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Dimensions and Degrees of Freedom

  1. Jan 2, 2004 #1
    When considering the three dimensions of space and our freedom of movement in that space, does our ability to change our state of motion (acceleration) imply an existence of a fourth dimension, ie. four space-time dimensions?

    Given three dimensions each mutually perpendicular, we can move up, down, left, right, forward and backward. We can also rotate around each axes. Is a fourth axes perpendicular to the other three necessary for going faster and slower?

    I know it's often debated whether time is really a physical dimension or just an abstraction. I also know that with regard to 4-D space-time, time isn't a dimension separate from the other three in an absolute sense; it depends on your orientation within space-time.

    To summarize my question: is a fourth dimension implicit by the fact that we can accelerate and would it be possible to change the motion of any object without this dimension?
    Last edited: Jan 2, 2004
  2. jcsd
  3. Jan 2, 2004 #2


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    Science Advisor

    Greetings Jimmy !

    Acceleration is not a dimension, and velocity is
    not a dimension either. When you describe a body
    in a 3D space (normal Cartesian coordinates' systems)
    you "break up" its location into the three axes
    which you define (as you please). Velocity is then
    the change in distance per unit of time relative
    to the coordiante system you defined. You can also
    "break" it up into velocity along each axis you define.
    Acceleration is the change in velocity per unit of time.
    So, if relative to your system I were moving along the
    X axis my location would be my distance from the
    center of your system (presumably - you), my velocity
    would be the extra feet I move per second (for example),
    and my acceleration would discribe by how much my velocity
    changes from one second to the next.

    BTW, that face looks awfully green, maybe you should cure it.

    Live long and prosper.
  4. Jan 2, 2004 #3
    Re: Re: Dimensions and Degrees of Freedom

    I understand what you are saying but I didn't suggest that velocity or acceleration were dimensions. I was asking if acceleration required another physical dimension along with the three dimensions of space. I was considering the fact that given three dimensions, we have certain degrees of freedom with regard to motion. I was curious if a fourth dimension was required to allow us the added degree of freedom, ie. acceleration.

    Thanks for your reply. :smile:
    Last edited: Jan 2, 2004
  5. Jan 2, 2004 #4
    i suppose that "fourth dimension" would be time as there is no motion without time

    just a thought ;)
  6. Jan 2, 2004 #5
    Yeah, good old Mr. Yuck. Lots of poison control centers in the US give out stickers of Mr. Yuck for parents to put on anything dangerous. I remember when I was younger, I saw lots of public service announcements from the West Virgina Poison control center which featured Mr. Yuck and warned children not to touch anything that had his face on it.

    If I chose a better avatar, I might get more responses.
    Last edited: Jan 2, 2004
  7. Jan 2, 2004 #6
    That's the general consensus. What I'm asking is, is a fourth, 'Physical' dimension necessary to accomodate all the degrees of freedom that we experience.
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