The inverse square law

[Andonyx]

No, suppose it extended uniformly in all directions, but it still were proportional to d instead of 1/d².

Well, then somehow something somewhere is creating more gravity...

The simple fact is anything, form gas, to solids, to plasma if it is spread out over four times it's original space gets four times less dense.

If it doesn't then you're adding some from somewhere.

The problem isn't with the inverse square law. We're just sayng that the inverse square law shows that anything traveling in a spherical expansion, at twice the radius is covering four times the area.

Fine and dandy.

But how that relates to its decrease in intensity is simple, and it has nothing to do with the inverse square law.

If you spread out something in a cookie pan, as you spread it out over four times the area, it will be 1/4 as dense.

Does that not make sense?

So as gravity gets to spread over four times the area from the same source, it's four times less intense.

What the problem?

 

[jj]

I'm just talking about gravity. Suppose, for example, that gravity were proportional to distance, like a spring, instead of being inversely proportional to the square of distance. So what? Can anyone describe why this violates energy conservation? (Springs don't violate it.) How would you go about extracting arbitrary amounts of energy from a system that obeyed this type of gravity?

Gravity spreads in 3 dimensions.

The spring pulls in one, and is connected at both ends.

 

[T'ai Chi]

Do you agree that you often troll this group, that you put yourself to total ridicule once, and that you continue with a new "identity" and continue to do so?

One can have a nickname, then stop using that nickname, then get a new nickname. Could you please find in the forum rules where one can't?

Do people acknowledge that other people have/had sock puppets? Or that "trolling" is an opinion and people usually call someone a troll who they don't agree with? Or that anyone can claim anyone else is a troll?

Do people deny that I've posted any worthwhile posts on this forum? I've only seen a very tiny amount (like 3 or 4) people saying that, and what do you know, these people are the same people that happen disagree with me on issues (which is fine of course)! An interesting observation.

Do people deny that I've said I was wrong about issues several times while I've been here, and that I've conceed that I see other peoples' ways, even in a heated, opinionated debate?

Do people believe those actions to be typical of most "trolls"?

Do people believe that once someone is labelled a troll they are always a troll?

Do you insist that it's "character assasination" to point out your continued misbehavior?

That's funny, because I asked some questions about the inverse square law in this thread, and then I get my nickname made fun of and Marx Brothers and Three Stooges quotes used, and I'm apparently misbehaving for doing that. If there is a God, he/she/it must have one heck of a sense of humor.

Does anyone here consider it "misbehavior" to ask questions about the inverse square law?

Does anyone here consider making fun of a nickname as an pointing out misbehavior?

Does anyone here consider making fun of nicknames as character assasination, except when a "troll's" name is being made fun of? Do people here think that rules have to be applied equally to all to be effective?

I thought you understood area. Primary among that would be understanding the meaning and definition of area, from which we wind up with units squared.

Yes, I do understand area. Again, I'm not interested in the 'area is defined like so... and the inverse law is related to area... thus the inverse law is the inverse squared law' as that, while true, is circular, definitional, fairly obvious, and doesn't interest me as a real explanation.

What I am wondering why in a universe we should expect it to come out in units squared, rather than some other unit. People can call me stupid, trollish, or whatever for wondering that; I could care less really, as the question is a reasonable one. If the answer is 'we don't know and how could we know?!', that is fine; I am just curious about why the universe is ordered the way it is and if we should expect it to be.

"regression"??? Why would "regression" be involved here?

Well, I know we measure area and there is error in measurements, so regression might be employed, especially involving areas (or whatever) of objects we cannot measure directly or accurately. Regression could also be used for verification of the inverse square law.

 

[phildonnia]

Gravity spreads in 3 dimensions.

The spring pulls in one, and is connected at both ends.

And the pressure of an explosive shock wave is inverse to the cube of the distance.

 

[69dodge]

Originally posted by jj
Gravity spreads in 3 dimensions.

The spring pulls in one, and is connected at both ends.

According to your reasoning, the force exerted by a spring should remain constant, like the intensity of a laser beam, rather than increase as the spring is stretched.

In any case, how similar my hypothetical gravity is to a spring is not really the important question. The important question is, how would you go about extracting arbitrary amounts of energy from a system that obeyed this type of gravity?

My answer is that you can't. It's a conservative field. Any central force is conservative if it depends only on distance, regardless of how it depends on distance.

 

[Andonyx]

According to your reasoning, the force exerted by a spring should remain constant, like the intensity of a laser beam, rather than increase as the spring is stretched.

In any case, how similar my hypothetical gravity is to a spring is not really the important question. The important question is, how would you go about extracting arbitrary amounts of energy from a system that obeyed this type of gravity?

My answer is that you can't. It's a conservative field. Any central force is conservative if it depends only on distance, regardless of how it depends on distance.

As for my response i guess, I didn't understand your question or where it was leading. But I think I agree with your conlusion.

As to the laser...It doesn't remain constant. It's still subject if nothing else to degredation by the mean free path, in which we can determine, due to the probability of any portion of its photons being absorbed or reflected in a medium that over distance it is degrading a certain amount over a certain distance.

It just isn't degrading by the same factor as the inverse square.

 

[69dodge]

Originally posted by Andonyx
Well, then somehow something somewhere is creating more gravity...

I suppose you could think about it that way if you wanted to. But then you run into the same problem even for the normal inverse-square type of gravity. What created the gravity 1000 miles up? It didn't come from the surface, getting thinner as it rose; the surface still has its own gravity.

If you integrated (the magnitude of) the force of gravity over all space (which is a fairly meaningless thing to do, but anyway . . .), you'd get infinity. Where did all that gravity come from?

Gravity isn't a substance that has to come from somewhere. It's a force field. It simply exists. A force field obeying a different law could simply exist just as easily.

 

[mattg]

Oh, and I can't resist:
The Earth is exactly 40000 km in circumference, from pole to pole. Not approximately, but exactly. This is irrefutable proof that God uses the metric system.

I can't resist either.
Measuring the EXACT circumference of the earth would be a lot like measuring the exact length of a coastline. You end up approaching infinity, due to all the surface variation.

(I apologize if the quoted comment was intended as sarcasm. I'm new here, and don't know everyone's personality yet.)

 

[69dodge]

Originally posted by Andonyx
As to the laser...It doesn't remain constant. [. . .] It just isn't degrading by the same factor as the inverse square.

Sure, no argument there. I was considering an idealized beam that didn't experience any spreading or scattering.

 

[Andonyx]

I suppose you could think about it that way if you wanted to. But then you run into the same problem even for the normal inverse-square type of gravity. What created the gravity 1000 miles up? It didn't come from the surface, getting thinner as it rose; the surface still has its own gravity.

If you integrated (the magnitude of) the force of gravity over all space (which is a fairly meaningless thing to do, but anyway . . .), you'd get infinity. Where did all that gravity come from?

Gravity isn't a substance that has to come from somewhere. It's a force field. It simply exists. A force field obeying a different law could simply exist just as easily.

Well, wait. That's what I'm saying, you can't have more gravity just created out of somewhere, and so the notion of gravity that doesn't obey the inverse square law is silly.

But I think I'm completely losing track of where you're going with this.

I mean are you trying to say that Gravity does violate conservation or not.

Because obviously in real life it doesn't.

And as you stated even in your world where it didn't dissapate by inverse square, it still didn't. (Your claim, not mine. I haven't thought about it enough although I suspect you're correct.)

So okay umm. Fine.

Now what's this about force fields?

Is this that old speculation on wether or not gravity actually trvales form a source to a thing?

Because the best evidence we have right now, is that YES, in fact it does. Recently evidence came ot light that not even gravity is instantaneous, and in fact if the sun suddenly popped out of existence the Earth wouldn't start to deviate from its orbit for eight minutes.

http://www.nature.com/nsu/030106/030106-8.html

The speed of gravity is most likely 'C'.

If that's the case, then it seems to me that there is no reason that gravity is not some force that starts at the gorund and radiates up.

But of course there is gravity from everything, so even in the absence of Earth's gravity there is various fields from the Sun and other stars, etc etc....

I'm not sure I have your line of reasoning right. Is there an earlier post of yours I missed that explains your ultimate conclusion?

My apologies if I missed this or am being obtuse. I just can't seem to grasp what you're getting at.

 

[roger]

I can't resist either.
Measuring the EXACT circumference of the earth would be a lot like measuring the exact length of a coastline. You end up approaching infinity, due to all the surface variation.

(I apologize if the quoted comment was intended as sarcasm. I'm new here, and don't know everyone's personality yet.)

The meter used to be defined as one ten millionth of the distance from the pole to the equator (great circle, passing through Paris). Thus, the comment was a joke based on this old definition.

Welcome to the boards, btw.

 

[jj]

According to your reasoning, the force exerted by a spring should remain constant, like the intensity of a laser beam, rather than increase as the spring is stretched.


Not at all. As far as I can tell, you just imagined that. You probably have some thought process that led up to it, but I can't even start to debug it until you explain.


In any case, how similar my hypothetical gravity is to a spring is not really the important question. The important question is, how would you go about extracting arbitrary amounts of energy from a system that obeyed this type of gravity?



Well, figure out what potential vs. kinetic energy works out to, for starters.


My answer is that you can't. It's a conservative field. Any central force is conservative if it depends only on distance, regardless of how it depends on distance.

Really?

How do you get both accileration and mv^2 to to equate properly?

 

[jj]

As to the laser...It doesn't remain constant. It's still subject if nothing else to degredation by the mean free path, in which we can determine, due to the probability of any portion of its photons being absorbed or reflected in a medium that over distance it is degrading a certain amount over a certain distance.

It just isn't degrading by the same factor as the inverse square.

Whoa, there, you can treat it as something coming from a distance that projects back to where it would be a point (you can figure this out from the coherence length and wavelenth of the beam), and then it obeys inverse-square just fine.

You just have to get the right point to treat as the source.

 

[jj]

Sure, no argument there. I was considering an idealized beam that didn't experience any spreading or scattering.

An idealized beam requires infinite energy per photon. This creates a number of interesting questions, eh?

 

[Andonyx]

Whoa, there, you can treat it as something coming from a distance that projects back to where it would be a point (you can figure this out from the coherence length and wavelenth of the beam), and then it obeys inverse-square just fine.

You just have to get the right point to treat as the source.

Is that point within say the silvered ruby slug?

I'm thinking of a classic ruby laser.

I need some further explanation to understand this.

And I would like to see some math on this because...well, I've been laboring under a different impression.

 

[Andonyx]

That and I have multiple sources that suggest you may be mistaken...

http://www.madsci.org/posts/archives/nov2000/973183458.Ph.r.html

The light in a laser beam does NOT obey the inverse-square law. The inverse-square law applies to energy that is emitted equally in all directions, while the laser light is directed.

http://www.unc.edu/~mrobin/notes/inverse.htm

This principle doesn't hold for fixtures like fresnel spotlights, flashlights, laser beams or car headlights. These are all focused fixtures - the drop off is much less noticeable. This feature is known as the columnation of the light source (how much the light is like a column). The best columnated source is a laser beam, which maintains its intensity over great distances.

Look I'm just saying of you're talking about the photons in the silvered ruby slug, or the emission of raditation...well, it isn't really a laser yet.

We both just aregued that the inverse square law is a function of something that spreads equally in all directions, Lasers simply dont' as a result of their coherent wavelengths.

I'm sorry jj I'm fairly certain the inverse square law does not apply here.

I remember learning this way back in Freshman year when we studied McCandless lighting theory which inolved the difference between focused lenses like fresnels, and flood lights like parcans.

 

[jj]

Is that point within say the silvered ruby slug?

I'm thinking of a classic ruby laser.

I need some further explanation to understand this.

And I would like to see some math on this because...well, I've been laboring under a different impression.

No, the virtual origin is usually well behind the laser.

 

[jj]

I'm sorry jj I'm fairly certain the inverse square law does not apply here.

It absolutely does, it's just that you have to figure out the right point of origin, which is NOT the laser, but some point way behind it. With a good, well-collimated, long-coherence-length laser, it can be WAY behind it.

You do note that the beam diffuses at some angle, yes? Small, but some angle.

Project the beam BACK from the source by that angle until the beam shrinks to a point, and you have your virtual origin.

THEN the inverse-square law works. Of course, it only works for 'x' in front of the laser, so you don't start at x=0 at the laser, it can be x=many miles at the point where the light exits the laser.

If there was a way to do drawings, it would be easier to see, perhaps. Just think of the laser beam (with no diffusion, atmospherics, etc, just free-space propagation) as diverging at a small but constant angle... So it gets slowly wider as it goes away form the laser.

So, when you go TOWARD the laser, and past it beyond the source, you can imagine a "virtual" beam that's gettin gsmaller and smaller, until it goes to a point. That is the virtual origin from where the inverse-square-law works.

And that becomes evident if you just figure out the area of the laser beam, too.

 

[jj]

I remember learning this way back in Freshman year when we studied McCandless lighting theory which inolved the difference between focused lenses like fresnels, and flood lights like parcans.

And same thing for lights that are virtually very far away. That's what spots, some kinds of focused instruments, etc, do.

And make sure you don't close the barn door too far


The virtual source is, of course, way behind the instrument...

 

[Walter Wayne]

Now I am going way back but ..., isn't the decay of a laser beam also have an additional spreading effect. I recall from my fourier optics course that a laser beam will slowly spread to a wider angle, even through free space. So in addition to inverse square from a virtual source, you have an additional effect since due to diffraction* the beam spreads of its own accord.

*oops, originally I said refrection which was in error

Walt


Edited to add: getting out old text book, maybe I'll remember more later.