Actually I consider dimensions as the number of degrees of freedom. Think of something (an imaginary particle) "in" a point, it can't move anywhere so there's no degree of freedom, and is therefore in 0 dimensions. On a line, it has one degree of freedom and hence one dimension. So on and so forth. Location CAN be defined by less dimensions than x, y, z, or "location" maybe require more, depending on the problem at hand and the constraints. For example, a pendulum with a fixed length has one degree of freedom and can be described in one dimension (the angle of the pendulum). I'm not sure where you're going with "gravity" has a single value. Gravitational acceleration varies by position, hence a non-uniform gravitational field which surrounds the Earth. For example, the acceleration is certainly different in NY than it is in Los Angeles...we generally need 3 dimensions to describe that. If we shift to General Relativity we need 4 dimensions.
You don't even understand the difference between center of mass and center of gravity, so there's no point in continuing.
10A....you posted this....Third, a true singularity is 0 dimensional. If it was 1 dimensional it would be a line. E.g. 0-D = point, 1-D = line, 2-D = plane, 3-D = cube. You continue to make that mistake over and over.[/QUOTE] Let's look at the first part of what you posted...."If it was 1 dimensional it would be a line."...end quote 10A. This statement is so stupid I am having a hard time deciding just WHAT I should point out what is wrong first!! Since YOU obviously do not comprehend that a LINE....by it's definition and REALITY CAN ONLY EXIST WITHIN A MINIMUM 10-D Universal Space-Time Reality...I will have to attempt to explain it to you. In order for anything to be defined or even exist as a word such as....a LINE....a PLANE....a CUBE...etc.....a Universal Reality with at least Matter and Energy MUST EXIST. For instance many years ago a book called FLAT LAND was written which described a World or Universe where only 2 Dimensions existed and where everything and all life was 2-D and just like a page on a book or drawing on a piece of paper.....that is how things existed but when this FLAT LAND was turned on it's edge sort of like attempting to look at the edge of a sheet of paper....IT NO LONGER EXISTED. Here and this post of yours as you detail out what YOU believe 1-D, 2-D, 3-D is....SHOWS ME HOW LITTLE YOU KNOW ABOUT THIS AND WHY YOU KEEP BUTTING HEADS WITH ME AS YOU REALLY DON'T UNDERSTAND. The REALITY is that 2-D....and a PLANE...as that is what you describe as being 2-D....CANNOT EXIST IN 2-D!!!! A Cube....cannot exist in 3-D!!! A LINE....cannot exist in 1-D!!! Everything you detail here can ONLY exist in at a MINIMUM 10-D. Reason? Because for a Line or Plane or Cube and even if that CUBE is simply drawn on a piece of paper....MATTER AND ENERGY MUST EXIST!!! You can't have a LINE without DISTANCE....and you can't have distance without POSITIONS OF MATTER AND ENERGY WITHIN SPACE-TIME.....and you can't have Matter and Energy without at a MINIMUM 10-D. Even a line drawn between two points on a piece of paper needs the matter and energy that the paper...the ink or graphite in the pen or pencil...TO EXIST!!! Any geometric structure or object be it real or represented MUST HAVE 10-D AT MINIMUM to exist. A 2-D can only exist as an ASPECT OF 10-D Plus. As far as 1-D being 0-D....NO....1-D we KNOW exists as a part or EXPRESSION within our Universal Space-Time as 1-D existing by itself and not within any 10-D plus Universal Space-Time would not allow Matter or Energy to exist. And 1-D CERTAINLY IS NOT a LINE as you posted as a Line denotes DISTANCE....and 1-D does not allow Distance. The Holy Grail of Space Travel Technology is to generate enough Energy to represent MASS....as Matter and Energy are Interchangeable...and since all Particles of Mass are completely comprised of Quantum Particle/Wave Forms of Energy....if the Human Race understood and developed the UFT...Unified Field Theory....we could basically....FOOL...the Universe into thinking that an enormous amount of generated Energy was indeed Mass. Thus by being able to DIRECTIONALLY GENERATING THIS ENERGY....we could FOLD SPACE-TIME....and thus instead of traveling distances in a Space Ship we would FOLD SPACE-TIME and travel without moving. Imagine having a string and YOU are located on one end of that string and a Planet you want to get to is located on the other end of that string....and that string represents space-time and DISTANCE. So...what is the shortest distance between two points? In school we were always taught the shortest distance was a STRAIGHT LINE...right? WRONG!!!! Take a string say 2 feet long representing the distance from Earth to a Planet 100 Light Years away in another Star System......and pull the string taunt. That 2 feet held taunt....is representing 100 Light Years or about 600 Trillion Miles. Now...take one end of the string and bring it to the other end of the string basically FOLDING THE STRING....or FOLDING SPACE-TIME. NOW...the shortest distance between 2 points is THE SAME POINT. What Dimensionality is EXPRESSED THIS WAY within a minimum 10-D Universal Space-Time? 1-D!!!!!! One Dimensional Expression!!! Thus what we are doing is WARPING OR FOLDING SPACE-TIME....which is what GRAVITATIONAL EFFECT IS!! The problem is that in order to generate such a massive amount of Energy to represent the required amount of Mass that would create the Gravity Effect....or Warp...or Fold Space....to cover 100 Light Years would take more Antimatter than exists in our entire Galaxy. So....what we have to do is create a Matter/Antimatter Reaction that Generates a Multiversal Cascade Energy Generation Reaction in INFINITE DIVERGENT UNIVERSAL STATES in a Multiversal System. AboveAlpha - - - Updated - - - PLEASE...by all means...tell me and the membership EXACTLY what it is I do not understand!!! This should be good! AboveAlpha
Man!!! You CANNOT have a Particle of Mass or Energy even EXIST in a 1-Dimensional State and a 0-D state means...NON-EXISTENCE. Gravity has NO VALUE....it is not a Particle Driven Force and in fact Gravity is not a Force at all....even though we call it the Weak Force as words fail us when describing Gravity. Gravity is simply an EFFECT....and that effect is specific to any amount of Mass warping the Space-Time around it in a manner that is indicative of a One Dimensional Expression. The Space-Time around the Mass is NOT 1-D....but it is WARPING INWARD UPON ITSELF....as if at it's center point of gravity Universal Space-Time Dimensionality breaks down to 1-D. AboveAlpha
Let's say I have a dimension, one dimension. I'll define it by X. I'll pick a point on X, that point I'll call zero, and notate it like X(0). I'll move an imaginary particle 2 meters along this dimension X, and notate it X(2). The distance it moved is X(2) - X(0). In this case, I picked the first point at zero so the DISTANCE it moved is 2 meters. I used one dimension for that distance. I think this was covered in elementary school, we called them number lines. The fact that there are more dimensions than 1 is totally irrelevant if a system is constrained to 1 dimension. A black hole singularity is a prime example, I can ignore 50 billion dimensions if the situation at hand confines itself to one, or zero dimensions. You have no problem ignoring all the other dimensions except one in describing your false singularity, but berate me for doing the same. You then continue to talk about a singularity as though it is 1-dimensional, and a singularity is 0-dimensional, as 1 dimension DOES allow for distance. I already explained you do not understand the difference between Center of Mass and Center of Gravity. The concepts are quite clear and fundamental, and your posts clearly, oh so clearly, indicate you have no clue as to the difference. That's ok, 15th century physics promoted the same concepts as you. I'll try to help you out though I don't know why. The Center of Mass is the mean location of a distribution of mass in space. Note "location", singular. In fact I can take a group of objects and determine the singular center of mass. There's a nifty formula for it. The Center of Mass exists with or without a gravitational field. If I take a peanut shaped object, and in empty space make it rotate, it will rotate around its Center of Mass. If that peanut happens to be of uniform density, it will rotate around its geometric center. If its not of uniform density, then it will rotate around whatever the mean location of its mass distribution is. Note that Center of Mass is not always inside the object. The Center of Gravity is a point (or points, it doesn't have to be unique unlike Center of Mass) where the sum of all torques due to gravity vanish. In other words, to even consider a Center of Gravity, there has to be a gravitational field. No field is required to compute the Center of Mass. The nature of the field has to be known as well, as most gravitational fields are non-uniform. For someone so "versed" in celestial mechanics, I would think this would be second nature. Our own satellites have to account for the difference between Center of Mass and Center of Gravity to maintain consistent orbits.
You don't understand 10A, my post about 5 dimensions must have been too long. Physics Dimensions and Art Dimensions are two separate things. The rules are different. You can't apply the simple geometry you learned in Grade School and High School to the Physics of Gravity. Gravity isn't a location. It's a physical dimension. When AboveAlpha tells you that Gravity is a one dimensional expression, Think about Expression in the mathematical sense. It comes from a mathematical equation. Here's the formula for Gravity: Inverse Square Law, Gravity
The Weak Force has nothing to do with gravity, and has to do with the emission and absorption of W and Z Bosons (in fact the W in a W Boson stands for Weak). I thought you knew all about particle physics? I'm still waiting for your 1 dimensional gravitational expression, and remember there are no appreciable black holes near the Earth.
Look...let me try to explain this to you so you won't post stuff like this as it does not make you look well educated in this field. You are confusing the CONCEPTS of Vertices as they apply in a 3-D ideology with Universal Space-Time REALITY. You see you are thinking along the lines of Vectors x, y and z....x=Horizontal....y=Vertical and z=Depth. Thus you are thinking as you look at the relationship of all 3 vertices that each is specific to a LINE of a particular distance determined by the other 2 vertices. Such a concept is for paper and compass and protractor Geometry we all learned in 5th grade. Universal Space-Time Geometry does not allow for any single defined aspect of Dimensional Geometry to exist in our Universal Space-Time. As example even a true aspect of 1-D or Singularity cannot and does not exist in our Universal Reality as 1-D rips through our minimum 10-D Universal Space-Time Dimensionality as a Black Hole's Singularity does NOT exist in our normal space-time. BUT....EXPRESSIONS of 1-D exist in the form of Gravity as Gravity being the effect of mass warping space-time is changing the 10-D or more closer to 1-D. As far as Center of Gravity....as I previously explained the farther away from a celestial body that possesses multiple Gravity Wells or Center of Gravity's.....the more congruent gravitational effect is to a single gravitational effect or center....but a complex celestial body either in form or density can have MULTIPLE centers of Gravity. Any you are NOT going to find Peanut Shaped Asteroids of uniform density or geometry. Now...in order to help you please define the manner you understand this statement of yours...."own satellites have to account for the difference between Center of Mass and Center of Gravity to maintain consistent orbits."...end quote 10A. AboveAlpha
Yes, I agree the rules are different between physical dimensions and art dimensions. I admittedly confine myself to the physics dimensions, though the art dimensions are cool. Ah yes the inverse square law. Well, the law as written there is a simplified model. It works for a lot of situations, perhaps most situations, but doesn't tell the whole story. For instance, it can't be used to compute tidal forces (you need more than one dimension for that), nor does it directly describe the gravitational forces inside a body. Also it's a Newtonian law that ignores relativity. We'll bypass relativity for now though. As written there, it's only valid for point masses or distributed masses that can be treated as point masses (see Gauss's Law for gravity). Now you can treat everything as a collection of point masses, but you need the vector version of Netwon's Law of Gravitation, which automatically puts the equation in 3 dimensions. Calculation of tidal forces require the computation over a distributed mass, e.g. in more than 1 dimension. If you have point masses distributed in 3 dimensions, you need 3 dimensions to calculate the net force due to gravity. The law doesn't quite hold up in some situations either, again its a model that works well most of the time, but not all the time. For example, once you are within the Earth the acceleration due to gravity decreases in proportion to the distance, not the square of the distance. We can also consider the interesting case of a planet consisting of a hollow shell. Outside the shell the inverse square law applies normally. Inside the shell, however, there is no gravitational acceleration despite the center of mass still at the center. A human would be weightless inside, everywhere inside. Again this is described by Gauss's law for gravity, which is most certainly expressed in 3 dimensions.
As I have already previously posted....GRAVITY IS NOT A FORCE. Gravity specific to the belief there existed a GRAVITON was the reason for naming Gravity the Weak Force as apposed to the Strong Force of Electromagnetism. Here is an explanation from a site WHY Gravitic Effect was labeled a Weak Force as they thought a GRAVITON EXISTED...it does NOT. Gravity Gravity, the weakest of the four forces, is about 10-36 times the strength of the strong force. This weakness is easily demonstrable - on a dry day, rub a comb across your shirt to give it static electricity, then hold it over a piece of paper on a desk. If you were successful, the piece of paper lifts off the desk. It takes an entire planet to keep the paper on the desk, but this force is easily overcome with everyday materials employing the electromagnetic force. However, the range of gravity is unlimited - every object in the universe exerts a gravitational force on everything else. The effects of gravity depend on two things: the mass of two bodies and the distance between them. In more precise terms, the attractive force between any two bodies is directly proportional to the product of the masses and inversely proportional to the square of the distance between the bodies. The dominance of gravity on macroscopic scales is due not to any intrinsic strength but instead to its enormous range and constant attractive nature, especially as compared to the other forces. These properties of gravity have made it extremely difficult to incorporate gravity into modern theoretical frameworks. The messenger particle of gravity is the graviton. It has not been experimentally verified, mainly because it is extremely hard to find the smallest denomination of the weakest force. Recent calculations show that it will likely be massless. Interestingly, all versions of modern string theory incorporate gravity (unlike previous quantum theories) and not only allow but require a particle with the properties of the graviton. Its discovery will likely represent a major victory for string theory, since previous quantum theories based on the model of point particles give illogical, infinite answers when gravity is incorporated. LINK...http://library.thinkquest.org/27930/forces.htm By the way....you are CONFUSING the WEAK AND STRONG NUCLEAR FORCES!!!!! The Gluon is responsible for the Strong Nuclear Force. The Weak Gauge Bosons are responsible for the Weak Nuclear Force. Look....I DO NOT ENJOY...making any member look the fool. Why don't you PLEASE first look things up BEFORE you post about things you have absolutely no idea or knowledge about? AboveAlpha
The Weak Force: http://hyperphysics.phy-astr.gsu.edu/hbase/forces/funfor.html http://www-project.slac.stanford.edu/e158/weakforce.html http://home.fnal.gov/~cheung/rtes/RTESWeb/LQCD_site/pages/weakforce.htm "...the belief there existed a GRAVITON was the reason for naming Gravity the Weak Force"- AboveAlpha By the way, what does "W" stand for in a W Boson?
10A...you posted this.... ....The law doesn't quite hold up in some situations either, again its a model that works well most of the time, but not all the time. For example, once you are within the Earth the acceleration due to gravity decreases in proportion to the distance, not the square of the distance. We can also consider the interesting case of a planet consisting of a hollow shell. Outside the shell the inverse square law applies normally. Inside the shell, however, there is no gravitational acceleration despite the center of mass still at the center. A human would be weightless inside, everywhere inside. Again this is described by Gauss's law for gravity, which is most certainly expressed in 3 dimensions.....end quote 10A. I have read this myself before but it is NOT TRUE. A person would have to remain STATIC and located directly dead center of a hollow sphere and that sphere would have to be PERFECT in it's geometry and distributed mass as well it could not be within any Gravitic Effect of any Celestial Bodies....for a person to remain weightless. Only at the very center of such a sphere could a person be weightless and even then since a person is NOT a small sphere and has arms and legs a persons non-spherical body would be attracted to and attract the sphere thus a person would eventually FALL....to a spot inside that sphere....as a Micro-Gravity would exist. AboveAlpha
Unbelievable!!!! You do realize that the statement of mine you first replied to was the one where I posted that we used to be taught that GRAVITY WAS THE WEAK FORCE....and I posted that GRAVITY WAS NOT A FORCE AT ALL!!! Then for some reason you challenged my statement saying GRAVITY WAS NOT A FORCE....for what reason I have no idea and stated....The Weak Force has nothing to do with gravity....which I AGREE WITH.....as THAT IS WHAT I WAS TALKING ABOUT TO BEGIN WITH!!!! But you were talking about the Weak Gauge Boson which has to do with the Weak Nuclear Force....NOT the incorrect Weak Force of Gravity. AboveAlpha
Well sorry but it is true. Naturally if you want to add more to the model that disturbs the gravitational flux, then things change. In the model I've given a person would be weightless in a hollow shell, whether at the edge or center. This is Gauss's LAW and is fundamental to understanding gravity, so color me surprised you don't know it. "4.8.3 Gauss’s Law for Gravity What is the gravitational field inside a spherical shell of radius and mass? Solution: Since the gravitational force is also an inverse square law, there is an equivalent Gauss’s law for gravitation. For r, the mass enclosed in a Gaussian surface is zero because the mass is all on the shell. Therefore the gravitational flux on the Gaussian surface is zero. This means that the gravitational field inside the shell is zero!" Source: http://web.mit.edu/viz/EM/visualizations/coursenotes/modules/guide04.pdf Page 4-34, the rest of the document mainly concerns Gauss's Law for electrical field flux, one of Maxwell's 4 equations.
Yes...I am well aware....but this will only result in true weightlessness for a perfect sphere at the center of this hollow sphere and as long as that hollow sphere is perfect geometrically and the material it is make of is perfectly distributed density wise. Do you understand WHY....a Human Beings body shape and distributed mass would cause it to obtain a micro-gravity and fall toward the interior shell? AboveAlpha
Nope. The shell is of perfect geometry spherical and the mass is evenly distributed. There is nothing inside or outside the shell, except for the human floating inside. Per Gauss's Law, there is no gravitational field inside due to the shell. As far as gravity is concerned the shell doesn't exist (ignoring relativity, it does sit in a potential well). The symmetry of whatever is inside doesn't matter one whit. The only possible gravity is due to the mass particles of the human on other mass particles of the human, which is not going to move her to the center of the shell.
Look....I will take this even a step further. Let's say we have a perfect 3 feet in diameter glass ball.....and we put this inside a perfect steel shell being 1000 feet in diameter on the inside and a perfectly distributed in density 3 feet thick wall for a shell. Now....if this glass ball is placed dead center it will float and not move as long as no other gravity issues outside the shell exist. If I place this Glass ball 30 feet away from the interior wall of the shell....the glass ball will FALL slowly but surely to that wall. WHY? Since the interior is hollow the congruence of Gravitic Effect specific to the Inverse Square Law is realized at a distance outside the sphere. At the center point of the sphere another sphere is being attracted to all matter around it equally thus an equilibrium exists and since the hollow sphere although also attracted to the glass ball is one structure...it as well will not move. But the MOMENT...that Glass Ball is removed from the center....where ever the closest inner wall is it will fall. As an example instead of a perfect hollow sphere we have positioned THOUSANDS of steel balls all equidistant from one another in a spherical lattice. We then place a ball at the center of this representative of a hollow sphere lattice....and that ball is the same size and mass and material of the other several thousand balls. The ball in the center will NOT move. But if we move that ball close to a wall just like in the other example say 30 feet away from a ball positioned on the lattice....that ball will FALL. This is based on the concept of how all Matter is mostly comprised of OPEN SPACE. AboveAlpha
You can place the glass ball near the wall, it won't move anywhere. There is much more mass on the far side of the wall than there is at the close side of the wall. The difference in mass offsets the difference in distance. That's a very simplistic version of Gauss's Law in spherical symmetry. It doesn't matter if the interior mass is distributed, or what symmetry it has, it can be a sphere, a hot dog, or Bette Davis. The lattice will have the same behavior, just that when the interior mass approaches the edge there's a point where the symmetry can break down due to the distributed masses, and that point is dependent upon the distance between the lattice masses. If that distance is tiny, then the distance from the wall would have to be tiny. Even then there's a path where the symmetry is maintained, and that should be a line through the collective center of mass of the balls that define an opening.
Here is the thing....Gauss's Law for Gravity in a sphere is a simplified method of Newton's law and both take into consideration Gravity as a force. Now the inverse square law also takes into account Gravity acting as a force and dictates the existence of a Graviton. However even though Gauss's Law can be proven with Calculus it is using an ASSUMPTION upon the very nature of Gravity. This Law has never been put to the test in any practical application and it has been suggested that if the construct of a earth sized sphere that was hollow was feeble it would in fact collapse upon itself and gather in a spherical manner. I personally do not believe in Gauss's Law of Gravity as it pertains to this topic. AboveAlpha
OMG, ROFL. Gauss's Law has nothing to do with any symmetry, spherical or otherwise, nor does it have anything to do with force. Pathetic, really pathetic. You want to invalidate Gauss's Law? You better start with the electric field version, which is one of Maxwell's Equations. Do you know what Maxwell's Equations are? Probably not, look them up on Wikipedia. Then you can move on to fluid mechanics, and prove the law wrong there. Along the way you're going to have to prove that the concept of divergence in math is flawed. You know I have a lot of patience, I like different points of view, I like to entertain other points of view, but to dismiss one of the fundamental laws of physics and mathematics in one post is unconscionable. There's people that know nothing, and they're great, they learn something. Then there's people who are like Penelope on SNL, and they're hopelessly lost. Guess which one you are?
Uhhh..... In classical mechanics, the shell theorem gives gravitational simplifications that can be applied to objects inside or outside a spherically symmetrical body. This theorem has particular application to astronomy. Isaac Newton proved the shell theorem[1] saying that: A spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its centre. If the body is a spherically symmetric shell (i.e., a hollow ball), no net gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell. LINK..http://en.wikipedia.org/wiki/Shell_theorem Want to try again? Gauss's Law specific to Gravity in a Sphere...is simply a easier way than using Newtonian Physics to calculate this concept and we are not talking about the other Gauss Laws. AboveAlpha.
I'll say it again, Gauss's Law has nothing to do with spheres or shells or symmetry. It's much more general than that. Gauss's Law is not "the shell theorem". If you had the least bit of inkling about calculus you would understand that, but I feel like I'm talking to my dog. I take that back, even he knows there's a multi-dimensional effect due to gravity on his urine stream when he hits his mark on the fire hydrant.
One other thing....every time I have asked you to explain some stupidity you have posted...such as your post stating I did not know the difference between Center of Mass and Center of Gravity....and I asked YOU to explain what it was I supposedly did not understand.....YOU DID NOT REPLY. You have done this CONSISTENTLY and during the part of our debate where you obviously could not understand the difference between 1-D 2-D and 3-D on paper compared to aspects of Universal Space-Time....you consistently would either refuse to reply or change the subject when you were shown to be way off the mark. Now this conversation keeps changing and changing to the point you are using a Law that has NEVER been physically proven. I at least admit this law can be proven with Calculus but it takes into consideration aspects of a FORCE rather than the Warping of Space-Time. You however keep moving along going here and there and change direction every time things and reality encircles you. AboveAlpha - - - Updated - - - OK...pray tell what does Gauss's law tell us other than what Newtonian Physics already tell us using the Inverse Square Law? And please provide proof. AboveAlpha
Your post #105 is the post where you among other things state a Peanut Shaped Asteroid would not have more than one center of Gravity. That...is NOT TRUE. AboveAlpha
