Please Sir, I don't understand relativity #1
Vonny N.
somebody here can answer my (possibly 'fuckin stooopid') questions
within the framework of the 'orthodox theory of relativity' (Read:
Cranks, please don't apply).
Consider a universe devoid of all matter and energy except for a test
body X and two observers A and B.
Let's suppose A is 'inertial' and (by definition, since X is free)
observes X to follow a straight world-line. Further, suppose that B is
'non-inertial' and (again, by definition) observes X to follow a
curved world-line. According to (my currently naive understanding of)
GTR, each observer can describe the observed world-line of X as a
geodesic of their spacetime with respect to a metric tensor field they
derive from Einstein's equation.
Now this makes sense for A, because there is (essentially) no matter
or energy in the universe, so Einstein's equation yields a flat metric
tensor (I imagine - I won't pretend to have demonstrated this claim).
But how does B explain the curvature in his metric tensor when his
universe (being the same as that of A) is also devoid of matter or
energy?
This question suggests to me that I don't even understand the goal,
let alone the training program.
Vonny N.
Tom Roberts
> Consider a universe devoid of all matter and energy except for a test
> body X and two observers A and B.
>
> Let's suppose A is 'inertial' and (by definition, since X is free)
> observes X to follow a straight world-line. Further, suppose that B is
> 'non-inertial' and (again, by definition) observes X to follow a
> curved world-line. According to (my currently naive understanding of)
> GTR, each observer can describe the observed world-line of X as a
> geodesic of their spacetime with respect to a metric tensor field they
> derive from Einstein's equation.
They will find THE SAME metric tensor field, because the geometry of the
manifold is a property of the manifold, not of any observer.
You seem to be confusing coordinates and/or tensor components with
tensors. This is common in older books, and can be a MAJOR stumbling
block for students, especially ones without a competent professor to
explain things to them. Several frequent contributors around here have
never understood the difference, and consequently get very confused and
keep making the same mistakes.
In your example the universe is devoid of all matter and energy (the
masses of X, A, and B are all negligible), so the metric will be flat,
and its timelike geodesics will be straight lines when referenced to
inertial coordinates [#]. As you state, they will not be straight lines
[@] when referenced to the non-inertial coordinates of B. But when B
looks at the components of the metric tensor projected onto his
(non-inertial) coordinates, he will find that they are not
diag(1,-1,-1,-1). When B works out the geodesic paths in his
coordinates, he will find they are not straight lines [@], and also that
X is following one of them, as is A.
[#] For once, I did not emphasize LOCALLY inertial coordinates.
Exercise for the reader: why not?
[@] By this I mean that the coordinates of the path are
not linear functions of the proper time of the path.
> But how does B explain the curvature in his metric tensor when his
> universe (being the same as that of A) is also devoid of matter or
> energy?
Even though B finds metric COMPONENTS that are not diag(1,-1,-1,-1), he
will find that the Riemann curvature computed from those components is
zero. So there _IS_ no curvature, even when computed using B's
non-inertial coordinates -- curvature is a geometric property of the
manifold and is independent of coordinates and observer.
About textbooks on GR: in 1973 Misner, Thorne, and Wheeler published
_Gravitation_, which emphasized the geometrical properties of tensors;
previous textbooks had dealt almost exclusively with tensor components
-- such textbooks can be EXTREMELY confusing. I strongly recommend not
using any textbook that works primarily in components, which is
basically any textbook older than 1973, including Weinberg's.
Here's a summary of the difference: the metric tensor g
has components g_ij when projected onto a given set of
coordinates. One has:
g = g_ij dx^i dx^j
where the {dx^i} are the basis co-vectors of the coordinates
{x^i}. Note that g, the {g_ij}, the {x^i}, and the {dx^i} ALL
depend on the point of the manifold at which they are evaluated
(but the standard notation omits this as implicitly understood).
In most books g and dx^i are typeset in bold, indicating their
tensor nature; the ASCII of this newsgroup prevents that -- if
your textbook does not do this, get a better one. Note
that each of the {g_ij} is a real function on the manifold,
but each of the {dx^i} is a TENSOR function on the manifold
(this is the notation of differential forms, not of elementary
calculus). Hence the equation above is an equality between
TENSORS. A tensor is an abstract geometrical object defined by
its properties; vectors and co-vectors are (rank 1) tensors.
If your textbook does not mention co-vectors, get a better one.
Tom Roberts
Androcles
"Vonny N." <von...@gmail.com> wrote in message
news:0c32bc78-d165-4877...@x41g2000hsb.googlegroups.com...
|I am just beginning to grapple with relativity theory and am hoping
| somebody here can answer my (possibly 'fuckin stooopid') questions
| within the framework of the 'orthodox theory of relativity' (Read:
| Cranks, please don't apply).
|
| Consider a universe devoid of all matter and energy except for a test
| body X and two observers A and B.
|
| Let's suppose A is 'inertial' and (by definition, since X is free)
| observes X to follow a straight world-line.
A's own motion allows for X to be "stationary".
| Further, suppose that B is
| 'non-inertial' and (again, by definition) observes X to follow a
| curved world-line.
B's own motion allows for X to be "stationary".
A observes B to follow a curve and X straight.
B observes A to follow a curve and X curved.
| According to (my currently naive understanding of)
| GTR, each observer can describe the observed world-line of X as a
| geodesic of their spacetime
| with respect to a metric tensor field they
| derive from Einstein's equation.
|
| Now this makes sense for A, because there is (essentially) no matter
| or energy in the universe, so Einstein's equation yields a flat metric
| tensor (I imagine - I won't pretend to have demonstrated this claim).
| But how does B explain the curvature in his metric tensor when his
| universe (being the same as that of A) is also devoid of matter or
| energy?
|
| This question suggests to me that I don't even understand the goal,
| let alone the training program.
|
| Vonny N.
The goal is to make the King's new clothes look very smart indeed.
"Isn't it grand! Isn't it fine! Look at the cut, the style, the line!
The suit of clothes is all together
But all together it's all together
The most remarkable suit of clothes that I have ever seen.
These eyes of mine at once determined
The sleeves are velvet, the cape is ermine
The hose are blue and the doublet is a lovely shade of green.
Somebody send for the Queen."
Well they sent for the Queen and they quickly explained to her about the
magic suit of clothes. And naturally, the Queen not wanting to appear a
fool, said,
"Well, isn't it oh! Isn't it rich! Look at the charm of every stitch!
The suit of clothes is all together
But all together it's all together
The most remarkable suit of clothes that I have ever seen.
These eyes of mine at once determined
The sleeves are velvet, the cape is ermine
The hose are blue and the doublet is a lovely shade of green.
Summon the court to convene."
Well the court convened, and you never saw in your life as many people as
were at that court. All the ambassadors, the dukes, the earls, the counts,
it was just black with people, and they were all told about the magic suit
of clothes. And after they were told they naturally didn't want to appear
fools and they said,
"Isn't it ohhh! Isn't it ahhh! Isn't it absolutely wheee(whistle sound)!
The suit of clothes is all together
But all together it's all together
The most remarkable suit of clothes a tailor ever made.
Now quickly, put it all together
With gloves of leather and hat and feather
It's all together the thing to wear in Saturday's parade.
Leading the royal brigade."
Now Saturday came and the streets were just lined with thousands, and
thousands, and thousands of people, and they all were cheering as the
artillery came by, the infantry marched by, the cavalry galloped by. And
everybody was cheering like mad, except one little boy. You see, he hadn't
heard about the magic suit and didn't know what he was supposed to see.
Well, as the King came by the little boy looked and, horrified, said,
"Look at the King! Look at the the King! Look at the King, the King, the
King!
The King is in the all together
But all together the all together
He's all together as naked as the day that he was born.
The King is in the all together
But all together the all together
It's all together the very least the King has ever worn."
All the courts positioned to call an intermission
His majesty is wide open to ridicule and scorn
The King is in the all together
But all together the all together
He's all together as naked as the day that he was born.
And it's all together too chilly a morn!
--
Androcles
Why did Einstein say
the speed of light from A to B is c-v,
the speed of light from B to A is c+v,
the "time" each way is the same?
Cranks, please don't apply.
Martin Hogbin
> I am just beginning to grapple with relativity theory and am hoping
> somebody here can answer my (possibly 'fuckin stooopid') questions
> within the framework of the 'orthodox theory of relativity' (Read:
> Cranks, please don't apply).
>
> Consider a universe devoid of all matter and energy except for a test
> body X and two observers A and B.
>
> Let's suppose A is 'inertial' and (by definition, since X is free)
> observes X to follow a straight world-line. Further, suppose that B is
> 'non-inertial' and (again, by definition) observes X to follow a
> curved world-line. According to (my currently naive understanding of)
> GTR, each observer can describe the observed world-line of X as a
> geodesic of their spacetime with respect to a metric tensor field they
> derive from Einstein's equation.
With some boundary condidtions. In general, the
Einstein field equations do not determine a unique
metric tensor field from starting conditions of just
the disposition of mass and energy. I think that this
is an interesting point worth mentioning.
For an answer to the question that you actually asked,
see Tom's reply and ignore the obvious crackpots.
Martin Hogbin
Dr. Henri Wilson
Einstein's relativity is total crap from start to finish.
>Vonny N.
Henri Wilson. ASTC,BSc,DSc(T)
www.users.bigpond.com/hewn/index.htm
....specialising in teaching physics to engineers and mathematicians....
Eric Gisse
A powerful argument, unfortunately undercut slightly by you not
knowing anything about relativity.
PD
"Wilson" is operating under the tactical mantra that the shorter the
statement from an uninformed amateur, the more compelling it sounds.
PD
Dr. Henri Wilson
Einstein's theory is a a load of crap from start to finish......a jumble of big
words and complicated maths, all following on from completely false initial
premises.
Naturally, its unique jargon is enough to hypnotize star-trek babies like geese
and draper.
PD
And here is where "Wilson" makes his fatal mistake of saying too much,
causing what was compelling in shorter form to be obvious
nincompoopery.
What big words? What complicated maths? There's not a thing
complicated about special relativity. What do you find confusing,
"Henri"?
> Henri Wilson. ASTC,BSc,DSc(T)
Oh, and for the record, the above line is entirely a fabrication.
Vonny N.
Good - that's what I was hoping: both observers agree on zero-
curvature. And thank you for such a perspicuous explanation.
My confusion, however, does not so much lie in the mixing of component/
component-free methods (I am teaching myself with modern,
mathematically rigorous books like Wald and Schutz), but rather in a
mis-understanding of the principle of equivalence. I was thinking that
the non-inertial observer could, by this principle, replace their
description of the world by an appropriate gravitational field. But
this would entail curvature, so that one observer declares space-time
to be curved, while the other does not. What is wrong with my use of
this principle here, and is it best to avoid this principle altogether
(which is my current thinking).
Cheers
Vonny N.
Dr. Henri Wilson
All religions rely heavily on their own unique jargon as a tool for
indoctrination.
Anyone who doesn't speak the language becomes the subject of ridicule...an
outcast... and eventually falls in line.
Henri Wilson. ASTC,BSc,DSc(T)
PD
> On Wed, 28 May 2008 15:49:04 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >On May 28, 5:35 pm, HW@....(Dr. Henri Wilson) wrote:
> >> On Wed, 28 May 2008 08:55:14 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >> >On May 28, 9:49 am, Eric Gisse <jowr...@gmail.com> wrote:
> >> >> > Einstein's relativity is total crap from start to finish.
>
> >> >> A powerful argument, unfortunately undercut slightly by you not
> >> >> knowing anything about relativity.
>
> >> >"Wilson" is operating under the tactical mantra that the shorter the
> >> >statement from an uninformed amateur, the more compelling it sounds.
>
> >> >PD
>
> >> Einstein's theory is a a load of crap from start to finish......a jumble of big
> >> words and complicated maths, all following on from completely false initial
> >> premises.
> >> Naturally, its unique jargon is enough to hypnotize star-trek babies like geese
> >> and draper.
>
> >And here is where "Wilson" makes his fatal mistake of saying too much,
> >causing what was compelling in shorter form to be obvious
> >nincompoopery.
>
> >What big words? What complicated maths? There's not a thing
> >complicated about special relativity. What do you find confusing,
> >"Henri"?
>
> All religions rely heavily on their own unique jargon as a tool for
> indoctrination.
What jargon? What big words? What complicated maths? You keep saying
these things are there, but you can't seem to point them out.
> Anyone who doesn't speak the language becomes the subject of ridicule...an
> outcast... and eventually falls in line.
Well, there's your approach as an alternative. When faced with
something you don't understand (even though it's really pretty
simple), you declare that it must be nonsense as a defense mechanism
(because you can't bear the thought there is something you can't
figure out on your own) rather than asking any questions about it or
trying to earnestly learn about it. Of course, when you do THAT, then
this meets with ridicule, which you misattribute to not belonging to
the "religion". This is the hallmark of a fragile ego. Seto does the
same thing. He figures that if he doesn't understand it, it must be
nonsense, and those who claim to understand it must be indoctrinated
zombies, and so it's easier for him to invent something else he *does*
understand, whether it's right or not.
>
> Henri Wilson. ASTC,BSc,DSc(T)www.users.bigpond.com/hewn/index.htm
Eric Gisse
So every technical field that has a vocabulary unique to it is a
religion?
Yea, /that/ makes sense.
Tom Roberts
> My confusion, however, does not so much lie in the mixing of component/
> component-free methods (I am teaching myself with modern,
> mathematically rigorous books like Wald and Schutz), but rather in a
> mis-understanding of the principle of equivalence. I was thinking that
> the non-inertial observer could, by this principle, replace their
> description of the world by an appropriate gravitational field.
Only to first order. The EP is a LOCAL statement about the equivalence
between acceleration and gravity that is valid only to the extent that
variations in either can be neglected.
> But
> this would entail curvature,
A perfectly uniform gravitational field has no curvature, but can have
non-zero connection coefficients.
[There is a solution to the field equation known as the
"domain wall", in which the manifold is flat everywhere
except on the infinitesimally-thin wall, but geodesics
are "attracted" to the wall.]
But the EP applies only locally, and only to the extent that variations
can be neglected. So, for instance, in a small elevator in freefall near
the earth, small test masses freefalling and essentially at rest inside
the elevator will converge (they fall radially toward the center of the
earth). For an elevator 2 meters wide, this convergence is quite small
(ratio of 2 meters to radius of the earth plus altitude of elevator).
Tom Roberts
Dr. Henri Wilson
...indoctrinated people never realise that they are the victims....
Einstein was wrong..... Accept it....
Henri Wilson. ASTC,BSc,DSc(T)
PD
Including the self-indoctrinated ones. Hint, hint, nudge, wink, wink.
>
> Einstein was wrong..... Accept it....
Sorry, first you need to explain to me where all the jargon and
complicated maths are. I just don't see them at all.
>
> Henri Wilson. ASTC,BSc,DSc(T)www.users.bigpond.com/hewn/index.htm
Dr. Henri Wilson
Read Roberts' posts.
.....big words about nothing.
....the bloke's a raving nutter.....
You Startrek babies lap it up....
Henri Wilson. ASTC,BSc,DSc(T)
PD
> On Fri, 30 May 2008 15:39:03 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >On May 30, 5:03 pm, HW@....(Dr. Henri Wilson) wrote:
> >> On Thu, 29 May 2008 15:31:30 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >> >On May 29, 5:06 pm, HW@....(Dr. Henri Wilson) wrote:
>
> >> ...indoctrinated people never realise that they are the victims....
>
> >Including the self-indoctrinated ones. Hint, hint, nudge, wink, wink.
>
> >> Einstein was wrong..... Accept it....
>
> >Sorry, first you need to explain to me where all the jargon and
> >complicated maths are. I just don't see them at all.
>
> Read Roberts' posts.
> .....big words about nothing.
WHAT big words?
Please, Henri, cite the big words you don't understand.
Dr. Henri Wilson
>On May 31, 5:54 pm, HW@....(Dr. Henri Wilson) wrote:
>> On Fri, 30 May 2008 15:39:03 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
>> >On May 30, 5:03 pm, HW@....(Dr. Henri Wilson) wrote:
>> >> On Thu, 29 May 2008 15:31:30 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
>> >> >On May 29, 5:06 pm, HW@....(Dr. Henri Wilson) wrote:
>>
>> >> ...indoctrinated people never realise that they are the victims....
>>
>> >Including the self-indoctrinated ones. Hint, hint, nudge, wink, wink.
>>
>> >> Einstein was wrong..... Accept it....
>>
>> >Sorry, first you need to explain to me where all the jargon and
>> >complicated maths are. I just don't see them at all.
>>
>> Read Roberts' posts.
>> .....big words about nothing.
>
>WHAT big words?
>Please, Henri, cite the big words you don't understand.
Henri Wilson. ASTC,BSc,DSc(T)
www.users.bigpond.com/hewn/index.htm
..Einstein created a brilliant and consistent theory about space and time. Unfortunately it was based on completely wrong principles.
Eric Gisse
> On Sun, 1 Jun 2008 11:35:32 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >On May 31, 5:54 pm, HW@....(Dr. Henri Wilson) wrote:
> >> On Fri, 30 May 2008 15:39:03 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >> >On May 30, 5:03 pm, HW@....(Dr. Henri Wilson) wrote:
> >> >> On Thu, 29 May 2008 15:31:30 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >> >> >On May 29, 5:06 pm, HW@....(Dr. Henri Wilson) wrote:
>
> >> >> ...indoctrinated people never realise that they are the victims....
>
> >> >Including the self-indoctrinated ones. Hint, hint, nudge, wink, wink.
>
> >> >> Einstein was wrong..... Accept it....
>
> >> >Sorry, first you need to explain to me where all the jargon and
> >> >complicated maths are. I just don't see them at all.
>
> >> Read Roberts' posts.
> >> .....big words about nothing.
>
> >WHAT big words?
> >Please, Henri, cite the big words you don't understand.
>
> Henri Wilson. ASTC,BSc,DSc(T)www.users.bigpond.com/hewn/index.htm
Do you actually expect us to believe you have any of those
certifications?
PD
OK, it appears you can't find any big words in Roberts' posts (or
anything in SR) after all, right? Or they're there, but you don't want
to admit which ones you don't understand.
PD
Dr. Henri Wilson
Henri Wilson. ASTC,BSc,DSc(T)
PD
So now you've resorted to the same penny-ante tactics that the
attention-whore NoEinstein uses. You can't resist responding (MUST.
HAVE. LAST. WORD.... RESPONSE. MANDATORY. TO. REFUSE. DEFEAT.) but
it's not necessary to actually say anything.
I think you let your guard down there a little, "Henri". Down went the
hubris and the macho, and you confessed that your real complaint with
relativity is that it uses words you don't understand and math you
don't understand (although it's really pretty easy after all). And
this you take to be a horrible slap to your tenuous ego.
What you don't seem to have a grip on is the fact that readers/mockers
of your posts can tell in an instant when you're telling the truth and
when you're just blustering and making it up as you go along. You are
fooling absolutely no one.
PD
PD
Dr. Henri Wilson
My time is too valuable to be wasted on trying to educate StarTrek babies.
>PD
Henri Wilson. ASTC,BSc,DSc(T)
www.users.bigpond.com/hewn/index.htm
..Einstein created a brilliant and consistent theory about space and time. Unfortunately it was based on completely wrong principles.
PD
> On Mon, 2 Jun 2008 15:41:43 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >On Jun 2, 5:27 pm, HW@....(Dr. Henri Wilson) wrote:
> >> On Mon, 2 Jun 2008 05:37:17 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >> >On Jun 1, 4:55 pm, HW@....(Dr. Henri Wilson) wrote:
> >> ..Einstein created a brilliant and consistent theory about space and time. Unfortunately it was based on completely wrong principles.
>
> >So now you've resorted to the same penny-ante tactics that the
> >attention-whore NoEinstein uses. You can't resist responding (MUST.
> >HAVE. LAST. WORD.... RESPONSE. MANDATORY. TO. REFUSE. DEFEAT.) but
> >it's not necessary to actually say anything.
>
> >I think you let your guard down there a little, "Henri". Down went the
> >hubris and the macho, and you confessed that your real complaint with
> >relativity is that it uses words you don't understand and math you
> >don't understand (although it's really pretty easy after all). And
> >this you take to be a horrible slap to your tenuous ego.
>
> >What you don't seem to have a grip on is the fact that readers/mockers
> >of your posts can tell in an instant when you're telling the truth and
> >when you're just blustering and making it up as you go along. You are
> >fooling absolutely no one.
>
> My time is too valuable to be wasted on trying to educate StarTrek babies.
Then stop posting here and do something more worthwhile with your
time. You've educated not a soul here. So what you're doing here is a
mystery.
If you DO want to post here, then be straightforward about it, rather
than this slime trail you've been leaving around. It's smelly and
unsightly and it besmirches the name of Australia.
>
> >PD
>
> Henri Wilson. ASTC,BSc,DSc(T)www.users.bigpond.com/hewn/index.htm
Eric Gisse
> On Mon, 2 Jun 2008 15:41:43 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >On Jun 2, 5:27 pm, HW@....(Dr. Henri Wilson) wrote:
> >> On Mon, 2 Jun 2008 05:37:17 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >> >On Jun 1, 4:55 pm, HW@....(Dr. Henri Wilson) wrote:
> >> ..Einstein created a brilliant and consistent theory about space and time. Unfortunately it was based on completely wrong principles.
>
> >So now you've resorted to the same penny-ante tactics that the
> >attention-whore NoEinstein uses. You can't resist responding (MUST.
> >HAVE. LAST. WORD.... RESPONSE. MANDATORY. TO. REFUSE. DEFEAT.) but
> >it's not necessary to actually say anything.
>
> >I think you let your guard down there a little, "Henri". Down went the
> >hubris and the macho, and you confessed that your real complaint with
> >relativity is that it uses words you don't understand and math you
> >don't understand (although it's really pretty easy after all). And
> >this you take to be a horrible slap to your tenuous ego.
>
> >What you don't seem to have a grip on is the fact that readers/mockers
> >of your posts can tell in an instant when you're telling the truth and
> >when you're just blustering and making it up as you go along. You are
> >fooling absolutely no one.
>
> My time is too valuable to be wasted on trying to educate StarTrek babies.
THEN SHUT THE FUCK UP.
>
> >PD
>
> Henri Wilson. ASTC,BSc,DSc(T)www.users.bigpond.com/hewn/index.htm
Koobee Wublee
> A perfectly uniform gravitational field has no curvature, but can have
> non-zero connection coefficients.
By definition, gravitation is a manifestation by the curvature in the
temporal axis. Gravitational time dilation gives gravity, and
gravitational time anti-dilation gives anti-gravity. Thus, what you
are saying does not make any sense.
> [There is a solution to the field equation known as the
> "domain wall", in which the manifold is flat everywhere
> except on the infinitesimally-thin wall, but geodesics
> are "attracted" to the wall.]
http://en.wikipedia.org/wiki/Domain_wall
You obviously mean something else. So, reference, please.
> But the EP applies only locally, and only to the extent that variations
> can be neglected. So, for instance, in a small elevator in freefall near
> the earth, small test masses freefalling and essentially at rest inside
> the elevator will converge (they fall radially toward the center of the
> earth). For an elevator 2 meters wide, this convergence is quite small
> (ratio of 2 meters to radius of the earth plus altitude of elevator).
Einstein’s re-iteration of Galileo’s principle of equivalence suits no
fundamental purpose at all. <shrug>
Koobee Wublee
> Vonny N. wrote:
> > Consider a universe devoid of all matter and energy except for a test
> > body X and two observers A and B.
>
> > Let's suppose A is 'inertial' and (by definition, since X is free)
> > observes X to follow a straight world-line. Further, suppose that B is
> > 'non-inertial' and (again, by definition) observes X to follow a
> > curved world-line. According to (my currently naive understanding of)
> > GTR, each observer can describe the observed world-line of X as a
> > geodesic of their spacetime with respect to a metric tensor field they
> > derive from Einstein's equation.
>
> They will find THE SAME metric tensor field, because the geometry of the
> manifold is a property of the manifold, not of any observer.
Since the geometry must be independent of any observer, it is most
likely that the metric, which is not a tensor but a mere matrix, of
each is not the same because of different choices in coordinate
systems.
> You seem to be confusing coordinates and/or tensor components with
> tensors.
The confusion is on your part. <shrug> You are forgetting the
observer has all the right to choose his own coordinate system. The
coordinate system alone is not enough to describe the geometry under
observation. You need the metric. Thus, the metric must be dependent
on the choice of coordinate system to describe the invariant geometry.
> This is common in older books, and can be a MAJOR stumbling
> block for students, especially ones without a competent professor to
> explain things to them.
Claiming the metric as invariant or the metric being the proper
presentation of the geometry is just plain wrong. <shrug> It takes a
choice of coordinate system and a metric to describe the geometry.
For example, given
ds^2 = g_ij dq^i dq^j
ds^2 is the geometry. g_ij are elements to the metric [g]. dq^i,
dq^j represent the coordinate system. In flat space, the following
can only be true if the choice of coordinate system is holonomic.
** (g_ij = 0) if (i != j)
If one chooses to employ a non-holonomic coordinate system, then the
following is true to describe flat space or spacetime.
** (g_ij != 0) if (i != j)
> Several frequent contributors around here have
> never understood the difference, and consequently get very confused and
> keep making the same mistakes.
You are one such person. <shrug>
> In your example the universe is devoid of all matter and energy (the
> masses of X, A, and B are all negligible), so the metric will be flat,
> and its timelike geodesics will be straight lines when referenced to
> inertial coordinates [#].
Even in GR, there exists no such special coordinate system. <shrug>
> As you state, they will not be straight lines
> [@] when referenced to the non-inertial coordinates of B.
You mean non-holonomic coordinate system. Of course, I have explained
so. See above.
> [#] For once, I did not emphasize LOCALLY inertial coordinates.
> Exercise for the reader: why not?
<shrug> is my answer. <shrug>
> [@] By this I mean that the coordinates of the path are
> not linear functions of the proper time of the path.
Please don’t pass non-holonomic coordinate systems as magic tricks.
<shrug>
> > But how does B explain the curvature in his metric tensor when his
> > universe (being the same as that of A) is also devoid of matter or
> > energy?
>
> Even though B finds metric COMPONENTS that are not diag(1,-1,-1,-1), he
> will find that the Riemann curvature computed from those components is
> zero.
The metric you mentioned above only defines a flat spacetime if the
choice of coordinate system is Euclidean and nothing else. <shrug>
> About textbooks on GR: in 1973 Misner, Thorne, and Wheeler published
> _Gravitation_, which emphasized the geometrical properties of tensors;
> previous textbooks had dealt almost exclusively with tensor components
That book is very disorganized! You are doing any novice any favor by
recommending that book. <shrug>
> -- such textbooks can be EXTREMELY confusing. I strongly recommend not
> using any textbook that works primarily in components,
Doing that will create even more mysticism. We already know both SR
and GR are Orwellian teaching of the following.
** MYSTICISM IS WISDOM
** PLAGIARISM IS CREATIVITY
** CONJECTURE IS REALITY
** FAITH IS THEORY
** LYING IS TEACHING
** BELIEVING IS LEARNING
> which is
> basically any textbook older than 1973, including Weinberg's.
So, is it why Mr. Tucker after reading Weinberg is still cluless as
what a Lagrangian is?
> Here's a summary of the difference: the metric tensor g
> has components g_ij when projected onto a given set of
> coordinates. One has:
> g = g_ij dx^i dx^j
No, this is not true. g, the metric tensor, is a matrix with special
properties. It is a collection of many numbers. g, in my
nomenclature, is [g], which indicates a matrix with multiple
elements. The elements to [g] are [g]_ij which is the same as g_ij.
Them what you have described makes absolutely no sense. It is
mathematically dead on arrival. <shrug>
> where the {dx^i} are the basis co-vectors of the coordinates
> {x^i}.
Your [dx^i] is merely a column or a row vector which should be more
properly represented by [dx] with elements [dx]_i. Presenting a
vector in a co-vector or not is merely how a vector is presented as a
column or a row. You are creating more mysticism here.
> Note that g, the {g_ij}, the {x^i}, and the {dx^i} ALL
> depend on the point of the manifold at which they are evaluated
> (but the standard notation omits this as implicitly understood).
> In most books g and dx^i are typeset in bold, indicating their
> tensor nature; the ASCII of this newsgroup prevents that -- if
> your textbook does not do this, get a better one. Note
> that each of the {g_ij} is a real function on the manifold,
> but each of the {dx^i} is a TENSOR function on the manifold
> (this is the notation of differential forms, not of elementary
> calculus). Hence the equation above is an equality between
> TENSORS. A tensor is an abstract geometrical object defined by
> its properties; vectors and co-vectors are (rank 1) tensors.
> If your textbook does not mention co-vectors, get a better one.
Oh, great. Now the deciding factor on a good physics book is if a
vector is presented by bold letters or not. <shrug> Did some authors
pay you money to endorse that?
Paul B. Andersen
> My time is too valuable to be wasted on trying to educate StarTrek babies.
'StarTrek babies', what's that?
--
Paul
Dr. Henri Wilson
<paul.b....@hiadeletethis.no> wrote:
>Dr. Henri Wilson wrote:
>> My time is too valuable to be wasted on trying to educate StarTrek babies.
>
>'StarTrek babies', what's that?
Idiots like geese and draper.
Dr. Henri Wilson
>On Jun 3, 5:33 pm, HW@....(Dr. Henri Wilson) wrote:
>> On Mon, 2 Jun 2008 15:41:43 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
>> >On Jun 2, 5:27 pm, HW@....(Dr. Henri Wilson) wrote:
>> >> On Mon, 2 Jun 2008 05:37:17 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
>> >> >On Jun 1, 4:55 pm, HW@....(Dr. Henri Wilson) wrote:
>>
>> >What you don't seem to have a grip on is the fact that readers/mockers
>> >of your posts can tell in an instant when you're telling the truth and
>> >when you're just blustering and making it up as you go along. You are
>> >fooling absolutely no one.
>>
>> My time is too valuable to be wasted on trying to educate StarTrek babies.
>
>Then stop posting here and do something more worthwhile with your
>time. You've educated not a soul here. So what you're doing here is a
>mystery.
>
>If you DO want to post here, then be straightforward about it, rather
>than this slime trail you've been leaving around. It's smelly and
>unsightly and it besmirches the name of Australia.
Well I think I have slaughtered all of relativity's sacred cows.
That's something the whole of Australia can be proud of..
Fizeau's experiment was my latest achievement.
....fully explained by BaTh and refuting SR.
>> >PD
>>
>> Henri Wilson. ASTC,BSc,DSc(T)www.users.bigpond.com/hewn/index.htm
>>
>> ..Einstein created a brilliant and consistent theory about space and time. Unfortunately it was based on completely wrong principles.
Henri Wilson. ASTC,BSc,DSc(T)
www.users.bigpond.com/hewn/index.htm
Eric Gisse
> On Wed, 04 Jun 2008 11:17:28 +0200, "Paul B. Andersen"
>
> >Dr. Henri Wilson wrote:
> >> My time is too valuable to be wasted on trying to educate StarTrek babies.
>
> >'StarTrek babies', what's that?
>
> Idiots like geese and draper.
>
> Henri Wilson. ASTC,BSc,DSc(T)www.users.bigpond.com/hewn/index.htm
>
> ..Einstein created a brilliant and consistent theory about space and time. Unfortunately it was based on completely wrong principles.
What happened to your valuable time, Ralph?
PD
> On Tue, 3 Jun 2008 15:38:11 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >On Jun 3, 5:33 pm, HW@....(Dr. Henri Wilson) wrote:
> >> On Mon, 2 Jun 2008 15:41:43 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >> >On Jun 2, 5:27 pm, HW@....(Dr. Henri Wilson) wrote:
> >> >> On Mon, 2 Jun 2008 05:37:17 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >> >> >On Jun 1, 4:55 pm, HW@....(Dr. Henri Wilson) wrote:
>
> >> >What you don't seem to have a grip on is the fact that readers/mockers
> >> >of your posts can tell in an instant when you're telling the truth and
> >> >when you're just blustering and making it up as you go along. You are
> >> >fooling absolutely no one.
>
> >> My time is too valuable to be wasted on trying to educate StarTrek babies.
>
> >Then stop posting here and do something more worthwhile with your
> >time. You've educated not a soul here. So what you're doing here is a
> >mystery.
>
> >If you DO want to post here, then be straightforward about it, rather
> >than this slime trail you've been leaving around. It's smelly and
> >unsightly and it besmirches the name of Australia.
>
> Well I think I have slaughtered all of relativity's sacred cows.
What you've accomplished in your own mind is hardly an achievement.
In my dreams, I've slept with Sandra Bullock and flown at 10,000 ft
without any mechanical assistance. Unlike you, I don't ascribe those
achievements to the level of reality.
What you think you've accomplished in PRIVATE is your business. Now,
what do you think you've accomplished HERE?
Dr. Henri Wilson
>On Jun 4, 5:11 pm, HW@....(Dr. Henri Wilson) wrote:
>> On Tue, 3 Jun 2008 15:38:11 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
>> >On Jun 3, 5:33 pm, HW@....(Dr. Henri Wilson) wrote:
>> >If you DO want to post here, then be straightforward about it, rather
>> >than this slime trail you've been leaving around. It's smelly and
>> >unsightly and it besmirches the name of Australia.
>>
>> Well I think I have slaughtered all of relativity's sacred cows.
>
>What you've accomplished in your own mind is hardly an achievement.
>In my dreams, I've slept with Sandra Bullock and flown at 10,000 ft
>without any mechanical assistance. Unlike you, I don't ascribe those
>achievements to the level of reality.
>
>What you think you've accomplished in PRIVATE is your business. Now,
>what do you think you've accomplished HERE?
Draper, one by one I have annihilated every so called argument against the
Ballistic theory of light.
Light is obviously ballistic. Einstein was a charleton....an aetherist in
disguise.
All he did was start with the conclusions of LET.......that, because of the
mythical 'Lorentz contractions', all observers would measure the OWLS as c,
irrespective of their own or the source's speed through the absolute
aether...... and then work backwards through the LET maths .
SR AND LET ARE THE SAME BLOODY THEORY....the wrong one.
Henri Wilson. ASTC,BSc,DSc(T)
Darwin123
> I am just beginning to grapple with relativity theory and am hoping
> somebody here can answer my (possibly 'fuckin stooopid') questions
> within the framework of the 'orthodox theory of relativity' (Read:
> Cranks, please don't apply).
>
> Consider a universe devoid of all matter and energy except for a test
> body X and two observers A and B.
>
> Let's suppose A is 'inertial' and (by definition, since X is free)
> observes X to follow a straight world-line. Further, suppose that B is
> 'non-inertial' and (again, by definition) observes X to follow a
> curved world-line. According to (my currently naive understanding of)
> GTR, each observer can describe the observed world-line of X as a
> geodesic of their spacetime with respect to a metric tensor field they
> derive from Einstein's equation.
>
> or energy in the universe, so Einstein's equation yields a flat metric
> tensor (I imagine - I won't pretend to have demonstrated this claim).
This can't make sense for A. If there is no matter or energy in
the universe, then there is no X. Since you have defined the metric in
terms of this X, there is no metric.
So how come you are making
> But how does B explain the curvature in his metric tensor when his
> universe (being the same as that of A) is also devoid of matter or
> energy?
I'll answer that when you tell us the quotient between 0 and 0.
This should be easy even for someone as naive as you.
0/0=?
PD
> On Wed, 4 Jun 2008 17:24:42 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >On Jun 4, 5:11 pm, HW@....(Dr. Henri Wilson) wrote:
> >> On Tue, 3 Jun 2008 15:38:11 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >> >On Jun 3, 5:33 pm, HW@....(Dr. Henri Wilson) wrote:
> >> >If you DO want to post here, then be straightforward about it, rather
> >> >than this slime trail you've been leaving around. It's smelly and
> >> >unsightly and it besmirches the name of Australia.
>
> >> Well I think I have slaughtered all of relativity's sacred cows.
>
> >What you've accomplished in your own mind is hardly an achievement.
> >In my dreams, I've slept with Sandra Bullock and flown at 10,000 ft
> >without any mechanical assistance. Unlike you, I don't ascribe those
> >achievements to the level of reality.
>
> >What you think you've accomplished in PRIVATE is your business. Now,
> >what do you think you've accomplished HERE?
>
> Draper, one by one I have annihilated every so called argument against the
> Ballistic theory of light.
Uh, no, you haven't. The evidence against the ballistic theory of
light is not an argument. It is experimental data. Your method for
dealing with this is to believe whatever data you want to believe.
Choosing which data you want to believe is not an acceptable method of
annihilating anything.
> Light is obviously ballistic.
Nature is rarely obvious. Just because you WANT nature to behave in
obvious ways (so that you can understand it) doesn't mean it's going
to.
But the real issue, of course, is that you don't like big words and
difficult maths. Problem is, you won't point out what you think are
the big words and difficult maths used.
Dr. Henri Wilson
>On Jun 5, 6:15 pm, HW@....(Dr. Henri Wilson) wrote:
>> On Wed, 4 Jun 2008 17:24:42 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
>> >On Jun 4, 5:11 pm, HW@....(Dr. Henri Wilson) wrote:
>> >What you think you've accomplished in PRIVATE is your business. Now,
>> >what do you think you've accomplished HERE?
>>
>> Draper, one by one I have annihilated every so called argument against the
>> Ballistic theory of light.
>
>Uh, no, you haven't. The evidence against the ballistic theory of
>light is not an argument. It is experimental data. Your method for
>dealing with this is to believe whatever data you want to believe.
>Choosing which data you want to believe is not an acceptable method of
>annihilating anything.
There is NO evidence against the BaTh.
There is NO evidence in support of Einstein's stupid theory.
You are a brainwashed fool Draper.
>> Light is obviously ballistic.
>
>Nature is rarely obvious. Just because you WANT nature to behave in
>obvious ways (so that you can understand it) doesn't mean it's going
>to.
>
>But the real issue, of course, is that you don't like big words and
>difficult maths. Problem is, you won't point out what you think are
>the big words and difficult maths used.
>
>> Einstein was a charleton....an aetherist in
>> disguise.
>>
>> All he did was start with the conclusions of LET.......that, because of the
>> mythical 'Lorentz contractions', all observers would measure the OWLS as c,
>> irrespective of their own or the source's speed through the absolute
>> aether...... and then work backwards through the LET maths .
>>
>> SR AND LET ARE THE SAME BLOODY THEORY....the wrong one.
>>
>> Henri Wilson. ASTC,BSc,DSc(T)www.users.bigpond.com/hewn/index.htm
>>
>> ..Einstein created a brilliant and consistent theory about space and time. Unfortunately it was based on completely wrong principles.
Henri Wilson. ASTC,BSc,DSc(T)
Eric Gisse
> On Thu, 5 Jun 2008 20:16:19 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >On Jun 5, 6:15 pm, HW@....(Dr. Henri Wilson) wrote:
> >> On Wed, 4 Jun 2008 17:24:42 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >> >On Jun 4, 5:11 pm, HW@....(Dr. Henri Wilson) wrote:
> >> >What you think you've accomplished in PRIVATE is your business. Now,
> >> >what do you think you've accomplished HERE?
>
> >> Draper, one by one I have annihilated every so called argument against the
> >> Ballistic theory of light.
>
> >Uh, no, you haven't. The evidence against the ballistic theory of
> >light is not an argument. It is experimental data. Your method for
> >dealing with this is to believe whatever data you want to believe.
> >Choosing which data you want to believe is not an acceptable method of
> >annihilating anything.
>
> There is NO evidence against the BaTh.
...that Ralph will accept.
> There is NO evidence in support of Einstein's stupid theory.
...that Ralph will accept.
PD
> On Thu, 5 Jun 2008 20:16:19 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >On Jun 5, 6:15 pm, HW@....(Dr. Henri Wilson) wrote:
> >> On Wed, 4 Jun 2008 17:24:42 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >> >On Jun 4, 5:11 pm, HW@....(Dr. Henri Wilson) wrote:
> >> >What you think you've accomplished in PRIVATE is your business. Now,
> >> >what do you think you've accomplished HERE?
>
> >> Draper, one by one I have annihilated every so called argument against the
> >> Ballistic theory of light.
>
> >Uh, no, you haven't. The evidence against the ballistic theory of
> >light is not an argument. It is experimental data. Your method for
> >dealing with this is to believe whatever data you want to believe.
> >Choosing which data you want to believe is not an acceptable method of
> >annihilating anything.
>
> There is NO evidence against the BaTh.
Of course there is. You choose not to believe it. That, of course, is
irrelevant.
> There is NO evidence in support of Einstein's stupid theory.
Of course there is. You choose not to believe it. That, of course, is
also irrelevant.
> You are a brainwashed fool Draper.
Well, of course you've brainwashed yourself to believe that. But once
again, that's irrelevant.
>
>
>
>
>
> >> Light is obviously ballistic.
>
> >Nature is rarely obvious. Just because you WANT nature to behave in
> >obvious ways (so that you can understand it) doesn't mean it's going
> >to.
>
> >But the real issue, of course, is that you don't like big words and
> >difficult maths. Problem is, you won't point out what you think are
> >the big words and difficult maths used.
You STILL haven't followed up on this, Ralph. Is there a reason why
you won't follow up on your own statements, other than you don't want
to? (Other than you're too busy to, though you're not too busy to post
that you're too busy to?)
>
> >> Einstein was a charleton....an aetherist in
> >> disguise.
>
> >> All he did was start with the conclusions of LET.......that, because of the
> >> mythical 'Lorentz contractions', all observers would measure the OWLS as c,
> >> irrespective of their own or the source's speed through the absolute
> >> aether...... and then work backwards through the LET maths .
>
> >> SR AND LET ARE THE SAME BLOODY THEORY....the wrong one.
>
> >> Henri Wilson. ASTC,BSc,DSc(T)www.users.bigpond.com/hewn/index.htm
>
> >> ..Einstein created a brilliant and consistent theory about space and time. Unfortunately it was based on completely wrong principles.
>
> Henri Wilson. ASTC,BSc,DSc(T)www.users.bigpond.com/hewn/index.htm
>
> ..Einstein created a brilliant and consistent theory about space and time. Unfortunately it was based on completely wrong principles.- Hide quoted text -
>
> - Show quoted text -
Dr. Henri Wilson
>On Jun 7, 3:15 am, HW@....(Dr. Henri Wilson) wrote:
>> On Thu, 5 Jun 2008 20:16:19 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
>> >On Jun 5, 6:15 pm, HW@....(Dr. Henri Wilson) wrote:
>> >> Draper, one by one I have annihilated every so called argument against the
>> >> Ballistic theory of light.
>>
>> >Uh, no, you haven't. The evidence against the ballistic theory of
>> >light is not an argument. It is experimental data. Your method for
>> >dealing with this is to believe whatever data you want to believe.
>> >Choosing which data you want to believe is not an acceptable method of
>> >annihilating anything.
>>
>> There is NO evidence against the BaTh.
>
>Of course there is. You choose not to believe it. That, of course, is
>irrelevant.
Give me some of that evidence Draper....instead of raving....
>
>> There is NO evidence in support of Einstein's stupid theory.
>
>Of course there is. You choose not to believe it. That, of course, is
>also irrelevant.
there is none.
>> You are a brainwashed fool Draper.
>
>Well, of course you've brainwashed yourself to believe that. But once
>again, that's irrelevant.
>
Henri Wilson. ASTC,BSc,DSc(T)
PD
> On Sat, 7 Jun 2008 07:09:43 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >On Jun 7, 3:15 am, HW@....(Dr. Henri Wilson) wrote:
> >> On Thu, 5 Jun 2008 20:16:19 -0700 (PDT), PD <TheDraperFam...@gmail.com> wrote:
> >> >On Jun 5, 6:15 pm, HW@....(Dr. Henri Wilson) wrote:
> >> >> Draper, one by one I have annihilated every so called argument against the
> >> >> Ballistic theory of light.
>
> >> >Uh, no, you haven't. The evidence against the ballistic theory of
> >> >light is not an argument. It is experimental data. Your method for
> >> >dealing with this is to believe whatever data you want to believe.
> >> >Choosing which data you want to believe is not an acceptable method of
> >> >annihilating anything.
>
> >> There is NO evidence against the BaTh.
>
> >Of course there is. You choose not to believe it. That, of course, is
> >irrelevant.
>
> Give me some of that evidence Draper....instead of raving....
Done that already. You say you don't believe it. That is, of course,
irrelevant. You know this, but you like denying reality. For you,
denying reality is fun.
>
> >> There is NO evidence in support of Einstein's stupid theory.
>
> >Of course there is. You choose not to believe it. That, of course, is
> >also irrelevant.
>
> there is none.
That's a denial of reality. I realize you find that fun, but it's also
completely irrelevant. You just make spurious noise, Ralph.