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The inverse square law

Iamme

Philosopher
I
Joined
Aug 5, 2003
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6,215
For all you math and physics buffs.

The very first time I learned of just one application of this law, I thought to myself that this practically proved the existance of God. To have such a formulation work out such that...well, the inverse square. It's of such exacting order, if you know what I mean. Very strange.

Your search engine will provide you with several interesting sites regarding this law, if you ask "inverse square law". But I will give you one site here:

hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html - 7k - Cached - More pages from this site
 
Hardly.

There have been plenty of people who have declared that god exists on mathematical coincidences alone, see Sagan's Broca's Brain for a very good example (Norman Bloom).

http://www.solarviews.com/eng/edu/invsquar.htm

Is an excellent explaination of the math behind the law.

It had to drop off at some rate, and this one certainly makes the most sense. The fact that it neatl fits into our number system is a result of the fact that we have a neat and efficient way to express exponents.
 
Iamme said:
The very first time I learned of just one application of this law, I thought to myself that this practically proved the existance of God.
Click to expand...
And what do you think now?

I guess it would be something along the lines of.....

"Well now, God explains the Inverse Square Law, now what explains God?"

After which you probably realised that all you had done was to give your mystery a name and that really nothing of value had been obtained.

Am I close?

BillyJoe
 
Iamme said:
For all you math and physics buffs.

The very first time I learned of just one application of this law, I thought to myself that this practically proved the existance of God. To have such a formulation work out such that...well, the inverse square. It's of such exacting order, if you know what I mean. Very strange.
Click to expand...
Not intricate at all, far from being sooooo impressive that only god(s) could explain why it is the way it is...

Dont be impressed the mathematics, it just describes (and predicts) natural occurences in the universe.

You wont prove the existence of god(s) with the inverse-square law...
 
You always hear that the laws of physics or the laws of mathematics govern the universe. I like to think it's the other way around. The universe governs the laws, wouldn't you say? Or am I just splitting hairs? :D In the end, they are just models of what is happening.
 
Man there's some cool " magic numbers" that will give you a mind cramp. The existances of such quantities give rise to the " it MUST be by design" senerio. Bottom line ? This stuff is cool ...Pi, e, perfect squares 3,4,5, primes, theres a suitcase full and in our effort to ascribe order to the universe we find them tickleing our imagination..ask a Math guy they have DEEP stories to tell.
 
Yeah, science describes and predicts but it doesn't explain.
I thought this was Iamme's point.

Why does the force of gravity between two objects change in proportion to the inverse square of the distance between them?
How can you even explain an "action at a distance" force such as Gravity.

For Iamme, in the first instance, this proved the existence of God.
I am waiting to hear if he still thinks that

(But I guess he's off for the weekend with his girlfriend :) after which he will likely burn in hell for eternity :( )

BillyJoe
 
I guess learning physics and making predictions about nature can give one a sense of power. Maybe some feel that there is a divine plan when they see nature quantified. I don't think about god much these days. I suppose I was 'burned' out after years of church and sunday school. I tend to leave god out of the equations. That's just me though.

As for action at a distance, I believe Newton was bothered by that concept. He didn't try to explain it. Einstein, when he generalized Relativity, did away with the force of gravity by using curved space-time. There is no 'action at a distance'. General Relativity is a more accurate model but it is still a model. It predicts the precession of mercury's perihelion more accurately than Newton's laws could and a host of other effects that were unknown in Newton's day. General Relativity takes into account the energy of gravity itself which adds to the overall curvature. This is why newton's law could not predict mercury's precession accurately. Of course, Newton's laws are still good as far as they go. They took us to the moon and physicist still use classical mechanics everyday. But I digress.

Of course, that leaves the questions: Why does mass/energy curve space-time? Why does curved space-time accelerate matter? Why can space-time be curved in the first place?

I'm not sure were god fits into all this if there is a god. I personally believe that man created god in his own image. I suppose we had to in order to relate to god.
 
BillyJoe said:
Yeah, science describes and predicts but it doesn't explain.
I thought this was Iamme's point.
Click to expand...
No, science doesnt explain the inverse-square law, it takes a chart to do that.

(Image "borrowed" then manipulated an image from here, I added my own commentary to the image)
 
Yahweh,

The chart is a model of what empirically has been shown to be the case. It is not an explanation.

Why doesn't gravitional force decrease in proportion to line (d) or volume (d<sup>3</sup>) rather than area (d<sup>2</sup>). Why does it decrease rather than remain constant with distance?

BillyJoe.
 
Yes, given that surface area is a square function, the inverse square law is no surprise (and crops up all in more places other than gravity). And if the inverse square law for gravity was of course shown to be an approximation by Einstein.

Walt
 
Jimmy,

I can't fault your physics.
Yes, Einstein is a closer approximation than Newton but not yet close enough because, as we know, it fails at the quantum level.
And, yes, the questions keep coming.....

Originally posted by jimmy
Why does mass/energy curve space-time? Why does curved space-time accelerate matter? Why can space-time be curved in the first place?
Click to expand...

As you say, it's all models of reality with no reason why.
And, yeah, God doesn't help.

Billy.
 
BillyJoe said:
Yahweh,

The chart is a model of what empirically has been shown to be the case. It is not an explanation.

Why doesn't gravitional force decrease in proportion to line (d) or volume (d<sup>3</sup>) rather than area (d<sup>2</sup>). Why does it decrease rather than remain constant with distance?

BillyJoe.
Click to expand...
Lets see if I can remember how to do this.

Suppose that we have a source which radiates power uniformly. If the power front moves at a constant rate, that power will be destributed uniformly over the surface of a sphere. Thus the energy density at a given distance is Power/4*pi*R<sup>2</sup> (assuming no power lost travelling out to that distance). Then look at the relation between energy and force. They are proportional.

As an analogy think of dropping a stone in a pond. A circular ripple goes out from the impact point. The energy of that wave is distributed over the circumfrance of that circle. Extend it to three dimension and you get the same thing.

I don't know if I explained it well, it's the best I can do at this time of night.

Walt
 
Iamme said:
For all you math and physics buffs.

The very first time I learned of just one application of this law, I thought to myself that this practically proved the existance of God. To have such a formulation work out such that...well, the inverse square. It's of such exacting order, if you know what I mean. Very strange.

Your search engine will provide you with several interesting sites regarding this law, if you ask "inverse square law". But I will give you one site here:

hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html - 7k - Cached - More pages from this site
Click to expand...

What's so surprising? If you take something and spread it out on a surface, you get inverse-square law.

Nothing more, nothing less. Not very surprising. Certainly not proof of anything but simple understanding!
 
Walt,

But why doesn't gravity act directly along a line joining the two objects rather than disperse through a surface?
Or why doesn't it disperse throughout the volume of the sphere rather than just through its surface?

If other possible universes, isn't it possible for gravity to be in proportion to d or d<sup>3</sup>?

If so, we still merely have a model of reality and the chart is a visual illustration of this model to help give us a feel for the empirically derived fact that gravity decreases in proportion to the distance (in Newton's framework).

We still have no explanation.

BillyJoe.
 
The inverse square law is just a close approximation. If you consider general relativity, then I suppose the answer is related to the local geometry and your velocity in space-time. If curved space-time is going to affect your motion (ie. acceleration), then you must have a motion to begin with. Does that make sense? Let me put it this way: In order for curved space-time to have an affect on something, that something must be moving through it in the first place. If gravity is a universal constant, does this mean that speed of matter in space-time is constant? Ah crap! I'm completely off topic now and possibly knocking on the gates of crankdom... Oh well, sorry.
 
Here's an interesting link I ran across:

Inverse Square Law

I'm not sure I agree with everything that is mentioned, however.

In a sense the inverse square law is the observational data that proves (1) our space is limited to three spacial dimensions, (2) space is not curved, the universe is flat, and (3) Euclidean geometry is sufficient.

An inverse square law is the natural law only in a space of three dimensions. The dimensionality of the law is always one less than the dimensionality of the space; inverse square in three dimensions, inverse cube in a space of four dimensions, and so on. The inverse square law is a by-product of the fact that the Universe has three spatial dimensions. William Paley saw this as an example of God's choice in designing a Universe suitable for human life.
Click to expand...

Considering that GR works very well using four dimensions and the inverse square law is a good approximation of how gravity works, something seems flawed with this assertion. *shrug*
 
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