A question with the readings of synchronized clocks

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In summary, the conversation discussed the synchronization of clocks in frame O and the arrival of a photon and particle at a specific point in O. The question was then changed to ask about the distance traveled by the moving particle. The conversation then delved into the use of Einstein's postulates and other concepts such as linearity, symmetry, isotropy, and reciprocity to derive the Lorentz transformations for space-time coordinates. The speaker also mentioned a similar derivation done by Levy and invited others to contribute to make it better.
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bernhard.rothenstein
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Consider that from the origin O of the inertial reference frame O start at the origin of time a particle that moves with speed u<c and a photon with speed c both in the positive direction of the OX axis. At each point of that axis we find a clock all the clocks being synchronized following the procedure proposed by Einstein. After a given time t of motion the photon arrives at the location of a clock C(x)[x=ct,y=0). What is the reading of a clock located where the particle arrives when the photon arrives at the location mentioned above?
Thanks.
 
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According to observers in frame O, when the photon arrives at point x = ct all frame O clocks, including the one at point x = ut, will read the same time t. Of course, since these points are spatially separated in O, other frames will disagree.
 
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clock readings

Doc Al said:
According to observers in frame O, when the photon arrives at point x = ct all frame O clocks, including the one at point x = ut, will read the same time t. Of course, since these points are spatially separated in O, other frames will disagree.
Thanks for helping me to change my question which becomes:"What is the distance traveled by the moving particle?" If it is ut=ux/c then consider the relative positions of the reference frames I and I' detected from I when the synchronized clocks of that frame read t. Let E(x=ct,y=0, t=x/c) and E'(x'=ct',y'=0, t'=x'/c) same events taking place on the overlapped axes OX(O'X'). Taking into account that relative motion distorts length and time intervals then adding only lengths measured in I we obtain
x-Vt=Ax' (1)
where A is a factor that accounts for the distorsion of lenghts. It could depend on the relative speed V but not on the space-time coordinates involved in the transformation process.
Considering the relative positions of I and I' detected from I' when the clocks of that frame read t' we obtain adding only lengths measured in I'
Ax=x'+Vt' (2)
Presenting (1) and (2) as
ct-Vt=Act' (3)
ct'+Vt'=Act (4)
the result is
A=sqrt(1-VV/cc) (5)
and so the Lorentz transformations for the space time coordinates are derived. Solving them for t and t' we obtain the Lorentz transformations for the time coordinates,
The problem is what was used above bedides Einstein's two postulates:
-Considering that the factor A is the same in I and I' as well we have involved linearity and simmetry.
-Considering that if I' moves with speed V relative to I and that I moves relative to I' with speed -V we took into account isotropy and reciprocity.
Did I use more?
A simillar derivation was presented recently by Levy (Am.J.Phys) consdiering that A is known from thought experiments.
Is the derivation free of flows?
Far from me to consider that was I have presented above is my contribution. I simply consider that it could be a standard, time saving and tranmsparent derivation of the LT. Please constribute to it in order to make it better!
 

1. How do synchronized clocks work?

Synchronized clocks use a master clock to send out a signal that is received by all other clocks in the system. This signal ensures that all clocks are set to the same time.

2. What is the purpose of synchronized clocks?

The purpose of synchronized clocks is to ensure that all clocks in a system are displaying the same time. This is especially important in scientific experiments and time-sensitive processes.

3. How accurate are synchronized clocks?

Synchronized clocks can be incredibly accurate, with some systems being able to synchronize clocks to within nanoseconds of each other. However, the accuracy also depends on the type of clock being used and the strength of the signal being sent.

4. Can synchronized clocks be used in different time zones?

Yes, synchronized clocks can be used in different time zones as long as the master clock is set to the correct time zone and all other clocks receive the signal accurately.

5. What are the benefits of using synchronized clocks?

Using synchronized clocks can eliminate confusion and discrepancies in time among different clocks. It also ensures accurate and precise time measurements, which is crucial in scientific research and other time-sensitive applications.

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