Paul B. Andersen wrote:

>> When Tom divides his displacement by his interval of time in his
>> universe--the only universe--it is not an illusion or mathematically
>> artifact that Tom's brain, operating at half the biological speed of
>> Trevor's brain, concludes that his velocity towards Trevor is
>> 3.4681689c or gama^2 times the proper velocity that Trevor calculates
>> for Tom.
>
> https://paulba.no/pdf/Mutual_time_dilation.pdf

you are a nigga.

On 10/8/22 10:47 PM, Paul Alsing wrote:
> It is NEVER the case that 2 observers observing their relative
> speeds can EVER determine their closing speed. The very definition
> of closing speed precludes such a situation. It just cannot be done.

This is just plain false, and I have no idea why you think it is true.
Any (locally) inertial frame can be used to determine the closing speed
between two objects, including either one of their rest frames (as long
as the object is moving inertially).

[Note that the value of the closing speed depends on which
(locally) inertial frame is used.]

Closing speed is the rate of change of the distance between the two
objects, as measured in the specified (locally) inertial frame. If one
uses the rest frame of either object, the closing speed is equal to the
relative speed of the other object.

Tom Roberts

On Sunday, October 9, 2022 at 9:03:47 AM UTC-7, tjrob137 wrote:
> On 10/8/22 10:47 PM, Paul Alsing wrote:
> > It is NEVER the case that 2 observers observing their relative
> > speeds can EVER determine their closing speed. The very definition
> > of closing speed precludes such a situation. It just cannot be done.
> This is just plain false, and I have no idea why you think it is true.
> Any (locally) inertial frame can be used to determine the closing speed
> between two objects, including either one of their rest frames (as long
> as the object is moving inertially).
>
> [Note that the value of the closing speed depends on which
> (locally) inertial frame is used.]
>
> Closing speed is the rate of change of the distance between the two
> objects, as measured in the specified (locally) inertial frame. If one
> uses the rest frame of either object, the closing speed is equal to the
> relative speed of the other object.
>
> Tom Roberts

I do not follow. 2 vehicles are approaching each other along the same axis. Let's say each is moving at .7c relative to my position in my chair on my balcony looking down on that axis. I can measure the rate of change of the distance between them and come up with a closing speed of 1.4c... but neither one of these guys can make any kind of measurement of the other that will ever exceed c... their measurements are limited by the LT... isn't that correct? Isn't that just basic relativity? Wouldn't this also be true even for much lower speeds? Even at, say, 50 mph each, their closing speed would be 100 mph but technically you could still apply the LT and find that from the frame of either car their perceived relative speed would be less than 100 mph by some incredibly small amount? Like 99.99999999 mph or some such? I am only talking about this one specific scenario, 2 objects moving directly towards each other and the measurements made from several different locations.

Please advise.

On Sunday, October 9, 2022 at 10:42:38 AM UTC-7, Paul Alsing wrote:
> Two vehicles are approaching each other along the same axis. Let's say
> each is moving at .7c relative to my position in my chair...

Speeds are not expressed "relative to positions", they are expressed in terms of specified coordinate systems, because objects have infinitely many different speeds "relative to your position", depending on the choice of coordinate systems, but they have just one speed in terms of (for example) the standard inertial coordinate system in which you are at rest.

> ...neither one of these guys can make any kind of measurement of the other
> that will ever exceed c... their measurements are limited by the LT... isn't that
> correct?

No, not at all. One of the worst aspects of many popular introductory expositions of special relativity is the conflating of the concepts of "observer" and "coordinate system". These books give young readers the impression that each observer is somehow magically linked to some particular system of coordinates, and any "measurement" performed by an observer somehow magically corresponds to the descriptions of events in terms of the standard inertial coordinate system in which that observer is (momentarily) at rest. Almost all the misunderstandings of special relativity -- on display daily in this newsgroup -- are due to this fundamental (and rather silly) misconception.

The actual situation, epistemologically, is much more sophisticated and frankly beyond your grasp or interest, but suffice it to say that a person need not be at rest in a coordinate system in order to make measurements in terms of that coordinate system. In fact, we do this all the time... you driving around in your car, measuring distances and times in terms of the ECI coordinate system (via GPS), and yet you are not at rest in terms of this system. Likewise we can make measurements in terms of accelerating coordinate system (such as systems rotating with the earth), even though those are not standard inertial coordinate systems. Astronomers make measurements of the solar system in terms of the barycentric system of the CoM, and yet the earth is not at rest in that system, and so on.

Moreover, you are only ever at a single location, so even when you naively think you are making measurements in terms of the standard inertial coordinates in which you are at rest, you are really making indirect inferences about other locations where you are not present. So there is no sense in which a person's measurements are locked to any particular system of coordinates. All measurements are indirect, and we can make measurements in terms of any system of coordinates we like. So, take all the books that conflate observers with coordinate systems and throw them in the trash, and start over trying to learn relativity.

On Sunday, October 9, 2022 at 1:42:38 PM UTC-4, Paul Alsing wrote:

> 2 vehicles are approaching each other along the same axis. Let's say each is moving at .7c relative to my
> position in my chair on my balcony looking down on that axis.

Thus, relative to your (inertial) coordinate system (CS) [it doesn't matter where you are located at in this CS], the speeds of the two "cars"
are 0.7c each, approaching each other. IOW, you [your CS] measures their speeds top be 0.7c.

> I can measure the rate of change of the distance between them and come up with a closing speed of 1.4c...

Correct.

> but neither one of these guys can make any kind of measurement of the other that will ever exceed c...

If one of the cars [also called an "observer", also called a CS; its associated (inertial) CS] measures the speed of the other (incoming) car,
he will get a value less than c.

> their measurements are limited by the LT... isn't that correct?

Yes.

> Wouldn't this also be true even for much lower speeds? Even at, say, 50 mph each, their closing
> speed would be 100 mph but technically you could still apply the LT and find that from the
> frame of either car their perceived relative speed would be less than 100 mph by some
> incredibly small amount? Like 99.99999999 mph or some such?

Yes.

rotchm wrote:

> On Sunday, October 9, 2022 at 1:42:38 PM UTC-4, Paul Alsing wrote:
> Thus, relative to your (inertial) coordinate system (CS) [it doesn't
> matter where you are located at in this CS], the speeds of the two
> "cars"
> are 0.7c each, approaching each other. IOW, you [your CS] measures their
> speeds top be 0.7c.
>
>> I can measure the rate of change of the distance between them and come
>> up with a closing speed of 1.4c...
>
> Correct.

what's the speed between them so, the time reach you and the time to reach
each other, you fucking stupid troll. You are a fucking crackpot. And that
yacht, is not yours.

On Sunday, 9 October 2022 at 22:12:19 UTC+2, rotchm wrote:
> On Sunday, October 9, 2022 at 1:42:38 PM UTC-4, Paul Alsing wrote:
>
> > 2 vehicles are approaching each other along the same axis. Let's say each is moving at .7c relative to my
> > position in my chair on my balcony looking down on that axis.
> Thus, relative to your (inertial) coordinate system (CS) [it doesn't matter where you are located at in this CS], the speeds of the two "cars"
> are 0.7c each, approaching each other. IOW, you [your CS] measures their speeds top be 0.7c.

> > I can measure the rate of change of the distance between them and come up with a closing speed of 1.4c...
> Correct.

In the meantimein the real world, however, forbidden
by your bunch of idiots GPS and TAI keep measuring
t'=t in forbidden by your bunch of idiots old seconds.

On 2022-10-10 06:01:24 +0000, Maciej Wozniak said:

>
> [ … ]
>
>
> In the meantimein the real world, however, forbidden
> by your bunch of idiots GPS and TAI keep measuring
> t'=t in forbidden by your bunch of idiots old seconds.

507
--
Athel -- French and British, living mainly in England until 1987.

On Sunday, October 9, 2022 at 1:02:05 AM UTC-7, Paul B. Andersen wrote:
> Den 08.10.2022 21:35, skrev patdolan:
> >
> > Trevor measures Tom Roberts' relative velocity along Trevor's x-axis as 0.8660243c. In Trevor's universe (the only universe(unless SR is a many-worlds theory)) Tom's co-moving x-axis which is parallel to Trevor's x-axis contains two meter marks for every one meter mark of Trevor's. This is not an illusion just because the two axes are moving wrt each other. Tom's meters really are only half as long as Trevor's meters. Therefore Tom must measure in his universe--the only universe--two meters of displacement for every one meter of displacement that Trevor measures.
> >
> > Furthermore, Trevor observers that Tom's clock is ticking at a rate only half as fast as Trevor's clock. This is not an illusion just because Tom's and Trevor's clocks are moving wrt each other. Tom's seconds really are twice as long as Trevor's seconds. Therefore Tom must measure in his universe--the only universe--one second for every two seconds that Trevor measures..
> >
> > When Tom divides his displacement by his interval of time in his universe--the only universe--it is not an illusion or mathematically artifact that Tom's brain, operating at half the biological speed of Trevor's brain, concludes that his velocity towards Trevor is 3.4681689c or gama^2 times the proper velocity that Trevor calculates for Tom.
> >
> https://paulba.no/pdf/Mutual_time_dilation.pdf" rel="nofollow" target="_blank">https://paulba.no/pdf/Mutual_time_dilation.pdf
>
> --
> Paul
>
> https://paulba.no/

Paul A#1, you have not squeezed all of the conclusions possible out of your three event, three clock scenario. For instance, at E1 there are d*gamma x-axis length units between clock A and clock B' on the x-axis as viewed from Frame K'. Therefore at E2 clock B' will have counted that d*gamma x-axis length units have passed it by since E1. According to your own calculation clock A reads d/(v*gamma) at E2. From our vantage point in Frame K' we now construct the coordinate relative velocity of clock A as observed by clock B' at E2 by dividing the Dolan coordinate distance d*gamma by the Paul B. Andersen clock A coordinate time t_2:

Conclusion #5 (d*gamma)/(d/(v*gamma)) = v*gamma^2

Which is exactly the Dolan coordinate relative velocity factor for relative velocity v. The symmetry is obvious.

On Monday, October 10, 2022 at 7:20:13 PM UTC-7, patdolan wrote:
> On Sunday, October 9, 2022 at 1:02:05 AM UTC-7, Paul B. Andersen wrote:
> > Den 08.10.2022 21:35, skrev patdolan:
> > >
> > > Trevor measures Tom Roberts' relative velocity along Trevor's x-axis as 0.8660243c. In Trevor's universe (the only universe(unless SR is a many-worlds theory)) Tom's co-moving x-axis which is parallel to Trevor's x-axis contains two meter marks for every one meter mark of Trevor's. This is not an illusion just because the two axes are moving wrt each other. Tom's meters really are only half as long as Trevor's meters. Therefore Tom must measure in his universe--the only universe--two meters of displacement for every one meter of displacement that Trevor measures.
> > >
> > > Furthermore, Trevor observers that Tom's clock is ticking at a rate only half as fast as Trevor's clock. This is not an illusion just because Tom's and Trevor's clocks are moving wrt each other. Tom's seconds really are twice as long as Trevor's seconds. Therefore Tom must measure in his universe--the only universe--one second for every two seconds that Trevor measures.
> > >
> > > When Tom divides his displacement by his interval of time in his universe--the only universe--it is not an illusion or mathematically artifact that Tom's brain, operating at half the biological speed of Trevor's brain, concludes that his velocity towards Trevor is 3.4681689c or gama^2 times the proper velocity that Trevor calculates for Tom.
> > >
> > https://paulba.no/pdf/Mutual_time_dilation.pdf" rel="nofollow" target="_blank">https://paulba.no/pdf/Mutual_time_dilation.pdf
> >
> > --
> > Paul
> >
> > https://paulba.no/
> Paul A#1, you have not squeezed all of the conclusions possible out of your three event, three clock scenario. For instance, at E1 there are d*gamma x-axis length units between clock A and clock B' on the x-axis as viewed from Frame K'. Therefore at E2 clock B' will have counted that d*gamma x-axis length units have passed it by since E1. According to your own calculation clock A reads d/(v*gamma) at E2. From our vantage point in Frame K' we now construct the coordinate relative velocity of clock A as observed by clock B' at E2 by dividing the Dolan coordinate distance d*gamma by the Paul B. Andersen clock A coordinate time t_2:
>
> Conclusion #5 (d*gamma)/(d/(v*gamma)) = v*gamma^2
>
> Which is exactly the Dolan coordinate relative velocity factor for relative velocity v. The symmetry is obvious.

Not to belabor the point, but coordinate relative velocity exceeds the speed of light for all proper relative velocities greater that .618c.

On Monday, October 10, 2022 at 7:44:29 PM UTC-7, patdolan wrote:
> On Monday, October 10, 2022 at 7:20:13 PM UTC-7, patdolan wrote:
> > On Sunday, October 9, 2022 at 1:02:05 AM UTC-7, Paul B. Andersen wrote:
> > > Den 08.10.2022 21:35, skrev patdolan:
> > > >
> > > > Trevor measures Tom Roberts' relative velocity along Trevor's x-axis as 0.8660243c. In Trevor's universe (the only universe(unless SR is a many-worlds theory)) Tom's co-moving x-axis which is parallel to Trevor's x-axis contains two meter marks for every one meter mark of Trevor's. This is not an illusion just because the two axes are moving wrt each other. Tom's meters really are only half as long as Trevor's meters. Therefore Tom must measure in his universe--the only universe--two meters of displacement for every one meter of displacement that Trevor measures.
> > > >
> > > > Furthermore, Trevor observers that Tom's clock is ticking at a rate only half as fast as Trevor's clock. This is not an illusion just because Tom's and Trevor's clocks are moving wrt each other. Tom's seconds really are twice as long as Trevor's seconds. Therefore Tom must measure in his universe--the only universe--one second for every two seconds that Trevor measures.
> > > >
> > > > When Tom divides his displacement by his interval of time in his universe--the only universe--it is not an illusion or mathematically artifact that Tom's brain, operating at half the biological speed of Trevor's brain, concludes that his velocity towards Trevor is 3.4681689c or gama^2 times the proper velocity that Trevor calculates for Tom.
> > > >
> > > https://paulba.no/pdf/Mutual_time_dilation.pdf" rel="nofollow" target="_blank">https://paulba.no/pdf/Mutual_time_dilation.pdf
> > >
> > > --
> > > Paul
> > >
> > > https://paulba.no/
> > Paul A#1, you have not squeezed all of the conclusions possible out of your three event, three clock scenario. For instance, at E1 there are d*gamma x-axis length units between clock A and clock B' on the x-axis as viewed from Frame K'. Therefore at E2 clock B' will have counted that d*gamma x-axis length units have passed it by since E1. According to your own calculation clock A reads d/(v*gamma) at E2. From our vantage point in Frame K' we now construct the coordinate relative velocity of clock A as observed by clock B' at E2 by dividing the Dolan coordinate distance d*gamma by the Paul B. Andersen clock A coordinate time t_2:
> >
> > Conclusion #5 (d*gamma)/(d/(v*gamma)) = v*gamma^2
> >
> > Which is exactly the Dolan coordinate relative velocity factor for relative velocity v. The symmetry is obvious.
> Not to belabor the point, but coordinate relative velocity exceeds the speed of light for all proper relative velocities greater that .618c.

Shut up Paddy!

Tell them what I say!

On Friday, October 7, 2022 at 11:02:15 AM UTC-7, Ross A. Finlayson wrote:
> On Friday, October 7, 2022 at 10:38:34 AM UTC-7, patdolan wrote:
> > On Thursday, October 6, 2022 at 3:26:16 PM UTC-7, tjrob137 wrote:
> > > On 10/1/22 12:58 PM, patdolan wrote:
> > > > On Saturday, October 1, 2022 at 10:02:56 AM UTC-7, tjrob137 wrote:
> > > >> On 9/30/22 10:17 PM, rotchm wrote:
> > > >>>>>> Since you talked about closing speeds, can you explain
> > > >>>>>> what you mean by such an expression?
> > > >>>> ... in this post he says..."Closing speed is the rate of
> > > >>>> change of the distance between two objects as they both move.
> > > >>>
> > > >>> Yes, that's basically it. The closing speed between two entities
> > > >>> is the rate of change of the distance (separation) between them,
> > > >>> as measured by a given frame (system of coordinates).
> > > >> Yes, but only for inertial coordinates. The closing speed for a
> > > >> given pair of objects varies, depending on which inertial frame is
> > > >> used to calculate/measure it.
> > > >>> Its "v1 ± v2" depending of sign conventions.
> > > >> Only when the two objects are moving along a single axis in the
> > > >> inertial frame used. If that isn't so, the calculation is MUCH
> > > >> more complicated.
> > > >>
> > > >> Tom Roberts
> > > > Now, Tom Roberts, provide this forum with the proper and coordinate
> > > > closing speeds, as calulated by observers on each closing object.
> > > Consider inertial frame S with coordinates (x,t) -- ignore y and z as
> > > they don't appear in this problem. Object A is located at x>0 and is
> > > moving inertially along the x axis of S with velocity Va, Va<0. Object B
> > > is located at x<0 and is moving inertially along the x axis of S with
> > > velocity Vb, Vb>0. These two objects are clearly approaching each other.
> > >
> > > In frame S, the closing speed of these two objects is |Va|+|Vb| = Vb-Va.
> > >
> > > (Remember my V's are 3-velocities along the x axis, with
> > > Va<0 and Vb>0.)
> > >
> > > In the rest frame of A, object B has velocity Vba such that
> > > Vb = (Va+Vba)/(1+Va*Vba/c^2)
> > > so
> > > Vba = (Vb-Va)/(1-Va*Vb/c^2)
> > > In the rest frame of A, their closing speed is |Vba| = Vba.
> > >
> > > In the rest frame of B, object A has velocity Vab such that
> > > Vb = (Va+Vab)/(1+Va*Vab/c^2)
> > > so
> > > Vab = (Va-Vb)/(1-Va*Vb/c^2)
> > > In the rest frame of B, their closing speed is |Vab| = -Vab.
> > >
> > > While the expressions are different, |Vab| = |Vba|, and the closing
> > > speeds in the two object's rest frames are the same.
> > >
> > > Note that if Va<<c and Vb<<c, the closing speeds in all three frames are
> > > approximately the same, |Va|+|Vb| = Vb-Va.
> > > > I will state up front that you won't/can't do it.
> > > As usual, you are wrong.
> > >
> > > Tom Roberts
> > Thank you Tom Roberts for deigning to respond to my challenge. So far we have been making our way up a 5.4 - 5.6 route. Time to find some 5.11 stuff. In your pedestrian implementation of the Einstein velocity addition formula, these are the two most interesting lines that you type:
> >
> > 1) "While the expressions are different, |Vab| = |Vba|, and the closing
> > speeds in the two object's rest frames are the same."
> > This result you arrive at is correct of course. But I will demonstrate that it rests on a completely unproved assumption.
> >
> > 2) "Note that if Va<<c and Vb<<c, the closing speeds in all three frames are
> > approximately the same, |Va|+|Vb| = Vb-Va."
> > Would you care to speculate on what the ramifications are of closing speeds that are a substantial fraction of c? Say .867c when gamma = 2?
> It's they saiy "there's an non-linear impulse", which adds to zero,
> then as it resonates, it adds to 1/2.
>
>
> That's where, "in a circle, the wave resonance observes itself",
> "yeah, radial is infinite and non-linear".
>
> So, it adds half up/down what is input.

Yeah, so non-linear input is atomic.

On Monday, October 10, 2022 at 8:34:19 PM UTC-7, Ross A. Finlayson wrote:
> On Monday, October 10, 2022 at 7:44:29 PM UTC-7, patdolan wrote:
> > On Monday, October 10, 2022 at 7:20:13 PM UTC-7, patdolan wrote:
> > > On Sunday, October 9, 2022 at 1:02:05 AM UTC-7, Paul B. Andersen wrote:
> > > > Den 08.10.2022 21:35, skrev patdolan:
> > > > >
> > > > > Trevor measures Tom Roberts' relative velocity along Trevor's x-axis as 0.8660243c. In Trevor's universe (the only universe(unless SR is a many-worlds theory)) Tom's co-moving x-axis which is parallel to Trevor's x-axis contains two meter marks for every one meter mark of Trevor's. This is not an illusion just because the two axes are moving wrt each other. Tom's meters really are only half as long as Trevor's meters. Therefore Tom must measure in his universe--the only universe--two meters of displacement for every one meter of displacement that Trevor measures.
> > > > >
> > > > > Furthermore, Trevor observers that Tom's clock is ticking at a rate only half as fast as Trevor's clock. This is not an illusion just because Tom's and Trevor's clocks are moving wrt each other. Tom's seconds really are twice as long as Trevor's seconds. Therefore Tom must measure in his universe--the only universe--one second for every two seconds that Trevor measures.
> > > > >
> > > > > When Tom divides his displacement by his interval of time in his universe--the only universe--it is not an illusion or mathematically artifact that Tom's brain, operating at half the biological speed of Trevor's brain, concludes that his velocity towards Trevor is 3.4681689c or gama^2 times the proper velocity that Trevor calculates for Tom.
> > > > >
> > > > https://paulba.no/pdf/Mutual_time_dilation.pdf" rel="nofollow" target="_blank">https://paulba.no/pdf/Mutual_time_dilation.pdf
> > > >
> > > > --
> > > > Paul
> > > >
> > > > https://paulba.no/
> > > Paul A#1, you have not squeezed all of the conclusions possible out of your three event, three clock scenario. For instance, at E1 there are d*gamma x-axis length units between clock A and clock B' on the x-axis as viewed from Frame K'. Therefore at E2 clock B' will have counted that d*gamma x-axis length units have passed it by since E1. According to your own calculation clock A reads d/(v*gamma) at E2. From our vantage point in Frame K' we now construct the coordinate relative velocity of clock A as observed by clock B' at E2 by dividing the Dolan coordinate distance d*gamma by the Paul B. Andersen clock A coordinate time t_2:
> > >
> > > Conclusion #5 (d*gamma)/(d/(v*gamma)) = v*gamma^2
> > >
> > > Which is exactly the Dolan coordinate relative velocity factor for relative velocity v. The symmetry is obvious.
> > Not to belabor the point, but coordinate relative velocity exceeds the speed of light for all proper relative velocities greater that .618c.
> Shut up Paddy!
>
> Tell them what I say!
Ross!...I don't think there's been a cross word between us since I challenged you to a duel 10 or 15 years ago. What gives? Better yet, meet me here tomorrow at sunrise. Mitch is my second, just like last time. Who is yours?

On Monday, October 10, 2022 at 8:39:53 PM UTC-7, patdolan wrote:
> On Monday, October 10, 2022 at 8:34:19 PM UTC-7, Ross A. Finlayson wrote:
> > On Monday, October 10, 2022 at 7:44:29 PM UTC-7, patdolan wrote:
> > > On Monday, October 10, 2022 at 7:20:13 PM UTC-7, patdolan wrote:
> > > > On Sunday, October 9, 2022 at 1:02:05 AM UTC-7, Paul B. Andersen wrote:
> > > > > Den 08.10.2022 21:35, skrev patdolan:
> > > > > >
> > > > > > Trevor measures Tom Roberts' relative velocity along Trevor's x-axis as 0.8660243c. In Trevor's universe (the only universe(unless SR is a many-worlds theory)) Tom's co-moving x-axis which is parallel to Trevor's x-axis contains two meter marks for every one meter mark of Trevor's. This is not an illusion just because the two axes are moving wrt each other. Tom's meters really are only half as long as Trevor's meters. Therefore Tom must measure in his universe--the only universe--two meters of displacement for every one meter of displacement that Trevor measures.
> > > > > >
> > > > > > Furthermore, Trevor observers that Tom's clock is ticking at a rate only half as fast as Trevor's clock. This is not an illusion just because Tom's and Trevor's clocks are moving wrt each other. Tom's seconds really are twice as long as Trevor's seconds. Therefore Tom must measure in his universe--the only universe--one second for every two seconds that Trevor measures.
> > > > > >
> > > > > > When Tom divides his displacement by his interval of time in his universe--the only universe--it is not an illusion or mathematically artifact that Tom's brain, operating at half the biological speed of Trevor's brain, concludes that his velocity towards Trevor is 3.4681689c or gama^2 times the proper velocity that Trevor calculates for Tom.
> > > > > >
> > > > > https://paulba.no/pdf/Mutual_time_dilation.pdf" rel="nofollow" target="_blank">https://paulba.no/pdf/Mutual_time_dilation.pdf
> > > > >
> > > > > --
> > > > > Paul
> > > > >
> > > > > https://paulba.no/
> > > > Paul A#1, you have not squeezed all of the conclusions possible out of your three event, three clock scenario. For instance, at E1 there are d*gamma x-axis length units between clock A and clock B' on the x-axis as viewed from Frame K'. Therefore at E2 clock B' will have counted that d*gamma x-axis length units have passed it by since E1. According to your own calculation clock A reads d/(v*gamma) at E2. From our vantage point in Frame K' we now construct the coordinate relative velocity of clock A as observed by clock B' at E2 by dividing the Dolan coordinate distance d*gamma by the Paul B. Andersen clock A coordinate time t_2:
> > > >
> > > > Conclusion #5 (d*gamma)/(d/(v*gamma)) = v*gamma^2
> > > >
> > > > Which is exactly the Dolan coordinate relative velocity factor for relative velocity v. The symmetry is obvious.
> > > Not to belabor the point, but coordinate relative velocity exceeds the speed of light for all proper relative velocities greater that .618c.
> > Shut up Paddy!
> >
> > Tell them what I say!
> Ross!...I don't think there's been a cross word between us since I challenged you to a duel 10 or 15 years ago. What gives? Better yet, meet me here tomorrow at sunrise. Mitch is my second, just like last time. Who is yours?

You think I duck? No, you duck.

Don't forget to duck!

On Thursday, October 6, 2022 at 6:57:27 PM UTC-7, Ross A. Finlayson wrote:
> On Thursday, September 29, 2022 at 7:44:29 PM UTC-7, Dono. wrote:
> > On Thursday, September 29, 2022 at 7:35:14 PM UTC-7, rotchm wrote:
> > > dono incited me to ask such a question.
> > >
> > > In the recent thread entitled "addition of velocities", the op
> > > inquired about closing speeds.
> > >
> > > An aggressive debate ensued.
> > >
> > > I (and others) maintained that closing speed (of two things)
> > > is simply "v1 ± v2" [depending of the sign conventions].
> > Well, you are an idiot, Stephane.
> > Time has made this only worse.
> > Closing speed is a convention, used to express the rate at which two objects, starting simultaneously, cover a distance L between them:
> >
> > v1*t+v2*t=L (see, "t" needs to be the SAME)
> > t=L/(v1+v2)
> >
> > By CONVENTION, UNDER the above conditions, u=v1+v2 is called closing speed
> > The concept is very useful when one of the "objects" is a pulse of light, say v1=c. Then the closing speed of covering a distance "L" is c+v. But cranks, of the type of Thomas Heger and Stephane Baune, call this "relative speed of light". This causes infinitely long debates about light speed not being constant. Most of such debates center around Einstein derivation of the Lorentz transforms in "On the Electrodynamics..." but also in the derivation of the phase difference in the Sagnac experiments where cranks like Stephane Baune will claim that light goes around at c+v in one direction and c-v in the opposite direction. Ergo, the Sagnac effect is "proof" that light speed is "variable".
>
>
> Or, ..., that it produces higher order objects as waves, ..., that reflect in eventual disposition in
> real wave collapse, ..., that c+v and c-v are "imaginary v".
>
> It's called resonance these days some guys just got a Nobel prize for it.

Right, Dono. Tell me I'm right!

On Thursday, October 6, 2022 at 6:55:41 PM UTC-7, Ross A. Finlayson wrote:
> On Thursday, September 29, 2022 at 7:35:14 PM UTC-7, rotchm wrote:
> > dono incited me to ask such a question.
> >
> > In the recent thread entitled "addition of velocities", the op
> > inquired about closing speeds.
> >
> > An aggressive debate ensued.
> >
> > I (and others) maintained that closing speed (of two things)
> > is simply "v1 ± v2" [depending of the sign conventions].
> > Or, the rate of change of the separation (distance) between the two things.
> > [We were discussing trajectories along the x_axis only btw].
> >
> > Dono however, maintains that the above are not the meaning of closing speed as used here (relativity and kinematics in general). And he reasons that:
> >
> > "v1+v2 is the closing speed of two objects that STARTED SIMULTANEOSLY. "
> >
> > " If the two objects don't start simultaneously, one cannot define closing speed."
> >
> > I am wondering as to what is the consensus here concerning the concept of
> > "closing speed".
>
> The objects meet or pass.
>
> Seems logic dictates "space contraction".

Seems logic dictates!

On Monday, October 10, 2022 at 8:41:46 PM UTC-7, Ross A. Finlayson wrote:
> On Monday, October 10, 2022 at 8:39:53 PM UTC-7, patdolan wrote:
> > On Monday, October 10, 2022 at 8:34:19 PM UTC-7, Ross A. Finlayson wrote:
> > > On Monday, October 10, 2022 at 7:44:29 PM UTC-7, patdolan wrote:
> > > > On Monday, October 10, 2022 at 7:20:13 PM UTC-7, patdolan wrote:
> > > > > On Sunday, October 9, 2022 at 1:02:05 AM UTC-7, Paul B. Andersen wrote:
> > > > > > Den 08.10.2022 21:35, skrev patdolan:
> > > > > > >
> > > > > > > Trevor measures Tom Roberts' relative velocity along Trevor's x-axis as 0.8660243c. In Trevor's universe (the only universe(unless SR is a many-worlds theory)) Tom's co-moving x-axis which is parallel to Trevor's x-axis contains two meter marks for every one meter mark of Trevor's. This is not an illusion just because the two axes are moving wrt each other. Tom's meters really are only half as long as Trevor's meters. Therefore Tom must measure in his universe--the only universe--two meters of displacement for every one meter of displacement that Trevor measures.
> > > > > > >
> > > > > > > Furthermore, Trevor observers that Tom's clock is ticking at a rate only half as fast as Trevor's clock. This is not an illusion just because Tom's and Trevor's clocks are moving wrt each other. Tom's seconds really are twice as long as Trevor's seconds. Therefore Tom must measure in his universe--the only universe--one second for every two seconds that Trevor measures.
> > > > > > >
> > > > > > > When Tom divides his displacement by his interval of time in his universe--the only universe--it is not an illusion or mathematically artifact that Tom's brain, operating at half the biological speed of Trevor's brain, concludes that his velocity towards Trevor is 3.4681689c or gama^2 times the proper velocity that Trevor calculates for Tom.
> > > > > > >
> > > > > > https://paulba.no/pdf/Mutual_time_dilation.pdf" rel="nofollow" target="_blank">https://paulba.no/pdf/Mutual_time_dilation.pdf
> > > > > >
> > > > > > --
> > > > > > Paul
> > > > > >
> > > > > > https://paulba.no/
> > > > > Paul A#1, you have not squeezed all of the conclusions possible out of your three event, three clock scenario. For instance, at E1 there are d*gamma x-axis length units between clock A and clock B' on the x-axis as viewed from Frame K'. Therefore at E2 clock B' will have counted that d*gamma x-axis length units have passed it by since E1. According to your own calculation clock A reads d/(v*gamma) at E2. From our vantage point in Frame K' we now construct the coordinate relative velocity of clock A as observed by clock B' at E2 by dividing the Dolan coordinate distance d*gamma by the Paul B. Andersen clock A coordinate time t_2:
> > > > >
> > > > > Conclusion #5 (d*gamma)/(d/(v*gamma)) = v*gamma^2
> > > > >
> > > > > Which is exactly the Dolan coordinate relative velocity factor for relative velocity v. The symmetry is obvious.
> > > > Not to belabor the point, but coordinate relative velocity exceeds the speed of light for all proper relative velocities greater that .618c.
> > > Shut up Paddy!
> > >
> > > Tell them what I say!
> > Ross!...I don't think there's been a cross word between us since I challenged you to a duel 10 or 15 years ago. What gives? Better yet, meet me here tomorrow at sunrise. Mitch is my second, just like last time. Who is yours?
> You think I duck? No, you duck.
>
> Don't forget to duck!

Duck...huh? So is it pistols or pillows?

On Monday, October 10, 2022 at 8:49:12 PM UTC-7, patdolan wrote:
> On Monday, October 10, 2022 at 8:41:46 PM UTC-7, Ross A. Finlayson wrote:
> > On Monday, October 10, 2022 at 8:39:53 PM UTC-7, patdolan wrote:
> > > On Monday, October 10, 2022 at 8:34:19 PM UTC-7, Ross A. Finlayson wrote:
> > > > On Monday, October 10, 2022 at 7:44:29 PM UTC-7, patdolan wrote:
> > > > > On Monday, October 10, 2022 at 7:20:13 PM UTC-7, patdolan wrote:
> > > > > > On Sunday, October 9, 2022 at 1:02:05 AM UTC-7, Paul B. Andersen wrote:
> > > > > > > Den 08.10.2022 21:35, skrev patdolan:
> > > > > > > >
> > > > > > > > Trevor measures Tom Roberts' relative velocity along Trevor's x-axis as 0.8660243c. In Trevor's universe (the only universe(unless SR is a many-worlds theory)) Tom's co-moving x-axis which is parallel to Trevor's x-axis contains two meter marks for every one meter mark of Trevor's. This is not an illusion just because the two axes are moving wrt each other. Tom's meters really are only half as long as Trevor's meters. Therefore Tom must measure in his universe--the only universe--two meters of displacement for every one meter of displacement that Trevor measures.
> > > > > > > >
> > > > > > > > Furthermore, Trevor observers that Tom's clock is ticking at a rate only half as fast as Trevor's clock. This is not an illusion just because Tom's and Trevor's clocks are moving wrt each other. Tom's seconds really are twice as long as Trevor's seconds. Therefore Tom must measure in his universe--the only universe--one second for every two seconds that Trevor measures.
> > > > > > > >
> > > > > > > > When Tom divides his displacement by his interval of time in his universe--the only universe--it is not an illusion or mathematically artifact that Tom's brain, operating at half the biological speed of Trevor's brain, concludes that his velocity towards Trevor is 3.4681689c or gama^2 times the proper velocity that Trevor calculates for Tom.
> > > > > > > >
> > > > > > > https://paulba.no/pdf/Mutual_time_dilation.pdf" rel="nofollow" target="_blank">https://paulba.no/pdf/Mutual_time_dilation.pdf
> > > > > > >
> > > > > > > --
> > > > > > > Paul
> > > > > > >
> > > > > > > https://paulba.no/
> > > > > > Paul A#1, you have not squeezed all of the conclusions possible out of your three event, three clock scenario. For instance, at E1 there are d*gamma x-axis length units between clock A and clock B' on the x-axis as viewed from Frame K'. Therefore at E2 clock B' will have counted that d*gamma x-axis length units have passed it by since E1. According to your own calculation clock A reads d/(v*gamma) at E2. From our vantage point in Frame K' we now construct the coordinate relative velocity of clock A as observed by clock B' at E2 by dividing the Dolan coordinate distance d*gamma by the Paul B. Andersen clock A coordinate time t_2:
> > > > > >
> > > > > > Conclusion #5 (d*gamma)/(d/(v*gamma)) = v*gamma^2
> > > > > >
> > > > > > Which is exactly the Dolan coordinate relative velocity factor for relative velocity v. The symmetry is obvious.
> > > > > Not to belabor the point, but coordinate relative velocity exceeds the speed of light for all proper relative velocities greater that .618c.
> > > > Shut up Paddy!
> > > >
> > > > Tell them what I say!
> > > Ross!...I don't think there's been a cross word between us since I challenged you to a duel 10 or 15 years ago. What gives? Better yet, meet me here tomorrow at sunrise. Mitch is my second, just like last time. Who is yours?
> > You think I duck? No, you duck.
> >
> > Don't forget to duck!
> Duck...huh? So is it pistols or pillows?

Nope, it's "die".

On Monday, October 10, 2022 at 8:56:24 PM UTC-7, Ross A. Finlayson wrote:
> On Monday, October 10, 2022 at 8:49:12 PM UTC-7, patdolan wrote:
> > On Monday, October 10, 2022 at 8:41:46 PM UTC-7, Ross A. Finlayson wrote:
> > > On Monday, October 10, 2022 at 8:39:53 PM UTC-7, patdolan wrote:
> > > > On Monday, October 10, 2022 at 8:34:19 PM UTC-7, Ross A. Finlayson wrote:
> > > > > On Monday, October 10, 2022 at 7:44:29 PM UTC-7, patdolan wrote:
> > > > > > On Monday, October 10, 2022 at 7:20:13 PM UTC-7, patdolan wrote:
> > > > > > > On Sunday, October 9, 2022 at 1:02:05 AM UTC-7, Paul B. Andersen wrote:
> > > > > > > > Den 08.10.2022 21:35, skrev patdolan:
> > > > > > > > >
> > > > > > > > > Trevor measures Tom Roberts' relative velocity along Trevor's x-axis as 0.8660243c. In Trevor's universe (the only universe(unless SR is a many-worlds theory)) Tom's co-moving x-axis which is parallel to Trevor's x-axis contains two meter marks for every one meter mark of Trevor's. This is not an illusion just because the two axes are moving wrt each other. Tom's meters really are only half as long as Trevor's meters. Therefore Tom must measure in his universe--the only universe--two meters of displacement for every one meter of displacement that Trevor measures.
> > > > > > > > >
> > > > > > > > > Furthermore, Trevor observers that Tom's clock is ticking at a rate only half as fast as Trevor's clock. This is not an illusion just because Tom's and Trevor's clocks are moving wrt each other. Tom's seconds really are twice as long as Trevor's seconds. Therefore Tom must measure in his universe--the only universe--one second for every two seconds that Trevor measures.
> > > > > > > > >
> > > > > > > > > When Tom divides his displacement by his interval of time in his universe--the only universe--it is not an illusion or mathematically artifact that Tom's brain, operating at half the biological speed of Trevor's brain, concludes that his velocity towards Trevor is 3.4681689c or gama^2 times the proper velocity that Trevor calculates for Tom.
> > > > > > > > >
> > > > > > > > https://paulba.no/pdf/Mutual_time_dilation.pdf" rel="nofollow" target="_blank">https://paulba.no/pdf/Mutual_time_dilation.pdf
> > > > > > > >
> > > > > > > > --
> > > > > > > > Paul
> > > > > > > >
> > > > > > > > https://paulba.no/
> > > > > > > Paul A#1, you have not squeezed all of the conclusions possible out of your three event, three clock scenario. For instance, at E1 there are d*gamma x-axis length units between clock A and clock B' on the x-axis as viewed from Frame K'. Therefore at E2 clock B' will have counted that d*gamma x-axis length units have passed it by since E1. According to your own calculation clock A reads d/(v*gamma) at E2. From our vantage point in Frame K' we now construct the coordinate relative velocity of clock A as observed by clock B' at E2 by dividing the Dolan coordinate distance d*gamma by the Paul B. Andersen clock A coordinate time t_2:
> > > > > > >
> > > > > > > Conclusion #5 (d*gamma)/(d/(v*gamma)) = v*gamma^2
> > > > > > >
> > > > > > > Which is exactly the Dolan coordinate relative velocity factor for relative velocity v. The symmetry is obvious.
> > > > > > Not to belabor the point, but coordinate relative velocity exceeds the speed of light for all proper relative velocities greater that .618c.
> > > > > Shut up Paddy!
> > > > >
> > > > > Tell them what I say!
> > > > Ross!...I don't think there's been a cross word between us since I challenged you to a duel 10 or 15 years ago. What gives? Better yet, meet me here tomorrow at sunrise. Mitch is my second, just like last time. Who is yours?
> > > You think I duck? No, you duck.
> > >
> > > Don't forget to duck!
> > Duck...huh? So is it pistols or pillows?
> Nope, it's "die".

"Like a giant lightning bolt from the center of the universe, ...".

"Like a giant lightning bolt, from the center of the universe, ...".

Straight to the head!

On Monday, October 10, 2022 at 8:58:29 PM UTC-7, Ross A. Finlayson wrote:
> On Monday, October 10, 2022 at 8:56:24 PM UTC-7, Ross A. Finlayson wrote:
> > On Monday, October 10, 2022 at 8:49:12 PM UTC-7, patdolan wrote:
> > > On Monday, October 10, 2022 at 8:41:46 PM UTC-7, Ross A. Finlayson wrote:
> > > > On Monday, October 10, 2022 at 8:39:53 PM UTC-7, patdolan wrote:
> > > > > On Monday, October 10, 2022 at 8:34:19 PM UTC-7, Ross A. Finlayson wrote:
> > > > > > On Monday, October 10, 2022 at 7:44:29 PM UTC-7, patdolan wrote:
> > > > > > > On Monday, October 10, 2022 at 7:20:13 PM UTC-7, patdolan wrote:
> > > > > > > > On Sunday, October 9, 2022 at 1:02:05 AM UTC-7, Paul B. Andersen wrote:
> > > > > > > > > Den 08.10.2022 21:35, skrev patdolan:
> > > > > > > > > >
> > > > > > > > > > Trevor measures Tom Roberts' relative velocity along Trevor's x-axis as 0.8660243c. In Trevor's universe (the only universe(unless SR is a many-worlds theory)) Tom's co-moving x-axis which is parallel to Trevor's x-axis contains two meter marks for every one meter mark of Trevor's. This is not an illusion just because the two axes are moving wrt each other. Tom's meters really are only half as long as Trevor's meters. Therefore Tom must measure in his universe--the only universe--two meters of displacement for every one meter of displacement that Trevor measures.
> > > > > > > > > >
> > > > > > > > > > Furthermore, Trevor observers that Tom's clock is ticking at a rate only half as fast as Trevor's clock. This is not an illusion just because Tom's and Trevor's clocks are moving wrt each other. Tom's seconds really are twice as long as Trevor's seconds. Therefore Tom must measure in his universe--the only universe--one second for every two seconds that Trevor measures.
> > > > > > > > > >
> > > > > > > > > > When Tom divides his displacement by his interval of time in his universe--the only universe--it is not an illusion or mathematically artifact that Tom's brain, operating at half the biological speed of Trevor's brain, concludes that his velocity towards Trevor is 3.4681689c or gama^2 times the proper velocity that Trevor calculates for Tom.
> > > > > > > > > >
> > > > > > > > > https://paulba.no/pdf/Mutual_time_dilation.pdf" rel="nofollow" target="_blank">https://paulba.no/pdf/Mutual_time_dilation.pdf
> > > > > > > > >
> > > > > > > > > --
> > > > > > > > > Paul
> > > > > > > > >
> > > > > > > > > https://paulba.no/
> > > > > > > > Paul A#1, you have not squeezed all of the conclusions possible out of your three event, three clock scenario. For instance, at E1 there are d*gamma x-axis length units between clock A and clock B' on the x-axis as viewed from Frame K'. Therefore at E2 clock B' will have counted that d*gamma x-axis length units have passed it by since E1. According to your own calculation clock A reads d/(v*gamma) at E2. From our vantage point in Frame K' we now construct the coordinate relative velocity of clock A as observed by clock B' at E2 by dividing the Dolan coordinate distance d*gamma by the Paul B. Andersen clock A coordinate time t_2:
> > > > > > > >
> > > > > > > > Conclusion #5 (d*gamma)/(d/(v*gamma)) = v*gamma^2
> > > > > > > >
> > > > > > > > Which is exactly the Dolan coordinate relative velocity factor for relative velocity v. The symmetry is obvious.
> > > > > > > Not to belabor the point, but coordinate relative velocity exceeds the speed of light for all proper relative velocities greater that .618c.
> > > > > > Shut up Paddy!
> > > > > >
> > > > > > Tell them what I say!
> > > > > Ross!...I don't think there's been a cross word between us since I challenged you to a duel 10 or 15 years ago. What gives? Better yet, meet me here tomorrow at sunrise. Mitch is my second, just like last time. Who is yours?
> > > > You think I duck? No, you duck.
> > > >
> > > > Don't forget to duck!
> > > Duck...huh? So is it pistols or pillows?
> > Nope, it's "die".
> "Like a giant lightning bolt from the center of the universe, ...".
>
> "Like a giant lightning bolt, from the center of the universe, ...".
>
> Straight to the head!

Ross, you are clearly in crisis tonight. Give us your coordinates and we will send assistance. If you are in Seattle, as I suspect, I will minister to you personally.

On Monday, October 10, 2022 at 9:14:37 PM UTC-7, patdolan wrote:
> On Monday, October 10, 2022 at 8:58:29 PM UTC-7, Ross A. Finlayson wrote:
> > On Monday, October 10, 2022 at 8:56:24 PM UTC-7, Ross A. Finlayson wrote:
> > > On Monday, October 10, 2022 at 8:49:12 PM UTC-7, patdolan wrote:
> > > > On Monday, October 10, 2022 at 8:41:46 PM UTC-7, Ross A. Finlayson wrote:
> > > > > On Monday, October 10, 2022 at 8:39:53 PM UTC-7, patdolan wrote:
> > > > > > On Monday, October 10, 2022 at 8:34:19 PM UTC-7, Ross A. Finlayson wrote:
> > > > > > > On Monday, October 10, 2022 at 7:44:29 PM UTC-7, patdolan wrote:
> > > > > > > > On Monday, October 10, 2022 at 7:20:13 PM UTC-7, patdolan wrote:
> > > > > > > > > On Sunday, October 9, 2022 at 1:02:05 AM UTC-7, Paul B. Andersen wrote:
> > > > > > > > > > Den 08.10.2022 21:35, skrev patdolan:
> > > > > > > > > > >
> > > > > > > > > > > Trevor measures Tom Roberts' relative velocity along Trevor's x-axis as 0.8660243c. In Trevor's universe (the only universe(unless SR is a many-worlds theory)) Tom's co-moving x-axis which is parallel to Trevor's x-axis contains two meter marks for every one meter mark of Trevor's. This is not an illusion just because the two axes are moving wrt each other. Tom's meters really are only half as long as Trevor's meters. Therefore Tom must measure in his universe--the only universe--two meters of displacement for every one meter of displacement that Trevor measures.
> > > > > > > > > > >
> > > > > > > > > > > Furthermore, Trevor observers that Tom's clock is ticking at a rate only half as fast as Trevor's clock. This is not an illusion just because Tom's and Trevor's clocks are moving wrt each other. Tom's seconds really are twice as long as Trevor's seconds. Therefore Tom must measure in his universe--the only universe--one second for every two seconds that Trevor measures.
> > > > > > > > > > >
> > > > > > > > > > > When Tom divides his displacement by his interval of time in his universe--the only universe--it is not an illusion or mathematically artifact that Tom's brain, operating at half the biological speed of Trevor's brain, concludes that his velocity towards Trevor is 3.4681689c or gama^2 times the proper velocity that Trevor calculates for Tom.
> > > > > > > > > > >
> > > > > > > > > > https://paulba.no/pdf/Mutual_time_dilation.pdf" rel="nofollow" target="_blank">https://paulba.no/pdf/Mutual_time_dilation.pdf
> > > > > > > > > >
> > > > > > > > > > --
> > > > > > > > > > Paul
> > > > > > > > > >
> > > > > > > > > > https://paulba.no/
> > > > > > > > > Paul A#1, you have not squeezed all of the conclusions possible out of your three event, three clock scenario. For instance, at E1 there are d*gamma x-axis length units between clock A and clock B' on the x-axis as viewed from Frame K'. Therefore at E2 clock B' will have counted that d*gamma x-axis length units have passed it by since E1. According to your own calculation clock A reads d/(v*gamma) at E2. From our vantage point in Frame K' we now construct the coordinate relative velocity of clock A as observed by clock B' at E2 by dividing the Dolan coordinate distance d*gamma by the Paul B. Andersen clock A coordinate time t_2:
> > > > > > > > >
> > > > > > > > > Conclusion #5 (d*gamma)/(d/(v*gamma)) = v*gamma^2
> > > > > > > > >
> > > > > > > > > Which is exactly the Dolan coordinate relative velocity factor for relative velocity v. The symmetry is obvious.
> > > > > > > > Not to belabor the point, but coordinate relative velocity exceeds the speed of light for all proper relative velocities greater that ..618c.
> > > > > > > Shut up Paddy!
> > > > > > >
> > > > > > > Tell them what I say!
> > > > > > Ross!...I don't think there's been a cross word between us since I challenged you to a duel 10 or 15 years ago. What gives? Better yet, meet me here tomorrow at sunrise. Mitch is my second, just like last time. Who is yours?
> > > > > You think I duck? No, you duck.
> > > > >
> > > > > Don't forget to duck!
> > > > Duck...huh? So is it pistols or pillows?
> > > Nope, it's "die".
> > "Like a giant lightning bolt from the center of the universe, ...".
> >
> > "Like a giant lightning bolt, from the center of the universe, ...".
> >
> > Straight to the head!
> Ross, you are clearly in crisis tonight. Give us your coordinates and we will send assistance. If you are in Seattle, as I suspect, I will minister to you personally.

NO, no, no, no, no, no, no, Pat.

You, you are in crisis.

On Tuesday, October 11, 2022 at 1:13:24 AM UTC-7, Ross A. Finlayson wrote:
> On Monday, October 10, 2022 at 9:14:37 PM UTC-7, patdolan wrote:
> > On Monday, October 10, 2022 at 8:58:29 PM UTC-7, Ross A. Finlayson wrote:
> > > On Monday, October 10, 2022 at 8:56:24 PM UTC-7, Ross A. Finlayson wrote:
> > > > On Monday, October 10, 2022 at 8:49:12 PM UTC-7, patdolan wrote:
> > > > > On Monday, October 10, 2022 at 8:41:46 PM UTC-7, Ross A. Finlayson wrote:
> > > > > > On Monday, October 10, 2022 at 8:39:53 PM UTC-7, patdolan wrote:
> > > > > > > On Monday, October 10, 2022 at 8:34:19 PM UTC-7, Ross A. Finlayson wrote:
> > > > > > > > On Monday, October 10, 2022 at 7:44:29 PM UTC-7, patdolan wrote:
> > > > > > > > > On Monday, October 10, 2022 at 7:20:13 PM UTC-7, patdolan wrote:
> > > > > > > > > > On Sunday, October 9, 2022 at 1:02:05 AM UTC-7, Paul B. Andersen wrote:
> > > > > > > > > > > Den 08.10.2022 21:35, skrev patdolan:
> > > > > > > > > > > >
> > > > > > > > > > > > Trevor measures Tom Roberts' relative velocity along Trevor's x-axis as 0.8660243c. In Trevor's universe (the only universe(unless SR is a many-worlds theory)) Tom's co-moving x-axis which is parallel to Trevor's x-axis contains two meter marks for every one meter mark of Trevor's. This is not an illusion just because the two axes are moving wrt each other. Tom's meters really are only half as long as Trevor's meters. Therefore Tom must measure in his universe--the only universe--two meters of displacement for every one meter of displacement that Trevor measures.
> > > > > > > > > > > >
> > > > > > > > > > > > Furthermore, Trevor observers that Tom's clock is ticking at a rate only half as fast as Trevor's clock. This is not an illusion just because Tom's and Trevor's clocks are moving wrt each other. Tom's seconds really are twice as long as Trevor's seconds. Therefore Tom must measure in his universe--the only universe--one second for every two seconds that Trevor measures.
> > > > > > > > > > > >
> > > > > > > > > > > > When Tom divides his displacement by his interval of time in his universe--the only universe--it is not an illusion or mathematically artifact that Tom's brain, operating at half the biological speed of Trevor's brain, concludes that his velocity towards Trevor is 3.4681689c or gama^2 times the proper velocity that Trevor calculates for Tom.
> > > > > > > > > > > >
> > > > > > > > > > > https://paulba.no/pdf/Mutual_time_dilation.pdf" rel="nofollow" target="_blank">https://paulba.no/pdf/Mutual_time_dilation.pdf
> > > > > > > > > > >
> > > > > > > > > > > --
> > > > > > > > > > > Paul
> > > > > > > > > > >
> > > > > > > > > > > https://paulba.no/
> > > > > > > > > > Paul A#1, you have not squeezed all of the conclusions possible out of your three event, three clock scenario. For instance, at E1 there are d*gamma x-axis length units between clock A and clock B' on the x-axis as viewed from Frame K'. Therefore at E2 clock B' will have counted that d*gamma x-axis length units have passed it by since E1. According to your own calculation clock A reads d/(v*gamma) at E2. From our vantage point in Frame K' we now construct the coordinate relative velocity of clock A as observed by clock B' at E2 by dividing the Dolan coordinate distance d*gamma by the Paul B. Andersen clock A coordinate time t_2:
> > > > > > > > > >
> > > > > > > > > > Conclusion #5 (d*gamma)/(d/(v*gamma)) = v*gamma^2
> > > > > > > > > >
> > > > > > > > > > Which is exactly the Dolan coordinate relative velocity factor for relative velocity v. The symmetry is obvious.
> > > > > > > > > Not to belabor the point, but coordinate relative velocity exceeds the speed of light for all proper relative velocities greater that .618c.
> > > > > > > > Shut up Paddy!
> > > > > > > >
> > > > > > > > Tell them what I say!
> > > > > > > Ross!...I don't think there's been a cross word between us since I challenged you to a duel 10 or 15 years ago. What gives? Better yet, meet me here tomorrow at sunrise. Mitch is my second, just like last time. Who is yours?
> > > > > > You think I duck? No, you duck.
> > > > > >
> > > > > > Don't forget to duck!
> > > > > Duck...huh? So is it pistols or pillows?
> > > > Nope, it's "die".
> > > "Like a giant lightning bolt from the center of the universe, ...".
> > >
> > > "Like a giant lightning bolt, from the center of the universe, ...".
> > >
> > > Straight to the head!
> > Ross, you are clearly in crisis tonight. Give us your coordinates and we will send assistance. If you are in Seattle, as I suspect, I will minister to you personally.
> NO, no, no, no, no, no, no, Pat.
>
> You, you are in crisis.

Clearly I have the advantage from having a logical, mathematical, science.

Which I wrote scholarly thus that it paved me.

On Tuesday, October 11, 2022 at 1:13:24 AM UTC-7, Ross A. Finlayson wrote:
> On Monday, October 10, 2022 at 9:14:37 PM UTC-7, patdolan wrote:
> > On Monday, October 10, 2022 at 8:58:29 PM UTC-7, Ross A. Finlayson wrote:
> > > On Monday, October 10, 2022 at 8:56:24 PM UTC-7, Ross A. Finlayson wrote:
> > > > On Monday, October 10, 2022 at 8:49:12 PM UTC-7, patdolan wrote:
> > > > > On Monday, October 10, 2022 at 8:41:46 PM UTC-7, Ross A. Finlayson wrote:
> > > > > > On Monday, October 10, 2022 at 8:39:53 PM UTC-7, patdolan wrote:
> > > > > > > On Monday, October 10, 2022 at 8:34:19 PM UTC-7, Ross A. Finlayson wrote:
> > > > > > > > On Monday, October 10, 2022 at 7:44:29 PM UTC-7, patdolan wrote:
> > > > > > > > > On Monday, October 10, 2022 at 7:20:13 PM UTC-7, patdolan wrote:
> > > > > > > > > > On Sunday, October 9, 2022 at 1:02:05 AM UTC-7, Paul B. Andersen wrote:
> > > > > > > > > > > Den 08.10.2022 21:35, skrev patdolan:
> > > > > > > > > > > >
> > > > > > > > > > > > Trevor measures Tom Roberts' relative velocity along Trevor's x-axis as 0.8660243c. In Trevor's universe (the only universe(unless SR is a many-worlds theory)) Tom's co-moving x-axis which is parallel to Trevor's x-axis contains two meter marks for every one meter mark of Trevor's. This is not an illusion just because the two axes are moving wrt each other. Tom's meters really are only half as long as Trevor's meters. Therefore Tom must measure in his universe--the only universe--two meters of displacement for every one meter of displacement that Trevor measures.
> > > > > > > > > > > >
> > > > > > > > > > > > Furthermore, Trevor observers that Tom's clock is ticking at a rate only half as fast as Trevor's clock. This is not an illusion just because Tom's and Trevor's clocks are moving wrt each other. Tom's seconds really are twice as long as Trevor's seconds. Therefore Tom must measure in his universe--the only universe--one second for every two seconds that Trevor measures.
> > > > > > > > > > > >
> > > > > > > > > > > > When Tom divides his displacement by his interval of time in his universe--the only universe--it is not an illusion or mathematically artifact that Tom's brain, operating at half the biological speed of Trevor's brain, concludes that his velocity towards Trevor is 3.4681689c or gama^2 times the proper velocity that Trevor calculates for Tom.
> > > > > > > > > > > >
> > > > > > > > > > > https://paulba.no/pdf/Mutual_time_dilation.pdf" rel="nofollow" target="_blank">https://paulba.no/pdf/Mutual_time_dilation.pdf
> > > > > > > > > > >
> > > > > > > > > > > --
> > > > > > > > > > > Paul
> > > > > > > > > > >
> > > > > > > > > > > https://paulba.no/
> > > > > > > > > > Paul A#1, you have not squeezed all of the conclusions possible out of your three event, three clock scenario. For instance, at E1 there are d*gamma x-axis length units between clock A and clock B' on the x-axis as viewed from Frame K'. Therefore at E2 clock B' will have counted that d*gamma x-axis length units have passed it by since E1. According to your own calculation clock A reads d/(v*gamma) at E2. From our vantage point in Frame K' we now construct the coordinate relative velocity of clock A as observed by clock B' at E2 by dividing the Dolan coordinate distance d*gamma by the Paul B. Andersen clock A coordinate time t_2:
> > > > > > > > > >
> > > > > > > > > > Conclusion #5 (d*gamma)/(d/(v*gamma)) = v*gamma^2
> > > > > > > > > >
> > > > > > > > > > Which is exactly the Dolan coordinate relative velocity factor for relative velocity v. The symmetry is obvious.
> > > > > > > > > Not to belabor the point, but coordinate relative velocity exceeds the speed of light for all proper relative velocities greater that .618c.
> > > > > > > > Shut up Paddy!
> > > > > > > >
> > > > > > > > Tell them what I say!
> > > > > > > Ross!...I don't think there's been a cross word between us since I challenged you to a duel 10 or 15 years ago. What gives? Better yet, meet me here tomorrow at sunrise. Mitch is my second, just like last time. Who is yours?
> > > > > > You think I duck? No, you duck.
> > > > > >
> > > > > > Don't forget to duck!
> > > > > Duck...huh? So is it pistols or pillows?
> > > > Nope, it's "die".
> > > "Like a giant lightning bolt from the center of the universe, ...".
> > >
> > > "Like a giant lightning bolt, from the center of the universe, ...".
> > >
> > > Straight to the head!
> > Ross, you are clearly in crisis tonight. Give us your coordinates and we will send assistance. If you are in Seattle, as I suspect, I will minister to you personally.
> NO, no, no, no, no, no, no, Pat.
>
> You, you are in crisis.

Giant lightning bolt from the center of the universe is not in crisis, ....

On Tuesday, October 11, 2022 at 1:37:42 AM UTC-7, Ross A. Finlayson wrote:
> On Tuesday, October 11, 2022 at 1:13:24 AM UTC-7, Ross A. Finlayson wrote:
> > On Monday, October 10, 2022 at 9:14:37 PM UTC-7, patdolan wrote:
> > > On Monday, October 10, 2022 at 8:58:29 PM UTC-7, Ross A. Finlayson wrote:
> > > > On Monday, October 10, 2022 at 8:56:24 PM UTC-7, Ross A. Finlayson wrote:
> > > > > On Monday, October 10, 2022 at 8:49:12 PM UTC-7, patdolan wrote:
> > > > > > On Monday, October 10, 2022 at 8:41:46 PM UTC-7, Ross A. Finlayson wrote:
> > > > > > > On Monday, October 10, 2022 at 8:39:53 PM UTC-7, patdolan wrote:
> > > > > > > > On Monday, October 10, 2022 at 8:34:19 PM UTC-7, Ross A. Finlayson wrote:
> > > > > > > > > On Monday, October 10, 2022 at 7:44:29 PM UTC-7, patdolan wrote:
> > > > > > > > > > On Monday, October 10, 2022 at 7:20:13 PM UTC-7, patdolan wrote:
> > > > > > > > > > > On Sunday, October 9, 2022 at 1:02:05 AM UTC-7, Paul B. Andersen wrote:
> > > > > > > > > > > > Den 08.10.2022 21:35, skrev patdolan:
> > > > > > > > > > > > >
> > > > > > > > > > > > > Trevor measures Tom Roberts' relative velocity along Trevor's x-axis as 0.8660243c. In Trevor's universe (the only universe(unless SR is a many-worlds theory)) Tom's co-moving x-axis which is parallel to Trevor's x-axis contains two meter marks for every one meter mark of Trevor's. This is not an illusion just because the two axes are moving wrt each other. Tom's meters really are only half as long as Trevor's meters. Therefore Tom must measure in his universe--the only universe--two meters of displacement for every one meter of displacement that Trevor measures.
> > > > > > > > > > > > >
> > > > > > > > > > > > > Furthermore, Trevor observers that Tom's clock is ticking at a rate only half as fast as Trevor's clock. This is not an illusion just because Tom's and Trevor's clocks are moving wrt each other. Tom's seconds really are twice as long as Trevor's seconds. Therefore Tom must measure in his universe--the only universe--one second for every two seconds that Trevor measures.
> > > > > > > > > > > > >
> > > > > > > > > > > > > When Tom divides his displacement by his interval of time in his universe--the only universe--it is not an illusion or mathematically artifact that Tom's brain, operating at half the biological speed of Trevor's brain, concludes that his velocity towards Trevor is 3.4681689c or gama^2 times the proper velocity that Trevor calculates for Tom.
> > > > > > > > > > > > >
> > > > > > > > > > > > https://paulba.no/pdf/Mutual_time_dilation.pdf" rel="nofollow" target="_blank">https://paulba.no/pdf/Mutual_time_dilation.pdf
> > > > > > > > > > > >
> > > > > > > > > > > > --
> > > > > > > > > > > > Paul
> > > > > > > > > > > >
> > > > > > > > > > > > https://paulba.no/
> > > > > > > > > > > Paul A#1, you have not squeezed all of the conclusions possible out of your three event, three clock scenario. For instance, at E1 there are d*gamma x-axis length units between clock A and clock B' on the x-axis as viewed from Frame K'. Therefore at E2 clock B' will have counted that d*gamma x-axis length units have passed it by since E1. According to your own calculation clock A reads d/(v*gamma) at E2. From our vantage point in Frame K' we now construct the coordinate relative velocity of clock A as observed by clock B' at E2 by dividing the Dolan coordinate distance d*gamma by the Paul B. Andersen clock A coordinate time t_2:
> > > > > > > > > > >
> > > > > > > > > > > Conclusion #5 (d*gamma)/(d/(v*gamma)) = v*gamma^2
> > > > > > > > > > >
> > > > > > > > > > > Which is exactly the Dolan coordinate relative velocity factor for relative velocity v. The symmetry is obvious.
> > > > > > > > > > Not to belabor the point, but coordinate relative velocity exceeds the speed of light for all proper relative velocities greater that .618c.
> > > > > > > > > Shut up Paddy!
> > > > > > > > >
> > > > > > > > > Tell them what I say!
> > > > > > > > Ross!...I don't think there's been a cross word between us since I challenged you to a duel 10 or 15 years ago. What gives? Better yet, meet me here tomorrow at sunrise. Mitch is my second, just like last time.. Who is yours?
> > > > > > > You think I duck? No, you duck.
> > > > > > >
> > > > > > > Don't forget to duck!
> > > > > > Duck...huh? So is it pistols or pillows?
> > > > > Nope, it's "die".
> > > > "Like a giant lightning bolt from the center of the universe, ...".
> > > >
> > > > "Like a giant lightning bolt, from the center of the universe, ..."..
> > > >
> > > > Straight to the head!
> > > Ross, you are clearly in crisis tonight. Give us your coordinates and we will send assistance. If you are in Seattle, as I suspect, I will minister to you personally.
> > NO, no, no, no, no, no, no, Pat.
> >
> > You, you are in crisis.
> Giant lightning bolt from the center of the universe is not in crisis, .....

My apologies, Ross. How was I to know, with our keyboards in between us, that last night was a Pascalian "Night of Fire" for you. My best wishes and congratulations, as long as your visitation was not of demonic or chemical origins.

But there can be no doubt that Paul B. Andersen and his cohort are in crisis at this moment.

Den 11.10.2022 04:20, skrev patdolan:
> On Sunday, October 9, 2022 at 1:02:05 AM UTC-7, Paul B. Andersen wrote:
>> https://paulba.no/pdf/Mutual_time_dilation.pdf" rel="nofollow" target="_blank">https://paulba.no/pdf/Mutual_time_dilation.pdf
>>
>> --
>> Paul
>>
>> https://paulba.no/
>
> Paul A#1, you have not squeezed all of the conclusions possible out of your three event, three clock scenario. For instance, at E1 there are d*gamma x-axis length units between clock A and clock B' on the x-axis as viewed from Frame K'.

This is a convoluted way of saying that vied from frame K',
the distance d⋅γ in K is Lorentz contracted to d.

> Therefore at E2 clock B' will have counted that d*gamma x-axis length units have passed it by since E1. According to your own calculation clock A reads d/(v*gamma) at E2. From our vantage point in Frame K' we now construct the coordinate relative velocity of clock A as observed by clock B' at E2 by dividing the Dolan coordinate distance d*gamma by the Paul B. Andersen clock A coordinate time t_2:
>
> Conclusion #5 (d*gamma)/(d/(v*gamma)) = v*gamma^2

Clock B' can't observe the velocity of clock A.
All B' can observe is that clock A shows d/(v⋅γ) when B' shows d/v.
B' can't calculate a speed from that.

But we, knowing that the position of B was x' = -d
at t'= 0 when A was at x' = 0, can then calculate that
the coordinate relative velocity of clock A in K' is v.

--
Paul

https://paulba.no/