Inverse Square Law

[Arnaud Antoine ANDRIEU]

The non-contact forces have an exchange particle, and that means you can apply the idea of the density of the exchange particles, or lines of force.

 

Even for neutrino?

[swansont]

 

Even for neutrino?

 

As I explained a few posts back, no. The weak interaction has a massive exchange particle.

[Arnaud Antoine ANDRIEU]

 

As I explained a few posts back, no. The weak interaction has a massive exchange particle.

 

How do you define density?

 

If you can see an object, it will be represented by magnitude. Everyone agrees.

 

However we can also say magnitude = density of matter that we can see.

 

If you can see neutrino, and this is already the case with the traps, how can you explain its magnitude?

[swansont]

How do you define density?

In this case, number per unit area.

 

If you can see an object, it will be represented by magnitude. Everyone agrees.

No, not everyone. I don't agree because I don't know what you're talking about.

 

However we can also say magnitude = density of matter that we can see.

 

If you can see neutrino, and this is already the case with the traps, how can you explain its magnitude?

What does this have to do with inverse-square laws? (also, wth?)

[Arnaud Antoine ANDRIEU]

No, not everyone. I don't agree because I don't know what you're talking about.

 

I have a Dr. Donald H. Menzel book. And he said exactly what I wrote. Can you explain?

 

wikipedia.org/wiki/Apparent_magnitude

Edited July 31, 2013 by Arnaud Antoine ANDRIEU

[michel123456]

The thing that the 1/r² forces have in common is they are action-at-a-distance forces. A rope is a contact force — there is a continuous object connecting you to the dog. The non-contact forces have an exchange particle, and that means you can apply the idea of the density of the exchange particles, or lines of force.

Yes.

Action at a distance is so bogus that scientists define it through an exchange of particles that travel through space (and time).

And as Strange said, action at a distance is ingested at a young age and becomes "intuitive"

 

Although I remember an example that I found most bizarre then.

It was when learning "resistance des materiaux" (resistance of materials) in the first year of architecture IIRC.

About a I beam

Where the professor explained that the up and down plates ( the flanges) take all the strength while the vertical plate (the web) takes almost nothing. In the beam, the important thing is the distance ( the depth) between the 2 up/down plates. Theoretically the web could even disappear, only the distance counts! (which is not entirely accurate because you need to make some contact between the 2 flanges, otherwise the beam falls apart)

 

The fact that the distance was the important thing blew my mind then.

But after a while I thought of a simple lever and thought it was exactly the same phenomena. And I swallowed the beam.

[swansont]

 

I have a Dr. Donald H. Menzel book. And he said exactly what I wrote. Can you explain?

 

wikipedia.org/wiki/Apparent_magnitude

 

Happy to. You post nonsense, out of context snippets, and I can't understand them. You don't even reference a book properly — what is the title of the book? What is the chapter discussing, from which you pulled the quote? What's the context of it?

 

You link to a celestial unit, which is apparent magnitude. What all does that have to do with observing a neutrino, and the connection of neutrinos to this discussion?

[michel123456]

The inverse square law follows from some vector calculus in 3-d. Specifically, if we have a vector field that is the gradient of some function, then the inverse square law corresponds to the divergence being zero outside the sources.

 

You get in general a [math]1/r^{n-1}[/math] law in n-dimensions.

So in 2 dimensions you get an inverse distance (not squared) relation. I guess.

[swansont]

So in 2 dimensions you get an inverse distance (not squared) relation. I guess.

Yes. That is what the 2-D cross section of a line source looks like. A line source drops off as 1/r in the other two dimensions.

[michel123456]

Yes. That is what the 2-D cross section of a line source looks like. A line source drops off as 1/r in the other two dimensions.

And in one dimension then?

[Greg H.]

In 1 dimension:

[math] 1/r^{1-1}[/math]

[math] 1/r^0[/math]

[math]1[/math]

 

If I understand the application correctly, it wouldn't drop off at all.

[swansont]

In 1 dimension:

[math] 1/r^{1-1}[/math]

[math] 1/r^0[/math]

[math]1[/math]

 

If I understand the application correctly, it wouldn't drop off at all.

 

Which is correct. The electric field of an infinite sheet of charge is a constant.

[michel123456]

 

Which is correct. The electric field of an infinite sheet of charge is a constant.

I don't understand (again)

One dimension is a line.

 

2 points on a line are separated by a distance.

 

The gravity that attracts those 2 points does not fall with the square of the distance in a 1 dimension universe?

Edited August 1, 2013 by michel123456

[swansont]

I don't understand (again)

One dimension is a line.

 

2 points on a line are separated by a distance.

 

The gravity that attracts those 2 points does not fall with the square of the distance in a 1 dimension universe?

 

Nope. If all you have is one dimension, you have one flux line along that dimension. You always have one flux line. Constant.

[michel123456]

 

Nope. If all you have is one dimension, you have one flux line along that dimension. You always have one flux line. Constant.

I was wondering a lot about your post.

 

I have always seet a Flatland world as a section of our 3D space. But it must not be so.

A section must retain the physical laws of the sectioned entity.

And you explanation states that gravitation follows a different law in 2D.

 

I am confused.

[studiot]

 

Although I remember an example that I found most bizarre then.

It was when learning "resistance des materiaux" (resistance of materials) in the first year of architecture IIRC.

About a I beam

Where the professor explained that the up and down plates ( the flanges) take all the strength while the vertical plate (the web) takes almost nothing. In the beam, the important thing is the distance ( the depth) between the 2 up/down plates. Theoretically the web could even disappear, only the distance counts! (which is not entirely accurate because you need to make some contact between the 2 flanges, otherwise the beam falls apart)

 

The fact that the distance was the important thing blew my mind then.

But after a while I thought of a simple lever and thought it was exactly the same phenomena. And I swallowed the beam.

 

 

I very much doubt the professor said exactly that.

 

The flanges take pretty well all the bending moment, but that is not the only load/stress acting.

 

To keep it simple I will ignore torsion and state that the other stress acting is vertical shear. This is taken pretty well completely by the web.

 

So much so that the beam has to be designed to resist the inevitable tendency to buckling that this vertical shear introduces.

 

You will see 'web stiffeners' welded into beams under particular load for just this reason

[swansont]

I was wondering a lot about your post.

 

I have always seet a Flatland world as a section of our 3D space. But it must not be so.

A section must retain the physical laws of the sectioned entity.

And you explanation states that gravitation follows a different law in 2D.

 

I am confused.

 

It depends on how you take that section of 3D space. You can't simply take an arbitrary slice of 3D space — what of you take a slice that doesn't have the sun in it? The 2D space will behave like 3D space if every slice is the same. That is, in 3D, the sun is contributing like a point, to see what it's like in 2D space that point has to be in any slice you take, so it is contributing like a line, perpendicular to the slice. In 3D space, with the 1/r² law, all of the line contributes, not just the point that's in the plane.

[michel123456]

If the slice is the orbital plane, the 1/r^2 law stands. And it is in this "slice" that Kepler's law is explained in all textbooks. As if Kepler's law was a result of 2D geometry.

Of course if you take a random "slice" that does not correspond to any orbit the result will be moot.

[swansont]

If the slice is the orbital plane, the 1/r^2 law stands. And it is in this "slice" that Kepler's law is explained in all textbooks. As if Kepler's law was a result of 2D geometry.

 

Orbital motion will be in a plane because there is no force to move it out of the plane (the force is radial and cannot exert a force that would change the velocity out of the plane. Looking at that plane is not the same as saying the analysis is in a 2D geometry. It's a 3D Geometry with one angle set to a constant (in spherical coordinates).

 

Of course if you take a random "slice" that does not correspond to any orbit the result will be moot.

Yes, precisely. You have to contrive a specific situation, and it does not apply generally.

[michel123456]

Orbital motion will be in a plane because there is no force to move it out of the plane (the force is radial and cannot exert a force that would change the velocity out of the plane. Looking at that plane is not the same as saying the analysis is in a 2D geometry. It's a 3D Geometry with one angle set to a constant (in spherical coordinates).

 

 

Yes, precisely. You have to contrive a specific situation, and it does not apply generally.

(emphasis mine)

But the analysis of Kepler's law is 2D.

It is stated that :(from wiki)

A line joining a planet and the Sun sweeps out equal areas during equal intervals of time^..

and (or)

[img=http://en.wikipedia.org/wiki/File:Kepler_laws_diagram.svg

Figure 1: Illustration of Kepler's three laws with two planetary orbits.

(1) The orbits are ellipses, with focal points ƒ₁ and ƒ₂ for the first planet and ƒ₁ and ƒ₃ for the second planet. The Sun is placed in focal point ƒ₁.

 

(2) The two shaded sectors A₁ and A₂ have the same surface area and the time for planet 1 to cover segment A₁ is equal to the time to cover segment A₂.

 

(3) The total orbit times for planet 1 and planet 2 have a ratio a₁^3/2 : a₂^3/2.

(All quoted from the same wiki article)

 

That is entirely 2D analysis.

I don't understand why it must be considered as a 3D by adding a constant. That looks like wishful thinking to me. One could then say it is a 11D geometry by adding other 9 constants out of nowhere.

[swansont]

(emphasis mine)

But the analysis of Kepler's law is 2D.

It is stated that :(from <a data-ipb="nomediaparse" data-cke-saved-href="http://en.wikipedia.org/wiki/Kepler" href="http://en.wikipedia.org/wiki/Kepler" s_laws_of_planetary_motion"="">wiki)

and (or)

[img=http://en.wikipedia.org/wiki/File:Kepler_laws_diagram.svg

(All quoted from the same wiki article)

 

That is entirely 2D analysis.

I don't understand why it must be considered as a 3D by adding a constant. That looks like wishful thinking to me. One could then say it is a 11D geometry by adding other 9 constants out of nowhere.

 

 

I explained why the motion must be 2D. But that's not the same as saying that the underlying geometry is 2D.

[michel123456]

 

 

I explained why the motion must be 2D. But that's not the same as saying that the underlying geometry is 2D.

So, you say that the underlying geometry is 3D, that the 3D geometry has a result an inverse squared law that is fully showed in a 2D diagram.

[swansont]

So, you say that the underlying geometry is 3D, that the 3D geometry has a result an inverse squared law that is fully showed in a 2D diagram.

 

I guess.