Proxima Centauri is 4.2 light-years away from Big Ben. Two distant observers A and B are racing past Proxima Centauri on their way to Big Ben at .867c relative to the Big Ben--Proxima Centauri frame of reference. For these two observers Proxima Centauri and Big Ben are only 2.1 light-years apart due to Lorentz contraction. Both observers also note that the little hand of Big Ben rotates only 365.25 times per year of their proper time instead of 730.5 rotations, due to Lorentz time dilation. Now this slowing of Big Ben is not some illusion or artifact of speed. SR assures us that Big Ben REALLY IS RUNNING SLOWER in their frame of reference.

Just as observer A passes Proxima Centauri he begins to count the 365.25 x 2.1 = 767 turns in the helical path of light emanating from the tip of Big Ben's little hand, which lie between Big Ben and Proxima Centauri at any given moment in that frame of reference. He also counts the 2.42 x 365.25 = 884 additional turns that Big Ben produces during the rest of his 2.42 year journey to Big Ben, for a total of 1651 turns during the entire trip.

Meanwhile, observer B decides to use the relativistic doppler formula instead, which relies on the oscillator's own proper frequency (in this case 730..5 turns per year) as the input. So observer B gets 3.747 x 2.42 x 730.5 = 6624 total turns of the helix during the trip from Proxima Centauri to Big Ben.

Observers A and B disagree on the total number of turns by a factor of 4 for the same helix on the same trip. The validity of the relativistic doppler formula is forever washed away.

On 12-Dec-23 5:19 pm, patdolan wrote:
> Proxima Centauri is 4.2 light-years away from Big Ben. Two distant
> observers A and B are racing past Proxima Centauri on their way to
> Big Ben at .867c relative to the Big Ben--Proxima Centauri frame of
> reference. For these two observers Proxima Centauri and Big Ben are
> only 2.1 light-years apart due to Lorentz contraction. Both observers
> also note that the little hand of Big Ben rotates only 365.25 times
> per year of their proper time instead of 730.5 rotations, due to
> Lorentz time dilation. Now this slowing of Big Ben is not some
> illusion or artifact of speed. SR assures us that Big Ben REALLY IS
> RUNNING SLOWER in their frame of reference.
>
> Just as observer A passes Proxima Centauri he begins to count the
> 365.25 x 2.1 = 767 turns in the helical path of light emanating from
> the tip of Big Ben's little hand, which lie between Big Ben and
> Proxima Centauri at any given moment in that frame of reference. He
> also counts the 2.42 x 365.25 = 884 additional turns that Big Ben
> produces during the rest of his 2.42 year journey to Big Ben, for a
> total of 1651 turns during the entire trip.

The observer has to consider where Big Ben was in his frame when the
light he's just seeing set out. Big Ben is now 2.1 light years away in
his frame, but it is moving, and the light has taken some time to
arrive, so the light he's just seen must have left Big Ben when it was
more than 2.1 light years away.

If we let the distance away that Big Ben was when the light departed be
d, we can see that the time that Big Ben took to get from distance d to
its present position of 2.1 light years must equal the time it took for
the light to get from distance d to the observer. That is:

(d - 2.1) / v = d / c

where v = is 0.867c, and c = 1.

(d - 2.1) / 0.867 = d / 1

d - 2.1 = 0.867 * d

d * (1 - 0.867) = 2.1

d = 2.1 / ( 1 - 0.867)

d = 15.79

So in the observer's frame the light has taken 15.79 years to arrive,
and there are many more than 2.1 years worth of rotations between Big
Ben and the observer.

Sylvia.

On Wednesday, December 13, 2023 at 12:51:44 AM UTC-8, Sylvia Else wrote:
> On 12-Dec-23 5:19 pm, patdolan wrote:
> > Proxima Centauri is 4.2 light-years away from Big Ben. Two distant
> > observers A and B are racing past Proxima Centauri on their way to
> > Big Ben at .867c relative to the Big Ben--Proxima Centauri frame of
> > reference. For these two observers Proxima Centauri and Big Ben are
> > only 2.1 light-years apart due to Lorentz contraction. Both observers
> > also note that the little hand of Big Ben rotates only 365.25 times
> > per year of their proper time instead of 730.5 rotations, due to
> > Lorentz time dilation. Now this slowing of Big Ben is not some
> > illusion or artifact of speed. SR assures us that Big Ben REALLY IS
> > RUNNING SLOWER in their frame of reference.
> >
> > Just as observer A passes Proxima Centauri he begins to count the
> > 365.25 x 2.1 = 767 turns in the helical path of light emanating from
> > the tip of Big Ben's little hand, which lie between Big Ben and
> > Proxima Centauri at any given moment in that frame of reference. He
> > also counts the 2.42 x 365.25 = 884 additional turns that Big Ben
> > produces during the rest of his 2.42 year journey to Big Ben, for a
> > total of 1651 turns during the entire trip.
> The observer has to consider where Big Ben was in his frame when the
> light he's just seeing set out. Big Ben is now 2.1 light years away in
> his frame, but it is moving, and the light has taken some time to
> arrive, so the light he's just seen must have left Big Ben when it was
> more than 2.1 light years away.

Agreed.
>
> If we let the distance away that Big Ben was when the light departed be
> d, we can see that the time that Big Ben took to get from distance d to
> its present position of 2.1 light years must equal the time it took for
> the light to get from distance d to the observer. That is:
>
> (d - 2.1) / v = d / c
>
> where v = is 0.867c, and c = 1.
>
> (d - 2.1) / 0.867 = d / 1
>
> d - 2.1 = 0.867 * d
>
> d * (1 - 0.867) = 2.1
>
> d = 2.1 / ( 1 - 0.867)
>
> d = 15.79
>
> So in the observer's frame the light has taken 15.79 years to arrive,
> and there are many more than 2.1 years worth of rotations between Big
> Ben and the observer.
If the first light to arrive at observer A was emitted from Big Ben 15.79 years ago (a very plausible assumption) then it stands to reason that the last light to arrive at the end of his 2.42 year trip was emitted from Big Ben 13.37 years ago. But this is a preposterous conclusion. For we know a priori in our souls and beyond any conclusion of algebraic reasoning that the last light to arrive was emitted the instant before observer A crashed into the clock face of Big Ben.

This is a teachable moment my children. The erroneous algebra of special relativity does not survive the move off the paper to the real world of empirical physical phact. You have been told this before Sylvia. And I have demonstrated this several ways now.

Thanks for the reply,

Patrick Dolan
Forensic Algebraicist
>
> Sylvia.

On Wednesday 13 December 2023 at 09:51:44 UTC+1, Sylvia Else wrote:
> On 12-Dec-23 5:19 pm, patdolan wrote:
> > Proxima Centauri is 4.2 light-years away from Big Ben. Two distant
> > observers A and B are racing past Proxima Centauri on their way to
> > Big Ben at .867c relative to the Big Ben--Proxima Centauri frame of
> > reference. For these two observers Proxima Centauri and Big Ben are
> > only 2.1 light-years apart due to Lorentz contraction. Both observers
> > also note that the little hand of Big Ben rotates only 365.25 times
> > per year of their proper time instead of 730.5 rotations, due to
> > Lorentz time dilation. Now this slowing of Big Ben is not some
> > illusion or artifact of speed. SR assures us that Big Ben REALLY IS
> > RUNNING SLOWER in their frame of reference.
> >
> > Just as observer A passes Proxima Centauri he begins to count the
> > 365.25 x 2.1 = 767 turns in the helical path of light emanating from
> > the tip of Big Ben's little hand, which lie between Big Ben and
> > Proxima Centauri at any given moment in that frame of reference. He
> > also counts the 2.42 x 365.25 = 884 additional turns that Big Ben
> > produces during the rest of his 2.42 year journey to Big Ben, for a
> > total of 1651 turns during the entire trip.
> The observer has to consider where Big Ben was in his frame when the
> light he's just seeing set out. Big Ben is now 2.1 light years away in
> his frame, but it is moving, and the light has taken some time to
> arrive, so the light he's just seen must have left Big Ben when it was
> more than 2.1 light years away.
>
> If we let the distance away that Big Ben was when the light departed be
> d, we can see that the time that Big Ben took to get from distance d to
> its present position of 2.1 light years must equal the time it took for
> the light to get from distance d to the observer. That is:
>
> (d - 2.1) / v = d / c
>
> where v = is 0.867c, and c = 1.
>
> (d - 2.1) / 0.867 = d / 1
>
> d - 2.1 = 0.867 * d
>
> d * (1 - 0.867) = 2.1
>
> d = 2.1 / ( 1 - 0.867)
>
> d = 15.79
>
> So in the observer's frame the light has taken 15.79 years to arrive,
> and there are many more than 2.1 years worth of rotations between Big
> Ben and the observer.

Fortunately we have GPS now, so anyone can check
that Your gedanken tales have nothing in common
with real clocks, real observers or real anything.

Sylvia Else wrote:

> The observer has to consider where Big Ben was in his frame when the
> light he's just seeing set out. Big Ben is now 2.1 light years away in
> his frame, but it is moving, and the light has taken some time to
> arrive, so the light he's just seen must have left Big Ben when it was
> more than 2.1 light years away.

not sure. One thing you people don't undrestand, is that Earth is not a an
earth from Sun. It's an earth from other sun exploding. Saying Earth is
5_𝗯𝗶𝗹𝗹𝗶𝗼𝗻_𝘆𝗲𝗮𝗿𝘀_𝗼𝗹𝗱, the old sun must have been exploded before that date.
Taking the age of Universe of 13_𝗯𝗶𝗹𝗹𝗶𝗼𝗻𝘀_𝘆𝗲𝗮𝗿𝘀_𝗼𝗹𝗱, this makes no sense, as
this Sun is already 5_𝗯𝗶𝗹𝗹𝗶𝗼𝗻𝘀_𝘆𝗲𝗮𝗿𝘀 old already. In this case you a 5 + 5 +
5 = 15_𝗯𝗶𝗹𝗹𝗶𝗼𝗻_𝘆𝗲𝗮𝗿𝘀_𝗼𝗹𝗱, as the minimum age required.

𝗨𝗸𝗿𝗮𝗶𝗻𝗲_𝘄𝗮𝘀_𝗻𝗲𝘃𝗲𝗿_𝗴𝗼𝗶𝗻𝗴_𝘁𝗼_𝘄𝗶𝗻_–_𝗨𝗦_𝘀𝗲𝗻𝗮𝘁𝗼𝗿
Tommy Tuberville has also dismissed the notion that Russia would invade
Europe, suggesting it was just 𝗮_“𝘀𝗲𝗹𝗹𝗶𝗻𝗴_𝗽𝗼𝗶𝗻𝘁”
https://r%74.com/news/588986-ukraine-never-win-senator/

Le 13/12/2023 à 09:51, Sylvia Else a écrit :
> On 12-Dec-23 5:19 pm, patdolan wrote:
>> Proxima Centauri is 4.2 light-years away from Big Ben. Two distant
>> observers A and B are racing past Proxima Centauri on their way to
>> Big Ben at .867c relative to the Big Ben--Proxima Centauri frame of
>> reference. For these two observers Proxima Centauri and Big Ben are
>> only 2.1 light-years apart due to Lorentz contraction. Both observers
>> also note that the little hand of Big Ben rotates only 365.25 times
>> per year of their proper time instead of 730.5 rotations, due to
>> Lorentz time dilation. Now this slowing of Big Ben is not some
>> illusion or artifact of speed. SR assures us that Big Ben REALLY IS
>> RUNNING SLOWER in their frame of reference.
>>
>> Just as observer A passes Proxima Centauri he begins to count the
>> 365.25 x 2.1 = 767 turns in the helical path of light emanating from
>> the tip of Big Ben's little hand, which lie between Big Ben and
>> Proxima Centauri at any given moment in that frame of reference. He
>> also counts the 2.42 x 365.25 = 884 additional turns that Big Ben
>> produces during the rest of his 2.42 year journey to Big Ben, for a
>> total of 1651 turns during the entire trip.

This is an interesting problem.
So I will answer it.
This will change all the relativistic nonsense that I notice on the
English and French forums in general,
where absolutely no one understands the theory correctly.

> The observer has to consider where Big Ben was in his frame when the
> light he's just seeing set out. Big Ben is now 2.1 light years away in
> his frame, but it is moving, and the light has taken some time to
> arrive, so the light he's just seen must have left Big Ben when it was
> more than 2.1 light years away.
>
> If we let the distance away that Big Ben was when the light departed be
> d, we can see that the time that Big Ben took to get from distance d to
> its present position of 2.1 light years must equal the time it took for
> the light to get from distance d to the observer. That is:
>
> (d - 2.1) / v = d / c
>
> where v = is 0.867c, and c = 1.
>
> (d - 2.1) / 0.867 = d / 1
>
> d - 2.1 = 0.867 * d
>
> d * (1 - 0.867) = 2.1
>
> d = 2.1 / ( 1 - 0.867)
>
> d = 15.79
>
> So in the observer's frame the light has taken 15.79 years to arrive,
> and there are many more than 2.1 years worth of rotations between Big
> Ben and the observer.
>
> Sylvia.

Everything you say seems very interesting, even logical.
Only, my very dear and remarkable Sylvia, like everyone else, you do
mathematical physics, but abstractly.
The universe is not made LIKE THAT.

R.H.

On Wednesday, December 13, 2023 at 8:03:34 AM UTC-8, Richard Hachel wrote:
> Le 13/12/2023 à 09:51, Sylvia Else a écrit :
> > On 12-Dec-23 5:19 pm, patdolan wrote:
> >> Proxima Centauri is 4.2 light-years away from Big Ben. Two distant
> >> observers A and B are racing past Proxima Centauri on their way to
> >> Big Ben at .867c relative to the Big Ben--Proxima Centauri frame of
> >> reference. For these two observers Proxima Centauri and Big Ben are
> >> only 2.1 light-years apart due to Lorentz contraction. Both observers
> >> also note that the little hand of Big Ben rotates only 365.25 times
> >> per year of their proper time instead of 730.5 rotations, due to
> >> Lorentz time dilation. Now this slowing of Big Ben is not some
> >> illusion or artifact of speed. SR assures us that Big Ben REALLY IS
> >> RUNNING SLOWER in their frame of reference.
> >>
> >> Just as observer A passes Proxima Centauri he begins to count the
> >> 365.25 x 2.1 = 767 turns in the helical path of light emanating from
> >> the tip of Big Ben's little hand, which lie between Big Ben and
> >> Proxima Centauri at any given moment in that frame of reference. He
> >> also counts the 2.42 x 365.25 = 884 additional turns that Big Ben
> >> produces during the rest of his 2.42 year journey to Big Ben, for a
> >> total of 1651 turns during the entire trip.
> This is an interesting problem.
> So I will answer it.

Dr. Hachel, I know that I speak for the entire forum when I type that we all await your solution to the Helical Path Paradox with unbridled enthusiasm..

> This will change all the relativistic nonsense that I notice on the
> English and French forums in general,
> where absolutely no one understands the theory correctly.
> > The observer has to consider where Big Ben was in his frame when the
> > light he's just seeing set out. Big Ben is now 2.1 light years away in
> > his frame, but it is moving, and the light has taken some time to
> > arrive, so the light he's just seen must have left Big Ben when it was
> > more than 2.1 light years away.
> >
> > If we let the distance away that Big Ben was when the light departed be
> > d, we can see that the time that Big Ben took to get from distance d to
> > its present position of 2.1 light years must equal the time it took for
> > the light to get from distance d to the observer. That is:
> >
> > (d - 2.1) / v = d / c
> >
> > where v = is 0.867c, and c = 1.
> >
> > (d - 2.1) / 0.867 = d / 1
> >
> > d - 2.1 = 0.867 * d
> >
> > d * (1 - 0.867) = 2.1
> >
> > d = 2.1 / ( 1 - 0.867)
> >
> > d = 15.79
> >
> > So in the observer's frame the light has taken 15.79 years to arrive,
> > and there are many more than 2.1 years worth of rotations between Big
> > Ben and the observer.
> >
> > Sylvia.
> Everything you say seems very interesting, even logical.
> Only, my very dear and remarkable Sylvia, like everyone else, you do
> mathematical physics, but abstractly.
> The universe is not made LIKE THAT.
>
> R.H.

On 14-Dec-23 12:12 am, patdolan wrote:
> On Wednesday, December 13, 2023 at 12:51:44 AM UTC-8, Sylvia Else
> wrote:
>> On 12-Dec-23 5:19 pm, patdolan wrote:
>>> Proxima Centauri is 4.2 light-years away from Big Ben. Two
>>> distant observers A and B are racing past Proxima Centauri on
>>> their way to Big Ben at .867c relative to the Big Ben--Proxima
>>> Centauri frame of reference. For these two observers Proxima
>>> Centauri and Big Ben are only 2.1 light-years apart due to
>>> Lorentz contraction. Both observers also note that the little
>>> hand of Big Ben rotates only 365.25 times per year of their
>>> proper time instead of 730.5 rotations, due to Lorentz time
>>> dilation. Now this slowing of Big Ben is not some illusion or
>>> artifact of speed. SR assures us that Big Ben REALLY IS RUNNING
>>> SLOWER in their frame of reference.
>>>
>>> Just as observer A passes Proxima Centauri he begins to count
>>> the 365.25 x 2.1 = 767 turns in the helical path of light
>>> emanating from the tip of Big Ben's little hand, which lie
>>> between Big Ben and Proxima Centauri at any given moment in that
>>> frame of reference. He also counts the 2.42 x 365.25 = 884
>>> additional turns that Big Ben produces during the rest of his
>>> 2.42 year journey to Big Ben, for a total of 1651 turns during
>>> the entire trip.
>> The observer has to consider where Big Ben was in his frame when
>> the light he's just seeing set out. Big Ben is now 2.1 light years
>> away in his frame, but it is moving, and the light has taken some
>> time to arrive, so the light he's just seen must have left Big Ben
>> when it was more than 2.1 light years away.
>
> Agreed.
>>
>> If we let the distance away that Big Ben was when the light
>> departed be d, we can see that the time that Big Ben took to get
>> from distance d to its present position of 2.1 light years must
>> equal the time it took for the light to get from distance d to the
>> observer. That is:
>>
>> (d - 2.1) / v = d / c
>>
>> where v = is 0.867c, and c = 1.
>>
>> (d - 2.1) / 0.867 = d / 1
>>
>> d - 2.1 = 0.867 * d
>>
>> d * (1 - 0.867) = 2.1
>>
>> d = 2.1 / ( 1 - 0.867)
>>
>> d = 15.79
>>
>> So in the observer's frame the light has taken 15.79 years to
>> arrive, and there are many more than 2.1 years worth of rotations
>> between Big Ben and the observer.
> If the first light to arrive at observer A was emitted from Big Ben
> 15.79 years ago (a very plausible assumption) then it stands to
> reason that the last light to arrive at the end of his 2.42 year trip
> was emitted from Big Ben 13.37 years ago. But this is a preposterous
> conclusion. For we know a priori in our souls and beyond any
> conclusion of algebraic reasoning that the last light to arrive was
> emitted the instant before observer A crashed into the clock face of
> Big Ben.

The long transit time for the first light is a consequence of the
distance it had to travel. The last light, just before the observer
crashes into Big Ben, has no distance to travel, and so has zero transit
time.

>
> This is a teachable moment my children. The erroneous algebra of
> special relativity does not survive the move off the paper to the
> real world of empirical physical phact. You have been told this
> before Sylvia. And I have demonstrated this several ways now.

Your "stands to reason" analysis is where things go awry. It is not the
fault of special relativity. In your formulation of your paradox, you
made a mistake, and mistakes happen. But now you're just being
intellectually dishonest.

Sylvia.

On 14-Dec-23 3:03 am, Richard Hachel wrote:
> Le 13/12/2023 à 09:51, Sylvia Else a écrit :
>> On 12-Dec-23 5:19 pm, patdolan wrote:
>>> Proxima Centauri is 4.2 light-years away from Big Ben. Two distant
>>> observers A and B are racing past Proxima Centauri on their way to
>>> Big Ben at .867c relative to the Big Ben--Proxima Centauri frame of
>>> reference. For these two observers Proxima Centauri and Big Ben are
>>> only 2.1 light-years apart due to Lorentz contraction. Both observers
>>> also note that the little hand of Big Ben rotates only 365.25 times
>>> per year of their proper time instead of 730.5 rotations, due to
>>> Lorentz time dilation. Now this slowing of Big Ben is not some
>>> illusion or artifact of speed. SR assures us that Big Ben REALLY IS
>>> RUNNING SLOWER in their frame of reference.
>>>
>>> Just as observer A passes Proxima Centauri he begins to count the
>>> 365.25 x 2.1 = 767 turns in the helical path of light emanating from
>>> the tip of Big Ben's little hand, which lie between Big Ben and
>>> Proxima Centauri at any given moment in that frame of reference. He
>>> also counts the 2.42 x 365.25 = 884 additional turns that Big Ben
>>> produces during the rest of his 2.42 year journey to Big Ben, for a
>>> total of 1651 turns during the entire trip.
>
>
> This is an interesting problem.
> So I will answer it.
> This will change all the relativistic nonsense that I notice on the
> English and French forums in general,
> where absolutely no one understands the theory correctly.
>
>
>
>> The observer has to consider where Big Ben was in his frame when the
>> light he's just seeing set out. Big Ben is now 2.1 light years away in
>> his frame, but it is moving, and the light has taken some time to
>> arrive, so the light he's just seen must have left Big Ben when it was
>> more than 2.1 light years away.
>>
>> If we let the distance away that Big Ben was when the light departed
>> be d, we can see that the time that Big Ben took to get from distance
>> d to its present position of 2.1 light years must equal the time it
>> took for the light to get from distance d to the observer. That is:
>>
>> (d - 2.1) / v = d / c
>>
>> where v = is 0.867c, and c = 1.
>>
>> (d - 2.1) / 0.867 = d / 1
>>
>> d - 2.1 = 0.867 * d
>>
>> d * (1 - 0.867) = 2.1
>>
>> d = 2.1 / ( 1 - 0.867)
>>
>> d = 15.79
>>
>> So in the observer's frame the light has taken 15.79 years to arrive,
>> and there are many more than 2.1 years worth of rotations between Big
>> Ben and the observer.
>>
>> Sylvia.
>
>
> Everything you say seems very interesting, even logical.
> Only, my very dear and remarkable Sylvia, like everyone else, you do
> mathematical physics, but abstractly.
> The universe is not made LIKE THAT.
>
> R.H.

This thread is about the theory of special relativity. Pat has alleged
that it contains a contradiction, because he got the math wrong.

Whether the theory properly describes the universe is a separate issue.

Sylvia.

Le 13/12/2023 à 22:42, Sylvia Else a écrit :
> This thread is about the theory of special relativity. Pat has alleged
> that it contains a contradiction, because he got the math wrong.
>
> Whether the theory properly describes the universe is a separate issue.
>
> Sylvia.

The problem with those who disprove special relativity in whole or in part
is that they do it very badly.

The worst being those who refute it in its entirety, even though multiple
experiments have shown that it is correct at least in part. These people
have remained at the level of Isaac Newton, and there is not much for them
to do.

Others, like me, understood very well that something was wrong, or even
proved it through certain theoretical contradictions (the Langevin paradox
has never been explained anywhere and proves that there is a contradiction
there theoretical for Galilean frames of reference, as Hachel's paradox
shows that there is exactly the same problem for accelerated frames: If A
accelerates towards B, then the time for B is greater than that of A,
since A expands its time, and more and more. But how can the time A for A
become smaller than that of B, while for him, it is B which approaches him
more and more quickly).

But those who understood this have been trying, desperately, for 120 years
now, to find out where the gigantic problem is.

Without succeeding.

It is with immense sadness that I read all of these, here, or on the
physics forums, or on YouTube.

They recognize special relativity as true, but sick, but do not know the
treatment that should be given to it.
Others flatly refuse to consider that there may sometimes be theoretical
and experimental imperfections.

The obvious cause is essentially human.

R.H.

On Wednesday, December 13, 2023 at 1:42:36 PM UTC-8, Sylvia Else wrote:
> On 14-Dec-23 3:03 am, Richard Hachel wrote:
> > Le 13/12/2023 à 09:51, Sylvia Else a écrit :
> >> On 12-Dec-23 5:19 pm, patdolan wrote:
> >>> Proxima Centauri is 4.2 light-years away from Big Ben. Two distant
> >>> observers A and B are racing past Proxima Centauri on their way to
> >>> Big Ben at .867c relative to the Big Ben--Proxima Centauri frame of
> >>> reference. For these two observers Proxima Centauri and Big Ben are
> >>> only 2.1 light-years apart due to Lorentz contraction. Both observers
> >>> also note that the little hand of Big Ben rotates only 365.25 times
> >>> per year of their proper time instead of 730.5 rotations, due to
> >>> Lorentz time dilation. Now this slowing of Big Ben is not some
> >>> illusion or artifact of speed. SR assures us that Big Ben REALLY IS
> >>> RUNNING SLOWER in their frame of reference.
> >>>
> >>> Just as observer A passes Proxima Centauri he begins to count the
> >>> 365.25 x 2.1 = 767 turns in the helical path of light emanating from
> >>> the tip of Big Ben's little hand, which lie between Big Ben and
> >>> Proxima Centauri at any given moment in that frame of reference. He
> >>> also counts the 2.42 x 365.25 = 884 additional turns that Big Ben
> >>> produces during the rest of his 2.42 year journey to Big Ben, for a
> >>> total of 1651 turns during the entire trip.
> >
> >
> > This is an interesting problem.
> > So I will answer it.
> > This will change all the relativistic nonsense that I notice on the
> > English and French forums in general,
> > where absolutely no one understands the theory correctly.
> >
> >
> >
> >> The observer has to consider where Big Ben was in his frame when the
> >> light he's just seeing set out. Big Ben is now 2.1 light years away in
> >> his frame, but it is moving, and the light has taken some time to
> >> arrive, so the light he's just seen must have left Big Ben when it was
> >> more than 2.1 light years away.
> >>
> >> If we let the distance away that Big Ben was when the light departed
> >> be d, we can see that the time that Big Ben took to get from distance
> >> d to its present position of 2.1 light years must equal the time it
> >> took for the light to get from distance d to the observer. That is:
> >>
> >> (d - 2.1) / v = d / c
> >>
> >> where v = is 0.867c, and c = 1.
> >>
> >> (d - 2.1) / 0.867 = d / 1
> >>
> >> d - 2.1 = 0.867 * d
> >>
> >> d * (1 - 0.867) = 2.1
> >>
> >> d = 2.1 / ( 1 - 0.867)
> >>
> >> d = 15.79
> >>
> >> So in the observer's frame the light has taken 15.79 years to arrive,
> >> and there are many more than 2.1 years worth of rotations between Big
> >> Ben and the observer.
> >>
> >> Sylvia.
> >
> >
> > Everything you say seems very interesting, even logical.
> > Only, my very dear and remarkable Sylvia, like everyone else, you do
> > mathematical physics, but abstractly.
> > The universe is not made LIKE THAT.
> >
> > R.H.
> This thread is about the theory of special relativity. Pat has alleged
> that it contains a contradiction, because he got the math wrong.

Sylvia, I'll brook no tongue-lashing from you about getting the math wrong. Let's examine the last two lines in your proof:

d = 2.1 / ( 1 - 0.867)

d = 15.79

Now let's change your value for v=0.867c to the non relativistic value of say v=.00001c. Now your last line becomes d = 2.1 light-years. Balderdash! At non-relativistic velocities d (the distance between Big Ben and Proxima Centauri) MUST revert to its non-relativistic distance of 4.2 light-years. You unknowingly smuggled Galilean relativity into a special relativity problem. This is where you went wrong and where I went right.

>
> Whether the theory properly describes the universe is a separate issue.
>
> Sylvia.

On 14-Dec-23 11:22 am, patdolan wrote:
> On Wednesday, December 13, 2023 at 1:42:36 PM UTC-8, Sylvia Else wrote:
>> On 14-Dec-23 3:03 am, Richard Hachel wrote:
>>> Le 13/12/2023 à 09:51, Sylvia Else a écrit :
>>>> On 12-Dec-23 5:19 pm, patdolan wrote:
>>>>> Proxima Centauri is 4.2 light-years away from Big Ben. Two distant
>>>>> observers A and B are racing past Proxima Centauri on their way to
>>>>> Big Ben at .867c relative to the Big Ben--Proxima Centauri frame of
>>>>> reference. For these two observers Proxima Centauri and Big Ben are
>>>>> only 2.1 light-years apart due to Lorentz contraction. Both observers
>>>>> also note that the little hand of Big Ben rotates only 365.25 times
>>>>> per year of their proper time instead of 730.5 rotations, due to
>>>>> Lorentz time dilation. Now this slowing of Big Ben is not some
>>>>> illusion or artifact of speed. SR assures us that Big Ben REALLY IS
>>>>> RUNNING SLOWER in their frame of reference.
>>>>>
>>>>> Just as observer A passes Proxima Centauri he begins to count the
>>>>> 365.25 x 2.1 = 767 turns in the helical path of light emanating from
>>>>> the tip of Big Ben's little hand, which lie between Big Ben and
>>>>> Proxima Centauri at any given moment in that frame of reference. He
>>>>> also counts the 2.42 x 365.25 = 884 additional turns that Big Ben
>>>>> produces during the rest of his 2.42 year journey to Big Ben, for a
>>>>> total of 1651 turns during the entire trip.
>>>
>>>
>>> This is an interesting problem.
>>> So I will answer it.
>>> This will change all the relativistic nonsense that I notice on the
>>> English and French forums in general,
>>> where absolutely no one understands the theory correctly.
>>>
>>>
>>>
>>>> The observer has to consider where Big Ben was in his frame when the
>>>> light he's just seeing set out. Big Ben is now 2.1 light years away in
>>>> his frame, but it is moving, and the light has taken some time to
>>>> arrive, so the light he's just seen must have left Big Ben when it was
>>>> more than 2.1 light years away.
>>>>
>>>> If we let the distance away that Big Ben was when the light departed
>>>> be d, we can see that the time that Big Ben took to get from distance
>>>> d to its present position of 2.1 light years must equal the time it
>>>> took for the light to get from distance d to the observer. That is:
>>>>
>>>> (d - 2.1) / v = d / c
>>>>
>>>> where v = is 0.867c, and c = 1.
>>>>
>>>> (d - 2.1) / 0.867 = d / 1
>>>>
>>>> d - 2.1 = 0.867 * d
>>>>
>>>> d * (1 - 0.867) = 2.1
>>>>
>>>> d = 2.1 / ( 1 - 0.867)
>>>>
>>>> d = 15.79
>>>>
>>>> So in the observer's frame the light has taken 15.79 years to arrive,
>>>> and there are many more than 2.1 years worth of rotations between Big
>>>> Ben and the observer.
>>>>
>>>> Sylvia.
>>>
>>>
>>> Everything you say seems very interesting, even logical.
>>> Only, my very dear and remarkable Sylvia, like everyone else, you do
>>> mathematical physics, but abstractly.
>>> The universe is not made LIKE THAT.
>>>
>>> R.H.
>> This thread is about the theory of special relativity. Pat has alleged
>> that it contains a contradiction, because he got the math wrong.
>
> Sylvia, I'll brook no tongue-lashing from you about getting the math wrong. Let's examine the last two lines in your proof:
>
> d = 2.1 / ( 1 - 0.867)
>
> d = 15.79
>
> Now let's change your value for v=0.867c to the non relativistic value of say v=.00001c. Now your last line becomes d = 2.1 light-years. Balderdash! At non-relativistic velocities d (the distance between Big Ben and Proxima Centauri) MUST revert to its non-relativistic distance of 4.2 light-years. You unknowingly smuggled Galilean relativity into a special relativity problem. This is where you went wrong and where I went right.

The 2.1 is the distance between the stars in the observer's frame, and
derives from the proper distance between the stars, and their velocity
relative to the observer.

You specified the parameters of the scenario, I'm just applying them. If
the velocity is not 0.867c, then the distance between stars in the
observer's frame is not 2.1 light years. Nothing turns on that.

Sylvia.

On Wednesday, December 13, 2023 at 4:30:11 PM UTC-8, Sylvia Else wrote:
> On 14-Dec-23 11:22 am, patdolan wrote:
> > On Wednesday, December 13, 2023 at 1:42:36 PM UTC-8, Sylvia Else wrote:
> >> On 14-Dec-23 3:03 am, Richard Hachel wrote:
> >>> Le 13/12/2023 à 09:51, Sylvia Else a écrit :
> >>>> On 12-Dec-23 5:19 pm, patdolan wrote:
> >>>>> Proxima Centauri is 4.2 light-years away from Big Ben. Two distant
> >>>>> observers A and B are racing past Proxima Centauri on their way to
> >>>>> Big Ben at .867c relative to the Big Ben--Proxima Centauri frame of
> >>>>> reference. For these two observers Proxima Centauri and Big Ben are
> >>>>> only 2.1 light-years apart due to Lorentz contraction. Both observers
> >>>>> also note that the little hand of Big Ben rotates only 365.25 times
> >>>>> per year of their proper time instead of 730.5 rotations, due to
> >>>>> Lorentz time dilation. Now this slowing of Big Ben is not some
> >>>>> illusion or artifact of speed. SR assures us that Big Ben REALLY IS
> >>>>> RUNNING SLOWER in their frame of reference.
> >>>>>
> >>>>> Just as observer A passes Proxima Centauri he begins to count the
> >>>>> 365.25 x 2.1 = 767 turns in the helical path of light emanating from
> >>>>> the tip of Big Ben's little hand, which lie between Big Ben and
> >>>>> Proxima Centauri at any given moment in that frame of reference. He
> >>>>> also counts the 2.42 x 365.25 = 884 additional turns that Big Ben
> >>>>> produces during the rest of his 2.42 year journey to Big Ben, for a
> >>>>> total of 1651 turns during the entire trip.
> >>>
> >>>
> >>> This is an interesting problem.
> >>> So I will answer it.
> >>> This will change all the relativistic nonsense that I notice on the
> >>> English and French forums in general,
> >>> where absolutely no one understands the theory correctly.
> >>>
> >>>
> >>>
> >>>> The observer has to consider where Big Ben was in his frame when the
> >>>> light he's just seeing set out. Big Ben is now 2.1 light years away in
> >>>> his frame, but it is moving, and the light has taken some time to
> >>>> arrive, so the light he's just seen must have left Big Ben when it was
> >>>> more than 2.1 light years away.
> >>>>
> >>>> If we let the distance away that Big Ben was when the light departed
> >>>> be d, we can see that the time that Big Ben took to get from distance
> >>>> d to its present position of 2.1 light years must equal the time it
> >>>> took for the light to get from distance d to the observer. That is:
> >>>>
> >>>> (d - 2.1) / v = d / c
> >>>>
> >>>> where v = is 0.867c, and c = 1.
> >>>>
> >>>> (d - 2.1) / 0.867 = d / 1
> >>>>
> >>>> d - 2.1 = 0.867 * d
> >>>>
> >>>> d * (1 - 0.867) = 2.1
> >>>>
> >>>> d = 2.1 / ( 1 - 0.867)
> >>>>
> >>>> d = 15.79
> >>>>
> >>>> So in the observer's frame the light has taken 15.79 years to arrive,
> >>>> and there are many more than 2.1 years worth of rotations between Big
> >>>> Ben and the observer.
> >>>>
> >>>> Sylvia.
> >>>
> >>>
> >>> Everything you say seems very interesting, even logical.
> >>> Only, my very dear and remarkable Sylvia, like everyone else, you do
> >>> mathematical physics, but abstractly.
> >>> The universe is not made LIKE THAT.
> >>>
> >>> R.H.
> >> This thread is about the theory of special relativity. Pat has alleged
> >> that it contains a contradiction, because he got the math wrong.
> >
> > Sylvia, I'll brook no tongue-lashing from you about getting the math wrong. Let's examine the last two lines in your proof:
> >
> > d = 2.1 / ( 1 - 0.867)
> >
> > d = 15.79
> >
> > Now let's change your value for v=0.867c to the non relativistic value of say v=.00001c. Now your last line becomes d = 2.1 light-years. Balderdash! At non-relativistic velocities d (the distance between Big Ben and Proxima Centauri) MUST revert to its non-relativistic distance of 4.2 light-years. You unknowingly smuggled Galilean relativity into a special relativity problem. This is where you went wrong and where I went right.
> The 2.1 is the distance between the stars in the observer's frame, and
> derives from the proper distance between the stars, and their velocity
> relative to the observer.
>
> You specified the parameters of the scenario, I'm just applying them. If
> the velocity is not 0.867c, then the distance between stars in the
> observer's frame is not 2.1 light years. Nothing turns on that.
>
> Sylvia.
Sylvia, you will never live this down. But don't take my word for it. Ask Dr. Hachel.

PS--I look forward to the Hachel's Helix solution to the Helical Path Paradox.

Le 14/12/2023 à 01:30, Sylvia Else a écrit :
> On 14-Dec-23 11:22 am, patdolan wrote:
>> On Wednesday, December 13, 2023 at 1:42:36 PM UTC-8, Sylvia Else wrote:
>>> On 14-Dec-23 3:03 am, Richard Hachel wrote:
>>>> Le 13/12/2023 à 09:51, Sylvia Else a écrit :
>>>>> On 12-Dec-23 5:19 pm, patdolan wrote:
>>>>>> Proxima Centauri is 4.2 light-years away from Big Ben. Two distant
>>>>>> observers A and B are racing past Proxima Centauri on their way to
>>>>>> Big Ben at .867c relative to the Big Ben--Proxima Centauri frame of
>>>>>> reference. For these two observers Proxima Centauri and Big Ben are
>>>>>> only 2.1 light-years apart due to Lorentz contraction. Both observers
>>>>>> also note that the little hand of Big Ben rotates only 365.25 times
>>>>>> per year of their proper time instead of 730.5 rotations, due to
>>>>>> Lorentz time dilation. Now this slowing of Big Ben is not some
>>>>>> illusion or artifact of speed. SR assures us that Big Ben REALLY IS
>>>>>> RUNNING SLOWER in their frame of reference.
>>>>>>
>>>>>> Just as observer A passes Proxima Centauri he begins to count the
>>>>>> 365.25 x 2.1 = 767 turns in the helical path of light emanating from
>>>>>> the tip of Big Ben's little hand, which lie between Big Ben and
>>>>>> Proxima Centauri at any given moment in that frame of reference. He
>>>>>> also counts the 2.42 x 365.25 = 884 additional turns that Big Ben
>>>>>> produces during the rest of his 2.42 year journey to Big Ben, for a
>>>>>> total of 1651 turns during the entire trip.
>>>>
>>>>
>>>> This is an interesting problem.
>>>> So I will answer it.
>>>> This will change all the relativistic nonsense that I notice on the
>>>> English and French forums in general,
>>>> where absolutely no one understands the theory correctly.
>>>>
>>>>
>>>>
>>>>> The observer has to consider where Big Ben was in his frame when the
>>>>> light he's just seeing set out. Big Ben is now 2.1 light years away in
>>>>> his frame, but it is moving, and the light has taken some time to
>>>>> arrive, so the light he's just seen must have left Big Ben when it was
>>>>> more than 2.1 light years away.
>>>>>
>>>>> If we let the distance away that Big Ben was when the light departed
>>>>> be d, we can see that the time that Big Ben took to get from distance
>>>>> d to its present position of 2.1 light years must equal the time it
>>>>> took for the light to get from distance d to the observer. That is:
>>>>>
>>>>> (d - 2.1) / v = d / c
>>>>>
>>>>> where v = is 0.867c, and c = 1.
>>>>>
>>>>> (d - 2.1) / 0.867 = d / 1
>>>>>
>>>>> d - 2.1 = 0.867 * d
>>>>>
>>>>> d * (1 - 0.867) = 2.1
>>>>>
>>>>> d = 2.1 / ( 1 - 0.867)
>>>>>
>>>>> d = 15.79
>>>>>
>>>>> So in the observer's frame the light has taken 15.79 years to arrive,
>>>>> and there are many more than 2.1 years worth of rotations between Big
>>>>> Ben and the observer.
>>>>>
>>>>> Sylvia.
>>>>
>>>>
>>>> Everything you say seems very interesting, even logical.
>>>> Only, my very dear and remarkable Sylvia, like everyone else, you do
>>>> mathematical physics, but abstractly.
>>>> The universe is not made LIKE THAT.
>>>>
>>>> R.H.
>>> This thread is about the theory of special relativity. Pat has alleged
>>> that it contains a contradiction, because he got the math wrong.
>>
>> Sylvia, I'll brook no tongue-lashing from you about getting the math wrong.
>> Let's examine the last two lines in your proof:
>>
>> d = 2.1 / ( 1 - 0.867)
>>
>> d = 15.79
>>
>> Now let's change your value for v=0.867c to the non relativistic value of say
>> v=.00001c. Now your last line becomes d = 2.1 light-years. Balderdash! At
>> non-relativistic velocities d (the distance between Big Ben and Proxima Centauri)
>> MUST revert to its non-relativistic distance of 4.2 light-years. You unknowingly
>> smuggled Galilean relativity into a special relativity problem. This is where you
>> went wrong and where I went right.
>
> The 2.1 is the distance between the stars in the observer's frame, and
> derives from the proper distance between the stars, and their velocity
> relative to the observer.
>
> You specified the parameters of the scenario, I'm just applying them. If
> the velocity is not 0.867c, then the distance between stars in the
> observer's frame is not 2.1 light years. Nothing turns on that.
>
> Sylvia.

There is a huge misunderstanding in this part of relativistic physics.

The problem posed here is:
The distance between Proxima Centauri is 4.2 ly.

A rocket passing near Proxima at speed Vo=0.867c in the Proxima-Earth
direction

At this very precise moment, the rocket captain looks through his
telescope.

At what distance does he see the earth.

Yanick Toutain (Newtonian) answers: 4.2 ly.

Sylvia Else (she is adorable) responds: 1.121 ly and affirms like Einstein
that there is a contraction of distances.

Doctor Hachel says : no.

The distance at this precise moment is 15,736 ly.

Earth is more than 15 light years away.

Theoretical proof: What is the apparent speed of the earth which
approaches the rocket in observable speed Vo=0.867c?

Vapp=Vo/(1+cosµ.Vo/c)=6.52c (calculation approved by physicists around
the world)

What is the proper time of the rocket to link Proxima and the earth?
Tr=2,414 years (calculation validated by all relativistic physicists in
the world).

What is the relationship between the distance traveled with the apparent
speed of the object and the subject's own time?
x=Vapp.Tr

Here x=6.52*2.414=15.736 ly

This is all fantastic logic.

L'=L.sqrt(1-Vo²/c²)/(1+cosµ.Vo/c) : Here, cosµ=-1 Vo=0.867c
L=4.2ly

R.H.

On 14-Dec-23 11:52 am, patdolan wrote:
> On Wednesday, December 13, 2023 at 4:30:11 PM UTC-8, Sylvia Else wrote:
>> On 14-Dec-23 11:22 am, patdolan wrote:
>>> On Wednesday, December 13, 2023 at 1:42:36 PM UTC-8, Sylvia Else wrote:
>>>> On 14-Dec-23 3:03 am, Richard Hachel wrote:
>>>>> Le 13/12/2023 à 09:51, Sylvia Else a écrit :
>>>>>> On 12-Dec-23 5:19 pm, patdolan wrote:
>>>>>>> Proxima Centauri is 4.2 light-years away from Big Ben. Two distant
>>>>>>> observers A and B are racing past Proxima Centauri on their way to
>>>>>>> Big Ben at .867c relative to the Big Ben--Proxima Centauri frame of
>>>>>>> reference. For these two observers Proxima Centauri and Big Ben are
>>>>>>> only 2.1 light-years apart due to Lorentz contraction. Both observers
>>>>>>> also note that the little hand of Big Ben rotates only 365.25 times
>>>>>>> per year of their proper time instead of 730.5 rotations, due to
>>>>>>> Lorentz time dilation. Now this slowing of Big Ben is not some
>>>>>>> illusion or artifact of speed. SR assures us that Big Ben REALLY IS
>>>>>>> RUNNING SLOWER in their frame of reference.
>>>>>>>
>>>>>>> Just as observer A passes Proxima Centauri he begins to count the
>>>>>>> 365.25 x 2.1 = 767 turns in the helical path of light emanating from
>>>>>>> the tip of Big Ben's little hand, which lie between Big Ben and
>>>>>>> Proxima Centauri at any given moment in that frame of reference. He
>>>>>>> also counts the 2.42 x 365.25 = 884 additional turns that Big Ben
>>>>>>> produces during the rest of his 2.42 year journey to Big Ben, for a
>>>>>>> total of 1651 turns during the entire trip.
>>>>>
>>>>>
>>>>> This is an interesting problem.
>>>>> So I will answer it.
>>>>> This will change all the relativistic nonsense that I notice on the
>>>>> English and French forums in general,
>>>>> where absolutely no one understands the theory correctly.
>>>>>
>>>>>
>>>>>
>>>>>> The observer has to consider where Big Ben was in his frame when the
>>>>>> light he's just seeing set out. Big Ben is now 2.1 light years away in
>>>>>> his frame, but it is moving, and the light has taken some time to
>>>>>> arrive, so the light he's just seen must have left Big Ben when it was
>>>>>> more than 2.1 light years away.
>>>>>>
>>>>>> If we let the distance away that Big Ben was when the light departed
>>>>>> be d, we can see that the time that Big Ben took to get from distance
>>>>>> d to its present position of 2.1 light years must equal the time it
>>>>>> took for the light to get from distance d to the observer. That is:
>>>>>>
>>>>>> (d - 2.1) / v = d / c
>>>>>>
>>>>>> where v = is 0.867c, and c = 1.
>>>>>>
>>>>>> (d - 2.1) / 0.867 = d / 1
>>>>>>
>>>>>> d - 2.1 = 0.867 * d
>>>>>>
>>>>>> d * (1 - 0.867) = 2.1
>>>>>>
>>>>>> d = 2.1 / ( 1 - 0.867)
>>>>>>
>>>>>> d = 15.79
>>>>>>
>>>>>> So in the observer's frame the light has taken 15.79 years to arrive,
>>>>>> and there are many more than 2.1 years worth of rotations between Big
>>>>>> Ben and the observer.
>>>>>>
>>>>>> Sylvia.
>>>>>
>>>>>
>>>>> Everything you say seems very interesting, even logical.
>>>>> Only, my very dear and remarkable Sylvia, like everyone else, you do
>>>>> mathematical physics, but abstractly.
>>>>> The universe is not made LIKE THAT.
>>>>>
>>>>> R.H.
>>>> This thread is about the theory of special relativity. Pat has alleged
>>>> that it contains a contradiction, because he got the math wrong.
>>>
>>> Sylvia, I'll brook no tongue-lashing from you about getting the math wrong. Let's examine the last two lines in your proof:
>>>
>>> d = 2.1 / ( 1 - 0.867)
>>>
>>> d = 15.79
>>>
>>> Now let's change your value for v=0.867c to the non relativistic value of say v=.00001c. Now your last line becomes d = 2.1 light-years. Balderdash! At non-relativistic velocities d (the distance between Big Ben and Proxima Centauri) MUST revert to its non-relativistic distance of 4.2 light-years. You unknowingly smuggled Galilean relativity into a special relativity problem. This is where you went wrong and where I went right.
>> The 2.1 is the distance between the stars in the observer's frame, and
>> derives from the proper distance between the stars, and their velocity
>> relative to the observer.
>>
>> You specified the parameters of the scenario, I'm just applying them. If
>> the velocity is not 0.867c, then the distance between stars in the
>> observer's frame is not 2.1 light years. Nothing turns on that.
>>
>> Sylvia.
> Sylvia, you will never live this down. But don't take my word for it. Ask Dr. Hachel.
>
> PS--I look forward to the Hachel's Helix solution to the Helical Path Paradox.

How about you reformulate you paradox taking into account the light
transit time.

Sylvia.

On Thursday 14 December 2023 at 01:30:11 UTC+1, Sylvia Else wrote:

> The 2.1 is the distance between the stars in the observer's frame, and
> derives from the proper distance between the stars, and their velocity
> relative to the observer.

And in the meantime in the real world improper clocks
keep measuring improper t'=t. Sorry, lady, You can
insist that the absurds of Your insane gurus are "proper"
and "right" and only right, sane people are going sane
way and Your chanting can do NOTHING about it.

On 14-Dec-23 11:55 am, Richard Hachel wrote:
> Le 14/12/2023 à 01:30, Sylvia Else a écrit :
>> On 14-Dec-23 11:22 am, patdolan wrote:
>>> On Wednesday, December 13, 2023 at 1:42:36 PM UTC-8, Sylvia Else wrote:
>>>> On 14-Dec-23 3:03 am, Richard Hachel wrote:
>>>>> Le 13/12/2023 à 09:51, Sylvia Else a écrit :
>>>>>> On 12-Dec-23 5:19 pm, patdolan wrote:
>>>>>>> Proxima Centauri is 4.2 light-years away from Big Ben. Two distant
>>>>>>> observers A and B are racing past Proxima Centauri on their way to
>>>>>>> Big Ben at .867c relative to the Big Ben--Proxima Centauri frame of
>>>>>>> reference. For these two observers Proxima Centauri and Big Ben are
>>>>>>> only 2.1 light-years apart due to Lorentz contraction. Both
>>>>>>> observers
>>>>>>> also note that the little hand of Big Ben rotates only 365.25 times
>>>>>>> per year of their proper time instead of 730.5 rotations, due to
>>>>>>> Lorentz time dilation. Now this slowing of Big Ben is not some
>>>>>>> illusion or artifact of speed. SR assures us that Big Ben REALLY IS
>>>>>>> RUNNING SLOWER in their frame of reference.
>>>>>>>
>>>>>>> Just as observer A passes Proxima Centauri he begins to count the
>>>>>>> 365.25 x 2.1 = 767 turns in the helical path of light emanating from
>>>>>>> the tip of Big Ben's little hand, which lie between Big Ben and
>>>>>>> Proxima Centauri at any given moment in that frame of reference. He
>>>>>>> also counts the 2.42 x 365.25 = 884 additional turns that Big Ben
>>>>>>> produces during the rest of his 2.42 year journey to Big Ben, for a
>>>>>>> total of 1651 turns during the entire trip.
>>>>>
>>>>>
>>>>> This is an interesting problem.
>>>>> So I will answer it.
>>>>> This will change all the relativistic nonsense that I notice on the
>>>>> English and French forums in general,
>>>>> where absolutely no one understands the theory correctly.
>>>>>
>>>>>
>>>>>
>>>>>> The observer has to consider where Big Ben was in his frame when the
>>>>>> light he's just seeing set out. Big Ben is now 2.1 light years
>>>>>> away in
>>>>>> his frame, but it is moving, and the light has taken some time to
>>>>>> arrive, so the light he's just seen must have left Big Ben when it
>>>>>> was
>>>>>> more than 2.1 light years away.
>>>>>>
>>>>>> If we let the distance away that Big Ben was when the light departed
>>>>>> be d, we can see that the time that Big Ben took to get from distance
>>>>>> d to its present position of 2.1 light years must equal the time it
>>>>>> took for the light to get from distance d to the observer. That is:
>>>>>>
>>>>>> (d - 2.1) / v = d / c
>>>>>>
>>>>>> where v = is 0.867c, and c = 1.
>>>>>>
>>>>>> (d - 2.1) / 0.867 = d / 1
>>>>>>
>>>>>> d - 2.1 = 0.867 * d
>>>>>>
>>>>>> d * (1 - 0.867) = 2.1
>>>>>>
>>>>>> d = 2.1 / ( 1 - 0.867)
>>>>>>
>>>>>> d = 15.79
>>>>>>
>>>>>> So in the observer's frame the light has taken 15.79 years to arrive,
>>>>>> and there are many more than 2.1 years worth of rotations between Big
>>>>>> Ben and the observer.
>>>>>>
>>>>>> Sylvia.
>>>>>
>>>>>
>>>>> Everything you say seems very interesting, even logical.
>>>>> Only, my very dear and remarkable Sylvia, like everyone else, you do
>>>>> mathematical physics, but abstractly.
>>>>> The universe is not made LIKE THAT.
>>>>>
>>>>> R.H.
>>>> This thread is about the theory of special relativity. Pat has alleged
>>>> that it contains a contradiction, because he got the math wrong.
>>>
>>> Sylvia, I'll brook no tongue-lashing from you about getting the math
>>> wrong. Let's examine the last two lines in your proof:
>>>
>>> d = 2.1 / ( 1 - 0.867)
>>>
>>> d = 15.79
>>>
>>> Now let's change your value for v=0.867c to the non relativistic
>>> value of say v=.00001c.  Now your last line becomes d = 2.1
>>> light-years.  Balderdash!  At non-relativistic velocities d (the
>>> distance between Big Ben and Proxima Centauri) MUST revert to its
>>> non-relativistic distance of 4.2 light-years.  You unknowingly
>>> smuggled Galilean relativity into a special relativity problem.  This
>>> is where you went wrong and where I went right.
>>
>> The 2.1 is the distance between the stars in the observer's frame, and
>> derives from the proper distance between the stars, and their velocity
>> relative to the observer.
>>
>> You specified the parameters of the scenario, I'm just applying them.
>> If the velocity is not 0.867c, then the distance between stars in the
>> observer's frame is not 2.1 light years. Nothing turns on that.
>>
>> Sylvia.
>
> There is a huge misunderstanding in this part of relativistic physics.
>
> The problem posed here is:
> The distance between Proxima Centauri is 4.2 ly.
>
> A rocket passing near Proxima at speed Vo=0.867c in the Proxima-Earth
> direction
>
> At this very precise moment, the rocket captain looks through his
> telescope.
>
> At what distance does he see the earth.
>
> Yanick Toutain (Newtonian) answers: 4.2 ly.
>
> Sylvia Else (she is adorable) responds: 1.121 ly and affirms like
> Einstein that there is a contraction of distances.

You're just making stuff up. I never said that.

Sylvia.

Le 14/12/2023 à 02:02, Sylvia Else a écrit :
> On 14-Dec-23 11:55 am, Richard Hachel wrote:
>> Le 14/12/2023 à 01:30, Sylvia Else a écrit :
>>> On 14-Dec-23 11:22 am, patdolan wrote:
>>>> On Wednesday, December 13, 2023 at 1:42:36 PM UTC-8, Sylvia Else wrote:
>>>>> On 14-Dec-23 3:03 am, Richard Hachel wrote:
>>>>>> Le 13/12/2023 à 09:51, Sylvia Else a écrit :
>>>>>>> On 12-Dec-23 5:19 pm, patdolan wrote:
>>>>>>>> Proxima Centauri is 4.2 light-years away from Big Ben. Two distant
>>>>>>>> observers A and B are racing past Proxima Centauri on their way to
>>>>>>>> Big Ben at .867c relative to the Big Ben--Proxima Centauri frame of
>>>>>>>> reference. For these two observers Proxima Centauri and Big Ben are
>>>>>>>> only 2.1 light-years apart due to Lorentz contraction. Both
>>>>>>>> observers
>>>>>>>> also note that the little hand of Big Ben rotates only 365.25 times
>>>>>>>> per year of their proper time instead of 730.5 rotations, due to
>>>>>>>> Lorentz time dilation. Now this slowing of Big Ben is not some
>>>>>>>> illusion or artifact of speed. SR assures us that Big Ben REALLY IS
>>>>>>>> RUNNING SLOWER in their frame of reference.
>>>>>>>>
>>>>>>>> Just as observer A passes Proxima Centauri he begins to count the
>>>>>>>> 365.25 x 2.1 = 767 turns in the helical path of light emanating from
>>>>>>>> the tip of Big Ben's little hand, which lie between Big Ben and
>>>>>>>> Proxima Centauri at any given moment in that frame of reference. He
>>>>>>>> also counts the 2.42 x 365.25 = 884 additional turns that Big Ben
>>>>>>>> produces during the rest of his 2.42 year journey to Big Ben, for a
>>>>>>>> total of 1651 turns during the entire trip.
>>>>>>
>>>>>>
>>>>>> This is an interesting problem.
>>>>>> So I will answer it.
>>>>>> This will change all the relativistic nonsense that I notice on the
>>>>>> English and French forums in general,
>>>>>> where absolutely no one understands the theory correctly.
>>>>>>
>>>>>>
>>>>>>
>>>>>>> The observer has to consider where Big Ben was in his frame when the
>>>>>>> light he's just seeing set out. Big Ben is now 2.1 light years
>>>>>>> away in
>>>>>>> his frame, but it is moving, and the light has taken some time to
>>>>>>> arrive, so the light he's just seen must have left Big Ben when it
>>>>>>> was
>>>>>>> more than 2.1 light years away.
>>>>>>>
>>>>>>> If we let the distance away that Big Ben was when the light departed
>>>>>>> be d, we can see that the time that Big Ben took to get from distance
>>>>>>> d to its present position of 2.1 light years must equal the time it
>>>>>>> took for the light to get from distance d to the observer. That is:
>>>>>>>
>>>>>>> (d - 2.1) / v = d / c
>>>>>>>
>>>>>>> where v = is 0.867c, and c = 1.
>>>>>>>
>>>>>>> (d - 2.1) / 0.867 = d / 1
>>>>>>>
>>>>>>> d - 2.1 = 0.867 * d
>>>>>>>
>>>>>>> d * (1 - 0.867) = 2.1
>>>>>>>
>>>>>>> d = 2.1 / ( 1 - 0.867)
>>>>>>>
>>>>>>> d = 15.79
>>>>>>>
>>>>>>> So in the observer's frame the light has taken 15.79 years to arrive,
>>>>>>> and there are many more than 2.1 years worth of rotations between Big
>>>>>>> Ben and the observer.
>>>>>>>
>>>>>>> Sylvia.
>>>>>>
>>>>>>
>>>>>> Everything you say seems very interesting, even logical.
>>>>>> Only, my very dear and remarkable Sylvia, like everyone else, you do
>>>>>> mathematical physics, but abstractly.
>>>>>> The universe is not made LIKE THAT.
>>>>>>
>>>>>> R.H.
>>>>> This thread is about the theory of special relativity. Pat has alleged
>>>>> that it contains a contradiction, because he got the math wrong.
>>>>
>>>> Sylvia, I'll brook no tongue-lashing from you about getting the math
>>>> wrong. Let's examine the last two lines in your proof:
>>>>
>>>> d = 2.1 / ( 1 - 0.867)
>>>>
>>>> d = 15.79
>>>>
>>>> Now let's change your value for v=0.867c to the non relativistic
>>>> value of say v=.00001c.  Now your last line becomes d = 2.1
>>>> light-years.  Balderdash!  At non-relativistic velocities d (the
>>>> distance between Big Ben and Proxima Centauri) MUST revert to its
>>>> non-relativistic distance of 4.2 light-years.  You unknowingly
>>>> smuggled Galilean relativity into a special relativity problem.  This
>>>> is where you went wrong and where I went right.
>>>
>>> The 2.1 is the distance between the stars in the observer's frame, and
>>> derives from the proper distance between the stars, and their velocity
>>> relative to the observer.
>>>
>>> You specified the parameters of the scenario, I'm just applying them.
>>> If the velocity is not 0.867c, then the distance between stars in the
>>> observer's frame is not 2.1 light years. Nothing turns on that.
>>>
>>> Sylvia.
>>
>> There is a huge misunderstanding in this part of relativistic physics.
>>
>> The problem posed here is:
>> The distance between Proxima Centauri is 4.2 ly.
>>
>> A rocket passing near Proxima at speed Vo=0.867c in the Proxima-Earth
>> direction
>>
>> At this very precise moment, the rocket captain looks through his
>> telescope.
>>
>> At what distance does he see the earth.
>>
>> Yanick Toutain (Newtonian) answers: 4.2 ly.
>>
>> Sylvia Else (she is adorable) responds: 1.121 ly and affirms like
>> Einstein that there is a contraction of distances.
>
> You're just making stuff up. I never said that.
>
> Sylvia.

Exact you said 2.093 ly.

But is the same approach : contraction of distances.

And is no true.

R.H.

On 14-Dec-23 12:27 pm, Richard Hachel wrote:
> Le 14/12/2023 à 02:02, Sylvia Else a écrit :
>> On 14-Dec-23 11:55 am, Richard Hachel wrote:
>>> Le 14/12/2023 à 01:30, Sylvia Else a écrit :
>>>> On 14-Dec-23 11:22 am, patdolan wrote:
>>>>> On Wednesday, December 13, 2023 at 1:42:36 PM UTC-8, Sylvia Else
>>>>> wrote:
>>>>>> On 14-Dec-23 3:03 am, Richard Hachel wrote:
>>>>>>> Le 13/12/2023 à 09:51, Sylvia Else a écrit :
>>>>>>>> On 12-Dec-23 5:19 pm, patdolan wrote:
>>>>>>>>> Proxima Centauri is 4.2 light-years away from Big Ben. Two distant
>>>>>>>>> observers A and B are racing past Proxima Centauri on their way to
>>>>>>>>> Big Ben at .867c relative to the Big Ben--Proxima Centauri
>>>>>>>>> frame of
>>>>>>>>> reference. For these two observers Proxima Centauri and Big Ben
>>>>>>>>> are
>>>>>>>>> only 2.1 light-years apart due to Lorentz contraction. Both
>>>>>>>>> observers
>>>>>>>>> also note that the little hand of Big Ben rotates only 365.25
>>>>>>>>> times
>>>>>>>>> per year of their proper time instead of 730.5 rotations, due to
>>>>>>>>> Lorentz time dilation. Now this slowing of Big Ben is not some
>>>>>>>>> illusion or artifact of speed. SR assures us that Big Ben
>>>>>>>>> REALLY IS
>>>>>>>>> RUNNING SLOWER in their frame of reference.
>>>>>>>>>
>>>>>>>>> Just as observer A passes Proxima Centauri he begins to count the
>>>>>>>>> 365.25 x 2.1 = 767 turns in the helical path of light emanating
>>>>>>>>> from
>>>>>>>>> the tip of Big Ben's little hand, which lie between Big Ben and
>>>>>>>>> Proxima Centauri at any given moment in that frame of
>>>>>>>>> reference. He
>>>>>>>>> also counts the 2.42 x 365.25 = 884 additional turns that Big Ben
>>>>>>>>> produces during the rest of his 2.42 year journey to Big Ben,
>>>>>>>>> for a
>>>>>>>>> total of 1651 turns during the entire trip.
>>>>>>>
>>>>>>>
>>>>>>> This is an interesting problem.
>>>>>>> So I will answer it.
>>>>>>> This will change all the relativistic nonsense that I notice on the
>>>>>>> English and French forums in general,
>>>>>>> where absolutely no one understands the theory correctly.
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>> The observer has to consider where Big Ben was in his frame when
>>>>>>>> the
>>>>>>>> light he's just seeing set out. Big Ben is now 2.1 light years
>>>>>>>> away in
>>>>>>>> his frame, but it is moving, and the light has taken some time to
>>>>>>>> arrive, so the light he's just seen must have left Big Ben when
>>>>>>>> it was
>>>>>>>> more than 2.1 light years away.
>>>>>>>>
>>>>>>>> If we let the distance away that Big Ben was when the light
>>>>>>>> departed
>>>>>>>> be d, we can see that the time that Big Ben took to get from
>>>>>>>> distance
>>>>>>>> d to its present position of 2.1 light years must equal the time it
>>>>>>>> took for the light to get from distance d to the observer. That is:
>>>>>>>>
>>>>>>>> (d - 2.1) / v = d / c
>>>>>>>>
>>>>>>>> where v = is 0.867c, and c = 1.
>>>>>>>>
>>>>>>>> (d - 2.1) / 0.867 = d / 1
>>>>>>>>
>>>>>>>> d - 2.1 = 0.867 * d
>>>>>>>>
>>>>>>>> d * (1 - 0.867) = 2.1
>>>>>>>>
>>>>>>>> d = 2.1 / ( 1 - 0.867)
>>>>>>>>
>>>>>>>> d = 15.79
>>>>>>>>
>>>>>>>> So in the observer's frame the light has taken 15.79 years to
>>>>>>>> arrive,
>>>>>>>> and there are many more than 2.1 years worth of rotations
>>>>>>>> between Big
>>>>>>>> Ben and the observer.
>>>>>>>>
>>>>>>>> Sylvia.
>>>>>>>
>>>>>>>
>>>>>>> Everything you say seems very interesting, even logical.
>>>>>>> Only, my very dear and remarkable Sylvia, like everyone else, you do
>>>>>>> mathematical physics, but abstractly.
>>>>>>> The universe is not made LIKE THAT.
>>>>>>>
>>>>>>> R.H.
>>>>>> This thread is about the theory of special relativity. Pat has
>>>>>> alleged
>>>>>> that it contains a contradiction, because he got the math wrong.
>>>>>
>>>>> Sylvia, I'll brook no tongue-lashing from you about getting the
>>>>> math wrong. Let's examine the last two lines in your proof:
>>>>>
>>>>> d = 2.1 / ( 1 - 0.867)
>>>>>
>>>>> d = 15.79
>>>>>
>>>>> Now let's change your value for v=0.867c to the non relativistic
>>>>> value of say v=.00001c.  Now your last line becomes d = 2.1
>>>>> light-years.  Balderdash!  At non-relativistic velocities d (the
>>>>> distance between Big Ben and Proxima Centauri) MUST revert to its
>>>>> non-relativistic distance of 4.2 light-years.  You unknowingly
>>>>> smuggled Galilean relativity into a special relativity problem.
>>>>> This is where you went wrong and where I went right.
>>>>
>>>> The 2.1 is the distance between the stars in the observer's frame,
>>>> and derives from the proper distance between the stars, and their
>>>> velocity relative to the observer.
>>>>
>>>> You specified the parameters of the scenario, I'm just applying
>>>> them. If the velocity is not 0.867c, then the distance between stars
>>>> in the observer's frame is not 2.1 light years. Nothing turns on that.
>>>>
>>>> Sylvia.
>>>
>>> There is a huge misunderstanding in this part of relativistic physics.
>>>
>>> The problem posed here is:
>>> The distance between Proxima Centauri is 4.2 ly.
>>>
>>> A rocket passing near Proxima at speed Vo=0.867c in the Proxima-Earth
>>> direction
>>>
>>> At this very precise moment, the rocket captain looks through his
>>> telescope.
>>>
>>> At what distance does he see the earth.
>>>
>>> Yanick Toutain (Newtonian) answers: 4.2 ly.
>>>
>>> Sylvia Else (she is adorable) responds: 1.121 ly and affirms like
>>> Einstein that there is a contraction of distances.
>>
>> You're just making stuff up. I never said that.
>>
>> Sylvia.
>
> Exact you said 2.093 ly.
>
> But is the same approach : contraction of distances.
> And is no true.
>
> R.H.

The significant context is "At what distance does he see the earth."

I never said that he sees the Earth at 2.1 light years. The closest I
got to saying anything about the distance at which Earth is seen is in
my calculation of the distance the light had travelled from the Earth,
and that number is nothing like 2.1 light years.

Sylvia.

On 2023-12-14 01:02:00 +0000, Sylvia Else said:

> On 14-Dec-23 11:55 am, Richard Hachel wrote:
>>
>> [ … ]
>>
>> Sylvia Else (she is adorable) responds: 1.121 ly and affirms like
>> Einstein that there is a contraction of distances.
>
> You're just making stuff up. I never said that.

Why on earth do you tolerate this misogynist twaddle from this ghastly
fake "Doctor"?

--
athel -- biochemist, not a physicist, but detector of crackpots

Le 14/12/2023 à 13:56, Athel Cornish-Bowden a écrit :
>> You're just making stuff up. I never said that.
>
> Why on earth do you tolerate this misogynist twaddle from this ghastly
> fake "Doctor"?

In one sentence, three lies.

I'm not mysopgynous, and I really like intelligent and feminine women.

I find that Sylvia often has scientifically interesting answers and so I
respond to her when I can.

I have never usurped anything, especially not a doctorate.

R.H.

On 2023-12-14 14:45:15 +0000, Richard Hachel said:

> Le 14/12/2023 à 13:56, Athel Cornish-Bowden a écrit :
>>> You're just making stuff up. I never said that.
>>
>> Why on earth do you tolerate this misogynist twaddle from this ghastly
>> fake "Doctor"?
>
> In one sentence, three lies.
>
> I'm not mysopgynous, and I really like intelligent and feminine women.
>
> I find that Sylvia often has scientifically interesting answers and so
> I respond to her when I can.
>
> I have never usurped anything, especially not a doctorate.

So you say, but you've never revealed which university awarded your
doctorate and what was the subject of your thesis. (I'm not referring
to your medical qualifications, but to your relevant qualifications.)

--
athel -- biochemist, not a physicist, but detector of crackpots

On Thursday, December 14, 2023 at 9:18:02 AM UTC-8, Athel Cornish-Bowden wrote:
> On 2023-12-14 14:45:15 +0000, Richard Hachel said:
>
> > Le 14/12/2023 à 13:56, Athel Cornish-Bowden a écrit :
> >>> You're just making stuff up. I never said that.
> >>
> >> Why on earth do you tolerate this misogynist twaddle from this ghastly
> >> fake "Doctor"?
> >
> > In one sentence, three lies.
> >
> > I'm not mysopgynous, and I really like intelligent and feminine women.
> >
> > I find that Sylvia often has scientifically interesting answers and so
> > I respond to her when I can.
> >
> > I have never usurped anything, especially not a doctorate.
> So you say, but you've never revealed which university awarded your
> doctorate and what was the subject of your thesis. (I'm not referring
> to your medical qualifications, but to your relevant qualifications.)
> --
> athel -- biochemist, not a physicist, but detector of crackpots
THAT IS ENGOUH! I don't want you two stags fighting over Sylvia on my thread. Now take it outside (chumps).

On Wednesday, December 13, 2023 at 12:51:44 AM UTC-8, Sylvia Else wrote:
> On 12-Dec-23 5:19 pm, patdolan wrote:
> > Proxima Centauri is 4.2 light-years away from Big Ben. Two distant
> > observers A and B are racing past Proxima Centauri on their way to
> > Big Ben at .867c relative to the Big Ben--Proxima Centauri frame of
> > reference. For these two observers Proxima Centauri and Big Ben are
> > only 2.1 light-years apart due to Lorentz contraction. Both observers
> > also note that the little hand of Big Ben rotates only 365.25 times
> > per year of their proper time instead of 730.5 rotations, due to
> > Lorentz time dilation. Now this slowing of Big Ben is not some
> > illusion or artifact of speed. SR assures us that Big Ben REALLY IS
> > RUNNING SLOWER in their frame of reference.
> >
> > Just as observer A passes Proxima Centauri he begins to count the
> > 365.25 x 2.1 = 767 turns in the helical path of light emanating from
> > the tip of Big Ben's little hand, which lie between Big Ben and
> > Proxima Centauri at any given moment in that frame of reference. He
> > also counts the 2.42 x 365.25 = 884 additional turns that Big Ben
> > produces during the rest of his 2.42 year journey to Big Ben, for a
> > total of 1651 turns during the entire trip.
> The observer has to consider where Big Ben was in his frame when the
> light he's just seeing set out. Big Ben is now 2.1 light years away in
> his frame, but it is moving, and the light has taken some time to
> arrive, so the light he's just seen must have left Big Ben when it was
> more than 2.1 light years away.
>
> If we let the distance away that Big Ben was when the light departed be
> d, we can see that the time that Big Ben took to get from distance d to
> its present position of 2.1 light years must equal the time it took for
> the light to get from distance d to the observer. That is:
>
> (d - 2.1) / v = d / c
>
> where v = is 0.867c, and c = 1.
>
> (d - 2.1) / 0.867 = d / 1
>
> d - 2.1 = 0.867 * d
>
> d * (1 - 0.867) = 2.1
>
> d = 2.1 / ( 1 - 0.867)
>
> d = 15.79
>
> So in the observer's frame the light has taken 15.79 years to arrive,
> and there are many more than 2.1 years worth of rotations between Big
> Ben and the observer.
>
> Sylvia.

Sylvia, in studying your approach to the problem I find that you have implicitly used the concept of absolute motion in your fundamental equation. You do this when you treat the Big Ben--Proxima Centauri complex as being in motion with respect to observer A by dividing the constant distance between BB and PC (2.1 ly) by v. So in a certain sense you claim that the distance between BB and PC is in motion with respect to, and approaching observer A while observer A is at rest. Don't believe me? read on.

Let's repeat the derivation, this time assuming that observer A is in motion and approaching the BB/PC complex which is at rest. Here's how in your own words:

If we let the distance away that observer A was when the light departed be
d, we can see that the time that observer A took to get from distance d to
its present position of 2.1 light years must equal the time it took for
the light to get from 2.1 to observer A. That is:

2.1/c = d/v

where v = is 0.867c, and c = 1.

2.1/1 = d/0.867

( 2.1 )( 0.867 ) = d

d = 1.82

BB <--------- 2.1 ------------> PC <--------------- d --------------> observer A
But this time it is observer A that moves at velocity v instead of the other way around.

On Thursday, December 14, 2023 at 12:07:13 PM UTC-8, patdolan wrote:
> On Wednesday, December 13, 2023 at 12:51:44 AM UTC-8, Sylvia Else wrote:
> > On 12-Dec-23 5:19 pm, patdolan wrote:
> > > Proxima Centauri is 4.2 light-years away from Big Ben. Two distant
> > > observers A and B are racing past Proxima Centauri on their way to
> > > Big Ben at .867c relative to the Big Ben--Proxima Centauri frame of
> > > reference. For these two observers Proxima Centauri and Big Ben are
> > > only 2.1 light-years apart due to Lorentz contraction. Both observers
> > > also note that the little hand of Big Ben rotates only 365.25 times
> > > per year of their proper time instead of 730.5 rotations, due to
> > > Lorentz time dilation. Now this slowing of Big Ben is not some
> > > illusion or artifact of speed. SR assures us that Big Ben REALLY IS
> > > RUNNING SLOWER in their frame of reference.
> > >
> > > Just as observer A passes Proxima Centauri he begins to count the
> > > 365.25 x 2.1 = 767 turns in the helical path of light emanating from
> > > the tip of Big Ben's little hand, which lie between Big Ben and
> > > Proxima Centauri at any given moment in that frame of reference. He
> > > also counts the 2.42 x 365.25 = 884 additional turns that Big Ben
> > > produces during the rest of his 2.42 year journey to Big Ben, for a
> > > total of 1651 turns during the entire trip.
> > The observer has to consider where Big Ben was in his frame when the
> > light he's just seeing set out. Big Ben is now 2.1 light years away in
> > his frame, but it is moving, and the light has taken some time to
> > arrive, so the light he's just seen must have left Big Ben when it was
> > more than 2.1 light years away.
> >
> > If we let the distance away that Big Ben was when the light departed be
> > d, we can see that the time that Big Ben took to get from distance d to
> > its present position of 2.1 light years must equal the time it took for
> > the light to get from distance d to the observer. That is:
> >
> > (d - 2.1) / v = d / c
> >
> > where v = is 0.867c, and c = 1.
> >
> > (d - 2.1) / 0.867 = d / 1
> >
> > d - 2.1 = 0.867 * d
> >
> > d * (1 - 0.867) = 2.1
> >
> > d = 2.1 / ( 1 - 0.867)
> >
> > d = 15.79
> >
> > So in the observer's frame the light has taken 15.79 years to arrive,
> > and there are many more than 2.1 years worth of rotations between Big
> > Ben and the observer.
> >
> > Sylvia.
> Sylvia, in studying your approach to the problem I find that you have implicitly used the concept of absolute motion in your fundamental equation. You do this when you treat the Big Ben--Proxima Centauri complex as being in motion with respect to observer A by dividing the constant distance between BB and PC (2.1 ly) by v. So in a certain sense you claim that the distance between BB and PC is in motion with respect to, and approaching observer A while observer A is at rest. Don't believe me? read on.
>
> Let's repeat the derivation, this time assuming that observer A is in motion and approaching the BB/PC complex which is at rest. Here's how in your own words:
>
> If we let the distance away that observer A was when the light departed be
> d, we can see that the time that observer A took to get from distance d to
> its present position of 2.1 light years must equal the time it took for
> the light to get from 2.1 to observer A. That is:
>
> 2.1/c = d/v
> where v = is 0.867c, and c = 1.
> 2.1/1 = d/0.867
>
> ( 2.1 )( 0.867 ) = d
>
> d = 1.82
>
> BB <--------- 2.1 ------------> PC <--------------- d --------------> observer A
> But this time it is observer A that moves at velocity v instead of the other way around.
BTW Sylvia, your method works out perfectly for the realistic doppler formula. But there is no denying the validity of my method. Which answer are we to choose? The principle of relativity claims that both answers are valid. In summation, we have achieved nothing less than a doppler test for absolute motion--the very thing that Einstein said couldn't exist.

I might--might, say you--decide to share my Nobel with you (I believe three or four are already as good as on their way to me already). But absolutely no dates at the Nobel banquet! I don't want either Athel or Dr. Hachel showing up and hogging my limelight.