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Understanding simultaneity

  1. Mar 12, 2007 #1
    I've picked up relativity, again after getting frustrated. I'm new but I need help understanding simultaneity. I tried to read further but it seems to be very important to all of Einstein’s other arguments. So here it goes.
    In relativity, the special and general theory, P 30 about halfway through to the end of the page, Einstein talks about light how 2 beams of light will reach the midpoint from where they started given that they travel at the same speed. This I understand. Then he talks about how if you are on a train moving toward one of the beams of light from the midpoint that you reach one of the beams of light before the other, and there for it will not appear simultaneous. This to I understand and agree with. But then he says that this means that the two events occur at different times if you are on the train rather than the embankment. I don't understand this leap of understanding from it appears to be to it is. I keep thinking that this is true because you change the distance between two points and therefore are no longer at the midpoint. I would really appreciate someone explaining this.
     
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  3. Mar 12, 2007 #2

    pervect

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    Given that the speed of light appears to be constant to all observers (which appears to be true from all experiments that have been done), one must conclude from the result of the thought experiment that the notion of simultaneous events depends on the observer. Two events that are simultaneous according to the train observer are not simultaneous according to the platform observer.

    I'm not sure how much this helps, but you'll have to accept that simultaneity is relative if you want to get very far with relativity. The only missing step from your description is the constancy of the speed of light - hopefully you can see how that prevents your notion from working.
     
  4. Mar 12, 2007 #3
    But I was wondering... isn't this a characteristic of changing your location away from the midpoint... isn't this the case because you are closer to one beam as compared to the other? Because Einstein said that the definition of simultaneous was when two photons would reach the midpoint between their starting locations at the exact same time not a point that once was at the midpoint. Sorry for being a pain but I can’t except things on faith, it’s not in my nature.
     
  5. Mar 12, 2007 #4

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    Einstein actually chose this method of clock synchronization (via light signals) in order to preserve isotropy. He mentioned this in his 1905 paper, but only very briefly.

    An isotropic clock synchronization is a fair clock synchronization.

    In order to measure velocities, one needs two clocks, and a means of synchronizing them. One lays out a course of known length, and puts one clock on the "starting line" and another clock on the "finish line".

    one then takes the difference between the time at which one crossed the starting line (measured on the clock at the start line) and the time at which one crosses the finish line (measured on the clock at the finish line) as the elapsed time for the trip, and one computes the velocity as the length of the course (measured with a ruler) divided by this time.

    Only when the clocks are synchronized "fairly" will one correctly measure the trip times (and hence the velocity) to be the same going in one direction over the course (say east-west) as in the other direction (west-east).

    The point that Einstein makes is that the clock synchronization that fairly measures the velocities of material objects is the same clock synchronization that makes the speed of light constant.

    This doesn't actually require "faith", it can be tested by experiment.

    For instance, one might say that for an object of a known mass, the clocks are synchronized properly when an east-west moving object of mass m has an equal and opposite momentum to a west-east moving object of mass m, such that they have a net velocity of zero when they collide.

    There are other methods of defining "fair" clock synchronization, including a comparison of "rapidity" measurements using only one clock to "velocity" measurements.

    A rapidity measurement requires a clock on the moving object. (this is possible for a physical moving object, but it's not possible to put a clock on a light beam, for instance). A fair clock synchronization scheme requires that a clock that transverses a course in a certain fixed amount of time E-W and the same fixed amount of time W-E as measured by an "onboard" clock also have equal trip times E-W and W-E using the "two clock" method.

    Because of relativistic time dilation, the times measured by the one-clock method (rapidity) and the two clock methods won't be the same. What is important is that the relation between the one-clock and two-clock methods is independent of the direction chosen, i.e. that the relationship is isotropic.

    As a consequence of this, and the constancy of the speed of light (also experimentally confirmed), the conclusion that a "fair" clock synchronization depends on the frame of reference can't be avoided.
     
  6. Mar 12, 2007 #5
    Note that a light beam already has a pretty good "clock" on board, namely the period of the wave of the photon. And the behaviour of this "clock" is completely consistent with relativity, it stands still between two events. :smile:
     
  7. Mar 12, 2007 #6
    wave as a clock

    Please let me know if you have seen that interesting idea mentioned or used somewhere. Thanks
     
  8. Mar 12, 2007 #7
    Honestly I do not remember ever seeing this particular illustration.

    In an Einstein synchronized frame of reference the photon is everywhere at the same time on the emission's line of simutaneity, i.e. the line following the direction of the photon. So then it follows that each observer on that line encountering the photon would have to measure the same phase of the wave.

    But, I would not mind to be proven wrong. :smile:
     
  9. Mar 12, 2007 #8

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    The wavelength of a beam of light is more of a measure of length than time. You can certainly use a "light clock" to keep time, but one can convert the natural "length" measurement of the wavelength into a time only by dividing by the speed.

    It turns out, of course, that the speed of light is constant, so there is a natural and constant conversion from wavelengths to times,

    Since I was trying to explain a bit about how we measure speed, it would have been a bit premature to assume without proof that the speed of light is constant. This is what we are trying to demonstrate, and to do this I think we should take an approach to defining clock synchronization that doesn't involve light signals at all, but only physical arguments about the "fair" way to synchronize clocks to insure a "fair" (isotropic) measurement of speed.
     
  10. Mar 14, 2007 #9
    I think I understand now... though not necessarily what you were saying... I think that what I was missing was the fact that Einstein just means that it appears to be at different times even though it really is simultaneous.
     
  11. Mar 14, 2007 #10

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    Ummm - nope, the point you should be getting is that there isn't any universally valid way to synchronize clocks.

    It's not just a matter of appearances.
     
  12. Mar 14, 2007 #11
    Couldn't you figure out the distance between things using simple trig. or a second reference followed by a few simple calculations by dividing the distance between you and the two given clocks by the speed of light compared to the time lapse? and does that not imply that there is in fact a universal view?
     
  13. Mar 14, 2007 #12
    clock synchronization

    Is there special relativity without clock synchronization?
    If observers located in an electromagnetic wave use the periodic e.m.
    oscillations as clocks should clock synchronization be involved?
    Consider the questions as rised by a humble physicist interested in teaching SR. Thanks
     
  14. Mar 15, 2007 #13
    I think I get it now and you can forget the universal view thing I said before... I found aphysics proffessor to explain it to me, and I think I understand now.
     
  15. Mar 15, 2007 #14
    Yes of course there is.

    Only if we insist on a kinematic and dynamic model where particles move in space over time we have to suffer "headaches" about clock synchronizations, spatial contractions and time dilations etc.

    However, if we view the relationships between particles from a space-time perspective, we don't need these.
     
  16. Mar 15, 2007 #15
    without clock synchronization?

    Please be more specific concerning your last sentence. Could you direct me to some literature? Thanks
     
  17. Mar 15, 2007 #16
    For instance when you insist on using 4-vectors and proper properties only you avoid relativistic confusion.

    There are no things like length contraction or time dilation for a 4-vector. You can define (in flat space) things like a space-time interval, velocity, acceleration, force and energy-momentum as 4-vectors and the nice property is that they are Lorentz invariant.
    Obviously you can do the same in curved space-time but then you need a bit more than 4-vectors.

    4-vectors are discussed very widely in the literature. A textbook example, relevant to relativity, which I particularly like for its transparency and being well organized, is 4-Vectors by David Morin, not a professor (yet?) from Harvard.

    He even includes a limerick:

    God said to his cosmos directors,
    “I’ve added some stringent selectors.
    One is the clause
    That your physical laws
    Shall be written in terms of 4-vectors.”

    :smile:
     
    Last edited: Mar 15, 2007
  18. Mar 16, 2007 #17
    Some relationship among clocks is necessary, but no particular relationship is inherently preferred. Synchronization of clocks at separate locations depends on establishing a convention for relating signals exchanged over distances with the readings of stationary clocks. The bottom line is that the proper interval will be invariant among all synchronization conventions.
     
  19. Mar 16, 2007 #18
    clock synchronization compulsory

    Thanks. As far as I know the construction of a four vector involves time dilation which at its turn involves clock synchronization at least in one of the involved reference frames. Am I right?
    Please give me an access to all the book by Morin.:smile:
     
  20. Mar 16, 2007 #19

    George Jones

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    In the URL, change "ch12" to any chapter at which you want to look.
     
  21. Mar 16, 2007 #20
    Why is it necessary?
    Can you give me an example where you think we need it?

    Apart from answering meaningless questions like "what time is it, right now, on Andromeda" I do not see any need whatsoever.
     
    Last edited: Mar 16, 2007
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