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

One-way tests of special relativity

  1. Sep 12, 2012 #1
    Assume Lorentz Aether Theory (supposedly equivalent mathematically to special relativity.)

    Lorentz considered there to exist an aether, with some stationary reference frame (though he considered it to be undiscoverable).

    Assume that the frame of reference in which the Cosmic Microwave Background Radiation is uniform is the stationary aether reference frame.

    Now a thought experiment (and - QUESTION #1 - I'd like to know if anything comparable to it has already been conducted).

    Let's consider ourselves to exist on a planet moving at constant velocity with respect to the aether. (The earth may be a reasonable facsimile.) We launch two identical rocketships, one going directly upstream against the aether, and the other in the opposite, downstream direction, such that the latter is now stationary in the aether frame. QUESTION #2: Do clocks on the former rocketship move more slowly, and those on the latter speed up?

    I strongly suspect the answer to this last question (#2) must be "no" (else an absolute reference frame *would* be discoverable), but I'd like to know the answer to #1 as well.
     
  2. jcsd
  3. Sep 12, 2012 #2
    #1 - Yes.

    #2 - No. Place an observer at rest with what is considered to be an aether frame. All observations will be as SR, with both of the ships time dilating and length contracting with their relative speed to the aether frame accordingly. Then have the two ships measure each other's time dilation with respect to what the stationary observer sees they must measure according to what the stationary observer observes of their rulers and clocks. The two ship observers will measure the same speed of each other, the same length contraction of each other, and the same time dilation of each other, same as SR.
     
  4. Sep 12, 2012 #3

    ghwellsjr

    User Avatar
    Science Advisor
    Gold Member

    You cannot observe or measure time dilation. It is calculated based on the selected reference frame and can be different for every reference frame. If you could observe or measure it, then you could identify the rest state of the aether.
     
  5. Sep 12, 2012 #4
    This is just SR, but one can indeed directly observe and measure time dilation. Ship A passes a single clock in frame B. Ship A records the time as the single clock directly passes the front of the ship and the time that the single clock passes the back of the ship, and also notes the readings on the single clock as it coincides with each of ship A's own two clocks at the front and the back. Ship A will observe that less time has passed upon the single clock than the time that passes between ship A's own two clocks. Ship B performs the same thing and observes the same.

    The reason is that two clocks must be used to measure the time that passes upon a single clock in motion, and while a frame says that their own clocks are synchronized, another frame says they are not. Each frame says that their own two clocks are synchronized and less time passes upon a single clock that passes by, while the other frame says that less time passed upon each of the first frame's two clocks, but that the first frame only measures a greater time between the two clocks because the first frame's clocks are not synchronized, with the back clock set to a greater time than the front clock, so measuring a greater time rather than lesser.
     
  6. Sep 12, 2012 #5

    PAllen

    User Avatar
    Science Advisor
    Gold Member

    All you have measured this way is a consequence of Einstein clock synchronization (used for the two clocks). Strictly, Doppler and differential aging are direct measurements; time dilation is not and is subject to convention both in SR and GR. Speaking of objective time dilation between distant observers is even more absurd (as opposed to speaking of Doppler and/or differential aging between paths that separate and come together).
     
  7. Sep 12, 2012 #6
    Well, right, it depends upon the convention for how one synchronizes clocks within frames. There is no absolute method for synchronizing clocks, so there is no absolute amount of time dilation that must be measured, no, but after having synchronized the clocks within each frame by some method, time dilation can be directly observed and measured between clocks as they coincide in the same places. That is all I am saying, although I am also considering the standard Einstein simultaneity convention where all frames measure c in my example where both frames measure the same thing. I'm not sure which ghwellsjr is referring to in terms of an aether.
     
  8. Sep 12, 2012 #7
    Certainly in the case of differential aging between paths that separate and come together, there is no way to meaningfully determine the relative rates at any point during passage. Which clock is faster is purely frame dependent.

    But regarding two clocks at different potential elevations in gravity, this does not seem to pertain.
    With the single condition of identical clocks at all locations , without arbitrary adjustment of rates, it appears to me that all frames would agree the clock at the higher potential was running faster.
    Simplest scenario: both clocks on the same radial path in gravity.
    A parallel path in flat space. All inertial frames on this path would agree the higher clock was running faster, independent of their speed, direction or synchronization convention.

    DO you see a reason this would not be the case?
     
  9. Sep 12, 2012 #8

    PAllen

    User Avatar
    Science Advisor
    Gold Member

    This is actually a measure of Doppler, as I define it. O1 sends time information to O2 as a sequence of signals defined by a physical mechanism (a light wave is just a form of this). The ability to define a 'time dilation as a function of positions' is unique to sufficiently static observers in a sufficiently static geometry. Given this you can (but are in no way required) choose to factor Doppler between different world lines into 'gravitational' and motion dependent. However 'gravitational' just means Doppler between colocated static observers. You are able to gloss over the arbitrary nature of simultaneity precisely (and only) because of the static character of the metric.

    Thus, this way of looking at things is a very special case in general GR scenarios, and one that some authors (and I) therefore thing should be discouraged.
     
  10. Sep 13, 2012 #9

    PAllen

    User Avatar
    Science Advisor
    Gold Member

    With these caveats, ok However, I prefer gwelljr's ways of looking at it: time dilation is a computed, conventional, quantity. Differential aging and Doppler are unambiguous physical measurements. Just as two way light speed measurement is unambiguous, while one way lightspeed can not be separated from simultaneity convention.
     
  11. Sep 13, 2012 #10

    ghwellsjr

    User Avatar
    Science Advisor
    Gold Member

    The OP of this thread asked us to assume the existence of aether and then asked about the clocks on two rocketships, one stationary in the aether and the other traveling. According to Lorentz Aether Theory, the stationary clock keeps track of true absolute time and is not, therefore, time dilated. The moving clock is time dilated and runs slow. However, as you correctly pointed out, the observers on each rocketship make all the same measurements of the other ones clocks and rulers, however, I was pointing out that those measurements do not include time dilation. If they did, they each would be able to determine which one was time dilated and which one was not, therefore being able to identify the rest state of the aether.

    Look at it this way: consider a single observer with a clock. In his rest frame, his clock is not time dilated. In a frame traveling with respect to him, his clock is time dilated. Can he tell any difference in the two situations? No, because he cannot measure time dilation. He can calculate it based on the different reference frames but those different reference frames do not in any way affect any of his measurements or observations.
     
  12. Sep 13, 2012 #11
    Yes of course: the phenomenon of time dilation can be observed - it's one of the confirmed predictions of SR, in disagreement with classical mechanics. And the amount of time dilation that one measures the other to have is a matter of convention/perspective. Moreover, how one exactly phrases this may depend on what one exactly means with "time dilation". :tongue2:
     
  13. Sep 13, 2012 #12
    This is very much a matter of formulation - and I don't find mine in the existing answers. So I'll add mine too. :tongue2:
    OK - in SR terms we can designate a CMBR based "stationary frame" and label it "the aether".
    Somewhat yes, see:
    http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html
    The answer on your second question (based on your assumptions), is Yes:

    a. Based on your assumption that the latter ship is now in True Rest (at rest in a true "stationary" frame), you must conclude that its clocks have sped up.
    b. On the other hand, if you assume that the first ship is now in true rest (so that you define another inertial frame as "stationary frame"), then it's the other way round.
    c. And if you assume that the Earth happened to be stationary at that time, then clocks on both ships have slowed down according to your assumption.
    That claim (starting with "else") is wrong, as nobody can determine if any of these assumptions is right.
     
    Last edited: Sep 13, 2012
  14. Sep 13, 2012 #13

    ghwellsjr

    User Avatar
    Science Advisor
    Gold Member

    So what exactly do you mean by "time dilation"?

    Time dilation refers to the slowing down of a moving clock (or time for any moving object) as determined by an inertial reference frame. It is a function of the speed of that clock/object as determined by that inertial reference frame. It is the ratio of a unit of time of the moving clock to the same unit of coordinate time. However, we usually like to talk about its reciprocal which is the ratio of the tick rate of a moving clock to the tick rate of the coordinate time. Pick a different inertial reference frame and the speed of the clock/object and therefore the time dilation is different. These are not observations or measurements.

    Any observer making an observation or measurement of any clock, either local or remote, either moving or stationary with respect to him will make the same observation or measurement no matter whether or not he is considering any reference frame. Reference frames have no influence on what observers observe or what they measure.

    Furthermore, any observer can use any reference frame they want to calculate the time dilation on any clock, local or remote, moving or stationary and it will be consistent with all observations and measurements.

    If you disagree with any of this, please provide a precise definition and an example.
     
  15. Sep 13, 2012 #14
    Yes indeed, I understand the same with it. Do you claim that "time dilation" as thus defined is not a predicted and verified phenomenon? :uhh:
    - http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

    At face value I disagree with some of the other things that you wrote, but I'm not going to distract from the topic by participating in what is likely a discussion over words (and others, please abstain too!)
     
  16. Sep 13, 2012 #15

    ghwellsjr

    User Avatar
    Science Advisor
    Gold Member

    In section 4 of Einstein's 1905 paper introducing Special Relativity, he asked the question, "What is the rate of this [moving] clock, when viewed from the stationary system?" He then derived the equation for the time on the moving clock, τ, as a function of the coordinate time, t, and the speed, v, of the moving clock, τ=t√(1-v2/c2) and then predicted that if you start with two clocks with the same time on them and take one of them on a curved path with speed, v, that eventually returns to the first clock that remained inertial, it would have a lesser time on it as predicted by his formula. This is the differential aging that PAllen mentioned in post #9. PAllen also mentioned Doppler.

    These are both measurements that are made independent of any particular reference frame. Both differential aging and Doppler require the proper formula for time dilation to arrive at the correct predictions of those measurements. But you can use any reference frame, not just the one in which the inertial clock is at rest or in which a Doppler observer is at rest to arrive at the correct predictions. In these other reference frames, the inertial clock can be time dilated and the moving clock can be time dilated in a different manner and the Doppler observer can view an object with different time dilation but the final outcome is the same.

    This is the whole point of Relativity. You can use any reference frame to make valid predictions about the measurements and observations that can be made and they all yield the same final results. But they can all yield different calculations for the time dilations but this has no bearing on what anyone can observe or measure.
     
  17. Sep 13, 2012 #16
    Time dilation is relative, yes, particular to the frame of reference that measures it, and dependent upon how clocks are synchronized, as are length contraction, RoS, speed, etc. Doppler is also frame dependent, but since it only requires a single clock within each frame to measure it, it is independent of the simultaneity convention. None of these things are absolute with or without an "absolute" aether frame, however, so I'm still not sure what you mean by stating that we would be able to identify the rest state of the aether, as the mathematics is still SR, dependent upon the frame of observation, which is relative.

    EDIT TO ADD - In your second paragraph, you are attempting to use a single clock to measure time dilation. A single observer with a single clock cannot, however, you're right about that. It requires two clocks within a frame to measure time dilation. Therefore it also depends upon how the two clocks within the observing frame are synchronized, but time dilation can be directly measured after performing the synchronization procedure.
     
    Last edited: Sep 13, 2012
  18. Sep 13, 2012 #17

    ghwellsjr

    User Avatar
    Science Advisor
    Gold Member

    First off, Doppler is not frame dependent and it requires two clocks (or their equivalent), a local one and a remote one. Doppler is the ratio of the observered tick rates of two clocks (or their equivalent).

    But to the main point: you say that time dilation is relative to the particular frame of reference that measures it. How does a frame of reference measure anything? Please describe what instruments you have in mind to make this measurement and how it is accomplished. I keep saying that time dilation can't measured or observed and you say that it can be. So please tell me how.

    If you can do that, then it will be obvious how to identify the rest state of the aether.
     
  19. Sep 13, 2012 #18
    Sorry, I edited my post after you posted apparently. Doppler only requires a single clock within each frame so is independent of synchronization procedures which only apply to two or more clocks within the same frame. It is frame dependent because light that is emitted by a frame will be measured to have a frequency that is dependent upon the frame that measures it.

    I explained how time dilation is measured earlier, but I will do so again, sure. Clocks within each frame are synchronized by some procedure, let's say the Einstein simultaneity convention. We have a ship A in an observing frame with two clocks, at the front and back of the ship. Clock B passes the front of the ship and we record the times upon clocks A_front and B1 as they coincide. Clock B travels along the ship to the back and we record the times upon clocks A_back and B2 as they coincide. B1 and B2 are the recorded readings upon clock B at the front and back of the ship. The time dilation ship observer A measures of clock B, then, is (B2 - B1) / (A_back - A_front). It is still relative, so the rest state of an aether cannot be identified from this.
     
  20. Sep 13, 2012 #19

    ghwellsjr

    User Avatar
    Science Advisor
    Gold Member

    I can see why you are having trouble understanding what I am saying because you seem to think, at least you talk like, clocks can only be stationary in a frame.

    For example, when talking about Doppler, you said (in post #18) that "Doppler only requires a single clock within each frame" and then you said "light that is emitted by a frame will be measured to have a frequency that is dependent upon the frame that measures it". You describe these two frames as one that emits light and another frame that measures it.

    Another example, when talking about two ships, you describe ship A as being in the observing frame A while frame B is for the time dilation ship B.

    You should think in terms of a single inertial frame with an infinite number of imaginary (as Einstein called them) coordinate clocks at every possible location. Now you can think in terms of a single physical clock that is moving at any speed and talk about its time dilation. Same thing for Doppler--two clocks moving apart or towards each other, each with an independent speed in the frame. Same thing for two ships--one stationary and the other moving or both moving, it doesn't matter. In each case, the time dilation for each observer/clock/ship is only dependent on its speed in the frame but the measurements and observations they make are independent of the frame that is used.
     
  21. Sep 13, 2012 #20
    Right, clocks within an inertial frame are considered stationary to that frame. We can fill the frame up with stationary clocks placed everywhere, yes, and we will need to use two or more of those clocks to actually measure time dilation, the clocks separated over a distance with the readings of each considered separately, not as one overall clock, which is why it is also synchronization dependent. The time dilation measured of a moving clock is the ratio of the time that passes upon that clock, the difference between readings, to that between the stationary clocks that coincide in the same places that the moving clock happens to be.

    As for measurements and observations being independent of the frame, I suppose you mean that all frames will agree upon the measurements that a particular frame will make, the actual readings upon that frame's rulers and clocks. That is fundamentally true, so it would not be saying anything about what is meant by measurements being frame dependent. The measurements themselves still depend upon the frame making the measurements. All frames will agree upon what measurements a particular frame makes, but each frame will themselves measure things differently.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook