GENIUS FORUMS

G-forum crew, I need your help. I thought about it long enough and I just can't wrap my head around Newton's inverse-square law theory.

The following is from how stuff works:

Newton was the first person to study Gravity seriously, and he came up with the law of universal gravitation:

Each particle of matter attracts every other particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The standard formula for gravity is:

Gravitational force = (G * m1 * m2) / (d2)

Ok, the presentation of the logic so far is clear enough. (although the part that confuses me is the inversely proportional to the square of the distance between them , part)

Where G is the gravitational constant, m1 and m2 are the masses of the two objects for which you are calculating the force, and d is the distance between the centers of gravity of the two masses.

and this is straight foward as well. Seems simple enough.

But then....

G has the value of 6.67 x 10E-8 dyne * cm2/gm2.

huh? Ok, I can accept that gravity is 6.67 without really having an explanation as to why........but what is this 10E-8 dyne * cm2/gm2? (I know what a dyne is)

--------------------------------------------------

This: (G * m1 * m2) / (d2)

does not seem to correspond to

this: 6.67 x 10E-8 dyne * cm2/gm2.

especially this part:

10E-8 dyne * cm2/gm2.


The rest of the article makes sense, superifically though, because I don't understand the main point.....

That means that if you put two 1-gram objects 1 centimeter apart from one another, they will attract each other with the force of 6.67 x 10E-8 dyne. A dyne is equal to about 0.001 gram weight, meaning that if you have a dyne of force available, it can lift 0.001 grams in Earth's gravitational field. So 6.67 x 10E-8 dyne is a miniscule force.

It's the 10E-8 that confuses me.

The formula (G * m1 * m2) / (d2) looks simple.

But when they plug the figures into the formula, where is m1 x m2?

Maybe this is just really obvious to most people, and perhaps I'm metaphorically color blind or tone deaf in regards to this sort of thing. (yes, thats right, a polite way of calling myself stupid)

Some help would be appreciated.

"E-8" is just another way of writing 10 ^ -8, which is another way of writing 1 / (10 ^ 8).

(although the part that confuses me is the inversely proportional to the square of the distance between them , part)

If Y is "inversely proportional" to X, that means that as X (distance [squared]) gets larger, Y (force of attraction) gets smaller, and as X gets smaller, Y gets larger.

ah-ha! you explained it very well, as I see it now. Thanks Philo.

I have the maths ability of about a 12 year old. I didn't do years 11 and 12 and have never used the maths I learnt in high school, so have forgotten same.

I never understand why there is a requirement for the distance to be squared. The same goes for E=MC2.

Gravitational force = (G * m1 * m2) / (d2)

I would have to say this is a formula not for gravitation, but for gravitational relativity.

I actually read E=Mc2 as something along the lines of -

The total potential sum of causal force contained within an object is equal to that objects gravitational force (the degree of contracting force in a spatial area) times?? the spatial area that would be taken up by the expansionary force if the gravitational force of the mass was removed.

Jamesh wrote:I never understand why there is a requirement for the distance to be squared. The same goes for E=MC2.

Because those are the formulas that actually model the behavior of objects observed.

Because those are the formulas that actually model the behavior of objects observed.

Sure, but there must be a very, very imple logical reason as to why the E=Mc2 formula will only work if the speed of light is squared. What part of nature does squaring the speed of light identify?

It might be easier to think of energy being from one universe and matter being from another universe, and we happen to live where various universes, such as the matter universe and the energy universe, intersect.

The using the speed of light as the constant in the formula causes the results to be actually slightly off, but it is such a minute difference that it does not matter for any practical purpose we have for it today - but it is important for the level of understanding that you are asking for to realize that the formula is lightly off.

In order to make a material measurement, we need something of the physical (matter) world to measure. Photons are so small that it's almost like they are not there, only observable when they are caught by energy, and so close to uniform in size, that they can manifest the properties of energy better than other matter, but this difference - the very existence of a photon which is what makes it possible for us to make a measurement - is enough to weigh down the energy.

Speed is a manifestation of energy, so in order to understand what energy is, we need energy as a unit on both sides of the equation
(A=A).
Since speed is only a manifestation of energy, we need something else on that side of the equation to cancel out everything that is not energy
(A=A + B - B)
The photon itself. despite being so small, weighs down the energy a lot - to the point that even though it is that small, the energy itself could go a squared amount faster if it were not weighed down by the photon.

This probably looks backwards to you at this point (it should, anyway) because the math is contrary to "common sense" (fortunatly Einstein didn't have any of that, so he wasn't weighed down with that barrier when he figured out E=mc^2). To understand it, please set aside everything i just said to see the next concept separately.

Matter is condsolidated energy. the gas in your car makes the car go, and after your car goes, the gas it used is gone (I'm oversimplifying for the sake of conveying the basic concept). Abstractly, the gas is the "going" of the car.

Now put the two concepts together and you should see how that relates to a quantity of mass being related to energy as a unit.

The conceptual flaw that is necessarily introduced to quantify it includes direction (which is a function of the physical universe) and time, which is not a function of the physical universe either, although its effects are observable in the physical universe where we are, as its universe and the physical univers intersect here. In order to use the physical universe to access the power of the energy universe we have to impose the laws that the physical universe must obey - laws that disguise the true nature of the energy universe. If we understand that the laws only apply to the physical universe, we can deduce the properties of energy itself.

If you look at the effects of the atomic bomb, you will see the squaring properties most easily.

Jamesh wrote:Sure, but there must be a very, very imple logical reason as to why the E=Mc2 formula will only work if the speed of light is squared. What part of nature does squaring the speed of light identify?

I'm not sure what you mean by this. Acceleration is specified in meters per second squared, but it does not make sense to ask, "What part of nature does squaring the seconds identify?" In both cases, the exponent is an artifact of the mathematical operations used to derive the formula / unit.

Yes thanks Elizabeth, I guess the problem arises because I tend to think of the E as a thing with properties, not a measurement of the causal power of an undescribed thing.

Comments one reads like "Dark energy is believed to make up 70% of the universe" lead one astray. They are all these different forms for energy, you know Gravitational, Electric, Magnetic, Thermal, Chemical, Elastic, Nuclear, all of which are attached to specific forms as if there was something fundamentally different with each, and it becomes natural to associate thingness with this type of energy, as if it were a wave of thingness converted from the destruction of mass, the electromagnetic spectrum, rather than limiting it to just the measurement factor.

The E in the equation relates to a Cause, not an effect, whereas the Mc2 is the various properties that make up the overall Effect that is physicalness - mass and spatial area and movement. The speed of light represents movement and squaring it represents movement within a flat spatial area.

"According to Einstein's theory of special relativity, mass and energy are equivalent."

Yes, if energy is merely a measurement not a thing, then he is saying that E=Mc2 is the definition of thingness, and that the essential or inherent nature of all things is not thingness but energy. It is an "A = the properties of A" statement. Energy is just causal power. It is an equalised equation, and it represents an equalisation of the contracting and expansionary forces. It is actually representing where there is no external causal power, it is representing the causal power contained in a balanced unit of existence. If the formula is out then it is out because only space itself is perfectly balanced, and the rest is not.

It seems that it is the squaring in this formula that creates the level of energy applicable to the level of the universe in which maths operates in, a two dimensional one, a flat spatial area. What I refer to as the expansionary force, can be imaged as just energy-as-a-thing in a three dimensional spatial area. The contracting force is energy as gravity.

Perhaps even our brain operates in a two dimensional manner. What I mean here is that even though we see three dimensionally, all the calculations at the bottom are all binary calculations. Information or data is essentially "strings of spatial units of logic" A unit of logic is a dualistic occurrence within a set spatial area, that is either on or off, full or empty, positive or negative, or anything else with A or Not-A dualistic qualities.

The artificial three dimensionality we create, is all based on single streams from different angles all coming together to form a three dimensional image. Three dimensionality is actually an effect. It is not the most basic nature of the universe, mere duality is, but it causes the 3 dimensional form of the universe because of the coming together from all angles, in the same way that two infinities have to be related, holistically. They don't have parts, so there can be no division, no dimensioning. They cause space, so they exist prior to the effect called space, they exist in a non-spatial state, and therefore no concept of distance and time could be applied.

Jamesh wrote:if energy is merely a measurement not a thing,

I'm not saying that energy is either a measurement or a thing. A measurement is a thing.

Jamesh wrote:Energy is just causal power.

That's exactly what I meant.

Jamesh wrote:It seems that it is the squaring in this formula that creates the level of energy applicable to the level of the universe in which maths operates in, a two dimensional one, a flat spatial area.

The way I'm thinking of it, yes and no. Math, like energy, is not of the physical universe. We can "do math" in the physical universe, and see causality most clearly with math as long as we enter everything into the equation that is supposed to go there (meaning, do the math correctly).

If we think of the physical universe as a toy with "some assembly required" we could think of math as accurate assembly instructions.

Jamesh wrote:Perhaps even our brain operates in a two dimensional manner. What I mean here is that even though we see three dimensionally, all the calculations at the bottom are all binary calculations. Information or data is essentially "strings of spatial units of logic" A unit of logic is a dualistic occurrence within a set spatial area, that is either on or off, full or empty, positive or negative, or anything else with A or Not-A dualistic qualities.

The artificial three dimensionality we create, is all based on single streams from different angles all coming together to form a three dimensional image. Three dimensionality is actually an effect. It is not the most basic nature of the universe, mere duality is, but it causes the 3 dimensional form of the universe because of the coming together from all angles, in the same way that two infinities have to be related, holistically. They don't have parts, so there can be no division, no dimensioning. They cause space, so they exist prior to the effect called space, they exist in a non-spatial state, and therefore no concept of distance and time could be applied.

I agree with all of that except the two-dimensional part (I consider math non-dimensional, but I am flexible in that consideration as math can be boiled down to a binary base. It is just easier for me to conceptualize it more completely as math being in, but not of, this universe). I do believe that even our brains - everything in fact - operate through a mathematecal function. We just don't yet have all of the variables to plug into the formulas, and in many cases have not yet discovered the formulas either.

I think we're essentially on the same page. Our difference of conceptualization of if math is 2 dimensional or non-dimensional is probably not a significant point.

Jamesh wrote:I never understand why there is a requirement for the distance to be squared. The same goes for E=MC2.

Gravitational force = (G * m1 * m2) / (d2)

I've been wondering the same thing, and I think I just figured it out. It's because gravity acts like acceleration, which changes speed in a parabolic curve.

E=mc^2 is the same in that the energy required to increase the speed of a mass increases as its speed increases in a parabolic curve, although it's weird that it's only the constant that's squared, because a squared constant is still only a constant. I would think that m should be squared.

On an unrelated tangent:

What's weird about the theory of relativity is that what is the speed increase supposed to be relative to? When they say a piece of matter can't reach the speed of light, what is this speed measured against? They seem to be talking in absolute speeds even though they say motion is relative.

Actually, the "tangent" is related.

Matt Gregory wrote:what is the speed increase supposed to be relative to?

It is relative to our reality. The constant (which is actually a tiny bit faster than the speed of light because the weight of the photon itself slows down the speed) is the measure of our baseline reality (the physical universe).

Matt Gregory wrote:it's weird that it's only the constant that's squared, because a squared constant is still only a constant.

The square of the constant of the physical universe is still just a constant, but it is the constant of the energy universe rather than the constant of the physical universe.
.

Matt Gregory wrote:When they say a piece of matter can't reach the speed of light, what is this speed measured against?

It is relative to any giveninertial frame of reference.

They seem to be talking in absolute speeds even though they say motion is relative.

No, the speed of something must always be measured relative to something else.

(fixed link)

If the mass of an object increases as its speed increases, then there must be a speed and direction of motion (assuming it's in motion relative to us on Earth) at which its mass is at a minimum, right? Couldn't they discover an absolute inertial frame of reference that way?

But I guess mass is relative, too, isn't it? Two objects sitting next to each other have no mass in relation to each other, but if you threw one at the other, they would exert a force on each other, which would be directly proportional to their masses, which could be calculated by determining how much force there was in the impact?

D- would you fix your link please?

Matt Gregory wrote:If the mass of an object increases as its speed increases

That's backwards, the mass decreases as its speed increases.
.

That would be Em=c^2.

I was thinking of this: length contraction

but length is different from mass. I'll have to get back to this at a later time when I can just concentrate on one thing at a time.
.

Matt Gregory wrote:Two objects sitting next to each other have no mass in relation to each other,

No, two objects near each other exert a gravitational force on each other, proportional to mass.

Matt Gregory wrote:If the mass of an object increases as its speed increases,

There is the rest mass of an object, which is what you would measure if you were at rest relative to that object.

A moving object has momentum, which is a form of energy. An object moving very quickly has more mass. This effect is normally very tiny, until you get up to extremely high velocities.

then there must be a speed and direction of motion (assuming it's in motion relative to us on Earth) at which its mass is at a minimum, right?

The mass is at a minimum when it is equal to the rest mass (i.e., the object being measured is not in motion relative to the measurer).

Couldn't they discover an absolute inertial frame of reference that way?

No.

Okay. I'm still confused about an object requiring increasing amounts of energy to gain speed the faster it goes. That doesn't make sense because the object is always stationary in relation to itself, so it seems to me that the increase would have to be linear.

If a space carrier took off from Earth and gained a speed of half light speed and then another ship launched off it in the same direction and then gained a speed of half light speed relative to the carrier, the smaller ship would be traveling at light speed relative to the Earth without requiring an infinite amount of energy.

Matt Gregory wrote:If a space carrier took off from Earth and gained a speed of half light speed and then another ship launched off it in the same direction and then gained a speed of half light speed relative to the carrier, the smaller ship would be traveling at light speed relative to the Earth without requiring an infinite amount of energy.

That certainly is the intuitive way we think about velocity, and it works fine when you are talking about normal (non-relativistic) velocities. However, when you are talking about speeds that are a significant fraction of the speed of light, you must use the Lorentz transformation, and its velocity addition law, instead of the ordinary addition that works so well and intuitively at ordinary speeds.

Using the Lorentz transform required by special relativity (being careful about the signs, and setting c=1), the velocity of the smaller ship relative to the Earth is not the speed of light, but is

V = 1 / [1 - (1/2)(-1/2)/(1*1)] = 1/(1+1/4) = 1/(5/4) = 4/5

Relative to Earth, the second ship is travelling at four fifths the speed of light.

I think you're just trying to rip me off a fifth!

That's pretty weird. I'll to think about that for awhile.

Thanks for the explanations . . . been wondering about that for a long time.