Local Conservation of Charge: Feynman's Thought Experiment Explained

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In summary, Feynman discusses the concept of conservation in his third messenger lecture and uses a thought experiment to demonstrate the conservation of charge. He explains that charge is conserved locally, meaning that any change in charge at a point must be balanced by a movement of charge in a smooth and continuous manner within a surrounding area. He also states that any conserved quantity must also be conserved locally.
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AlchemistK
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I was watching the messenger lectures by Feynman and in the third lecture he talks about conservation. In the beginning he talks about the conservation of charge, and at one point demonstrates a thought experiment in which two observers, one stationary and the other moving, see a charge disappear at one point in front of them and another similar charge reappear behind them. The person stationary with respect to the charges see the charge appear at the same time it disappears, but the second person disagrees because of his movement.
Then Feynman states that charge is conserved locally.
What does he mean by that?

(He also states that if something is conserved, it must also be conserved locally.)
 
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It means something like this: if the amount of charge at some point in space changes value from Q1 to Q2 in a time interval from T1 to T2, then there exists a surface surrounding the point such that an amount of charge equal to Q2-Q1 passes through the surface in the same time interval. It's just a way of saying that for a conserved quantity such as charge to change value at a point, it must do so by moving in a smooth and continuous way to some nearby point(s).
 

1. What is local conservation of charge?

Local conservation of charge is a fundamental principle in physics that states that the total amount of electric charge within a closed system remains constant over time. This means that charge cannot be created or destroyed, only transferred between objects within the system.

2. Who is Feynman and why is his thought experiment important?

Richard Feynman was a renowned physicist who made significant contributions to the field of quantum mechanics. His thought experiment on local conservation of charge, also known as Feynman's paradox, is important because it challenges the traditional understanding of electric charge and helped pave the way for the development of quantum electrodynamics.

3. Can you explain the thought experiment in simple terms?

In Feynman's thought experiment, he imagines two charged particles approaching each other and then repelling each other. According to classical physics, this would require an infinite amount of energy. However, using quantum mechanics, Feynman showed that the energy required is actually finite, and this is due to the exchange of virtual particles between the two particles.

4. How does Feynman's thought experiment relate to the concept of virtual particles?

In the thought experiment, Feynman explains that the repulsion between the two particles is due to the exchange of virtual particles, which are particles that pop in and out of existence in a vacuum. This exchange of virtual particles allows for the transfer of charge between the two particles, while still preserving the overall conservation of charge within the system.

5. What are the implications of Feynman's thought experiment?

Feynman's thought experiment helped to reconcile the concept of local conservation of charge with the principles of quantum mechanics. It also led to the development of quantum electrodynamics, which is a powerful theory that describes the interactions between charged particles and electromagnetic fields. Additionally, it highlights the importance of considering the quantum nature of particles when studying fundamental principles in physics.

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