Vector Potential: Reality or Tool?

In summary, vector potential is a useful mathematical tool in classical electrodynamics, as only the electric and magnetic fields have physical meaning. However, in quantum electrodynamics, it is considered a physical primitive constituent of the electromagnetic field, as shown by the Aharonov-Bohm Effect. In QM, vector potential is physical but not observable, similar to wave functions. It is essentially one of the wave functions in QED. However, the problem with non-observable quantities in QM is that it is difficult to determine if they are true physical quantities or just mathematical representations. Therefore, while vector potential is a real physical object, it is not directly observable. Its circulation around a closed loop is equivalent to the magnetic flux, and
  • #1
curupira
5
0
Has vector potential in classical electrodynamics a physical reality or it's just a mathematical tool?
 
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  • #2
It's just a (very useful) tool. Only the electric and magnetic fields have physical meaning. That's why you can make a Gauge transformation on the potentials (they change the potentials but not the fields) without altering the results.
 
  • #3
But in quantum electrodynamics it is physical in the sense that it is now the primitive constituents of the electromagnetic field. This was proven with the Aharonov-Bohm Effect which showed that while there may not be any fields in a region, a non-zero vector potential (and scalar potential too since you need both to describe the fields) can have measurable effects. This is not true in classical electrodynamics but if you have heard of such things this is probably where it came from.
 
  • #4
In QM, vector potential is physical, but not observable. In that sense, it is not unlike wave functions. In fact, in QED, it is essentially one of the wave functions.

Of course, the problem with non-observable quantities in QM is that you cannot tell if these are true physical quantities, or merely convenient mathematical representations for something else. So this doesn't mean that vector potential is "real". Merely that there is a real physical object that it represents.
 
  • #5
Vector potential don't but circulation of vector potential

[tex]\oint_L\vec{A}\cdot d\vec{l}=\int_S\vec{B}\cdot d\vec{S}=\Phi_B[/tex]

is magnetic flux.
 
  • #6
E,B and A,phi are two alternate ways of calculating physical observables. Neither are observable in themselves.
 

1. What is vector potential?

Vector potential is a mathematical quantity used in electromagnetism to describe the direction and magnitude of a magnetic field. It is a vector field that is derived from the electric and magnetic fields.

2. Is vector potential a real physical quantity?

There is some debate among scientists about whether vector potential is a physically real quantity or simply a mathematical tool. Some argue that it represents a physically real magnetic field, while others believe it is simply a mathematical construct.

3. How is vector potential related to magnetic fields?

The vector potential is related to magnetic fields through the equation B = ∇ x A, where B is the magnetic field and A is the vector potential. This equation is known as the Biot-Savart law, and it shows that the magnetic field is the curl of the vector potential.

4. What are the practical applications of vector potential?

Vector potential is used in many practical applications, including designing and optimizing electromagnets, modeling the behavior of electric motors, and calculating the magnetic fields produced by electric currents. It is also used in quantum mechanics to describe the behavior of particles with spin.

5. Is vector potential a useful tool in scientific research?

Yes, vector potential is a useful tool in scientific research, particularly in the fields of electromagnetism and quantum mechanics. It allows scientists to mathematically describe and understand the behavior of magnetic fields and particles with spin, and it is essential in many practical applications.

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