By: Adrian (a.delete@this.acm.org), December 18, 2021 4:17 am
Room: Moderated Discussions
Adrian (a.delete@this.acm.org) on December 18, 2021 2:54 am wrote:
> ⚛ (0xe2.0x9a.0x9b.delete@this.gmail.com) on December 17, 2021 1:49 pm wrote:
> >
> > - The shortest distance (shortest possible path) between the
> > switch and the light bulb (LED) is approximately 1 meter
> >
> >
> >
> > The video is implicitly claiming that information about
> > the space-time event "the switch has just been closed"
> > is being transmitted from the switch to the LED using the
> > shortest possible path of approximately 1 meter (such
> > as: via radio waves), instead of being transmitted in/along/via the wire of length 300e6 meters.
> >
> > Given your knowledge of the theory/theories of electromagnetism:
> > Does the theory support the claim that information
> > about the space-time event "the switch has just been closed" travels to the LED via the shortest path?
> >
Sorry, I have omitted to answer this part of your message.
The event "the switch has just been closed" does not travel to the LED via the geometrically shortest path, but through the path that takes the shortest time for the electromagnetic potential to propagate, which depends on the dielectric and magnetic properties of the materials present around.
However there should not be much difference between those 2 paths, especially when the experiment is done in an environment where most of the space is filled with air.
In electromagnetic problems, you have 2 things that mathematically behave like fluids, the electric charge and the electric potential, which is what you measure with a voltmeter.
In electrostatic problems, you have only stationary distributions of electric charge and electric potential. The potential is not of much use, as it is completely determined by the charge, so it is redundant.
On the other hand, if you have moving parts or other things that cause variations in time, the electric charge flows and its flow is the electric current and the electric potential also flows and its flow is the magnetic potential.
Unlike in the electrostatic case, the 4-vector electromagnetic potential, i.e. electric potential together with its flow, acquires an independence of the 4-vector electric charge density together with its flow, because it is no longer determined by the current charge and current distribution but also by the past history. The potential tries to follow the flow of the charge, but there is a delay between the flow of the potential and the charge movements that caused it.
To determine the exact path of propagation from the power supply to the bulb, you need a 3-dimensional geometric model of the environment, with the material parameters of everything present.
Than you can compute the evolution in time of the charge density 4-vector and electromagnetic potential 4-vector, after switching on the power supply. Then you can see the exact path.
However such an approach is seldom needed, as the actual path will not be too different from the geometrically shortest path through the air, so you can approximate it like that.
> ⚛ (0xe2.0x9a.0x9b.delete@this.gmail.com) on December 17, 2021 1:49 pm wrote:
> >
> > - The shortest distance (shortest possible path) between the
> > switch and the light bulb (LED) is approximately 1 meter
> >
> >
> > +----150e6--------battery--switch-------150e6------+
> > |##################################################| 1
> > +----150e6--------------LED-------------150e6------+
> > > >
> > The video is implicitly claiming that information about
> > the space-time event "the switch has just been closed"
> > is being transmitted from the switch to the LED using the
> > shortest possible path of approximately 1 meter (such
> > as: via radio waves), instead of being transmitted in/along/via the wire of length 300e6 meters.
> >
> > Given your knowledge of the theory/theories of electromagnetism:
> > Does the theory support the claim that information
> > about the space-time event "the switch has just been closed" travels to the LED via the shortest path?
> >
Sorry, I have omitted to answer this part of your message.
The event "the switch has just been closed" does not travel to the LED via the geometrically shortest path, but through the path that takes the shortest time for the electromagnetic potential to propagate, which depends on the dielectric and magnetic properties of the materials present around.
However there should not be much difference between those 2 paths, especially when the experiment is done in an environment where most of the space is filled with air.
In electromagnetic problems, you have 2 things that mathematically behave like fluids, the electric charge and the electric potential, which is what you measure with a voltmeter.
In electrostatic problems, you have only stationary distributions of electric charge and electric potential. The potential is not of much use, as it is completely determined by the charge, so it is redundant.
On the other hand, if you have moving parts or other things that cause variations in time, the electric charge flows and its flow is the electric current and the electric potential also flows and its flow is the magnetic potential.
Unlike in the electrostatic case, the 4-vector electromagnetic potential, i.e. electric potential together with its flow, acquires an independence of the 4-vector electric charge density together with its flow, because it is no longer determined by the current charge and current distribution but also by the past history. The potential tries to follow the flow of the charge, but there is a delay between the flow of the potential and the charge movements that caused it.
To determine the exact path of propagation from the power supply to the bulb, you need a 3-dimensional geometric model of the environment, with the material parameters of everything present.
Than you can compute the evolution in time of the charge density 4-vector and electromagnetic potential 4-vector, after switching on the power supply. Then you can see the exact path.
However such an approach is seldom needed, as the actual path will not be too different from the geometrically shortest path through the air, so you can approximate it like that.