On Monday 18 December 2023 at 04:14:09 UTC+1, 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.

Sorry, lady, nobody has to obey Your absurds.
It's just another delusion of Yours (and Your insane
gurus as well).

Den 18.12.2023 01:13, skrev patdolan:
> Prof. Paul are vanquished.

You haven't addressed my derivations with a single word.

I challenge you to find any errors or absurdities in the following:

Problem:
An observer O is racing past Proxima Centauri on her way to Big Ben
at .867c relative to the Big Ben.

Question to answer:
How many rotations will the little hand of Big-Ben make
from the observer O is passing Proxima Centauri to she hits
the Earth?

Let's call Earth's rest frame K(t,x).
We will call the position of the Earth E, and the position of
Proxima Centauri P in this frame.

O->v
K: P-----------------E
0 L
At t = t₀ = 0, the observer O is at P.
At t = t₁ the observer O is at E

L = 4.2 [ly] proper distance Earth - Proxima Centauri in K
v = 0.867c
γ = 2.0068
f₀ = 730.5 [cycles/y], proper frequency of the BB clock.
T = 1/f₀ = 0.001369 [y], proper duration of a cycle

t₁ = L/v = 4.844 y

So the answer to the question above is:
N₀ = f₀⋅t₁ = f₀⋅L/v = 3538.75 cycles
===================================

This is the same as what NM predicts, because we
have not asked what is measured in O's rest frame.
____________________________________________________

The observer's clock is moving in K:
--------------------------------------

Let K'(t',x') be O's rest frame.

There are two events of interest:
E0: The observer is at P
In K: t₀ = 0, x₀ = 0
In K': t₀' = 0, x₀' = 0

E1: The observer is at E
In K: t₁ = L/v = 4.84429 y, x₁ = L = 4.2 ly
In K':
t₁' = γ(t₁-v⋅x₁/c²) = L/γv = 2.41395 y
x₁' = γ(x₁-v⋅t₁) = 0

In K: t₂ = T = 0.001369 y, x₂ = L/v = 2.09289 ly
In K': t₂'= γ(t₂-v⋅x₂/c²) = T/γ = 0.00068215 y

f₀' = γ⋅f₀ = 1465.96 cycles/y , the frequency measured in K'

So SR predicts that O will measure (count):
N₁ = f₀'⋅t₁' = γ⋅f₀⋅L/γv = f₀⋅L/v = 3538.75 cycles
=================================================>

Note this:
The observer's clock advances the proper time:
τ' = t₁'- t₀'= 2.41395 y
while the difference between the coordinate time
t₀ at x₀ and t₁ at x₁ changes by:
(t₁ - t₀) = L/v = 4.84429 y.

The observer's moving clock appears to run slow as measured in K.
________________________________________________________________

Big Ben is moving in K':
-------------------------

t₄' = 0
O
P-----------E
0 x₄'

At Event E₄ is E at x₄' when t₄' = 0

We know that E always is at x = L in K
t₄' = γ(t₄-v⋅L/c²) = 0 => t₄ = v⋅L/c² = 3.6414 y
x₄' = γ(x₄-v⋅t₄) = γ(L-L(v²/c²)) = L/γ = 2.09289 ly

So measured in K' at the time t' = 0, E is at the position L/γ
and BB is showing the proper time τ₄ = v⋅L/c² = 3.6414 y

At Event E1, when E is at P, we have from above:
BB is showing the the proper time τ₁ = t₁ = L/v = 4.84429 y

We still have:
f₀' = γ⋅f₀ = 1465.96 cycles/y , the frequency measured in K'
t₁' = L/γv = 2.41395 y

So SR predicts that O will measure (count):
N₁ = f₀'⋅t₁' = γ⋅f₀⋅L/γv = f₀⋅L/v = 3538.75 cycles
=================================================>

Note this:
Big Ben advances the proper time:
(τ₁-τ₄) = L/v-v⋅L/c² = (L/v)(1-v²/c²) = L/γ²v = 1.20289 y
while the difference between the coordinate time t₄' at x₄'
and t₁' at x₁' changes by:
(t₁' - t₄') = L/γv = 2.41395 y

The moving Big Ben appears to run slow as measured in K'.
_________________________________________________________________

Calculation with Doppler shift.

O-v
P-----------------E
0 L

Since O is approaching the Earth, he will measure
(see above) the frequency of BB to be f₀' = γ⋅f₀.

He will visually observe this frequency to Doppler shifted:
f = sqrt((1+v/c)/(1-v/c))f₀' = f₀/(1-v/c)

He will observe this frequency for the time L/v.
But when he is at P, he will see the light emitted from BB
at a time L/c before he arrived at P, so he must subtract
the counts he received the first time L/c.
That means that he must count the cycles received during
the time Δt = L/v - L/c = (L/v)(1-v/c)

The number of counts emitted from BB during this time is:
N = f⋅Δt = (f₀/(1-v/c))(L/v)(1-v/c) = f₀⋅L/v = 3538.75 cycles
==============================================================

############################################################

BOTTOM LINE:

You, Pat Dolan, claim that it is possible to make SR make
different predictions for the same scenario, and that SR
therefore is inconsistent.

What SR predicts is not a matter of opinion, it is a matter of fact.

And I have shown you the fact that SR give the same answer calculated
several ways.

Since you have demonstrated that you are unable to calculate what
SR predicts, my calculations are probably way above your head.
But my calculations are correct (but for possible typos).

Case closed.

I will be away from home for the Holidays, and will not send
any posts to s.f.relativity for some time.

--
Paul

https://paulba.no/

On 19-Dec-23 1:19 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,
> You have unknowingly assumed absolute motion right here. So let's
> use your assumption of the existence of absolute motion. But this
> time we will assume that the observer is moving while Big Ben is
> stationary in the observer's frame.
>
> We start with your conclusion that the distance between Big Ben and
> the observer is 15.79 light-years in the observer's frame when Big
> Ben emits the first light the observer will see. So we also know
> that at the instant the first light is emitted from BB, the distance
> between the observer and Proxima Centauri is [ 15.79 - 2.1 = ] 13.69
> light-years in the observer's frame because the separation between BB
> and PC is always a constant in any frame. But the observer is moving
> towards the stationary Proxima Centauri at .867c. Therefore after
> 2.1 light-years, just as the first light emitted by the stationary BB
> is passing the stationary PC, the moving observer will have cut the
> total distance down by only [ 2.1 x .867 = ] 1.82 light-years. So
> there can be no physical rendezvous of the first light and the
> observer at Proxima Centauri according to your assumption that d =
> 15.79.

The flaw in your reasoning here is the assumption that, in the
observer's frame, it will take 2.1 years for the light emitted from Big
Ben (BB) to reach Proxima Centauri (PC). This assumption is incorrect
because in the observer's frame PC is moving at 0.867c away from the
light that is heading towards it. In the 15.79 years light takes for the
journey, PC moves 13.69 light years. When added to the 2.l light year
separation from BB, that adds up to the 15.79 light years that the light
has to travel.

At some point, I'm going to tire of explaining to you where your
analyses have gone wrong, and stop doing it. No doubt you will then
claim it's because I cannot. Other readers, if there are any, will
likely see the true situation, which is that you consistently get this
stuff wrong, and that your "contradiction" is nothing but your piling
mistake on mistake.

Sylvia.

On Monday, December 18, 2023 at 2:59:28 PM UTC-8, Sylvia Else wrote:
> On 19-Dec-23 1:19 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,
> > You have unknowingly assumed absolute motion right here. So let's
> > use your assumption of the existence of absolute motion. But this
> > time we will assume that the observer is moving while Big Ben is
> > stationary in the observer's frame.
> >
> > We start with your conclusion that the distance between Big Ben and
> > the observer is 15.79 light-years in the observer's frame when Big
> > Ben emits the first light the observer will see. So we also know
> > that at the instant the first light is emitted from BB, the distance
> > between the observer and Proxima Centauri is [ 15.79 - 2.1 = ] 13.69
> > light-years in the observer's frame because the separation between BB
> > and PC is always a constant in any frame. But the observer is moving
> > towards the stationary Proxima Centauri at .867c. Therefore after
> > 2.1 light-years, just as the first light emitted by the stationary BB
> > is passing the stationary PC, the moving observer will have cut the
> > total distance down by only [ 2.1 x .867 = ] 1.82 light-years. So
> > there can be no physical rendezvous of the first light and the
> > observer at Proxima Centauri according to your assumption that d =
> > 15.79.
> The flaw in your reasoning here is the assumption that, in the
> observer's frame, it will take 2.1 years for the light emitted from Big
> Ben (BB) to reach Proxima Centauri (PC). This assumption is incorrect
> because in the observer's frame PC is moving at 0.867c away from the
> light that is heading towards it.

Wrong! In my version of the observer's frame, the coordinate system is attached to the earth (and therefore Proxima Centauri). And it is the observer who is moving with respect to that Lorentz-contracted frame. Is this possible? Sure. That's the principle of relativity. The co-moving coordinate system can be attached to either the observer or the thing observed. If not, why not?

Look at it this way: special relativity demands that we treat as equivalent 1) the observer racing along a Lorentz contracted coordinate system attached to a Lorentz contracted Earth-gap-Proxima Centauri, and 2) a Lorentz contracted Earth-gap-Proxima Centauri racing along the observer's proper coordinate system attached to the observer.

In the 15.79 years light takes for the
> journey, PC moves 13.69 light years. When added to the 2.l light year
> separation from BB, that adds up to the 15.79 light years that the light
> has to travel.
>
> At some point, I'm going to tire of explaining to you where your
> analyses have gone wrong, and stop doing it. No doubt you will then
> claim it's because I cannot.
Yes, I will. And I will enjoy doing so.
Other readers, if there are any, will
> likely see the true situation, which is that you consistently get this
> stuff wrong, and that your "contradiction" is nothing but your piling
> mistake on mistake.
>
> Sylvia.

On 19-Dec-23 10:28 am, patdolan wrote:
> On Monday, December 18, 2023 at 2:59:28 PM UTC-8, Sylvia Else wrote:
>> On 19-Dec-23 1:19 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,
>>> You have unknowingly assumed absolute motion right here. So let's
>>> use your assumption of the existence of absolute motion. But this
>>> time we will assume that the observer is moving while Big Ben is
>>> stationary in the observer's frame.
>>>
>>> We start with your conclusion that the distance between Big Ben
>>> and the observer is 15.79 light-years in the observer's frame
>>> when Big Ben emits the first light the observer will see. So we
>>> also know that at the instant the first light is emitted from
>>> BB, the distance between the observer and Proxima Centauri is [
>>> 15.79 - 2.1 = ] 13.69 light-years in the observer's frame because
>>> the separation between BB and PC is always a constant in any
>>> frame. But the observer is moving towards the stationary Proxima
>>> Centauri at .867c. Therefore after 2.1 light-years, just as the
>>> first light emitted by the stationary BB is passing the
>>> stationary PC, the moving observer will have cut the total
>>> distance down by only [ 2.1 x .867 = ] 1.82 light-years. So
>>> there can be no physical rendezvous of the first light and the
>>> observer at Proxima Centauri according to your assumption that d
>>> = 15.79.
>> The flaw in your reasoning here is the assumption that, in the
>> observer's frame, it will take 2.1 years for the light emitted
>> from Big Ben (BB) to reach Proxima Centauri (PC). This assumption
>> is incorrect because in the observer's frame PC is moving at
>> 0.867c away from the light that is heading towards it.
>
> Wrong! In my version of the observer's frame, the coordinate system
> is attached to the earth (and therefore Proxima Centauri). And it
> is the observer who is moving with respect to that
> Lorentz-contracted frame. Is this possible? Sure. That's the
> principle of relativity. The co-moving coordinate system can be
> attached to either the observer or the thing observed. If not, why
> not?

Each inertial frame has its own coordinate system. Special relativity
describes the transformation (the Lorentz transformation) between the
coordinate systems of relatively moving inertial frames.

You can analyse a scenario in any inertial frame, but you need to be
consistent about it, and not mix results between frames.

You also cannot arbitrarily say that the coordinate system of a
particular inertial frame is the one applicable to an observer in a
different inertial frame. Nothing in special relativity says you can do
that, and especially not the principle of relativity.

Your attempt to save your paradox is looking increasingly desperate.

Sylvia.

On Monday 18 December 2023 at 23:59:28 UTC+1, Sylvia Else wrote:
> On 19-Dec-23 1:19 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,
> > You have unknowingly assumed absolute motion right here. So let's
> > use your assumption of the existence of absolute motion. But this
> > time we will assume that the observer is moving while Big Ben is
> > stationary in the observer's frame.
> >
> > We start with your conclusion that the distance between Big Ben and
> > the observer is 15.79 light-years in the observer's frame when Big
> > Ben emits the first light the observer will see. So we also know
> > that at the instant the first light is emitted from BB, the distance
> > between the observer and Proxima Centauri is [ 15.79 - 2.1 = ] 13.69
> > light-years in the observer's frame because the separation between BB
> > and PC is always a constant in any frame. But the observer is moving
> > towards the stationary Proxima Centauri at .867c. Therefore after
> > 2.1 light-years, just as the first light emitted by the stationary BB
> > is passing the stationary PC, the moving observer will have cut the
> > total distance down by only [ 2.1 x .867 = ] 1.82 light-years. So
> > there can be no physical rendezvous of the first light and the
> > observer at Proxima Centauri according to your assumption that d =
> > 15.79.
> The flaw in your reasoning here is the assumption that, in the
> observer's frame, it will take 2.1 years for the light emitted from Big
> Ben (BB) to reach Proxima Centauri (PC). This assumption is incorrect
> because in the observer's frame PC is moving at 0.867c away from the
> light that is heading towards it. In the 15.79 years light takes for the
> journey, PC moves 13.69 light years. When added to the 2.l light year
> separation from BB, that adds up to the 15.79 light years that the light
> has to travel.

Gedanken, lady. Fabricated. Anyone can check GPS, these absurds
have nothing in common with real clocks, real observations,
real anything.

On 12/18/2023 6:28 PM, patdolan wrote:

> Wrong! In my version of the observer's frame, the coordinate system is attached to the earth (and therefore Proxima Centauri). And it is the observer who is moving with respect to that Lorentz-contracted frame.

You are frame jumping all over the place. No wonder you are so confused.

Le 19/12/2023 à 01:01, Sylvia Else a écrit :

> Your attempt to save your paradox is looking increasingly desperate.

What is this paradox that bothers you?

I solved Langevin's paradox (it took a flash of genius and it took me
thirty years to solve it), I solved the paradox of accelerated frames of
reference (which is the same paradox but in an accelerated environment), I
I resolved the paradox of observable time segments incompatible with
instantaneous speeds. Perhaps I won't be useless if a fourth has to be
solved. What is this paradox?

> Sylvia.

R.H.

On 19-Dec-23 9:28 pm, Richard Hachel wrote:
> Le 19/12/2023 à 01:01, Sylvia Else a écrit :
>
>> Your attempt to save your paradox is looking increasingly desperate.
>
> What is this paradox that bothers you?
>
> I solved Langevin's paradox (it took a flash of genius and it took me
> thirty years to solve it), I solved the paradox of accelerated frames of
> reference (which is the same paradox but in an accelerated environment),
> I I resolved the paradox of observable time segments incompatible with
> instantaneous speeds. Perhaps I won't be useless if a fourth has to be
> solved. What is this paradox?
>
>> Sylvia.
>
> R.H.
> Look at the top of the thread.

But there is no paradox. Pat just doesn't know his special relativity.

Sylvia.

On 12/12/23 12:19 AM, patdolan wrote:
> [...]

As I showed in "Demolishing Doppler Part One", you used the wrong frame
in calculating the Doppler shift approach to counting turns. As I
showed, when one calculates it correctly the two approaches give the
same number of turns, so it does NOT show any problem with Sr.

The problem is YOUR MISUNDERSTANDING OF SPECIAL RELATIVITY.

Tom Roberts

On Saturday 23 December 2023 at 06:19:09 UTC+1, Tom Roberts wrote:
> On 12/12/23 12:19 AM, patdolan wrote:
> > [...]
>
> As I showed in "Demolishing Doppler Part One", you used the wrong frame
> in calculating the Doppler shift approach to counting turns. As I
> showed, when one calculates it correctly the two approaches give the
> same number of turns, so it does NOT show any problem with Sr.
>
> The problem is YOUR MISUNDERSTANDING OF SPECIAL RELATIVITY.

And you don't understand that we're FORCED!!!
To THE BEST WAY!!!!!

Le 23/12/2023 à 06:18, Tom Roberts a écrit :
> On 12/12/23 12:19 AM, patdolan wrote:
>> [...]
>
> As I showed in "Demolishing Doppler Part One", you used the wrong frame
> in calculating the Doppler shift approach to counting turns. As I
> showed, when one calculates it correctly the two approaches give the
> same number of turns, so it does NOT show any problem with Sr.
>
> The problem is YOUR MISUNDERSTANDING OF SPECIAL RELATIVITY.
>
> Tom Roberts

Ah?

Parce que vous avez compris la théorie de la relativité, vous?

Un moment d'espérance.

R.H.

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.

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.

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.

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.

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?

Le 27/12/2023 à 23:46, Sylvia Else a écrit :
> On 28-Dec-23 5:37 am, patdolan wrote:

> I expect that you will now claim that I cannot point to flaw in your
> reasoning. Do your worst. I'm done with this.

No, no, you're not done with this.

One day, an admirer came to see Hachel for a signing of his book "Saint
Paul or the Antichrist of Light", one of the most important theological
reflections in the history of humanity and he took the opportunity to ask
him if It was true that only three people clearly understood the theory of
special relativity. Doctor Hachel raised his head, looking surprised, and
replied, “And who are the other two?”

No, no, Sylvia, you're not done yet.

You must be able to learn and teach this theory correctly.

Women are generally more disciplined and less dissipated than men, which
could be an advantage for you.

> Sylvia.

R.H.

On Thursday, December 28, 2023 at 12:26:25 AM UTC-8, Richard Hachel wrote:
> Le 27/12/2023 à 23:46, Sylvia Else a écrit :
> > On 28-Dec-23 5:37 am, patdolan wrote:
>
> > I expect that you will now claim that I cannot point to flaw in your
> > reasoning. Do your worst. I'm done with this.
> No, no, you're not done with this.
>
> One day, an admirer came to see Hachel for a signing of his book "Saint
> Paul or the Antichrist of Light", one of the most important theological
> reflections in the history of humanity

Dr. Hachel, I am intrigued by Hachel's Heresy. Can you deliver to this forum the three most salient points of your claim that St. Paul was the Antichrist of Light?

and he took the opportunity to ask
> him if It was true that only three people clearly understood the theory of
> special relativity. Doctor Hachel raised his head, looking surprised, and
> replied, “And who are the other two?”
>
> No, no, Sylvia, you're not done yet.
>
> You must be able to learn and teach this theory correctly.
>
> Women are generally more disciplined and less dissipated than men, which
> could be an advantage for you.
>
> > Sylvia.
>
> R.H.