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Light sphere question 
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#577
Dec909, 05:23 PM

P: 687

So, I am saying that is not the way to approach the SR light sphere. If it is approached as t increases and each point is transformed to satisfy, x'² + y'² + z'² = τ²c² then we have logical consistancy. On the other hand, if we include ±x', we get different length radii for each directiion due to the simultaneity difference in each direction of the light ray in O. It can only be approached as taking each spacetime coord in O and LT'ing it, then applying x'² + y'² + z'² = τ²c² That is why I say the normal logic of ct' = ±x' does not work. The following points in O satisify that condition t1=r/(λ(cv)) for the ray point right and t2=r/(λ(c+v)) for the ray point left. If you run these through LT with x=+ct and x=ct as appropriate, you will find two different satisfactions of the equation ct' = ±x' at two different times in O which creates two different light spheres which is a logical inconsistancy. 


#578
Dec909, 05:29 PM

P: 687

I have concluded LT will not give me the center of the light sphere after and time t in the frame of O.
I realize Einstein assumed it is at vt. Does anyone have anything else on this that I am not seeing? 


#579
Dec909, 05:34 PM

P: 687

Also, if you run this point through LT,
x = λvt/(1+λ) t' = t( t  vx/c² )λ You will find t' = t with collinear relative motion. Thus, we must be very careful not to conclude LT decides time dilation between frames. 


#580
Dec909, 05:48 PM

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#581
Dec909, 05:50 PM

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#582
Dec909, 05:56 PM

P: 687




#583
Dec909, 06:00 PM

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x = gamma*(x' + vt') = gamma*vT' t = gamma*(t' + vx'/c^2) = gamma*T' So, x/t = (gamma*vT')/(gamma*T') = v, and if x/t=v then x=vt. 


#584
Dec909, 06:02 PM

P: 687

It does not achieve anything. I created two different light spheres in O' because of the simultaneity differential of the direction of the light rays in O. Yet, if I do strictly point by point transforms as suggested by Einstein, I have a consistant resolution. 


#585
Dec909, 06:03 PM

P: 687

Thanks. That works. 


#586
Dec909, 06:15 PM

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#587
Dec909, 06:20 PM

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#588
Dec909, 06:48 PM

P: 687

That was my argument. You did not prove anything to me about this. Then, I discovered it created two light spheres. You agreed. The question for you is how do you create logical consistancy with ct' = +x'? I would like to see this. 


#589
Dec909, 06:48 PM

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#590
Dec909, 07:22 PM

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#591
Dec909, 10:07 PM

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#592
Dec909, 10:47 PM

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Thus t1=r/(λ(cv)), x1R=ct1 is one side of the light sphere in O at t1, whose other side must be t1=r/(λ(cv)), x1L=ct1, which by the LT you can check does lie on a light sphere of O'. Smilarly, t2=r/(λ(c+v)), x2L=ct2 is one side of the light sphere in O at t2, whose other side must be t2=r/(λ(c+v)), x2R=ct2, which by the LT you can check does lie on a light sphere of O'. 


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