Teaching GR right after intermediate mechanics
PD
advocating teaching GR a whole lot earlier than it presently is in most
places.
In all classes above junior level, he notes that the standard approach
to teaching a subject in physics is to:
a) introduce the necessary mathematical tools
b) motivate and explain the basic (field) equations
c) solve the (field) equations in interesting circumstances
d) apply the solutions to make predictions and compare with observation
and experiment
This strict deductive approach is useful for producing an in-depth and
"rigorous" understanding of things. However, it also has the
disadvantage of discouraging application of physical good sense and
visualization. He also points out that we don't do that in an
introductory survey course; we don't need to be able to do surface
integrals and Gauss's law to look at electric field configurations.
He suggests that for GR, one can dispense (at least at first) with
differential geometry, instead focusing on the metric and the fact that
a geodesic is stationary with respect to some variation of the path
between two spacetime endpoints A and B. The latter looks very much
like the principle of least action, with the proper time taking the
role of the lagrangian.
Using this principle and starting with the Schwarzchild metric, he
shows that one can very quickly come up with an "effective" potential
for orbits, complete with the relativistic term. From that, he quickly
gets the inner diameter of the accretion disk, as well as the
perihelion advance for (pseudo-)closed orbits.
This approach looks good to me, and it would be good to try to do the
same thing if possible for quantum mechanics and other difficult
subjects. Anyone up fror writing a book?
PD
Koobee Wublee
news:1144818063....@t31g2000cwb.googlegroups.com...
> Hartle...
> suggests that for GR, one can dispense (at least at first) with
> differential geometry, instead focusing on the metric and the fact that
> a geodesic is stationary with respect to some variation of the path
> between two spacetime endpoints A and B. The latter looks very much
> like the principle of least action, with the proper time taking the
> role of the lagrangian.
The current understanding of GR using calculus of variations is through
a principle (more like a postulate) of stationary action where the
stationary condition is the traversed spacetime of the event. A more
well proven principle is the principle of least time or action as you
have pointed out where every event taking place must obey the least
amount of elapsed time. The example is the Snell's Law. I went
through a series of discussions with Dr. Roberts, Dr. Carlip, and Mr.
Most a while back on this subject. They all suggested if calculus of
variations is to be taken, the segment of spacetime must be stationary.
Of course, they all failed to explain photons which always travel with
a stationary spacetime of zero. If you subscribe to the principle of
least time, you must use a slightly different Lagrangian for the
geodesics. The results are almost the same for Schwarzschild metric
but are definitely different for the general case. Using the same
mathematical method, principle of least time does not yield the same
correct Mercury's orbital motion as the pinciple of stationary
spacetime. You have to decide which interpretation of GR is correct
first. And then, I hope you would not fudge your answer like
Besso/Einstein did.
> Using this principle and starting with the Schwarzchild metric, he
> shows that one can very quickly come up with an "effective" potential
> for orbits, complete with the relativistic term. From that, he quickly
> gets the inner diameter of the accretion disk, as well as the
> perihelion advance for (pseudo-)closed orbits.
Calculus of variations is much a better approach than geometric stuff.
Riemann and Christoffel must be geniuses to ever derive the goedesics
without using calculus of variations.
Given a segment of spacetime below.
ds^2 = g_ij dq^i dq^j
The traditional (principle of stationary spacetime) Lagrangian is
derived by dividing both side by ds^2 which yields
L = g_ij dq^i/ds dq^j/ds = 1
I believe in the principle of least time in which the Lagrangian should
be a function of (dq^i/dq^0) and (dq^j/dq^0) instead of (dq^i/ds) and
(dq^j/ds). In doing so, the tight connection between the temporal axis
and the spatial axes is weakened tremendously which is violating the
essence of the concept of spacetime.
> This approach looks good to me, and it would be good to try to do the
> same thing if possible for quantum mechanics and other difficult
> subjects. Anyone up fror writing a book?
I would love to write a book about this subject if time permits. I am
just a blue collar worker working all day long to support my growing
family.
Eric Gisse
PD wrote:
> Hartle has written a paper in a recent AJP (Vol 74, No. 1, p. 14),
> advocating teaching GR a whole lot earlier than it presently is in most
> places.
[snip good idea]
My expectation is that nobody teaches GR to undergrads. That is the
impression I get from not only the books about GR, but the general
expectation of the mathematics required to suitably understand it.
PD
This is precisely Hartle's purpose in writing the paper. He sees no
sound reason for that.
PD
Len Gaasenbeek
To PD,
To teach students general relativity at any time, is to teach them pseudo
science. Once they come to believe that illogical reasoning is all right,
they will be ruined for life. It is like teaching children that to become a
suicide bomber is the greatest religious sacrifice a person can make and
will cause the perpetrator to go straight to heaven.
More damage is done to susceptible students by teachers than any other group
I can think off, whether they are relativists or religious. Of course
relativists are religious too, in that any one who questions their illogical
postulates (faith) is branded a heretic, who doesn't understand 'modern
relativistic physics' and consequently should be ostracized.
The only people Christ didn't have a good word to say about were the
Pharisees, the self-righteous religious-establishment teachers of his day.
It is sad to think, that things haven't improved in 2000 years!
Len.
..................................................
"PD" <TheDrap...@gmail.com> wrote in message
news:1144818063....@t31g2000cwb.googlegroups.com...
..................................................
Bilge
>advocating teaching GR a whole lot earlier than it presently is in most
>places.
[...]
>He suggests that for GR, one can dispense (at least at first) with
>differential geometry, instead focusing on the metric and the fact that
>a geodesic is stationary with respect to some variation of the path
>between two spacetime endpoints A and B. The latter looks very much
>like the principle of least action, with the proper time taking the
>role of the lagrangian.
>
>Using this principle and starting with the Schwarzchild metric, he
>shows that one can very quickly come up with an "effective" potential
>for orbits, complete with the relativistic term. From that, he quickly
>gets the inner diameter of the accretion disk, as well as the
>perihelion advance for (pseudo-)closed orbits.
>This approach looks good to me, and it would be good to try to do the
>same thing if possible for quantum mechanics and other difficult
>subjects. Anyone up fror writing a book?
Except for one thing. In order to teach such courses, one would
have do so at the expense of the courses that serve as a foundation
for the real physics in those courses. Better to teach the differential
geometry first along with some other mathematics which has become
important to modern physics than introduce yet another topic which has
to e astardized in order to present some phenomenology. In the end,
teaching the mathematical tools first means not having to explain things
like a covariant derivative N different times in N diferent contexts
so that it appears to e two different concepts with a vague resemblence.
Just think how much simpler it would have been to study general relativity
and field theory if you already knew that you need to specify a connection
to differentiate.
Bilge
>news:1144818063....@t31g2000cwb.googlegroups.com...
>> Hartle...
>> suggests that for GR, one can dispense (at least at first) with
>> differential geometry, instead focusing on the metric and the fact that
>> a geodesic is stationary with respect to some variation of the path
>> between two spacetime endpoints A and B. The latter looks very much
>> like the principle of least action, with the proper time taking the
>> role of the lagrangian.
>
>The current understanding of GR using calculus of variations is through
>a principle (more like a postulate) of stationary action where the
>stationary condition is the traversed spacetime of the event. A more
mathematics rather than be given some overly simplified material that
only facillitates misconceptions.
Bilge
>To PD,
>
>To teach students general relativity at any time, is to teach them pseudo
>science.
and all of your demands to reintroduce mysticism and magic into
science are going to go unheeded. Deal with it.
Eric Gisse
What it seems he is proposing is a "GR-lite" course for undergrads.
Of course I'm not going to get the full power of electromagnetism,
mechanics, and quantum theory with my undergrad physics education! Why
would I expect to get all of general relativity?
Personally, my understanding of GR currently sits at about the level
Hartle seems to be proposing. I am very comfortable with the
justification, derivation, and usage of [well, some of it but enough]
of the Schwarzschild metric. But the full power of GR eludes me because
I'm still off-put by all the mathematics required [I finally get on
speaking terms with tensors, then I have to learn calculus of
variations to vary the metric. Arggh.]
I'm liking this idea, if only to get folks to have some understanding
of general relativity if they don't choose to continue to graduate
school. If the physics classes at UAF are any indication of the overall
way physics is taught, you will learn everything BUT general relativity
to one degree or another. Having investigated what is taught, I see
plenty of special relativity from start to finish but GR is restricted
to places like the back of my mechanics book explained in vague detail.
Yea. I like this idea.
But who is going to write the damn book? I shill for Carroll so much on
here if only because he has been the one to make GR the most
presentable for me at my current understanding of mathematics. Did he
have anyone in mind or was he just floating a trial balloon?
>
> PD
Igor
Len Gaasenbeek wrote:
> To PD,
>
> To teach students general relativity at any time, is to teach them pseudo
> science.
No, it's called modern physics. And the fact that you don't understand
a word of it is betrayed by your jealous ignorance.
>Once they come to believe that illogical reasoning is all right,
> they will be ruined for life.
You wish you had the ability to be ruined in this way.
>It is like teaching children that to become a
> suicide bomber is the greatest religious sacrifice a person can make and
> will cause the perpetrator to go straight to heaven.
Oh, that's brilliant! Equating modern physics with suicide bombing.
What kind of drugs are you on?
JanPB
> "PD" <TheDrap...@gmail.com> wrote in message
> news:1144818063....@t31g2000cwb.googlegroups.com...
> > Hartle...
> > suggests that for GR, one can dispense (at least at first) with
> > differential geometry, instead focusing on the metric and the fact that
> > a geodesic is stationary with respect to some variation of the path
> > between two spacetime endpoints A and B. The latter looks very much
> > like the principle of least action, with the proper time taking the
> > role of the lagrangian.
>
> The current understanding of GR using calculus of variations is through
> a principle (more like a postulate) of stationary action where the
> stationary condition is the traversed spacetime of the event.
You mean proper time (to get a geodesic). Replace "stationary
spacetime" with "stationary proper time" in what follows.
> A more
> well proven principle is the principle of least time or action as you
> have pointed out where every event taking place must obey the least
> amount of elapsed time. The example is the Snell's Law. I went
> through a series of discussions with Dr. Roberts, Dr. Carlip, and Mr.
> Most a while back on this subject. They all suggested if calculus of
> variations is to be taken, the segment of spacetime must be stationary.
> Of course, they all failed to explain photons which always travel with
> a stationary spacetime of zero. If you subscribe to the principle of
> least time, you must use a slightly different Lagrangian for the
> geodesics.
It looks to me like a confusion between two principles of stationary
action: Hamilton's and Maupertuis'. The first varies Lagrangian with
fixed endpoints and endtimes, the second varies reduced action (the "p
q-dot") with fixed endpoints and fixed Hamiltonian (this forces the
endtimes to vary). It is the latter which reduces more directly to the
familar Fermat and Snell.
> The results are almost the same for Schwarzschild metric
> but are definitely different for the general case. Using the same
> mathematical method, principle of least time does not yield the same
> correct Mercury's orbital motion as the pinciple of stationary
> spacetime.
If the variation is done correctly, both cases should yield the same
result - they are mathematically equivalent (for systems of constant
Hamiltonian). The Maupertuis variation process is different than the
standard "fix endpoints and endtimes" Hamilton routine - perhaps that's
where the discrepancy came from? I haven't looked into this in detail
though.
> Calculus of variations is much a better approach than geometric stuff.
> Riemann and Christoffel must be geniuses to ever derive the goedesics
> without using calculus of variations.
>
> Given a segment of spacetime below.
>
> ds^2 = g_ij dq^i dq^j
>
> The traditional (principle of stationary spacetime) Lagrangian is
> derived by dividing both side by ds^2 which yields
>
> L = g_ij dq^i/ds dq^j/ds = 1
>
> I believe in the principle of least time in which the Lagrangian should
> be a function of (dq^i/dq^0) and (dq^j/dq^0) instead of (dq^i/ds) and
> (dq^j/ds). In doing so, the tight connection between the temporal axis
> and the spatial axes is weakened tremendously which is violating the
> essence of the concept of spacetime.
This is what happens with the Maupertuis-type of variation - the time
parameter is forced on you by the condition that the Hamiltonian remain
constant during the variation.
At the end of the day all these approaches must be equivalent anyway.
--
Jan Bielawski
Bill Hobba
Nor do I - see my direct response.
Thanks
Bill
>
> PD
>
Bill Hobba
Not me. But the approach looks sound. I have always been of the belief
exactly as Feynman did in his famous lectures one can introduce SR to first
year physics/math students using excerpts from Taylor and Wheeler -
Space-time Physics and Wheeler - Journey into Gravity and Space-time and of
course the lectures.
http://www.amazon.com/gp/product/0716760347/104-0328048-9592740?v=glance&n=283155
http://www.amazon.com/gp/product/071670336X/sr=8-5/qid=1144886037/ref=sr_1_5/104-0328048-9592740?%5Fencoding=UTF8
The math of those sources looks minimal.
I would not study GR without SR first. In second year more detail can
given with a deeper study of relativity adding Taylor and Wheeler -
Exploring Black Holes - Introduction to General Relativity.
http://www.amazon.com/gp/product/020138423X/sr=8-7/qid=1144886086/ref=sr_1_7/104-0328048-9592740?%5Fencoding=UTF8
And having the machinery of SR available in second year would simplify EM -
one can start with SR and Coulombs law which all students would be familiar
with from even grade 8 science and develop Maxwell's equations, the
existence of magnetic fields etc.
http://www.cse.secs.oakland.edu/haskell/SpecialRelativity.htm
Much less ad-hoc introduction of facts you need to take on face value.
Indeed Taylors and Wheelers approach does seem very similar to Hartles:
http://www.eftaylor.com/general.html
'Learning general relativity usually requires mastering Einstein's field
equations, which are expressed in the complicated mathematics of tensors or
differential forms. But big chunks of general relativity require only
calculus if one starts with the metric describing spacetime around Earth or
black hole. Expressions for energy and angular momentum follow, along with
predictions for the motions of particles and light. Students study the
Global Positioning system, precession of Mercury's orbit, gravitational red
shift, orbits of light and deflection of light by Sun, the gravitational
retardation of light, and frame-dragging near a rotating body.'
Actually Taylor has a lot to say about the approach of basing things on the
PLA.
http://www.eftaylor.com/leastaction.html
In fact I have been a long advocate is teaching mechanics using the PLA with
supplemental reading for the Feynman Lecture. Feynmans explanation of what
force is for example is IMHO simply the best their is - indeed much of the
lectures are like that. For actually solving problems I think the Schaum
outline series is the go rather than rely on an actual text - which is the
major weakness of the lectures.
Third year students could have a course based on say Sean Carols notes.
I strongly suspect undergrads would appreciate relativity being available in
all years of their physics/math education. If that elective was offered to
me I would have jumped at it. In my math degree the physics was classical
mechanics, EM and good old methods of mathematical physics. I did subjects
like methods of mathematical economics and operations research - relativity
would have been much more interesting. Indeed I remember one lecturer
mentioning he had to leave a little early to go to a symposium on GR. The
response of the class was overwhelming - they would have loved to study it.
Thanks
Bill
>
> PD
>
Bill Hobba
"Bilge" <dub...@radioactivex.lebesque-al.net> wrote in message
news:slrne3q0j2...@radioactivex.lebesque-al.net...
Valid point - no very valid point. The issue I have however is to motivate
students. From my experience physics/math students are really really
interested in relativity - partially I think due to the myth only a handful
of people understand it - wouldn't it be neat to be one of those. Of course
when you learn it you soon find it is just that - a myth. I believe we
have at least two relativity texts accessible to first year students -
Wheeler and Taylor Space-time physics and Wheeler - Journey into Gravity
and Space-time. Wheeler and Taylor's - Black Holes - Introduction to
General Relativity looks accessible to second year students. For third year
normal introductory texts like Sean Carols notes looks fine. My temperance
of uni was keeping student interest in the material is always a problem.
But I seem to recall Bilge has actually taught the stuff - so his opinion
carries much more weight than mine. I only ever taught calculus and then to
drongoes (a bit harsh - they were all much better with the opposite sex than
me) who could not grasp the idea of a limit but needed calculus to study
engineering and was a TA/tutor for some introductory stats classes.
Thanks
Bill
JanPB
It looks like the article is a result of Hartle's experiences in
teaching from his own book perhaps: http://tinyurl.com/qk527
His book is just 3 years old and has a very "undergrad-friendly" look
and feel to it. I've only scanned it but it looks very nice.
--
Jan Bielawski
Bill Hobba
"JanPB" <fil...@gmail.com> wrote in message
news:1144891406.3...@u72g2000cwu.googlegroups.com...
Yes indeed it does. My only concern is 'The aim of this groundbreaking new
text is to bring general relativity into the undergraduate curriculum and
make this fundamental theory accessible to all physics majors.'. I think
math majors would be interested as well. I know I was.
Thanks
Bill
>
> --
> Jan Bielawski
>
Koobee Wublee
>> The current understanding of GR using calculus of variations is through
>> a principle (more like a postulate) of stationary action where the
>> stationary condition is the traversed spacetime of the event.
>
> You mean proper time (to get a geodesic). Replace "stationary
> spacetime" with "stationary proper time" in what follows.
I actually do not mean proper time. Your definition of proper time is
the spacetime itself divided by the speed of light which is just
spacetime multiplied by a constant. My concept of a proper time is a
lot different. It has the context of the relationship between the
observed (coordinate) time and observed (coordinate) space.
>> A more
>> well proven principle is the principle of least time or action as you
>> have pointed out where every event taking place must obey the least
>> amount of elapsed time. The example is the Snell's Law. I went
>> through a series of discussions with Dr. Roberts, Dr. Carlip, and Mr.
>> Most a while back on this subject. They all suggested if calculus of
>> variations is to be taken, the segment of spacetime must be stationary.
>> Of course, they all failed to explain photons which always travel with
>> a stationary spacetime of zero. If you subscribe to the principle of
>> least time, you must use a slightly different Lagrangian for the
>> geodesics.
>
> It looks to me like a confusion between two principles of stationary
> action: Hamilton's and Maupertuis'. The first varies Lagrangian with
> fixed endpoints and endtimes, the second varies reduced action (the "p
> q-dot") with fixed endpoints and fixed Hamiltonian (this forces the
> endtimes to vary). It is the latter which reduces more directly to the
> familar Fermat and Snell.
No, I have not. The Euler-Lagrange Equations only specify when a
stationary condition occurs. It is still up to you to argue for a
least action with this stationary condition. To argue a minimal
action, you must find a stationary condition first. The fixed points
approach also works for the least action.
>> The results are almost the same for Schwarzschild metric
>> but are definitely different for the general case. Using the same
>> mathematical method, principle of least time does not yield the same
>> correct Mercury's orbital motion as the pinciple of stationary
>> spacetime.
>
> If the variation is done correctly, both cases should yield the same
> result - they are mathematically equivalent (for systems of constant
> Hamiltonian). The Maupertuis variation process is different than the
> standard "fix endpoints and endtimes" Hamilton routine - perhaps that's
> where the discrepancy came from? I haven't looked into this in detail
> though.
Please do. You seem to be the only one here who can understand what I
am talking about.
>> Calculus of variations is much a better approach than geometric stuff.
>> Riemann and Christoffel must be geniuses to ever derive the goedesics
>> without using calculus of variations.
>>
>> Given a segment of spacetime below.
>>
>> ds^2 = g_ij dq^i dq^j
>>
>> The traditional (principle of stationary spacetime) Lagrangian is
>> derived by dividing both side by ds^2 which yields
>>
>> L = g_ij dq^i/ds dq^j/ds = 1
>>
>> I believe in the principle of least time in which the Lagrangian should
>> be a function of (dq^i/dq^0) and (dq^j/dq^0) instead of (dq^i/ds) and
>> (dq^j/ds). In doing so, the tight connection between the temporal axis
>> and the spatial axes is weakened tremendously which is violating the
>> essence of the concept of spacetime.
>
> This is what happens with the Maupertuis-type of variation - the time
> parameter is forced on you by the condition that the Hamiltonian remain
> constant during the variation.
>
> At the end of the day all these approaches must be equivalent anyway.
Since the Euler-Lagrange Equations are very sensitive to the choice of
Lagrangians. In the general case, the Lagrangians serving as the
densities that minimize a segment of spacetime and an elapsed amount of
time do not yield the same result at the quintessential scale (quoting
from Dr. Roberts). Why don't try it yourself?
Koobee Wublee
news:1144859249.9...@e56g2000cwe.googlegroups.com...
>> This is precisely Hartle's purpose in writing the paper. He sees no
>> sound reason for that.
>
> What it seems he is proposing is a "GR-lite" course for undergrads.
If anyone promotes the principle of least action to solve the geodesic
equations, it will be the end of GR. The reason is that the foundng
fathers of GR decided on the proper time which is just spacetime
divided by the speed of light as the common coordinate. That was
before photons were properly characterized. Since then we know a
photon always travels with a spacetime of zero. In doing so, it is
already a stationary action. So, using the Euler-Lagrange Equations
for something that is already stationary with any trajectory does not
make any sense. For example, when a photon travels from point A to
point B, this photon can take any course it likes. In doing so, the
spacetime is always zero. There is no special path that will allow a
least amount of spacetime. Thus, that is why Dr. Carlip and Dr.
Roberts do not even talk about the principle of least action on
geodesics. They choose to settle on Riemann/Christoffel's work on this
subject.
> Of course I'm not going to get the full power of electromagnetism,
> mechanics, and quantum theory with my undergrad physics education! Why
> would I expect to get all of general relativity?
The differential geometric approach of GR is the legacy of Grossmann's
work. That did not get anywhere until Hilbert used the calculus of
variations to find the field equations. Although Hilbert's Lagrangian
requires an understanding of Riemann/Christoffel's work, GR is actually
very simple if you take your time to understand the calculus of
variations which is also a very simple subject by itself. Speaking of
Hilbert's Lagrangian that give rise to the field equations, it does not
satisfy any physically meaningful action. Gravity is not caused by the
curvature in spacetime as commonly believed, but gravity is caused
solely by gravitational time dilation. Without gravitational time
dilation, a curvature in space does not yield gravitation as Riemann
had discovered. Gravitational time dilation is enough to explain
gravitation. Adding an irrelavant condition such as the curvature of
space does not bode very well to argue for a stationary or a least
amount of any action.
JanPB
>
> The differential geometric approach of GR is the legacy of Grossmann's
> work.
Well, yes and no. I mean Grossmann or no Grossmann, differential
geometry is the language of GR and you cannot bypass it in any way -
it's really the essence of the equivalence principle.
> That did not get anywhere until Hilbert used the calculus of
> variations to find the field equations.
Just a historical note - Hilbert got his equations *after* Einstein.
The somewhat embarrassing (to Hilbert) smoking gun regarding this
matter has been found few years ago. Hilbert actually *changed* the
galley proofs of his article after he saw Einstein's equations but *did
not change the original date* on those proofs. Very below the belt.
> Speaking of
> Hilbert's Lagrangian that give rise to the field equations, it does not
> satisfy any physically meaningful action.
What do you mean by "satisfying an action"?
> Gravity is not caused by the
> curvature in spacetime as commonly believed, but gravity is caused
> solely by gravitational time dilation. Without gravitational time
> dilation, a curvature in space does not yield gravitation as Riemann
> had discovered. Gravitational time dilation is enough to explain
> gravitation.
Not all of gravitation.
> Adding an irrelavant condition such as the curvature of
> space does not bode very well to argue for a stationary or a least
> amount of any action.
So why is there spatial curvature in, say, the Schwarzschild metric?
--
Jan Bielawski
JanPB
> "JanPB" <fil...@gmail.com> wrote in message
> news:1144883216.7...@z34g2000cwc.googlegroups.com...
>
> >> The current understanding of GR using calculus of variations is through
> >> a principle (more like a postulate) of stationary action where the
> >> stationary condition is the traversed spacetime of the event.
> >
> > You mean proper time (to get a geodesic). Replace "stationary
> > spacetime" with "stationary proper time" in what follows.
>
> I actually do not mean proper time. Your definition of proper time is
> the spacetime itself divided by the speed of light which is just
> spacetime multiplied by a constant.
OK, the only conclusion I can make based on this is that you either
don't know what you are talking about or that you use a non-standard
terminology. You should at least define what you mean by:
"spacetime divided by the speed of light",
"spacetime multiplied by a constant".
What I mean by proper time is speed integrated over the (timelike)
path.
> My concept of a proper time is a
> lot different. It has the context of the relationship between the
> observed (coordinate) time and observed (coordinate) space.
Don't call it "proper time" then.
> >> A more
> >> well proven principle is the principle of least time or action as you
> >> have pointed out where every event taking place must obey the least
> >> amount of elapsed time. The example is the Snell's Law. I went
> >> through a series of discussions with Dr. Roberts, Dr. Carlip, and Mr.
> >> Most a while back on this subject. They all suggested if calculus of
> >> variations is to be taken, the segment of spacetime must be stationary.
> >> Of course, they all failed to explain photons which always travel with
> >> a stationary spacetime of zero. If you subscribe to the principle of
> >> least time, you must use a slightly different Lagrangian for the
> >> geodesics.
> >
> > It looks to me like a confusion between two principles of stationary
> > action: Hamilton's and Maupertuis'. The first varies Lagrangian with
> > fixed endpoints and endtimes, the second varies reduced action (the "p
> > q-dot") with fixed endpoints and fixed Hamiltonian (this forces the
> > endtimes to vary). It is the latter which reduces more directly to the
> > familar Fermat and Snell.
>
> No, I have not.
?
> The Euler-Lagrange Equations only specify when a
> stationary condition occurs.
What do you mean by "only"? What else do you need?
> It is still up to you to argue for a
> least action with this stationary condition. To argue a minimal
> action, you must find a stationary condition first.
> The fixed points approach also works for the least action.
What do you need the *minimal* action for? The difference between
stationary and minimal lies in the global structure of spacetime and
nothing you've said so far had anything to do with it.
> >> The results are almost the same for Schwarzschild metric
> >> but are definitely different for the general case. Using the same
> >> mathematical method, principle of least time does not yield the same
> >> correct Mercury's orbital motion as the pinciple of stationary
> >> spacetime.
> >
> > If the variation is done correctly, both cases should yield the same
> > result - they are mathematically equivalent (for systems of constant
> > Hamiltonian). The Maupertuis variation process is different than the
> > standard "fix endpoints and endtimes" Hamilton routine - perhaps that's
> > where the discrepancy came from? I haven't looked into this in detail
> > though.
>
> Please do. You seem to be the only one here who can understand what I
> am talking about.
I cannot add anything to it - there can be no contradiction between
equivalent definitions of geodesics.
> Since the Euler-Lagrange Equations are very sensitive to the choice of
> Lagrangians. In the general case, the Lagrangians serving as the
> densities that minimize a segment of spacetime and an elapsed amount of
> time do not yield the same result at the quintessential scale (quoting
> from Dr. Roberts). Why don't try it yourself?
I cannot parse the last paragraph. It would be better if you used
standard terminology. What Lagrangians do not yield the same result?
Obviously two random Lagrangians won't yield the same result - why is
it such a surprise?
--
Jan Bielawski
Bilge
>news:1144859249.9...@e56g2000cwe.googlegroups.com...
>
>>> This is precisely Hartle's purpose in writing the paper. He sees no
>>> sound reason for that.
>>
>> What it seems he is proposing is a "GR-lite" course for undergrads.
>
>If anyone promotes the principle of least action to solve the geodesic
>equations, it will be the end of GR.
a geodesic on a sphere is a great circle? The procedure is
_exactly_ the same as finding a geodesic in general relativity.
>The reason is that the foundng
>fathers of GR decided on the proper time which is just spacetime
>divided by the speed of light as the common coordinate.
You have to be as stupid as the day is long. It's a coordinate
system, imbecile. Do you really think that the coefficients in
dr^2 = (adx)^2 + (bdy)^2 with a = 1cm/10mm and b = 2.54cm/in
have physical significance? Sheeesh. How long have you been taxing
your brain without figuring this out? It just is not that hard.
>That was before photons were properly characterized. Since then we
>know a photon always travels with a spacetime of zero.
Whatever that means.
>In doing so, it is already a stationary action. So, using the
>Euler-Lagrange Equations
Go learn something about variational calculus and lagrangians.
Your attempt to use the ``power of the Lagrangian Method'' amounts
using the lagrangian as it used when introducing it to college sophomores,
except that college sophomores will have probably have been given
some prepratory material in the way of variational calculus to insure
they don't end up with the same misconceptions you have.
[...]
>had discovered. Gravitational time dilation is enough to explain
>gravitation. Adding an irrelavant condition such as the curvature of
>space does not bode very well to argue for a stationary or a least
>amount of any action.
Why are you trying to explain something related to general relativity?
You've een working on the perihelion of mercury for what, a year now?
After a year, you are still convinced that everyone else used general
relativitity incorrectly to get the right answer while you used general
relativity correctly to get the wrong answer? That kind of logic alone
ought to suggest to anyone that your sole area of expertise is
overestimating your expertise.
PD
Indeed, he refers to the book in his paper (naturally) as an attempt to
do just that. It's called a "physics first" approach to GR.
PD
>
> --
> Jan Bielawski
PD
I understand your point. However, I think there is in fact value in
explaining things like a covariant derivative N different times in N
different contexts. There is a reason why the *same* subjects in
mechanics are generally taught at least three times to physics
students: in the introductory course, in a 2nd year undergrad course,
and in a graduate level course. There are different tools brought to
bear, but the same *physics* is revisited.
One way of thinking about this is that the physics is integrated
vertically through the curriculum, while the mathematical tools and
concepts are integrated horizontally.
This encourages skill at synthesis as well as a deeper physical
intuition, which are always hallmarks of an excellent physical mind.
It was always an enormous frustration to me to have a grad student
doing his/her orals and I would ask a basic conceptual question, and
the first thing the candidate would do would be to try to write down
the Lagrangian. Pulling out the pneumatic socket wrench when the pair
of sliplock pliers in the back pocket will do just fine.
PD
Bill Hobba
Bill Hobba
Whoops - sorry guys for accidentally posting a blank message.
I learnt Faradays law in grade 8, grade 10, grade 12, vector analysis, and
at uni in courses on EM if I would have took them. And then again in
graduate school (if you took it - it was an elective for me being a math
student). This used to annoy the hell out of me. But a quote from
chwinger - Classical Electrodynamics page 1 put it in perspective:
'The teaching of electrodynamics theory is something like that of American
History is school; you get it again and again. Well this is the end of the
line. Here we will put it all together and yet not quite since it is still
classical electrodynamics and the final goal is quantum electrodynamics.
This preoccupation reflects the all pervasive nature of electromagnetism,
with implications ranging from the futherest galaxies to the interiors of
fundamental particles. In particular the properties of ordinary matter,
including those properties classified as chemical and biological, depend
only on electromagnetic forces, in conjunction with the microscopic laws of
quantum mechanics.'
And that I think sums it up - early on we take a lot of things on face
value. As your mathematical sophistication and knowledge of physics
improves we take less and less on faith and understand how it is all
interconnected eg once one knows SR then one can introduce Maxwell's
equations in a much more elegant fashion. I see no reason GR could not
follow similar lines until we get the 'end of the line' either in final year
or graduate school.
As an aside I notice people tend to prefer Jackson as the standard advanced
EM textbook. I don't have a copy of that but after reading a number my
favorite is Schwinger (by a smidgen over Landau - Classical theory of
Fields) - yet I never seem to see it used as a text. Interesting.
Thanks
Bill
>
> PD
>
Koobee Wublee
> >If anyone promotes the principle of least action to solve the geodesic
> >equations, it will be the end of GR.
>
> In other words, you believe it is impossile to determine that
> a geodesic on a sphere is a great circle? The procedure is
> _exactly_ the same as finding a geodesic in general relativity.
Calculus of Variations fails to determines the geodesics for photons
based on minimal traversed spacetime. However, properly interpreted,
Calculus of Variations should have no problems to arrive at the
geodesic equations based on minimal elapsed coordinate time.
The procedures are not the same. It is fudged to be the same. <shrug>
> >The reason is that the foundng
> >fathers of GR decided on the proper time which is just spacetime
> >divided by the speed of light as the common coordinate.
>
> You have to be as stupid as the day is long. It's a coordinate
> system, imbecile. Do you really think that the coefficients in
> dr^2 = (adx)^2 + (bdy)^2 with a = 1cm/10mm and b = 2.54cm/in
> have physical significance? Sheeesh. How long have you been taxing
> your brain without figuring this out? It just is not that hard.
I think you are misunderstanding something. I have no idea what you
are referring to. Try to bark up a different tree. <shrug>
> >That was before photons were properly characterized. Since then we
> >know a photon always travels with a spacetime of zero.
>
> Whatever that means.
In another words, you fail to understand the nature of photons.
<shrug>
> >In doing so, it is already a stationary action. So, using the
> >Euler-Lagrange Equations
>
> Go learn something about variational calculus and lagrangians.
> Your attempt to use the ``power of the Lagrangian Method'' amounts
> using the lagrangian as it used when introducing it to college sophomores,
> except that college sophomores will have probably have been given
> some prepratory material in the way of variational calculus to insure
> they don't end up with the same misconceptions you have.
It sounds like you need to learn with the sophomores. <shrug>
> [...]
> >had discovered. Gravitational time dilation is enough to explain
> >gravitation. Adding an irrelavant condition such as the curvature of
> >space does not bode very well to argue for a stationary or a least
> >amount of any action.
>
> Why are you trying to explain something related to general relativity?
> You've een working on the perihelion of mercury for what, a year now?
> After a year, you are still convinced that everyone else used general
> relativitity incorrectly to get the right answer while you used general
> relativity correctly to get the wrong answer? That kind of logic alone
> ought to suggest to anyone that your sole area of expertise is
> overestimating your expertise.
You need to back up your comments with mathematics. Without it, you
are just babbling. <shrug>
Koobee Wublee
>> The differential geometric approach of GR is the legacy of Grossmann's
>> work.
>
> Well, yes and no. I mean Grossmann or no Grossmann, differential
> geometry is the language of GR and you cannot bypass it in any way -
> it's really the essence of the equivalence principle.
Grossmann's work led to dead end as Riemann tried to do almost half a
century earlier. The language of GR does not have to be differential
geometry as Grossmann tried to impose it to be. The Principle of
Equivalence does not show any useful purpose. The field equations can
only be derived after the Lagrangian leading to the Einstein-Hilbert
Action is materialized. With the solution to the field equations
presetned as the metric, solving the geodesics using Calculus of
Variations is much simpler. This is the exact point which Dr. Draper
is trying to make referring to Dr. Hartle's work.
>> That did not get anywhere until Hilbert used the calculus of
>> variations to find the field equations.
>
> Just a historical note - Hilbert got his equations *after* Einstein.
> The somewhat embarrassing (to Hilbert) smoking gun regarding this
> matter has been found few years ago. Hilbert actually *changed* the
> galley proofs of his article after he saw Einstein's equations but *did
> not change the original date* on those proofs. Very below the belt.
It is astronomically improbable (again quoting from Dr. Roberts) that
two persons within a couple weeks of each other would have conjured up
the same Lagrangian leading to the Einstein-Hilbert Action. This was
achieved without proper derivation of this Lagrangian. You can say
Hilbert pulled it out of his *ss which Einstein eagerly licked it up.
Your belief of the historical account is totally biased. Stachel's
job, thus his career, depends very much on glorifying Eisntein to no
end. In doing so, he seems to be willing to stretch the truth. The
forensic evidence is embedded in the mathematics involved. To
blatantly alter the history disregarding what mathematical evidence is
as you have said "hitting below the belt".
>> Speaking of
>> Hilbert's Lagrangian that give rise to the field equations, it does not
>> satisfy any physically meaningful action.
>
> What do you mean by "satisfying an action"?
I don't understand what any physically meaningful action this
Einstein-Hilbert Action serves. If you do, perhaps you can enlighten
me.
>> Gravity is not caused by the
>> curvature in spacetime as commonly believed, but gravity is caused
>> solely by gravitational time dilation. Without gravitational time
>> dilation, a curvature in space does not yield gravitation as Riemann
>> had discovered. Gravitational time dilation is enough to explain
>> gravitation.
>
> Not all of gravitation.
So, how many types of gravitation do you know of? I only know of one.
>> Adding an irrelavant condition such as the curvature of
>> space does not bode very well to argue for a stationary or a least
>> amount of any action.
>
> So why is there spatial curvature in, say, the Schwarzschild metric?
Try to connect the dots between a bogus Lagrangian and the solutions to
field equations based on this bogus Lagrangian.
Koobee Wublee
>> I actually do not mean proper time. Your definition of proper time is
>> the spacetime itself divided by the speed of light which is just
>> spacetime multiplied by a constant.
>
> OK, the only conclusion I can make based on this is that you either
> don't know what you are talking about or that you use a non-standard
> terminology. You should at least define what you mean by:
>
> "spacetime divided by the speed of light",
dtau = ds / c
> "spacetime multiplied by a constant".
dtau = k * ds
Where
** k = 1 / c
This is as simple as you can get it.
> What I mean by proper time is speed integrated over the (timelike)
> path.
You either don't understand the concept of spacetime or choose to hide
your comments in fancy vacabularies.
>> My concept of a proper time is a
>> lot different. It has the context of the relationship between the
>> observed (coordinate) time and observed (coordinate) space.
>
> Don't call it "proper time" then.
I don't. Spacetime is a meaningless quantity to an observer. Keep in
mind that an observer observes an event with his measurement system and
not with an alien one nor God's.
>> >> A more
>> >> well proven principle is the principle of least time or action as you
>> >> have pointed out where every event taking place must obey the least
>> >> amount of elapsed time. The example is the Snell's Law. I went
>> >> through a series of discussions with Dr. Roberts, Dr. Carlip, and Mr.
>> >> Most a while back on this subject. They all suggested if calculus of
>> >> variations is to be taken, the segment of spacetime must be stationary.
>> >> Of course, they all failed to explain photons which always travel with
>> >> a stationary spacetime of zero. If you subscribe to the principle of
>> >> least time, you must use a slightly different Lagrangian for the
>> >> geodesics.
>> >
>> > It looks to me like a confusion between two principles of stationary
>> > action: Hamilton's and Maupertuis'. The first varies Lagrangian with
>> > fixed endpoints and endtimes, the second varies reduced action (the "p
>> > q-dot") with fixed endpoints and fixed Hamiltonian (this forces the
>> > endtimes to vary). It is the latter which reduces more directly to the
>> > familar Fermat and Snell.
>>
>> No, I have not.
>
> ?
Geodesics have fixed end-points.
>> The Euler-Lagrange Equations only specify when a
>> stationary condition occurs.
>
> What do you mean by "only"? What else do you need?
Given a functon f(x), to find the minimum of this function, you solve
for x of the following.
df(x)/dx = 0
x only shows a stationary condition. It is still up to your dilligence
to show
d^2f(x)/dx^2 < 0
In doing so, you can then claim a minimum of f(x). This is as basic as
you can get.
>> It is still up to you to argue for a
>> least action with this stationary condition. To argue a minimal
>> action, you must find a stationary condition first.
>> The fixed points approach also works for the least action.
>
> What do you need the *minimal* action for? The difference between
> stationary and minimal lies in the global structure of spacetime and
> nothing you've said so far had anything to do with it.
To repeat, the Calculus of Variations only deliver the stationary
condition to you. It is still up to you to show it is indeed a
minimum.
>> >> The results are almost the same for Schwarzschild metric
>> >> but are definitely different for the general case. Using the same
>> >> mathematical method, principle of least time does not yield the same
>> >> correct Mercury's orbital motion as the pinciple of stationary
>> >> spacetime.
>> >
>> > If the variation is done correctly, both cases should yield the same
>> > result - they are mathematically equivalent (for systems of constant
>> > Hamiltonian). The Maupertuis variation process is different than the
>> > standard "fix endpoints and endtimes" Hamilton routine - perhaps that's
>> > where the discrepancy came from? I haven't looked into this in detail
>> > though.
>>
>> Please do. You seem to be the only one here who can understand what I
>> am talking about.
>
> I cannot add anything to it - there can be no contradiction between
> equivalent definitions of geodesics.
If you have no comments to my argument, I have none as well. <shrug>
>> Since the Euler-Lagrange Equations are very sensitive to the choice of
>> Lagrangians. In the general case, the Lagrangians serving as the
>> densities that minimize a segment of spacetime and an elapsed amount of
>> time do not yield the same result at the quintessential scale (quoting
>> from Dr. Roberts). Why don't try it yourself?
>
> I cannot parse the last paragraph. It would be better if you used
> standard terminology. What Lagrangians do not yield the same result?
> Obviously two random Lagrangians won't yield the same result - why is
> it such a surprise?
It sounds like you do not understand the Calculus of Variations fully
and the roles Largangians play. The only advice to you is to go and
study it thoroughly. True me. It is one of the easiest subjects in
the many treatises of mathematics.
JanPB
> "JanPB" <fil...@gmail.com> wrote in message
> news:1144907101.5...@i39g2000cwa.googlegroups.com...
>
> >> >> well proven principle is the principle of least time or action as you
> >> >> have pointed out where every event taking place must obey the least
> >> >> amount of elapsed time. The example is the Snell's Law. I went
> >> >> through a series of discussions with Dr. Roberts, Dr. Carlip, and Mr.
> >> >> Most a while back on this subject. They all suggested if calculus of
> >> >> variations is to be taken, the segment of spacetime must be stationary.
> >> >> Of course, they all failed to explain photons which always travel with
> >> >> a stationary spacetime of zero. If you subscribe to the principle of
> >> >> least time, you must use a slightly different Lagrangian for the
> >> >> geodesics.
> >> >
> >> > It looks to me like a confusion between two principles of stationary
> >> > action: Hamilton's and Maupertuis'. The first varies Lagrangian with
> >> > fixed endpoints and endtimes, the second varies reduced action (the "p
> >> > q-dot") with fixed endpoints and fixed Hamiltonian (this forces the
> >> > endtimes to vary). It is the latter which reduces more directly to the
> >> > familar Fermat and Snell.
> >>
> >> No, I have not.
> >
> > ?
>
> Geodesics have fixed end-points.
I meant your answer didn't fit grammatically with anything that went on
before. I said that Maupertuis' principle lead to Snell's law and the
like, and you answered: "No, I have not".
> >> The Euler-Lagrange Equations only specify when a
> >> stationary condition occurs.
> >
> > What do you mean by "only"? What else do you need?
>
> Given a functon f(x), to find the minimum of this function, you solve
> for x of the following.
>
> df(x)/dx = 0
>
> x only shows a stationary condition. It is still up to your dilligence
> to show
>
> d^2f(x)/dx^2 < 0
>
> In doing so, you can then claim a minimum of f(x). This is as basic as
> you can get.
This is true except it's not relevant to this situation:
1. The stuff you wrote above is about finding minimum of a function of
*one variable*.
2. Variational calculus OTOH uses functions of *infinitely many*
variables which on top of that come from a manifold that's not
necessarily linear. The second derivative criterion you wrote doesn't
apply.
3. Which doesn't matter anyway because geodesics - and motion
trajectories in mechanics in general - are not paths of minimal action
but paths of *extremal* (aka. stationary) action (these paths are
called "extremals" for a reason). That's why Euler-Lagrange and/or
Hamilton's principle, etc., are sufficient to describe the motion. For
example, in Newtonian mechanics the Euler-Lagrange equation basically
says "F=ma as far as applied forces are concerned".
(Of course there are situations in which you really want to know
whether certain path actually minimises certain integral but these are
specific questions regarding specific action values like the classic
brachistochrone problem. Then you need a much more intricate criterion
- e.g. the necessary condition for min/max due to Weierstrass - than
the basic 2nd derivative test.)
> >> It is still up to you to argue for a
> >> least action with this stationary condition. To argue a minimal
> >> action, you must find a stationary condition first.
> >> The fixed points approach also works for the least action.
> >
> > What do you need the *minimal* action for? The difference between
> > stationary and minimal lies in the global structure of spacetime and
> > nothing you've said so far had anything to do with it.
>
> To repeat, the Calculus of Variations only deliver the stationary
> condition to you.
That's all you need to determine motion in general.
> It is still up to you to show it is indeed a minimum.
No, that's unnecessary (except in special cases).
> >> Since the Euler-Lagrange Equations are very sensitive to the choice of
> >> Lagrangians. In the general case, the Lagrangians serving as the
> >> densities that minimize a segment of spacetime and an elapsed amount of
> >> time do not yield the same result at the quintessential scale (quoting
> >> from Dr. Roberts). Why don't try it yourself?
> >
> > I cannot parse the last paragraph. It would be better if you used
> > standard terminology. What Lagrangians do not yield the same result?
> > Obviously two random Lagrangians won't yield the same result - why is
> > it such a surprise?
>
> It sounds like you do not understand the Calculus of Variations fully
> and the roles Largangians play. The only advice to you is to go and
> study it thoroughly. True me. It is one of the easiest subjects in
> the many treatises of mathematics.
I know it backwards and forwards but the way you write about it makes
it hard to follow. Obviously different Lagrangians yield different
results. But you'd have to provide details of the integrations Tom was
telling you about if you want people to comment on it.
--
Jan Bielawski
JanPB
> "JanPB" <fil...@gmail.com> wrote in message
> news:1144906012.4...@z34g2000cwc.googlegroups.com...
>
> >> The differential geometric approach of GR is the legacy of Grossmann's
> >> work.
> >
> > Well, yes and no. I mean Grossmann or no Grossmann, differential
> > geometry is the language of GR and you cannot bypass it in any way -
> > it's really the essence of the equivalence principle.
>
> Grossmann's work led to dead end as Riemann tried to do almost half a
> century earlier. The language of GR does not have to be differential
> geometry as Grossmann tried to impose it to be.
Nonsense.
> The Principle of Equivalence does not show any useful purpose.
Nonsense.
> The field equations can
> only be derived after the Lagrangian leading to the Einstein-Hilbert
> Action is materialized.
Nonsense.
> With the solution to the field equations
> presetned as the metric, solving the geodesics using Calculus of
> Variations is much simpler.
Well, of course, given a solution it's much easier to derive the
motion. That's deep :-)
> This is the exact point which Dr. Draper
> is trying to make referring to Dr. Hartle's work.
>
> >> That did not get anywhere until Hilbert used the calculus of
> >> variations to find the field equations.
> >
> > Just a historical note - Hilbert got his equations *after* Einstein.
> > The somewhat embarrassing (to Hilbert) smoking gun regarding this
> > matter has been found few years ago. Hilbert actually *changed* the
> > galley proofs of his article after he saw Einstein's equations but *did
> > not change the original date* on those proofs. Very below the belt.
>
> It is astronomically improbable (again quoting from Dr. Roberts) that
> two persons within a couple weeks of each other would have conjured up
> the same Lagrangian leading to the Einstein-Hilbert Action. This was
> achieved without proper derivation of this Lagrangian. You can say
> Hilbert pulled it out of his *ss which Einstein eagerly licked it up.
Any reason why you are so stuck on the Lagrangian derivation? Just
curious.
> Your belief of the historical account is totally biased. Stachel's
> job, thus his career, depends very much on glorifying Eisntein to no
> end. In doing so, he seems to be willing to stretch the truth. The
> forensic evidence is embedded in the mathematics involved.
That too. But the changes are indefensible. It all points to the
conclusion above.
> To
> blatantly alter the history disregarding what mathematical evidence is
> as you have said "hitting below the belt".
The changes are all there - what do you mean by "blatantly alter the
history"? You mean somebody broke into the archives few decades ago and
forged Hilbert's handwriting in order to discredit him and elevate
Einstein? Who was it? Hilbert's disgruntled servant? A janitor at the
archive who was bored one day and decided to mess with Stachel's head
just for fun? George W. Bush? Space aliens? Who?
> >> Speaking of
> >> Hilbert's Lagrangian that give rise to the field equations, it does not
> >> satisfy any physically meaningful action.
> >
> > What do you mean by "satisfying an action"?
>
> I don't understand what any physically meaningful action this
> Einstein-Hilbert Action serves. If you do, perhaps you can enlighten
> me.
Even in standard classical mechanics action is not particularly
intuitive: integrated excess of the kinetic energy over the potential -
what does this mean? The sum of the two energies makes much more
intuitive sense.
> >> Gravity is not caused by the
> >> curvature in spacetime as commonly believed, but gravity is caused
> >> solely by gravitational time dilation. Without gravitational time
> >> dilation, a curvature in space does not yield gravitation as Riemann
> >> had discovered. Gravitational time dilation is enough to explain
> >> gravitation.
> >
> > Not all of gravitation.
>
> So, how many types of gravitation do you know of? I only know of one.
>
> >> Adding an irrelavant condition such as the curvature of
> >> space does not bode very well to argue for a stationary or a least
> >> amount of any action.
> >
> > So why is there spatial curvature in, say, the Schwarzschild metric?
>
> Try to connect the dots between a bogus Lagrangian and the solutions to
> field equations based on this bogus Lagrangian.
You didn't answer my question. Let me ask again: if you claim curvature
of space does not yield gravitation then what does curvature of space
do in the Schwarzschild metric?
--
Jan Bielawski
JanPB
>
> brachistochrone problem. Then you need a much more intricate criterion
> - e.g. the necessary condition for min/max due to Weierstrass - than
> the basic 2nd derivative test.)
I meant the Weierstrass _sufficient_ condition, of course.
--
Jan Bielawski
Koobee Wublee
> I meant your answer didn't fit grammatically with anything that went on
> before. I said that Maupertuis' principle lead to Snell's law and the
> like, and you answered: "No, I have not".
The principle of least time is Snell's Law.
>> >> The Euler-Lagrange Equations only specify when a
>> >> stationary condition occurs.
>> >
>> > What do you mean by "only"? What else do you need?
>>
>> Given a functon f(x), to find the minimum of this function, you solve
>> for x of the following.
>>
>> df(x)/dx = 0
>>
>> x only shows a stationary condition. It is still up to your dilligence
>> to show
>>
>> d^2f(x)/dx^2 < 0
>>
>> In doing so, you can then claim a minimum of f(x). This is as basic as
>> you can get.
>
> This is true except it's not relevant to this situation:
You are wrong. It is still relevant.
> 1. The stuff you wrote above is about finding minimum of a function of
> *one variable*.
Ever heard of partial differential derivatives?
> 2. Variational calculus OTOH uses functions of *infinitely many*
> variables which on top of that come from a manifold that's not
> necessarily linear. The second derivative criterion you wrote doesn't
> apply.
Apparently, you don't understand what a Lagrangian is and the action
this Largrangian is related to. <shrug>
The Lagrangian is not what you take the 2nd derivative to find the
curvature at the stationary point. For example, the elapsed time is
described as
delta T = integral of (ds / v)
Since (v = ds/dt), you get
delta T = integral of (dt) = integral( L dt)
Where the Lagrangian is just (1).
> 3. Which doesn't matter anyway because geodesics - and motion
> trajectories in mechanics in general - are not paths of minimal action
> but paths of *extremal* (aka. stationary) action (these paths are
> called "extremals" for a reason). That's why Euler-Lagrange and/or
> Hamilton's principle, etc., are sufficient to describe the motion. For
> example, in Newtonian mechanics the Euler-Lagrange equation basically
> says "F=ma as far as applied forces are concerned".
Again, your mechanics fails to describe the geodesics for photons.
This should sound an alarm, but apparently you choose to ignore it.
> (Of course there are situations in which you really want to know
> whether certain path actually minimises certain integral but these are
> specific questions regarding specific action values like the classic
> brachistochrone problem. Then you need a much more intricate criterion
> - e.g. the necessary condition for min/max due to Weierstrass - than
> the basic 2nd derivative test.)
With 2 variables, try using the determinants. Everything else is still
the same.
>> >> It is still up to you to argue for a
>> >> least action with this stationary condition. To argue a minimal
>> >> action, you must find a stationary condition first.
>> >> The fixed points approach also works for the least action.
>> >
>> > What do you need the *minimal* action for? The difference between
>> > stationary and minimal lies in the global structure of spacetime and
>> > nothing you've said so far had anything to do with it.
>>
>> To repeat, the Calculus of Variations only deliver the stationary
>> condition to you.
>
> That's all you need to determine motion in general.
>
>> It is still up to you to show it is indeed a minimum.
>
> No, that's unnecessary (except in special cases).
There is no known event that follows a stationary action. On the other
hand, the principle of least time is responsible for most of the laws
of physics we know including (f = m a), (Torque = I d^2w/d^2t), Snell's
Law, geodesics, etc. Your two simple sentenses are just nonsense.
>> >> Since the Euler-Lagrange Equations are very sensitive to the choice of
>> >> Lagrangians. In the general case, the Lagrangians serving as the
>> >> densities that minimize a segment of spacetime and an elapsed amount of
>> >> time do not yield the same result at the quintessential scale (quoting
>> >> from Dr. Roberts). Why don't try it yourself?
>> >
>> > I cannot parse the last paragraph. It would be better if you used
>> > standard terminology. What Lagrangians do not yield the same result?
>> > Obviously two random Lagrangians won't yield the same result - why is
>> > it such a surprise?
>>
>> It sounds like you do not understand the Calculus of Variations fully
>> and the roles Largangians play. The only advice to you is to go and
>> study it thoroughly. True me. It is one of the easiest subjects in
>> the many treatises of mathematics.
>
> I know it backwards and forwards but the way you write about it makes
> it hard to follow. Obviously different Lagrangians yield different
> results.
That is my point. Euler-Lagrange Equations are very sensitive to the
choice of Lagrangian. Just how difficult is it to understand that?
Any slight variations on the Lagrangian would lead to different result.
So, when Hilbert pulled one out of nowhere, you cannot say it is valid
(again quoting from Dr. Roberts) whithout justifying if it is derived
from well known qualified sources. If you do not question where a
Lagrangian comes from, you are embracing alchemy and not physics.
There is a difference between the disciplines of alchemy and physics.
> But you'd have to provide details of the integrations Tom was
> telling you about if you want people to comment on it.
You lost me on this. What integrations are you talking about? The
operation of integration is mechanical. Once you set up a rule (or a
procedure) to do so, it is just a matter of followig instructions.
Koobee Wublee
>> Grossmann's work led to dead end as Riemann tried to do almost half a
>> century earlier. The language of GR does not have to be differential
>> geometry as Grossmann tried to impose it to be.
>
> Nonsense.
>
>> The Principle of Equivalence does not show any useful purpose.
>
> Nonsense.
>
>> The field equations can
>> only be derived after the Lagrangian leading to the Einstein-Hilbert
>> Action is materialized.
>
> Nonsense.
I still maintain the following points.
** Grossmann's work led to dead end as Riemann tried to do almost half
a century earlier. The language of GR does not have to be differential
geometry as Grossmann tried to impose it to be.
** The Principle of Equivalence does not show any useful purpose.
** The field equations can only be derived after the Lagrangian
leading to the Einstein-Hilbert Action is materialized.
>> With the solution to the field equations
>> presetned as the metric, solving the geodesics using Calculus of
>> Variations is much simpler.
>
> Well, of course, given a solution it's much easier to derive the
> motion. That's deep :-)
Well, you can also derive the goedesic equations using the general
metric.
> Any reason why you are so stuck on the Lagrangian derivation? Just
> curious.
Lagrangian is the density of an action you are trying to find a
stationary condition to. You'd better justify the reason for the
validity to find a stationary condition of this action. Also, the
Euler-Lagrange Equations are very sensitive to the choice of
Lagrangian. You'd better derive your Lagrangian instead of patching it
together like the Monster created by Dr. Frankenstein.
>> Your belief of the historical account is totally biased. Stachel's
>> job, thus his career, depends very much on glorifying Eisntein to no
>> end. In doing so, he seems to be willing to stretch the truth. The
>> forensic evidence is embedded in the mathematics involved.
>
> That too. But the changes are indefensible. It all points to the
> conclusion above.
>
>> To
>> blatantly alter the history disregarding what mathematical evidence is
>> as you have said "hitting below the belt".
>
> The changes are all there - what do you mean by "blatantly alter the
> history"? You mean somebody broke into the archives few decades ago and
> forged Hilbert's handwriting in order to discredit him and elevate
> Einstein? Who was it? Hilbert's disgruntled servant? A janitor at the
> archive who was bored one day and decided to mess with Stachel's head
> just for fun? George W. Bush? Space aliens? Who?
You just make yourself a suspect to mutilate a historic document.
>> >> Speaking of
>> >> Hilbert's Lagrangian that give rise to the field equations, it does not
>> >> satisfy any physically meaningful action.
>> >
>> > What do you mean by "satisfying an action"?
>>
>> I don't understand what any physically meaningful action this
>> Einstein-Hilbert Action serves. If you do, perhaps you can enlighten
>> me.
>
> Even in standard classical mechanics action is not particularly
> intuitive: integrated excess of the kinetic energy over the potential -
> what does this mean? The sum of the two energies makes much more
> intuitive sense.
You are still talking nonsense.
>> Try to connect the dots between a bogus Lagrangian and the solutions to
>> field equations based on this bogus Lagrangian.
>
> You didn't answer my question. Let me ask again: if you claim curvature
> of space does not yield gravitation then what does curvature of space
> do in the Schwarzschild metric?
The fault lies in the choice of Lagrangian. Therefore, the curvature
in space resulted in the Schwarzschild metric is bogus. The curvature
of space in the Schwarzschild metric does not affect anything except
adding a greater angle of defelction to a photon, and possibly
Mercury's orbital anomaly ( I have not worked out the metric similar to
Schwarzschild with only the gravitational time dilation part and
without the curvature in space).
JanPB
> "JanPB" <fil...@gmail.com> wrote in message
> news:1145064495....@e56g2000cwe.googlegroups.com...
>
> > I meant your answer didn't fit grammatically with anything that went on
> > before. I said that Maupertuis' principle lead to Snell's law and the
> > like, and you answered: "No, I have not".
>
> The principle of least time is Snell's Law.
It's not.
> >> >> The Euler-Lagrange Equations only specify when a
> >> >> stationary condition occurs.
> >> >
> >> > What do you mean by "only"? What else do you need?
> >>
> >> Given a functon f(x), to find the minimum of this function, you solve
> >> for x of the following.
> >>
> >> df(x)/dx = 0
> >>
> >> x only shows a stationary condition. It is still up to your dilligence
> >> to show
> >>
> >> d^2f(x)/dx^2 < 0
> >>
> >> In doing so, you can then claim a minimum of f(x). This is as basic as
> >> you can get.
> >
> > This is true except it's not relevant to this situation:
>
> You are wrong. It is still relevant.
No, it's not. You don't need the minimum to compute motion. Have you
ever read a book on classical mechanics?
> > 1. The stuff you wrote above is about finding minimum of a function of
> > *one variable*.
>
> Ever heard of partial differential derivatives?
And how is this an answer to my objection? The point is what you wrote
above quoting the undergrad 2nd derivative test does not apply to
variational calculus.
> > 2. Variational calculus OTOH uses functions of *infinitely many*
> > variables which on top of that come from a manifold that's not
> > necessarily linear. The second derivative criterion you wrote doesn't
> > apply.
>
> Apparently, you don't understand what a Lagrangian is and the action
> this Largrangian is related to. <shrug>
So you claim that action is a function of single variable for which a
simple 2nd derivative test is applicable.
I'll tell you what. Why don't we just stop this thread here? It's
obvious you have no idea what you are talking about and it's simply not
feasible for me to teach you physics over the Internet. My advice for
you would be to learn the basics first.
--
Jan Bielawski
JanPB
> "JanPB" <fil...@gmail.com> wrote in message
> news:1145065821.4...@e56g2000cwe.googlegroups.com...
>
> >> Grossmann's work led to dead end as Riemann tried to do almost half a
> >> century earlier. The language of GR does not have to be differential
> >> geometry as Grossmann tried to impose it to be.
> >
> > Nonsense.
> >
> >> The Principle of Equivalence does not show any useful purpose.
> >
> > Nonsense.
> >
> >> The field equations can
> >> only be derived after the Lagrangian leading to the Einstein-Hilbert
> >> Action is materialized.
> >
> > Nonsense.
>
> I still maintain the following points.
>
> ** Grossmann's work led to dead end as Riemann tried to do almost half
> a century earlier. The language of GR does not have to be differential
> geometry as Grossmann tried to impose it to be.
>
> ** The Principle of Equivalence does not show any useful purpose.
>
> ** The field equations can only be derived after the Lagrangian
> leading to the Einstein-Hilbert Action is materialized.
Yes, I heard you first time around and there is no need to repeat it.
It's still incorrect.
> >> With the solution to the field equations
> >> presetned as the metric, solving the geodesics using Calculus of
> >> Variations is much simpler.
> >
> > Well, of course, given a solution it's much easier to derive the
> > motion. That's deep :-)
>
> Well, you can also derive the goedesic equations using the general
> metric.
That wasn't the point.
> > Any reason why you are so stuck on the Lagrangian derivation? Just
> > curious.
>
> Lagrangian is the density of an action you are trying to find a
> stationary condition to. You'd better justify the reason for the
> validity to find a stationary condition of this action. Also, the
> Euler-Lagrange Equations are very sensitive to the choice of
> Lagrangian. You'd better derive your Lagrangian instead of patching it
> together like the Monster created by Dr. Frankenstein.
And who defines what constitutes "derivation of a Lagrangian"? You?
> >> Your belief of the historical account is totally biased. Stachel's
> >> job, thus his career, depends very much on glorifying Eisntein to no
> >> end. In doing so, he seems to be willing to stretch the truth. The
> >> forensic evidence is embedded in the mathematics involved.
> >
> > That too. But the changes are indefensible. It all points to the
> > conclusion above.
> >
> >> To
> >> blatantly alter the history disregarding what mathematical evidence is
> >> as you have said "hitting below the belt".
> >
> > The changes are all there - what do you mean by "blatantly alter the
> > history"? You mean somebody broke into the archives few decades ago and
> > forged Hilbert's handwriting in order to discredit him and elevate
> > Einstein? Who was it? Hilbert's disgruntled servant? A janitor at the
> > archive who was bored one day and decided to mess with Stachel's head
> > just for fun? George W. Bush? Space aliens? Who?
>
> You just make yourself a suspect to mutilate a historic document.
All your answers are like that - sort of on topic but really not
addressing the issue. I ASKED: what do you mean by "blatantly alter the
history"? In what way exactly is your answer ("You just make yourself a
suspect to mutilate a historic document") relevant to my question? How
can you say history has been "blatantly altered" without addressing it
further? "Oh, yes, all the documents have been altered by Stachel,
oops, sorry old chap, got a train to catch - good bye!"
> >> >> Speaking of
> >> >> Hilbert's Lagrangian that give rise to the field equations, it does not
> >> >> satisfy any physically meaningful action.
> >> >
> >> > What do you mean by "satisfying an action"?
> >>
> >> I don't understand what any physically meaningful action this
> >> Einstein-Hilbert Action serves. If you do, perhaps you can enlighten
> >> me.
> >
> > Even in standard classical mechanics action is not particularly
> > intuitive: integrated excess of the kinetic energy over the potential -
> > what does this mean? The sum of the two energies makes much more
> > intuitive sense.
>
> You are still talking nonsense.
So please explain to us what is so "physically meaningful" (your words)
about the Lagrangian in classical Newtonian mechanics?
> >> Try to connect the dots between a bogus Lagrangian and the solutions to
> >> field equations based on this bogus Lagrangian.
> >
> > You didn't answer my question. Let me ask again: if you claim curvature
> > of space does not yield gravitation then what does curvature of space
> > do in the Schwarzschild metric?
>
> The fault lies in the choice of Lagrangian.
What fault?
> Therefore, the curvature
> in space resulted in the Schwarzschild metric is bogus. The curvature
> of space in the Schwarzschild metric does not affect anything except
> adding a greater angle of defelction to a photon, and possibly
> Mercury's orbital anomaly
And it doesn't bother you that the actual Schwarzschild metric matches
observational data?
> ( I have not worked out the metric similar to
> Schwarzschild with only the gravitational time dilation part and
> without the curvature in space).
That should be easy - look up MTW, pp. 505-508 on how to set up
spacetime metrics out of prescribed curvatures in spatial slices piled
up across time. I bet this was attempted countless times before with
the same result (failure to match observations).
--
Jan Bielawski
Bilge
>explaining things like a covariant derivative N different times in N
>different contexts.
The reason I gave that particular example is precisely because
it is an example which illustrates a complete waste of time in
``unlearning'' and relearning, until realizing that the entire
idea was made to appear N times as difficult because it was
made to appear as N different concepts which look vaguely similar.
>There is a reason why the *same* subjects in mechanics are generally
>taught at least three times to physics students: in the introductory
>course, in a 2nd year undergrad course, and in a graduate level course.
>There are different tools brought to bear, but the same *physics* is
>revisited.
With a little improvement in the curriculum, some of the redundancy
could be reduced. In any case, we aren't talking about a hypothetical
case where the physics being taught is the physics inherent in the
theory. We are talking aout a case where the physics is intentionally
being subverted as an expedient to teaching the course.
>One way of thinking about this is that the physics is integrated
>vertically through the curriculum, while the mathematical tools and
>concepts are integrated horizontally.
That's a nice slogan, but it doesn't really mean anything.
>This encourages skill at synthesis as well as a deeper physical
>intuition, which are always hallmarks of an excellent physical mind.
Personally, I think ``deeper thought'' occurs in _spite_ of the
way a physics curriculum is typically designed, not because of it.
For example, the classic ``dilemna'' of ``how can light be a particle
_and_ a wave - not to mention a wave without a medium - only arises
because the concept of ``lightwaves'' was intoduced in the first place and
then reinforced using examples like water waves in ripple tanks. The
entire dilemna should never come up, since it was artificially created as
an artifact of ``simplifying'' the initial presentation.
Bilge
>news:slrne3scj3...@radioactivex.lebesque-al.net...
>
>> >If anyone promotes the principle of least action to solve the geodesic
>> >equations, it will be the end of GR.
>>
>> In other words, you believe it is impossile to determine that
>> a geodesic on a sphere is a great circle? The procedure is
>> _exactly_ the same as finding a geodesic in general relativity.
>
>Calculus of Variations fails to determines the geodesics for photons
>based on minimal traversed spacetime.
Since ``minimal traversed spacetime'' is a non-sequitur, I would
expect that.
>However, properly interpreted,
>Calculus of Variations should have no problems to arrive at the
>geodesic equations based on minimal elapsed coordinate time.
Are you stoned or just stupid? The point of variational calculus is
to find curves of _extremal_ length, not just the ones with minimal
length. Sheesh.
>The procedures are not the same.
Sure they are. Just write down s = \integral sqrt(g_uv dx^u dx^v)
without assuming anything about g_uv or the numer of dimensions.
After obtaining a general result, plug in different metrics.
>It is fudged to be the same. <shrug>
In other words, you are the lone genius who discovered that general
relativity is wrong because general relativity correctly predicts the
perihelion shift of mercury and your proof consists of being unable to get
the same result that tens of thousands of people have otained over the
last 75 years? Saaay - that really does sound convincing...
>> You have to be as stupid as the day is long. It's a coordinate
>> system, imbecile. Do you really think that the coefficients in
>> dr^2 = (adx)^2 + (bdy)^2 with a = 1cm/10mm and b = 2.54cm/in
>> have physical significance? Sheeesh. How long have you been taxing
>> your brain without figuring this out? It just is not that hard.
>
>I think you are misunderstanding something.
Not unless you are about to tell me that all of your posts were
intended to be a joke that I misunderstood as stupidity.
>I have no idea what you are referring to.
Of course you don't. If you did, you would realize that you stand
a better chance of success at basket weaving than at physics.
>Try to bark up a different tree. <shrug>
>
>> >That was before photons were properly characterized. Since then we
>> >know a photon always travels with a spacetime of zero.
>>
>> Whatever that means.
>
>In another words, you fail to understand the nature of photons.
No, I understand photons just fine and certainly a great deal
better than you do. I'll be perfectly happy to have you try and
prove that I'm wrong at the same time you try and prove that
you know something about lagrangian formalism. Start with relativity
and derive electromagnetism.
><shrug>
>
>> >In doing so, it is already a stationary action. So, using the
>> >Euler-Lagrange Equations
>>
>> Go learn something about variational calculus and lagrangians.
>> Your attempt to use the ``power of the Lagrangian Method'' amounts
>> using the lagrangian as it used when introducing it to college sophomores,
>> except that college sophomores will have probably have been given
>> some prepratory material in the way of variational calculus to insure
>> they don't end up with the same misconceptions you have.
>
>It sounds like you need to learn with the sophomores. <shrug>
I'm still waiting for you to demonstrate your proficiency by solving
the previous simple examples you've been given. Basically, you are
all bullshit, no action.
>> Why are you trying to explain something related to general relativity?
>> You've een working on the perihelion of mercury for what, a year now?
>> After a year, you are still convinced that everyone else used general
>> relativitity incorrectly to get the right answer while you used general
>> relativity correctly to get the wrong answer? That kind of logic alone
>> ought to suggest to anyone that your sole area of expertise is
>> overestimating your expertise.
>
>You need to back up your comments with mathematics.
Sure. I've previously given you the terms under which we can
ojectively determine who is doing the babbling. Pick any topic
in physics and we'll arrive at some question for which both of
us will present solutions along with the physics which goes into
each step of the solution. So far, you have evaded any response
to that offer.
>Without it, you are just babbling. <shrug>
I'm perfectly willing to let who is babbling be settled by
comparing explanations of physical phenomena.
PD
Bilge wrote:
> PD:
> >I understand your point. However, I think there is in fact value in
> >explaining things like a covariant derivative N different times in N
> >different contexts.
>
> The reason I gave that particular example is precisely because
> it is an example which illustrates a complete waste of time in
> ``unlearning'' and relearning, until realizing that the entire
> idea was made to appear N times as difficult because it was
> made to appear as N different concepts which look vaguely similar.
>
> >There is a reason why the *same* subjects in mechanics are generally
> >taught at least three times to physics students: in the introductory
> >course, in a 2nd year undergrad course, and in a graduate level course.
> >There are different tools brought to bear, but the same *physics* is
> >revisited.
>
> With a little improvement in the curriculum, some of the redundancy
> could be reduced.
I'm not sure that's a worthy goal. I think the redundancy is necessary.
Students don't really get a good grip on a concept until they've walked
around it three or four times, like a dog curling up for a nap.
> In any case, we aren't talking about a hypothetical
> case where the physics being taught is the physics inherent in the
> theory. We are talking aout a case where the physics is intentionally
> being subverted as an expedient to teaching the course.
I don't know what you mean here.
>
> >One way of thinking about this is that the physics is integrated
> >vertically through the curriculum, while the mathematical tools and
> >concepts are integrated horizontally.
>
> That's a nice slogan, but it doesn't really mean anything.
Allow me to explain my meaning. Vertical integration means the same
physics concepts are revisited time and time again, but with different
mathematical apparatus and depth of application each time. Horizontal
integration means that the same mathematical tool set is applied to
different physical conceptual frameworks; the Fourier transform, for
example.
>
> >This encourages skill at synthesis as well as a deeper physical
> >intuition, which are always hallmarks of an excellent physical mind.
>
> Personally, I think ``deeper thought'' occurs in _spite_ of the
> way a physics curriculum is typically designed, not because of it.
>
> For example, the classic ``dilemna'' of ``how can light be a particle
> _and_ a wave - not to mention a wave without a medium - only arises
> because the concept of ``lightwaves'' was intoduced in the first place and
> then reinforced using examples like water waves in ripple tanks. The
> entire dilemna should never come up, since it was artificially created as
> an artifact of ``simplifying'' the initial presentation.
Here I agree with you, but I think that fixing it can be accomplished
without sacrificing simplicity. It is sufficient, for example, to
introduce particle-wave duality the same way that Feynman was careful
to do: pointing out that electrons or photons are not "like" things
they have seen before, and that they are completely different animals
than the things they have seen in ripple tanks or pool tables.
PD
Ken S. Tucker
PD wrote:
> Hartle has written a paper in a recent AJP (Vol 74, No. 1, p. 14),
> advocating teaching GR a whole lot earlier than it presently is in most
> places.
>
> to teaching a subject in physics is to:
> a) introduce the necessary mathematical tools
> b) motivate and explain the basic (field) equations
> c) solve the (field) equations in interesting circumstances
> d) apply the solutions to make predictions and compare with observation
> and experiment
>
> This strict deductive approach is useful for producing an in-depth and
> "rigorous" understanding of things. However, it also has the
> disadvantage of discouraging application of physical good sense and
> visualization. He also points out that we don't do that in an
> introductory survey course; we don't need to be able to do surface
> integrals and Gauss's law to look at electric field configurations.
>
> differential geometry, instead focusing on the metric and the fact that
> a geodesic is stationary with respect to some variation of the path
> between two spacetime endpoints A and B. The latter looks very much
> like the principle of least action, with the proper time taking the
> role of the lagrangian.
>
> Using this principle and starting with the Schwarzchild metric, he
> shows that one can very quickly come up with an "effective" potential
> for orbits, complete with the relativistic term. From that, he quickly
> gets the inner diameter of the accretion disk, as well as the
> perihelion advance for (pseudo-)closed orbits.
>
> This approach looks good to me, and it would be good to try to do the
> same thing if possible for quantum mechanics and other difficult
> subjects. Anyone up fror writing a book?
>
I can only speak from my own experience, a fella
who averaged B's in an *ontario* Public School.
My interest in relativity became important in Gr.7,
and read all the encyclopedia article's available in
the 60's, but the best was Martin Gardners pocket
book, "Relativity for the Million", that was certainly
superseded by much more sophisicated works in
High School.
My personal breakthough on GR could be done in
an article that explains the Gravitational Red-shift,
as a consequence of Conservation of Energy, and
that is common sense if one accepts, light energy
is proportion to frequency embodied simply by
Qunatum Theory's,
E=h*f
and using,
E=mc^2, (solar energy source)
then GR follows.
The E=h*f equation obligates a departure from
Newton's theory wherein the frequency and relative
rates of time were unaffected by gravitation.
I went on to produce essay on the subject and was
- on that basis - invited to study at the U of T in the
1960's.
Weinberg later on in 1972 wrote that up in his book,
"Grav & Cosmo" on page 84,
(starting with "Incidentally" on that page), well I
didn't think it was Incidental !!!
(note there is no reference to source :-).
Have a look at that article, it requires only Public
School algebra, yet it relates General Relativity to
Quantum Theory using the Principle of Equivalence,
in one page!
Chances are, only about 100 GR reserchers will
ever exist on Earth able to advance GR and only
about a 1000 will be capable of being aware of
that advance. So I'd introduce GR only as an
incremental interesting adjuncture to Newtonian
Physics that is sufficient for 99.999% of kids.
GR ought to be introduced as a 30 minute filler.
I may be wrong, (last time I thought that I was wrong),
during the 60's was a significant democratic movement
to provide equality, and from the standpoint of
General Covariance, which is really the basis of GR,
each person is equally entitled to regard their Frame
of Reference as as valid as anyone one elses, thus
establishing and equating the Principle of Democracy
and the Principle of General Covariance, that may be
possible philosophically.
Regards
Ken S. Tucker
FrediFizzx
news:1145130349.7...@j33g2000cwa.googlegroups.com...
Yep, I think I have seen an alteration of that that derives Planck's
constant from relativity. Relativity and QT are connected, aren't they?
A marriage made in "heaven"; Quantum Vacuum Charge = +,- sqrt(hbar*c) =
QFT. ;-)
FrediFizzx
http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.pdf
or postscript
http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.ps
Koobee Wublee
>> > I meant your answer didn't fit grammatically with anything that went on
>> > before. I said that Maupertuis' principle lead to Snell's law and the
>> > like, and you answered: "No, I have not".
>>
>> The principle of least time is Snell's Law.
>
> It's not.
Do you even know what Snell's Law is?
http://physics.nmt.edu/~raymond/classes/ph13xbook/node36.html
>> >> >> The Euler-Lagrange Equations only specify when a
>> >> >> stationary condition occurs.
>> >> >
>> >> > What do you mean by "only"? What else do you need?
>> >>
>> >> Given a functon f(x), to find the minimum of this function, you solve
>> >> for x of the following.
>> >>
>> >> df(x)/dx = 0
>> >>
>> >> x only shows a stationary condition. It is still up to your dilligence
>> >> to show
>> >>
>> >> d^2f(x)/dx^2 < 0
>> >>
>> >> In doing so, you can then claim a minimum of f(x). This is as basic as
>> >> you can get.
>> >
>> > This is true except it's not relevant to this situation:
>>
>> You are wrong. It is still relevant.
>
> No, it's not. You don't need the minimum to compute motion. Have you
> ever read a book on classical mechanics?
So, moving from point A to point B, if you don't need a minimum time
elapsed, then you can have an infinite number of ways to do so. The
laws of physics exist because moving from point A to point B only
allows one path.
>> > 1. The stuff you wrote above is about finding minimum of a function of
>> > *one variable*.
>>
>> Ever heard of partial differential derivatives?
>
> And how is this an answer to my objection?
You can apply the partial derivatives for each variable to find the
extremum.
> The point is what you wrote
> above quoting the undergrad 2nd derivative test does not apply to
> variational calculus.
I never said the 2nd derivative test applies to the calculus of
variations. I said the calculus of variations only delivers the
extremum. It is still up to your dilligence to argue for a minimal
condition.
>> > 2. Variational calculus OTOH uses functions of *infinitely many*
>> > variables which on top of that come from a manifold that's not
>> > necessarily linear. The second derivative criterion you wrote doesn't
>> > apply.
>>
>> Apparently, you don't understand what a Lagrangian is and the action
>> this Largrangian is related to. <shrug>
>
> So you claim that action is a function of single variable for which a
> simple 2nd derivative test is applicable.
No.
> I'll tell you what. Why don't we just stop this thread here?
Why? Our discussions have not ended.
> It's
> obvious you have no idea what you are talking about and it's simply not
> feasible for me to teach you physics over the Internet. My advice for
> you would be to learn the basics first.
I have heard that before many times over. How do you know what you
have learned is anything valid (agian quoting from Dr. Roberts) if you
shut your eyes on opposing arguments. At least, I have reached out to
understand what GR is all about.
Koobee Wublee
>> I still maintain the following points.
>>
>> ** Grossmann's work led to dead end as Riemann tried to do almost half
>> a century earlier. The language of GR does not have to be differential
>> geometry as Grossmann tried to impose it to be.
>>
>> ** The Principle of Equivalence does not show any useful purpose.
>>
>> ** The field equations can only be derived after the Lagrangian
>> leading to the Einstein-Hilbert Action is materialized.
>
> Yes, I heard you first time around and there is no need to repeat it.
> It's still incorrect.
What is wrong? And how so?
>> >> With the solution to the field equations
>> >> presetned as the metric, solving the geodesics using Calculus of
>> >> Variations is much simpler.
>> >
>> > Well, of course, given a solution it's much easier to derive the
>> > motion. That's deep :-)
>>
>> Well, you can also derive the goedesic equations using the general
>> metric.
>
> That wasn't the point.
Then, what is your point?
>> > Any reason why you are so stuck on the Lagrangian derivation? Just
>> > curious.
>>
>> Lagrangian is the density of an action you are trying to find a
>> stationary condition to. You'd better justify the reason for the
>> validity to find a stationary condition of this action. Also, the
>> Euler-Lagrange Equations are very sensitive to the choice of
>> Lagrangian. You'd better derive your Lagrangian instead of patching it
>> together like the Monster created by Dr. Frankenstein.
>
> And who defines what constitutes "derivation of a Lagrangian"? You?
Not just me. This is what physics is all about. You need to justify
every single equation without any BS. If not, you are just an
alchemist.
>> >> Your belief of the historical account is totally biased. Stachel's
>> >> job, thus his career, depends very much on glorifying Eisntein to no
>> >> end. In doing so, he seems to be willing to stretch the truth. The
>> >> forensic evidence is embedded in the mathematics involved.
>> >
>> > That too. But the changes are indefensible. It all points to the
>> > conclusion above.
>> >
>> >> To
>> >> blatantly alter the history disregarding what mathematical evidence is
>> >> as you have said "hitting below the belt".
>> >
>> > The changes are all there - what do you mean by "blatantly alter the
>> > history"? You mean somebody broke into the archives few decades ago and
>> > forged Hilbert's handwriting in order to discredit him and elevate
>> > Einstein? Who was it? Hilbert's disgruntled servant? A janitor at the
>> > archive who was bored one day and decided to mess with Stachel's head
>> > just for fun? George W. Bush? Space aliens? Who?
>>
>> You just make yourself a suspect to mutilate a historic document.
>
> All your answers are like that - sort of on topic but really not
> addressing the issue. I ASKED: what do you mean by "blatantly alter the
> history"? In what way exactly is your answer ("You just make yourself a
> suspect to mutilate a historic document") relevant to my question? How
> can you say history has been "blatantly altered" without addressing it
> further? "Oh, yes, all the documents have been altered by Stachel,
> oops, sorry old chap, got a train to catch - good bye!"
I don't accuse Stachel of mutilating the document. However, I am not
surprised if he is very happy that document is mutilated. This way he
can justify how Hilbert copied Einstein's field equations. Again,
however, the forensic evidence of the derivations of the field
equations clearly indicates Einstein copied Hilbert. How so you may
ask? I have already answered that in the previous posts in this
thread.
>> >> >> Speaking of
>> >> >> Hilbert's Lagrangian that give rise to the field equations, it does not
>> >> >> satisfy any physically meaningful action.
>> >> >
>> >> > What do you mean by "satisfying an action"?
>> >>
>> >> I don't understand what any physically meaningful action this
>> >> Einstein-Hilbert Action serves. If you do, perhaps you can enlighten
>> >> me.
>> >
>> > Even in standard classical mechanics action is not particularly
>> > intuitive: integrated excess of the kinetic energy over the potential -
>> > what does this mean? The sum of the two energies makes much more
>> > intuitive sense.
>>
>> You are still talking nonsense.
>
> So please explain to us what is so "physically meaningful" (your words)
> about the Lagrangian in classical Newtonian mechanics?
Bingo! How is the classical Lagrangian derived? This is the most
relevant question you have raised. After all, the classical Lagrangian
works for the Newtonian mechanics down to every little detail. Well,
to derive the classical Lagrangian, you have to acknowledge the fact
that geodesics obeys the principle of least time. If you still refuse
to accept that, the classical Lagrangian remains a mystery to you. In
doing so, you paint Lagrangians with a divine mask. That is why you
cannot recognize the BS nature of the Lagrangian that leads to the
field equations. And that is your loss.
>> >> Try to connect the dots between a bogus Lagrangian and the solutions to
>> >> field equations based on this bogus Lagrangian.
>> >
>> > You didn't answer my question. Let me ask again: if you claim curvature
>> > of space does not yield gravitation then what does curvature of space
>> > do in the Schwarzschild metric?
>>
>> The fault lies in the choice of Lagrangian.
>
> What fault?
Let me try to answer your petty question again. The curvature of space
as indicated by the Schwarzschild metric exhibits a fault in the theory
of GR. What fault? Hilbert's Lagrangian is supposed to minimize the
Einstein-Hilbert Action whatever it is. If you cannot answer what this
action is and why the minimum or stationary condition to this action
results in the laws of physics covering this subject, that is a fault
to the theory of GR. A stionary condition should be where there is no
curvature in space.
>> Therefore, the curvature
>> in space resulted in the Schwarzschild metric is bogus. The curvature
>> of space in the Schwarzschild metric does not affect anything except
>> adding a greater angle of defelction to a photon, and possibly
>> Mercury's orbital anomaly
>
> And it doesn't bother you that the actual Schwarzschild metric matches
> observational data?
Not at all, an observation was edited to fit the prediction, and other
preditions were cooked to match the observations. Whould you like to
go through one by one?
Does Einstein's pre-GR prediction of Mercury's orbital anomaly which is
totally nonsense not bother you?
>> ( I have not worked out the metric similar to
>> Schwarzschild with only the gravitational time dilation part and
>> without the curvature in space).
>
> That should be easy - look up MTW, pp. 505-508 on how to set up
> spacetime metrics out of prescribed curvatures in spatial slices piled
> up across time. I bet this was attempted countless times before with
> the same result (failure to match observations).
I don't have that book. However, I am very capable of deriving the
result. Thank you.
Koobee Wublee
> Koobee Wublee:
> >"Bilge" <dub...@radioactivex.lebesque-al.net> wrote in message
> >news:slrne3scj3...@radioactivex.lebesque-al.net...
> >
> >> >If anyone promotes the principle of least action to solve the geodesic
> >> >equations, it will be the end of GR.
> >>
> >> In other words, you believe it is impossile to determine that
> >> a geodesic on a sphere is a great circle? The procedure is
> >> _exactly_ the same as finding a geodesic in general relativity.
> >
> >Calculus of Variations fails to determines the geodesics for photons
> >based on minimal traversed spacetime.
>
> Since ``minimal traversed spacetime'' is a non-sequitur, I would
> expect that.
You are still not making any sense. The spacetime is always zero for
photons. Do you even know what photons are?
> >However, properly interpreted,
> >Calculus of Variations should have no problems to arrive at the
> >geodesic equations based on minimal elapsed coordinate time.
>
> Are you stoned or just stupid? The point of variational calculus is
> to find curves of _extremal_ length, not just the ones with minimal
> length. Sheesh.
I do know the Calculus of Variations only deliver the extremums.
> >The procedures are not the same.
>
> Sure they are. Just write down s = \integral sqrt(g_uv dx^u dx^v)
> without assuming anything about g_uv or the numer of dimensions.
> After obtaining a general result, plug in different metrics.
Apparently, you don't even know how Euler-Lagange Equations are
derived. There are differences between the following two.
** d(@Ls/@(dq^i/ds)/ds = @Ls/@q^i
** d(@Lt/@(dq^i/dt)/dt = @Lt/@q^i
Where
** Ls =/= Lt
> >It is fudged to be the same. <shrug>
>
> In other words, you are the lone genius who discovered that general
> relativity is wrong because general relativity correctly predicts the
> perihelion shift of mercury and your proof consists of being unable to get
> the same result that tens of thousands of people have otained over the
> last 75 years? Saaay - that really does sound convincing...
Being a genius is not what any one would call himself. It has to be
earned. However, I do have discovered the voodoo-ness in mathematics
that leads to predictions able to match observations in GR. You should
not be convinced by anyone. You should try to understand the material
yourself.
> >> You have to be as stupid as the day is long. It's a coordinate
> >> system, imbecile. Do you really think that the coefficients in
> >> dr^2 = (adx)^2 + (bdy)^2 with a = 1cm/10mm and b = 2.54cm/in
> >> have physical significance? Sheeesh. How long have you been taxing
> >> your brain without figuring this out? It just is not that hard.
> >
> >I think you are misunderstanding something.
>
> Not unless you are about to tell me that all of your posts were
> intended to be a joke that I misunderstood as stupidity.
No. I don't play games like you have trying to redirect my post to
alt.troll.
> >I have no idea what you are referring to.
>
> Of course you don't. If you did, you would realize that you stand
> a better chance of success at basket weaving than at physics.
I don't even know how to start with basket weaving. Again, you are
making another mistake. <shrug>
> >Try to bark up a different tree. <shrug>
> >
> >> >That was before photons were properly characterized. Since then we
> >> >know a photon always travels with a spacetime of zero.
> >>
> >> Whatever that means.
> >
> >In another words, you fail to understand the nature of photons.
>
> No, I understand photons just fine and certainly a great deal
> better than you do. I'll be perfectly happy to have you try and
> prove that I'm wrong at the same time you try and prove that
> you know something about lagrangian formalism.
Your comments strongly indicate your failure to even understand the
characters of photons.
> Start with relativity and derive electromagnetism.
That is another chapter of discussion. <shrug>
> ><shrug>
> >
> >> >In doing so, it is already a stationary action. So, using the
> >> >Euler-Lagrange Equations
> >>
> >> Go learn something about variational calculus and lagrangians.
> >> Your attempt to use the ``power of the Lagrangian Method'' amounts
> >> using the lagrangian as it used when introducing it to college sophomores,
> >> except that college sophomores will have probably have been given
> >> some prepratory material in the way of variational calculus to insure
> >> they don't end up with the same misconceptions you have.
> >
> >It sounds like you need to learn with the sophomores. <shrug>
>
> I'm still waiting for you to demonstrate your proficiency by solving
> the previous simple examples you've been given. Basically, you are
> all bullshit, no action.
What simple examples?
> >> Why are you trying to explain something related to general relativity?
> >> You've een working on the perihelion of mercury for what, a year now?
> >> After a year, you are still convinced that everyone else used general
> >> relativitity incorrectly to get the right answer while you used general
> >> relativity correctly to get the wrong answer? That kind of logic alone
> >> ought to suggest to anyone that your sole area of expertise is
> >> overestimating your expertise.
> >
> >You need to back up your comments with mathematics.
>
> Sure. I've previously given you the terms under which we can
> ojectively determine who is doing the babbling. Pick any topic
> in physics and we'll arrive at some question for which both of
> us will present solutions along with the physics which goes into
> each step of the solution. So far, you have evaded any response
> to that offer.
I have seen the contrary. <shrug>
> >Without it, you are just babbling. <shrug>
>
> I'm perfectly willing to let who is babbling be settled by
> comparing explanations of physical phenomena.
Meaning what, troll?
va...@cox.net
Wheeler and Edwin Taylor.
Dirk Van de moortel
"Koobee Wublee" <koobee...@gmail.com> wrote in message news:1145161498....@i39g2000cwa.googlegroups.com...
"The reason why the laws of physics exist":
http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/ReasonLaws.html
Dirk Vdm
Dirk Van de moortel
<va...@cox.net> wrote in message news:1145163328....@j33g2000cwa.googlegroups.com...
> The book has already been written. Exploring Black Holes by John
> Wheeler and Edwin Taylor.
Yes of course, but I'm sure PD meant a ditto book about QM.
Dirk Vdm
Bilge
>"Bilge" <dub...@radioactivex.lebesque-al.net> wrote in message
>news:slrne41hfp...@radioactivex.lebesque-al.net...
>> Koobee Wublee:
>> >"Bilge" <dub...@radioactivex.lebesque-al.net> wrote in message
>> >news:slrne3scj3...@radioactivex.lebesque-al.net...
>> >
>> >> >If anyone promotes the principle of least action to solve the geodesic
>> >> >equations, it will be the end of GR.
>> >>
>> >> In other words, you believe it is impossile to determine that
>> >> a geodesic on a sphere is a great circle? The procedure is
>> >> _exactly_ the same as finding a geodesic in general relativity.
>> >
>> >Calculus of Variations fails to determines the geodesics for photons
>> >based on minimal traversed spacetime.
>>
>> Since ``minimal traversed spacetime'' is a non-sequitur, I would
>> expect that.
>
>You are still not making any sense. The spacetime is always zero for
>photons. Do you even know what photons are?
Photons aren't the issue. Your non-sensical personalized terminology
is the the issue.
>> >However, properly interpreted,
>> >Calculus of Variations should have no problems to arrive at the
>> >geodesic equations based on minimal elapsed coordinate time.
>>
>> Are you stoned or just stupid? The point of variational calculus is
>> to find curves of _extremal_ length, not just the ones with minimal
>> length. Sheesh.
>
>I do know the Calculus of Variations only deliver the extremums.
Then why did you write what you wrote above?
>> Sure they are. Just write down s = \integral sqrt(g_uv dx^u dx^v)
>> without assuming anything about g_uv or the numer of dimensions.
>> After obtaining a general result, plug in different metrics.
>
>Apparently, you don't even know how Euler-Lagange Equations are
>derived.
Since you had no idea what,
\delta L = (dL/dq)\delta q + (dL/d(d_u q))\delta (d_u q)
the last time I wrote down the variation, obviously it is you who has no
idea how to derive the euler-lagrange equations.
>There are differences between the following two.
>
>** d(@Ls/@(dq^i/ds)/ds = @Ls/@q^i
>** d(@Lt/@(dq^i/dt)/dt = @Lt/@q^i
What is your point? Did you just figure out that varying different
parameters gives you an extremem for for the parameter being varies or
what? The reason that it is so ovious that you know nothing about
this suject (or any other topic in math and physics) is that you
post the most trivial observations and act as though you have discovered
something profound. Except for one thing. You have to get the same physical
result regardless of how you solve the equations. Jesus, you dumb.
[...]
>> In other words, you are the lone genius who discovered that general
>> relativity is wrong because general relativity correctly predicts the
>> perihelion shift of mercury and your proof consists of being unable to get
>> the same result that tens of thousands of people have otained over the
>> last 75 years? Saaay - that really does sound convincing...
>
>Being a genius is not what any one would call himself.
Well, certainly no one else is going to call you a genius. Indeed,
from all of the evidence in your posts, you should be thrilled to
get a consensus of dumabss.
>It has to be
>earned. However, I do have discovered the voodoo-ness in mathematics
>that leads to predictions able to match observations in GR. You should
>not be convinced by anyone. You should try to understand the material
>yourself.
Any time you want to stop evading the opportunity I gave you to
prove which one of understands this material, feel free. I assume
you haven't the cajones to put up and you are too much of loud
mouth hillbilly to shut up.
[...]
>> No, I understand photons just fine and certainly a great deal
>> better than you do. I'll be perfectly happy to have you try and
>> prove that I'm wrong at the same time you try and prove that
>> you know something about lagrangian formalism.
>
>Your comments strongly indicate your failure to even understand the
>characters of photons.
Feel free to prove that instead of evading your chance to do so
as you did in bailing out just below:
>> Start with relativity and derive electromagnetism.
>
>That is another chapter of discussion. <shrug>
OK, then I assume you have no idea that photons have something
to do with electromagnetism. You've proved my point. You are
clueless.
[...]
>> I'm still waiting for you to demonstrate your proficiency by solving
>> the previous simple examples you've been given. Basically, you are
>> all bullshit, no action.
>
>What simple examples?
Well, there is the one that I've given you at least three times and
each time you've evaded it: Given the lagrangian,
L = \psibar(p/ - m)\psi
use noether's theorem to find the consereved current if \psi is a
doublet of states and is invariant under an SU(2) rotation.
Another poster gave you a trivial classical scenario and asked you
to construct the lagrangian and obtain the equations of motion.
You bailed out on that one too.
[...]
>> Sure. I've previously given you the terms under which we can
>> ojectively determine who is doing the babbling. Pick any topic
>> in physics and we'll arrive at some question for which both of
>> us will present solutions along with the physics which goes into
>> each step of the solution. So far, you have evaded any response
>> to that offer.
>
>I have seen the contrary. <shrug>
OK, cite the article in which you accepted that offer and
posted the evidence to which you refer.
>> >Without it, you are just babbling. <shrug>
>>
>> I'm perfectly willing to let who is babbling be settled by
>> comparing explanations of physical phenomena.
>
>Meaning what, troll?
Just what it says. Anytime you wish to demonstrate that I don't
know what I'm talking about, I'll be happy to make the comparison
and even let _you_ decide which branch of physics you think gives
you the best shot to prove it. That way, I'll end up with a
permanent reference to you complete and utter failure to prove
you are anything but an overpressurized windbag and couch potato.
Dirk Van de moortel
"Bilge" <dub...@radioactivex.lebesque-al.net> wrote in message news:slrne448ds...@radioactivex.lebesque-al.net...
> Koobee Wublee, the idiot:
> >"Bilge" <dub...@radioactivex.lebesque-al.net> wrote in message
> >news:slrne41hfp...@radioactivex.lebesque-al.net...
> >> Koobee Wublee:
> >> >"Bilge" <dub...@radioactivex.lebesque-al.net> wrote in message
> >> >news:slrne3scj3...@radioactivex.lebesque-al.net...
> >> >
> >> >> >If anyone promotes the principle of least action to solve the geodesic
> >> >> >equations, it will be the end of GR.
> >> >>
> >> >> In other words, you believe it is impossile to determine that
> >> >> a geodesic on a sphere is a great circle? The procedure is
> >> >> _exactly_ the same as finding a geodesic in general relativity.
> >> >
> >> >Calculus of Variations fails to determines the geodesics for photons
> >> >based on minimal traversed spacetime.
> >>
> >> Since ``minimal traversed spacetime'' is a non-sequitur, I would
> >> expect that.
> >
> >You are still not making any sense. The spacetime is always zero for
> >photons. Do you even know what photons are?
>
> Photons aren't the issue. Your non-sensical personalized terminology
> is the the issue.
Remember, Australopitecus Afarensis personally re-invented
the Lagrangian:
http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/NewLagrangian.html
and the gravitational potential:
http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/NewPotential.html
Dirk Vdm
JanPB
> "JanPB" <fil...@gmail.com> wrote in message
> news:1145083775....@i39g2000cwa.googlegroups.com...
>
> > obvious you have no idea what you are talking about and it's simply not
> > feasible for me to teach you physics over the Internet. My advice for
> > you would be to learn the basics first.
>
> I have heard that before many times over.
No doubt.
> How do you know what you have learned is anything valid
This question tells me more about you than my answer could explain as
the saying goes.
> (agian quoting from Dr. Roberts) if you
> shut your eyes on opposing arguments.
You have no "opposing arguments". Your main arguments are framed almost
exclusively in terms of Lagrangians and action which you keep throwing
around without understanding. If you don't know that Euler-Lagrange is
a condition for extremality and so are the two main variational
principles of mechanics, and insist on applying the 2nd derivative test
there (!), and refuse to accept a correction (easily verifiable) then
we have nothing to discuss.
And no, Snell's law is not Fermat's principle, it's a corollary to it -
just try to apply Snell's law to continuously varying media.
--
Jan Bielawski
Koobee Wublee
>> > It's
>> > obvious you have no idea what you are talking about and it's simply not
>> > feasible for me to teach you physics over the Internet. My advice for
>> > you would be to learn the basics first.
>>
>> I have heard that before many times over.
>
> No doubt.
Yes, and I have all thanks to your (plural) kindly directions.
>> How do you know what you have learned is anything valid
>
> This question tells me more about you than my answer could explain as
> the saying goes.
I would love to read about your profiling of me. Please do. I might
help you if you want to write a biography about me. So, the next
generations would remember me.
>> (agian quoting from Dr. Roberts) if you
>> shut your eyes on opposing arguments.
>
> You have no "opposing arguments". Your main arguments are framed almost
> exclusively in terms of Lagrangians and action which you keep throwing
> around without understanding.
Principle of Least Time is the most powerful principle in physics.
That is why I drilled it to the ground. One must understand that
before attempting to branch out into other disciplines.
> If you don't know that Euler-Lagrange is
> a condition for extremality and so are the two main variational
> principles of mechanics, and insist on applying the 2nd derivative test
> there (!), and refuse to accept a correction (easily verifiable) then
> we have nothing to discuss.
Geodesics describes how an object moves from point A, which is fixed,
to point B, which is also fixed. The Lagangian involved is not what
you want to take the 2nd derivative of to find a true minimum. This
concept is very simple. I don't understand why you are trying very
hard to confuse yourself.
> And no, Snell's law is not Fermat's principle,
This is utterly nonsense. It does not take GR to understand this.
Fermat's Principle is the Principle of Least Time. Snell Law obeys the
Principle of Least Time.
> it's a corollary to it -
> just try to apply Snell's law to continuously varying media.
A beam of light travels through several mediums each with its own value
of the speed of light in the medium (not vacuum) does still obey the
Principle of Least Time and thus the Snell's Law. This also applies to
continuous mediums. This beam of light should also obey the Principle
of Least Time as well as Snell's Law. I still don't understand your
objection to Snell's Law under a continuous medium. This should be
very basic. It does not take GR to understand this as well.
Koobee Wublee
> >You are still not making any sense. The spacetime is always zero for
> >photons. Do you even know what photons are?
>
> Photons aren't the issue. Your non-sensical personalized terminology
> is the the issue.
The spacetime of non-photons is not zero. The spacetime for photons is
zero. I still do not understand your objections. Can you follow
logic?
> >> Are you stoned or just stupid? The point of variational calculus is
> >> to find curves of _extremal_ length, not just the ones with minimal
> >> length. Sheesh.
> >
> >I do know the Calculus of Variations only deliver the extremums.
>
> Then why did you write what you wrote above?
You quoted a small section of something I wrote and interpret it as
whatever evil wish you have. It is not my fault.
> >Apparently, you don't even know how Euler-Lagange Equations are
> >derived.
>
> Since you had no idea what,
>
> \delta L = (dL/dq)\delta q + (dL/d(d_u q))\delta (d_u q)
>
> the last time I wrote down the variation, obviously it is you who has no
> idea how to derive the euler-lagrange equations.
Your terminology using ascii codes is not what I am familiar with. In
fact with very liberal interpretations to whatever garbage you wrote
above, I cannot make out anything intelligible. Again, this should not
be my fault.
> >There are differences between the following two.
> >
> >** d(@Ls/@(dq^i/ds)/ds = @Ls/@q^i
> >** d(@Lt/@(dq^i/dt)/dt = @Lt/@q^i
>
> What is your point? Did you just figure out that varying different
> parameters gives you an extremem for for the parameter being varies or
> what?
My point is that there is a different Lagrangian for a different
parameter you want to find an extremum of.
> The reason that it is so ovious that you know nothing about
> this suject (or any other topic in math and physics) is that you
> post the most trivial observations and act as though you have discovered
> something profound. Except for one thing. You have to get the same physical
> result regardless of how you solve the equations. Jesus, you dumb.
Whatever you want to judge my understanding, it is out of my control.
> [...]
> >> In other words, you are the lone genius who discovered that general
> >> relativity is wrong because general relativity correctly predicts the
> >> perihelion shift of mercury and your proof consists of being unable to get
> >> the same result that tens of thousands of people have otained over the
> >> last 75 years? Saaay - that really does sound convincing...
> >
> >Being a genius is not what any one would call himself.
>
> Well, certainly no one else is going to call you a genius. Indeed,
> from all of the evidence in your posts, you should be thrilled to
> get a consensus of dumabss.
Then, don't call me a genius then. It is no big deal to me. Why do
you make it into a big deal?
> >It has to be
> >earned. However, I do have discovered the voodoo-ness in mathematics
> >that leads to predictions able to match observations in GR. You should
> >not be convinced by anyone. You should try to understand the material
> >yourself.
>
> Any time you want to stop evading the opportunity I gave you to
> prove which one of understands this material, feel free. I assume
> you haven't the cajones to put up and you are too much of loud
> mouth hillbilly to shut up.
I have done so. You just do not accept my logical answers without any
logical criticisms like Dr. Roberts, Dr. Carlip, Mr. Bielawski,
Mr.Most, etc. Your trait is a bigotry.
> >> No, I understand photons just fine and certainly a great deal
> >> better than you do. I'll be perfectly happy to have you try and
> >> prove that I'm wrong at the same time you try and prove that
> >> you know something about lagrangian formalism.
> >
> >Your comments strongly indicate your failure to even understand the
> >characters of photons.
>
> Feel free to prove that instead of evading your chance to do so
> as you did in bailing out just below:
I do not understand your babbling. It is getting late. I don't even
care. My question to you is would I lose sleep over what you wrote
above.
> >> Start with relativity and derive electromagnetism.
> >
> >That is another chapter of discussion. <shrug>
>
> OK, then I assume you have no idea that photons have something
> to do with electromagnetism. You've proved my point. You are
> clueless.
I never said photons have nothing to do with electromagnetism.
> [...]
> >> I'm still waiting for you to demonstrate your proficiency by solving
> >> the previous simple examples you've been given. Basically, you are
> >> all bullshit, no action.
> >
> >What simple examples?
>
> Well, there is the one that I've given you at least three times and
> each time you've evaded it: Given the lagrangian,
>
> L = \psibar(p/ - m)\psi
>
> use noether's theorem to find the consereved current if \psi is a
> doublet of states and is invariant under an SU(2) rotation.
> Another poster gave you a trivial classical scenario and asked you
> to construct the lagrangian and obtain the equations of motion.
> You bailed out on that one too.
I refuse to do homework for you with your belligerent attitude.
> [...]
> >> Sure. I've previously given you the terms under which we can
> >> ojectively determine who is doing the babbling. Pick any topic
> >> in physics and we'll arrive at some question for which both of
> >> us will present solutions along with the physics which goes into
> >> each step of the solution. So far, you have evaded any response
> >> to that offer.
> >
> >I have seen the contrary. <shrug>
>
> OK, cite the article in which you accepted that offer and
> posted the evidence to which you refer.
I don't accept babbling as anything intelligible. Thus, I cannot give
you any articles. Your comments are all babbling. It is only due to
my dilligence to give you the courtesy to understand what you are
babbling. So, consider yourself lucky.
> >> >Without it, you are just babbling. <shrug>
> >>
> >> I'm perfectly willing to let who is babbling be settled by
> >> comparing explanations of physical phenomena.
> >
> >Meaning what, troll?
>
> Just what it says. Anytime you wish to demonstrate that I don't
> know what I'm talking about, I'll be happy to make the comparison
> and even let _you_ decide which branch of physics you think gives
> you the best shot to prove it. That way, I'll end up with a
> permanent reference to you complete and utter failure to prove
> you are anything but an overpressurized windbag and couch potato.
Who is more of a couch potato? Your posting window is much broader
than mine. My opportunity to do so is limited to late at night due to
my work for making a living, my work to keep my growing family running,
and my work to understand more about the subjects I don't know of.
Why do you give up on redirecting my post to alt.troll?
Dirk Van de moortel
"Koobee Wublee" <koobee...@gmail.com> wrote in message news:1145253126....@z34g2000cwc.googlegroups.com...
> "JanPB" <fil...@gmail.com> wrote in message
> news:1145215822.6...@j33g2000cwa.googlegroups.com...
>
> >> > It's
> >> > obvious you have no idea what you are talking about and it's simply not
> >> > feasible for me to teach you physics over the Internet. My advice for
> >> > you would be to learn the basics first.
> >>
> >> I have heard that before many times over.
> >
> > No doubt.
>
> Yes, and I have all thanks to your (plural) kindly directions.
>
> >> How do you know what you have learned is anything valid
> >
> > This question tells me more about you than my answer could explain as
> > the saying goes.
>
> I would love to read about your profiling of me. Please do. I might
> help you if you want to write a biography about me. So, the next
> generations would remember me.
The next generations will remember you as Australopithecus
Afarensis, Scholarly Fungi, Time Traveler, Lordly Amoeba,
Ibn Battuta, Marco Polo, all names for one coward who
proudly declared:
http://groups.google.co.uk/groups?&threadm=V1r09.661180$352.138570@sccrnsc02
| "Scholarly Fungi" <scholar...@yahoo.com> wrote in message
| news:bdq09.28353$Fq6.2...@news2.west.cox.net...
| > It is also unfortunate that most of the folks blindly embracing this
| > holohaux come from the white supremacists. I don't see what this would gain
| > for them other than trying to antagonize the Jews. However, this is
| > history. When I was in my early high school years, I independently came up
| > with what Butz was saying without knowing his existence. Hey, I am very
| > proud of my humble analytical skills.
So, you don't have to worry, do you?
Dirk Vdm
Ken S. Tucker
> > Weinberg later on in 1972 wrote that up in his book,
> > "Grav & Cosmo" on page 84,
> > (starting with "Incidentally" on that page), well I
> > didn't think it was Incidental !!!
> > (note there is no reference to source :-).
> >
> > Have a look at that article, it requires only Public
> > School algebra, yet it relates General Relativity to
> > Quantum Theory using the Principle of Equivalence,
> > in one page!
>
> Yep, I think I have seen an alteration of that that derives Planck's
> constant from relativity. Relativity and QT are connected, aren't they?
Absolutely Fred, it's truly amazing the're practically
the same theory, especially in terms of *action*,
I don't separate them anymore.
Here's a story that I think is particularily well
suited to your working interest in light and photons.
Suppose to start, we're back in the 1800's and
we assume Newtonian physics applies in the universe
and gravity does NOT affect light in any way.
Now I'm going to situate Freddi the astronaut at a
pythagorean radius "r" from the Sun.
(You can pick this up in Weinberg's "Grav & Cosmo"
pg.181, mid page, R=r-GM , GM=1.47 kms for Sun).
Freddi measures the light intensity, from the Sun
at "r" to be "f"
Well then Einstein phones up God and tells him
that light needs to obey the Law of Conservation
of Energy, well God agreed and flicked the GR
switch.
Suddenly Freddi's light intensity meter reading reduced
to "f' " (red-shifted) and he finds he needs to move 1.47 kms
toward the Sun to get the same intensity reading, "f".
(Recall sqrt(g_00) ~ 1 - GM/r ).
So Freddi phones up God, asks "what's up?",
God explains that Einstein kicked up a stink about
light needing to obey the Law of Conservation of
Energy so He set energy proportional to frequency,
and went back to bed, (likely with Mrs. God to make
many new Gods, but I don't like to gossip in groups).
Turns out later some guy named Planck invented
something called Planck's constant denoted "h"
that sets Energy proportional to frequency using,
E=h*f.
Recall frequency can be "N cycles per second",
== N/sec = 1/period, with period =t seconds meaning
E*t = E' *t' = h = h' .
When Freddi descended that 1.47 kms, his Energy
changed from E' to E and the frequency reading on his
intensitymeter changed from f' back to f , but "h"
remained constant.
Now Einstein kicks up a fuss again and predicts
t' = t sqrt(g_00)
and so
E' = E/sqrt(g_00)
so that QT's "h" is constant and invariant.
When E' is differentiated w.r.t to "r" sure enough
a minor correction to orbits is required and predicts
a perihelion advance of 43" of arc per century for the
orbit of Mercury, similiar reasoning applies to the
deflection of light.
To summarize: Fred, when God flicked the GR switch
he also turned on Planck's "h", and QT, it's the same.
Weird thing is, most guys are trying to unify QT and
GR, but as I explain in the story, I haven't even figured
out the difference yet!
> marriage made in "heaven"; Quantum Vacuum Charge = +,- sqrt(hbar*c) =
> QFT. ;-)
Again, absolutely Yes!
I fall back on the classical Energy = q*Q/r.
Well as always,
Best Regards
Ken S. Tucker
FrediFizzx
Not quite exactly the same. Close but no cigar yet. ;-)
> Weird thing is, most guys are trying to unify QT and
> GR, but as I explain in the story, I haven't even figured
> out the difference yet!
The difference is trying to get hbar/2 from GR. It's easy to get hbar,
but not so easy to get the one for spinors. ;-) Hmm... But of course I
did get that many moons ago by by just doing (hbar*w/2)(E) +
(hbar*w/2)(B) = hbar*w; read (E) and (B) as a function of a photon's
electric field and magnetic field assuming they are equal in energy.
But how to get from GR?
> > marriage made in "heaven"; Quantum Vacuum Charge = +,- sqrt(hbar*c)
=
> > QFT. ;-)
>
> Again, absolutely Yes!
> I fall back on the classical Energy = q*Q/r.
Ya still have to get hbar/2 from that using GR.
> Well as always,
> Best Regards
> Ken S. Tucker
FrediFizzx
Ken S. Tucker
Well I do SR with respect to "c" being an invariant
constant.
I do GR with respect to "h" being an invariant constant,
i.e. *energy proportional to EM frequency*
> > Weird thing is, most guys are trying to unify QT and
> > GR, but as I explain in the story, I haven't even figured
> > out the difference yet!
>
> The difference is trying to get hbar/2 from GR. It's easy to get hbar,
> but not so easy to get the one for spinors. ;-) Hmm... But of course I
> did get that many moons ago by by just doing (hbar*w/2)(E) +
> (hbar*w/2)(B) = hbar*w; read (E) and (B) as a function of a photon's
> electric field and magnetic field assuming they are equal in energy.
> But how to get from GR?
Well let's expressing those equations in a tensor form,
that is generally covariant.
> > > marriage made in "heaven"; Quantum Vacuum Charge = +,- sqrt(hbar*c)
> =
> > > QFT. ;-)
> >
> > Again, absolutely Yes!
> > I fall back on the classical Energy = q*Q/r.
>
> Ya still have to get hbar/2 from that using GR.
Agreed, and even better, derive those (h,c,q) from
a theory of the dimensionality of the unverse.
While we now accept Length, Time and Mass
to be relative, we connect L and T using "c" and
we connect T (and or L) and M by "h", the latter
being equally useful in GR and QT.
Bilge
>news:slrne448ds...@radioactivex.lebesque-al.net...
>
>> >You are still not making any sense. The spacetime is always zero for
>> >photons. Do you even know what photons are?
>>
>> Photons aren't the issue. Your non-sensical personalized terminology
>> is the the issue.
>
>The spacetime of non-photons is not zero. The spacetime for photons is
>zero. I still do not understand your objections. Can you follow
>logic?
Can you read? If so, why did you just repeat the same non-standard
terminology?
[...]
>> Since you had no idea what,
>>
>> \delta L = (dL/dq)\delta q + (dL/d(d_u q))\delta (d_u q)
>>
>> the last time I wrote down the variation, obviously it is you who has no
>> idea how to derive the euler-lagrange equations.
>
>Your terminology using ascii codes is not what I am familiar with.
It's standard TeX/LaTeX, the markup format used for type setting
scientific articles (for example, 99% of the articles on arXiv are
submitted and stored in this format, the pdf and ps files being generated
on the fly). Since this is a science newsgroup and you have been posting
here for years, it should be familiar by now. Moreover, since TeX/ LaTeX
is much better than word processing programs like m$word, word defect,
etc., for writing documents of any kind which need to look professionally
written (in terms of structure, layout, ease of use and typeset quality
finish) it ought to be familiar to anyone who cares about the documents
they write, for any purpose.
[...]
>> What is your point? Did you just figure out that varying different
>> parameters gives you an extremem for for the parameter being varies or
>> what?
>
>My point is that there is a different Lagrangian for a different
>parameter you want to find an extremum of.
Does that mean you think you get different physics by merely changing
parameters? If you think so, you've seriously missed the point of the
lagrangian formalism and variational calculus in general. The entire
reason for using an affine parameter like \tau or s, is to insure that
the lagrangian has _no_ _explicit_ coordinate dependence, since physics
has _no_ _explicit_ coordinate dependence. Go uy a textbook on elementary
classical mechanics.
[...]
>
>Whatever you want to judge my understanding, it is out of my control.
Only if your lack of understanding is beyond your control. While that
might very well be true, you should at least realize it.
[...]
>> Well, certainly no one else is going to call you a genius. Indeed,
>> from all of the evidence in your posts, you should be thrilled to
>> get a consensus of dumabss.
>
>Then, don't call me a genius then. It is no big deal to me. Why do
>you make it into a big deal?
I don't call you a genius, except in the same context the dog in the
movie ``A Boy and His Dog,'' referred to his owner as ``Albert'' in
a mocking reference to einstein, because his owner was so dense.
[...]
>> Any time you want to stop evading the opportunity I gave you to
>> prove which one of understands this material, feel free. I assume
>> you haven't the cajones to put up and you are too much of loud
>> mouth hillbilly to shut up.
>
>I have done so. You just do not accept my logical answers without any
>logical criticisms like Dr. Roberts, Dr. Carlip, Mr. Bielawski,
>Mr.Most, etc. Your trait is a bigotry.
I have given you explicit reasons why you are wrong, but as you yourself
just made perfectly obvious, you persist in being stupid despite the
criticisms even you acknowledge as logical. Apparently, I am considerably
less optimistic that logic can be used persuasively on someone who goes
out of his way to be stupid than they do.
[...]
>> >> Start with relativity and derive electromagnetism.
>> >
>> >That is another chapter of discussion. <shrug>
>>
>> OK, then I assume you have no idea that photons have something
>> to do with electromagnetism. You've proved my point. You are
>> clueless.
>
>I never said photons have nothing to do with electromagnetism.
Then you should have no difficulty answering the question.
[...]
>> use noether's theorem to find the consereved current if \psi is a
>> doublet of states and is invariant under an SU(2) rotation.
>> Another poster gave you a trivial classical scenario and asked you
>> to construct the lagrangian and obtain the equations of motion.
>> You bailed out on that one too.
>
>I refuse to do homework for you with your belligerent attitude.
So much for your self-professed expertise with noether's theorem.
[...]
>> >I have seen the contrary. <shrug>
>>
>> OK, cite the article in which you accepted that offer and
>> posted the evidence to which you refer.
>
>I don't accept babbling as anything intelligible. Thus, I cannot give
>you any articles. Your comments are all babbling. It is only due to
>my dilligence to give you the courtesy to understand what you are
>babbling. So, consider yourself lucky.
OK, then oviously, you made up the previous comment.
[...]
>> Just what it says. Anytime you wish to demonstrate that I don't
>> know what I'm talking about, I'll be happy to make the comparison
>> and even let _you_ decide which branch of physics you think gives
>> you the best shot to prove it. That way, I'll end up with a
>> permanent reference to you complete and utter failure to prove
>> you are anything but an overpressurized windbag and couch potato.
>
>Who is more of a couch potato? Your posting window is much broader
>than mine. My opportunity to do so is limited to late at night due to
>my work for making a living, my work to keep my growing family running,
>and my work to understand more about the subjects I don't know of.
If you were really interested in understanding anything, you would
not go out of your way to be ineducable.
Koobee Wublee
> >The spacetime of non-photons is not zero. The spacetime for photons is
> >zero. I still do not understand your objections. Can you follow
> >logic?
>
> Can you read? If so, why did you just repeat the same non-standard
> terminology?
Yes, I can read. The question is if you can understand.
> [...]
> >> Since you had no idea what,
> >>
> >> \delta L = (dL/dq)\delta q + (dL/d(d_u q))\delta (d_u q)
> >>
> >> the last time I wrote down the variation, obviously it is you who has no
> >> idea how to derive the euler-lagrange equations.
> >
> >Your terminology using ascii codes is not what I am familiar with.
>
> It's standard TeX/LaTeX, the markup format used for type setting
> scientific articles (for example, 99% of the articles on arXiv are
> submitted and stored in this format, the pdf and ps files being generated
> on the fly). Since this is a science newsgroup and you have been posting
> here for years, it should be familiar by now. Moreover, since TeX/ LaTeX
> is much better than word processing programs like m$word, word defect,
> etc., for writing documents of any kind which need to look professionally
> written (in terms of structure, layout, ease of use and typeset quality
> finish) it ought to be familiar to anyone who cares about the documents
> they write, for any purpose.
It sounds like you have issues with Microsoft Word and whoever Word
Perfect. I don't, and I prefer to present my equation in the old
fashion way where even the 1st year calculus student should have no
problem understanding my terminology. Since this newsgroup reaches
much wider audience, I do appreciate it if you write it in such a way
that could be understood by a wider audience.
> >My point is that there is a different Lagrangian for a different
> >parameter you want to find an extremum of.
>
> Does that mean you think you get different physics by merely changing
> parameters?
No.
> If you think so, you've seriously missed the point of the
> lagrangian formalism and variational calculus in general. The entire
> reason for using an affine parameter like \tau or s, is to insure that
> the lagrangian has _no_ _explicit_ coordinate dependence, since physics
> has _no_ _explicit_ coordinate dependence. Go uy a textbook on elementary
> classical mechanics.
What is your argument towards 'no'?
> >Whatever you want to judge my understanding, it is out of my control.
>
> Only if your lack of understanding is beyond your control. While that
> might very well be true, you should at least realize it.
Have you ever applied what you wrote to yourself? You will find that
answer within you.
> >Then, don't call me a genius then. It is no big deal to me. Why do
> >you make it into a big deal?
>
> I don't call you a genius, except in the same context the dog in the
> movie ``A Boy and His Dog,'' referred to his owner as ``Albert'' in
> a mocking reference to einstein, because his owner was so dense.
I have never even heard of that movie "A Boy and His Dog". From what
you have briefly described, it sounds like the boy is correct by
referring his dog as 'Albert'. It is a good mocking of Einstein.
Well, I do also have a dog. I name him 'Kublai'. Do I mock 'Kublai
Khan'? No, I admire Kublai Khan. This means your analogy can mean the
opposite which you even cannot comprehend.
> [...]
> >> Any time you want to stop evading the opportunity I gave you to
> >> prove which one of understands this material, feel free. I assume
> >> you haven't the cajones to put up and you are too much of loud
> >> mouth hillbilly to shut up.
> >
> >I have done so. You just do not accept my logical answers without any
> >logical criticisms like Dr. Roberts, Dr. Carlip, Mr. Bielawski,
> >Mr.Most, etc. Your trait is a bigotry.
>
> I have given you explicit reasons why you are wrong, but as you yourself
> just made perfectly obvious, you persist in being stupid despite the
> criticisms even you acknowledge as logical. Apparently, I am considerably
> less optimistic that logic can be used persuasively on someone who goes
> out of his way to be stupid than they do.
What is so explicit of reasons such as the following quoted from what
you said?
"...you haven't the cajones to put up and you are too much of loud
mouth hillbilly to shut up."
We are talking about physics here and not about some mindless idiot
pointing.
> >I never said photons have nothing to do with electromagnetism.
>
> Then you should have no difficulty answering the question.
That is correct.
> [...]
> >> use noether's theorem to find the consereved current if \psi is a
> >> doublet of states and is invariant under an SU(2) rotation.
> >> Another poster gave you a trivial classical scenario and asked you
> >> to construct the lagrangian and obtain the equations of motion.
> >> You bailed out on that one too.
> >
> >I refuse to do homework for you with your belligerent attitude.
>
> So much for your self-professed expertise with noether's theorem.
I said I am not placing Noether Theorem, which is very redundant in the
first place, as the highest quality in the study of GR. That does not
mean I have to do your homework for you.
> >I don't accept babbling as anything intelligible. Thus, I cannot give
> >you any articles. Your comments are all babbling. It is only due to
> >my dilligence to give you the courtesy to understand what you are
> >babbling. So, consider yourself lucky.
>
> OK, then oviously, you made up the previous comment.
I don't know what statement you are referring to. Don't expect me to
even look up your petty accusation.
> If you were really interested in understanding anything, you would
> not go out of your way to be ineducable.
So, you are very educable. You accept everything the 'experts' tell it
at face value. You are the one who does not understand physics. You
are just a troll.
FrediFizzx
But that doesn't get us all the way there. There is more do it than
just E = hbar*w.
> > > Weird thing is, most guys are trying to unify QT and
> > > GR, but as I explain in the story, I haven't even figured
> > > out the difference yet!
> >
> > The difference is trying to get hbar/2 from GR. It's easy to get
hbar,
> > but not so easy to get the one for spinors. ;-) Hmm... But of
course I
> > did get that many moons ago by by just doing (hbar*w/2)(E) +
> > (hbar*w/2)(B) = hbar*w; read (E) and (B) as a function of a photon's
> > electric field and magnetic field assuming they are equal in energy.
> > But how to get from GR?
>
> Well let's expressing those equations in a tensor form,
> that is generally covariant.
I guess we need to put spacetime into this somehow. OK from QVC, we
have,
hbar*w/2 = Cvac*Vvac^2/2 = Lvac*Ivac^2/2
Cvac is just lambda/2pi and Lvac is lambda/(2pi*c^2) so that gets us
space and time; Vvac is "vacuum" volts and Ivac is "vacuum" current.
The electric field component only has space involved so it is like a
"static" potential. The B field component has both space and time
involved so it is not a static potential. OK, where do we go from here?
In order to make this work for spinors, we have to bring in the QVC
relativistic medium so that hbar*w/2 can be defined by them.
> > > > marriage made in "heaven"; Quantum Vacuum Charge = +,-
sqrt(hbar*c)
> > =
> > > > QFT. ;-)
> > >
> > > Again, absolutely Yes!
> > > I fall back on the classical Energy = q*Q/r.
> >
> > Ya still have to get hbar/2 from that using GR.
>
> Agreed, and even better, derive those (h,c,q) from
> a theory of the dimensionality of the unverse.
> While we now accept Length, Time and Mass
> to be relative, we connect L and T using "c" and
> we connect T (and or L) and M by "h", the latter
> being equally useful in GR and QT.
It is not so hard to get (h,c,q) since sqrt(hbar*c) = q or hbar*c = q^2
and our Spin Matrix can generate mass from that. It's when you toss in
Newton's G that things don't seem quite right. ;-)
brian a m stuckless
-=-
> If you were really interested in understanding anything,
> you would not go out of your way to be ineducable.
$$ ^.
$$ COSMiC relief.
$$ Poor FLUFFY, under his GR CONE-of-EMPTiNESS
$$ (..which doesN'T get any BiGGER along it's axis).
$$ [i.e. Bilge "explains": 'Why KAOS isN'T GR-reachable'].
Re: Teaching GR right after intermediate mechanics
Re: Why KAOS isN'T GR-reachable ..by Bilge.
Bilge
>"Bilge" <dub...@radioactivex.lebesque-al.net> wrote in message
>news:slrne4e7l3...@radioactivex.lebesque-al.net...
>
>> >The spacetime of non-photons is not zero. The spacetime for photons is
>> >zero. I still do not understand your objections. Can you follow
>> >logic?
>>
>> Can you read? If so, why did you just repeat the same non-standard
>> terminology?
>
>Yes, I can read. The question is if you can understand.
Obviously, I do understand. You deliberately use non-standard
terminology in order to insure your statements are meaningless.
I recognize what you write as meaningless.
[...]
[...]
>> >My point is that there is a different Lagrangian for a different
>> >parameter you want to find an extremum of.
>>
>> Does that mean you think you get different physics by merely changing
>> parameters?
>
>No.
Then why did you try to arguew differently? Obviously if you don't
think that diffrent paramaterizations give different physics, your
entire argument was irrelevant, since the only difference between
\tau and t is that \tau is coordinate independent and t, by definition
is a timelike coordinate for one particular coordinate system. That
means, the only failure here is your failure to know what you are doing
or what physics is represented by the equations you mindlessly post.
>> If you think so, you've seriously missed the point of the
>> lagrangian formalism and variational calculus in general. The entire
>> reason for using an affine parameter like \tau or s, is to insure that
>> the lagrangian has _no_ _explicit_ coordinate dependence, since physics
>> has _no_ _explicit_ coordinate dependence. Go uy a textbook on elementary
>> classical mechanics.
>
>What is your argument towards 'no'?
None. I'm flexible. If you have no interest in understanding basic
physics and think you can make up for it with bullshit, I'll reward
you for your effort.
[...]
>> I have given you explicit reasons why you are wrong, but as you yourself
>> just made perfectly obvious, you persist in being stupid despite the
>> criticisms even you acknowledge as logical. Apparently, I am considerably
>> less optimistic that logic can be used persuasively on someone who goes
>> out of his way to be stupid than they do.
>
>What is so explicit of reasons such as the following quoted from what
>you said?
>
>"...you haven't the cajones to put up and you are too much of loud
>mouth hillbilly to shut up."
That is another example of your inability to be truthful, even to
yourself. You'll have to go a lot further back than that post to
find a reply where I made the mistake of taking you seriously and
I never claimed that I have replied to all of your posts seriously.
Indeed, I readily admit to not taking you seriously after the first
couple of replies. Taking you seriously would actually lend credibility to
your thesis that physicists can't think for themselves by not recognizing
you as the troll you are. You used up your benefit of the doubt credits
long ago and I have no intention of taking you seriously until you
post something serious.
[...]
>We are talking about physics here and not about some mindless idiot
>pointing.
Right - I'm pointing at a mindless idiot. If you don't want to
be treated as a mindless idiot, don't work so hard at being a
mindless idiot. It's that simple.
>> >I never said photons have nothing to do with electromagnetism.
>>
>> Then you should have no difficulty answering the question.
>
>That is correct.
But apparently, you cannot.
[...]
>> So much for your self-professed expertise with noether's theorem.
>
>I said I am not placing Noether Theorem, which is very redundant in the
>first place, as the highest quality in the study of GR.
Then use the opportunity you were just given to prove that.
>That does not mean I have to do your homework for you.
Again, you are unable to be truthful. I did not ask you do my homework.
I gave you the opportunity to demonstrate that you aren't all hot air
by applying noether's theorem to a simple lagrangian. You certainly
don't have to do anything. Indeed, I'm counting on your inability to
answer that question every time I ask it (as well as the even simpler
question posed to you by someone else) to support my claim that you are
a mindless windbag.
>>
>> OK, then oviously, you made up the previous comment.
>
>I don't know what statement you are referring to. Don't expect me to
>even look up your petty accusation.
Since you don't bother to look up anything, why would I expect you
change strategies now?
>> If you were really interested in understanding anything, you would
>> not go out of your way to be ineducable.
>
>So, you are very educable. You accept everything the 'experts' tell it
>at face value.
Once again, you are unable to e truthful, even to yourself. I'm
educable because I don't accept or reject something until I study it.
On the other hand, you are the embodiment of your own criticism,
except that reject everything you think an expert tells you because
you have some inferiority complex that has led to your delusion of
expertise in things you know absolutely zero about. My 13 year old
nephew knows more math than you do, and he doesn't know a lot of math.
>You are the one who does not understand physics.
I have given you numerous opportunities to try and prove that, but
you keep evading them. Why is that? I've even offered to let you choose
any branch of physics you want so that you would have the advantage,
unless of course, your best understanding of any topic in physics
is far below my understanding of any topic in physics. I don't expect you
to take the opportunity to prove you're anything but a windbag any more
than I expect you solve a simple lagrangian.
Ken S. Tucker
out a reasonable reply at the end...
I hear you...
Fred, you know I'm more comfortable to reply with
references, but I'm afraid our discussion enters the
*Twilight Zone* of GR that's a bit slippery, we're
entering the *Dark Side of the Force*.
Let me conjure Planck's invariant "h" as,
h = p_u x^u
with p_u being the energy-momentum 4-vector,
and x^u being a finite quantity, for example,
h = {p_0} * [x^0] = (6.625*10^-27) {ergs} * [seconds]
where the {erg} and [second] are finite,
that you know is assumable.
>From what I understand, the "continuum" only
allows differentials and proportionality constants,
like "c", (used in the familiar context of SR to
relate dr = c*dt), so using "x^u" maybe off the
continuum, not sure about that.
I've read that space & time has a *natural*
expression using the contravariant terms
"x^u", but energy and momentum are more
naturally expressed by covariant "p_u" terms,
and I used that above to define "h", so I'll stay
with that.
Moving to AE's GR, you're familiar with mass
being expressed as a length, for example, the
Sun has a length of 1.47 kms is conventional,
from,
L = (G/c^2) (Mass of Sun) = 1.47 kms.
The problem arises when the relativistic
dimensionality of Newton's "G" is considered.
It looks to me like G is a 2nd rank tensor,
let me explain...I'll use K in place of G to
keep conventions straight, and use,
x^u = K^uv p_v
to be the GR relation converting mass (or
energy-momentum p_v) to a length "x^u"
keeping the natural indexs, I explained above
that work for defining Planck's "h" to be
invariant.
Me thinks G is not an invariant but a tensor
to convert mass to length using K^uv.
Keep an eye on that possiblity, it could help.
Best Regards
Ken S. Tucker
> FrediFizzx