Re: Uncle assAl: (SR) Lorentz t', x' = Intervals

From: J.E. (troubled6man_at_yahoo.com)
Date: 11/23/04 

Date: 23 Nov 2004 08:28:03 -0800

"Androcles" <dummy@dummy.net> wrote in message news:<kyrod.48545$Y7.18998@fe1.news.blueyonder.co.uk>...
> "J.E." <troubled6man@yahoo.com> wrote in message
> news:39d6e584.0411220955.4fbf3db5@posting.google.com...
> > "Androcles" <dummy@dummy.net> wrote in message
> > news:<2Wsld.9814$P7.2027@fe2.news.blueyonder.co.uk>...
> >> "J.E." <troubled6man@yahoo.com> wrote in message
> >> news:39d6e584.0411130738.31fb5b90@posting.google.com...
> >
> > [snip the part you proabbly read, the reference is above if you need
> > it]
> >
> >> : Terrance SEES 60*60*24*365*[7-sqrt(48)]*[7+sqrt(48)] +
> >> : 60*60*24*375*[7+sqrt(48)]*[7-sqrt(48)] = 60*60*24*365*[2] ticks of
> >> : Stella's clock.
> >>
> >> For how long? She's gone 14 years, right?
> >> How many ticks does Terence count?
> >> I'll stop here and see what you say.
> >> Androcles.
> >
> > I'll take pity on you, the answer to "how many ticks did Terrance
> > count on Stella's clock" is "Terrance SEES
> > 60*60*24*365*[7-sqrt(48)]*[7+sqrt(48)] +
> > 60*60*24*375*[7+sqrt(48)]*[7-sqrt(48)] = 60*60*24*365*[2] ticks of
> > Stella's clock". (I wonder where I got that from? :> )
> >
> > Your question "for how long? She's gone 14 years, right?" is not EVEN
> > a question about what Terrance or Stella SEES (neither can SEE a
> > "year"). Terrance does count 60*60*24*365*[14] ticks on his OWN clock
> > between the event when Stella leaves and when she returns, and he ALSO
> > counts 60*60*24*365*[2] ticks on Stella's clock between the event when
> > Stella leaves and when she returns. That's the facts of the
> > prediction.
>
> Why dont you come baklc when you can count to 14?
> Androcles.

I can count Androcles, and you KNOW it too. Stella wasn't GONE for 14
years. Stella didn't transmit 14 years worth of signal. Stella was
gone for 60*60*24*365*[14] ticks of Terrance's clock and
60*60*24*365*[2] ticks of her own clock. There is no such thing as "a
year". You are a SCAREDY CAT that is AFRAID of reading the real math
because then you'd have to ADMIT that I'm NOT fudging anything.
Coward.

The real irony is that you are so closed minded that you won't even
READ the correct SR predictions so you CANNOT even compare them to
data.

> > If you had read the rationale (or the rest of the post) you would see
> > the SR predicts that Stella does count 60*60*24*365*[2] ticks on her
> > own clock between the event when she leaves and when she returns, and
> > she ALSO counts 60*60*24*365*[14] ticks on Terrance's clock between
> > the event when she leaves and when she returns, that is the whole
> > POINT of the LACK of a paradox, they agree and WHAT HAPPENED. If they
> > start MAKING UP concepts like "time" and "length" THEN they will
> > discover that both were relative, but there IS NO NEED TO DO SO for
> > science. P.S. I shortened up the parts you didn't read last time
> > because I think they might be interesting and/or helpful to you.
> >
> >> : Rationale: he saw a doppler shifted rate (factor [7-sqrt(48)]) for
> >> : most of the time, specifical until his "come home" signal was returned
> >> : by her "I'm turning around signal" which took [7+sqrt(48)]
> >> : terrance-years for him to SEE, for the short amount of remaining time
> >> : ((14-[7+sqrt(48)]) = [7-sqrt(48)] terrance-years) he saw a blue
> >> : doppler shifted signal (factor [7+sqrt(48)]).
> >> :
> >> : Terrance SEES 60*60*24*365*14 ticks of HIS OWN clock.
> >> :
> >> : How many ticks of Terrance's clock does Stella SEE? Stella SEES the
> >> : 60*60*24*365*[7-sqrt(48)] ticks that Terrance sent BEFORE sending the
> >> : "come home" signal, but she saw them REDshifted at a rate f' such that
> >> : 60*60*24*365*[7-sqrt(48)] ticks = f'*[X Stella-years], but we KNOW
> >> : what the numerical value of f' is since the relative velocity v is
> >> : such that v/c= sqrt(48/49), the numerical value of f' is
> >> : 60*60*24*365*[7-sqrt(48)], so X must be 1. But we haven't finished
> >> : computing how many ticks Stella SEES of Terrance's clock on the way
> >> : back. She SEES the 60*60*24*365*[7+sqrt(48)] ticks of his clock AFTER
> >> : he sent the "come home" signal on her way back. Which we expect to
> >> : take just as many stella-years (e.g. 1), is that CONSISTENT? Yes,
> >> : here's why, she SEES an f' on the way back with a numerical value of
> >> : 60*60*24*365*[7+sqrt(48)], which means over 1 stella-year she SEES
> >> : 60*60*24*365*[7+sqrt(48)] ticks of Terrance's clock, so over the whole
> >> : trip she SEES 60*60*24*365*[7-sqrt(48)] + 60*60*24*365*[7+sqrt(48)]
> >> : 60*60*24*365*14 ticks of Terrance's clock, the SAME NUMBER Terrance
> >> : SAW of HIS OWN clock. Yeah! No paradox.
> >> :
> >> : How many ticks of Stella's clock does Stella SEE? Stella SEES
> >> : 60*60*24*365*1 on her way out, and 60*60*24*365*1 on her way back, so
> >> : 60*60*24*365*2 ticks total, the SAME NUMBER Terrance SAW of Stella's
> >> : clock. Yeah! No paradox.
> >> :
> >> : Let's do the algebra so that you can see that this is ALWAYS the case,
> >> : without EVER having to fudge. Assume a doppler shift factor of g
> >> : (red) and 1/g (blue), and Stella gone for X stella-years, and Y
> >> : terrance-years, and a rest frequency of f for each twin's clock.
> >> :
> >> : Then Stella SEES [f*g*(X/2)+ f*(1/g)*(X/2)] = [f*(X/2)*(g+(1/g))]
> >> : ticks of Terrance's clock, and f*X ticks of her own clock.
> >> :
> >> : And Terrance SEES f*Y ticks of his own clock, so since
> >> : f*Y=f*(X/2)*(g+(1/g)) we get that the equation 2*Y*g=X*g*g+X must
> >> : hold. But we want to solve for v/c, so we first need to solve for g
> >> : (g^2=[1-v/c]/[1+v/c] is the REDshift factor (from the relativisitic
> >> : doppler formula), so we know v/c = (1-g^2)/(g^2+1)). If X=0 then Y=0
> >> : and all ticks SEEN are zero, so assume that it is not the case that
> >> : X=0 and complete the square to go from X*(g*g-2*(Y/X)*g + 1 + (Y/X)^2
> >> : - (Y/X)^2)=0 into (g-(Y/X))^2=-1+(Y/X)^2, so we have g = (Y/X) +
> >> : sqrt(-1+(Y/X)^2) or g = (Y/X) + sqrt(-1+(Y/X)^2) (so in the numerical
> >> : example above Y/X is 7 and we have g=7+sqrt(48) or g=7-sqrt(48)), why
> >> : two results? Well notice that the equation f*Y=f*(X/2)*(g+(1/g)) only
> >> : had the term (g+(1/g)) in it, if g=h or g=1/h the expression (g+(1/g))
> >> : is the same, and that is EXACTLY the case here, (Y/X) +
> >> : sqrt(-1+(Y/X)^2) = 1/ [(Y/X) + sqrt(-1+(Y/X)^2)], so the differance is
> >> : the fact that one was a redshift, and the other the blueshift).
> >> : Blueshifts are greater than one, and g was called the redshift, so g=
> >> : (Y/X) - sqrt(-1+(Y/X)^2), and thence v/c = (1-[(Y/X) -
> >> : sqrt(-1+(Y/X)^2)]^2)/([(Y/X) - sqrt(-1+(Y/X)^2)]^2+1).
> >> :
> >> : Whew, showing consistency in COvariant manner is WAY harder than just
> >> : using an INvariant 4-vector analysis, glad we ONLY have to do this for
> >> : skeptics like Androcles.
> >> :
> >> : v/c = (X^2-[Y - sqrt(-X^2+Y^2)]^2)/([Y - sqrt(-X^2+Y^2)]^2+X^2)
> >> : v/c = (2*X^2-2*Y^2 + 2*Y*sqrt(Y^2-X^2))/(2*Y^2 -2*Y*sqrt(-X^2+Y^2))
> >> : v/c = [(X^2-Y^2 + Y*sqrt(Y^2-X^2))(Y+sqrt(Y*Y-X*X)]/[(Y^2
> >> : -Y*sqrt(-X^2+Y^2))(Y+sqrt(Y*Y-X*X))]
> >> :
> >> : v/c = [(X^2-Y(Y - sqrt(Y^2-X^2)))(Y+sqrt(Y*Y-X*X))]/[Y*(Y*Y
> >> : -(Y*Y-X*X))]
> >> :
> >> : v/c = [X*X*(Y+sqrt(Y*Y-X*X))-Y*(Y -
> >> : sqrt(Y*Y-X*X))(Y+sqrt(Y*Y-X*X))]/[Y*X*X]
> >> :
> >> : v/c = [X*X*(Y+sqrt(Y*Y-X*X))-Y*X*X]/[Y*X*X]
> >> :
> >> : v/c = sqrt(1-(X/Y)^2)
> >> :
> >> : So it's amazing, it's just like I can do algebra like a "real little
> >> : boy" because when X=2 and Y=14 we get v/c = sqrt(1-(1/7)^2) =
> >> : sqrt((49-1)/49) = sqrt(48/49) a familiar number from the numerical
> >> : example.
> >> :
> >> : So now that we know v/c, we know that if Terrance waits Z
> >> : terrance-years, then sends a light signal to Stella then she will get
> >> : it EXACTLY when she turns around IF AND ONLY IF [Y/2]*v=[Y/2-Z]*c,
> >> : solving for Z, we get:
> >> : Z= [Y/2]-[Y/2]*[v/c]
> >> :
> >> : So Z = [Y/2]-[Y/2]*sqrt(1-(X/Y)^2) = [Y/2]-sqrt((Y*Y-X*X)/4)
> >> :
> >> : (so when Y=14 and X=2, we get 7-sqrt(48)! Amazing, no fudging)
> >> :
> >> : OK, everything else actually assumed consistency, now that we have an
> >> : expression for Z we know that Terrance SEES [f*g*(Y-Z) f*(1/g)*Z]
> >> : ticks from Stella's clock. So the test for consistency (paradox
> >> : avoidance) come down to ONE equation after all this symbolic work (but
> >> : NOW we've done it for ANY amount of stella-time X and any amount of
> >> : Terrance-time Y where Terrance can send a light signal to Stella to
> >> : tell her to turn around).
> >> :
> >> : Solve:
> >> : [f*g*(Y-Z) + f*(1/g)*Z]
> >> :
> >> : We will use the substitutions
> >> : g=sqrt([Y-sqrt(Y*Y-X*X)]/[Y+sqrt(Y*Y-X*X)]) and Z = Y/2 -
> >> : sqrt((Y*Y-X*X)/4). The latter we just derived, but let's show the
> >> : former.
> >> :
> >> : g*g=((Y/X) - sqrt(-1+(Y/X)^2))*((Y/X) - sqrt(-1+(Y/X)^2))
> >> : g*g=(Y/X)*(Y/X) - 2*(Y/X)*sqrt(-1+(Y/X)^2) + (-1+(Y/X)^2)
> >> : g*g=[Y*Y - 2*Y*sqrt(Y*Y-X*X) + (Y*Y-X*X)]/(X*X)
> >> : g*g=[Y*Y - 2*Y*sqrt(Y*Y-X*X) + (Y*Y-X*X)]/(X*X)
> >> : g*g=([Y - sqrt(Y*Y-X*X)]^2)/(X*X)
> >> :
> >> : But
> >> : [Y-sqrt(Y*Y-X*X)]/[Y+sqrt(Y*Y-X*X)]=
> >> : ([Y-sqrt(Y*Y-X*X)]^2)/([Y+sqrt(Y*Y-X*X)]*[Y-sqrt(Y*Y-X*X)])=
> >> : ([Y-sqrt(Y*Y-X*X)]^2)/(Y*Y-(Y*Y-X*X))=
> >> : [Y-sqrt(Y*Y-X*X)]^2)/(X*X)
> >> :
> >> : so the conclusion that g=sqrt(([Y-sqrt(Y*Y-X*X)]/[Y+sqrt(Y*Y-X*X)]) is
> >> : fine, (it could have been independantly computed since we know v/c
> >> : now, but the point is that we have this form that is simpler for the
> >> : next computation).
> >> :
> >> : So given g=sqrt([Y-sqrt(Y*Y-X*X)]/[Y+sqrt(Y*Y-X*X)]) and Z = Y/2 -
> >> : sqrt((Y*Y-X*X)/4), solve:
> >> : [f*g*(Y-Z) + f*(1/g)*Z]
> >> :
> >> : OK
> >> : [f*g*(Y-Z) + f*(1/g)*Z]=
> >> : f*[g*(Y-[Y/2-sqrt((Y*Y-X*X)/4)]) + (1/g)*[Y/2-sqrt((Y*Y-X*X)/4)]]=
> >> : f*[(g/2)*(Y+sqrt(Y*Y-X*X)]) + (1/g)*[Y-sqrt(Y*Y-X*X)]*(1/2)]=
> >> : (f/2)*[g*(Y+sqrt(Y*Y-X*X)]) + (1/g)*[Y-sqrt(Y*Y-X*X)]]=
> >> : (f/2)*[sqrt((Y - sqrt(Y*Y-X*X))*(Y + sqrt(Y*Y-X*X))) +
> >> : (1/g)*[Y-sqrt(Y*Y-X*X)]]=
> >> : (f/2)*[sqrt(Y*Y - (Y*Y-X*X)) + (1/g)*[Y-sqrt(Y*Y-X*X)]]=
> >> : (f/2)*[X + (1/g)*[Y-sqrt(Y*Y-X*X)]]=
> >> : (f/2)*[X + sqrt([Y+sqrt(Y*Y-X*X)]*[Y-sqrt(Y*Y-X*X)])]=
> >> : (f/2)*[X + sqrt(Y*Y-(Y*Y-X*X))]=
> >> : (f/2)*[X + X]= f*X
> >> :
> >> : So Terrance SEES f*X ticks from Stella's clock, the SAME number of
> >> : ticks from Stella's clock that Stella SEES. No paradox. And this was
> >> : done for any X,Y where 0 < X < Y, well the case where X=0 reduces to
> >> : X=Y=0 which is ALSO no paradox and then in all cases the number of
> >> : ticks SEEN is 0 as well, so no paradox in that case either. No
> >> : fudging, no paradox.
> >
> > [snip about Androcles accusing me of ranting]
> >
> >> : > Rant rant rant.
> >> : > I'm still confident you haven't a clue.
> >> :
> >> : It was a response to you, it was a response to you, it was a response
> >> : to you. Just move on to an actual critic of my post which you
> >> : probably *still* haven't read. Now that you agree that my numbers are
> >> : right, I've showed you (if you read it) the NON-fudging way to compute
> >> : the twin-paradox setup. So you know how to compute how many ticks
> >> : Terrance SEES on his own clock, and on Stella's clock. And how many
> >> : Stella SEES on Terrance's clock and on her own clock. And they each
> >> : AGREE about how many ticks each clock made, that's THE WHOLE POINT of
> >> : the exercise.
> >> :
> >> : > : > That's fine, you're allow to make errors sometime
> >> : > : > : Androcles, just come clean and admit it and move on and that's all
> >> : > : > : fine. Persist, and the lurkers will judge you accordingly.
> >> : > : >
> >> : > : > I'm sure they will. ROFL!
> >> : > :
> >> : > : This is supposed to be a debate Androcles, I'm just feeling bad for
> >> : > : allowing you to dig yourself such a deep hole, if this were in person
> >> : > : I would have "excused myself" to go to the bathroom after passing you
> >> : > : a private note explaining your error so that you wouldn't make
> >> : > : yourself look so dumb. For your own image just TRY to PRETEND that I
> >> : > : am an honest person who can do his math, and who WANTS to debate SR
> >> : > : with you FAIRLY, and ACT accordingly.
>
> >> : > I'm still confident you haven't a clue.
> >> :
> >> : Let's get this straight, you admit that my numbers were correct when
> >> : you were wrong, but you still think I haven't a clue? Why can't we
> >> : just MOVE ON with the example now that you agree that my speed, time
> >> : and doppler shift are correct to discussion the CONCLUSION about how I
> >> : COMPUTE (rather than assume) how many ticks of Stella's clock Terrance
> >> : SEES?
> >> :
> >> : I think at this point if you agree to the time of 14 terrance-years,
> >> : and a speed of sqrt(48/49) speed of light that all I need is a
> >> : concrete frequency of how many ticks Terrance SEES on his own clock
> >> : during the 14 terrance-years Stella is gone. I wanted to say
> >> : 60*60*24*365*14 ticks, is that OK? It makes the +/- 1 tick cause by
> >> : YOU forcing ME to use Koks numbers to have only a small error, and
> >> : it's not REALLY that hard to toss around Androcles, loosen up a bit,
> >> : bigger numbers won't bite you.
> >
> > [snip Androcles ranting about claims he made that I believe things
> > that I never said I believed]
> >
> >> : > : I personally don't care AT ALL what Einstein wrote
> >> : >
> >> : > Ah...
> >> : > No point in continuing, then, is there?
> >> : > Glad you've admitted it.
> >> : > Remaining rant snipped unread.
> >> : > Androcles.
> >> :
> >> : Androcles I feel sorry for you that reading is apparantly so hard for
> >> : you, but you aren't a fair debater at all. You make fun of people
> >> : that read Einstein even Einstein is a man and can be wrong. And
> >> : people who base SR on SET THEORY instead of Einstein are MUCH less
> >> : likely to be wrong but you APPARANTLY have NO INTEREST in the more
> >> : TRUSTED and MODERN theory?
> >> :
> >> : Why could this be? I'm sure there are many motivations, but I keep
> >> : being suspicious that it is your sense of unfair debating things by
> >> : (purposely) misrepresenting it, and you find that easier to do with
> >> : Einstein than cold hard set theory. The modern theory of SR is based
> >> : not on a website that Einstein didn't write, but on a structure proven
> >> : to exist in the set theoretical universe. So if the modern theory is
> >> : internally inconsistent, then SO is set theory.

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