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Re: The Helical Path Paradox

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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.

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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 Patrick Dolan <pd8441303@gmail.com> - 2023-12-23 09:56 -0800
                Re: The Helical Path Paradox "pdolan@adsistor.com" <pdolan@adsistor.com> - 2023-12-27 00:02 -0800
                Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-27 00:21 -0800
                Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-27 10:37 -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
  Re: The Helical Path Paradox Tom Roberts <tjoberts137@sbcglobal.net> - 2023-12-22 23:18 -0600
    Re: The Helical Path Paradox Maciej Wozniak <maluwozniak@gmail.com> - 2023-12-23 01:31 -0800
    Re: The Helical Path Paradox Richard Hachel <r.hachel@tiscali.fr> - 2023-12-23 16:03 +0000

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