As we know, Bondi derives the Lorentz transformations (LT) via the radar detection of the space-time coordinates of a distant event.(adsbygoogle = window.adsbygoogle || []).push({});

Once derived from other starting points the LT should account for the results obtained by Bondi expressing them as a function of the Doppler factor

D=sqrt[(1+b)/(1-b)] which can be derived without using the LT (b=V/c). The outgoing radar signal generates the event E(x,y=0,t=x/c) when detected from I and E'(x'=ct',y'=0,t'=x'/c). In accordance with the LT we have

x=(x'+cbt')/sqrt(1-b^2). (1)

But

b=(D^2-1)/1+D^2

sqrt(1-b^2)=2D/(1+D^2)

with which (1) becomes

x=[x'(1+D^2)+ct'(D^2-1)]/2D=Dx'=Dct' (2)

In a simillar way we obtain

t=[(1+D^2)x'+(D^2-1)x'/c]/2D=Dt'=Dx'/c. (3)

If the event is generated by a tardyon moving with speed u(u') the generated events are

E(x=ut,y=0,t=x/u) and E'(x'=u't',y'=0,t'=x'/u') and the corresponding LT could be espressed again as a function of D.

Do you find flows above? Do you consider that it could be a good exercise for the beginner teaching him to handle the LT?

Thanks in advance for your answers.

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# From Lorentz transformatios to Bondi's approach

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