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

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  •  dimensions... (5+ / 0-)
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    vcmvo2, kbman, grasshopper, linkage, drache

    ...as I was taught, are "axes of measurement," a subtle but significant difference from the common understanding that they refer to something qualitative about spacetime.  

    This might enable people to understand the idea that linear motion is one-dimensional.  Motion in a straight (for all intents & purposes) line is motion along a single axis of measurement: thus, one dimension.  

    Motion that includes a change of direction (as I understand, "change of direction" is also a form of acceleration) would be motion in two dimensions: two axes of measurement, the original direction and the new direction.  

    So far, the original direction and the new direction have occurred on a plane: by analogy like driving down a main street and making a turn: you are still on flat ground, which is roughly a plane.  

    Another change of direction that takes one off that plane, is motion in a third dimension:  by analogy if you begin to drive up a hill so you have left the flat plane of the city roads below, you need a third axis of measurement to describe your direction of travel.  

    •  a very concise and brilliant explaination (2+ / 0-)
      Recommended by:
      vcmvo2, G2geek

      my goal now is to imitate that in my writings I think.

      You are right that change of direction is a form of acceleration. But I don't want to spoil a future topic ;) (if you are curious look up centripetal acceleration)  

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

      by drache on Sun Jun 07, 2009 at 08:01:50 AM PDT

      [ Parent ]

    •  depends on how you regard time, (1+ / 0-)
      Recommended by:
      G2geek

      I suppose.  Can't have motion without it.

      Is it a "dimension"?

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

      by Deward Hastings on Sun Jun 07, 2009 at 11:00:49 PM PDT

      [ Parent ]

      •  Yes, it is, but slightly different. (1+ / 0-)
        Recommended by:
        drache

        According to modern physics, time and space are seen as part of a unified whole; thus the term "spacetime" to refer to "what it is that we live in."  

        Remember that a dimension is an axis of measurement, nothing more.  Since you can measure time along a linear axis, it's a dimension.

        Ordinarily we think of time as a vector, which is to say, a quantity that has a definite direction:  the proverbial "arrow of time" that only goes forward.

        However in quantum physics, time is actually a scalar, whis is a quantity without a definite or necessary direction:  just like the three spatial dimensions.   Certain equations in quantum physics work "both ways" in time: forward and backward, with equally viable results.  

        At the cutting edge (or the fringe, depending on your opinion), there are hypotheses that call for information to be able to propagate "backward" in time.  The entire area of quantum entanglement brings this up indirectly: if you have an entangled photon pair that demonstrate simultaneous changes in behavior, does this imply that a state-value has propagated through normal spacetime instantaneously (faster than light), or that it has somehow operated "retrocausally" (backward in time).   Faster than light is forbidden by Einstein, but retrocausality is allowed in quantum physics.  Either way appears to violate common sense, but that's only because common sense hasn't caught up yet.

        Interestingly, some of these concepts have parallels or equivalents in religion and general philosophy.  

        The Calvinist doctrine of "predestination," whereby a person's destination in Heaven or Hell is fixed before they are born, makes sense if you assume that time is traversible by God: thus God knows in advance the overall trajectory of your life, even though those details are not known by you until they unfold.  And somehow this is still consistent with the overall Christian doctrine of individual free will.  

        Buddhism speaks of timelessness and the timeless void that precedes the ordinary world of appearances: the idea here is that everything "happens" simultaneously rather than sequentially, which is consistent with the simultaneity of entanglement.  

        Of course it's foolish to try to equate science and religion, as it would be to equate a symphony and a sculpture (one has melody and rhythm, the other has shape and texture).  However in a philosophical sense, it's interesting that humans have seemed to arrive at a kind of intuitive understanding of certain aspects of reality that were later elucidated and fleshed out by science on its own terms.  

        This makes sense in the context that certain underlying characteristics of the physical universe are observable in subtle ways from everyday experience.  As a close friend of mine says, Nature builds with few and simple rules.  

        •  in the diarist's (1+ / 0-)
          Recommended by:
          G2geek

          "equations of motion" "delta s" and "delta t" are not distinguished . . . you can solve for one, or the other.  If either is a constant then . . .

          If I were doing a Bridgman style "dimensional analysis" I'd list "time" as a . . .

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

          by Deward Hastings on Mon Jun 08, 2009 at 06:58:51 AM PDT

          [ Parent ]

          •  say more.... (1+ / 0-)
            Recommended by:
            drache

            ...don't just leave us hanging by the tail of three dots.  

            •  the answers become your own (0+ / 0-)

              only if you figure them out yourself.  "Science" isn't about "authority" . . .

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

              by Deward Hastings on Mon Jun 08, 2009 at 07:29:18 AM PDT

              [ Parent ]

              •  you just me personally (1+ / 0-)
                Recommended by:
                G2geek

                I don't like this answer. Science may not be about authority, but this is not a class room and even as a physicist I am not entirely sure what you are getting at.

                Time can really only be represented in so many ways.

                Please don't be coy, state your thoughts.

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

                by drache on Mon Jun 08, 2009 at 07:34:58 AM PDT

                [ Parent ]

                •  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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