Particle-field(wave) duality

  • Thread starter Kolahal Bhattacharya
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In summary, Griffiths and Jackson discuss the validity of the superposition principle for electrostatic energy. While the principle holds for point charges, it fails for larger magnitudes. This leads to a discussion about the relationship between stored energy and fields, and whether charges and particles can be considered condensed forms of energy. The concept of wave-particle duality is also brought up, with the understanding that while fields follow the principle of superposition, energies do not.
  • #1
Kolahal Bhattacharya
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Griffiths says the superposition principle is not valid for electrostatic energy.I understood this concept,remembering that energy,unlike potential(point function),is a field function.Is Griffiths's conclusion still correct for point charge distribution (rqn.2.43)?
I think it's correct: we know electromagnetic energy grows larger as the charge is localised more & more(Jackson).So, when we are dealing with point charges,which are localised themselves, magnitude of W is very large so that it cannot obey superposition principle.I think the principle fails when huge magnitudes are involved.Any conceptual mistake?Please help.
Next, will it be wrong to consider stored energy creates appropriate field & condensed field creates appropriate particle?i.e. can we regard a charge as a condensed form of electromagnetic energy? or, a mass particle as a condensed form of gravitational energy?I use appropriate subscripts to distinguish betweeen the fields.Can any light be thrown from here to wave -particle duality?
 
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  • #2
Electric and Magnetic *fields* are the Sum of individual source contributions [which is superposition] (says classical E&M, anyway).
But the *Energies* involved go as E^2 + B^2 , even for sparse fields.
Obviously a quadratic cannot be a superposition of source contributions.

The sources themselves are additive (Q = q1 + q2 + q3 ...), so are distinct
from the NON-additive Field Energies that they engender [promulgate].
A source is most closely related to the additive Field that diverges from it.
 
  • #3


I can say that the concept of particle-field (wave) duality is a fundamental principle in quantum mechanics. It states that particles can exhibit both wave-like and particle-like behavior, depending on how they are observed or measured. This principle has been experimentally verified through various experiments, such as the double-slit experiment.

Regarding Griffiths' statement that the superposition principle is not valid for electrostatic energy, I believe it is still correct for point charge distributions. This is because the superposition principle states that the total energy of a system is the sum of the energies of its individual components. However, for point charges, the energy can become infinitely large as the charges get closer together, making it impossible to apply the superposition principle.

In terms of considering stored energy as creating appropriate fields and condensed fields as creating particles, this is a valid way of thinking about it. In the case of a charge, it can be seen as a condensed form of electromagnetic energy. Similarly, a mass particle can be seen as a condensed form of gravitational energy. However, it is important to note that these are just conceptual models and do not fully explain the complex nature of these phenomena.

As for any connection to wave-particle duality, it is important to understand that quantum mechanics is a probabilistic theory and does not necessarily have a direct connection to classical concepts such as fields and particles. The wave-particle duality is a unique property of quantum systems and cannot be fully explained using classical concepts. So while there may be some connections between the two, it is not a direct correlation.

In conclusion, the concepts of particle-field (wave) duality and the superposition principle are both important in understanding the behavior of particles at the quantum level. While there may be some connections between these concepts and classical ones, it is important to remember that quantum mechanics operates on a different level and cannot be fully explained using classical concepts.
 

1. What is particle-field duality?

Particle-field duality refers to the concept in quantum mechanics where particles can exhibit properties of both waves and particles depending on the experimental setup. This means that particles, such as electrons or photons, can behave as discrete, localized objects (particles) or diffuse, spread out entities (waves) depending on how they are observed.

2. Who first proposed the idea of particle-field duality?

The idea of particle-field duality was first proposed by French physicist Louis de Broglie in his doctoral thesis in 1924. He suggested that particles, such as electrons, could exhibit wave-like behavior and have a wavelength associated with them.

3. What is the double-slit experiment and how does it demonstrate particle-field duality?

The double-slit experiment is a famous experiment that demonstrates particle-field duality. It involves shooting particles, such as electrons, through two slits and observing the resulting interference pattern on a screen. This interference pattern is similar to the pattern formed by waves passing through two slits, suggesting that the particles have wave-like properties.

4. How does particle-field duality relate to the uncertainty principle?

The uncertainty principle, proposed by Werner Heisenberg, states that it is impossible to know both the position and momentum of a particle with absolute certainty. This is because the act of measuring one property affects the other. Particle-field duality plays a role in this principle, as the wave-like behavior of particles means that their position and momentum cannot be known simultaneously.

5. How has the concept of particle-field duality impacted our understanding of the physical world?

The concept of particle-field duality has greatly impacted our understanding of the physical world, particularly in the field of quantum mechanics. It has challenged our traditional understanding of particles as solely discrete, solid objects and has led to new theories and experiments in the field. It has also played a role in the development of modern technologies, such as transistors and lasers, which rely on the wave-like behavior of particles.

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