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Are length contraction and time dilation conventions?

  1. Apr 19, 2014 #1
    Since many authors call simultaneity between events a convention, and that under the specific set of rules we may choose a convention or a coordinate system relative to an IRF (or non-inertial) to describe space time, I wonder what's the relation between this and the effects of length contraction and time dilation. Are lengths contracting and time running slower relative to an IRF also conventions, and by that I don't mean that the total elapsed time between events is a convention also. Suppose that in the case of the twin paradox we use a different convention, like Dolby and Gull's radar coordinates. Since the lines of simultaneity are different, this must imply that time dilates differently and lengths contract differently than in the original setup. So are length contraction and time dilation also conventions, and we may choose how clocks run and rods contract, depending on the reference system we use, or the coordinate chart we use.

  2. jcsd
  3. Apr 19, 2014 #2

    Simon Bridge

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    Short answer: no.

    The other "convention"s you talk about are more a matter of being careful about definitions that we don't normally think about.

    Note: time dilation and length contraction are relationships between measurements in two inertial reference frames. Not "relative to an inertial reference frame".

    Reference for Dolby and Gull. JIC.
    ... they appear to be reformulating the problem as a teaching exercise.
  4. Apr 19, 2014 #3
    So in Dulby and Gull coordinates, from the perspective of the travelling twin, time dilates and lenghts contract just like in the ordinary description where the lines of simultaneity are straight, the only differences is the different 'shape' of the lines of simultaneity? Or is it the case that the lines aren't straight because time dilates differently, of course from the perspective of the moving twin? Thanks.
  5. Apr 19, 2014 #4

    Simon Bridge

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    D&G coordinates are a convenience of calculation.
    Two observers with a constant relative velocity will each see the other as having the slow clock.
    In the twin's paradox, both twins agree that the accelerated twin returns younger.
    D&G coordinates do not change this.
    Last edited: Apr 19, 2014
  6. Apr 19, 2014 #5
    I understand that, I understand that the travelling twin will elapsed less proper time. But from the perspective of the moving twin, the Earth twin's clock won't dilate time by the same rate. And by that I mean that in the classical setup with the straight lines of simultaneity, on the outbound trip the moving twin will see the Earth twin's clock run slower by a constant rate through the whole trip. In this case, when using Dolby and Gull coordinates, it won't, right? So relative to him the time will dilate differently but they will agree on how much proper time has elapsed for both of them. Correct me please if I'm wrong, and explain why I am. Thanks in advance.
  7. Apr 19, 2014 #6

    Simon Bridge

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    There appear to be a number of misunderstandings here...
    1. clocks do not "dilate time" - they just measure it.
    2. There is no absolute motion: in the frame of the "travelling" twin, the Earthbound twin is the "moving twin".
    3. The travelling twin observes the normal time dilation for the entire time the velocity is a constant.

    This is not correct.
    The travelling twin will observe the Earth clocks slow only during the constant velocity parts of the trip. During the turn-around, the Earth clocks speed up.
    This will happen no matter how the speed-up is calculated.

    This is also incorrect - the proper time is a matter of physics not mathematics.
    The clocks tick off however much time they do no matter what method we use to calculate it.
    They even tick off time when we don't do any calculations at all.
    The maths is just book-keeping.

    Thus the proper time is whatever the stationary clock measures.
    This does not depend on the coordinate system we use.

    I thin that D&G coordinates are not particularly useful - they just add to the problems of teaching special relativity instead of making some go away.
  8. Apr 19, 2014 #7
    @Simon, sorry for my bad language, I understand that motion nor time are absolute, I just want to know do moving clocks tick slower no matter what simultaneity convention we use, and do lenghts behave similarly regarding contraction. So do the Earth clocks behave at the same way regarding time dilation relative to the moving twin's frame, as if the lines of simultaneity are straight.
    Last edited: Apr 19, 2014
  9. Apr 19, 2014 #8

    Simon Bridge

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    I understand - I have to check though.
    A lot of misunderstandings come from not being careful with language, and that goes double for special relativity.

    That is right - as far as the inertial observer is concerned, moving clocks run slow even without having a formal convention for what counts as "simultaneous".
    In fact, time dilation and length contraction are commonly taught before "simultaniety".

    The linear convention is just a careful wording of what most people mean when they say two things happen at the same time.

    What the paper appears to be saying is that they can take some weird non-intuitive convention and give it the label "simultaneous" so that two events simultaneous in one frame will be simultaneous in all frames. But this convention of "simultaneous" is not particularly useful.

    The main thing here is to distinguish between physical and mathematical effects.
    Last edited: Apr 19, 2014
  10. Apr 19, 2014 #9


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    The physical phenomena are not conventional. The standard formulas for them are conventional. This is easy to see when using radar based simultaneity conventions (convince yourself of this).
  11. Apr 19, 2014 #10


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    Wow! Very well said.
  12. Apr 20, 2014 #11

    But what does this imply? I know, as all of you also know, the standard formula for time dilation and length contraction, and in the classical case scenario, the clock of the Earth twin ticks slower by a constant rate throughout the trip, the same applies to length which is contracted during the trip to a constant size. Using radar coordinates, or a different simultaneity convention, it seems that both agree how much time has passed for each one of them, but now time may not pass slowly by a constant rate throughout the trip. Please correct me if I'm wrong.
  13. Apr 20, 2014 #12

    Simon Bridge

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    But which time to the twins agree about?
    Are they the same age after the trip just because they suddenly decided to do their math by a different convention?
  14. Apr 20, 2014 #13
    They agree how much proper time has elapsed for each one of them. But really the question is do different simultaneity conventions affect length and time measurements for an inertial observer, or to say it better relative to his inertial reference frame.
  15. Apr 20, 2014 #14


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    One of the great findings in Einstein's famous 1905 paper was that one has to properly define what one means by measuring a distance in space or the time elapsed between two events. Due to the finite speed of light (or any other possible signal used to compare distant events) the simultaneity of events is a frame-dependent notion, i.e., two observers in relative motion (in special relativity the most simple case is, of course, unifrom relative motion) do not agree upon whether two events that do not take place at the same position are simultaneous or not.

    Thus, one has to define what one means by measuring the length of an object, and by the conventional definition as observer will assign the length of an extended object by reading the position of its end points simultaneously with respect to his clock. This implies, as is easily to calculate from the Lorentz-transformation formulas, that the length of a moving rod will turn out to be shorter than in its rest frame by the inverse Lorentz factor, [itex]\sqrt{1-v^2/c^2}[/itex].

    Another question is, how an object appears when you watch it flying by. Here the question is, whether you'd see an object which is a sphere in its rest frame as a length-contracted object, like an ellipsoid. The answer is clearly no! You see just a sphere. If painted somehow you'd see it rotated with respect to the same sphere if it was at rest. The reason is that the light reaching your eyes at a given instant of (your local) time from different points of the surface of the sphere was not emitted at the same time due to the finite speed of light. Thus you don't measure the diameter of the sphere along different directions in the sense of the length measurement defined above but you detect the light emitted at different times from its surface hitting your eye "now".
  16. Apr 20, 2014 #15


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    It doesn't imply anything. All observers agree on the invariant and finite two-way speed of light-time dilation falls right out of that as is intuitively clear. The actual formulas for time dilation simply depend on our convention for the one-way speed of light because we need a simultaneity convention to setup coordinates and relate global time coordinates of different frames.
  17. Apr 20, 2014 #16


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    When you measure the length of a moving object, you need to find the distance between the location of the front of the object at a certain time and the back of the object at the same time, by definition.

    If you change your notion of "at the same time", you change the measured length.

    For a stationary object, this won't be an issue.

    If you make a measurement of any time interval but proper time, you need two clocks, and the time difference between the two clocks depends on how you synchronize them. This implies that the time difference depends also on the synchronization.

    Proper time doesn't suffer from this issue, you only use one clock, so you don't need to concern yourself with the synchornization issue.

    Because different inertial frames have different notions of how clocks should be synchronized, the above affects are important when you change frames.
  18. Apr 20, 2014 #17
    @Pervect, @WBN, @vanhees, thanks for the answers. I have to examine them more closely but reading them quickly I think I got the point of eache of your 3 replies.
  19. Apr 20, 2014 #18

    Simon Bridge

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    Short answer:
    The way you define "simultaniety", the convention you chose, makes no difference the the the outcome of a physical measurement. The Universe does not notice or care about our conventions.

    Calculating some "radar time" or any other convention of time makes no difference to the amount of aging a twin undergoes before he next meets his brother.

    Long answer:
    You have to say what you mean by "measurements". How do the measurements happen? What measurement is important to the problem in hand?

    This is core to what the others have been saying.

    This is why the relativity lessons are careful to talk specifically about rulers and clocks and set up special clocks (light-clocks ferinstance) etc to illustrate the relationships they want to talk about.

    It's why the twins paradox statement ties the conventions of relativity to the amount of physical aging that a human being undergoes and why causality arguments talk about killing things. It's probably the toughest thing to grasp in special relativity: the need to be achingly and pedantically specific.

    However, whatever you are calling a measurement, whichever convention you settle on, to deserve the term "measurement", it has to be some physical process involving some sort of comparison - a ruler to a length etc. And it has to be done in some stated reference frame. You may define a convention to decide what process to use in your measurement but the actual measurement process itself is unaffected by that choice because the UNiverse does not care about our conventions.

    The naive convention is: when you ask someone to measure a time period - they look at their watch. When you ask someone to measure a length they get a ruler out and place it right next to the length to be measured. This is the starting point of where we get the idea of "proper" lengths and times from. It's what you get when you do an experiment in the lab.

    We can make some other convention - but, in order for the convention to be useful, we still have to be able to relate that to the results of experiments, and to human experience.


    1. Simple example - the unit of length is a convention - I am free to call anything I like a meter. I will get a different number of meters by changing the convention but the actual physical distance I have to walk is not affected by that. The physical length of the road is unaffected by the size of my meter-ruler.

    More to the point:
    2. In the twins paradox example - the aging process of the human body is a physical event. If you want to ask how much the twins have physically aged with respect to each other - then you have one kind of measurement. Expressing that in terms of "proper time" or anything else is the convention - the amount of physical deterioration,aging, the twins see when they look at each other when they meet up is independent of that convention.

    The twins may agree on a convention where they have a standard clock which ticks off the same amount for both of them ... in which case, they will notice that they age at different rates against that standard clock. But the same can be said for pretty much any clock. When they finally meet up, they still have the same difference in the amount of aging they have undergone.

    Well done.

    Your questions seem to indicate that you are making a common mistake called "mistaking the map for the territory".

    You need to separate the physical processes from the mathematical ones used to predict/calculate them.
  20. Apr 21, 2014 #19
    I think that time dilation which is in other words a different clock rate which depends on clock speed relative to the stationary system by the factor of γ, is separate issue to relative simultaneity, although somehow related by transformation equations.

    Relativistic simultaneity is the result of coordinate time dependency on distance from the 4 D coordinate system origin as seen in Lorentz transformation equations.

    Time dilation effects i.e. slower aging are lasting and irreversible after the relative motion stops and therefore unlikely to be the product of a convention while relativistic simultaneity effects cease to exist then.
  21. Apr 21, 2014 #20


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    Differential aging is an entirely different phenomenon from time dilation.
  22. Apr 21, 2014 #21

    Simon Bridge

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    ... so long as you realize that the term "stationary system" doesn't mean anything special here.

    I'm puzzled that you think real physical processes that are ongoing and irreversible, like aging, are just a matter of convention.
  23. Apr 21, 2014 #22

    I said aging in the usual sense of this word.
    The time dilation concept to my best knowledge applies to a time interval between two co-local events measured by the local clock in the moving system comparing to the corresponding interval of the stationary system. It must be relevant to aging as clock's age will be the time indication counted from 0.
    Let us consider a clock which is at rest with the moving system K'. The time t' which it indicates in K' is its proper time τ and we can put its coordinate x' equal to 0. It then follows from the inverse Lorentz transformation that t=τ/[itex]\sqrt{1-v^{2}/c^{2}}[/itex] hence clock time τ=t[itex]\sqrt{1-v^{2}/c^{2}}[/itex]

    I assumed the clock of the observer in the moving system started at synchronisation point t=t'=0 after acceleration to a velocity v had been completed.

    Let the stationary system predict the position of the moving clock at its own clock indication t and bring it to a halt and destruction level which retains last recorded time.
    It seems logical that the last recorded time on the clock is t[itex]\sqrt{1-v^{2}/c^{2}}[/itex] with an immediate conclusion the moving clock has aged less and the result is lasting and irreversible.
    Whether you call it dilation or differential aging it does not matter in this case
    Last edited: Apr 21, 2014
  24. Apr 21, 2014 #23
    This is a misunderstanding. I have said "unlikely to be the product of a convention" which when translated to common language means "is not". It is hard for me to say anything categorically about reality without at least a grain of doubt. Sorry if it was not clear enough
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