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Re: The Helical Path Paradox

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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?  read on.
> 
> Let's repeat the derivation, this time assuming that observer A is in
> motion and approaching the BB/PC complex which is at rest.  Here's
> how in your own words:
> 
> If we let the distance away that observer A was when the light
> departed be d, we can see that the time that observer A took to get
> from distance d to its present position of 2.1 light years must equal
> the time it took for the light to get from 2.1 to observer A. That
> is:
> 
> 2.1/c = d/v
> 
> where v = is 0.867c, and c = 1.
> 
> 2.1/1 = d/0.867
> 
> ( 2.1 )( 0.867 ) = d
> 
> d = 1.82
> 
> BB <--------- 2.1 ------------> PC <--------------- d -------------->
> observer A But this time it is observer A that moves at velocity v
> instead of the other way around.


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.

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The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-11 22:19 -0800
  Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-12 11:28 -0800
    Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-12 17:55 -0800
  Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-13 19:51 +1100
    Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-13 05:12 -0800
      Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-14 08:40 +1100
    Re: The Helical Path Paradox Maciej Wozniak <maluwozniak@gmail.com> - 2023-12-13 05:19 -0800
    Re: The Helical Path Paradox Ryker Habibulaev Balanda <enaa@brdaaeea.ye> - 2023-12-13 13:32 +0000
    Re: The Helical Path Paradox Richard Hachel <r.hachel@frite.fr> - 2023-12-13 16:03 +0000
      Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-13 09:50 -0800
      Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-14 08:42 +1100
        Re: The Helical Path Paradox Richard Hachel <r.hachel@frite.fr> - 2023-12-13 22:32 +0000
        Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-13 16:22 -0800
          Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-14 11:30 +1100
            Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-13 16:52 -0800
              Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-14 11:56 +1100
            Re: The Helical Path Paradox Richard Hachel <r.hachel@frite.fr> - 2023-12-14 00:55 +0000
              Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-14 12:02 +1100
                Re: The Helical Path Paradox Richard Hachel <r.hachel@frite.fr> - 2023-12-14 01:27 +0000
                Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-14 12:58 +1100
                Re: The Helical Path Paradox Athel Cornish-Bowden <me@yahoo.com> - 2023-12-14 13:56 +0100
                Re: The Helical Path Paradox Richard Hachel <r.hachel@frite.fr> - 2023-12-14 14:45 +0000
                Re: The Helical Path Paradox Athel Cornish-Bowden <me@yahoo.com> - 2023-12-14 18:17 +0100
                Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-14 10:03 -0800
            Re: The Helical Path Paradox Maciej Wozniak <maluwozniak@gmail.com> - 2023-12-13 17:00 -0800
    Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-14 12:07 -0800
      Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-14 12:49 -0800
      Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-15 11:10 +1100
        Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-14 19:21 -0800
        Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-14 19:23 -0800
        Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-14 19:33 -0800
          Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-15 15:07 +1100
            Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-14 20:40 -0800
              Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-15 16:07 +1100
                Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-15 00:26 -0800
                Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-15 19:45 +1100
                Re: The Helical Path Paradox "Paul B. Andersen" <relativity@paulba.no> - 2023-12-15 14:45 +0100
                Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-15 12:06 -0800
                Re: The Helical Path Paradox "Paul B. Andersen" <relativity@paulba.no> - 2023-12-16 10:24 +0100
                Re: The Helical Path Paradox Maciej Wozniak <maluwozniak@gmail.com> - 2023-12-16 01:47 -0800
            Re: The Helical Path Paradox Maciej Wozniak <maluwozniak@gmail.com> - 2023-12-15 13:37 -0800
    Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-16 13:20 -0800
      Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-17 16:13 -0800
        Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-18 11:25 +1100
          Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-17 16:48 -0800
            Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-18 13:09 +1100
              Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-17 18:31 -0800
                Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-18 14:14 +1100
                Re: The Helical Path Paradox Maciej Wozniak <maluwozniak@gmail.com> - 2023-12-18 06:29 -0800
        Re: The Helical Path Paradox "Paul B. Andersen" <relativity@paulba.no> - 2023-12-18 20:43 +0100
    Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-18 06:19 -0800
      Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-19 09:59 +1100
        Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-18 15:28 -0800
          Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-19 11:01 +1100
            Re: The Helical Path Paradox Richard Hachel <r.hachel@tiscali.fr> - 2023-12-19 10:28 +0000
              Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-19 21:37 +1100
          Re: The Helical Path Paradox Volney <volney@invalid.invalid> - 2023-12-19 01:03 -0500
        Re: The Helical Path Paradox Maciej Wozniak <maluwozniak@gmail.com> - 2023-12-18 21:17 -0800
  Re: The Helical Path Paradox "Paul B. Andersen" <relativity@paulba.no> - 2023-12-15 14:45 +0100
    Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-15 11:28 -0800
      Re: The Helical Path Paradox "Paul B. Andersen" <relativity@paulba.no> - 2023-12-16 10:24 +0100

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