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A very basic question

  1. Jul 14, 2012 #1
    Could someone please explain to me both technically and intuitively why the heart slows down as one nears the speed of light relative to an arbitrarily defined stationary observer? I feel rather silly for asking this because I've read the special relativity chapters in 5 different books (feynman,griffiths,taylor,rindler,french) and I am still unable to answer this simple question.
     
  2. jcsd
  3. Jul 14, 2012 #2
    Let's try a little analogy.

    Say there's a road that runs north and an intersection 1 mile north of the origin. If you're facing north, then you say the road extends 1 mile in the direction you face, and you're done. But if instead you're facing northwest, you'd say it goes .7 miles in the direction you're facing and .7 miles to your right. The part that goes in the direction you're facing is shorter, just because you turned. The same vector or interval is being measured, but it's been resolved into a different set of components.

    The same goes for relativity. Here, "the direction you're facing" becomes "the direction you're moving through spacetime". If it takes 1 second for your heart to beat, then obviously that's what you measure. But someone else, moving at a speed relative to you, has a different direction they're traveling through spacetime, and like with the road analogy, when they measure the spacetime interval between two events, they resolve it into different components. In relativity, unlike Euclidean geometry, the time component they measure is increased instead of decreased. They think it takes more time for your heart to beat. But this is all just because they measure the components of a vector with respect to a different basis.
     
  4. Jul 14, 2012 #3
    Yeah looking at the problem from the perspective of Minkowski spacetime clears up a lot of things.Thanks.

    The problem I have with textbooks is that they use a thought experiment with a mechanism involving light to explain time dilation and then extrapolate it to ALL mechanisms in that IF.
     
  5. Jul 14, 2012 #4
    Following up on Muphrid's excellent and efficient response I'll sketch the Minkowski space-time diagram for the clocks. Using the Loedel form of the diagram we have red and blue observers moving off in opposite directions with the same speed with respect to a black rest frame. The distance and time measurements then have the same calibration in the sketches. The upper sketch is used to derive the time dilation equation (Lorentz transformation). In this derivation we embrace the concept that all observers move along their respective worldlines (along their 4th dimension) at the speed of light): dx4 = c(dt).

    The lower sketch shows the different cross-section views of space-time for red and blue observers--this makes clear the explanation underlying the length contraction and time dilation phenomena of special relativity.
    Loedel-Diagrams_2.jpg
     
    Last edited: Jul 14, 2012
  6. Jul 14, 2012 #5

    Dale

    Staff: Mentor

    The heart works by EM, so iif EM slows down then so does the heart
     
  7. Jul 14, 2012 #6

    A.T.

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    Different reference frames are not parallel universes with alternative realities.

    If a light clock and some other mechanism placed at rest next to eachother stay in a certain sync in their rest frame, then they must stay in the same sync in every other frame. Otherwise you would get paradoxes.

    So any change in the rate of the light clock must also happen to the rate of any other mechanism, that is at rest to the light clock.
     
  8. Jul 15, 2012 #7

    As Dalespam suggests, If light in a vacuum slows down wouldn't you expect ALL electromagnetic signals to slow down.... Like the electrical impulses in a heart?

    You can pick any physical phenomena....they all slow down, even 'aging'...that is, cellular function [chemical processes]. And radioactive decay, and.......all
     
  9. Jul 15, 2012 #8
    This sketch might help to visualize the loedel diagram Bobc2 talked about:
    For pink observer his 10 pink heartbeats for 7 blue heartbeats.
    For blue observer his 7 blue heartbeats for 4,9 pink heartbeats.
    For blue observer his 10 blue heartbeats for 7 pink heartbeats.

    The world of simultaneous events for both observers is different. That's relativity of simultanaeity. Event blue heart at 7th beat and event pink heart at 4,9th beat are simultaneous for blue observer (they happen in one blue world if simultaneous events), but those two events do not happen simultaneously for pink observer (i.e. not both in one pink world of simultaneous events; they happen one before/after the other)
    7-10.jpg
     
  10. Jul 15, 2012 #9

    pervect

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    You've seen a lot of more detailed explanations, I thought I'd give a shorter overview. In pre-relativistic physics, if you have two events, both the distance between them and the time between them (which I will call the duration, the duration simpy being the magnitude of the time difference), are independent of the observer.

    In relativity, this is not the case.

    To complicate matters further, the definition of "at the same time" in relativity becomes observer dependent.

    "Why" this all happens is a consequence of the speed of light being a universal speed limit. Some of the previous posts, or, better yet, a textbook (apparently you've read a few - good for you!) will explain why the general principle that the speed of light is constant for all observers implies that duration and length are both observer dependent.

    It's a very common mistake to think that special relativity implies that time flows at different rates, but to cling to the idea that it can be defined in an observer independent manner. The way your question is phrased suggests to me that you might be making this very common error. It's not just a matter of clocks slowing down or speeding up. The notion of time has gone a fundamental shift, from being observer independent to observer dependent.

    What becomes the same for all the observers, and can be used to communicate between them without changing value, is the concept of the Lorentz Interval. The Lorentz interval is a combination of duration and distance (the square of the interval is given by distance^2 - c^2 * duration^2). In relativistis physics, the Lorentz interval between two events is the same for all observers. Neither distance or duration can make the same claim.
     
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