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   sci.physics.research      Current physics research. (Moderated)      17,516 messages   

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   Message 16,656 of 17,516   
   richalivingston@gmail.com to Nicolaas Vroom   
   Re: The rigid rod paradox with 8 clocks.   
   14 Nov 19 20:51:24   
   
   Nicholaas,  See my commentary below:   
      
   On Wednesday, November 13, 2019 at 10:26:30 AM UTC-6, Nicolaas Vroom wrote:   
   > Consider a rod with 8 clocks, equally spaced, a distance l apart.   
   > The rod is considered at rest. This implies that the speed of light c=20   
   > in all directions is the same. We call this rule 1.=20   
   > The clocks are numbered from #1 to #8.   
   > The strategy is to perform a certain number of experiments.   
   >=20   
   > The first experiment is called clock synchronisation.=20   
   > Halfway in between clock #4 and #5, there is a light source which emits a=   
   =20   
   > reset signal. The setup is such that the length lightpath to each clock i=   
   s   
   > the same. Using rule 1 the light signal will reach all the clocks simulta=   
   neous.   
   > This is important because all the clocks at any moment will all show the =   
   same=20   
   > count.   
      
   As stated this implies the clocks are in a circle.  If they were in a strai=   
   ght line they could not all be the same distance from the source of the lig=   
   ht pulse.  However I accept that the clocks can be synchronized with the re=   
   sult you state by using a slightly more elaborate procedure.   
      
   >=20   
   > The second experiment starts with making an exact copy of rod #1. Also   
   > attached to each clock there is an engine which can be fired with a stand=   
   ard   
   > burst in either the forward or backward direction. Each clock also has   
   > an observer.=20   
   > The second experiment consists that each observer on rod #2 fires his eng=   
   ine   
   > with a standard burst in the same direction when his clock is reset.=20   
   > This burst will give the rod a certain speed v.   
   > The now moving observers will perform the next tasks when they reach the =   
   next   
   > clock at rest: They will write down the reading of the clock at rest and   
   > the reading of their own moving clock.=20   
   > This is the result:=20   
   > They are the same for all observers. The number of counts of the moving   
   > clocks is less than the number of counts of the clocks at rest.   
   > This is not so strange because it means that the physical forces which   
   > influence the behaviour of each clock are identical. Specific what this   
   > means is that all the moving clocks stay synchronised. This is rule 2.   
   > You can repeat this experiment, but still, rule 2 applies.=20   
      
   This is where you are misunderstanding SR.  You are applying an impulse to =   
   each clock/observer on rod #2 and the result is that each clock/observer is=   
    instantaneously accelerated to some speed, and they all start at the same =   
   time in this frame.  Also, in this frame, they remain the same distance apa=   
   rt and synchronized as you say, BUT ONLY IN THIS FRAME.  In the frame of th=   
   e observers on the accelerated clocks the other clocks are no longer synchr=   
   onized, and the spacing between the clocks on rod #2 is no longer the same =   
   as on rod #1.   
      
   >=20   
   > Experiment 3 is almost identical to experiment 2. That means all   
   > the engines are fired after the reset signal is received.   
   > This defines the starting condition of experiment 3. The starting   
   > condition of experiment 3 is a moving rod with the speed v.   
   > Experiment 3 involves that a certain moment the light signal between   
   > clock #4 and #5 of the moving rod issues a reset signal.=20   
   > Like before the moving observers write down the results when they reach   
   > the next clock at rest. This is the result:   
   > All the observers write down the same number of counts for the clocks   
   > at rest. For the moving clocks, the results are different. The clock   
   > in front will have the lowest count. The clock at the back the highest   
   > count. Physical the clock in the back is reset the first.=20   
      
   This experiment is not so clear what you intend.  I believe you are saying =   
   that rod #2 is initially moving as speed v and that when alongside rod #1 t=   
   hat the engines are fired "simultaneously" to cause rod #2 to stop alongsid=   
   e rod #1.  It is important to be clear what you mean by simultaneous, i.e. =   
   in what frame are they simultaneous?  If in the rod #1 frame, and if rod #2=   
    was accelerated as in experiment #1, then yes, all the clocks will show th=   
   e same time differences.  But be aware that the engines are not being fired=   
    simultaneously in the moving rod #2 frame.  Nor is the initial spacing bet=   
   ween the clocks on rod #2 in the moving frame the same as on rod #1 measure=   
   d in its rest frame.   
      
   >=20   
   > Experiment 4 is the same as Experiment 3 with the difference that   
   > we again make an exact copy of rod #2 before the reset signal is issued.   
   > This is rod #3.=20   
   > The extra complication is that in experiment 4 both the moving rod #2=20   
   > and #3 receive the same reset signal.=20   
   > The next complication is that when each of the clocks of rod #3 receives =   
   a=20   
   > reset signal also the engine is fired in the same direction as experiment=   
    #2.   
   > However, this will also give a physical complication, because the engine   
   > in the back will start first and in front of the latest. As such the phys=   
   ical   
   > forces will try to compress the rod.=20   
      
   You don't mention, and maybe are not aware, that in experiment 1 that rod #=   
   2 will be stretched, under tension, immediately after firing the engines th=   
   at accelerated the rod.   
      
   > The opposite case is also possible. That means physical forces will try t=   
   o   
   > expand the length of the physical rod.   
   >  =20   
   > Experiment 2 belongs to what you can call a symmetrical experiment.   
   > This is the case if you start from a state at rest than in either directi=   
   on=20   
   > the results are the same i.e. how higher the speed how slower the=20   
   > moving clock ticks.   
   > What is also the case, after reaching a certain speed and the speed is=20   
   > decreased the clock starts to run faster until the speed reaches zero.   
      
   I'm not following what you are intending to say here.  If you are seeing so=   
   me inconsistency, that is because you are not appreciating all the effects =   
   of the accelerations and SR.  Rod #2 will be stretched immediately after th=   
   e impulse and, in the frame moving with rod #2, the clocks will no longer b=   
   e synchronized IN THAT FRAME.  They will remain synchronized in the rest fr=   
   ame of rod #1 however, and will continue to be spaced the same distance, un=   
   til the stiffness of rod #2 pulls the clocks back to their "normal" spacing=   
   .  There are three effects:  time dilation, change in synchonization and ch=   
   ange in spacing.  If you correctly understand all of these there is no para=   
   dox or inconsistency.   
      
   >=20   
   > Experiment 4 belongs to what you can call an asymmetrical experiment.   
   > This is the case when the starting condition involves a moving rod.   
   > In that case when a clock receives a burst in the same direction as the   
   > original speed the clock will start to run slower.=20   
      
   [continued in next message]   
      
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