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Re: The Helical Path Paradox

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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
>>>>>>>>> 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.
>> 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.

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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 Sylvia Else <sylvia@email.invalid> - 2023-12-28 09:46 +1100
      Re: The Helical Path Paradox Richard Hachel <r.hachel@tiscali.fr> - 2023-12-28 08:26 +0000
        Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-28 09:12 -0800

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