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What is a point?

  1. Jul 22, 2014 #1
    hi there...

    what is a point in a space?

    classical math tells us that a point is:

    - an exact location on a plane surface
    - it has zero dimension

    but it can be viewed of as

    - an origin of fundamental forces operating within a dimension. all forces in a dimension must have an origin, thus, it is logical that a point within that dimension must be responsible to create the force.

    - it has no dimension but movement or activity can be observed. this follows that a point though it has no dimension, the only way that activity is evident is for the point to have rotation. it also follows that it can rotate either left handed, or right handed.

    - the point's spin also, is not confined to a certain plane in a dimension only. for example, in a three dimensional "space", the left handed or right handedness of the point's spin only denotes orientation since the point can spin in all directions.

    can you please help me on this if my observations are correct or not beacuse recent physics experiments clearly are going to the direction of this observation.
     
  2. jcsd
  3. Jul 22, 2014 #2

    bhobba

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    An object in a mathematical model, usually in basic QM, but not always otherwise, Euclidean geometry.

    And your source of such a claim is?

    Before answering that be aware of our forum rules:
    https://www.physicsforums.com/showthread.php?t=733933

    Thanks
    Bill
     
  4. Jul 22, 2014 #3
    my origin of the claim is from the central force problem of classical mechanics which aims is to determine the motion of a particle under the influence of a single central force. A central force is a force that points from the particle directly towards (or directly away from) a fixed point in space, the center, and whose magnitude only depends on the distance of the object to the center. (from wiki pedia).

    the problem applies for bodies having mass (thus having their own dimension in the case within three dimensional space as having length, width and height) but can it be extended to the smallest unit of space available within a dimension (ie the distance between two zero dimensional points in a one dimension subset or dissection in a 3d space) and the interaction of the forces transferred from one point to the next.
     
  5. Jul 22, 2014 #4

    Drakkith

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    Per wiki: http://en.wikipedia.org/wiki/Point_(geometry [Broken])

    Note the last sentence. A point is not a physical object. It is a mathematical concept. We can consider objects and events to be located at a point, but we cannot say that the point itself creates anything or is responsible for anything, nor can it have a spin. It's just a way to keep track of the location of things in space.
     
    Last edited by a moderator: May 6, 2017
  6. Jul 22, 2014 #5
    so how does a force act upon a point in space? does it only transiently convey ; transmit the force into space since it is implied in classical math that it is only a notion to keep track of location of things in space?
     
  7. Jul 22, 2014 #6

    Drakkith

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    A force does not act on a point in space, it acts on an object located at that point in space. These interactions are governed by well understood laws.
     
  8. Jul 23, 2014 #7
    but those laws as i researched does not have conformity when describing forces within very small objects and forces that govern massive objects why is that so?? i believe in the notion that all forces operating in a dimension must be the same whether the force is acting on a small object or it acts on a massive object and everything in between.

    thus it follows that in order for forces acting on objects are the same, the medium in which the objects exist must be of the same "viscosity", (i am describing viscosity because it is observed that space acts like it and is documented in various scientific journals.) but as objects tend to be more massive than others it is logical that the space encompassing massive objects tend to be more stretched than less massive objects.

    now, what does space comprises of? is it just a region of nothingness or does space have a very intricate structure? then if it is, it follows that every point in space, which it is a subset of must comprise of a structure so that the space will behave accordingly so as to what the point in space behaves.
     
  9. Jul 23, 2014 #8

    bhobba

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    Forces operating in a dimension? I have zero idea what you mean.

    The modern view of forces comes from Quantum Field theory:
    https://www.princeton.edu/~achaney/tmve/wiki100k/docs/Quantum_field_theory.html
    'In perturbative quantum field theory, the forces between particles are mediated by other particles. The electromagnetic force between two electrons is caused by an exchange of photons. Intermediate vector bosons mediate the weak force and gluons mediate the strong force. There is currently no complete quantum theory of the remaining fundamental force, gravity, but many of the proposed theories postulate the existence of a graviton particle that mediates it. These force-carrying particles are virtual particles and, by definition, cannot be detected while carrying the force, because such detection will imply that the force is not being carried. In addition, the notion of "force mediating particle" comes from perturbation theory, and thus does not make sense in a context of bound states.'

    It has a very intricate structure - the vacuum is a very interesting, weird and wonderful thing in Quantum Field Theory.

    And general relativity says its dynamical as well - in fact that's the very essence of General Relativity - no prior geometry - meaning geometry itself is dynamical.

    And meshing these insights together is one of the greatest challenges of modern physics.

    Thanks
    Bill
     
    Last edited: Jul 23, 2014
  10. Jul 23, 2014 #9
    yes general relativity says that space has no geometry but it has structure. so, if space has structure, then the points which comprises space also has structure. although in mathematics the point is only used as a notion to depict a location, it does not mean that a point is non existent.
     
  11. Jul 23, 2014 #10

    Drakkith

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    I'm with Bhobba. I don't know what this means. Honestly I can't really make heads or tails of most of your post.
     
  12. Jul 23, 2014 #11

    Drakkith

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    Each point itself cannot have a structure, but the way they are arranged can be the result of the structure of space.
     
  13. Jul 23, 2014 #12

    bhobba

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    That's not what it says - it says it has no PRIOR geometry - meaning the space-time geometry (not space - but space-time) is determined by the Einstein Field Equations (EFE's).

    Its a very interesting fact of GR that that assumption alone, and a few reasonable physical assumptions, leads to the EFE's.

    But this thread is not the place to discuss that - the relativity section is where it belongs.

    And Drakkith is correct - points have no structure - they are one of the concepts used in defining what a geometry is. Specifically in GR the geometry is known as a Pseudo Riemannian geometry - but that is just by the by.

    Thanks
    Bill
     
    Last edited: Jul 23, 2014
  14. Jul 23, 2014 #13
    in a way that is correct. because points have zero dimension to begin with. but how is it that matter be created from a point in space and in that point only and not elsewhere?
     
  15. Jul 23, 2014 #14

    Drakkith

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    You seem to be thinking that a point is some sort of physical object. It is not. It is a mathematical construct used in various branches of math, including being one of the building blocks of basic geometry. However, it is possible to have geometry without points: http://en.wikipedia.org/wiki/Noncommutative_geometry

    It is important to remember that mathematical concepts do not always apply to the real world, and even when they do, it is only because they happen to be useful in describing reality, not because they are fundamentally true.
     
  16. Jul 23, 2014 #15

    bhobba

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    Conceptually matter occupies a point in space - it isn't created from a point.

    That is both VERY important and VERY true.

    Our theories are basically mathematical models.

    A point is simply an object in the model.

    Thanks
    Bill
     
  17. Jul 23, 2014 #16

    Drakkith

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    Matter is not created from a point in space, but at a point in space. I don't mean to be nitpicky, but I want to make sure we don't get confused. Matter is only created at that point because that's where the creation event is happening.
     
  18. Jul 23, 2014 #17
    its alright sir drakkith. i only observed that when matter is created at a point in space and not from it, then matter will be created at all points in space resulting in non variability. but in reality, this never happened. it is clearly observed that some regions in space have more matter than in some areas. this also is observed here on earth thus resulting in the variability in the forms of matter existing in our planet. even in outer space there are some regions which are more dense than other areas. if we make the the second statement into account then variability can exist since matter will be created more massive from one point and less massive on the other in relation to the space that governs both points.

    so it leads us to wonder if those points in space are static or not.
     
  19. Jul 23, 2014 #18
    i am not describing the interaction of the points but the interaction of the space surrounding both points, assuming that the distance of the points are far enough to be observed.
     
  20. Jul 23, 2014 #19

    bhobba

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    By definition a point is static.

    And the variability of the density of matter has a lot to do with gravitational clumping - meaning tiny variations in density get magnified over time by gravitational attraction.

    It is believed the universe started out fairly homogeneous.

    Thanks
    Bill
     
  21. Jul 23, 2014 #20

    bhobba

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    I have zero idea what you mean by that.

    Thanks
    Bill
     
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