• #### Re: The Helical Path Paradox

From Sylvia Else@21:1/5 to patdolan on Wed Dec 13 19:51:39 2023
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.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Richard Hachel@21:1/5 to All on Wed Dec 13 16:03:31 2023
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.
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.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Sylvia Else@21:1/5 to Richard Hachel on Thu Dec 14 08:42:32 2023
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.
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.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Sylvia Else@21:1/5 to patdolan on Thu Dec 14 08:40:16 2023
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
made a mistake, and mistakes happen. But now you're just being
intellectually dishonest.

Sylvia.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Richard Hachel@21:1/5 to All on Wed Dec 13 22:32:20 2023
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
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

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.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Sylvia Else@21:1/5 to patdolan on Thu Dec 14 11:30:06 2023
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.
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.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Sylvia Else@21:1/5 to patdolan on Thu Dec 14 11:56:00 2023
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.
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.

transit time.

Sylvia.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Richard Hachel@21:1/5 to All on Thu Dec 14 00:55:59 2023
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.
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.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Sylvia Else@21:1/5 to Richard Hachel on Thu Dec 14 12:02:00 2023
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.
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.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Richard Hachel@21:1/5 to All on Thu Dec 14 01:27:19 2023
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.
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.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Sylvia Else@21:1/5 to Richard Hachel on Thu Dec 14 12:58:03 2023
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.
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.
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.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Athel Cornish-Bowden@21:1/5 to Sylvia Else on Thu Dec 14 13:56:47 2023
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

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Richard Hachel@21:1/5 to All on Thu Dec 14 14:45:15 2023
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.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Athel Cornish-Bowden@21:1/5 to Richard Hachel on Thu Dec 14 18:17:56 2023
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

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

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Sylvia Else@21:1/5 to patdolan on Fri Dec 15 11:10:24 2023
On 15-Dec-23 7:07 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.

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.

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

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.

When analysing in the BB/PC frame, you should not be applying the length contraction.

But in any case, I do not see the significance of d here. In the
previous analysis, the purpose of d was to allow a determination of how
long ago, in the observer's frame, the light set out that the observer
will eventually see when passing PC, because the light has to traverse
distance d. In the current analysis, the light traversing distance d is
of no interest, because the analysis doesn't even start until the
observer reaches PC.

We know that in the BB/PC frame, it took 4.2 years for that light to
make the transit from BB to PC.

It will then take a further 4.2 / 0.867 years for the observer to reach
BB, bringing the total to a bit over 9 years, which is entirely
consistent with my analysis in the observer's frame, and with the
relativistic Doppler effect.

In your original post you said:

"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."

This is clearly wrong, with the correct number being nothing like that
low. The conceptual flaw appears to lie in the assumption that one can
just apply time dilation and length contraction to a snapshot of time
and distance. Both time dilation and length contraction are special
cases of the Lorentz transform, and one has to be very careful not to
seek to use them in situations that do not match those cases. Doing so
has led many a poster down a rabbit hole. This is why I have
consistently suggested to one particular poster that he use the Lorentz transform instead.

Sylvia.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Sylvia Else@21:1/5 to patdolan on Fri Dec 15 15:07:52 2023
On 15-Dec-23 2:33 pm, patdolan wrote:
On Thursday, December 14, 2023 at 4:10:29 PM UTC-8, Sylvia Else wrote:
On 15-Dec-23 7:07 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.

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.

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

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.
When analysing in the BB/PC frame, you should not be applying the length
contraction.

But in any case, I do not see the significance of d here. In the
previous analysis, the purpose of d was to allow a determination of how
long ago, in the observer's frame, the light set out that the observer
will eventually see when passing PC, because the light has to traverse
distance d. In the current analysis, the light traversing distance d is
of no interest, because the analysis doesn't even start until the
observer reaches PC.

We know that in the BB/PC frame, it took 4.2 years for that light to
make the transit from BB to PC.

It will then take a further 4.2 / 0.867 years for the observer to reach
BB, bringing the total to a bit over 9 years, which is entirely
consistent with my analysis in the observer's frame, and with the
relativistic Doppler effect.
In your original post you said:

"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."
This is clearly wrong, with the correct number being nothing like that
low. The conceptual flaw appears to lie in the assumption that one can
just apply time dilation and length contraction to a snapshot of time
and distance. Both time dilation and length contraction are special
cases of the Lorentz transform, and one has to be very careful not to
seek to use them in situations that do not match those cases. Doing so
has led many a poster down a rabbit hole. This is why I have
consistently suggested to one particular poster that he use the Lorentz

Sylvia.

My greatest oversight was assuming that just because Big Ben churns out 365.25 turns of the helix per year, and Proxima Centauri received 365.25 turns per year, it follows that the 2.1 light-year gap between the two can only contain 2.1 x 365.25 = 767
total turns. Your d-analysis wisened me up. Your d-analysis demonstrated that helical turns can stack up in the gap. BUT ONLY when the gap is in motion while observer A is at rest. And the gap is moving towards observer A. Yes, you read the last
sentence correctly. Because if you repeat the Sylvia d-analysis with the gap at rest and observer A in motion, as I did, you get a validly derived answer 4 times smaller than the relativistic doppler formula answer. While the Sylvia d-analysis gives
precisely the relativistic doppler formula value. That claim that absolute motion has been resurrected from the tomb is beyond conceptual ability of most of the denizen's of this forum and may require a new subject post.

In short, I found at the heart of special relativity the same contradiction that Einstein claimed to have found at the heart of electrodynamics. I have raised absolute motion from the dead. As for your wordy post, Sylvia, get back to us when you can
put all of that chatter into a few equations. Prove what you say with what you can calculate, as I always do.

I'm probably repeating myself here.

In the frame in which the gap is not moving, it is 4.2 light years long,
and always contains 4.2 years worth of spirals, so at the point were the observer reaches PC, the gap still contains 4.2 years worth of spirals.

It then takes the observer 4.2/0.867 years to reach BB, during which
another 4.85 years worth of spirals are created. So the observer
traverses 4.2 + 4.85 = 9.05 years worth of spirals.

In this frame, we don't even need special relativity to reach the right conclusion.

Sylvia.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Sylvia Else@21:1/5 to patdolan on Fri Dec 15 16:07:57 2023
On 15-Dec-23 3:40 pm, patdolan wrote:
On Thursday, December 14, 2023 at 8:07:57 PM UTC-8, Sylvia Else wrote:
On 15-Dec-23 2:33 pm, patdolan wrote:
On Thursday, December 14, 2023 at 4:10:29 PM UTC-8, Sylvia Else wrote: >>>> On 15-Dec-23 7:07 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.

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.

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

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.
When analysing in the BB/PC frame, you should not be applying the length >>>> contraction.

But in any case, I do not see the significance of d here. In the
previous analysis, the purpose of d was to allow a determination of how >>>> long ago, in the observer's frame, the light set out that the observer >>>> will eventually see when passing PC, because the light has to traverse >>>> distance d. In the current analysis, the light traversing distance d is >>>> of no interest, because the analysis doesn't even start until the
observer reaches PC.

We know that in the BB/PC frame, it took 4.2 years for that light to
make the transit from BB to PC.

It will then take a further 4.2 / 0.867 years for the observer to reach >>>> BB, bringing the total to a bit over 9 years, which is entirely
consistent with my analysis in the observer's frame, and with the
relativistic Doppler effect.
In your original post you said:

"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."
This is clearly wrong, with the correct number being nothing like that >>>> low. The conceptual flaw appears to lie in the assumption that one can >>>> just apply time dilation and length contraction to a snapshot of time
and distance. Both time dilation and length contraction are special
cases of the Lorentz transform, and one has to be very careful not to
seek to use them in situations that do not match those cases. Doing so >>>> has led many a poster down a rabbit hole. This is why I have
consistently suggested to one particular poster that he use the Lorentz >>>> transform instead.

Sylvia.

My greatest oversight was assuming that just because Big Ben churns out 365.25 turns of the helix per year, and Proxima Centauri received 365.25 turns per year, it follows that the 2.1 light-year gap between the two can only contain 2.1 x 365.25 =
767 total turns. Your d-analysis wisened me up. Your d-analysis demonstrated that helical turns can stack up in the gap. BUT ONLY when the gap is in motion while observer A is at rest. And the gap is moving towards observer A. Yes, you read the last
sentence correctly. Because if you repeat the Sylvia d-analysis with the gap at rest and observer A in motion, as I did, you get a validly derived answer 4 times smaller than the relativistic doppler formula answer. While the Sylvia d-analysis gives
precisely the relativistic doppler formula value. That claim that absolute motion has been resurrected from the tomb is beyond conceptual ability of most of the denizen's of this forum and may require a new subject post.

In short, I found at the heart of special relativity the same contradiction that Einstein claimed to have found at the heart of electrodynamics. I have raised absolute motion from the dead. As for your wordy post, Sylvia, get back to us when you can
put all of that chatter into a few equations. Prove what you say with what you can calculate, as I always do.
I'm probably repeating myself here.

In the frame in which the gap is not moving, it is 4.2 light years long,
and always contains 4.2 years worth of spirals, so at the point were the
observer reaches PC, the gap still contains 4.2 years worth of spirals.

It then takes the observer 4.2/0.867 years to reach BB, during which
another 4.85 years worth of spirals are created. So the observer
traverses 4.2 + 4.85 = 9.05 years worth of spirals.

In this frame, we don't even need special relativity to reach the right
conclusion.

Yes, I see that. No length contraction, no time dilation (BB still makes 730.5 revolutions per year). You've figured how many turns would hit observer A as viewed by a stationary observer in the gap's proper frame. Your answer is not even
recognizable as anywhere near relativistic. Even at .867c. Now have the courage to due the calculation of what the moving observer A apprehends using the special theory of relativity.

Sylvia.

I did most of that already. You even conceded that it gave a result that matched that of the relativistic Doppler effect calculation.

The only result you've ever got that differs involves using the special
case time dilation and length contraction concepts in a scenario which
does not mach the special case requirements.

Sylvia.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Sylvia Else@21:1/5 to patdolan on Fri Dec 15 19:45:13 2023
On 15-Dec-23 7:26 pm, patdolan wrote:
On Thursday, December 14, 2023 at 9:08:01 PM UTC-8, Sylvia Else
wrote:
On 15-Dec-23 3:40 pm, patdolan wrote:
On Thursday, December 14, 2023 at 8:07:57 PM UTC-8, Sylvia Else
wrote:
On 15-Dec-23 2:33 pm, patdolan wrote:
On Thursday, December 14, 2023 at 4:10:29 PM UTC-8, Sylvia
Else wrote:
On 15-Dec-23 7:07 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.

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?

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.
When analysing in the BB/PC frame, you should not be
applying the length contraction.

But in any case, I do not see the significance of d here.
In the previous analysis, the purpose of d was to allow a
determination of how long ago, in the observer's frame, the
light set out that the observer will eventually see when
passing PC, because the light has to traverse distance d.
In the current analysis, the light traversing distance d
is of no interest, because the analysis doesn't even start
until the observer reaches PC.

We know that in the BB/PC frame, it took 4.2 years for that
light to make the transit from BB to PC.

It will then take a further 4.2 / 0.867 years for the
observer to reach BB, bringing the total to a bit over 9
years, which is entirely consistent with my analysis in the
observer's frame, and with the relativistic Doppler
effect. In your original post you said:

"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." This is clearly wrong,
with the correct number being nothing like that low. The
conceptual flaw appears to lie in the assumption that one
can just apply time dilation and length contraction to a
snapshot of time and distance. Both time dilation and
length contraction are special cases of the Lorentz
transform, and one has to be very careful not to seek to
use them in situations that do not match those cases. Doing
so has led many a poster down a rabbit hole. This is why I
have consistently suggested to one particular poster that
he use the Lorentz transform instead.

Sylvia.

My greatest oversight was assuming that just because Big Ben
churns out 365.25 turns of the helix per year, and Proxima
Centauri received 365.25 turns per year, it follows that the
2.1 light-year gap between the two can only contain 2.1 x
365.25 = 767 total turns. Your d-analysis wisened me up. Your
d-analysis demonstrated that helical turns can stack up in
the gap. BUT ONLY when the gap is in motion while observer A
is at rest. And the gap is moving towards observer A. Yes,
you read the last sentence correctly. Because if you repeat
the Sylvia d-analysis with the gap at rest and observer A in
motion, as I did, you get a validly derived answer 4 times
smaller than the relativistic doppler formula answer. While
the Sylvia d-analysis gives precisely the relativistic
doppler formula value. That claim that absolute motion has
been resurrected from the tomb is beyond conceptual ability
of most of the denizen's of this forum and may require a new
subject post.

In short, I found at the heart of special relativity the same
contradiction that Einstein claimed to have found at the
heart of electrodynamics. I have raised absolute motion from
the dead. As for your wordy post, Sylvia, get back to us when
you can put all of that chatter into a few equations. Prove
what you say with what you can calculate, as I always do.
I'm probably repeating myself here.

In the frame in which the gap is not moving, it is 4.2 light
years long, and always contains 4.2 years worth of spirals, so
at the point were the observer reaches PC, the gap still
contains 4.2 years worth of spirals.

It then takes the observer 4.2/0.867 years to reach BB, during
which another 4.85 years worth of spirals are created. So the
observer traverses 4.2 + 4.85 = 9.05 years worth of spirals.

In this frame, we don't even need special relativity to reach
the right conclusion.

Yes, I see that. No length contraction, no time dilation (BB
still makes 730.5 revolutions per year). You've figured how many
turns would hit observer A as viewed by a stationary observer in
anywhere near relativistic. Even at .867c. Now have the courage
to due the calculation of what the moving observer A apprehends
using the special theory of relativity.

Sylvia.
I did most of that already. You even conceded that it gave a result
that matched that of the relativistic Doppler effect calculation.

The only result you've ever got that differs involves using the
special case time dilation and length contraction concepts in a
scenario which does not mach the special case requirements.

Sylvia.

Yes Sylvia, I conceded that your first calculation of d = 15.79 ly
along with the additional 2.1 ly of the gap, perfectly account for
the 6650 turns which are also generated by the famous relativistic
doppler formula. BUT ONLY WHEN THE GAP IS IN MOTION AND THE OBSERVER
IS AT REST. (The proceeding sentence could not even be uttered 48
more precious. I have been vouchsafed the knowledge of the ultimate contradiction at the heart of relativity: the existence of absolute
motion and a test for same in the guise of relativistic doppler.

And, as discussed, we get the same result in the frame of BB/PC, which
is to say when the gap is not in motion. So what's left to address?

I do not see where you get the "absolute motion" from.

Sylvia.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Paul B. Andersen@21:1/5 to All on Fri Dec 15 14:45:52 2023
Den 12.12.2023 07:19, skrev patdolan:
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.

I will interpret this as the question to answer is:

How many rotations will the little hand of Big-Ben make
from the observer is passing Proxima Centauri to he hits
the Earth?

Let's call Earth's rest frame K(t,x).
We will call the position of the Earth E, and the position of
Proxima Centauri P in this frame.

O->v
K: P-----------------E
0 L
At t = t₀ = 0, the observer O is at P.
At t = t₁ the observer O is at E

L = 4.2 [ly] proper distance Earth - Proxima Centauri in K
v = 0.867c
γ = 2.0068
f₀ = 730.5 [cycles/y], proper frequency of the BB clock.
T = 1/f₀ = 0.001369 [y], proper duration of a cycle

t₁ = L/v = 4.844 y

So the answer to the question above is:
N₀ = f₀⋅t₁ = f₀⋅L/v = 3538.75 cycles
===================================

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.

It's not quite clear what this is supposed to mean, but I will
interpret it as: What will SR predict that the observer will
measure the number of turns will be?

Let K'(t',x') be O's rest frame.

There are two events of interest:
E0: The observer is at P
In K: t₀ = 0, x₀ = 0
In K': t₀' = 0, x₀' = 0

E1: The observer is at E
In K: t₁ = L/v, x₁ = L
In K':
t₁' = γ(t₁-v⋅x₁/c²) = L/γv
x₁' = γ(x₁-v⋅t₁) = 0

In K: t₂ = T, x₂ = T/v
In K': t₂'= γ(t₂-v⋅x₂/c²) = T/γ

f₀' = γ⋅f₀, the frequency measured in K'

So SR predicts that O will measure (count):
N₁ = f₀'⋅t₁' = γ⋅f₀⋅L/γv = f₀⋅L/v = 3538.75 cycles
=================================================

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.

So we are talking about visual observation of the BB clock.

O-v
P-----------------E
0 L

Since O is approaching the Earth, he will measure
(see above) the frequency of BB to be f₀' = γ⋅f₀.

He will visually observe this frequency to Doppler shifted:
f = sqrt((1+v/c)/(1-v/c))f₀' = f₀/(1-v/c)

He will observe this frequency for the time L/v.
But when he is at P, he will see the light emitted from BB
at a time L/c before he arrived at P, so he must subtract
the counts he received the first time L/c.
That means that he must count the cycles received during
the time Δt = L/v - L/c = (L/v)(1-v/c)

The number of counts emitted from BB during this time is:
N = f⋅Δt = (f₀/(1-v/c))(L/v)(1-v/c) = f₀⋅L/v = 3538.75 cycles ==============================================================

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.

--
Paul

https://paulba.no/

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Paul B. Andersen@21:1/5 to All on Sat Dec 16 10:24:06 2023
Den 15.12.2023 20:28, skrev patdolan:
On Friday, December 15, 2023 at 5:43:13 AM UTC-8, Paul B. Andersen wrote:
Den 12.12.2023 07:19, skrev patdolan:
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.
I will interpret this as the question to answer is:

How many rotations will the little hand of Big-Ben make
from the observer is passing Proxima Centauri to he hits
the Earth?

Let's call Earth's rest frame K(t,x).
We will call the position of the Earth E, and the position of
Proxima Centauri P in this frame.

v
K: P-----------------E
0 L
At t = t₀ = 0, the observer O is at P.
At t = t₁ the observer O is at E

L = 4.2 [ly] proper distance Earth - Proxima Centauri in K
v = 0.867c
γ = 2.0068
f₀ = 730.5 [cycles/y], proper frequency of the BB clock.
T = 1/f₀ = 0.001369 [y], proper duration of a cycle

t₁ = L/v = 4.844 y

So the answer to the question above is:
N₀ = f₀⋅t₁ = f₀⋅L/v = 3538.75 cycles
===================================

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.
It's not quite clear what this is supposed to mean, but I will
interpret it as: What will SR predict that the observer will
measure the number of turns will be?

Let K'(t',x') be O's rest frame.

There are two events of interest:
E0: The observer is at P
In K: t₀ = 0, x₀ = 0
In K': t₀' = 0, x₀' = 0

E1: The observer is at E
In K: t₁ = L/v, x₁ = L
In K':
t₁' = γ(t₁-v⋅x₁/c²) = L/γv
x₁' = γ(x₁-v⋅t₁) = 0

In K: t₂ = T, x₂ = T/v
In K': t₂'= γ(t₂-v⋅x₂/c²) = T/γ

f₀' = γ⋅f₀, the frequency measured in K'

So SR predicts that O will measure (count):
N₁ = f₀'⋅t₁' = γ⋅f₀⋅L/γv = f₀⋅L/v = 3538.75 cycles
=================================================

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.

So we are talking about visual observation of the BB clock.

O-v
P-----------------E
0 L

Since O is approaching the Earth, he will measure
(see above) the frequency of BB to be f₀' = γ⋅f₀.

He will visually observe this frequency to Doppler shifted:
f = sqrt((1+v/c)/(1-v/c))f₀' = f₀/(1-v/c)

He will observe this frequency for the time L/v.
But when he is at P, he will see the light emitted from BB
at a time L/c before he arrived at P, so he must subtract
the counts he received the first time L/c.
That means that he must count the cycles received during
the time Δt = L/v - L/c = (L/v)(1-v/c)

The number of counts emitted from BB during this time is:
N = f⋅Δt = (f₀/(1-v/c))(L/v)(1-v/c) = f₀⋅L/v = 3538.75 cycles
==============================================================

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.

--
Paul

https://paulba.no/

Paul, the only Roman numerals that appear in the above submission to this forum, appear in your conclusion. Please have the courtesy and the courage to publish a numerical version of each of your algebraic schema directly below that schem >
Now why am I requesting this of you? I am requesting this so that you yourself will reveal your to yourself your own absurdities. How will this forum know that you have successfully educated yourself in your own absurdities? By the simple fact that
you will not do as I request, out of embarrassment. But that's okay.

I will definitely not give the answers in Roman numerals as you request.

Do you really not understand the decimal numeral system?

I defined the constants in the decimal system:

L = 4.2 [ly] proper distance Earth - Proxima Centauri in K
v = 0.867c
γ = 2.0068
f₀ = 730.5 [cycles/y], proper frequency of the BB clock.
T = 1/f₀ = 0.001369 [y], proper duration of a cycle

Are you really not able to put these values into the my
three answers to the same question?

----------
t₁ = L/v = 4.844 y

So the answer to the question above is:
N₀ = f₀⋅t₁ = f₀⋅L/v = 3538.75 cycles
===================================
-----------------

t₁' = γ(t₁-v⋅x₁/c²) = L/γv

f₀' = γ⋅f₀, the frequency measured in K'

So SR predicts that O will measure (count):
N₁ = f₀'⋅t₁' = γ⋅f₀⋅L/γv = f₀⋅L/v = 3538.75 cycles
=================================================

-------------------------

f = sqrt((1+v/c)/(1-v/c))f₀' = f₀/(1-v/c)

Δt = L/v - L/c = (L/v)(1-v/c)

The number of counts emitted from BB during this time is:
N = f⋅Δt = (f₀/(1-v/c))(L/v)(1-v/c) = f₀⋅L/v = 3538.75 cycles ==============================================================

I challenger you to point out any absurdities in my calculations.

Or don't you understand them because they ar not written in
Roman numerals? :-D

--

Paul

https://paulba.no/

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Sylvia Else@21:1/5 to patdolan on Mon Dec 18 11:25:00 2023
On 18-Dec-23 11:13 am, patdolan wrote:
On Saturday, December 16, 2023 at 1:20:04 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.
In his latest post to this thread Paul has challenged me to find
any absurdities in his calculations, of which I'm sure there are
many. But at present I am concentrating on an absurdity that I
found in Sylvia's brilliant derivation above. And it reminds me to
remind you all of the first rule of relativism, which is: whatever
conclusion you reach while employing the principle of special
relativity, there will always be a contradiction associated with
that conclusion--all you have to do is look for it long enough.

Back to Sylvia's derivation of d, which represents the distance at
which the first light has to leave the tip of Big Ben's little hand
in order to make a timely rendezvous with the distant observer A at
Proxima Centauri. The reader will recall that the distant observer
and the light from BB race towards each other for a meetup at
Proxima Centauri. This meetup signals the start of the helical turn
counting by the distant observer. The light from BB travels at c
whilst the distant observer travels at 0.867c. As you can read
above, Sylvia brilliantly calculates that the first particle of
light that will eventually meetup with the distant observer will
have to emanate from Big Ben no less than 15.79 light years prior
to the meetup. This brilliant solution exactly accounts for the
stacking up of helical turns in the gap between Big Ben ( the earth
) and Proxima Centauri, such that 6651 helical turns ( the solution
yielded by the relativistic doppler formula ) will be measured by
the observer in the time it takes for him to traverse the distance
between Proxima and the clock face of Ben.

Here is the absurdity. The guy who just installed the radio
telescope on the top of Big Ben knows that he can send a signal,
bounce it off of Proxima Centauri and have it return to him in just
8.4 years. In Sylvia's world that signal won't even arrive at
Proxima until 15.8 years have passed. So Albert requires that we
now entertain the absurdity of two beams of light simultaneously
launched from BB towards the same target Proxima Centauri; one of
the beams completes a round trip [ 15.8 - 8.4 = ] 7.4 years before
the other beam even arrives at PC.

Now you're adding periods of time from different frames. I'd have
thought even you would know that you cannot meaningfully do that.

Further, the 15.8 years is in the frame of the observer, not the frame

How many times do you expect people to disentangle your mistakes before
you'll accept that you do not know what you are doing?

Sylvia.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Sylvia Else@21:1/5 to patdolan on Mon Dec 18 13:09:17 2023
On 18-Dec-23 11:48 am, patdolan wrote:
On Sunday, December 17, 2023 at 4:25:04 PM UTC-8, Sylvia Else wrote:
On 18-Dec-23 11:13 am, patdolan wrote:
On Saturday, December 16, 2023 at 1:20:04 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.
In his latest post to this thread Paul has challenged me to find
any absurdities in his calculations, of which I'm sure there are
many. But at present I am concentrating on an absurdity that I
found in Sylvia's brilliant derivation above. And it reminds me to
remind you all of the first rule of relativism, which is: whatever
conclusion you reach while employing the principle of special
relativity, there will always be a contradiction associated with
that conclusion--all you have to do is look for it long enough.

Back to Sylvia's derivation of d, which represents the distance at
which the first light has to leave the tip of Big Ben's little hand
in order to make a timely rendezvous with the distant observer A at
Proxima Centauri. The reader will recall that the distant observer
and the light from BB race towards each other for a meetup at
Proxima Centauri. This meetup signals the start of the helical turn
counting by the distant observer. The light from BB travels at c
whilst the distant observer travels at 0.867c. As you can read
above, Sylvia brilliantly calculates that the first particle of
light that will eventually meetup with the distant observer will
have to emanate from Big Ben no less than 15.79 light years prior
to the meetup. This brilliant solution exactly accounts for the
stacking up of helical turns in the gap between Big Ben ( the earth
) and Proxima Centauri, such that 6651 helical turns ( the solution
yielded by the relativistic doppler formula ) will be measured by
the observer in the time it takes for him to traverse the distance
between Proxima and the clock face of Ben.

Here is the absurdity. The guy who just installed the radio
telescope on the top of Big Ben knows that he can send a signal,
bounce it off of Proxima Centauri and have it return to him in just
8.4 years. In Sylvia's world that signal won't even arrive at
Proxima until 15.8 years have passed. So Albert requires that we
now entertain the absurdity of two beams of light simultaneously
launched from BB towards the same target Proxima Centauri; one of
the beams completes a round trip [ 15.8 - 8.4 = ] 7.4 years before
the other beam even arrives at PC.
Now you're adding periods of time from different frames. I'd have
thought even you would know that you cannot meaningfully do that.

Further, the 15.8 years is in the frame of the observer, not the frame
Yes, I know Sylvia. But the the difference is even more absurd when you consider the difference from the Big Ben, Proxima Centauri proper frame.

So you say, but what are the numbers? In particular, what are they when
you get the math right?

Sylvia.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Sylvia Else@21:1/5 to patdolan on Mon Dec 18 14:14:05 2023
On 18-Dec-23 1:31 pm, patdolan wrote:
On Sunday, December 17, 2023 at 6:09:22 PM UTC-8, Sylvia Else wrote:
On 18-Dec-23 11:48 am, patdolan wrote:
On Sunday, December 17, 2023 at 4:25:04 PM UTC-8, Sylvia Else wrote:
On 18-Dec-23 11:13 am, patdolan wrote:
On Saturday, December 16, 2023 at 1:20:04 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.
In his latest post to this thread Paul has challenged me to find
any absurdities in his calculations, of which I'm sure there are
many. But at present I am concentrating on an absurdity that I
found in Sylvia's brilliant derivation above. And it reminds me to >>>>>> remind you all of the first rule of relativism, which is: whatever >>>>>> conclusion you reach while employing the principle of special
relativity, there will always be a contradiction associated with
that conclusion--all you have to do is look for it long enough.

Back to Sylvia's derivation of d, which represents the distance at >>>>>> which the first light has to leave the tip of Big Ben's little hand >>>>>> in order to make a timely rendezvous with the distant observer A at >>>>>> Proxima Centauri. The reader will recall that the distant observer >>>>>> and the light from BB race towards each other for a meetup at
Proxima Centauri. This meetup signals the start of the helical turn >>>>>> counting by the distant observer. The light from BB travels at c
whilst the distant observer travels at 0.867c. As you can read
above, Sylvia brilliantly calculates that the first particle of
light that will eventually meetup with the distant observer will
have to emanate from Big Ben no less than 15.79 light years prior
to the meetup. This brilliant solution exactly accounts for the
stacking up of helical turns in the gap between Big Ben ( the earth >>>>>> ) and Proxima Centauri, such that 6651 helical turns ( the solution >>>>>> yielded by the relativistic doppler formula ) will be measured by
the observer in the time it takes for him to traverse the distance >>>>>> between Proxima and the clock face of Ben.

Here is the absurdity. The guy who just installed the radio
telescope on the top of Big Ben knows that he can send a signal,
bounce it off of Proxima Centauri and have it return to him in just >>>>>> 8.4 years. In Sylvia's world that signal won't even arrive at
Proxima until 15.8 years have passed. So Albert requires that we
now entertain the absurdity of two beams of light simultaneously
launched from BB towards the same target Proxima Centauri; one of
the beams completes a round trip [ 15.8 - 8.4 = ] 7.4 years before >>>>>> the other beam even arrives at PC.
Now you're adding periods of time from different frames. I'd have
thought even you would know that you cannot meaningfully do that.

Further, the 15.8 years is in the frame of the observer, not the frame >>>> of the radio telescope.
Yes, I know Sylvia. But the the difference is even more absurd when you consider the difference from the Big Ben, Proxima Centauri proper frame.
So you say, but what are the numbers? In particular, what are they when
you get the math right?

Sylvia.
In the BB-PC rest frame your d expands to 31.6 years. ( 2 x 15.8 years ). The Big Ben radio telescope signal round trip to PC remains 8.4 years ( 2 x 4.2 years ). Just an incredible absurdity.

Sylvia, cut the small talk. Either find a way to save relativity or cry uncle.

You're talking about two events separated in space and time. You can't
just multiply the time difference by γ and call it good. You have to
apply the Lorentz transform.

One event consists of the light arriving at the observer. Let that be at
time t1 = 0 and position x1 = 0.

The other event consists of the light being emitted from Big Ben. That
happens 15.8 years earlier, so let that be at time t2 = -15.8. It also
happens 15.8 light years away, in the opposite direction to the velocity
vector of Big Ben, so let that be at x2 = -15.8.

Now we the Lorentz transform on both events to get into the t' frame,
being the frame of Big Ben. Taking γ to be 2, and v as 0.867, we get:

t'2 = 2 * [-15.8 - (0.867 * -15.8)] = -4.2
t'1 = 2 * [0 - 0.867 * 0] = 0

So in the t' frame (i.e. the Big Ben frame) the difference in time
between the two events, t'1 - t'2, is 4.2 years, which is exactly what
one would expect.

Sylvia.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Paul B. Andersen@21:1/5 to All on Mon Dec 18 20:43:59 2023
Den 18.12.2023 01:13, skrev patdolan:
Prof. Paul are vanquished.

You haven't addressed my derivations with a single word.

I challenge you to find any errors or absurdities in the following:

Problem:
An observer O is racing past Proxima Centauri on her way to Big Ben
at .867c relative to the Big Ben.

How many rotations will the little hand of Big-Ben make
from the observer O is passing Proxima Centauri to she hits
the Earth?

Let's call Earth's rest frame K(t,x).
We will call the position of the Earth E, and the position of
Proxima Centauri P in this frame.

O->v
K: P-----------------E
0 L
At t = t₀ = 0, the observer O is at P.
At t = t₁ the observer O is at E

L = 4.2 [ly] proper distance Earth - Proxima Centauri in K
v = 0.867c
γ = 2.0068
f₀ = 730.5 [cycles/y], proper frequency of the BB clock.
T = 1/f₀ = 0.001369 [y], proper duration of a cycle

t₁ = L/v = 4.844 y

So the answer to the question above is:
N₀ = f₀⋅t₁ = f₀⋅L/v = 3538.75 cycles
===================================

This is the same as what NM predicts, because we
have not asked what is measured in O's rest frame. ____________________________________________________

The observer's clock is moving in K:
--------------------------------------

Let K'(t',x') be O's rest frame.

There are two events of interest:
E0: The observer is at P
In K: t₀ = 0, x₀ = 0
In K': t₀' = 0, x₀' = 0

E1: The observer is at E
In K: t₁ = L/v = 4.84429 y, x₁ = L = 4.2 ly
In K':
t₁' = γ(t₁-v⋅x₁/c²) = L/γv = 2.41395 y
x₁' = γ(x₁-v⋅t₁) = 0

In K: t₂ = T = 0.001369 y, x₂ = L/v = 2.09289 ly
In K': t₂'= γ(t₂-v⋅x₂/c²) = T/γ = 0.00068215 y

f₀' = γ⋅f₀ = 1465.96 cycles/y , the frequency measured in K'

So SR predicts that O will measure (count):
N₁ = f₀'⋅t₁' = γ⋅f₀⋅L/γv = f₀⋅L/v = 3538.75 cycles
=================================================>

Note this:
The observer's clock advances the proper time:
τ' = t₁'- t₀'= 2.41395 y
while the difference between the coordinate time
t₀ at x₀ and t₁ at x₁ changes by:
(t₁ - t₀) = L/v = 4.84429 y.

The observer's moving clock appears to run slow as measured in K. ________________________________________________________________

Big Ben is moving in K':
-------------------------

t₄' = 0
O
P-----------E
0 x₄'

At Event E₄ is E at x₄' when t₄' = 0

We know that E always is at x = L in K
t₄' = γ(t₄-v⋅L/c²) = 0 => t₄ = v⋅L/c² = 3.6414 y
x₄' = γ(x₄-v⋅t₄) = γ(L-L(v²/c²)) = L/γ = 2.09289 ly

So measured in K' at the time t' = 0, E is at the position L/γ
and BB is showing the proper time τ₄ = v⋅L/c² = 3.6414 y

At Event E1, when E is at P, we have from above:
BB is showing the the proper time τ₁ = t₁ = L/v = 4.84429 y

We still have:
f₀' = γ⋅f₀ = 1465.96 cycles/y , the frequency measured in K'
t₁' = L/γv = 2.41395 y

So SR predicts that O will measure (count):
N₁ = f₀'⋅t₁' = γ⋅f₀⋅L/γv = f₀⋅L/v = 3538.75 cycles
=================================================>

Note this:
Big Ben advances the proper time:
(τ₁-τ₄) = L/v-v⋅L/c² = (L/v)(1-v²/c²) = L/γ²v = 1.20289 y
while the difference between the coordinate time t₄' at x₄'
and t₁' at x₁' changes by:
(t₁' - t₄') = L/γv = 2.41395 y

The moving Big Ben appears to run slow as measured in K'. _________________________________________________________________

Calculation with Doppler shift.

O-v
P-----------------E
0 L

Since O is approaching the Earth, he will measure
(see above) the frequency of BB to be f₀' = γ⋅f₀.

He will visually observe this frequency to Doppler shifted:
f = sqrt((1+v/c)/(1-v/c))f₀' = f₀/(1-v/c)

He will observe this frequency for the time L/v.
But when he is at P, he will see the light emitted from BB
at a time L/c before he arrived at P, so he must subtract
the counts he received the first time L/c.
That means that he must count the cycles received during
the time Δt = L/v - L/c = (L/v)(1-v/c)

The number of counts emitted from BB during this time is:
N = f⋅Δt = (f₀/(1-v/c))(L/v)(1-v/c) = f₀⋅L/v = 3538.75 cycles ==============================================================

############################################################

BOTTOM LINE:

You, Pat Dolan, claim that it is possible to make SR make
different predictions for the same scenario, and that SR
therefore is inconsistent.

What SR predicts is not a matter of opinion, it is a matter of fact.

And I have shown you the fact that SR give the same answer calculated
several ways.

Since you have demonstrated that you are unable to calculate what
But my calculations are correct (but for possible typos).

Case closed.

I will be away from home for the Holidays, and will not send
any posts to s.f.relativity for some time.

--
Paul

https://paulba.no/

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Sylvia Else@21:1/5 to patdolan on Tue Dec 19 09:59:24 2023
On 19-Dec-23 1:19 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,
You have unknowingly assumed absolute motion right here. So let's
use your assumption of the existence of absolute motion. But this
time we will assume that the observer is moving while Big Ben is
stationary in the observer's frame.

the observer is 15.79 light-years in the observer's frame when Big
Ben emits the first light the observer will see. So we also know
that at the instant the first light is emitted from BB, the distance
between the observer and Proxima Centauri is [ 15.79 - 2.1 = ] 13.69 light-years in the observer's frame because the separation between BB
and PC is always a constant in any frame. But the observer is moving
towards the stationary Proxima Centauri at .867c. Therefore after
2.1 light-years, just as the first light emitted by the stationary BB
is passing the stationary PC, the moving observer will have cut the
total distance down by only [ 2.1 x .867 = ] 1.82 light-years. So
there can be no physical rendezvous of the first light and the
observer at Proxima Centauri according to your assumption that d =
15.79.

The flaw in your reasoning here is the assumption that, in the
observer's frame, it will take 2.1 years for the light emitted from Big
Ben (BB) to reach Proxima Centauri (PC). This assumption is incorrect
because in the observer's frame PC is moving at 0.867c away from the
light that is heading towards it. In the 15.79 years light takes for the journey, PC moves 13.69 light years. When added to the 2.l light year separation from BB, that adds up to the 15.79 light years that the light
has to travel.

At some point, I'm going to tire of explaining to you where your
analyses have gone wrong, and stop doing it. No doubt you will then
claim it's because I cannot. Other readers, if there are any, will
likely see the true situation, which is that you consistently get this
mistake on mistake.

Sylvia.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Sylvia Else@21:1/5 to patdolan on Tue Dec 19 11:01:42 2023
On 19-Dec-23 10:28 am, patdolan wrote:
On Monday, December 18, 2023 at 2:59:28 PM UTC-8, Sylvia Else wrote:
On 19-Dec-23 1:19 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,
You have unknowingly assumed absolute motion right here. So let's
use your assumption of the existence of absolute motion. But this
time we will assume that the observer is moving while Big Ben is
stationary in the observer's frame.

and the observer is 15.79 light-years in the observer's frame
when Big Ben emits the first light the observer will see. So we
also know that at the instant the first light is emitted from
BB, the distance between the observer and Proxima Centauri is [
15.79 - 2.1 = ] 13.69 light-years in the observer's frame because
the separation between BB and PC is always a constant in any
frame. But the observer is moving towards the stationary Proxima
Centauri at .867c. Therefore after 2.1 light-years, just as the
first light emitted by the stationary BB is passing the
stationary PC, the moving observer will have cut the total
distance down by only [ 2.1 x .867 = ] 1.82 light-years. So
there can be no physical rendezvous of the first light and the
observer at Proxima Centauri according to your assumption that d
= 15.79.
The flaw in your reasoning here is the assumption that, in the
observer's frame, it will take 2.1 years for the light emitted
from Big Ben (BB) to reach Proxima Centauri (PC). This assumption
is incorrect because in the observer's frame PC is moving at
0.867c away from the light that is heading towards it.

Wrong! In my version of the observer's frame, the coordinate system
is attached to the earth (and therefore Proxima Centauri). And it
is the observer who is moving with respect to that
Lorentz-contracted frame. Is this possible? Sure. That's the
principle of relativity. The co-moving coordinate system can be
attached to either the observer or the thing observed. If not, why
not?

Each inertial frame has its own coordinate system. Special relativity
describes the transformation (the Lorentz transformation) between the coordinate systems of relatively moving inertial frames.

You can analyse a scenario in any inertial frame, but you need to be
consistent about it, and not mix results between frames.

You also cannot arbitrarily say that the coordinate system of a
particular inertial frame is the one applicable to an observer in a
different inertial frame. Nothing in special relativity says you can do
that, and especially not the principle of relativity.

Sylvia.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Volney@21:1/5 to patdolan on Tue Dec 19 01:03:34 2023
On 12/18/2023 6:28 PM, patdolan wrote:

Wrong! In my version of the observer's frame, the coordinate system is attached to the earth (and therefore Proxima Centauri). And it is the observer who is moving with respect to that Lorentz-contracted frame.

You are frame jumping all over the place. No wonder you are so confused.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Richard Hachel@21:1/5 to All on Tue Dec 19 10:28:53 2023
Le 19/12/2023 à 01:01, Sylvia Else a écrit :

What is this paradox that bothers you?

I solved Langevin's paradox (it took a flash of genius and it took me
thirty years to solve it), I solved the paradox of accelerated frames of reference (which is the same paradox but in an accelerated environment), I
I resolved the paradox of observable time segments incompatible with instantaneous speeds. Perhaps I won't be useless if a fourth has to be

Sylvia.

R.H.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Sylvia Else@21:1/5 to Richard Hachel on Tue Dec 19 21:37:10 2023
On 19-Dec-23 9:28 pm, Richard Hachel wrote:
Le 19/12/2023 à 01:01, Sylvia Else a écrit :

What is this paradox that bothers you?

I solved Langevin's paradox (it took a flash of genius and it took me
thirty years to solve it), I solved the paradox of accelerated frames of reference (which is the same paradox but in an accelerated environment),
I I resolved the paradox of observable time segments incompatible with instantaneous speeds. Perhaps I won't be useless if a fourth has to be solved. What is this paradox?

Sylvia.

R.H.
Look at the top of the thread.

But there is no paradox. Pat just doesn't know his special relativity.

Sylvia.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Tom Roberts@21:1/5 to patdolan on Fri Dec 22 23:18:56 2023
On 12/12/23 12:19 AM, patdolan wrote:
[...]

As I showed in "Demolishing Doppler Part One", you used the wrong frame
in calculating the Doppler shift approach to counting turns. As I
showed, when one calculates it correctly the two approaches give the
same number of turns, so it does NOT show any problem with Sr.

The problem is YOUR MISUNDERSTANDING OF SPECIAL RELATIVITY.

Tom Roberts

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Richard Hachel@21:1/5 to All on Sat Dec 23 16:03:25 2023
Le 23/12/2023 à 06:18, Tom Roberts a écrit :
On 12/12/23 12:19 AM, patdolan wrote:
[...]

As I showed in "Demolishing Doppler Part One", you used the wrong frame
in calculating the Doppler shift approach to counting turns. As I
showed, when one calculates it correctly the two approaches give the
same number of turns, so it does NOT show any problem with Sr.

The problem is YOUR MISUNDERSTANDING OF SPECIAL RELATIVITY.

Tom Roberts

Ah?

Parce que vous avez compris la théorie de la relativité, vous?

Un moment d'espérance.

R.H.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Sylvia Else@21:1/5 to patdolan on Thu Dec 28 09:46:14 2023
On 28-Dec-23 5:37 am, patdolan wrote:
On Saturday, December 23, 2023 at 9:56:26 AM UTC-8, Patrick Dolan
wrote:
On Sunday, December 17, 2023 at 7:14:09 PM UTC-8, Sylvia Else
wrote:
On 18-Dec-23 1:31 pm, patdolan wrote:
On Sunday, December 17, 2023 at 6:09:22 PM UTC-8, Sylvia Else
wrote:
On 18-Dec-23 11:48 am, patdolan wrote:
On Sunday, December 17, 2023 at 4:25:04 PM UTC-8, Sylvia
Else wrote:
On 18-Dec-23 11:13 am, patdolan wrote:
On Saturday, December 16, 2023 at 1:20:04 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.
In his latest post to this thread Paul has challenged
me to find any absurdities in his calculations, of
which I'm sure there are many. But at present I am
concentrating on an absurdity that I found in
Sylvia's brilliant derivation above. And it reminds
me to remind you all of the first rule of relativism,
which is: whatever conclusion you reach while
employing the principle of special relativity, there
will always be a contradiction associated with that
conclusion--all you have to do is look for it long
enough.

Back to Sylvia's derivation of d, which represents
the distance at which the first light has to leave
the tip of Big Ben's little hand in order to make a
timely rendezvous with the distant observer A at
Proxima Centauri. The reader will recall that the
distant observer and the light from BB race towards
each other for a meetup at Proxima Centauri. This
meetup signals the start of the helical turn counting
by the distant observer. The light from BB travels at
c whilst the distant observer travels at 0.867c. As
you can read above, Sylvia brilliantly calculates
that the first particle of light that will eventually
meetup with the distant observer will have to emanate
from Big Ben no less than 15.79 light years prior to
the meetup. This brilliant solution exactly accounts
for the stacking up of helical turns in the gap
between Big Ben ( the earth ) and Proxima Centauri,
such that 6651 helical turns ( the solution yielded
by the relativistic doppler formula ) will be
measured by the observer in the time it takes for him
to traverse the distance between Proxima and the
clock face of Ben.

Here is the absurdity. The guy who just installed the
radio telescope on the top of Big Ben knows that he
can send a signal, bounce it off of Proxima Centauri
Sylvia's world that signal won't even arrive at
Proxima until 15.8 years have passed. So Albert
requires that we now entertain the absurdity of two
beams of light simultaneously launched from BB
towards the same target Proxima Centauri; one of the
beams completes a round trip [ 15.8 - 8.4 = ] 7.4
years before the other beam even arrives at PC.
Now you're adding periods of time from different frames.
I'd have thought even you would know that you cannot
meaningfully do that.

Further, the 15.8 years is in the frame of the observer,
not the frame of the radio telescope.
Yes, I know Sylvia. But the the difference is even more
absurd when you consider the difference from the Big Ben,
Proxima Centauri proper frame.
So you say, but what are the numbers? In particular, what are
they when you get the math right?

Sylvia.
In the BB-PC rest frame your d expands to 31.6 years. ( 2 x
15.8 years ). The Big Ben radio telescope signal round trip to
PC remains 8.4 years ( 2 x 4.2 years ). Just an incredible
absurdity.

Sylvia, cut the small talk. Either find a way to save
relativity or cry uncle.
You're talking about two events separated in space and time. You
can't just multiply the time difference by γ and call it good.
You have to apply the Lorentz transform.

One event consists of the light arriving at the observer. Let
that be at time t1 = 0 and position x1 = 0.

The other event consists of the light being emitted from Big Ben.
That happens 15.8 years earlier, so let that be at time t2 =
-15.8. It also happens 15.8 light years away, in the opposite
direction to the velocity vector of Big Ben, so let that be at x2
= -15.8.

Now we the Lorentz transform on both events to get into the t'
frame, being the frame of Big Ben. Taking γ to be 2, and v as
0.867, we get:

t'2 = 2 * [-15.8 - (0.867 * -15.8)] = -4.2 t'1 = 2 * [0 - 0.867 *
0] = 0

So in the t' frame (i.e. the Big Ben frame) the difference in
time between the two events, t'1 - t'2, is 4.2 years, which is
exactly what one would expect.

Sylvia.
Sylvia, you have missed the entire point of the helical path
paradox. You correctly use the LTs to demonstrate the equivalence
of the spacetime intervals between the same two events in the S'
frame and in the S frame. So? The point of the helical path paradox
is that it can be demonstrated that for the same oscillator there
is disagreement between the number of turns in a light path helix
for the same spacetime interval:

15.8 light-years x 365.25 turns/light-year = 5571 turns in the
spacetime interval ( or alternatively, using the relativistic
doppler formula 3.747 x 730.5 x 2.1 = 5748 turns )

and

4.2 light-years x 730.5 turns/light-year = 3068 turns in the same
spacetime interval.

Both values cannot be correct for the same spacetime interval in
the same universe. It would destroy conservations of energy, for
one thing.

Sylvia, you have had enough of time to think over the above. What is
your response? How can the same spacetime interval contain different
numbers of helical turns? Or different numbers of waves?

It's become apparent that you're incapable of applying relativity
properly, and unable, or unwilling, to be corrected. You will continue
to believe that there's an issue with your paradox, despite all attempts
to disabuse you.

I expect that you will now claim that I cannot point to flaw in your
reasoning. Do your worst. I'm done with this.

Sylvia.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From Richard Hachel@21:1/5 to All on Thu Dec 28 08:26:22 2023
Le 27/12/2023 à 23:46, Sylvia Else a écrit :
On 28-Dec-23 5:37 am, patdolan wrote:

I expect that you will now claim that I cannot point to flaw in your reasoning. Do your worst. I'm done with this.

No, no, you're not done with this.

One day, an admirer came to see Hachel for a signing of his book "Saint
Paul or the Antichrist of Light", one of the most important theological reflections in the history of humanity and he took the opportunity to ask
him if It was true that only three people clearly understood the theory of special relativity. Doctor Hachel raised his head, looking surprised, and replied, “And who are the other two?”

No, no, Sylvia, you're not done yet.

You must be able to learn and teach this theory correctly.

Women are generally more disciplined and less dissipated than men, which
could be an advantage for you.

Sylvia.

R.H.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)