The inverse square law

[BillHoyt]

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.

Just google for the Apollo laser reflector experiments. They are still running them.

 

[BillHoyt]

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.

The overwhelming majority of your posts are weany, scared, lame attempts to insinuate science has got it all wrong and to try to point others to some kind of mystical interpretation of reality. Your next most frequent posts are of this wooish whine sort. Not a whine for tasting, but a whine for laying down and avoiding. And with a bouquet like an aborigine's armpit. Give your lips a rest. Your mouth'll thank you.

Would you prefer me to simply list all your past handles? Would you prefer to be called T'ai Chi / Whodini / Sherlock Holmes? I think Tr'olldini is both succinct and accurate.

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. ...
wah wah wah wah wah wah wah

Let's get back to your "substance," eh?

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.

If you understood area, you would understand that there is nothing circular about it. If you understood area. If you understood inverse square, you would understand that it derives from the underlying definitions, and that deriving from underlying definitions is not the same as tautological.

"You are a nitwit" derives from two things. First, observation of your posts at JREF. Second, the syntax of the English language. Third, the definitions of "you", "are", "a" and "nitwit." That is not circular. "You are a nitwit because you are a nitwit," on the other hand, is circular.

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.

You continue to evince a puerile understanding of mathematics, statistics and science. If you stopped whining long enough and started readig for understanding here, the world might open for you. If not, expect more challenges to your inane questions and comments.

 

[CurtC]

Walter Wayne wrote:
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.

There are not two effects - they are one and the same. The diffraction causes the laser beam to spread out over long distances, and this spreading obeys the inverse square law. If you shine a laser dot on the Moon, the dot will no longer be a skinny 1/4" beam - it will have spread out considerably. If you go twice as far as the Moon, it will have spread to a diameter twice as wide, or four times the area, with the same amount of laser power, so the intensity at any point there is 1/4 what it was on the Moon's surface.

 

[Iconoclast]

If you took a finite quantity of Jello-brand Jello gelatin snacks and tried to make a hollow sphere out of it, then tried to stretch that sphere evenly to twice its original radius, the gelatin comprising the sphere would then be 1/4 the thickness of its original size.

I haven't bothered to do the math, and I'm sure this'll come back to haunt me, but surely your jello analogy works with a disc and not a sphere.

No

Hmmm, you say I'm wrong, so that probably means I'm not. Lets look a little deeper.

Well, no. It's a sphere, that's kind of how you get to the inverse square law. We're talking about three dimensions, not two.

3 dimensions, thanks for the tip.

What I did state wrongly was that it's thickness would be 1/4 which is misleading.

Well, that was everything you stated. That the shell thickness would now be 1/4 of it's original value is not misleading, it's simply wrong.

If you have a shell of mean radius R and thickness D, it would have a volume of V. If you then double the radius and kept the thickness constant the resulting shell volume would be 2V, which implies that if the Volume is required to stay constant the thickness of the shell must halve.

Which is to say, the volume of a shell varies linearly with radius, which is nothing like your original statement. I was merely pointing out that if you changed you model to a disk, say a pita bread -- that bread that looks like somebody's ironed it -- then the thickness of the disk would be 1/4 of it's original value if you doubled the radius of the disk and kept the volume of it constant.

 

[CurtC]

Here's another practical application: the radar range equation. A radar pulse goes from the source antenna, reducing in intensity by the inverse square law, until it hits its target and bounces back. At this point, the target is acting as its own point source and has to go back an equal distance to the antenna to receive it. Since these effects get multplied together, the power of the reflected signal that the radar station receives is inversely proportional to the distance to the fourth power. A target twice as far away presents only 1/16 the signal on the receive side.

 

[CurtC]

Iconoclast wrote:
Hmmm, you say I'm wrong, so that probably means I'm not. Lets look a little deeper...

That the shell thickness would now be 1/4 of it's original value is not misleading, it's simply wrong.

If you have a shell of mean radius R and thickness D, it would have a volume of V. If you then double the radius and kept the thickness constant the resulting shell volume would be 2V...

If you're going to be insulting, it helps if you're technically correct, but your analysis is wrong. A spherical shell of radius R and thickness D - what's its volume? It would be the surface area times the thickness. The surface area is 4 * pi * R^2, so the volume would be (4piDR^2). Now double the radius. The new volume is (4piD(2R)^2), or (16piDR^2). Notice that the volume has increased by a factor of four, not simply doubled. The Jello would be 1/4 the thickness.

 

[Iconoclast]

If you're going to be insulting, it helps if you're technically correct, but your analysis is wrong. A spherical shell of radius R and thickness D - what's its volume? It would be the surface area times the thickness. The surface area is 4 * pi * R^2, so the volume would be (4piDR^2). Now double the radius. The new volume is (4piD(2R)^2), or (16piDR^2). Notice that the volume has increased by a factor of four, not simply doubled. The Jello would be 1/4 the thickness.

Fair Dinkum! How could I balls that up so badly? And I was being a smarta** to boot. Sincere apologies Curt and Andonyx. I think I'll go self flagellate for a while then have a lie down. dickhead wanker jerkoff smartass tosser a'hole bleh...

 

[BillHoyt]

Tr'olldini,

You out there? Can you read? Can you count?

 

[Vorticity]

The inverse square law applies to light, sound, and ANYTHING that travels outward equally in all directions.

I was flipping through this thread, and saw this comment. For light and sound (and gravity) it's true, but it's NOT true for anything that travels outward equally in all directions.

Take, for example, the strong nuclear force. It is isotropic (i.e. it "travels outward equally in all directions"), but it's potential falls off roughly like:

V(r) ~ (1/r)Exp(-m r)

(it's much easier to think of these things in terms of the potential rather than the force) This does NOT generate an inverse square law.

At any rate, it can be shown via elementary quantum field theory that for any force that is mediated by a massless particle (photon, graviton, etc) whose associated field has the requisite symmetries, the potential will always fall off like

V(r) ~ +- 1/r

which generates the force

F(r) ~ -+1/r^2

So, inverse square is NOT purely descriptive. It can be derived from a few basic assumptions.

 

[Andonyx]

I was flipping through this thread, and saw this comment. For light and sound (and gravity) it's true, but it's NOT true for anything that travels outward equally in all directions.

Take, for example, the strong nuclear force. It is isotropic (i.e. it "travels outward equally in all directions"), but it's potential falls off roughly like:

V(r) ~ (1/r)Exp(-m r)

Okay when you get into particle physics or anything that doesn't operate plainly in the Newtonian realm, you can count me right out of it.

I apologize for not making that clear earlier, or If I confused anyone with bad generalizations.

But thank you for the new info.

 

[CFLarsen]

90 posts and not a peep from Steve Grenard about the Inverse Square Law.

I suspect he is learning something....

 

[T'ai Chi]

Tr'olldini,

There is the character assination by making fun of names again... that only seems to apply to some people some of the time..

I guess that means you have some issue, not me.

You out there?

Uh, yeah.

Can you read?

Uh, yeah.

Can you count?

Uh yeah. Your questions are much easier than Claus'.

You going somewhere with this, or somewhere further away from talking about the inverse square law?

 

[BillHoyt]

Uh yeah. Your questions are much easier than Claus'.

Only when you ignore them, Tr'olldini

 

[T'ai Chi]

The overwhelming majority of your posts are weany, scared, lame attempts to insinuate science has got it all wrong and to try to point others to some kind of mystical interpretation of reality.

Whatever. I don't think science has it all wrong, sorry you misunderstood. I think some of its more dogmatic followers have their beliefs about science very wrong.

And with a bouquet like an aborigine's armpit. Give your lips a rest. Your mouth'll thank you.

Good use of imagery, but you flunk on content.

Would you prefer me to simply list all your past handles? Would you prefer to be called T'ai Chi / Whodini / Sherlock Holmes? I think Tr'olldini is both succinct and accurate.

Uh huh. You don't think that is just an excuse so you can get away with character assasination by making fun of a nickname?

I can list multiple handles of many users here that they have used here and elsewhere based on knowledge from conversations around here. Do you have a point?

If you understood area, you would understand that there is nothing circular about it. If you understood area. If you understood inverse square, you would understand that it derives from the underlying definitions, and that deriving from underlying definitions is not the same as tautological.

The "underlying definitions" that you are talking about comes down to saying 'area is measured in units squared, the inverse law depends on area, therefore the inverse law is the inverse squared law'. Again, no kidding, but I'm interested in why the universe has it so we are measuring area in units squared to begin with. If you don't know or believe no one can know, feel free to say that.

Unless, of course, you can explain how your "underlying definitions" are different from tautologies.

"You are a nitwit" derives from two things. First, observation of your posts at JREF. Second, the syntax of the English language. Third, the definitions of "you", "are", "a" and "nitwit." That is not circular. "You are a nitwit because you are a nitwit," on the other hand, is circular.

I'm not too impressed by bullies or self-appointed policemen. The fact that they dream themself to be scary is the only scary part.

You continue to evince a puerile understanding of mathematics, statistics and science.

Interesting belief, when you've evaded all of the statistics questions I asked you. Why is that? Feel free to ignore that again Bill. We know you probably will.

(from a while back)

I suggest we stick to the topics, follow Randi's guidance and improve the signal-to-noise ratio.

Perhaps you should follow your own advice, and get back to talking about the inverse squared law?

 

[T'ai Chi]

Only when you ignore them, Tr'olldini

Sorry sir, I don't respond to bully tactics. It simply won't ever work on me.

 

[BillHoyt]

The "underlying definitions" that you are talking about comes down to saying 'area is measured in units squared, the inverse law depends on area, therefore the inverse law is the inverse squared law'. Again, no kidding, but I'm interested in why the universe has it so we are measuring area in units squared to begin with. If you don't know or believe no one can know, feel free to say that.

Unless, of course, you can explain how your "underlying definitions" are different from tautologies.

Tr'oll, this has been done repeatedly here for you. You just don't get it. Right now, you are arguing at the level of the cretinists who claim that natural selection is a tautology. It isn't This isn't. The magic that is there is in the equations and the physics. The magic you seek is in your head.

[/b]I'm not too impressed by bullies or self-appointed policemen. The fact that they dream themself to be scary is the only scary part.[/b]

Really? Then why do you feel compelled to hide behind short, cryptic remarks? Why do find yourself unable to defend against the inevitable challenges when you do give voice to your woo claims?

Perhaps you should follow your own advice, and get back to talking about the inverse squared law?

Only three pages and you've already lost sense of the thread? The thread was not opened as a simple discussion of the law, but as a discussion of the law as proof of god. I have been trying to challenge your claims that the scientific explanations are "just-so" stories. You, of course, have been trying to duck the challenge.

 

[T'ai Chi]

Tr'oll, this has been done repeatedly here for you. You just don't get it. Right now, you are arguing at the level of the cretinists who claim that natural selection is a tautology. It isn't This isn't. The magic that is there is in the equations and the physics. The magic you seek is in your head.

Sorry, you failed to answer the question. In Larsen List style, will you either answer, or state that you refuse to answer:

1. How are your "underlying definitions" different from tautologies?

You, of course, have been trying to duck the challenge.

That is funny coming from someone who refused to answer, even ignored, ALL of my statistics questions, then claim I got my responses off the Internet after I answered all of his correctly.

*shrug* Whatever.

 

[BillHoyt]

Sorry, you failed to answer the question. In Larsen List style, will you either answer, or state that you refuse to answer:

1. How are your "underlying definitions" different from tautologies?
[/B]

You need to look up the definition of "tautology," tr'olldini. I already answered the question. Yahweh already answered the question.

 

[T'ai Chi]

You need to look up the definition of "tautology," tr'olldini. I already answered the question. Yahweh already answered the question.

We'll chalk that up as a "refuse to answer" response.

 

[jj]

We'll chalk that up as a "refuse to answer" response.

I'll open my discourse with you with a simple question:

Why did you start your participation here with a chip on your shoulder and a handfull of inexplicable conclusions that you won't explain. What was your point about the spring? It's wrong, but I have no idea why you concluded it, and you ignored my request for discourse by engaging in ad-homs against someone else.

Are you truly here to learn or are you just here to disrupt?