Simulation of smoothness using discrete quantities

[Kharakov]

That is actually a good question. In the early days of glass CRT disdplays algoriithms to plot graphics with limited resolution was a hot topic. Even a simple line.Visually I'd say it is the eye's resolution.Plot a straight line on a high res display and put a straight edge against it.

Mechanicaly there is no such thing as a true flat surface. Draw a line with a straight edge on paper. Look at it from 5 feet away, then look at it with a magnifying glass. The edge of the line will apear rough. Same general idea with quantization.

Digitize an audio signal the reconstruct it with digital to analog converters. Filter it with a low pass filter and the digital reconstruction appears smooth. Artifacts of the finite quantization, coarseness, exist put are very low. Digital audio is quantized.

Not that the thread is going anywhere now that unter has ahold of it, but one point of the thread is that an infinite amount of discrete elements are required to describe something smooth, like nature.

A presumably natural consciousness would by its nature have a tendency towards smoothing, because of field strength drop off and the like.

Don't know what you mean. Our brains are quantized by brain cells. Brain cells are quantized by molecules. And so on.

Conceptually the models say reality is discrete particles interacting through fields. Smoothness is an illusion of perception. Solid is a relative term.

Individual particles are not "separate" from the continuum, they are part of the whole. There are smooth gradients of field strengths, but nothing in nature is discrete. Except me farting in a jet.

 

[steve_bank]

Don't know what you mean. Our brains are quantized by brain cells. Brain cells are quantized by molecules. And so on.

Conceptually the models say reality is discrete particles interacting through fields. Smoothness is an illusion of perception. Solid is a relative term.

Individual particles are not "separate" from the continuum, they are part of the whole. There are smooth gradients of field strengths, but nothing in nature is discrete. Except me farting in a jet.

Thoughtful post.

Then it is a matter of subjective interpretation. Models based on particles produce results consistent with the models. You could say it is continuous because particles in matter are not truly isolated and form a continuum. Never looked at it that way before. So the words continuous and quantized regarding matter may be equally subjective.

 

[Kharakov]

There is divergence of field gradient at the particle, where the field force --->approaches----> infinity.

It doesn't matter... I'm still too poor to get laid by a hot chick while on a bunch of drugs.....

 

[steve_bank]

There is divergence of field gradient at the particle, where the field force --->approaches----> infinity.

It doesn't matter... I'm still too poor to get laid by a hot chick while on a bunch of drugs.....

Divergence tells you whether a volume is a sink sorce, or passive??? Graduent tells you at a point where the force vector is poinmting ???

 

[Kharakov]

ehh, where the net divergence is 0? I was thinking of change in direction of gradient, where the gradient changes directions at full strength.

At a point source, I think the correct interpretation would be divergence=0.

 

[steve_bank]

ehh, where the net divergence is 0? I was thinking of change in direction of gradient, where the gradient changes directions at full strength.

At a point source, I think the correct interpretation would be divergence=0.

In an electric circuit the divergennce of the volume of a resistor is zero, passive. A local sorce is positive. The volume of a battery has positve divergence.

Curl, divergence, and gradient apply to any situation where energy and or mass flows. EM fields, water flow, or gavity fields.

Gradient at full strength?

 

[Kharakov]

My brain is fucking evil. I was envisioning a pointlike particle as an actual point in space where field strength flipped direction- like it approached a particle, approached infinite force as it approached the "point particle" (which is just a mathematical convenience, everything that exists is spread out over space), blah blah blah.

In other words, I took the "elementary school" particle view of things. I am quite retarded, so it shouldn't surprise you that I still view things as elementary school particles. Sort of like I'm not part of the collective.

 

[steve_bank]

My brain is fucking evil. I was envisioning a pointlike particle as an actual point in space where field strength flipped direction- like it approached a particle, approached infinite force as it approached the "point particle" (which is just a mathematical convenience, everything that exists is spread out over space), blah blah blah.

In other words, I took the "elementary school" particle view of things. I am quite retarded, so it shouldn't surprise you that I still view things as elementary school particles. Sort of like I'm not part of the collective.

A common text book example for gradient is a ball rolling down a mountain in a gravity field. Gradient yields the instantaneous vector at any point.

What you are describing is analogous to a black hole. It tries to compress to an infinitely small point, but can never get there.

No idea what you are talking about. The thing to do is write an equation then apply calculus, and take limits to infinity.

 

[Kharakov]

I was mangling language. Ignore it. I'll try and reexplain it from the beginning later.

 

[Kharakov]

I was thinking of particles as actual particles, instead of fields. So particles, with inverse square law relationship of force strength  Coulomb's law, has a force that approaches infinity as you get closer to the particle. It's just sloppy thinking. Disregard it, unless you want to talk about it for some weird reason (maybe say why it's incorrect thinking, so others understand).


force is proportional to 1/r^2 as r-->0

 

[steve_bank]

I was thinking of particles as actual particles, instead of fields. So particles, with inverse square law relationship of force strength  Coulomb's law, has a force that approaches infinity as you get closer to the particle. It's just sloppy thinking. Disregard it, unless you want to talk about it for some weird reason (maybe say why it's incorrect thinking, so others understand).


force is proportional to 1/r^2 as r-->0

You can apply divergence and gradient to complex static electric fields. It becomes complicated quickly. Numerical solvers are used to solve Maxwell's Equations.

I do not know if an electron has a size estimate. In theory electrons are particles not divisible.

Maxwell's Demon, an infinitely small observer. Imagine yourself inside an electric field and what do you see?

https://en.wikipedia.org/wiki/Maxwell's_demon

Look at the differential form of Gauss Law.

https://en.wikipedia.org/wiki/Gauss's_law

Then look at the del operator in Cartesian coordinates . Then put it together to answer your question. I used Scilab, free online download, you can set up a simulation.

There is also a demo version of a partial differential equation solver PDE Solutions that has examples in electrostatics.

https://en.wikipedia.org/wiki/Gradient

 

[steve_bank]

It went over my head, In electrostatics charges are treated as points in space, distributed along a line like a wire , distributed on a surface like a copper sheet, or distributed within a surface.

 

[Kharakov]

I do not know if an electron has a size estimate. In theory electrons are particles not divisible.

Next post:
In electrostatics charges are treated as points in space, distributed along a line like a wire , distributed on a surface like a copper sheet, or distributed within a surface.

I'm under the distinct impression that the particle treatment is a mathematical simplification rather than a physical truth.

Like how in the (simple) Schwarzschild metric of GR the gravity well of the Earth is treated like it comes from a point source, rather than a complex entity with constantly changing gravitational field due to magma flows, etc. (the change is not even enough to impact measurements for the most part, but the point is, it is there).

 

[steve_bank]

I do not know if an electron has a size estimate. In theory electrons are particles not divisible.

Next post:
In electrostatics charges are treated as points in space, distributed along a line like a wire , distributed on a surface like a copper sheet, or distributed within a surface.

I'm under the distinct impression that the particle treatment is a mathematical simplification rather than a physical truth.

Like how in the (simple) Schwarzschild metric of GR the gravity well of the Earth is treated like it comes from a point source, rather than a complex entity with constantly changing gravitational field due to magma flows, etc. (the change is not even enough to impact measurements for the most part, but the point is, it is there).

I do not know much about relativity but I agree. In astronomy distant stars are treated like a point source, In EM it is called an isotropic radiator. We treat stars like theoretical point sources radiating equally in all directions. At light years away it works for radiated power estimates for stars.

Trying to do practicay electrostatics at the electron level would be impossible.

What a particle is is open to speculation. What we know is we can do things with the concepts and the models. Using electrostatics a capacitor can be designed.

IN QM operations can be at the particle level. Transistors are an example.

In an electrostatic field force at any point is determined by moving a theoretical unit charge around the field, field mapping. In differential equations a vector field.

It is an expensive book these days the book Electromagnetics by Krauss is a goo. Written as a physics text.

There is a series of books called Problem Solvers. There is one for EM and is a thick book of worked out problems. Cheaper than a text. I used to have a copy.

 

[steve_bank]

There is a little more about inverse square. Imagine you are at a point on a sphere expanding around a star. As the sphere gets bigger the local energy density around the point decreases, but the total energy passing through the sphere's surface stays constant, ignoring absorption and scattering.

Conservation says total energy can not diminish. It should be the same for fields around point charges.