Groups > sci.physics.relativity > #625664

Re: The Helical Path Paradox

From	Sylvia Else <sylvia@email.invalid>
Newsgroups	sci.physics.relativity
Subject	Re: The Helical Path Paradox
Date	2023-12-13 19:51 +1100
Message-ID	<ktt9krFi5muU1@mid.individual.net> (permalink)
References	<500ab0c4-e0fd-4dd9-8e00-6654a154e0cen@googlegroups.com>

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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.

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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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