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Re: The Helical Path Paradox

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

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

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

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

Sylvia.

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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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