On Tuesday, June 20, 2023 at 6:52:13 AM UTC-7, Trevor Lange wrote:
> On Tuesday, June 20, 2023 at 3:30:08 AM UTC-7, patdolan wrote:
> > When...
>
> That's your crucial mistake. Remember, in terms of S, the word "when" refers to a particular value of the time coordinate t, whereas in terms of S' the word "when" refers to a particular value of the time coordinate t'. Events that are simultaneous (A occurs "when" B occurs) in terms of S are not simultaneous (A does not occur "when" B occurs) in terms of S', and vice versa. This is crucial for understanding what relativistic time dilation even means, which is why I took the troubler to explain it using the two rows of clocks... which you ran away from. Remember?
> > the following equations ALWAYS hold true:
> > ∆E = the change in the earth's orbital position in radians
> > ∆B = the change in position of Big Ben's little hand in radians
> > ∆w = the change in position of the little hand on a distant observer's wristwatch in radians
> Again, you failed to specify what time interval you are referring to (and you continue to propagate the idiocy of carrying along both the earth's position and the hands of the earth clock, like a small child who imagines that maybe those two things do not advance proportionally in the magical wonderland of grown-up relativity. Also, you continue to ignore the fact that the wristwatch is running slow in terms of S, just as the earth clock is running slow in terms of S'.
>
> Look, to make any kind of rationally coherent statement, you need to refer to the *rates* of the clocks, which are *ratios* of changes in angular positions to changes in time, and the relavant relations are
>
> ∆B/∆t' < ∆w/∆t'
> ∆B/∆t > ∆w/∆t
>
> Remember the two rows of clocks that you ran away from? Now do you understand?

This should fix your problem with the BBP eqns:

A distant observer possesses a constant velocity relative to the solar system which is also normal to the solar system's plane of rotation, along line that is collinear with the sun's axis of rotation the following equations ALWAYS hold true:

∆E = the change in the earth's orbital position in radians
∆B = the change in position of Big Ben's little hand in radians
∆w = the change in position of the little hand on a distant observer's wristwatch in radians

∆E = ∆B/730.5 [ coupling equation ]
∆w = 𝛾∆B = 𝛾( ∆E x 730.5 ) [ orbital dilation equation ]

From these a priori true equations the Big Ben Paradox is easily derived.

Also note that the need for a "rate" and/or time intervals, is abolished in this BBP because we are examining pure angular displacement at ever instance. Angular displacement of watch hands. Angular displacement of planets in orbit. The only intervals we need consider are angular intervals. Do you understand why rates and time intervals no longer apply? This is your and Einstein's biggest weakness--the need to work with rates of time which is a compound fallacy. I have transcended that fallacy with the BBP. This is a brand new conceptualization which your relativity-besotted mind will reject for awhile.

Where is your re-write, Legion? What's keep back relativity's last stand?

On Tuesday, June 20, 2023 at 8:02:16 AM UTC-7, patdolan wrote:
> On Tuesday, June 20, 2023 at 6:52:13 AM UTC-7, Trevor Lange wrote:
> > On Tuesday, June 20, 2023 at 3:30:08 AM UTC-7, patdolan wrote:
> > > When...
> >
> > That's your crucial mistake. Remember, in terms of S, the word "when" refers to a particular value of the time coordinate t, whereas in terms of S' the word "when" refers to a particular value of the time coordinate t'. Events that are simultaneous (A occurs "when" B occurs) in terms of S are not simultaneous (A does not occur "when" B occurs) in terms of S', and vice versa. This is crucial for understanding what relativistic time dilation even means, which is why I took the troubler to explain it using the two rows of clocks... which you ran away from. Remember?
> > > the following equations ALWAYS hold true:
> > > ∆E = the change in the earth's orbital position in radians
> > > ∆B = the change in position of Big Ben's little hand in radians
> > > ∆w = the change in position of the little hand on a distant observer's wristwatch in radians
> > Again, you failed to specify what time interval you are referring to (and you continue to propagate the idiocy of carrying along both the earth's position and the hands of the earth clock, like a small child who imagines that maybe those two things do not advance proportionally in the magical wonderland of grown-up relativity. Also, you continue to ignore the fact that the wristwatch is running slow in terms of S, just as the earth clock is running slow in terms of S'.
> >
> > Look, to make any kind of rationally coherent statement, you need to refer to the *rates* of the clocks, which are *ratios* of changes in angular positions to changes in time, and the relavant relations are
> >
> > ∆B/∆t' < ∆w/∆t'
> > ∆B/∆t > ∆w/∆t
> >
> > Remember the two rows of clocks that you ran away from? Now do you understand?
> This should fix your problem with the BBP eqns:
>
> A distant observer possesses a constant velocity relative to the solar system which is also normal to the solar system's plane of rotation, along line that is collinear with the sun's axis of rotation the following equations ALWAYS hold true:
> ∆E = the change in the earth's orbital position in radians
> ∆B = the change in position of Big Ben's little hand in radians
> ∆w = the change in position of the little hand on a distant observer's wristwatch in radians
> ∆E = ∆B/730.5 [ coupling equation ]
> ∆w = 𝛾∆B = 𝛾( ∆E x 730.5 ) [ orbital dilation equation ]
>
> From these a priori true equations the Big Ben Paradox is easily derived.
> Also note that the need for a "rate" and/or time intervals, is abolished in this BBP because we are examining pure angular displacement at ever instance. Angular displacement of watch hands. Angular displacement of planets in orbit. The only intervals we need consider are angular intervals. Do you understand why rates and time intervals no longer apply? This is your and Einstein's biggest weakness--the need to work with rates of time which is a compound fallacy. I have transcended that fallacy with the BBP. This is a brand new conceptualization which your relativity-besotted mind will reject for awhile.
>
> Where is your re-write, Legion? What's keep back relativity's last stand?

We are tired of waiting, Legion. Close your eyes and imagine you and I are in our own lovely Paramount Theater (free tours every 1st Saturday) speaking to a packed house of 3,000. These three thousand Seattleites are of more or less average intelligence. They have come downtown, braving the sidewalk tents, dung, urine, needles, drug-addicted panhandling crazies, to hear about the newest scientific sensation, the Big Ben Paradox. I have just wrapped up my presentation, including CGI demonstrations and a thorough explanation of the BBP equation set. Now it is your turn to tell them why and where the BBP is fallacious. Go!

On 2023-06-20 17:29:17 +0000, patdolan said:

> On Tuesday, June 20, 2023 at 8:02:16 AM UTC-7, patdolan wrote:
>> On Tuesday, June 20, 2023 at 6:52:13 AM UTC-7, Trevor Lange wrote:> >
>> On Tuesday, June 20, 2023 at 3:30:08 AM UTC-7, patdolan wrote:> > >
>> When...> >> > That's your crucial mistake. Remember, in terms of S, the
>> word "when" refers to a particular value of the time coordinate t,
>> whereas in terms of S' the word "when" refers to a particular value of
>> the time coordinate t'. Events that are simultaneous (A occurs "when" B
>> occurs) in terms of S are not simultaneous (A does not occur "when" B
>> occurs) in terms of S', and vice versa. This is crucial for
>> understanding what relativistic time dilation even means, which is why
>> I took the troubler to explain it using the two rows of clocks... which
>> you ran away from. Remember?> > > the following equations ALWAYS hold
>> true:> > > ∆E = the change in the earth's orbital position in radians>
>> > > ∆B = the change in position of Big Ben's little hand in radians> >
>> > ∆w = the change in position of the little hand on a distant
>> observer's wristwatch in radians> > Again, you failed to specify what
>> time interval you are referring to (and you continue to propagate the
>> idiocy of carrying along both the earth's position and the hands of the
>> earth clock, like a small child who imagines that maybe those two
>> things do not advance proportionally in the magical wonderland of
>> grown-up relativity. Also, you continue to ignore the fact that the
>> wristwatch is running slow in terms of S, just as the earth clock is
>> running slow in terms of S'.> >> > Look, to make any kind of rationally
>> coherent statement, you need to refer to the *rates* of the clocks,
>> which are *ratios* of changes in angular positions to changes in time,
>> and the relavant relations are> >> > ∆B/∆t' < ∆w/∆t'> > ∆B/∆t > ∆w/∆t>
>> >> > Remember the two rows of clocks that you ran away from? Now do you
>> understand?
>> This should fix your problem with the BBP eqns:>> A distant observer
>> possesses a constant velocity relative to the solar system which is
>> also normal to the solar system's plane of rotation, along line that is
>> collinear with the sun's axis of rotation the following equations
>> ALWAYS hold true:
>> ∆E = the change in the earth's orbital position in radians> ∆B = the
>> change in position of Big Ben's little hand in radians> ∆w = the change
>> in position of the little hand on a distant observer's wristwatch in
>> radians
>> ∆E = ∆B/730.5 [ coupling equation ]> ∆w = 𝛾∆B = 𝛾( ∆E x 730.5 ) [
>> orbital dilation equation ]>> From these a priori true equations the
>> Big Ben Paradox is easily derived.
>> Also note that the need for a "rate" and/or time intervals, is
>> abolished in this BBP because we are examining pure angular
>> displacement at ever instance. Angular displacement of watch hands.
>> Angular displacement of planets in orbit. The only intervals we need
>> consider are angular intervals. Do you understand why rates and time
>> intervals no longer apply? This is your and Einstein's biggest
>> weakness--the need to work with rates of time which is a compound
>> fallacy. I have transcended that fallacy with the BBP. This is a brand
>> new conceptualization which your relativity-besotted mind will reject
>> for awhile.>> Where is your re-write, Legion? What's keep back
>> relativity's last stand?
>
> We are tired

"We" implies more than one person. Who is the other one?

> of waiting, Legion. Close your eyes and imagine you and I are in our
> own lovely Paramount Theater (free tours every 1st Saturday) speaking
> to a packed house of 3,000. These three thousand Seattleites are of
> more or less average intelligence. They have come downtown, braving
> the sidewalk tents, dung, urine, needles, drug-addicted panhandling
> crazies, to hear about the newest scientific sensation, the Big Ben
> Paradox. I have just wrapped up my presentation, including CGI
> demonstrations and a thorough explanation of the BBP equation set. Now
> it is your turn to tell them why and where the BBP is fallacious. Go!

--
Athel -- French and British, living in Marseilles for 36 years; mainly
in England until 1987.

On Tuesday, June 20, 2023 at 8:02:16 AM UTC-7, patdolan wrote:
> The following equations ALWAYS hold true:

Nope, they are trivially underspecified, as explained to you before. Remember?

> ∆E = ∆B/730.5 [ coupling equation ]

That is underspecified, because (again) you have not stated the time intervals over which ∆E and ∆B occur. For example, if ∆E is the angular change over 45 minutes of t, and ∆B is the angular change over 72 minutes of t, that relation is false. Likewise if ∆E occurs over 45 minutes of t, and ∆B occurs over 45 minutes of t', that relation is false. And so on.

> ∆w = 𝛾∆B [ orbital dilation equation ]

Again, that relation is underspecified, because you have not stated the time intervals over which ∆w and ∆B occur. For example, if ∆w occurs over 45 minutes of t, and ∆B occurs over 72 minutes of t, that relation is false. Likewise if ∆w occurs over 45 minutes of t, and ∆B occurs over 45 minutes of t', that relation is false. Of course, if ∆w occurs over 45 minutes of t', and ∆B occurs over 45 minutes of t', that relation is true. On the other hand (so to speak), if ∆w occurs over 45 minutes of t, and ∆B occurs over 45 minutes of t, the correct relation is 𝛾∆w = ∆B.

Now do you understand?

On Tuesday, June 20, 2023 at 11:48:37 AM UTC-7, Trevor Lange wrote:
> On Tuesday, June 20, 2023 at 8:02:16 AM UTC-7, patdolan wrote:
> > The following equations ALWAYS hold true:
>
> Nope, they are trivially underspecified, as explained to you before. Remember?
> > ∆E = ∆B/730.5 [ coupling equation ]
> That is underspecified, because (again) you have not stated the time intervals over which ∆E and ∆B occur. For example, if ∆E is the angular change over 45 minutes of t, and ∆B is the angular change over 72 minutes of t, that relation is false. Likewise if ∆E occurs over 45 minutes of t, and ∆B occurs over 45 minutes of t', that relation is false. And so on.

Let's take this one first, Legion. The coupling equation is a definition, a premise. Just like any of the four Maxwell Equations are definitions/premises.

Demonstrate to this forum that the BBP coupling equation ∆E = ∆B/730.5 isn't a priori true beyond any reasonable doubt. And furthermore it is true in all inertial frames of reference. Otherwise, if Big Ben could decouple from the the earth's orbital period, then minutes, hours, days, seasons, years, and centuries could have different durations from what Big Ben indicates.

>
> > ∆w = 𝛾∆B [ orbital dilation equation ]
>
> Again, that relation is underspecified, because you have not stated the time intervals over which ∆w and ∆B occur. For example, if ∆w occurs over 45 minutes of t, and ∆B occurs over 72 minutes of t, that relation is false. Likewise if ∆w occurs over 45 minutes of t, and ∆B occurs over 45 minutes of t', that relation is false. Of course, if ∆w occurs over 45 minutes of t', and ∆B occurs over 45 minutes of t', that relation is true. On the other hand (so to speak), if ∆w occurs over 45 minutes of t, and ∆B occurs over 45 minutes of t, the correct relation is 𝛾∆w = ∆B.
>
> Now do you understand?

On Tuesday, June 20, 2023 at 12:09:56 PM UTC-7, patdolan wrote:
> [Sorry for being so dense, but I still don't understand. Please tell me, even more
> s.l.o.w.l.y why] equation ∆E = ∆B/730.5 isn't a priori true beyond any reasonable
> doubt.

Again, the "equation" you've typed has no definite meaning (let alone truth) because you have not defined what the symbols represent. For example: If ∆E is defined as the change in E over 45 minutes of t, and ∆B is defined as the change in B over 72 minutes of t, then the "equation" you typed is false.

> [Again, I apologize for being so dense, but could you also explain why the following string of symbols is also meaningless because I have not defined the symbols?]: ∆w = 𝛾∆B

Sure, that too is meaningless, because you have not defined the symbols. For example, if ∆w is the change in w over 45 minutes of t, and ∆B i the change in B over 72 minutes of t, that relation is false. Likewise if ∆w is the change in w over 45 minutes of t, and ∆B is the change in B over 45 minutes of t', that relation is false. Of course, if ∆w is the change in w over 45 minutes of t', and ∆B is the change in B over 45 minutes of t', that relation is true. On the other hand, if ∆w is the change in w over 45 minutes of t, and ∆B is the change in B over 45 minutes of t, the correct relation is 𝛾∆w = ∆B.

On Tuesday, June 20, 2023 at 6:04:14 PM UTC-7, Trevor Lange wrote:
> On Tuesday, June 20, 2023 at 12:09:56 PM UTC-7, patdolan wrote:
> > [Sorry for being so dense, but I still don't understand. Please tell me, even more
> > s.l.o.w.l.y why] equation ∆E = ∆B/730.5 isn't a priori true beyond any reasonable
> > doubt.
>
> Again, the "equation" you've typed has no definite meaning (let alone truth) because you have not defined what the symbols represent. For example: If ∆E is defined as the change in E over 45 minutes of t, and ∆B is defined as the change in B over 72 minutes of t, then the "equation" you typed is false.
>
> > [Again, I apologize for being so dense, but could you also explain why the following string of symbols is also meaningless because I have not defined the symbols?]: ∆w = 𝛾∆B
>
> Sure, that too is meaningless, because you have not defined the symbols. For example, if ∆w is the change in w over 45 minutes of t, and ∆B i the change in B over 72 minutes of t, that relation is false. Likewise if ∆w is the change in w over 45 minutes of t, and ∆B is the change in B over 45 minutes of t', that relation is false. Of course, if ∆w is the change in w over 45 minutes of t', and ∆B is the change in B over 45 minutes of t', that relation is true. On the other hand, if ∆w is the change in w over 45 minutes of t, and ∆B is the change in B over 45 minutes of t, the correct relation is 𝛾∆w = ∆B.

Nobody knows what you are typing about, Legion. Some sort of tortured logic to serve as your extinction burst before you and relativity sustain total and complete defeat. You might as well make the same tortured argument agains E = mc^2 or F = ma. I knew in the end you would break.

But I am not quite done with you yet. I prefer to toy with my prey a bit before dispatching them. So let's review were we are at:

So far I have established the a prior & tautologous coupling equation as being at the heart of the Big Ben Paradox. Now I will apply the principle of relativity to the coupling equation to arrive at the orbital time dilation equation, which is the conclusion of the argument and the end of either the earth or special relativity. Here we go.

∆E = the change in the earth's orbital position in radians
∆B = the change in position of Big Ben's little hand in radians
∆w = the change in position of the little hand on a distant observer's wristwatch in radians

∆E = ∆B/730.5 [ coupling equation ] to which we apply the principle of relativity

∆w = 𝛾∆B, to arrive at

∆w = 𝛾∆B = 𝛾( ∆E x 730.5 ) [ orbital dilation equation ]

which dooms the earth to fiery disaster as it orbits through the ever unchanging and invariant spacetime curvature in the vicinity of the sun.

Now Legion, there is one faint glimmer of hope for relativity. And that lies in the possibly that the dance of the magic tensors and Christoffels causes the invariant spacetime curvature in the vicinity of the sun to decrease as 1/𝛾. With such a decrease the earth would continue to orbit the sun in all inertial frames of reference, no matter how dilated the orbital velocity. But as I indicated, that hope is a false hope. Because with such a decrease in spacetime curvature, at the lim of the sun the curvature would be zero for a beam of starlight by definition. So the Chritoffels and the tensors in that case would predict zero curvature. But they don't, do they. The Christensors in fact predict 1.75 arc secs. This leaves us with the antinomous conclusion that if GR is true, then GR is false.

So the BBP really does take away all hope for the two relativities. Surely some illustrious scientist must have come up with this argument long before little Pat Dolan. Someone should have a look.

On Tuesday, June 20, 2023 at 7:35:26 PM UTC-7, patdolan wrote:
> > > [Again, I apologize for being so dense, but could you also explain why the following string of symbols is also meaningless because I have not defined the symbols?]: ∆w = 𝛾∆B
> >
> > Sure, that too is meaningless, because you have not defined the symbols.. For example, if ∆w is the change in w over 45 minutes of t, and ∆B i the change in B over 72 minutes of t, that relation is false. Likewise if ∆w is the change in w over 45 minutes of t, and ∆B is the change in B over 45 minutes of t', that relation is false. Of course, if ∆w is the change in w over 45 minutes of t', and ∆B is the change in B over 45 minutes of t', that relation is true. On the other hand, if ∆w is the change in w over 45 minutes of t, and ∆B is the change in B over 45 minutes of t, the correct relation is 𝛾∆w = ∆B.
>
> [Once again, I will totally disregard what you just explained to me, and simply re-iterate my infantile gibberish.]

> I have established the a prior & tautologous coupling equation

Nope, we've explained why the string of characters you typed are meaningless, because you refuse to define the symboIs ∆w and ∆B, and hence there is no particular relation between them. For example, if you define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we define them as the changes during a given interval of time ∆t, then we have the relation 𝛾∆w = ∆B.

> [Relativity would be valid if] tensors and Christoffel [symbols] cause the
> invariant spacetime curvature in the vicinity of the sun to decrease as 1/𝛾.

As explained to you numerous times, the components of the Riemann curvature tensor are obviously coordinate-dependent, and of course the Christoffel symbols (not tensors) are also highly coordinate dependent, and the field equations of general relativity are generally covariant, meaning that the components of all the tensors vary in precisely the way necessary to compensate for whatever coordinate system we choose, and preserve the same invariant intervals along every path, and hence preserve all geodesics, and so on. This is trivial and self-evident.

> With such [covariance], at the lim of the sun the curvature would be
> zero for a beam of starlight by definition.

No, as stated above, geodesics are preserved under any diffeomorphic transformation of the coordinate system. Needless to say, a pulse of light follows a geodesic, just as does a material body.

Now, clueless newbies are sometimes puzzled momentarily about the difference in the extrinsic curvature of various paths in the same gravitational field. For example, they see the parabolic trajectory of a baseball thrown between two people, and then they see the nearly straight trajectory of a bullet fired between those same two people. Of course, they are just thinking of the spatial paths, and then they are told (homework exercise) to compute the extrinsic curvature of those two paths in space and TIME. They discover that the extrinsic curvatures of those two paths are actually the same. (Of course, this is completely different from the intrinsic curvature that actually determines the trajectories.)

> Surely someone must have come up with this argument [before]...

LOL. The fallacy you are expressing occurs to many of the more dim-witted beginning students. It's an old chestnut, a cliche.

How about a little ben clock?

if you
put on
a watch
on the wrist
of a light
particle
traveling
at the
speed of light
what time would it be?

--
The Starmaker -- To question the unquestionable, ask the unaskable,
to think the unthinkable, mention the unmentionable, say the unsayable,
and challenge
the unchallengeable.

On Tuesday, June 20, 2023 at 8:41:43 PM UTC-7, Trevor Lange wrote:
> On Tuesday, June 20, 2023 at 7:35:26 PM UTC-7, patdolan wrote:
> > > > [Again, I apologize for being so dense, but could you also explain why the following string of symbols is also meaningless because I have not defined the symbols?]: ∆w = 𝛾∆B
> > >
> > > Sure, that too is meaningless, because you have not defined the symbols. For example, if ∆w is the change in w over 45 minutes of t, and ∆B i the change in B over 72 minutes of t, that relation is false. Likewise if ∆w is the change in w over 45 minutes of t, and ∆B is the change in B over 45 minutes of t', that relation is false. Of course, if ∆w is the change in w over 45 minutes of t', and ∆B is the change in B over 45 minutes of t', that relation is true. On the other hand, if ∆w is the change in w over 45 minutes of t, and ∆B is the change in B over 45 minutes of t, the correct relation is 𝛾∆w = ∆B.
> >
> > [Once again, I will totally disregard what you just explained to me, and simply re-iterate my infantile gibberish.]
> > I have established the a prior & tautologous coupling equation
> Nope, we've explained why the string of characters you typed are meaningless, because you refuse to define the symboIs ∆w and ∆B, and hence there is no particular relation between them. For example, if you define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we define them as the changes during a given interval of time ∆t, then we have the relation 𝛾∆w = ∆B.
>
> > [Relativity would be valid if] tensors and Christoffel [symbols] cause the
> > invariant spacetime curvature in the vicinity of the sun to decrease as 1/𝛾.
> As explained to you numerous times, the components of the Riemann curvature tensor are obviously coordinate-dependent, and of course the Christoffel symbols (not tensors) are also highly coordinate dependent, and the field equations of general relativity are generally covariant, meaning that the components of all the tensors vary in precisely the way necessary to compensate for whatever coordinate system we choose, and preserve the same invariant intervals along every path, and hence preserve all geodesics, and so on. This is trivial and self-evident.
>
> > With such [covariance], at the lim of the sun the curvature would be
> > zero for a beam of starlight by definition.
> No, as stated above, geodesics are preserved under any diffeomorphic transformation of the coordinate system. Needless to say, a pulse of light follows a geodesic, just as does a material body.
>
> Now, clueless newbies are sometimes puzzled momentarily about the difference in the extrinsic curvature of various paths in the same gravitational field. For example, they see the parabolic trajectory of a baseball thrown between two people, and then they see the nearly straight trajectory of a bullet fired between those same two people. Of course, they are just thinking of the spatial paths, and then they are told (homework exercise) to compute the extrinsic curvature of those two paths in space and TIME. They discover that the extrinsic curvatures of those two paths are actually the same. (Of course, this is completely different from the intrinsic curvature that actually determines the trajectories.)
>
> > Surely someone must have come up with this argument [before]...
>
> LOL. The fallacy you are expressing occurs to many of the more dim-witted beginning students. It's an old chestnut, a cliche.

Prove it. Cite a link or a book or an article or a paper or a video. I say you are lying again Legion.

On Wednesday, June 21, 2023 at 9:41:16 AM UTC-7, patdolan wrote:
> > > > > [Again, I apologize for being so dense, but could you also explain why the following string of symbols is also meaningless because I have not defined the symbols?]: ∆w = 𝛾∆B
> > > >
> > > > Sure, that too is meaningless, because you have not defined the symbols. For example, if ∆w is the change in w over 45 minutes of t, and ∆B i the change in B over 72 minutes of t, that relation is false. Likewise if ∆w is the change in w over 45 minutes of t, and ∆B is the change in B over 45 minutes of t', that relation is false. Of course, if ∆w is the change in w over 45 minutes of t', and ∆B is the change in B over 45 minutes of t', that relation is true. On the other hand, if ∆w is the change in w over 45 minutes of t, and ∆B is the change in B over 45 minutes of t, the correct relation is 𝛾∆w = ∆B.
> > >
> > > [Once again, I will totally disregard what you just explained to me, and simply re-iterate my infantile gibberish.]
> > > I have established the a prior & tautologous coupling equation
> > Nope, we've explained why the string of characters you typed are meaningless, because you refuse to define the symboIs ∆w and ∆B, and hence there is no particular relation between them. For example, if you define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we define them as the changes during a given interval of time ∆t, then we have the relation 𝛾∆w = ∆B.
> >
> > > [Relativity would be valid if] tensors and Christoffel [symbols] cause the
> > > invariant spacetime curvature in the vicinity of the sun to decrease as 1/𝛾.
> > As explained to you numerous times, the components of the Riemann curvature tensor are obviously coordinate-dependent, and of course the Christoffel symbols (not tensors) are also highly coordinate dependent, and the field equations of general relativity are generally covariant, meaning that the components of all the tensors vary in precisely the way necessary to compensate for whatever coordinate system we choose, and preserve the same invariant intervals along every path, and hence preserve all geodesics, and so on. This is trivial and self-evident.
> >
> > > With such [covariance], at the lim of the sun the curvature would be
> > > zero for a beam of starlight by definition.
> > No, as stated above, geodesics are preserved under any diffeomorphic transformation of the coordinate system. Needless to say, a pulse of light follows a geodesic, just as does a material body.
> >
> > Now, clueless newbies are sometimes puzzled momentarily about the difference in the extrinsic curvature of various paths in the same gravitational field. For example, they see the parabolic trajectory of a baseball thrown between two people, and then they see the nearly straight trajectory of a bullet fired between those same two people. Of course, they are just thinking of the spatial paths, and then they are told (homework exercise) to compute the extrinsic curvature of those two paths in space and TIME. They discover that the extrinsic curvatures of those two paths are actually the same.. (Of course, this is completely different from the intrinsic curvature that actually determines the trajectories.)
> >
> > > Surely someone must have come up with this argument [before]...
> >
> > LOL. The fallacy you are expressing occurs to many of the more dim-witted beginning students. It's an old chestnut, a cliche.
>
> Prove it. Cite a link or a book or an article or a paper or a video.

Prove what? That if you define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we define them as the changes during a given interval of time ∆t, then we have the relation 𝛾∆w = ∆B ?

Or that the components of the Riemann curvature tensor are coordinate-dependent, or that the Christoffel symbols (not tensors) are also highly coordinate dependent?

Or that the field equations of general relativity are generally covariant, meaning that the components of all the tensors vary in precisely the way necessary to compensate for whatever coordinate system we choose? Or that they yield the same invariant intervals along every path, and hence preserve all geodesics.

Or that pulses of light follow geodesics just as do material particles?

Or that the extrinsic curvatures of the trajectories of a baseball and a bullet in space-TIME are the same?

Or that the relation (-1)^2 = (1)^2 does not imply -1 = 1?

Or that the hackneyed fallacies and misunderstandings you recite here are very familiar to any knowledgeable person because they commonly occur to dim-witted beginners, to the point of being cliches ?

On Wednesday, June 21, 2023 at 6:46:07 PM UTC-7, Trevor Lange wrote:
> On Wednesday, June 21, 2023 at 9:41:16 AM UTC-7, patdolan wrote:
> > > > > > [Again, I apologize for being so dense, but could you also explain why the following string of symbols is also meaningless because I have not defined the symbols?]: ∆w = 𝛾∆B
> > > > >
> > > > > Sure, that too is meaningless, because you have not defined the symbols. For example, if ∆w is the change in w over 45 minutes of t, and ∆B i the change in B over 72 minutes of t, that relation is false. Likewise if ∆w is the change in w over 45 minutes of t, and ∆B is the change in B over 45 minutes of t', that relation is false.. Of course, if ∆w is the change in w over 45 minutes of t', and ∆B is the change in B over 45 minutes of t', that relation is true. On the other hand, if ∆w is the change in w over 45 minutes of t, and ∆B is the change in B over 45 minutes of t, the correct relation is 𝛾∆w = ∆B.
> > > >
> > > > [Once again, I will totally disregard what you just explained to me, and simply re-iterate my infantile gibberish.]
> > > > I have established the a prior & tautologous coupling equation
> > > Nope, we've explained why the string of characters you typed are meaningless, because you refuse to define the symboIs ∆w and ∆B, and hence there is no particular relation between them. For example, if you define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we define them as the changes during a given interval of time ∆t, then we have the relation 𝛾∆w = ∆B.
> > >
> > > > [Relativity would be valid if] tensors and Christoffel [symbols] cause the
> > > > invariant spacetime curvature in the vicinity of the sun to decrease as 1/𝛾.
> > > As explained to you numerous times, the components of the Riemann curvature tensor are obviously coordinate-dependent, and of course the Christoffel symbols (not tensors) are also highly coordinate dependent, and the field equations of general relativity are generally covariant, meaning that the components of all the tensors vary in precisely the way necessary to compensate for whatever coordinate system we choose, and preserve the same invariant intervals along every path, and hence preserve all geodesics, and so on. This is trivial and self-evident.
> > >
> > > > With such [covariance], at the lim of the sun the curvature would be
> > > > zero for a beam of starlight by definition.
> > > No, as stated above, geodesics are preserved under any diffeomorphic transformation of the coordinate system. Needless to say, a pulse of light follows a geodesic, just as does a material body.
> > >
> > > Now, clueless newbies are sometimes puzzled momentarily about the difference in the extrinsic curvature of various paths in the same gravitational field. For example, they see the parabolic trajectory of a baseball thrown between two people, and then they see the nearly straight trajectory of a bullet fired between those same two people. Of course, they are just thinking of the spatial paths, and then they are told (homework exercise) to compute the extrinsic curvature of those two paths in space and TIME. They discover that the extrinsic curvatures of those two paths are actually the same. (Of course, this is completely different from the intrinsic curvature that actually determines the trajectories.)
> > >
> > > > Surely someone must have come up with this argument [before]...
> > >
> > > LOL. The fallacy you are expressing occurs to many of the more dim-witted beginning students. It's an old chestnut, a cliche.
> >
> > Prove it. Cite a link or a book or an article or a paper or a video.
> Prove what? That if you define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we define them as the changes during a given interval of time ∆t, then we have the relation 𝛾∆w = ∆B ?

𝛾∆w = ∆B has not physical consequences for either the distant observer or the solar system.

∆w = 𝛾∆B has catastrophic consequences for the solar system. Why? Because of the coupling equation ∆B = ∆E/730.5. Let's make the substitution.

∆w = 𝛾( ∆E/730.5 )

In the distant observer's inertial frame, hurdling towards the solar system at v(𝛾), the earth's orbital velocity is now decreased by 𝛾 to 𝛾∆E/730.5/∆t'. The earth no longer has the orbital velocity to remain stable orbit.

Granted, in the solar system's frame the Earth still has the orbital velocity sufficient to keep it in orbit. But now we have two equally valid physical situations, both predicted by the principle of relativity. These situations cannot both exist in one universe. Either the earth falls from orbit or it remains in orbit.

Choose Legion. Choose.

>
> Or that the components of the Riemann curvature tensor are coordinate-dependent, or that the Christoffel symbols (not tensors) are also highly coordinate dependent?
>
> Or that the field equations of general relativity are generally covariant, meaning that the components of all the tensors vary in precisely the way necessary to compensate for whatever coordinate system we choose? Or that they yield the same invariant intervals along every path, and hence preserve all geodesics.
>
> Or that pulses of light follow geodesics just as do material particles?
>
> Or that the extrinsic curvatures of the trajectories of a baseball and a bullet in space-TIME are the same?
>
> Or that the relation (-1)^2 = (1)^2 does not imply -1 = 1?
>
> Or that the hackneyed fallacies and misunderstandings you recite here are very familiar to any knowledgeable person because they commonly occur to dim-witted beginners, to the point of being cliches ?

On Thursday, June 22, 2023 at 10:25:55 AM UTC-7, patdolan wrote:
> > If you define ∆w and ∆B as the changes in w and B respectively during a
> > given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we
> > define them as the changes during a given interval of time ∆t, then we
> > have the relation 𝛾∆w = ∆B.
>
> 𝛾∆w = ∆B has not physical consequences for either the distant observer or the solar system.

Again, any such equations is meaningless unless you define the symbols. For example, if we define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we define them as the changes during a given interval of time ∆t, then we have the relation 𝛾∆w = ∆B. Both of these are objectively verifiable physical facts. They can both be verified by anyone in any state of motion.

On Thursday, June 22, 2023 at 4:51:46 PM UTC-7, Trevor Lange wrote:
> On Thursday, June 22, 2023 at 10:25:55 AM UTC-7, patdolan wrote:
> > > If you define ∆w and ∆B as the changes in w and B respectively during a
> > > given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we
> > > define them as the changes during a given interval of time ∆t, then we
> > > have the relation 𝛾∆w = ∆B.
> >
> > 𝛾∆w = ∆B has not physical consequences for either the distant observer or the solar system.
> Again, any such equations is meaningless unless you define the symbols. For example, if we define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we define them as the changes during a given interval of time ∆t, then we have the relation 𝛾∆w = ∆B. Both of these are objectively verifiable physical facts. They can both be verified by anyone in any state of motion.
No arguments. But one equation leads to the end of the earth. The other, mathematically simultaneous equation does not. Now tell this forum which the Universe will choose.

On 6/22/2023 6:51 PM, Trevor Lange wrote:
> On Thursday, June 22, 2023 at 10:25:55 AM UTC-7, patdolan wrote:
>>> If you define ∆w and ∆B as the changes in w and B respectively during a
>>> given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we
>>> define them as the changes during a given interval of time ∆t, then we
>>> have the relation 𝛾∆w = ∆B.
>>
>> 𝛾∆w = ∆B has not physical consequences for either the distant observer or the solar system.
>
> Again, any such equations is meaningless unless you define the symbols. For example, if we define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we define them as the changes during a given interval of time ∆t, then we have the relation 𝛾∆w = ∆B. Both of these are objectively verifiable physical facts. They can both be verified by anyone in any state of motion.
The race for the title of most incompetent poster in
sci.physics.relativity has finally been settled. Dolan
has the honor he's worked so hard to achieve.

On Thursday, June 22, 2023 at 6:48:12 PM UTC-7, whodat wrote:
> On 6/22/2023 6:51 PM, Trevor Lange wrote:
> > On Thursday, June 22, 2023 at 10:25:55 AM UTC-7, patdolan wrote:
> >>> If you define ∆w and ∆B as the changes in w and B respectively during a
> >>> given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we
> >>> define them as the changes during a given interval of time ∆t, then we
> >>> have the relation 𝛾∆w = ∆B.
> >>
> >> 𝛾∆w = ∆B has not physical consequences for either the distant observer or the solar system.
> >
> > Again, any such equations is meaningless unless you define the symbols. For example, if we define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we define them as the changes during a given interval of time ∆t, then we have the relation 𝛾∆w = ∆B. Both of these are objectively verifiable physical facts. They can both be verified by anyone in any state of motion.
> The race for the title of most incompetent poster in
> sci.physics.relativity has finally been settled. Dolan
> has the honor he's worked so hard to achieve.

You'll never fool me again, Starmaker.

On Thursday, June 22, 2023 at 5:51:23 PM UTC-7, patdolan wrote:
> > If we define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we define them as the changes during a given interval of time ∆t, then we have the relation 𝛾∆w = ∆B. Both of these are objectively verifiable physical facts.
>
> No arguments.... [but] which [will] the Universe will choose?

Again, both of those are objective facts, along with infinitely many others.. For example, there is a system of coordinates S" such that if we define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t", then we have the relation ∆w = ∆B. The equations of physics take the same form in terms of each of the infinitely many such systems of coordinates. The descriptions of events are perfectly consistent in terms of each of these systems.

On Friday, 23 June 2023 at 04:40:01 UTC+2, Trevor Lange wrote:
> On Thursday, June 22, 2023 at 5:51:23 PM UTC-7, patdolan wrote:
> > > If we define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we define them as the changes during a given interval of time ∆t, then we have the relation 𝛾∆w = ∆B. Both of these are objectively verifiable physical facts.
> >
> > No arguments.... [but] which [will] the Universe will choose?
>
> Again, both of those are objective facts, along with infinitely many others.

And in the meantime in the real world, forbidden
by your bunch of idiots "improper" clocks keep
measuring improper t'=t in improper seconds.

On 2023-06-23 01:48:07 +0000, whodat said:

> On 6/22/2023 6:51 PM, Trevor Lange wrote:
>> On Thursday, June 22, 2023 at 10:25:55 AM UTC-7, patdolan wrote:
>>>> If you define ∆w and ∆B as the changes in w and B respectively during a
>>>> given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we
>>>> define them as the changes during a given interval of time ∆t, then we
>>>> have the relation 𝛾∆w = ∆B.
>>>
>>> 𝛾∆w = ∆B has not physical consequences for either the distant observer
>>> or the solar system.
>>
>> Again, any such equations is meaningless unless you define the symbols.
>> For example, if we define ∆w and ∆B as the changes in w and B
>> respectively during a given interval of time ∆t', then we have the
>> relation ∆w = 𝛾∆B, but if we define them as the changes during a given
>> interval of time ∆t, then we have the relation 𝛾∆w = ∆B. Both of
>> these are objectively verifiable physical facts. They can both be
>> verified by anyone in any state of motion.
> The race for the title of most incompetent poster in
> sci.physics.relativity has finally been settled. Dolan
> has the honor he's worked so hard to achieve.

You're probably right, though the competition for that title is pretty
severe, with Ken Seto, Richard Hachel, Richard Hertz, Maciej Wozniak,
Laurence Clark Crossen and Thomas Heger also in the running.

--
Athel -- French and British, living in Marseilles for 36 years; mainly
in England until 1987.

On Friday, 23 June 2023 at 11:13:15 UTC+2, Athel Cornish-Bowden wrote:
> On 2023-06-23 01:48:07 +0000, whodat said:
>
> > On 6/22/2023 6:51 PM, Trevor Lange wrote:
> >> On Thursday, June 22, 2023 at 10:25:55 AM UTC-7, patdolan wrote:
> >>>> If you define ∆w and ∆B as the changes in w and B respectively during a
> >>>> given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we
> >>>> define them as the changes during a given interval of time ∆t, then we
> >>>> have the relation 𝛾∆w = ∆B.
> >>>
> >>> 𝛾∆w = ∆B has not physical consequences for either the distant observer
> >>> or the solar system.
> >>
> >> Again, any such equations is meaningless unless you define the symbols..
> >> For example, if we define ∆w and ∆B as the changes in w and B
> >> respectively during a given interval of time ∆t', then we have the
> >> relation ∆w = 𝛾∆B, but if we define them as the changes during a given
> >> interval of time ∆t, then we have the relation 𝛾∆w = ∆B. Both of
> >> these are objectively verifiable physical facts. They can both be
> >> verified by anyone in any state of motion.
> > The race for the title of most incompetent poster in
> > sci.physics.relativity has finally been settled. Dolan
> > has the honor he's worked so hard to achieve.
> You're probably right, though the competition for that title is pretty
> severe, with Ken Seto, Richard Hachel, Richard Hertz, Maciej Wozniak,
> Laurence Clark Crossen and Thomas Heger also in the running.

And in the meantime in the real world, forbidden by your
bunch of idiots "improper" clocks keep measuring t'=t, just
like all serious clocks always did.
Your insane screams of being FORCED to THE BEST WAY
somehow didn't work.

On 6/22/2023 9:06 PM, patdolan wrote:
> On Thursday, June 22, 2023 at 6:48:12 PM UTC-7, whodat wrote:
>> On 6/22/2023 6:51 PM, Trevor Lange wrote:
>>> On Thursday, June 22, 2023 at 10:25:55 AM UTC-7, patdolan wrote:
>>>>> If you define ∆w and ∆B as the changes in w and B respectively during a
>>>>> given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we
>>>>> define them as the changes during a given interval of time ∆t, then we
>>>>> have the relation 𝛾∆w = ∆B.
>>>>
>>>> 𝛾∆w = ∆B has not physical consequences for either the distant observer or the solar system.
>>>
>>> Again, any such equations is meaningless unless you define the symbols. For example, if we define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we define them as the changes during a given interval of time ∆t, then we have the relation 𝛾∆w = ∆B. Both of these are objectively verifiable physical facts. They can both be verified by anyone in any state of motion.

>> The race for the title of most incompetent poster in
>> sci.physics.relativity has finally been settled. Dolan
>> has the honor he's worked so hard to achieve.
>
> You'll never fool me again, Starmaker.

ibid

On Thursday, June 22, 2023 at 7:40:01 PM UTC-7, Trevor Lange wrote:
> On Thursday, June 22, 2023 at 5:51:23 PM UTC-7, patdolan wrote:
> > > If we define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we define them as the changes during a given interval of time ∆t, then we have the relation 𝛾∆w = ∆B. Both of these are objectively verifiable physical facts.
> >
> > No arguments.... [but] which [will] the Universe will choose?
>
> Again, both of those are objective facts, along with infinitely many others. For example, there is a system of coordinates S" such that if we define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t", then we have the relation ∆w = ∆B.

Yes, that eqn is true if and only if the distant observer is in the rest frame of the solar system. In ALL other cases the earth no longer has sufficient orbital velocity to remain in stable orbit.

So here is a philosophical question: suppose it's just the distant observer's wristwatch hurtling towards the SS, does the earth still spiral into the sun? Or must that wristwatch be observed by a sentient being for relativity to be true. If the former, then any space rock traveling towards the earth should be able to cause the earth's orbit to destabilize. How about 'dem apples, Paul B. Anderson?

The equations of physics take the same form in terms of each of the infinitely many such systems of coordinates. The descriptions of events are perfectly consistent in terms of each of these systems.

On Friday, June 23, 2023 at 7:57:04 AM UTC-7, patdolan wrote:
> > If we define ∆w and ∆B as the changes in w and B respectively during a
> > given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we
> > define them as the changes during a given interval of time ∆t, then we
> > have the relation 𝛾∆w = ∆B.
> >
> > Likewise, there is a system of coordinates S" such that if we define ∆w
> > and ∆B as the changes in w and B respectively during a given interval of
> > time ∆t", then we have the relation ∆w = ∆B.
>
> Yes, that eqn is true if and only if the distant observer is in the rest frame
> of the solar system.

No, not at all. Regardless of the relative motion of the two clocks, there is a system of coordinates S" in terms of which the clocks have equal velocities (in opposite directions), and if we define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t", then we have the relation ∆w = ∆B.

So, for the two clocks you asked about, in any state of relative motion, all three of those relations (and infinitely many others) are valid descriptions of the relation between ∆w and ∆B, where those quantities are defined as the changes in those variables for a given interval of coordinate time in terms of any of the infinitely many different systems of coordinates.

> In ALL other cases the earth no longer has sufficient orbital velocity
> to remain in stable orbit.

Look, consider a well-manicured sloping green at your local golf course, and suppose someone takes some white chalk and draws a grid of lines on the green, and then they take some yellow chalk and draw a different grid of yellow lines on the green. Now, an expert golfer strikes the ball and it rolls along the sloping surface and happily drops into the cup. We can describe the trajectory of the ball in terms of the white coordinate system, or in terms of the yellow coordinate system, but that doesn't change the trajectory of the ball or the fact that it drops into the cup.

You keep claiming that the ball goes into the cup when described in terms of the white coordinate system, but if we describe its path in terms of the yellow coordinate system we find that it karooms off into the sandtrap! Well, that's just insane. You should stop saying dumb stuff like that. Grow up.

> Suppose it's just the distant observer's wristwatch hurtling towards the SS,
> does the earth still spiral into the sun?

Again, this has nothing to do with "observers". Relativity is not a subjectivist theory. Some terrible popularizations of relativity (of which there are many) habitually speak in terms of "observers" when they really mean coordinate systems, and this pedagogical travesty has been calamitous, producing generations of hardcore crackpots. All of your beliefs about the meaning of relativity are utterly wrong.

Remember, in terms of coordinates in which the sun is spatially stationary, it's trajectory is a straight line path in the time direction, and the earth's trajectory is a very elongated helix with its axis pointing in the time direction. Now, we can describe this helix in terms of a rotated system of coordinates, so that the axis is not pointing purely in the time t' direction, it is tilted and points partly in the z' direction. So, the t'-extent of a certain number of windings of the helix is not the same as the t extent, because it is tilted. Same for the z and z' extents. Mind you, it's the very same helix, it's just described in terms of mutually tilted systems of coordinates, like the white and yellow coordinates on the green.

On Friday, June 23, 2023 at 4:37:40 PM UTC-7, Trevor Lange wrote:
> On Friday, June 23, 2023 at 7:57:04 AM UTC-7, patdolan wrote:
> > > If we define ∆w and ∆B as the changes in w and B respectively during a
> > > given interval of time ∆t', then we have the relation ∆w = 𝛾∆B, but if we
> > > define them as the changes during a given interval of time ∆t, then we
> > > have the relation 𝛾∆w = ∆B.
> > >
> > > Likewise, there is a system of coordinates S" such that if we define ∆w
> > > and ∆B as the changes in w and B respectively during a given interval of
> > > time ∆t", then we have the relation ∆w = ∆B..
> >
> > Yes, that eqn is true if and only if the distant observer is in the rest frame
> > of the solar system.
> No, not at all. Regardless of the relative motion of the two clocks, there is a system of coordinates S" in terms of which the clocks have equal velocities (in opposite directions), and if we define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t", then we have the relation ∆w = ∆B.
>
> So, for the two clocks you asked about, in any state of relative motion, all three of those relations (and infinitely many others) are valid descriptions of the relation between ∆w and ∆B, where those quantities are defined as the changes in those variables for a given interval of coordinate time in terms of any of the infinitely many different systems of coordinates.
> > In ALL other cases the earth no longer has sufficient orbital velocity
> > to remain in stable orbit.
> Look, consider a well-manicured sloping green at your local golf course, and suppose someone takes some white chalk and draws a grid of lines on the green, and then they take some yellow chalk and draw a different grid of yellow lines on the green. Now, an expert golfer strikes the ball and it rolls along the sloping surface and happily drops into the cup. We can describe the trajectory of the ball in terms of the white coordinate system, or in terms of the yellow coordinate system, but that doesn't change the trajectory of the ball or the fact that it drops into the cup.
>
> You keep claiming that the ball goes into the cup when described in terms of the white coordinate system, but if we describe its path in terms of the yellow coordinate system we find that it karooms off into the sandtrap! Well, that's just insane.

Agreed, it's insane. It's also reductio ad absurdum, viz.,, it is a disproof of the original set of premises. Those premises that have fallen to this particular RAA are 1) special relativity, and/or 2) general relativity. It hit Paul B. Anderson like a ton of bricks. Now he gets it; he may still not agree with it, but he gets it. You don't even understand what is at stake and what is being tested in the BBP. Keep working on it, from a pragmatist point of view. Forget about the math for now.

You should stop saying dumb stuff like that. Grow up.
>
> > Suppose it's just the distant observer's wristwatch hurtling towards the SS,
> > does the earth still spiral into the sun?
> Again, this has nothing to do with "observers". Relativity is not a subjectivist theory. Some terrible popularizations of relativity (of which there are many) habitually speak in terms of "observers" when they really mean coordinate systems, and this pedagogical travesty has been calamitous, producing generations of hardcore crackpots. All of your beliefs about the meaning of relativity are utterly wrong.
>
> Remember, in terms of coordinates in which the sun is spatially stationary, it's trajectory is a straight line path in the time direction, and the earth's trajectory is a very elongated helix with its axis pointing in the time direction. Now, we can describe this helix in terms of a rotated system of coordinates, so that the axis is not pointing purely in the time t' direction, it is tilted and points partly in the z' direction. So, the t'-extent of a certain number of windings of the helix is not the same as the t extent, because it is tilted. Same for the z and z' extents. Mind you, it's the very same helix, it's just described in terms of mutually tilted systems of coordinates, like the white and yellow coordinates on the green.

Tom Roberts once tried the helix escape, but he couldn't make it work. Just hand waving, as you have just done. But it does show the extent you will go, fueled by growing desperation over the fall of relativity.

Denial
Anger
Depression
Acceptance
Moving On

On Friday, June 23, 2023 at 5:45:09 PM UTC-7, patdolan wrote:
> > Likewise, there is a system of coordinates S" such that if we define ∆w
> > and ∆B as the changes in w and B respectively during a given interval of
> > time ∆t", then we have the relation ∆w = ∆B.
>
> Yes, that eqn is true if and only if the distant observer is in the rest frame
> of the solar system.

No, not at all. Regardless of the relative motion of the two clocks, there's a system of coordinates S" in terms of which the clocks have equal velocities (in opposite directions), and if we define ∆w and ∆B as the changes in w and B respectively during a given interval of time ∆t", then we have the relation ∆w = ∆B. This alone eviscerates all your beliefs. Agreed?

> > You keep claiming that the ball goes into the cup when described in terms of the white coordinate system, but if we describe its path in terms of the yellow coordinate system we find that it karooms off into the sandtrap! Well, that's just insane.
>
> Agreed, [what I've been claiming for years] is insane. [Thank you for so clearly describing my insanity.]

You're welcome. Now the question becomes: Why do you keep repeating something that you know is self-evidently insane?

> > Remember, in terms of coordinates in which the sun is spatially stationary, it's trajectory is a straight line path in the time direction, and the earth's trajectory is a very elongated helix with its axis pointing in the time direction. Now, we can describe this helix in terms of a rotated system of coordinates, so that the axis is not pointing purely in the time t' direction, it is tilted and points partly in the z' direction. So, the t'-extent of a certain number of windings of the helix is not the same as the t extent, because it is tilted. Same for the z and z' extents. Mind you, it's the very same helix, it's just described in terms of mutually tilted systems of coordinates, like the white and yellow coordinates on the green.
>
> [I'm going to claim that I don't understand that, and that I think it is] just hand waving.

Well, the obvious problem here is that when I explain things to you rigorously, proving the vanishing of the contracted Ricci tensor (the vacuum field equations), and how geodesic paths map to geodesic paths, under every diffeomorphism, and the covariance of the Riemann curvature tensor, and the coordinate dependence of the Christoffel symbols, and when I even give you the explcit coordinate systems S and S' and the relationship between them, and how the laws of physics are satisfied in terms of each, and so on, and anticipate and patiently explode every one of your juvenile dodges and evasions, you reply TL;dr. But when I give you the dumbed down version, tailored to the level of your pre-school mentality, you complain that it is hand-waving and insufficiently rigorous (this from the dolt who claims the relation (-1)^2 = (1)^2 rigorously implies -1 = 1 LOL).