From: nicolaas.vroom@pandora.be   
      
   On Thursday, 28 May 2020 20:14:03 UTC+2, Tom Roberts  wrote:   
   > On 5/25/20 8:38 AM, Nicolaas Vroom wrote:   
   >   
   > > What is the reason that you cannot use one reference frame for the   
   > > whole experiment from start to finish i.e. when both clocks again   
   > > can be compared at point O?   
   >   
   > There is no such reason, and my discussion explicitly showed using the   
   > inertial frame of A for the entire analysis.   
      
   In fact, there are two issues:   
   1) Is it wise to select only one reference frame?   
   2) Which is the best reference frame to select?   
   Apparently you agree with issue 1.   
   I would prefer point O, as indicated in the text.   
      
   > >> T = \integral sqrt(1-v^2/c^2) dt   
      
   > > My understanding is that t represents the time (clock count) of a   
   > > clock at rest and T the (time) clock count of a moving clock.   
   >   
   > Not quite. t is the time coordinate of the inertial frame,   
      
   This raises a new question: What is the difference my 't represents the   
   time of a clock in a reference frame' versus 'the time coordinate of   
   the inertial frame'   
      
   > So it is clear that the time coordinate   
   > of the inertial frame is the same as the elapsed proper time of a clock   
   > at rest in it (reset the clock to zero at t=0). They are conceptual   
   > different but numerically equal.   
      
   My philosophy is to use as many concepts as possible   
      
   > 	A clock can only indicate its proper time, and only   
   > 	along its worldline; the time coordinate of an inertial   
   > 	frame can indicate the frame's coordinate time anywhere   
   > 	the frame is valid. Of course, such coordinates are   
   > 	models, and to implement them requires physical clocks   
   > 	located where events of interest occur; all such clocks   
   > 	must, of course, be synchronized to the coordinate time.   
      
   That means IMO that all the clocks should be synchronized with   
   one standard clock. IMO at the origin O   
      
   > > The question is how is v (the speed of the clock) measured?   
   >   
   > In the usual way: v=dx/dt, where x(t) is the position of the object at   
   > time t, and t is the time coordinate of the inertial frame.   
      
   In practice, this means that t is the time of the nearest physical clock.   
      
   > > IMO in order to do that, you need a reference rod in the frame at   
   > > rest with two clocks at backend x1 and the frontend x2 of this rod,   
   > > also at rest. When you do that you can calculate the speed v by   
   > > applying the following formula: v = (x2-x1) / (t2-t1) where t1 is   
   > > the time that the moving clock coincides with the backend x1 and t2   
   > > the time that the clock coincides with the front end x2 of the   
   > > clock.   
   >   
   > That works, too.   
   >   
   > Note this is a gedanken, and we implicitly presume that when we use a   
   > given inertial frame, we can identify its coordinate values for all   
   > events of interest. This, of course, includes the events occupied by the   
   > clock as it moves around.   
      
   IMO this is not a gedanken.   
   It should be a description (a plan) of a possible experiment,   
   as detailed as possible.   
   When you start such a description with one reference frame   
   which consists of a 3D grid and at each crossing point a clock,   
   'everything' becomes much simpler to understand.   
      
      
   > >> Note that neither position nor acceleration appears in this   
   > >> equation; all that matters is the speed of the twin relative to   
   > >> the inertial frame being used to calculate.   
   > >   
   > > That is correct. But if the speed varies along this path you need   
   > > more clocks to calculate the time T correctly.   
   >   
   > Hmmm. I repeat: this is a gedanken, and we implicitly presume that when   
   > we use a given inertial frame, we can identify its coordinate values for   
   > all events of interest. This, of course, includes the events occupied by   
   > the clock as it moves around.   
      
   IMO it is not clear what you really mean with 'a Gedanken'.   
   What is in my mind and within the mind of anybody else can be completely   
   different.   
   Each person, in general, can have its own experience and its own   
   understanding. That implies to compare, what different people mean,   
   is difficult. That is why I prefer to start with experiments is IMO   
   much more practical and to wait with mathematics and any theory.   
      
   > If you want to place clocks at rest in the inertial frame, located along   
   > the path of the moving clock, that is fine, but it provides no   
   > additional information than is contained in the coordinates themselves.   
      
   IMO to discuss a real experiment first and then to explain, that the same   
   information also is 'contained in the coordinates themselves', seems   
   to me, much more logical.   
   IMO often by only studying an experiment is enough to derive the mathematics   
   that explains what is observed.   
   When you do that is a good start to unravel the laws that describe   
   similar experiments.   
      
   > > But there is another issue: How do you know that the equation to   
   > > calculate T is correct?   
   >   
   > This is NOT an issue. We are using SR to model this Gedanken, and that   
   > is the correct equation of SR. We know this because it has been derived   
   > many times in many textbooks.   
      
   The issue is what these thoughts are about and if all textbooks have the   
   same thoughts in mind.   
      
   > > The only way is when the calculated T at the end can be verified by   
   > > means of an actual experiment.   
   >   
   > Hmmmm. The model itself has no need of experiments because it is merely   
   > a set of postulates and theorems, plus definitions of the symbols that   
   > appear in them.   
      
   hmmm. 'The' model is always a model of something. Its that something that   
   is the most important.   
      
   > Testing the model and validating it certainly does require experiments.   
      
   > For this equation of SR, that has been done many   
   > times, for many different types of clocks and many different physical   
   > situations.   
      
   It is important at least to describe one clock in detail because   
   each different type could require its own mathematics.   
      
   > > Using different experiments etc   
   >   
   > Hmmm. If you can apply different types of clocks in the same physical   
   > situation, yes. But in general, that is not practical, and what is   
   > required is to show agreement with the theory; after all, it is the   
   > theory we are testing.   
      
   You cannot test a theory on its own. You must have an example   
   which require the theory to make predictions.   
   You can use Newton's Law to verify the movement of the planet Mercury.   
   You will fail. The next possibility is to try GR.   
      
   There are different types of clocks i.e. clocks based on time signals,   
   atomic clocks or nuclear optical clocks.   
   The above-mentioned equation can be verified with a clock based   
   on light signals. Of such a clock there are two types:   
   One in which the light signal at rest moves vertical and a different   
   one in which the light signal moves horizontally. The mathematics   
   that describes each is different.   
      
   Nicolaas Vroom   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)