Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A question about the rationale of SR?

  1. Jun 13, 2006 #1
    Hello, I have a question about special relativity.

    According to the Lorentz transformation, if a coordinate system K' is moving with respect to a coordinate system K, then a rod fixed with respect to K' will appear to be more lengthy with respect to K than that with respect to K'.

    The equations are true .. Ok, but I don't understand the rationale behind that. Why does the motion change the measured length? If somebody can give me a real world meaning, I will be very thankful.
  2. jcsd
  3. Jun 13, 2006 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    (distance^2) - (c*time^2) remains constant in relativity - it's known as the Lorentz invariant. Note that when the Lorentz interval is zero, the constancy of the Lorentz interval implies that the speed of light is the same for all observers.

    It can be shown that time changes via various arguments (such as the light clock). In order to keep the Lorentz interval invariant, distance must change as well.
  4. Jun 13, 2006 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Lorentz boosts are strongly analogous to ordinary rotations in Euclidean space. (In fact, mathematically, the only real difference is a sign)

    So, it might help to think of a similar situation in Euclidean 3-space. Actually, let's look at 2-space, since it's simpler.

    Suppose I draw two parallel lines on a sheet of paper. You want to measure how far apart the lines are. (This is analogous to wanting to measure the length of an object)

    Suppose you first place your ruler so that it's perpendicular to the lines, and you measure a distance of 1". (This is analogous to measuring the length in a frame where the object is at rest)

    Now, suppose that you oriented your ruler differently. Say, making an angle of 60° with the lines. In this case, you'd measure a distance of 1.15". (This is analogous to measuring the length in a different frame where it is moving)

    In Euclidean space, when you make a measurement that is perpendicular to the lines, you get a certain length, and if you make your measurements along a different direction, you see a bigger length.

    In Minowski space-time, it's the same, except for a sign. When you make a measurement that is perpendicular to the objects motion through space-time (that is, in a frame where the object is at rest), you get a certain length. If you make the measurement along some other direction (that is, in a frame where the object is moving), you get a shorter length.
  5. Jun 15, 2006 #4
    Here is the simplest explanation I've found yet...

    Your friend is moving. You are not. Yet you both see light at the same speed! Something's gotta give .... length and time.
  6. Jun 18, 2006 #5
    In a 3 dimensional coordinate space, all the directions in which a rod can be arranged are fully defined by its physical length L = (x^2 + y^2 + z^2)^1/2 But if the universe has another dimension, then the length of the rod has one more factor (ict)^2. This means that L is really a spacetime composite rather than a spatial thing, and this spacetime configuration undergoes a change when put in motion - but it is not a physical change. It is an accompanying circumstance of the motion - it changes its situation with respect to the system K. Contraction is only a consequence of how things are measured - it is not a physical reality and related per se to cause and effect - the statical or proper length of the rod in the K frame is the greatest, but the measurement of length in the K' frame is equally real. The total spacetime length in K has only a temporal term, the measurement in K' has both a temporal and a spatial term - therefore the measurement in two relatively moving frames will be different.
  7. Jul 3, 2006 #6
    Any change of distance or angle between two or more objects will have an impact on the appearance of time and space measurements between them. Both will measure time to go slower and length to be shorter for the other object.

    Does nature requrires a rationale? I do not believe so, It is simply the way it is. :)
  8. Jul 3, 2006 #7


    User Avatar
    Science Advisor
    Gold Member

    You can understand the rationale driving nature at deeper levels though, and the constancy of the speed of light is a consequence of the SR metric.

    If you unite time and 3D space as dimensions in a space-time continuum you need a conversion factor to convert the seconds into metres or vice versa.

    Such a conversion factor is a velocity, or its reciprocal.

    So there is a velocity, always called c, built into the fabric of space-time.

    As you said elsewhere, because photons are massless they have to travel at this velocity, and so c is identified with the speed of light in a vacuum. :smile:

    Last edited: Jul 3, 2006
  9. Jul 3, 2006 #8
    Well that's not the way I see it all all, but then we are getting in the area of philosophy. :)
    Reason is a definitly not useless figment of the human imagination but it has absolutel nothing to do with nature.
    Last edited: Jul 3, 2006
  10. Jul 3, 2006 #9
    I couldn't disagree any more strongly. If theory has taught us just one thing it's that nature has an uncanny way of behaving according to rational rules and principles. Pretty much all of theoretical physics is "reasonable" in the sense that we have yet to observe anything which cannot be described in terms of a rigorous mathematical framework.
  11. Jul 3, 2006 #10
    Funny, so if something can be described or approximated by a mathematical famework it must be reasonable? How many perfectly round and mathematicaly pure circles are there in nature?
    Don't you realize that all Platonic and other metaphysical ideas are really abstractions and idealizations? They are most certainly not identical with reality and in fact cannot possibly be real. Math is a tool that can be used to make predictions about nature's behaviour, however math does not explain it let alone declare it reasonable.
    Anyway, this really belongs in the philosophy section if you ask me, I only respond to it since you brought up the "nature is reason" belief. :)
  12. Jul 3, 2006 #11
    How about you go back and read my post again in the context of your pretty strange comment that "reason has nothing to do with nature."
  13. Jul 3, 2006 #12
    No kidding, it must be me :uhh:

    You implied that nature behaves according to rules and principles and is rationale driven, hence my reply.

    Every theory I am aware of is an approximation of nature not a description. Nature is not a mathematical model!
  14. Jul 3, 2006 #13


    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2018 Award

    If people wish to carry on this type of discussion, please continue in the philosophy forum. Do NOT hijack this thread into this line of conversation.

  15. Jul 3, 2006 #14
    Yes, nature does appear to behave according to very definite rules and principles. Logically, it does not follow (nor did I claim) that this behaviour is driven by some underlying "spooky" rationale. It is indisputable, however, that the observed behaviour of physical systems can be accurately described by theories based on rational assumptions; it is in this context that one could claim that nature is rational.

    This is plainly incorrect. Physical theories are both approximations and descriptions. The descriptive nature of a physical theory follows by assumption: if it's not a description of the behaviour of nature then what's the point of the theory? Secondly, the approximate nature of all physical models is simply a function of our inability to perform experiments to arbitrarily high precision. If you really need to be convinced that this is so, you need look no further than the countless phenomenological predictions of QED.
  16. Jul 3, 2006 #15
    Right, next you are going to tell us that QED is based on, how did you put it, "a rigorous mathematical framework", afteral what is scratching out an infinity left and right among Appolonians. :biggrin:
  17. Jul 3, 2006 #16
    It would perhaps help if you knew how renormalization worked before implying that it's not rigorous.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook