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Different Clock Rates Throughout Accelerating Spaceship 
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#55
Feb513, 05:57 PM

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You've got boulders expelled by identical springs at t0 per starting rest frame. This means they must be the same distance apart and moving at the same speed per this starting rest frame. If they each expel another boulder at t0+1 per their own watches (which are still in synch per the rest frame (but slow), but not per each other), again their speed and distance and clocks are in synch per the starting rest frame. Per each other, their clocks are out of synch and they have moved further apart. 


#56
Feb513, 07:13 PM

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Either I went wrong somewhere, or else this cannot be situation #2. 1) Once both boulders *begin* to be pressed backward, both vehicles are in motion. 2) From that moment on, moving wrt the rest frame, their clocks appear out of synch in the rest frame. 3) Therefore, the final moment of boulder release from the spring will be different between the vehicles as seen by the rest frame. I am describing the case where the apparatus, the program, the intent of the two vehicles is the same, but I think that they end up out of synch at then end of the acceleration period, as seen in the rest frame, therefore we can't in a general way say that they have "accelerated in exactly the same way in the rest frame." The intended so, they began so, but because the acceleration takes time, and they are moving during that time, they have not ended up so. They *began* accelerating in exactly the same way in the rest frame. They entire acceleration process did not take place in exactly the same way in the rest frame. 


#57
Feb513, 07:22 PM

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#58
Feb513, 07:33 PM

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#59
Feb513, 07:36 PM

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#60
Feb513, 07:59 PM

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ok. thanks.



#61
Feb513, 11:59 PM

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How do they determine these effects within the frame??? Measure relative clock rates and distance?? 


#62
Feb613, 08:35 AM

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ok hope this is ok for this same thread. I'm moving in a more basic direction for understanding acceleration+SR:
For two intertial frames in relative motion, we can use gamma to describe how each observer measures the other's clock speed. Complete parity. Closely related to relativity of simultaneity. Fine. Given an inertial frame RF, and someone moving in a circle AF at velocity v with associated Lorentz gamma, as far as I understand, RF still use gamma to determine rate of AF's clock? what will AF use for RF's clock  1/gamma ? 


#63
Feb613, 08:38 AM

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They can detect time difference between front and back clocks by exchanging signals. 


#64
Feb613, 08:49 AM

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There are different philosophy's on this. To understand anything accelerating observers will measure (including see or photograph), it is simplest just to use any convenient inertial frame. The results of observations are invariant. To try to come up with a frame for the accelerating observer, you run into the same issues as in GR: there is well defined local accelerated frame, just as there are well defined local frames in GR. However, there is no global frame for an accelerated observer in SR, just as there are no global frames in GR. What you can do, if you insist, is set up a coordinate system in which the accelerated observer remains at fixed coordinate position. Such a coordinate system may not be able to cover all of spacetime. Unfortunately, there are many ways to do this, none preferred. Once you have defined such coordinates (via transform from inertial frame), you can compute the metric in them. Then, using the metric, you can compute time dilation etc. per this coordinate system. It won't be as simple as a constant in place of gamma. The constant gamma results from the fact that the metric in the inertial SR frame is diag(1,1,1,1). With a metric that varies by position and time, you need to integrate contraction of metric with path tangent vectors, instead of having a simple constant. The up shot of all this is that there is no (preferred) answer to your question (what does the accelerated observer use in place of gamma?). It depends on what coordinate system you set up. On the other hand, let me stress again, if you want to know anything about what the accelerated observer measures or sees, just compute this in any convenient inertial frame. 


#65
Feb613, 09:09 AM

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What RF calls gamma can be used to determine the click speed on AF and its inverse can be used to determine RF's click speed measured from AF. I mean if RF measures one second while AF is making a revolution, and RF find AF's clock to have moved forward by .5 second, then it's a given that AF will find RFs clock to have clicked twice as fast as his own. I just want to verify it is this simple. I don't see how this can't be true. 


#66
Feb613, 09:19 AM

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For AO, the behavior they see on clocks in the inertial frame depend on where in the inertial frame they are, and the visual rates vary in time. That is, the observed behavior of inertial clocks will be both position and time dependent. The rates on these clocks averaged over time will show them (per the AO) to fast compared to AO clock. It is true that for pure circular motion at constant speed, the averaged rate seen on the inertial clocks will be gamma (as determined by RF) times faster than AO's clock. 


#67
Feb613, 09:27 AM

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#68
Feb613, 09:33 AM

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#69
Feb613, 09:46 AM

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1) for uniform linear motion, gamma is purely "subjective"  nobody's clock is moving slower than anyone else's in a meaningful way. it is all wrapped up with planes of simultaneity. 2) for uniform circular motion, gamma gains a clear "objective" meaning  RF can use it to describe *all* of AO's time dilation, and AO can use the inverse to describe *average* time antidilation of RF. It is similar to the gravity situation where there are agreed differences in time dilations. 3) The next part is harder for me to work out  the linearly accelerating observer  how RF and AO can measure their relative clock speeds. I gather than RF can calculate AO's relative time dilation by simply integrating ever changing gamma with ever changing velocity? But to ask how AO determines RF's clock speed, this situation is neither the simple 'subjective' or 'objective' case above. 


#70
Feb613, 10:22 AM

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For AO, this simple example raises one of the SR concepts difficult to grasp on first encounter. This is the so called Rindler horizon. If you try to ask about how AO would model RF clocks by factoring out light delay using some simultaneity convention, you face the following observation: RF clocks that AO is accelerating away from appear to red shift until they disappear, at a fixed distance behind the AO. Any RF clock further away cannot be seen or communicate in any way with the AO, so mutual clock comparison is impossible. Note that there is a one way aspect to this (as for all horizons): any RF clock can eventually receive a signal from any point in AO's history; however, there is a last time, for every clock in RF, after which it cannot send any signals to AO. Visually, you can certainly say the case is more like your (1): any clock at rest in RF and AO's clock each eventually see the other clock freezing and red shifting to infinity. 


#71
Feb613, 10:37 AM

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For normal SR we can use gamma for both observers to determine that they see each other's clocks as ticking slower by gamma. This works for clocks they are passing or any other clocks in either frame.
I understand that it becomes more complex doing this between RF and AO for remote clocks, so I would just wish to focus on RF clocks being passed by the AO observer, all of which are deemed simultaneous and synchronized by RF. RF uses integrating gamma to watch AO's single clock continually slow down relative to the RF network of clocks as v and gamma increase. What does AO decide passing these RF clocks. How fast does this network of RF clocks tick? The same method? 


#72
Feb613, 11:12 AM

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To try to create an symmetric situation for AO, we need a configuration of coaccelerating clocks, with one RF clock going past them. For this, we have to decide the acceleration profile of each clock, and also how to synchronize them. For the latter, unfortunately, there is no preferred approach (what is special about inertially comoving clocks is that any reasonable synchronization procedure produces the same result; this is not true for a family of accelerating clocks. In particular, Einstein clock synch using light signals, and Born rigidity based simultaneity, disagree.) I urge you to focus on questions about what AO observes, and stop trying to treat AO as defining a frame of reference. 


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