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View Diary: Weekly Physics: Equations of Motion (63 comments)

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  •  You have created an interesting conundrum, (0+ / 0-)

    in that readers who understand your mathematical formulations already understand what you attempt to explain.  In effect the presence of the "mathematics" becomes an appeal to (claim of) authority directed to those who don’t understand . . . a "believe what I say, because I understand the math" directed to those readers.  That's not necessarily a bad thing, but there is (considerable) room for disagreement as to what the words used mean . . . "dimension" being one example.  To be sure one can ("mathematically") describe "position" on a one-dimensional scale . . . but can one describe "motion" without adding another . . . something ? ? ?  The "mathematics" sampled in the diary suggests "not" . . .

    As geek's examples above indicate this question goes directly to our understanding of space-time, and how our simple (mathematical) models map (or fail to map) to it.  What was it that Haldane said?  Something like:  "the Universe is not only queerer than we suppose, but queerer than we can suppose" . . .

    Fake Left, Drive Right . . . not my idea of a Democrat . . .

    by Deward Hastings on Mon Jun 08, 2009 at 08:16:40 AM PDT

    [ Parent ]

    •  Ps. (0+ / 0-)

      What does "you just me personally" mean ? ? ?

      Fake Left, Drive Right . . . not my idea of a Democrat . . .

      by Deward Hastings on Mon Jun 08, 2009 at 08:17:53 AM PDT

      [ Parent ]

    •  asdf (0+ / 0-)

      First, that was a mistake on my part, it was supposed to be "you know just me personally". I even thought that was what I wrote.

      As to your point, honestly you are mostly wrong but do have a point.

      Linear motion is defined as 1 dimensional motion and it doesn't matter how many dimensions you add on. They are extraneous as in any properly defined frame of reference all the other dimensions collapse to 1 dimension.

      Even if you view time as a vector (which it can be) in this equation time is implicitly a scalar as there is no need to complicate matters. The vector quality literally would fall out of any official derivation just like the higher dimensions would.

      There is no need to needlessly do higher math, it's like taking a howitzer to hunt geese. Sure it works but it's messy and way over kill.

      As to the appeal to authority, I understand that it might seem that way but really it's not. Look to tomorrow for my diary redux on this where I actually derive the equations.  Frankly how I am presenting is exactly how I first was introduced to them. Namely introduce the simplest case first as mere fact and then go back to actually prove it later. Of course I am horribly condensing the time between things but the principle should hold.

      I completely agree that the universe is very queer, but there is no reason to go too fast and deluge people. And frankly in some cases even these equations hold so well that there is no need to get further complicated.

      To quote a professor of mine 'there's no need to calculate the uncertainity of a baseball when it's going to be less then what you can see'.

      A song about life
      Why aren't you more like Gandhi? Why aren't I?

      by drache on Mon Jun 08, 2009 at 08:34:57 AM PDT

      [ Parent ]

      •  implicit in your use of words, (0+ / 0-)

        but absent from the equations presented, is the assumption (definition?) that time is not a "dimension".  But without a variable "quantity" of time there can be no description of motion . . . such a (mathematical) description requires both a spatial "dimension" and a temporal "dimension" (in the Bridgman sense), and both are present in your equations of motion.  You seem not to want to call time a "dimension", but you offer no other word for it . . . making "dimension" a synonym for "position", which raises again the question "how do you account for "motion" with only "position" as referant?"

        Fake Left, Drive Right . . . not my idea of a Democrat . . .

        by Deward Hastings on Mon Jun 08, 2009 at 08:57:23 AM PDT

        [ Parent ]

        •  I am avoiding time as a dimension (0+ / 0-)

          solely because there is little point to doing so unless we are invoking relativity, advanced electromagnetic dynamics or quantum theory (I think that covers things).

          Outside of those sub fields time is just a scalar that must always be positive.

          Anything more is over thinking the problem.

          You could of course create an axis known as 'time' this wouldn't be hard (and in fact time is often treated as such) but to an extent this is more tricks with math then actual physics. And has more to do with an efficient intuitive way to track a motions path as time elapses. But strictly speaking I would not call that a dimension.

          Questions on time are tricky because in many ways time like mass is considered a fundamental assumption of science. And yet within fields like relativity it's not exactly true.

          What I am trying to get at is that while you have good points on time they are not of impact here. Because in the simple classical (or Newtonian) physics I have presented time flows forward at a constant predictable rate. And there is nothing in the problem that can impact that.

          A song about life
          Why aren't you more like Gandhi? Why aren't I?

          by drache on Mon Jun 08, 2009 at 10:59:27 AM PDT

          [ Parent ]

          •  "time flows forward" (0+ / 0-)

            or so it seems to us.  But that is not apparent from your "equations of motion", where it is treated as a variable no different from position.

            And position also is "just a scalar" if confined to one (spatial) dimension (in one sense of the word).

            Of course one does "create an axis known as "time"" . . . it is an essential component of any mathematical description of motion.  You can also note that in some restricted views of "reality" it seems always to be "positive", or uni-directional, but that is not a necessary assumption for equations of motion.  Any mathematical description of motion in space/time has of necessity four variables (or "dimensions"), and usually five, regardless whether (or not) it is assumed one (or more) of those dimensions must be somehow constrained for it to map to "reality" as we perceive it.  That there is no apparent "negative time" or no apparent "negative mass" is (perhaps) just an artifact of our (very) parochial view of the universe . . . neither assumption is necesitated by the mathematics.

            If you want to "avoid time as a dimension" perhaps you should try leaving it out of your "equations of motion" . . .

            Fake Left, Drive Right . . . not my idea of a Democrat . . .

            by Deward Hastings on Mon Jun 08, 2009 at 01:10:18 PM PDT

            [ Parent ]

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