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Simplified Twin Paradox Resolution.



 
 
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  #21  
Old January 7th 13, 06:39 PM posted to sci.physics.relativity,sci.physics,sci.math,sci.astro
Koobee Wublee
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Posts: 815
Default Simplified Twin Paradox Resolution.

On Jan 7, 6:41 am, Vilas Tamhane wrote:
Koobee Wublee wrote:


Instead of v, let’s say (B = v / c) for simplicity. The earth is
Point #0, outbound spacecraft is Point #1, and inbound spacecraft is
Point #2.


According to the Lorentz transform, relative speeds a


** B_00^2 = 0, speed of #0 as observed by #0
** B_01^2 = B^2, speed of #1 as observed by #0
** B_02^2 = B^2, speed of #2 as observed by #0


** B_10^2 = B^2, speed of #0 as observed by #1
** B_11^2 = 0, speed of #1 as observed by #1
** B_12^2 = 4 B^2 / (1 – B^2), speed of #2 as observed by #1


** B_20^2 = B^2, speed of #0 as observed by #2
** B_21^2 = 4 B^2 / (1 – B^2), speed of #1 as observed by #2
** B_22^2 = 0, speed of #2 as observed by #2


When Point #0 is observed by all, the Minkowski spacetime (divided by
c^2) is:


** dt_00^2 (1 – B_00^2) = dt_10^2 (1 – B_10^2) = dt_20^2 (1 – B_20^2)


When Point #1 is observed by all, the Minkowski spacetime (divided by
c^2) is:


** dt_01^2 (1 – B_01^2) = dt_11^2 (1 – B_11^2) = dt_21^2 (1 – B_21^2)


When Point #2 is observed by all, the Minkowski spacetime (divided by
c^2) is:


** dt_02^2 (1 – B_02^2) = dt_12^2 (1 – B_12^2) = dt_22^2 (1 – B_22^2)


Where


** dt_00 = Local rate of time flow at Point #0
** dt_01 = Rate of time flow at #1 as observed by #0
** dt_02 = Rate of time flow at #2 as observed by #0


** dt_10 = Rate of time flow at #0 as observed by #1
** dt_11 = Local rate of time flow at Point #1
** dt_12 = Rate of time flow at #2 as observed by #1


** dt_20 = Rate of time flow at #0 as observed by #2
** dt_21 = Rate of time flow at #1 as observed by #2
** dt_22 = Local rate of time flow at Point #2


So, with all the pertinent variables identified, the contradiction of
the twins’ paradox is glaring right at anyone with a thinking brain.
shrug


- - -


From the Lorentz transformations, you can write down the following
equation per Minkowski spacetime. Points #1, #2, and #3 are
observers. They are observing the same target.


** c^2 dt1^2 – ds1^2 = c^2 dt2^2 – ds2^2 = c^2 dt3^2 – ds3^2


Where


** dt1 = Time flow at Point #1
** dt2 = Time flow at Point #2
** dt3 = Time flow at Point #3


** ds1 = Observed target displacement segment by #1
** ds2 = Observed target displacement segment by #2
** ds3 = Observed target displacement segment by #3


The above spacetime equation can also be written as follows.


** dt1^2 (1 – B1^2) = dt2^2 (1 – B2^2) = dt3^2 (1 – B3^2)


Where


** B^2 = (ds/dt)^2 / c^2


When #1 is observing #2, the following equation can be deduced from
the equation above.


** dt1^2 (1 – B1^2) = dt2^2 . . . (1)


Where


** B2^2 = 0, #2 is observing itself


Similarly, when #2 is observing #1, the following equation can be
deduced.


** dt1^2 = dt2^2 (1 – B2^2) . . . (2)


Where


** B1^2 = 0, #1 is observing itself


According to relativity, the following must be true.


** B1^2 = B2^2


Thus, equations (1) and (2) become the following equations
respectively.


** dt1^2 (1 – B^2) = dt2^2 . . . (3)
** dt2^2 = dt1^2 (1 – B^2) . . . (4)


Where


** B^2 = B1^2 = B2^2


The only time the equations (3) and (4) can co-exist is when B^2 = 0.
Thus, the twins’ paradox is very real under the Lorentz transform.
shrug


Stuff is so simple that it is a big surprise when all
the so-called bright minds in the scientific communities
have so much trouble understanding.


Stuff is simple and they don’t have any trouble in understanding. But
they cannot go against the politics of people belonging to one race
and same people who happen to hold the strings of economy of great
America.


After all these years trying to talk sense out of the likes, Koobee
Wublee would have to disagree with you. They are indeed fvcking
morons who cannot understand basic algebra and basic concept of what
science is all about. The strong language is indeed very
appropriate. shrug

Coming back to Paul, he will never consider the example you suggested,
that, A and B both go away from C and come back to C. In this case,
there is no way to show difference in time in the clocks of A and B,
though, according to Einstein, each other’s clock was running slow and
still their own were running at proper rate. This proposed reciprocity
is exactly the foolishness that SR is based on.


Koobee Wublee would tend to agree on this one. paul is so busy
justifying why he has said the Doppler effect from GR needed to be
corrected for the carrier frequencies of downlink signals. The recent
excuse is that he did not meant what he said in the past. We will see
what other excuses that he can come up with. In the meantime, try not
to hold your breath for paul to modify his JAVA applet to allow for
both twins to travel with identical acceleration profile and also an
arbitrary time period for the twins to coast (with no acceleration).
It would be interesting to see how paul copes with the mutual time
dilation building up. If he had any brain at all, it would be like
similar to Zed holding his hands to his forehead yelling “no” in the
movie “Zardoz” after “the Wizard of Oz” was exposed to him. shrug

http://en.wikipedia.org/wiki/Zardoz


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  #22  
Old January 8th 13, 03:07 AM posted to sci.physics.relativity,sci.physics,sci.math,sci.astro
1treePetrifiedForestLane
external usenet poster
 
Posts: 974
Default Simplified Twin Paradox Resolution.

do you not see that the angular momentum
of atoms, has to be condsidered if a prefered direction
is taken?

taht is to say, lightwaves do not have a velocity,
only a speed.

Situation IS asymmetrical if we tag a frame that undergoes actual
acceleration. But this is against the basic principles of SR which
deals with uniform relative motion and nothing else.


thus:
my main concern, for using diadians (or tau) is that
the simplicity of (viz) radar distances is obscured;
also, how to avoid confusion with radians (or "pi+pi"),
since pi is generally considered to be a dimensionless constant,
by some argument or other.

--yay; a new proof of Fermat's 'little' theorm!
  #23  
Old January 8th 13, 04:10 AM posted to sci.physics.relativity,sci.physics,sci.math,sci.astro
Vilas Tamhane
external usenet poster
 
Posts: 52
Default Simplified Twin Paradox Resolution.

On Jan 7, 10:39*pm, Koobee Wublee wrote:
On Jan 7, 6:41 am, Vilas Tamhane wrote:









Koobee Wublee wrote:
Instead of v, let’s say (B = v / c) for simplicity. *The earth is
Point #0, outbound spacecraft is Point #1, and inbound spacecraft is
Point #2.


According to the Lorentz transform, relative speeds a


** *B_00^2 = 0, speed of #0 as observed by #0
** *B_01^2 = B^2, speed of #1 as observed by #0
** *B_02^2 = B^2, speed of #2 as observed by #0


** *B_10^2 = B^2, speed of #0 as observed by #1
** *B_11^2 = 0, speed of #1 as observed by #1
** *B_12^2 = 4 B^2 / (1 – B^2), speed of #2 as observed by #1


** *B_20^2 = B^2, speed of #0 as observed by #2
** *B_21^2 = 4 B^2 / (1 – B^2), speed of #1 as observed by #2
** *B_22^2 = 0, speed of #2 as observed by #2


When Point #0 is observed by all, the Minkowski spacetime (divided by
c^2) is:


** *dt_00^2 (1 – B_00^2) = dt_10^2 (1 – B_10^2) = dt_20^2 (1 – B_20^2)


When Point #1 is observed by all, the Minkowski spacetime (divided by
c^2) is:


** *dt_01^2 (1 – B_01^2) = dt_11^2 (1 – B_11^2) = dt_21^2 (1 – B_21^2)


When Point #2 is observed by all, the Minkowski spacetime (divided by
c^2) is:


** *dt_02^2 (1 – B_02^2) = dt_12^2 (1 – B_12^2) = dt_22^2 (1 – B_22^2)


Where


** *dt_00 = Local rate of time flow at Point #0
** *dt_01 = Rate of time flow at #1 as observed by #0
** *dt_02 = Rate of time flow at #2 as observed by #0


** *dt_10 = Rate of time flow at #0 as observed by #1
** *dt_11 = Local rate of time flow at Point #1
** *dt_12 = Rate of time flow at #2 as observed by #1


** *dt_20 = Rate of time flow at #0 as observed by #2
** *dt_21 = Rate of time flow at #1 as observed by #2
** *dt_22 = Local rate of time flow at Point #2


So, with all the pertinent variables identified, the contradiction of
the twins’ paradox is glaring right at anyone with a thinking brain..
shrug


- - -


*From the Lorentz transformations, you can write down the following
equation per Minkowski spacetime. *Points #1, #2, and #3 are
observers. *They are observing the same target.


** *c^2 dt1^2 – ds1^2 = c^2 dt2^2 – ds2^2 = c^2 dt3^2 – ds3^2


Where


** *dt1 = Time flow at Point #1
** *dt2 = Time flow at Point #2
** *dt3 = Time flow at Point #3


** *ds1 = Observed target displacement segment by #1
** *ds2 = Observed target displacement segment by #2
** *ds3 = Observed target displacement segment by #3


The above spacetime equation can also be written as follows.


** *dt1^2 (1 – B1^2) = dt2^2 (1 – B2^2) = dt3^2 (1 – B3^2)


Where


** *B^2 = (ds/dt)^2 / c^2


When #1 is observing #2, the following equation can be deduced from
the equation above.


** *dt1^2 (1 – B1^2) = dt2^2 . . . (1)


Where


** *B2^2 = 0, #2 is observing itself


Similarly, when #2 is observing #1, the following equation can be
deduced.


** *dt1^2 = dt2^2 (1 – B2^2) . . . (2)


Where


** *B1^2 = 0, #1 is observing itself


According to relativity, the following must be true.


** *B1^2 = B2^2


Thus, equations (1) and (2) become the following equations
respectively.


** *dt1^2 (1 – B^2) = dt2^2 . . . (3)
** *dt2^2 = dt1^2 (1 – B^2) . . . (4)


Where


** *B^2 = B1^2 = B2^2


The only time the equations (3) and (4) can co-exist is when B^2 = 0.

  #24  
Old January 8th 13, 04:20 AM posted to sci.physics.relativity,sci.physics,sci.math,sci.astro
1treePetrifiedForestLane
external usenet poster
 
Posts: 974
Default Simplified Twin Paradox Resolution.

Einsteimania is no solely the fault
of herr doktor-proffesor E. --
see the book on fractals and power-laws e.g.

anyway, do you see that teh angular momentum
of atoms, at least, explains inertia,
relativistically?

I was not referring to the die-hard Einstein supporters


thus:
the Grace datum clearly shows that thoswe two icesheets
are still rising, but it can't be by very much;
they have always been stacked to the gills.

The ice sheets of Greenland and Antarctica contain about 99.5 per cent
of the Earth's glacier ice and could raise sea levels by 65 metres if
they melted completely – although experts think this is highly
unlikely in the foreseeable future. However, a survey of the world's
top 26 glaciologists found most believe melting of the ice sheets
could be more rapid and severe than previously estimated. They believe


thus:
GR is no more of a theory
about the curvature of space, which is clearly manifest
to geometers (viz, Eratosthenes and Gauss),
than it explains what causes gravity, the same as Fig Newton.

however, it is simplicity, itself, to adduce the curvature
of space from Newton's "decategorified" equation
of "universal gravity." (obviously,
Kepler did all of the legwork .-)

thus:
the sole determinant of the speed (not velocity) of light,
is the index of refraction of the medium,
viz Snell's law.

the classsical problem was Liebniz's *brachistochrone*, although
one has to realize that the ray-tracing idealization is not a natter
of importance; just of interpretation ... and
thr same applies to Minkowskian ligthconeheads, like Feynman.

thus:
read the original write-up of the "two-pihole experiment"
by Young, which totally exposed Newton's untheory
of "corpuscles" of light, a 100 years after he screwed-up Snell's law
-- just like Descartes, did.

see http://science.larouchepac.com/fermat/

thus:
my main concern, for using diadians (or tau) is that
the simplicity of (viz) radar distances is obscured;
also, how to avoid confusion with radians (or "pi+pi"),
since pi is generally considered to be a dimensionless constant,
by some argument or other.

--yay; a new proof of Fermat's 'little' theorm!
  #25  
Old January 8th 13, 07:51 AM posted to sci.physics.relativity,sci.physics,sci.math,sci.astro
Lord Androcles, Zeroth Earl of Medway[_6_]
external usenet poster
 
Posts: 58
Default Simplified Twin Paradox Resolution.

"Vilas Tamhane" wrote in message
...

On Jan 7, 10:39 pm, Koobee Wublee wrote:
After all these years trying to talk sense out of the likes, Koobee
Wublee would have to disagree with you. They are indeed fvcking
morons who cannot understand basic algebra and basic concept of what
science is all about. The strong language is indeed very
appropriate. shrug

Coming back to Paul, he will never consider the example you suggested,
that, A and B both go away from C and come back to C. In this case,
there is no way to show difference in time in the clocks of A and B,
though, according to Einstein, each other’s clock was running slow and
still their own were running at proper rate. This proposed reciprocity
is exactly the foolishness that SR is based on.


Koobee Wublee would tend to agree on this one. paul is so busy
justifying why he has said the Doppler effect from GR needed to be
corrected for the carrier frequencies of downlink signals. The recent
excuse is that he did not meant what he said in the past. We will see
what other excuses that he can come up with. In the meantime, try not
to hold your breath for paul to modify his JAVA applet to allow for
both twins to travel with identical acceleration profile and also an
arbitrary time period for the twins to coast (with no acceleration).
It would be interesting to see how paul copes with the mutual time
dilation building up. If he had any brain at all, it would be like
similar to Zed holding his hands to his forehead yelling “no” in the
movie “Zardoz” after “the Wizard of Oz” was exposed to him. shrug

http://en.wikipedia.org/wiki/Zardoz


I was not referring to the die-hard Einstein supporters on this NG. It
is clear to me that for more than a century, top most brains in
physics were deliberately trying to maintain Einstein’s deified image.
It is the American government that owes answers to public.
So far as Paul Anderson is concerned, he has spent lot of time in
justifying SR and in later twists given to SR. By doing so, he reduces
himself to a dishonest bigot.
=================================
Kinky Wobbly is no less a dishonest bigot. His only excuse for his
luminiferous mechanical ectoplasm is "It obviously must exist" without
giving any reason or mathematical argument why it must exist, nor can can he
point to any experiment supporting his blind faith.

-- This message is brought to you from the keyboard of
Lord Androcles, Zeroth Earl of Medway.
When I get my O.B.E. I'll be an earlobe.


 




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