g = c*s / r^2
As I've been sitting here and getting a bit hung up on the F=G(M+m)/r^2-Kepler-Centripetal-angular momentum stuff, I've decided to just get right to the meat of my theory that gravity is not an applied external force.
This is my theory (and put on your Relativity thinking caps and hold them down tightly!):
If bodies in free-fall in gravitational field are in a state of inertial rest, then gravity is not an applied external force. And, if gravity is not an external force then what the heck is it?
Electromagnetic radiation (light) that has been released as pure energy expands as a light sphere in all accessible directions. Sometimes the photon-wave is reflected, other times it's absorbed by matter and becomes a part of that matter.
Light expands at a constant speed (c) of 299,792,458 m/s in a vacuum.
When light is absorbed by matter it does not expand at c anymore. It's previous latent energy now contributes to the structure and mass of whatever particle absorbed it; it becomes matter.
Electromagnet energy and matter have already been theoretically united as matter-energy by E=mc^2 (much as space and time have been united as space-time).
But unifying gravity with the other elements and forces of physics has been a tough go. But, I have an idea.
If motion is relative, then the speed of light is, too. Now, I hear you say "c is a constant." Yes, in any frame of reference, c is a constant. And so is mass, time, and all of the fundamental principles of classical mechanics.
But light (energy) that has been absorbed and is now a part of a particle (matter), has entered a very different frame of reference for itself. It now has mass, it's staying reasonably still...it can be pushed around.
So, what happened to it's unstoppable urge to expand at the speed of light?
My answer: It never lost it.
Just as a photon-wave can't do anything but expand at c, so can't a particle of matter. The difference is the frame of reference. Rather than the energy expanding through space at c, the particle is *ahem* expanding through space at c.
Gravity obeys an inverse-square law. If one planet is twice as far away from the sun as another, then the gravitational effect of the sun on that planet is 1/4 of that planet that's twice as close. If it's 3 times further away then the effect is 1/9. 4 times? 1/16, etc.
This is due to the simple Euclidian law of geometry; that the surface of a sphere grows as the square of the radius.
Let's assume a standard sphere where we call the radius 1 and the surface area 1. If the radius of another sphere is 2, then the surface area of that sphere is 4. If the radius = 3, then surface area = 9, etc.
If the force g = 1 at a radius r = 1, then the same progression applies.
Imagine a sphere at any given radius from a mass (body) as a shell.
The force of gravity at any given spherical shell at a given radius from the center of the source mass is the same as it is at any other shell at any given radius from that body,.but it's effect is dispersed -- by an inverse square law -- as the shells become larger at greater distances.
(Expanding light spheres do the same thing. Let's say there are two stars of equal mass and brightness, but one is twice as far away as the other. The star that is twice as far away is four times as dim as the one that is twice as close.)
That matter is "expanding through space at c" -- causing the effect we call gravity -- is perfectly sensical if we can just picture in our minds a light sphere expanding through space at c; then picture the light sphere frozen; then (since that can't happen, can it?) the relative velocity of that "frozen" sphere through space.
Or, let me try it this way: Imagine that we have a really expensive camera that can zoom back to follow the light sphere as it expands, so it's always the same size on the screen. The sphere will look to be at rest (like a particle mass), while the space around it would seem to be getting sucked in.
Here's the cool part: If we were to pan back fast enough to keep the expanding light sphere at a constant size in the center of our screen, we would have to retreat at the speed of light. This would mean that the sphere would always be frozen in time as far as we could tell. The nearest matter around it that's being "sucked in" would seem to just sit there; time has stopped. But there would be new stars buzzing by us at the speed of light, seemingly rushing at c to get to that light sphere; and it would appear to us to be progressing as some kind of crazy backward inverse law.
As you get closer to a mass it's gravity effect increases according to the inverse-square law. I decided, one day, to assume that a particle's radius was determined by (or, in proportion to) it's mass and gravity effect. I further assumed that, at it's "surface radius," it's g-force would produce an acceleration of c*s. Then I wondered; what size would a particle of 1 Earth-mass be when it's surface g was equal to c*s?
First; here are some basic facts:
c*s = 299,792,458 m/s^2
g = 9.78 m/s^2
c*s/g = 30,653,625.56
1 / (c*s/g) = 0.000000032
surface area of a sphere = 4*pi*r^2
radius of Earth = 6,378,000 meters
surface area of Earth = 511,185,500,700 meters^2
So, let's take the actual measurements for the Earth's surface:
r = 6,378,000 meters
g = 9,78 m/s^2
surface area is 511,185,500,700 meters^2
and reduced them to the point where g=c*s:
r = 1,151.976424 meters
g = c*s
surface area is 16,676,184.03 meters^2
As expected:
If you divide the surface area of the Earth by the reduced surface area you get:
30,653,625.54
Dividing the radius of the Earth by the reduced radius:
5,536.571641 (the sq.rt. of 30,653,625.54)
and dividing actual sea-level g by c*s:
0.000000032
There are several ways of playing with the numbers, but there's a kicker.
Looking through the results, here's how gravity finally gets to be in an equation with c:
r^2 = c*s / g
c*s = g*r^2
g = c*s / r^2
(c*s is how I write the speed of light as an acceleration; it means 186,000 m/s^2.)
These equations are only for supra-atomic bodies like the Earth, and G(m) for other bodies would have to be factered in to get a concrete answer; and it may not tranlate to subatomic particles. Also, relativistic time dialations might skew the effects (i.e. the reduction represents a "Black Hole").
It's a hypothesis in progress that may lead to nowhere else, but I'll crunch some numbers (for electrons and protons) and see what happens.
Daniel has a critique of the gravity posts so far here, and I responded in the comments. I want to explain more precisely what I'm trying to prove, as it might be a bit unclear so far.
I'm attempting to show that Isaac Newton's equation
F = G(Mm) / r^2
should be replaced with
a = G(M+m) / r^2.
Also, since Newton's Principle of Equivalence was first theorized only because Galileo's Law of Falling Bodies seemed irrefutable (and I refute it!), the Principle of Equivalence is unneccessary.
But let me explain exactly what I mean by a=G(M+m)/r^2.
(And I like to use visual examples rather than just deal with cold abstract point particles. I'm like that.)
Imagine that we are in a space ship that is at rest relative to a distant planet called M1. We have a very powerful spy-telescope than not only see the planet clearly, but also any incoming meteors that are only the size of bowling ball.
The planet is just sitting out there in the void of space and doesn't even seem to be moving against the background stars.
We then notice a small meteor heading straight for M1 on a collision course. We know how far away these bodies are from us, and from each other. Observing m2's motion against the background stars, we quickly calculate that the meteor is "falling" toward M1 acording to F=G(M1)/r^2.
We don't notice M1 moving at all.
We call our fellow astronaut, who's camping on M1's surface, and tell him to look up through his telescope at the incoming meteor. "Yep," he says, "Here it comes, and with the exact same rate of acceleration we expect all falling bodies to have here.
Eventually the meteor hits the planet, but misses the astronaut, and M1 seems to still be in the exact same place it was before the meteor ever showed up.
The next day we look out again from our spaceship and... holy cow, look what's coming in now! It's another planet with exactly the same mass as M1 (we're physic, too btw) heading on the same path that the meteor followed! We call this planet: M2.
Observing M2's motion against the background stars we calculate that M2 is falling with an acceleration toward M1 according to F=G(M1)/r^2, as expected.
Now we turn our telescope to M1 an notice that it's moving across the background stars, in a straight line toward M2, with an acceleration in accordance with F=G(M2)/r^2.
We call our astronaut who's camping on M1 and tell him to look up. "What the..." he says. That thing is heading toward me with an acceleration rate that's TWICE what it should be! I mean, all bodies are supposed to fall at the same rate!"
"Uh, Dave?" we say, "M1 -- where you are -- is accelerating toward M2 at the same rate that M2 is accelerating toward M1."
"But, I don't feel any differant. How can you tell me I'm accelerating?"
"Because we can see it happening!"
To Dave the Astronaut, in his frame of reference he is still where we was along along, in a state of rest; and the incoming bodies were all in a state of acceleration. He has no idea why that falling planet is coming in at twice the rate of acceleration that's twice the rate with which he's seen every other falling body fall.
The two forces at work are defined by F=G(M1)/r^2 and F=G(M2)/r^2. The total acceleration due to those "forces" involved in the M1-M2 system is a=G(M1+M2)/r^2. The accelerations due to the masses of the two components of the system are additive; and the relative acceleration of M2 toward M1 is twice the rate than that of the insignificant meteor toward M1.
Newton's F=G(Mm)/r^2 (along with the corresponding Principle of Equivalence that negates the accelerating effects resulting from the large product: F) assumes that two bodies are "action-reaction pairs," and that the force exerted on M1 by a meteor is "equal and opposite" to that exerted on the meteor by M1.
This comes from Newton's hypothesis that gravity is essentially an "action-at-a-distance" where the bodies somehow detect each other's mass, and then act accordingly.
All of this is based on the idea that gravity is an applied external force.
Einstein demonstrated via the elevator experiment that, without a frame of reference, a body falling in a gravitational field is indistiguishable from a body at rest outside of a gravitational field. Therefore; bodies fall (accelerate toward other bodies) not because they are being acted upon by an external force, but because they are at rest in a gravitational field.
Stephen Hawking, in his book A Brief History of Time, attempted to explain the Principle of Equivalence (between Gravitational and Inertial mass) with an analogy invoking the different sized engines required to move a light car versus a heavy car; that the inertia mass of the heavier car needs a stronger engine to move it.
Hawking wrote, as Newton had, that greater energy is needed to move the heavier car and thus, it followed that the greater gravitational mass of a heavier body is needed to overcome the body's greater resistance to a change in it's inertia.
Why the analogy fails -- I contend -- is that the car needs a force applied to it in order to accelerate it (F=ma), but a body in free-fall does not; it is in an inertial state of rest even as it appears to be accelerating.
As I wrote before: Even though a falling body appears to be accelerating, it is not. It is WE, standing on the ground in the gravitational field, that are undergoing an acceleration.
Just to belabor the point one more time (egad!): The presumption that gravity is an applied external force is the entire premise behind Newton's "action-reaction pairs" idea that led to F=G(Mm)/r^2 and the Principle of Equivalence.
Next post will be in a little while! Yay!
Okay, I said I was gonna put part three up tonight, but I had a long day at work and right now I just feel like kickin' back and surfin' the blogosphere which I haven't been able to do in a couple o' days.
Writing is hard when it's important (at least to the writer). So many phrases and clauses ("conjuction junction...what's your function?...") running through my head. But how to get to them, and in what order; aye, there's the rub. Building an argument for a clique of newbies and wonks is problematic. You don't want to get too bogged down in obscurity that you alienate some, but you also don't want to get so vague and general that you insult/bore/leave-unfullfilled others.
Maybe, when I write about all this physics stuff, I sometimes assume a level of familiarity on the part of the reader that isn't neccessarily there; and the thread of logic can seem presumptuous and inapproachable.
If any holes need filling just let me know.
(No, that's not a come-on!)
I'll continue tomorrow...or, at least, over the weekend.
One fine day in school my sixth grade teacher taught the class that two objects of different weights fell at exactly the same rate of acceleration. I clearly remember Mr. Weatherby standing atop his desk and simultaneously dropping a text book and a #2 pencil, and we all watched very closely to make absolutely certain that they hit the floor at the same time. I couldn't be sure that they had, although they did seem to. But, with the assurance from Mr. Weatherby, I accepted that they had.
He then explained that this enchanted reality was known as Galileo's Law of Falling Bodies. Maybe it struck me at the time that if it was good enough for Galileo then it was good enough for me.
But I've always felt a nagging uneasiness whenever I thought about it. As I grew older and more interested in the finer points of physics, my curiosity about this basic law increased.
"This can not be!" I kept muttering to myself when I was sure I was alone. "More mass means more gravity. And more gravity means more acceleration, dag nab it!"
F = G(M+m) / r^2
One mass does not unilaterally attract another, the other mass is also attracting the first, even if it's one particle at a time. (Specifically; two bodies are attracted to their common center of mass.)
The Earth attracts a 1kg body with the same gravity effect as it attracts a .25kg body. But the 1kg and .25kg bodies each attract the Earth proportional to their mass. They have different masses and must attract the Earth to different degree as surely as the Moon would attract the bodies to a differing degree.
(I keep using the word "attract". It's completely inaccurate, but it's an old habit.)
If Newton's Principle of Equivalence is correct then it's a body's resistance to the applied force of gravity that counter-balances it's gravitational attraction, and each body's mass -- no matter what it is -- counters in the same way, and so they fall at the same rate of acceleration.
Assuming that's true, I wondered, then why wouldn't g on a planet of similar size but twice the mass (we'll call it Planet X) be identical to Earth's? On Planet X, a bowling ball would fall twice as fast, right?
Let's crunch some numbers, not quite planetary-sized, but varied enough to vividly make the point.
UPDATE: Daniel has pointed out to me that the following example does not make the point I was trying to make. F2 and F3 are equal, but it's because the mass and acceleration are just reversed in the two instances. That's what I get for posting an idea that struck me as I stared at the monitor, and before I thought it through.
I'll try and come up with an appropriate example (if it's even neccessary).
In this example M1=1,000,000; m1=1; M2=2,000,000; and m2=2.
There are four combinations:
F1 = G(M1m1) / r^2......F1 = G(1,000,000) / r^2
F2 = G(M1m2) / r^2......F2 = G(2,000,000) / r^2
F3 = G(M2m1) / r^2......F3 = G(2,000,000) / r^2
F4 = G(M2m2) / r^2......F4 = G(4,000,000) / r^2
F2 and F3 resolve identically, even though the two massive bodies, M1 and M2, should give very different results for the lesser bodies, m1 and m2. Substituting Earth-mass and Planet X-mass for the M1 and M2, two rocks (one twice as heavy as the other) for m1 and m2, would give the same result: F2 = F3, even though observation tells us they don't.
But, I can hear you saying "But, Spork, the Principle of Equivalence takes care of this. It's M1 and M2's resistance to moving toward m1 and m2. The inertia is almost entirely put on the lesser masses."
Okay. Then the next question is: What evidence is there that a body in free-fall in a gravitational field is, in fact, resisting?
EINSTEIN'S PRINCIPLE OF EQUIVALENCE
Albert Einstein, while developing his own theories of gravity, had tried many ideas before focusing on Newton's old Principle of Equivalence. He did not accept, at the time, that gravity could propogate across the void of space without any real, and hopefully discoverable communication between masses.
The "action-at-distance" that Newton had resigned himself to was illogical and inadequate. He sought for years to expand Relativity into a working theory of gravity.
Then Einstein was intriqued by a newspaper item about a man who had fallen some distance and survived to tell about it. The man, describing his descent to the reporter, mentioned that while he was falling he could feel no effects of gravity. He described what it was like to be weightless.
Einstein made the connection that a free-fall in gravitational field and weightlessness are indistinguishable without a frame of reference.
That Newton's Principle of Equivalence was the way to explain the Law of Falling Bodies was accepted for hundreds of years before Einstein, but it offered no real understanding of why this was so. Using his General Theory of Relativity, Einstein tried to settle the matter.
THE ELEVATOR EXPERIMENT
The elevator experiment is the most famous of Einstein's "thought experiments" that he used to explain Relativity, as well as explore it's implications.
It's important to note that it is not merely an analogy or metaphor. It's a real working example of how the world works.
An elevator carrying a few scientists is suspended at some altitude above the Earth's surface. There are no windows.
The scientists know that they are at rest in the Earth's gravitational field. They can sense up from down, and their pencils fall to the floor when dropped.
Suddenly the cables are released and they begin a free-fall toward the ground. Now they float weightlessly. One scientist takes a pencil from his pocket-protector and releases it. It floats in mid-air; an object at rest and remaining at rest. He gives it a nudge, and it moves at a constant speed -- an object in motion and remaing in motion -- until acted upon by an external force: the wall of the elevator.
The scientists conclude that they have either a) been magically transported to a zero-gravity system, obeying all of Newton's laws of motion, or b) are about to crash.
Now imagine that they have indeed been transported, still floating around, into a vast region of empty space. Suddenly the cables begin to reel in the car at a constant rate of acceleration.
Once again their feet can plant firmly on the floor, and pencil accelerate at a constant rate when dropped.
The scientists could then conclude that they are, once again, at rest in Earth's gravitational field.
The elevator thought experiment illustrates the central premise of the General Theory of Relativity; that rest within a gravitational field in indistiguishable from a constant acceleration without a frame of reference. They are relative states of inertia. This is Einstein's Principle of Equivalence.
F = G(M+m) / r^2 RETURNS
One important element of the elevator experiment is that Einstein used it to confirm the Law of Falling Bodies. When the elevator was accelerated by the cables in the void of space, all the objects met the floor with the same urgency regardless of each one's individual mass.
But, as I wrote earlier, the experiment isn't just an analogy but an example of how the world works. The gravitational effects between the walls of the elevator and the pencils is so negligible that they are, for all practical observational purposes, meaningless. (And, if the elevator were a uniform sphere, the effects would be zero.)
To say that the elevator experiment proves the Law of Falling Bodies is no different than saying that dropping two unequal masses from the Leaning Tower of Piza proves it. The difference would be too irrelevant to matter.
In an effort to test Newton's principle of equivalence (which Einstein claimed to validate) a man named Baron von Eotvos came up with an experiment in which he attempted to observe any discrepancy between the velocity of falling unequal masses. He devised an apparatus -- known as a tension fiber balance -- and an experiment whose results seemed to indicate that the Law of Falling Bodies is valid to at least 5 parts per billion.
In the mid-60's the experiment was refined by Robert Dicke by a factor of several hundred. It was regarded as rock solid evidence that Galileo's Law, and Newton's Principle of Equivalence, were scientifically canonical.
However, if we invoke the principle that all forces are additive and look at the example of two bodies -- one 1kg, the other .25kg -- falling toward the surface of the Earth (with a mass of approximately 6 x 10^24kg, we can calculate the difference between the two rates of acceleration in free-fall.
The mass of the Earth-1kg body system:
6,000,000,000,000,000,000,000,001.kg
The mass of the Earth-.25kg body system:
6,000,000,000,000,000,000,000,000.25kg
The difference, being a mere .75kg -- or, one part per 8 trillion trillion -- is a smaller difference than the Eotvos/Dicke experiments could measure by a factor of about 40 thousand trillion. No wonder they didn't notice it.
QUICK CLEAN-UP Q&A BEFORE WE MOVE ON:
Q: If F=G(Mm)/r^2 is wrong, then why is a 1kg body 4 times as heavy as a .25kg body?
A: The weight of the body is what it is because of the force needed to keep it from falling. But what's at work here is F=ma.
When you hold out a hammer and release it, it wall fall until it hits the ground. This event is not due to a force (gravity) acting on the hammer; it's due to the sudden absence of force (you, holding it) and the sudden reappearance of force (the ground) that are the only forces at work.
Einstein showed that a body in free-fall is in an inertial state of rest. It's the act of holding it that creates an acceleration.
Even though a falling body appears to be accelerating, it is actually WE, standing still on the ground, who are experiencing an acceleration.
("a" is the acceleration cause by "g", and varies at different altitudes. So the force needed to hold up a body -- while "at rest" in a gravitational field (it's "weight")-- is specifically described by F=mg.)
CLIFF-HANGER
But, I hear you thinking, this is all academic. All of the discrepancies so far are debatable, and the "evidence" is on a scale too small to allow any confirmation. Where is some real observable evidence? Surely there are macrocosmic examples that could justify a radical change in such long-held physical laws.
Yep, there are! Coming tomorrow!!
(Kepler, Cavendish, Jupiter, light spheres, Hawking, and the fact that gravity is not an applied external force. And maybe, just maybe, some of my working hypothesis of what gravity actually is!)
Hey, c'mon, I love this stuff, but I'm not about to give myself carpal-tunnel syndrome for it!!! ;)
This is mainly a primer to the classical theories of gravity that I intend to refute. For anyone well-versed in such things, you wont learn anything here. :(
But it'll be handy info for everybody else!
Among the many cornerstones of the classical and modern theories of physics lay Galileo's Law of Falling Bodies and Isaac Newton's Principle of Equivalence. For centuries they have both been tested, re-tested, built upon and held to be irrefutably confirmed.
My mission is to present an argument, through reason and observation, that these two gravitational laws are fallacies.
I invite any and all challenges and input! I'm not proud, just curious. ;)
THE LAW OF FALLING BODIES
Prior to Galileo's experiments with falling bodies at about the year 1590, the predominant wisdom was that heavier bodies fell faster than lighter ones. Aristotle, some twenty centuries earlier, decreed that this was the case based on the obvious fact that rocks fell faster than feathers.
He failed, of course, to consider the effect of air resistence. He also failed to test his theory (assumption, really) by experimenting, i.e.: dropping rocks of different weights from significant heights.
What seemed completely sensical and obvious to Aristotle in the 4th Century B.C. was rejected by Galileo on the strength of observation. By dropping two unequal masses from a great height he could demonstrate that, all common sense and expectation aside, these two unequal masses would fall at precisely the same rate of acceleration. This he defined as the Law of Falling Bodies, and it is probably the oldest classical theory left standing to date.
Well, 'til now anyway. ;)
GALILEO'S PARADOX
Even as he championed this new and exciting discovery Galileo was at a loss to explain how it could be so, and he attempted to disprove it through thought experiments.
One of his experiments was to imagine two bodies of unequal mass dropping from a great height while tethored loosely by a piece of string. Assuming that these two masses would fall at different rates he posed to himself some questions:
Would the lighter, slower-falling object slow the descent of the heavier?
Would the heavier, faster-falling object speed up the lighter one?
Or, would the two -- being connected by the string -- make yet a heavier object and fall faster than either of the two would seperately?
Since Galileo could find no way to justify choosing one over the others, he decided that the assumption that unequal masses fell at different rates presented a paradox which the Law of Falling Bodies took care of nicely.
He then reached the further conclusion that gravity attracts each individual particle in each body seperately, thus the bodies, as a whole, fall at the same rate.
This assertion was echoes by both Newton and Einstein, and is held to be one of the most irrefutable facts of the laws of gravity.
NEWTON'S PRINCIPLE OF EQUIVALENCE
A century after Galileo, Isaac Newton assured us that the Law of Falling Bodies was valid.
It was during Sir Isaac's efforts to understand and describe the Moon's orbital characteristics that he applied the equation
F = G(Mm) / r^2
On an Eartbound horizontal plane the force neccessary to roll a 5kg rock a certain distance is less than the force needed to roll a 20kg rock the same distance. Newton's Second Law of Motion describes this as F=ma (force = mass times accelleration).
In an Earthbound vertical plane, however, objects in a free-fall seem to accelerate at only one possible speed; approximately 32fps^2 at sea level.
Newton wondered that, curiously, it could be argued that the force of the Earth's gravity on two unequal masses in free-fall could actually make the lighter object fall faster due to it's lesser resistance to a change in it's inertial state than the heavier body. While applying the Law of Falling Bodies to this, he attempted to explain it by defining two kinds of mass; Gravitational mass, and Inertial mass.
Gravitational mass (due to the amount of matter) determines the body's gravitational attractiveness. A more massive (heavier) body has a stronger gravitational effect.
Inertial mass (due to the amount of matter) determines a body's resistance to a change in it's inertial state. A more massive (heavier) body is more resistant to moving it if it's a rest, and stopping it if it's in motion. (Of course, motion is relative and these two phrases are really saying the same thing.)
Newton then theorized that the Gravitational mass and the Inertial mass of any body, and in any system of bodies, are equivalent.
While his equation
F = G(Mm) / r^2
This concludes the introduction to the classical theory of gravity. Einstein's Principle of Equivalence (the "elevator experiment") will be next.
Okay, I've made up my mind. Now's the time to sink or swim.
Beginning tomorrow evening I'm going to begin posting -- in installments -- my working theory of Gravity.
It may be sleepy for some, creepy for others. But, I promise it'll be food for thought.
And I invite, nay, DEMAND critique!!
heh, this is gonna be fun. :D
