenoid "far away" outside of these two paths, you obviously have no magnetic flux going through this surface (neglecting fringe effects of course), and therefore no relative phase shift.
 
  • #5
Matterwave
You misunderstand Quantum mechanics.
You say "If you move your solenoid "far away" outside of these two paths..."
But, the solenoid can be in these two paths. You can draw the two paths which include the the solenoid.
How about that case?
You think only the case that the solenoid is outside of the two pathes.
 
  • #6
The contribution to the interference is mainly from the 2 straight paths (the light rays). The paths you have to draw to include this solenoid far away do not contribute much to the interference pattern.
 
  • #7
Matterwave
2 straight paths?
I don't see what you say in QM book. Many QM books don't say about the shape of pathes. I can't believe what you say is true.
 
  • #8
How do you usually describe 2 slit interference?
 
  • #9
If you want a reference, you can read Gottfried and Yan's Quantum Mechanics Fundamentals Page 196. They tell you there that the main contributions to the interference is due to the classical (straight-line) paths and their close neighbors.
 
  • #10
Thank you
 
  • #11
Matterwave
Thank you for discussing this subject and saying me something useful.
I want to talk to you with the other quantum mechanical problem.
If you see this comment, contact me. mrhun@hanmail.net
 

Related to A question on the Aharonov-Bohm effect

1. What is the Aharonov-Bohm effect?

The Aharonov-Bohm effect is a quantum mechanical phenomenon that occurs when a charged particle is influenced by a magnetic field despite the fact that the particle does not actually pass through the field. This effect demonstrates that the electromagnetic potential, rather than the magnetic field itself, is responsible for the behavior of charged particles.

2. Who discovered the Aharonov-Bohm effect?

The Aharonov-Bohm effect was first proposed by Yakir Aharonov and David Bohm in 1959. They were working on developing a quantum theory of the electromagnetic field and came across this unexpected result in their calculations.

3. How does the Aharonov-Bohm effect challenge traditional concepts of electromagnetism?

The Aharonov-Bohm effect challenges the traditional concept that the behavior of charged particles is solely determined by the electric and magnetic fields in which they are located. This effect shows that the electromagnetic potential, which was previously thought to be a mere mathematical construct, also has a physical influence on charged particles.

4. What are some applications of the Aharonov-Bohm effect?

The Aharonov-Bohm effect has several potential applications in the field of quantum information and technology. It has been proposed as a way to create non-local interactions between quantum systems, which could be useful for quantum computing and communication. It has also been suggested as a way to manipulate the spin of electrons, which could have applications in spintronics.

5. How has the Aharonov-Bohm effect been experimentally verified?

The Aharonov-Bohm effect has been experimentally verified through various experiments, including the famous electron interference experiment conducted by Tonomura et al. in 1986. In this experiment, electrons were observed to interfere with each other even though they did not pass through the regions of the magnetic field where the interference should have occurred. This and other experiments have confirmed the existence of the Aharonov-Bohm effect and its role in quantum mechanics.

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