Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



TruthWhy all atoms fall at the same rate in vacuumjohnreed
Posted:
Sep 15, 2011 3:38 AM


Robert Allan> What is truth? I think that it's fair to say that truth is what can be proved and the rest is just...conjecture?
johnreed> In brief: It appears that if we can envisage it as the truth and the closer we come to believing it is the truth; the greater is the likelihood that we are wrong. This is not an iron clad rule, but consider: We think we have proved that a universal force that we call gravity exists as a property of inanimate matter. We believe it exists because we feel our weight. We believe it acts on us because we feel our weight. We define it in units of what we feel, our weight; as the product of mass and acceleration [mg]. We postulate that inertial mass [ma] and so called gravitational mass [mg] are equivalent with respect to the celestial universe because they are equivalent with respect to what we feel as, our weight [mg] and force [ma].
So developing logic through the lens provided by our senses allows us to define the least action consistent universe after our own least action consistent image. Our weight [mg] and a force that we feel [ma]. Both [g] and [a] represent acceleration[1].
Note: Where we place a balance scale is immaterial to the balance scale. Wherever we place it the magnitude of [g] will be the same on each pan regardless of the mass magnitudes placed on the pans (this is true except in theoretical cases where extreme magnitudes that exist in mathematical fantasies are projected to vary greatly in very short distances). So when we define an object in units of [mg] the only quantity we are comparing is the quantity of mass [m], on the balance scale. [g] is a consequence of location. That's pretty simple isn't it? So you might wonder why I bother to point it out.
If [g] was not a consequence of location then mass [m] and [g] acceleration could not be separated into the components of weight [mg]. In such a case the balance scale would only give us weight as [w]. In fact we used the balance scale to give us weight for 6000 years and for 6000 years we believed that heavy objects fell faster than lighter objects. So when Galileo showed that all objects fall at the same rate we were amazed and we have remained amazed for 450 years.
This is because our normal use for the balance scale is to compare weight [mg]. Weight is specific to location and specific to what we feel at that location. Weight, [mg], and what we feel varies according to a location in space. Given any mass [m] all three, weight, [mg] and what we feel, depend on the magnitude of [g]. We can change locations and our mass [m] remains unchanged but our weight, [mg] and what we feel varies according to a location in space. Again its pretty simple stuff. High school physics. So why do I discuss it? Because we have defined the universe in terms of what we feel.
We say that a force we feel as weight [mg] is universally generated by inanimate and animate matter as an inate property of matter itself. I say this is false. The force we feel is generated by us (our effort) and we apply it to inanimate matter and/or feel it through physically interacting with inanimate and animate matter. The force we feel does not act at a distance. The force we feel does depend on our location in space. So "something" acts at a distance.
We think that it is proportional everywhere in the universe (in terms of mass, distance and time), to the magnitudes we feel and measure on the surface of planets and moons. Where mass is conserved independent of the action of planets, stars and moons.
All atoms fall at the same rate in a vacuum. Therefore I conclude that the planet attractor acts uniformly on each atom (Einstein proposed a uniform gravitational field). This is the "level" playing field we are born in and the field that contains the atoms from which we are built. Given the level playing field that acts on all atoms 'uniformly'; we feel the cumulative 'non'uniform resistance of those atoms when we 'work' against the direction the field of atoms is uniformly pulled. When we 'travel' in the direction the field uniformly pulls on our atoms, we experience free fall, or no resistance other than air resistance. The 'universal 'attractive action is uniform on the non uniform atoms that make up animate and inanimate matter. This is why all atoms fall at the same rate in vacuum. The pull on each is uniform. This uniform pull allows us to feel variance in the resistance of the nonuniform atoms we work against. An object we lift offers its weight as resistance to our effort. It offers no resistance to the pull of the planet, relative to us.
Gravitational force is a legacy concept based solely on what we feel; our weight, and the quantitative least action consistent mathematical convenience of its definition [mg]. Nothing pulls on us. The pull is uniform on our atoms which we would not feel during freefall in a vacuum. We feel our total weight when we are in contact with the planet; or when we accelerate away from the planet. We feel the resistance of our nonuniform atoms when we work in opposition to the direction the planet uniformly pulls on our nonuniform atoms. We feel the resistance of our nonuniform atoms when we act in opposition to a state of rest or in opposition to a state of constant motion. In all cases of inertial mass [ma] and gravitational mass [mg] the force we feel is the resistance of nonuniform atoms in response to our effort. We act on this nonuniform resistance and we feel an equal and opposite force because our effort is equal and opposite to the resistance we act on. We have defined it that way. [F=mg] and [F=ma].
The force we apply when we lift an object at any location, will always be equal to the weight of the object's atoms that resist the force we apply at that location. We generate the force. Matter provides the resistance we must counter. We feel and generate the force. It begins and ends in our body and effort. We lift objects. Objects can strike us. [F=mg] and/or [F=ma]. This does not even imply that mass generates a universal gravitational force, much less at a distance.
We have heretofore attributed this phenomenon to Newton's 3rd law. The "equal and opposite" law because the force we generate is equal and opposite to the resistance we work against. Again we have defined the universe through the lens of our own image.
There is nothing universal about the force we feel [mg] except the resistance [m] and the location in space [g] that causes it. Our effort cannot be generalized to the effort of the planet. Inanimate objects exert no effort. Nonetheless we assign the force we feel to all inanimate objects based solely on their objective resistance. The planet attractor acts on atoms. All atoms fall at the same rate. We lift or work against the cumulative sum of the nonuniform resistance of the atoms in an object. The planet attractor pulls uniformly on the object's nonuniform atoms and on our nonuniform atoms as we lift the object. To assign the force we feel and generate, to inanimate object resistance is error.
If you are perplexed and think that this is not what you were taught in school, you are correct. This is what I have learned and what I am attempting to explain. I am redefining gravitational force as a force we feel as living objects in response to resistance. We act on resistance and we feel the force we generate. The cause of that resistance is undoubtably universal, it just is not the force we call gravity. It is the planet attractor's uniform action on nonuniform atoms. The uniform action on nonuniform atoms by the planet attractor is why all atoms fall at the same rate. The atoms have no resistance falling in a vacuum. We feel the resistance we call force and weight when we interact with matter. We can quantify this resistance in units as a product of mass and acceleration [ma] and/or [mg]. I will further explain why this works when I continue. johnreed, Saturday, 10 September, 2011
Related notes: [1] The simplest case of acceleration can be expressed as a change of speed over time. Take the most familiar US definition for speed as miles per hour or [m/h]. This is [distance/time] or [d/t]. [Speed] over [time] then becomes [d/t]/[t] which is [d/t^2]. [1] Where mass is the conserved cumulative resistance of nonuniform planet and moon surface atoms and is conserved independent of the celestial least action motion: Recall that we have spin angular momentum and linear momentum from Newton?s first law. We don?t have orbital angular momentum from that law. We acquire orbital angular momentum from Newton?s mathematical derivation for centripetal force where he used a perfect circle and perfect motion to argue for centripetal acceleration. The spinning perfect circle angular velocity is an artifact of the uniformly spinning circle itself. The angular velocity of a spinning disk, sphere, or solid object, is an artifact of the uniformly spinning disk, sphere, or solid. So we have least action consistent single object spin angular momentum as an artifact of the spinning perfect circle angular velocity. Newton then used the least action consistent angular velocity of Kepler?s empirical time controlled law of areas for 2 body planet orbital motion, to mathematically carry his perfectly circular 2 body uniform motion, spin angular momentum analog, to the planet?s nonuniform 2 body orbital motion. It?s based solely on timespace parameters where the emergent conserved cumulative resistance of nonuniform planet and moon surface atoms is either designated as the cause of the least action consistent celestial motion (Newton?s gravity), or as the consequence of the least action consistent motion, as spacetime curvature (Albert Einstein and peers). johnreed
I have made it easier to reference my supporting work by creating a Google Science and Technology Group titled: "The Least Action Consistent Universe and the Mathematics". Currently it contains Sections 1 through 9 for reference. The many subsections and work prior to 2007 has not been included. I will develop it further as I have the time and gain familiarity with the venue. Meanwhile my more recent work is available for public review to all, and open to criticism and discussion by any person who joins the group. The latter is a condition established by Google and newsgroups in general. I provide information. I seek no recruits. However, there are no restrictions or requirements to join.
Current web address: http://groups.google.com/group/thejohnreed
If you respond to this post from a newsgroup other than the above, please send a copy to Randamajor@yahoo.com, if you want a timely response. Thanks. johnreed Wednesday, 14 September, 2011



