Anyone good with Tensors?
gu...@hotmail.com
I think long ago I read (anyone have the link and Einstein's words on
it) that Einstein believed there was an Aether (is there any
relationship of the Aether with his cosmological constant mistake)?
*****When**** Einstein wrote his GR theory, did he still believe in an
Aether?
If so then it seems his warped space, rubber sheet model and Einstein's
math for tensors could have based on an Aether (or space as a fabric),
if no then why not?
Koobee Wublee
news:1149575015.9...@g10g2000cwb.googlegroups.com...
> I think long ago I read (anyone have the link and Einstein's words on
> it) that Einstein believed there was an Aether (is there any
> relationship of the Aether with his cosmological constant mistake)?
It is very simple. The curvature in space was Karl Gauss's idea.
However, it was his student Bernhardt Riemann (a genius just like his
teacher) who characterized how an object would behave under the
curvature of space. Christoffel actually was the one completed
Riemann's work and wrote down the geodesic equations describing exactly
how objects are going to behave under the curvature of space. This is
no surprising because the Aether actually allows the curvature in
space.
The Cosmological Constant is just a fudge figure (a bandaide) to be
used if beneficial in an applied circumstance.
> *****When**** Einstein wrote his GR theory, did he still believe in an
> Aether?
No, he did not. His original GR theory was a mirror image of the
observation where Newton observed a falling apple under the influence
of gravity. Einstein's approach was to fancy himself falling under the
influence of gravity. Unlike Newton's logical approach to the mystery
of gravitation, Einstein's Equivalence Principle did not get anywhere.
So, Einstein, disgusted with himself for his failure, cooperated with
his long time classmate Marcel Grossmann to take another look at the
nature of gravity after Grossman applied Riemann's curvature of space
in the the equations. Grossmann's approach again did not get anywhere.
Dumping Grossman and looking for help at Goettingen, Einstein
conducted a series of lectures. The bait finally was taken. David
Hilbert started working on the problem. The Einstein Field Equations
were discovered only after Hilbert patched together a Lagrangian
(similar how Dr. Frankenstein patched together that monster) and
applied with the Calculus of Variations discovered several centuries
prior by Euler and Lagrange. Without Hilbert's Lagrangian, there would
be no field equations and thus GR. To claim Einstein and Hilbert
arrived at the field equations independently would mean the Lagrangian
is also patched together independently by Hilbert and Einstein. The
odds for two persons to pull out the same BS within a week of each
other is astronomically unlikely.
> If so then it seems his warped space, rubber sheet model and Einstein's
> math for tensors could have based on an Aether (or space as a fabric),
> if no then why not?
Yes, indeed. However, the misconception is that gravitation is caused
by the curvature in spacetime. If you examine the mathematics of GR
thoroughly, you will discover that the curvature of space along would
not cause a gravitation. Only a dilation (or curvature) in time would
cause gravitation regardless wether if space is curved or not.
So, the cause of gravity is only the gravitational time dilation. The
justification for gravitation being caused by the curvature in
spacetime would dictate more work for mother nature. As we know,
mother nature always follows the path of least resistance. That is why
we have Snell's Law. Thus, GR is utterly bogus in nature.
Sue...
you can bend the rest of the world around to make it happen.
That isn't bogus. It may be useless but it is not bogus. ;-)
Sue...
Dead Paul
<snip>
if you want the low down on tensors as they "pertain" to GR in a form
that most can understand then have a look at
http://www.physicsdeconstructed.com/
chapter 6 p 339
It show just how tensors were/are misused in the GR formulation.
surrealis...@hotmail.com
An ether is any space-filling thing which has some physical property.
An abstract space-filling entity, such as the metric function, can be
considered as a field. Fields don't have to "really exist" to be useful
in physics. Remember that space itself is an abstract, made-up concept
whose properties are defined by some physical theory.
Physics deals with made-up models which live inside made-up theories.
If the theory works, the model is justified by being useful, though no
inference can be made that the model is "true of reality." (If one
chooses to do that, it's a personal choice.)
What Einstein did not believe in after 1905 was a space-filling
mechanical medium as a carrier for electrodynamical phenomena.
John C. Polasek
wrote:
I didn't find that: between pg 339 and 353 nothing but windy rhetoric.
Who is this anonymous author? I refuse to deal with his attorney.
JP
Igor
It's not warped space, it's curved spacetime. The rubber sheet model
is a poor analogy used in popular treatments and can lead to tremendous
misunderstandings. Tensors already existed as mathematical objects
prior to Einstein, and they are just generalizations of vectors. And
no, Einstein never believed in an aether after his first papers on
relativity were published.
Koobee Wublee
news:1149614665.8...@c74g2000cwc.googlegroups.com...
>
> It's not warped space, it's curved spacetime. The rubber sheet model
> is a poor analogy used in popular treatments and can lead to tremendous
> misunderstandings. Tensors already existed as mathematical objects
> prior to Einstein, and they are just generalizations of vectors. And
> no, Einstein never believed in an aether after his first papers on
> relativity were published.
Poincare did not believe in the Aether years before Einstein. Unlike
Poincare, Einstein never rejected the Aether. The correct historic
credit to Einstein in the subject of relativity should be his role as a
promoter of Poincare's idea or SR and as a catalist that sped up the
development of GR. Without Einstein, SR and GR would take a longer
time before acceptance. The true nature of physics dealing with the
subject of relativity maybe discovered even before that.
gu...@hotmail.com
Check my other post, in 1920 Einstein said he based his GR on the
Ether.
gu...@hotmail.com
Koobee Wublee wrote:
> <gu...@hotmail.com> wrote in message
> news:1149575015.9...@g10g2000cwb.googlegroups.com...
>
> > I think long ago I read (anyone have the link and Einstein's words on
> > it) that Einstein believed there was an Aether (is there any
> > relationship of the Aether with his cosmological constant mistake)?
>
> It is very simple. The curvature in space was Karl Gauss's idea.
> However, it was his student Bernhardt Riemann (a genius just like his
> teacher) who characterized how an object would behave under the
> curvature of space. Christoffel actually was the one completed
> Riemann's work and wrote down the geodesic equations describing exactly
> how objects are going to behave under the curvature of space. This is
> no surprising because the Aether actually allows the curvature in
> space.
>
> The Cosmological Constant is just a fudge figure (a bandaide) to be
> used if beneficial in an applied circumstance.
>
> > *****When**** Einstein wrote his GR theory, did he still believe in an
> > Aether?
>
> No, he did not.
Check my other post, in 1920 Einstein said he based GR on the Ether.
He ended by saying the Ethe is not a concrete/tangeable
substance....maybe to protect his behind?
Igor
No he did not. I think you must have your wires crossed and are taking
him out of context.
Igor
Koobee Wublee wrote:
> "Igor" <thoo...@excite.com> wrote in message
> news:1149614665.8...@c74g2000cwc.googlegroups.com...
> >
> > It's not warped space, it's curved spacetime. The rubber sheet model
> > is a poor analogy used in popular treatments and can lead to tremendous
> > misunderstandings. Tensors already existed as mathematical objects
> > prior to Einstein, and they are just generalizations of vectors. And
> > no, Einstein never believed in an aether after his first papers on
> > relativity were published.
>
> Poincare did not believe in the Aether years before Einstein.
Correct.
> Unlike Poincare, Einstein never rejected the Aether.
Can you back that up?
>The correct historic
> credit to Einstein in the subject of relativity should be his role as a
> promoter of Poincare's idea or SR and as a catalist that sped up the
> development of GR.
People have debated this for years and have gotten nowhere.
>Without Einstein, SR and GR would take a longer
> time before acceptance. The true nature of physics dealing with the
> subject of relativity maybe discovered even before that.
Wishful thinking. It's also been said that had he continued his
research, William R Hamilton could have discovered both SR and QM
several decades prior to their actual appearance, but those didn't
happen either.
Tom Roberts
> The Cosmological Constant is just a fudge figure (a bandaide) to be
> used if beneficial in an applied circumstance.
The cosmological constant is a legitimate part of the field equation,
and cannot be ruled out a priori. It is a constant to be fit to
observations and measurements. Its value must be extremely small in
order for the equations of GR to agree with Newtonian gravity in the
appropriate limit -- it is so small that effects are observable only on
very large scales, hence it's name.
> However, the misconception is that gravitation is caused
> by the curvature in spacetime.
Nobody who has thought about it very much at all thinks that. Your usage
of naive causality is completely unwarranted. Gravitation is, however,
well modeled by curvature in spacetime.
> If you examine the mathematics of GR
> thoroughly, you will discover that the curvature of space along would
> not cause a gravitation. Only a dilation (or curvature) in time would
> cause gravitation regardless wether if space is curved or not.
Actually it takes curvature in spacetime. Many results come out wrong if
one ignores the curvature of space; among them is the bending of
starlight by the sun.
> The
> justification for gravitation being caused by the curvature in
> spacetime would dictate more work for mother nature. As we know,
> mother nature always follows the path of least resistance. That is why
> we have Snell's Law.
And why we have GR. The field equation of GR is simply the Lagrange
equation for the Hilbert action. Indeed, _every_ major fundamental
theory of physics can be expressed as a principle of least action for
which the Lagrangian is an appropriate geometrical curvature. This
includes Maxwell's equations, QED, the standard model, and GR. For GR
the Hilbert action has a Lagrangian density consisting of simply the
Ricci curvature scalar.
Tom Roberts
Tom Roberts
> gu...@hotmail.com wrote:
>> Check my other post, in 1920 Einstein said he based his GR on the
>> Ether.
>
> No he did not. I think you must have your wires crossed and are taking
> him out of context.
This is indeed out of context. In 1920 Einstein attended a conference on
the aether, and made remarks that essentially say that the "aether" of
GR is utterly unlike any other aether, in that it has no physical
properties (density, temperature, pressure, etc.), and no state of rest
can be ascribed to it.
To consider GR as an "aether theory" requires an incredible PUN on the
word that robs it of all meaning. Einstein knew this. But he spoke in
the style of his time, not ours. <shrug>
Tom Roberts
gu...@hotmail.com
you shrug to claim innocence and ambiguity. Einstein's specific words
to the same link I gave:
"GR without an ETHER IS UNTHINKABLE"
His further claims that is the Ether is not a tangeable substance
(perhaps the same way photon has no mass or not a particle,etc...) is
to cover his own behind.
In the very debts of your shrugging you know both above are correct.
>
> Tom Roberts
gu...@hotmail.com
> This is indeed out of context. In 1920 Einstein attended a conference on
> the aether, and made remarks that essentially say that the "aether" of
> GR is utterly unlike any other aether, in that it has no physical
> properties (density, temperature, pressure, etc.), and no state of rest
> can be ascribed to it.
>
> To consider GR as an "aether theory" requires an incredible PUN on the
> word that robs it of all meaning. Einstein knew this. But he spoke in
> the style of his time, not ours. <shrug>
>
Einstein's own words in 1920 from the link I gave: "GR without an ETHER
IS UNTHINKABLE"
His further claims that the Ether is not a tangeable substance (perhaps
the same way photon has no mass or not a particle,etc...) is to cover
his behind on this claim.
Example: The air is hot but from another perspective the air is also
cold (say comparing it to the temperature of the sun) = covering one's
behind (pride, honour, and fame) if any contradicting info is found in
the future.
dda1
gu...@hotmail.com wrote:
> >
> > To consider GR as an "aether theory" requires an incredible PUN on the
> > word that robs it of all meaning. Einstein knew this. But he spoke in
> > the style of his time, not ours. <shrug>
> >
>
> you shrug to claim innocence and ambiguity. Einstein's specific words
> to the same link I gave:
>
> "GR without an ETHER IS UNTHINKABLE"
>
> His further claims that is the Ether is not a tangeable substance
> (perhaps the same way photon has no mass or not a particle,etc...) is
> to cover his own behind.
>
No cretin, Einstein did not need to cover anything. You need to have a
brain transplant such that you "get" the meaning of things.
>
>
> >
> > Tom Roberts
gu...@hotmail.com
Ah cretin! Louis the bastards are at the GATE!
> >
> >
> > >
> > > Tom Roberts
Koobee Wublee
news:TaIhg.112084$dW3....@newssvr21.news.prodigy.com...
> The cosmological constant is a legitimate part of the field equation,
> and cannot be ruled out a priori. It is a constant to be fit to
> observations and measurements. Its value must be extremely small in
> order for the equations of GR to agree with Newtonian gravity in the
> appropriate limit -- it is so small that effects are observable only on
> very large scales, hence it's name.
The Cosmological Constant is patched after the field equation are
derived. The field equations are derived through the Hilbert
Lagrangian (the Lagrangian to Hilbert-Einstein Action). The modified
field equations are NOT Euler-Lagrange equations to the Hilbert
Lagrangian. Then, how can you say the Cosmological Constant is a
legitimate part of the field equations?
>> However, the misconception is that gravitation is caused
>> by the curvature in spacetime.
>
> Nobody who has thought about it very much at all thinks that. Your usage
> of naive causality is completely unwarranted. Gravitation is, however,
> well modeled by curvature in spacetime.
Let's say instead of the Hilbert Lagrangian. I find another one
resulted in the field equations that yield a metric similar to the
Schwarzschild metric except with unity term (1) associated with dr^2
(instead of (1 -2 U)^-1). Can this new metric explain gravity? Yes,
it does. Does this new metric indicate a curvature in space? No.
Space is flat described by this new metric. So, how can you claim
gravitation can only be modeled by a curvature in spacetime?
Gravitation is there as long as there is a gravitational time dilation
regardless if space is curved or flat! It gets better. Why does the
least action dictates a curvature in time after all? The whole concept
of using a Lagrangian to derive the field equations is absolutely silly
and absurd beyond imagination?
> Actually it takes curvature in spacetime. Many results come out wrong if
> one ignores the curvature of space; among them is the bending of
> starlight by the sun.
I am not arguing that GR deals with a curvature in spacetime. GR is a
special case of hypotheses dealing with spacetime directly or
indirectly. There are other hypotheses that do not manifest a
curvature in spacetime but only time. With a gravitational time
dilation, it is more than adequate to explain gravitation. So, how can
you argue a set of physical laws actually represents the least amout of
action dealing with the curvature in both space and time but not
another set of physical laws only dealing with curvature in time and
flat space?
> And why we have GR. The field equation of GR is simply the Lagrange
> equation for the Hilbert action. Indeed, _every_ major fundamental
> theory of physics can be expressed as a principle of least action for
> which the Lagrangian is an appropriate geometrical curvature. This
> includes Maxwell's equations, QED, the standard model, and GR. For GR
> the Hilbert action has a Lagrangian density consisting of simply the
> Ricci curvature scalar.
And what makes this Hilbert Lagrangian valid except through
experimentation? It is a very complicated Lagrangian as you have to
admit. How can you vouche for its validity other than through
experimentation?
Ilja Schmelzer
"Koobee Wublee" <koobee...@gmail.com> schrieb
> "Tom Roberts" <tjrobe...@sbcglobal.net> wrote
> > The cosmological constant is a legitimate part of the field equation,
> > and cannot be ruled out a priori. It is a constant to be fit to
> > observations and measurements. Its value must be extremely small in
> > order for the equations of GR to agree with Newtonian gravity in the
> > appropriate limit -- it is so small that effects are observable only on
> > very large scales, hence it's name.
>
> The Cosmological Constant is patched after the field equation are
> derived. The field equations are derived through the Hilbert
> Lagrangian (the Lagrangian to Hilbert-Einstein Action). The modified
> field equations are NOT Euler-Lagrange equations to the Hilbert
> Lagrangian.
They are Euler-Lagrange equations to a slightly modified Hilbert
Lagrangian.
L = R sqrt{-g} is the Hilbert Lagrangian,
L = (R + const) sqrt{-g} is the Hilbert Lagrangian with cosmological
constant.
> Then, how can you say the Cosmological Constant is a
> legitimate part of the field equations?
The basic idea is that the Lagrangian should be a covariant function
of the metric g_mn(x). (R + const) sqrt{-g} are the lowest order
terms with this property. (There are others, like R^2 sqrt{-g} and
so on, but there was no need to include them.)
> And what makes this Hilbert Lagrangian valid except through
> experimentation? It is a very complicated Lagrangian as you have to
> admit.
It depends how you look at it. It is the second simple expression
(after the cosmological constant) which fulfills a nice covariance
property.
Ilja
Ilja Schmelzer
<surrealis...@hotmail.com> schrieb
> An ether is any space-filling thing which has some physical property.
> An abstract space-filling entity, such as the metric function, can be
> considered as a field. Fields don't have to "really exist" to be useful
> in physics. Remember that space itself is an abstract, made-up concept
> whose properties are defined by some physical theory.
Whatever "really exists", other people, stones, animals, the Sun, are
also abstract, made-up concepts, defined by some human theory
(the "theory" named "common sense"), in the same sense as fields.
Therefore I would prefer to say that the fields really exist.
The question was if these fields describe properties of some
"mechanical ether" in such a way as thermodynamic fields
(temperature, entropy, pressure and so on) describe properties
of large numbers of atoms moving in space.
Ilja
Ilja Schmelzer
"Koobee Wublee" <koobee...@gmail.com> schrieb
> Poincare did not believe in the Aether years before Einstein. Unlike
> Poincare, Einstein never rejected the Aether.
Can you give a quote where Poincare rejected the Aether?
Ilja
Igor
In his lifetime, Einstein did apparently say a few things
professionally that he later wished he would have never uttered. I
think that this was one of them. That's mostly because he didn't mean
it the way you think he did. I think he meant it in sort of the same
sense that "fabric" is often used to describe spacetime, which is a
poor analogy also. He also regretted that the theory came to be known
as Relativity, since this led to more mistunderstandings and was often
confused, and still is, with the philosophy of Relativism.
Igor
Koobee Wublee wrote:
> "Tom Roberts" <tjrobe...@sbcglobal.net> wrote in message
> news:TaIhg.112084$dW3....@newssvr21.news.prodigy.com...
>
> > The cosmological constant is a legitimate part of the field equation,
> > and cannot be ruled out a priori. It is a constant to be fit to
> > observations and measurements. Its value must be extremely small in
> > order for the equations of GR to agree with Newtonian gravity in the
> > appropriate limit -- it is so small that effects are observable only on
> > very large scales, hence it's name.
>
> The Cosmological Constant is patched after the field equation are
> derived. The field equations are derived through the Hilbert
> Lagrangian (the Lagrangian to Hilbert-Einstein Action). The modified
> field equations are NOT Euler-Lagrange equations to the Hilbert
> Lagrangian. Then, how can you say the Cosmological Constant is a
> legitimate part of the field equations?
Ever heard of Lagrange multipliers? The Einstein tensor is required to
be covariantly divergenceless. However, so is the metric tensor.
Hence, any linear combination of the two should be also.
> >> However, the misconception is that gravitation is caused
> >> by the curvature in spacetime.
> >
> > Nobody who has thought about it very much at all thinks that. Your usage
> > of naive causality is completely unwarranted. Gravitation is, however,
> > well modeled by curvature in spacetime.
>
> Let's say instead of the Hilbert Lagrangian. I find another one
> resulted in the field equations that yield a metric similar to the
> Schwarzschild metric except with unity term (1) associated with dr^2
> (instead of (1 -2 U)^-1). Can this new metric explain gravity? Yes,
> it does.
First, you'd have a hard time reconciling that solution with the vacuum
field equations. The only way to really do it would be to redefine the
radial coordinate so that it comes out that way. But this would
consequences for the rest of the metric. And even if you could get
away with it, the space part of the curvature is only half the factor
for gravitation anyway. The temporal part is essentially Newtonian and
provides the other half.
>Does this new metric indicate a curvature in space? No.
Not necessarily. You would just be rearraging things. But even if the
spatial part of the curvature disappears, it wouldn't matter much. You
can't get rid of spacetime curvature anyway. It's a tensor and so, if
it's curved in one frame it must be curved in all of them.
> Space is flat described by this new metric. So, how can you claim
> gravitation can only be modeled by a curvature in spacetime?
Spacetime is still curved.
> Gravitation is there as long as there is a gravitational time dilation
> regardless if space is curved or flat!
No gravitation or gravitational dilation in flat spacetime.
>It gets better. Why does the
> least action dictates a curvature in time after all?
It doesn't. A space is either curved or flat. The variational
principle alone can''t dictate that.
>The whole concept
> of using a Lagrangian to derive the field equations is absolutely silly
> and absurd beyond imagination?
You have something better?
> > Actually it takes curvature in spacetime. Many results come out wrong if
> > one ignores the curvature of space; among them is the bending of
> > starlight by the sun.
>
> I am not arguing that GR deals with a curvature in spacetime. GR is a
> special case of hypotheses dealing with spacetime directly or
> indirectly. There are other hypotheses that do not manifest a
> curvature in spacetime but only time. With a gravitational time
> dilation, it is more than adequate to explain gravitation. So, how can
> you argue a set of physical laws actually represents the least amout of
> action dealing with the curvature in both space and time but not
> another set of physical laws only dealing with curvature in time and
> flat space?
Don't think of it that way. Spacetime is curved, period. You might be
able to perform transformations that make the spatial part flat or the
temporal part flat, but overall, a flat spacetime remains flat and a
curved spacetime remains curved.
> > And why we have GR. The field equation of GR is simply the Lagrange
> > equation for the Hilbert action. Indeed, _every_ major fundamental
> > theory of physics can be expressed as a principle of least action for
> > which the Lagrangian is an appropriate geometrical curvature. This
> > includes Maxwell's equations, QED, the standard model, and GR. For GR
> > the Hilbert action has a Lagrangian density consisting of simply the
> > Ricci curvature scalar.
>
> And what makes this Hilbert Lagrangian valid except through
> experimentation? It is a very complicated Lagrangian as you have to
> admit. How can you vouche for its validity other than through
> experimentation?
I think that's all we have. If you have a better way to derive all
these effects, we'd love to hear it.
Tom Roberts
> "Tom Roberts" <tjrobe...@sbcglobal.net> wrote in message
> news:TaIhg.112084$dW3....@newssvr21.news.prodigy.com...
>> The cosmological constant is a legitimate part of the field equation,
>
> The Cosmological Constant is patched after the field equation are
> derived.
Hmmm. The indefinite integral of x^2 is (1/3)x^3 + C. Do you think that
C is "patched after the equation is derived"? The cosmological constant
in the EFE is directly analogous to the C in an indefinite integral.
>>> However, the misconception is that gravitation is caused
>>> by the curvature in spacetime.
>> Nobody who has thought about it very much at all thinks that. Your usage
>> of naive causality is completely unwarranted. Gravitation is, however,
>> well modeled by curvature in spacetime.
>
> Let's say instead of the Hilbert Lagrangian. I find another one
> resulted in the field equations that yield a metric similar to the
> Schwarzschild metric except with unity term (1) associated with dr^2
> (instead of (1 -2 U)^-1). Can this new metric explain gravity? Yes,
> it does. Does this new metric indicate a curvature in space? No.
> Space is flat described by this new metric. So, how can you claim
> gravitation can only be modeled by a curvature in spacetime?
Because the underlying manifold is spacetime, not simply space. The
foliation of spacetime into space and time is of no physical
significance, because it is the same symmetry as changing coordinates.
> Gravitation is there as long as there is a gravitational time dilation
> regardless if space is curved or flat!
Sure -- the foliation of spacetime into space and time is arbitrary. But
spaceTIME is not flat. Attempting to discuss the curvature of space as a
fundamental entity is hopeless.
> And what makes this Hilbert Lagrangian valid except through
> experimentation?
Welcome to physics.
> It is a very complicated Lagrangian as you have to
> admit.
Actually, it is the simplest possible Lagrangian that satisfies the
clear and obvious symmetries.
Tom Roberts
Tom Roberts
> Tom Roberts wrote:
>> In 1920 Einstein attended a conference on
>> the aether, and made remarks that essentially say that the "aether" of
>> GR is utterly unlike any other aether, in that it has no physical
>> properties (density, temperature, pressure, etc.), and no state of rest
>> can be ascribed to it.
>>
>> To consider GR as an "aether theory" requires an incredible PUN on the
>> word that robs it of all meaning. Einstein knew this. But he spoke in
>> the style of his time, not ours. <shrug>
>>
> you shrug to claim innocence and ambiguity.
Not at all. I merely claim Einstein's words do not mean what you think
they mean.
> Einstein's specific words
> to the same link I gave:
> "GR without an ETHER IS UNTHINKABLE"
Sure. But simply pulling quotes out of context is useless. You need to
_READ_THE_ARTICLE_ and you will see that what I said above is a
reasonable synopsis of this aspect of his statements.
Tom Roberts
Koobee Wublee
> Koobee Wublee wrote:
>> The Cosmological Constant is patched after the field equation are
>> derived.
>
> Hmmm. The indefinite integral of x^2 is (1/3)x^3 + C. Do you think that
> C is "patched after the equation is derived"? The cosmological constant
> in the EFE is directly analogous to the C in an indefinite integral.
What is this integral you are referring to? EFE are the results of
differentiation.
>> Let's say instead of the Hilbert Lagrangian. I find another one
>> resulted in the field equations that yield a metric similar to the
>> Schwarzschild metric except with unity term (1) associated with dr^2
>> (instead of (1 -2 U)^-1). Can this new metric explain gravity? Yes,
>> it does. Does this new metric indicate a curvature in space? No.
>> Space is flat described by this new metric. So, how can you claim
>> gravitation can only be modeled by a curvature in spacetime?
>
> Because the underlying manifold is spacetime, not simply space. The
> foliation of spacetime into space and time is of no physical
> significance, because it is the same symmetry as changing coordinates.
I don't understand what you are saying. Is this an ancient verse out
of a GR bible?
>> Gravitation is there as long as there is a gravitational time dilation
>> regardless if space is curved or flat!
>
> Sure -- the foliation of spacetime into space and time is arbitrary. But
> spaceTIME is not flat. Attempting to discuss the curvature of space as a
> fundamental entity is hopeless.
Again, foliation? There is not even such a word in the English
language. Please stop talking in riddles to justify your points.
>> It is a very complicated Lagrangian as you have to
>> admit.
>
> Actually, it is the simplest possible Lagrangian that satisfies the
> clear and obvious symmetries.
I don't see the simplicity in Hilbert Lagrangian. Simplicity is
awefully subjective. What guarantees it being the valid one? What
does the Hilbert-Einstein Action have to be minimized?
Koobee Wublee
>
> Koobee Wublee wrote:
>> The Cosmological Constant is patched after the field equation are
>> derived. The field equations are derived through the Hilbert
>> Lagrangian (the Lagrangian to Hilbert-Einstein Action). The modified
>> field equations are NOT Euler-Lagrange equations to the Hilbert
>> Lagrangian. Then, how can you say the Cosmological Constant is a
>> legitimate part of the field equations?
>
> Ever heard of Lagrange multipliers? The Einstein tensor is required to
> be covariantly divergenceless. However, so is the metric tensor.
> Hence, any linear combination of the two should be also.
Yes, I have heard of Lagrangian Multipliers. I still don't see what
these have anything convincingly to do with the Cosmological Constant.
>> >> However, the misconception is that gravitation is caused
>> >> by the curvature in spacetime.
>> >
>> > Nobody who has thought about it very much at all thinks that. Your usage
>> > of naive causality is completely unwarranted. Gravitation is, however,
>> > well modeled by curvature in spacetime.
>>
>> Let's say instead of the Hilbert Lagrangian. I find another one
>> resulted in the field equations that yield a metric similar to the
>> Schwarzschild metric except with unity term (1) associated with dr^2
>> (instead of (1 -2 U)^-1). Can this new metric explain gravity? Yes,
>> it does.
>
> First, you'd have a hard time reconciling that solution with the vacuum
> field equations. The only way to really do it would be to redefine the
> radial coordinate so that it comes out that way. But this would
> consequences for the rest of the metric. And even if you could get
> away with it, the space part of the curvature is only half the factor
> for gravitation anyway. The temporal part is essentially Newtonian and
> provides the other half.
Your concern is grossly unjustified. I am looking for mathematical
disproof of the metric I presented not handwaving with riddles added in
between each waving.
>>Does this new metric indicate a curvature in space? No.
>
> Not necessarily. You would just be rearraging things. But even if the
> spatial part of the curvature disappears, it wouldn't matter much. You
> can't get rid of spacetime curvature anyway. It's a tensor and so, if
> it's curved in one frame it must be curved in all of them.
>
>> Space is flat described by this new metric. So, how can you claim
>> gravitation can only be modeled by a curvature in spacetime?
>
> Spacetime is still curved.
Again, I showed mathematical proof that gravitation is adequate with
only gravitational time dilation regardless if space is curved or not.
>> Gravitation is there as long as there is a gravitational time dilation
>> regardless if space is curved or flat!
>
> No gravitation or gravitational dilation in flat spacetime.
Yes, but time can be curved, and space can be flat.
>>It gets better. Why does the
>> least action dictates a curvature in time after all?
>
> It doesn't. A space is either curved or flat. The variational
> principle alone can''t dictate that.
According to Hilbert Lagrange, it does.
>> I am not arguing that GR deals with a curvature in spacetime. GR is a
>> special case of hypotheses dealing with spacetime directly or
>> indirectly. There are other hypotheses that do not manifest a
>> curvature in spacetime but only time. With a gravitational time
>> dilation, it is more than adequate to explain gravitation. So, how can
>> you argue a set of physical laws actually represents the least amout of
>> action dealing with the curvature in both space and time but not
>> another set of physical laws only dealing with curvature in time and
>> flat space?
>
> Don't think of it that way. Spacetime is curved, period. You might be
> able to perform transformations that make the spatial part flat or the
> temporal part flat, but overall, a flat spacetime remains flat and a
> curved spacetime remains curved.
This is merely a postulate that spacetime is curved. Hilbert
Lagrangian is not proven to be valid. Thus, the result of the
curvature in spacetime according to the Calculus of Variations based on
the Lagrangian is questionable.
>> And what makes this Hilbert Lagrangian valid except through
>> experimentation? It is a very complicated Lagrangian as you have to
>> admit. How can you vouche for its validity other than through
>> experimentation?
>
> I think that's all we have. If you have a better way to derive all
> these effects, we'd love to hear it.
I promise that it'll come. I never bluff.
Ilja Schmelzer
"Tom Roberts" <tjrobe...@sbcglobal.net> schrieb
> > The Cosmological Constant is patched after the field equation are
> > derived.
>
> Hmmm. The indefinite integral of x^2 is (1/3)x^3 + C. Do you think that
> C is "patched after the equation is derived"? The cosmological constant
> in the EFE is directly analogous to the C in an indefinite integral.
??? Very different from this C, the functional derivative
delta S/delta g_mn (the Einstein equations) changes if
we introduce the cosmological constant.
Ilja
Aetherist
>
>Tom Roberts wrote:
>> Igor wrote:
>> > gu...@hotmail.com wrote:
>> >> Check my other post, in 1920 Einstein said he based his GR on the
>> >> Ether.
>> >
>> > No he did not. I think you must have your wires crossed and are taking
>> > him out of context.
>>
>> This is indeed out of context. In 1920 Einstein attended a conference on
>> the aether, and made remarks that essentially say that the "aether" of
>> GR is utterly unlike any other aether, in that it has no physical
>> properties (density, temperature, pressure, etc.), and no state of rest
>> can be ascribed to it.
>>
>> To consider GR as an "aether theory" requires an incredible PUN on the
>> word that robs it of all meaning. Einstein knew this. But he spoke in
>> the style of his time, not ours. <shrug>
>>
>
> you shrug to claim innocence and ambiguity. Einstein's specific words
> to the same link I gave:
>
> "GR without an ETHER IS UNTHINKABLE"
"Never attempt to teach a pig to sing, it's a waste of time
and annoys the pig"
In other words, there exist NO! way to reach Tom and/or convince him
that Einstein's essay should be taken at face value... Don't try to
confuse him with actual historical fact, his mind is simply made up!
> His further claims that is the Ether is not a tangeable substance
> (perhaps the same way photon has no mass or not a particle,etc...) is
> to cover his own behind.
Actually that's not true. Let's quote the whole sentence,
"According to the general theory of relativity space
without ether is unthinkable; for in such space there
not only wonld be no propagation of light, but also no
possibility of existence for standards of space and
time (measuring-rods and clocks), nor therefore any
space-time intervals in the physical sense. ..."
If matter (measuring-rods) are tangeable the one must think that
this sentence makes it clear that Einstein thought that ether
was a tangible, substantive, media. What also thought, and I
agree, was that the individual particles making up the ether
can not be individually identified and tracked through time.
We can only deal with these in a collective, statistical manner.
Quote,
"But this ether may not be thought of as endowed with
the quality characteristic of ponderable inedia, ..."
Like a rock or pebble...
"... as consisting of parts which may be tracked
through time."
When you can conceive how to track an individual molecules of
hydrogen in a multi-molar sea of hydrogen through time you'll
come to grips with this concept. Thus his earlier comment,
"They may not be thought of as consisting of particles
WHICH ALLOW themselves to be separately tracked through
time. ..."
Ref: http://www.tu-harburg.de/rzt/rzt/it/Ether.html
> In the very debts of your shrugging you know both above are correct.
Of course he does. He cannot change Einstein's written words
those are immutable facts...
Paul Stowe
gu...@hotmail.com
He finishes off by saying the ether is not a tangeable substance
perhaps the same way mechanics is tangeable and relatvity is not
tangeable (perspective related) or to cover himself and honour to
whatever new theory might unsubstanciate his own.
Example: hot water is cold (if you compare it to the sun's
temperature.) ( Ether is there (GR would exist without it) and the
Ether is also not there = untangeable)
>
> Tom Roberts
gu...@hotmail.com
Since light has no mass similar to sound, I think both light and the
ether are untangeable....you cannot see the ether and only the ripples
(waves) in it and these ripples are photons (and perhaps electrons,
partilces, hence matter) which are only waves (ripples) in the ether =
untangeable.
Igor
Koobee Wublee wrote:
> "Igor" <thoo...@excite.com> wrote in message
> news:1149788333....@h76g2000cwa.googlegroups.com...
> >
> > Koobee Wublee wrote:
> >> The Cosmological Constant is patched after the field equation are
> >> derived. The field equations are derived through the Hilbert
> >> Lagrangian (the Lagrangian to Hilbert-Einstein Action). The modified
> >> field equations are NOT Euler-Lagrange equations to the Hilbert
> >> Lagrangian. Then, how can you say the Cosmological Constant is a
> >> legitimate part of the field equations?
> >
> > Ever heard of Lagrange multipliers? The Einstein tensor is required to
> > be covariantly divergenceless. However, so is the metric tensor.
> > Hence, any linear combination of the two should be also.
>
> Yes, I have heard of Lagrangian Multipliers. I still don't see what
> these have anything convincingly to do with the Cosmological Constant.
You may have heard of them, but I doubt that you've ever really used
them. If you had, you'd most likely understand what I mean. The whole
point is that the Einstein tensor has be covariant divergence free.
Since the metric tensor already meets this criterion, this means that
we can always form a new divergence free Einstein tensor by adding a
constant multiple of the metric tensor. For that reason, the
cosmological constant doesn't necessarily have to be there, but it
could be there. Nature would have the final say.
> >> >> However, the misconception is that gravitation is caused
> >> >> by the curvature in spacetime.
> >> >
> >> > Nobody who has thought about it very much at all thinks that. Your usage
> >> > of naive causality is completely unwarranted. Gravitation is, however,
> >> > well modeled by curvature in spacetime.
> >>
> >> Let's say instead of the Hilbert Lagrangian. I find another one
> >> resulted in the field equations that yield a metric similar to the
> >> Schwarzschild metric except with unity term (1) associated with dr^2
> >> (instead of (1 -2 U)^-1). Can this new metric explain gravity? Yes,
> >> it does.
> >
> > First, you'd have a hard time reconciling that solution with the vacuum
> > field equations. The only way to really do it would be to redefine the
> > radial coordinate so that it comes out that way. But this would
> > consequences for the rest of the metric. And even if you could get
> > away with it, the space part of the curvature is only half the factor
> > for gravitation anyway. The temporal part is essentially Newtonian and
> > provides the other half.
>
> Your concern is grossly unjustified. I am looking for mathematical
> disproof of the metric I presented not handwaving with riddles added in
> between each waving.
But where is it?
> >>Does this new metric indicate a curvature in space? No.
> >
> > Not necessarily. You would just be rearraging things. But even if the
> > spatial part of the curvature disappears, it wouldn't matter much. You
> > can't get rid of spacetime curvature anyway. It's a tensor and so, if
> > it's curved in one frame it must be curved in all of them.
> >
> >> Space is flat described by this new metric. So, how can you claim
> >> gravitation can only be modeled by a curvature in spacetime?
> >
> > Spacetime is still curved.
>
> Again, I showed mathematical proof that gravitation is adequate with
> only gravitational time dilation regardless if space is curved or not.
No problem there. But spacetime must still be curved overall in order
tor this to work. Remember, no spacetime curvature -- no gravity.
> >> Gravitation is there as long as there is a gravitational time dilation
> >> regardless if space is curved or flat!
> >
> > No gravitation or gravitational dilation in flat spacetime.
>
> Yes, but time can be curved, and space can be flat.
If you're saying that R_00 is the only only nonzero component of the
Ricci tensor, then yes, that could be possible, But that's what I've
been saying all along.
> >>It gets better. Why does the
> >> least action dictates a curvature in time after all?
> >
> > It doesn't. A space is either curved or flat. The variational
> > principle alone can''t dictate that.
>
> According to Hilbert Lagrange, it does.
I don't know where you're getting this. The Hilbert action has the
form: Int R sqrt (-g) d^4V . This can be optimized whether R is zero
or finite, or whether the space is flat or curved.
> >> I am not arguing that GR deals with a curvature in spacetime. GR is a
> >> special case of hypotheses dealing with spacetime directly or
> >> indirectly. There are other hypotheses that do not manifest a
> >> curvature in spacetime but only time. With a gravitational time
> >> dilation, it is more than adequate to explain gravitation. So, how can
> >> you argue a set of physical laws actually represents the least amout of
> >> action dealing with the curvature in both space and time but not
> >> another set of physical laws only dealing with curvature in time and
> >> flat space?
> >
> > Don't think of it that way. Spacetime is curved, period. You might be
> > able to perform transformations that make the spatial part flat or the
> > temporal part flat, but overall, a flat spacetime remains flat and a
> > curved spacetime remains curved.
>
> This is merely a postulate that spacetime is curved. Hilbert
> Lagrangian is not proven to be valid. Thus, the result of the
> curvature in spacetime according to the Calculus of Variations based on
> the Lagrangian is questionable.
It's perfectly fine for GR alone. Additional terms have to be added
when there are external fields. AFAIK, there has never been anything
shown to be wrong with it.
> >> And what makes this Hilbert Lagrangian valid except through
> >> experimentation? It is a very complicated Lagrangian as you have to
> >> admit. How can you vouche for its validity other than through
> >> experimentation?
> >
> > I think that's all we have. If you have a better way to derive all
> > these effects, we'd love to hear it.
>
> I promise that it'll come. I never bluff.
Tell me what you have. Otherwise, you're just saying it's not valid
without any rigorous proof.
Dirk Van de moortel
"Koobee Wublee" <koobee...@gmail.com> wrote in message news:1149830195.1...@i39g2000cwa.googlegroups.com...
>
> "Tom Roberts" <tjrobe...@sbcglobal.net> wrote in message
> news:bm%hg.93221$H71....@newssvr13.news.prodigy.com...
>
> > Koobee Wublee wrote:
> >> The Cosmological Constant is patched after the field equation are
> >> derived.
> >
> > Hmmm. The indefinite integral of x^2 is (1/3)x^3 + C. Do you think that
> > C is "patched after the equation is derived"? The cosmological constant
> > in the EFE is directly analogous to the C in an indefinite integral.
>
> What is this integral you are referring to? EFE are the results of
> differentiation.
>
> >> Let's say instead of the Hilbert Lagrangian. I find another one
> >> resulted in the field equations that yield a metric similar to the
> >> Schwarzschild metric except with unity term (1) associated with dr^2
> >> (instead of (1 -2 U)^-1). Can this new metric explain gravity? Yes,
> >> it does. Does this new metric indicate a curvature in space? No.
> >> Space is flat described by this new metric. So, how can you claim
> >> gravitation can only be modeled by a curvature in spacetime?
> >
> > Because the underlying manifold is spacetime, not simply space. The
> > foliation of spacetime into space and time is of no physical
> > significance, because it is the same symmetry as changing coordinates.
>
> I don't understand what you are saying.
That is because you are an obnoxious imbecile.
> Is this an ancient verse out
> of a GR bible?
>
> >> Gravitation is there as long as there is a gravitational time dilation
> >> regardless if space is curved or flat!
> >
> > Sure -- the foliation of spacetime into space and time is arbitrary. But
> > spaceTIME is not flat. Attempting to discuss the curvature of space as a
> > fundamental entity is hopeless.
>
> Again, foliation? There is not even such a word in the English
> language.
Like for instance in Webster:
http://www.webster.com/dictionary/foliation
> Please stop talking in riddles to justify your points.
Please continue behaving like an obnoxious imbecile.
Dirk Vdm
JanPB
> "Tom Roberts" <tjrobe...@sbcglobal.net> wrote in message
> news:bm%hg.93221$H71....@newssvr13.news.prodigy.com...
> > Sure -- the foliation of spacetime into space and time is arbitrary. But
> > spaceTIME is not flat. Attempting to discuss the curvature of space as a
> > fundamental entity is hopeless.
>
> Again, foliation? There is not even such a word in the English
> language. Please stop talking in riddles to justify your points.
Hahaha! Poor Tom (again).
> >> It is a very complicated Lagrangian as you have to
> >> admit.
If you don't know "foliation" perhaps you should lay off field
Lagrangians. Just a suggestion.
--
Jan Bielawski
surrealis...@hotmail.com
Relativists should make peace with Einstein's notion of "ether." This
causes no harm. And constantly bickering over the term "ether" seems to
accomplish nothing good for either side. However, Einstein's
metric-field ether is neither Maxwell's ether nor Lorentz's ether, both
of which were mechanical.
Einstein was originally impressed by the similarity between the
immobile Lorentzian ether and SR's flat spacetime. So, his "ether"
exists as a theoretical construct because Einstein first drew this
immobility analogy between Lorentz's ether and flat spacetime. It was
then just one small step to go from flat spacetime to dynamic, curved
spacetime, and voila: the metric field tensor is also an "ether."
What do these three ethers have in common? 1) they're all space
filling, and 2) they're all used in some physical theory to explain
electrodynamic phenomena.
Koobee Wublee
>
> Koobee Wublee wrote:
>> Yes, I have heard of Lagrangian Multipliers. I still don't see what
>> these have anything convincingly to do with the Cosmological Constant.
>
> You may have heard of them, but I doubt that you've ever really used
> them. If you had, you'd most likely understand what I mean. The whole
> point is that the Einstein tensor has be covariant divergence free.
> Since the metric tensor already meets this criterion, this means that
> we can always form a new divergence free Einstein tensor by adding a
> constant multiple of the metric tensor. For that reason, the
> cosmological constant doesn't necessarily have to be there, but it
> could be there. Nature would have the final say.
Do you have an example of whatever not covariantly divergenceless?
>> Your concern is grossly unjustified. I am looking for mathematical
>> disproof of the metric I presented not handwaving with riddles added in
>> between each waving.
>
> But where is it?
Try the following spacetime.
ds^2 = c^2 (1 - 2 U) dt^2 - dr^2 - r^2 dH^2 ...
It has a flat space but with gavitational time dilation. It explains
gravity just as good as the Schwarzschild spacetime. Thus, the cause
of gravitation is not and none other than gravitational time dilation
regardless if space is curved or not.
>> >>It gets better. Why does the
>> >> least action dictates a curvature in time after all?
>> >
>> > It doesn't. A space is either curved or flat. The variational
>> > principle alone can''t dictate that.
>>
>> According to Hilbert Lagrange, it does.
>
> I don't know where you're getting this. The Hilbert action has the
> form: Int R sqrt (-g) d^4V . This can be optimized whether R is zero
> or finite, or whether the space is flat or curved.
Since the metric is indirectly derived from the Hilbert Lagrangian
through the calculus of variations, you still have to justify the
reason behind that. What is extremizing the Hilbert-Einstein Action
necessary for a particular metric to exist?
Aetherist
>> If matter (measuring-rods) are tangible the one must think that
>> this sentence makes it clear that Einstein thought that ether
>> was a tangible, substantive, media. What he also thought, and I
>> agree, was that the individual particles making up the ether
>> can not be individually identified and tracked through time.
>> We can only deal with these in a collective, statistical manner.
>> Quote,
>>
>> "But this ether may not be thought of as endowed with
>> the quality characteristic of ponderable inedia, ..."
>>
>> Like a rock or pebble...
>>
>> "... as consisting of parts which may be tracked
>> through time."
>>
>> When you can conceive how to track an individual molecule of
>> hydrogen in a multi-molar sea of hydrogen through time you'll
>> come to grips with this concept. Thus his earlier comment,
>>
>> "They may not be thought of as consisting of particles
>> WHICH ALLOW themselves to be separately tracked through
>> time. ..."
>>
>> Ref: http://www.tu-harburg.de/rzt/rzt/it/Ether.html
>>
>>> In the very debts of your shrugging you know both above are correct.
>>
>> Of course he does. He cannot change Einstein's written words
>> those are immutable facts...
>>
>> Paul Stowe
>
> Relativists should make peace with Einstein's notion of "ether." This
> causes no harm. And constantly bickering over the term "ether" seems to
> accomplish nothing good for either side.
I agree, and modernists should make peace with aetherists. They are
simply differeent metaphysical perspectives.
> However, Einstein's metric-field ether is neither Maxwell's ether nor
> Lorentz's ether, both of which were mechanical.
That's funny given Einstein's comment in the introduction of his
1905 paper. Which was, to accept Maxwell's model as valid as a
start. Doing so inherits the only physical model Maxwell ever
provided for deriving these equations.
>
> Einstein was originally impressed by the similarity between the
> immobile Lorentzian ether and SR's flat spacetime. So, his "ether"
> exists as a theoretical construct because Einstein first drew this
> immobility analogy between Lorentz's ether and flat spacetime. It was
> then just one small step to go from flat spacetime to dynamic, curved
> spacetime, and voila: the metric field tensor is also an "ether."
>
> What do these three ethers have in common? 1) they're all space
> filling, and 2) they're all used in some physical theory to explain
> electrodynamic phenomena.
I'd say concepts, not ethers... There is only one space filling substance
who's properties include all of these.
Spoonfed
n-dimensional subspace of a greater than n dimensional space. The
questions which are answered by tensors have to do with objects falling
in gravity, light bending in gravity, and time slowing in gravity, and
(maybe) space expanding in gravity.
I don't actually know what these questions are... only that they have
to do with gravitational potential fields and gradients. In
particular, non-zero gradients and non-constant fields.
I have no idea what Einstein "thought" but it seems to me, he may have
gone off the deep end for a little while. I've read two books now that
pointed out that Einstein tried to fit his theory in with the Machian
principles, which claimed such things as "rotation and acceleration do
not exist without outside reference." Martin Gardner even used the
notion of "the average motion of all objects in the universe" in his
description of the twin paradox.
Though obviously the average motion of all objects in the universe has
no bearing on the twin paradox, there still could be such an average
motion. If you assume the universe is finite, then there is an average
momentum. Also, there is a center of gravity, and thus a nonzero
gravitational gradient at every point except the center.
However, a finite mass universe, if Heisenberg's uncertainty principle
(HUP) is accurate, means a finite initial size. I believe Hawking
showed that the universe had to begin with a singularity, and I agree
since an initial finite size in one reference frame means an
arbitrarily extended (across time and space) creation in every other
reference frame. Only a singularity will appear the same in all
reference frames.
So with an infinite universe, there does not need to be an average
momentum, center of mass, or universal nonzero gravitational gradient.
So what am I saying?
Whether or not you think there is an ether, there does seem to be
something quantifiable about gravitational potential. One can create a
space or spacetime map of gravitational potential across the universe,
just as you can make a map of the stars. This spacetime map of
gravitational potential at all points and times is just like a map of
events at all points and times, so it can be transformed through
Lorentz Transformations just like any other spacetime diagram. So if
the ether transforms just like a set of events transforms, I'm not sure
if there's any reason to argue ether or no ether. Except Noether had a
really good method of solving classical mechanics problems, so let's
stick with Noether.
There has been some attempt to redefine straight lines arout the idea
that straight lines are geodesics or paths which light takes. At the
very same time, or in the very same paragraph, sometimes, it is noted
that objects accelerate, and light bends in gravitational fields.
Well, straight lines obviously don't bend or change directions, whereas
geodesics and paths of light in gravitational fields do. The trouble is
there is some ambiguity of context. If an object turns or accelerates,
it is clearly not moving in a straight line. But through massive
contortions of algebraic manipulation and origami, you can put together
a representation of reality where all objects move in straight lines at
the speed of light. But it requires a two dimensional surface in three
dimensional space just to represent one dimension of motion. (See
"Relativity Visualized")
Igor
Koobee Wublee wrote:
> "Igor" <thoo...@excite.com> wrote in message
> news:1149872824....@u72g2000cwu.googlegroups.com...
> >
> > Koobee Wublee wrote:
> >> Yes, I have heard of Lagrangian Multipliers. I still don't see what
> >> these have anything convincingly to do with the Cosmological Constant.
> >
> > You may have heard of them, but I doubt that you've ever really used
> > them. If you had, you'd most likely understand what I mean. The whole
> > point is that the Einstein tensor has be covariant divergence free.
> > Since the metric tensor already meets this criterion, this means that
> > we can always form a new divergence free Einstein tensor by adding a
> > constant multiple of the metric tensor. For that reason, the
> > cosmological constant doesn't necessarily have to be there, but it
> > could be there. Nature would have the final say.
>
> Do you have an example of whatever not covariantly divergenceless?
The Einstein tensor and the metric tensor.
>
> >> Your concern is grossly unjustified. I am looking for mathematical
> >> disproof of the metric I presented not handwaving with riddles added in
> >> between each waving.
> >
> > But where is it?
>
> Try the following spacetime.
>
> ds^2 = c^2 (1 - 2 U) dt^2 - dr^2 - r^2 dH^2 ...
>
> It has a flat space but with gavitational time dilation. It explains
> gravity just as good as the Schwarzschild spacetime. Thus, the cause
> of gravitation is not and none other than gravitational time dilation
> regardless if space is curved or not.
But this is not a solution of the weak field equations. The Ricci
tensor won't vanish for this "solution", so it's not a good example..
> >> >>It gets better. Why does the
> >> >> least action dictates a curvature in time after all?
> >> >
> >> > It doesn't. A space is either curved or flat. The variational
> >> > principle alone can''t dictate that.
> >>
> >> According to Hilbert Lagrange, it does.
> >
> > I don't know where you're getting this. The Hilbert action has the
> > form: Int R sqrt (-g) d^4V . This can be optimized whether R is zero
> > or finite, or whether the space is flat or curved.
>
> Since the metric is indirectly derived from the Hilbert Lagrangian
> through the calculus of variations, you still have to justify the
> reason behind that. What is extremizing the Hilbert-Einstein Action
> necessary for a particular metric to exist?
No. The metric is already part of the Lagrangian in the more general
sense. It's not derived. The functional shape of the metric
components is determined by the field equations, which are based on
the variational principle. Classical mechanics is also derived using
variational principles. There are metrics there also. Note the metric
tensors for flat spaces described by polar and speherical coordinates.
But notice there is no talk of curvature there at all.
Igor
Spoonfed wrote:
> Tensors have to do with parallel transport of vectors along an
> n-dimensional subspace of a greater than n dimensional space.
No. Those are called affine connections. And they are not tensors at
all.
>The
> questions which are answered by tensors have to do with objects falling
> in gravity, light bending in gravity, and time slowing in gravity, and
> (maybe) space expanding in gravity.
Actually, a tensor is a generalization of a vector, which can be
described as a tensor of rank one. There are tensors of rank zero
(scalars) which are invariant. And there are higher rank tensors (some
matrices can be called second rank tensors).
> I don't actually know what these questions are... only that they have
> to do with gravitational potential fields and gradients. In
> particular, non-zero gradients and non-constant fields.
GR, as a tensor theory, is based on the equivalence principle, which
states that, gravitational acceleration cannot be locally distinguished
from any arbitrary acceleration.
> I have no idea what Einstein "thought" but it seems to me, he may have
> gone off the deep end for a little while. I've read two books now that
> pointed out that Einstein tried to fit his theory in with the Machian
> principles, which claimed such things as "rotation and acceleration do
> not exist without outside reference." Martin Gardner even used the
> notion of "the average motion of all objects in the universe" in his
> description of the twin paradox.
Well, there was a period where he certainly was obsessed with Mach and
tried very hard to make Mach's ideas fit into the theory. He
eventually gave up when solutions to his GR equations were found that
completely disagreed with all of Mach's concepts.
> Though obviously the average motion of all objects in the universe has
> no bearing on the twin paradox, there still could be such an average
> motion. If you assume the universe is finite, then there is an average
> momentum. Also, there is a center of gravity, and thus a nonzero
> gravitational gradient at every point except the center.
Center of what?
> However, a finite mass universe, if Heisenberg's uncertainty principle
> (HUP) is accurate, means a finite initial size.
Not necessarily.
> I believe Hawking
> showed that the universe had to begin with a singularity, and I agree
> since an initial finite size in one reference frame means an
> arbitrarily extended (across time and space) creation in every other
> reference frame. Only a singularity will appear the same in all
> reference frames.
Depends on what type of singularity it actually is. There are some
types that are merely artefacts of the geometry and can be removed by a
simple coordinate transformation. A good example is the poles in
Mercator projection. Then there are those intrinsic singularities that
do persist no matter how you remap the system.
> So with an infinite universe, there does not need to be an average
> momentum, center of mass, or universal nonzero gravitational gradient.
Why not? These ideas should still be valid for an infinite universe.
>
> So what am I saying?
>
> Whether or not you think there is an ether, there does seem to be
> something quantifiable about gravitational potential. One can create a
> space or spacetime map of gravitational potential across the universe,
> just as you can make a map of the stars. This spacetime map of
> gravitational potential at all points and times is just like a map of
> events at all points and times, so it can be transformed through
> Lorentz Transformations just like any other spacetime diagram. So if
> the ether transforms just like a set of events transforms, I'm not sure
> if there's any reason to argue ether or no ether. Except Noether had a
> really good method of solving classical mechanics problems, so let's
> stick with Noether.
A lot of people miss the point that has been done to death in the last
hundred years. Whether or not the aether exists in some form is
irrelevant. So far as we have been able to observe, not only have we
not been able to find any aether, it doesn't even seem to be necessary.
> There has been some attempt to redefine straight lines arout the idea
> that straight lines are geodesics or paths which light takes. At the
> very same time, or in the very same paragraph, sometimes, it is noted
> that objects accelerate, and light bends in gravitational fields.
> Well, straight lines obviously don't bend or change directions, whereas
> geodesics and paths of light in gravitational fields do. The trouble is
> there is some ambiguity of context. If an object turns or accelerates,
> it is clearly not moving in a straight line. But through massive
> contortions of algebraic manipulation and origami, you can put together
> a representation of reality where all objects move in straight lines at
> the speed of light. But it requires a two dimensional surface in three
> dimensional space just to represent one dimension of motion. (See
> "Relativity Visualized")
Actually, the notion of geodesic is a generalization of the concept of
a straight line and in most cases, as in GR, geodesics are never
straight lines. But they are the path of least effort for a body to
move through the geometry. In GR, planetary orbits become elliptical
geodesics and the path of light is bent when it nears a massive object
like the sun. No one pretends that these are straight lines. They are
merely geodesics for the curved spacetime generated by the sun.
Spoonfed
> Spoonfed wrote:
> > Tensors have to do with parallel transport of vectors along an
> > n-dimensional subspace of a greater than n dimensional space.
>
> No. Those are called affine connections. And they are not tensors at
> all.
>
Phew! Thank you.
> >The
> > questions which are answered by tensors have to do with objects falling
> > in gravity, light bending in gravity, and time slowing in gravity, and
> > (maybe) space expanding in gravity.
>
> Actually, a tensor is a generalization of a vector, which can be
> described as a tensor of rank one. There are tensors of rank zero
> (scalars) which are invariant. And there are higher rank tensors (some
> matrices can be called second rank tensors).
>
Which ones?
> > I don't actually know what these questions are... only that they have
> > to do with gravitational potential fields and gradients. In
> > particular, non-zero gradients and non-constant fields.
>
> GR, as a tensor theory, is based on the equivalence principle, which
> states that, gravitational acceleration cannot be locally distinguished
> from any arbitrary acceleration.
>
Right. "locally." If you look past your eyebrows, you know you've got
arbitrarily acceleration when
a) the stars in one direction get more blue-shifted and the others get
more red-shifted
b) you drill a hole in the floor and there are people hanging off the
other side.
c) the propellant runs out
I will say, the equivalence principle itself leads to some interesting
ideas in that gravity doesn't seem to have any kind of conceptual
handle you can grab onto to do gedanken--best you can do is rely on
experiment. But it is comparitively easy to think about a rig under
constant acceleration and consider what would happen to raindrops,
light beams, and watches in such an environment, (absent of gravity).
I can see a definite appeal to establishing that the two are
equivalent, as long as you keep in mind the environment you're dealing
with. And I suppose the tensor mathematics is just the tool you need
to keep precisely this in mind, if you know how to use them.
> > I have no idea what Einstein "thought" but it seems to me, he may have
> > gone off the deep end for a little while. I've read two books now that
> > pointed out that Einstein tried to fit his theory in with the Machian
> > principles, which claimed such things as "rotation and acceleration do
> > not exist without outside reference." Martin Gardner even used the
> > notion of "the average motion of all objects in the universe" in his
> > description of the twin paradox.
>
> Well, there was a period where he certainly was obsessed with Mach and
> tried very hard to make Mach's ideas fit into the theory. He
> eventually gave up when solutions to his GR equations were found that
> completely disagreed with all of Mach's concepts.
>
I would say that Galilean relativity and Special Relativity also
completely disagree with all of Mach's concepts but I don't have an
elegant proof on hand.
> > Though obviously the average motion of all objects in the universe has
> > no bearing on the twin paradox, there still could be such an average
> > motion. If you assume the universe is finite, then there is an average
> > momentum. Also, there is a center of gravity, and thus a nonzero
> > gravitational gradient at every point except the center.
>
> Center of what?
>
If the universe has a finite mass, then along any given direction,
there must be a particle which has traveled further than any other in
that direction. Why? Because if there aren't, it either means there
are no particles in that direction, or there are an infinite number.
Point in the opposite direction, and there must be a similar particle.
Halfway between these two particles is the center of the universe in
that line.
I would be interested in an example of a finite mass universe that has
no center of mass/center of gravity if you have one.
> > However, a finite mass universe, if Heisenberg's uncertainty principle
> > (HUP) is accurate, means a finite initial size.
>
> Not necessarily.
>
If my interpretation of HUP is accurate, finite mass implies finite
momentum between every pair of particles. Finite momentum * zero
initial size of universe < hbar/2. In order for the universe to start
as a singularity, you need the momenta to span an infinite set.
Not sure what your "not necessarily" is getting at, but it might be
gravity... If you are thinking of how gravity warps space to bring down
to a singularity regions that defy HUP. But with perfect symmetry and
infinite mass, there is no gradient... It doesn't matter how strong the
gravitational field is if it doesn't vary from point to point.
> > I believe Hawking
> > showed that the universe had to begin with a singularity, and I agree
> > since an initial finite size in one reference frame means an
> > arbitrarily extended (across time and space) creation in every other
> > reference frame. Only a singularity will appear the same in all
> > reference frames.
>
> Depends on what type of singularity it actually is. There are some
> types that are merely artefacts of the geometry and can be removed by a
> simple coordinate transformation. A good example is the poles in
> Mercator projection. Then there are those intrinsic singularities that
> do persist no matter how you remap the system.
>
Good point. I wasn't aware of the ambiguity with which the word
"singularity" was used in GR. The big bang singularity means singular
event--a geometric point in spacetime. And certainly, if you want to
map all timelines (or worldlines) extending from it as vertical then it
would appear as a horizontal line, just as the north and south poles
appear as horizontal line segments in a mercator projection.
However, under a Lorentz transformation, an event will remain an event,
and should persist as a point in a spacetime diagram no matter what
Lorentz transformation you do.
The instantaneous appearance of a finite size universe (no matter how
small) is a set of independent events.
> > So with an infinite universe, there does not need to be an average
> > momentum, center of mass, or universal nonzero gravitational gradient.
>
> Why not? These ideas should still be valid for an infinite universe.
>
No, not necessarily. Imagine an infinite length ruler. Where is the
center? At the zero mark? No, the zero mark is arbitrarily placed.
No matter where you observe the ruler, there is always an equal amount
in both directions.
> >
> > So what am I saying?
> >
> > Whether or not you think there is an ether, there does seem to be
> > something quantifiable about gravitational potential. One can create a
> > space or spacetime map of gravitational potential across the universe,
> > just as you can make a map of the stars. This spacetime map of
> > gravitational potential at all points and times is just like a map of
> > events at all points and times, so it can be transformed through
> > Lorentz Transformations just like any other spacetime diagram. So if
> > the ether transforms just like a set of events transforms, I'm not sure
> > if there's any reason to argue ether or no ether. Except Noether had a
> > really good method of solving classical mechanics problems, so let's
> > stick with Noether.
>
> A lot of people miss the point that has been done to death in the last
> hundred years. Whether or not the aether exists in some form is
> irrelevant. So far as we have been able to observe, not only have we
> not been able to find any aether, it doesn't even seem to be necessary.
>
I agree.
>
> > There has been some attempt to redefine straight lines arout the idea
> > that straight lines are geodesics or paths which light takes. At the
> > very same time, or in the very same paragraph, sometimes, it is noted
> > that objects accelerate, and light bends in gravitational fields.
> > Well, straight lines obviously don't bend or change directions, whereas
> > geodesics and paths of light in gravitational fields do. The trouble is
> > there is some ambiguity of context. If an object turns or accelerates,
> > it is clearly not moving in a straight line. But through massive
> > contortions of algebraic manipulation and origami, you can put together
> > a representation of reality where all objects move in straight lines at
> > the speed of light. But it requires a two dimensional surface in three
> > dimensional space just to represent one dimension of motion. (See
> > "Relativity Visualized")
>
> Actually, the notion of geodesic is a generalization of the concept of
> a straight line and in most cases, as in GR, geodesics are never
> straight lines. But they are the path of least effort for a body to
> move through the geometry. In GR, planetary orbits become elliptical
> geodesics and the path of light is bent when it nears a massive object
> like the sun. No one pretends that these are straight lines. They are
> merely geodesics for the curved spacetime generated by the sun.
Maybe it's not a widespread idea, but I think I've talked to people who
pretended this.
Tom Roberts
> "Tom Roberts" <tjrobe...@sbcglobal.net> wrote in message
> news:bm%hg.93221$H71....@newssvr13.news.prodigy.com...
>> Koobee Wublee wrote:
>>> The Cosmological Constant is patched after the field equation are
>>> derived.
>> Hmmm. The indefinite integral of x^2 is (1/3)x^3 + C. Do you think that
>> C is "patched after the equation is derived"? The cosmological constant
>> in the EFE is directly analogous to the C in an indefinite integral.
>
> What is this integral you are referring to? EFE are the results of
> differentiation.
It is an _example_ of a similar phenomenon -- where the usual
mathematical "derivation" does not necessarily provide the complete
solution.
>>> Let's say instead of the Hilbert Lagrangian. I find another one
>>> resulted in the field equations that yield a metric similar to the
>>> Schwarzschild metric except with unity term (1) associated with dr^2
>>> (instead of (1 -2 U)^-1). Can this new metric explain gravity? Yes,
>>> it does. Does this new metric indicate a curvature in space? No.
>>> Space is flat described by this new metric. So, how can you claim
>>> gravitation can only be modeled by a curvature in spacetime?
>> Because the underlying manifold is spacetime, not simply space. The
>> foliation of spacetime into space and time is of no physical
>> significance, because it is the same symmetry as changing coordinates.
>
> I don't understand what you are saying.
That's quite clear. You do not understand much about GR at all. This is
very basic.
And I don't claim that gravitation can _only_ be modeled by curvature in
spacetime. Such curvature has proven to be an excellent model of
gravitation. But of course that does not rule out the possibility that
other models can be found; indeed, Newtonian gravitation is also a
pretty good model.
> Again, foliation? There is not even such a word in the English
> language. Please stop talking in riddles to justify your points.
Clearly you do not know the standard vocabulary, so how can you expect
to be taken seriously?
Foliation is the word used to indicate the separating of an N
dimensional manifold into submanifolds whose dimensions add up to N. It
is a normal part of the standard vocabulary of differential geometry and
GR. <shrug>
>>> It is a very complicated Lagrangian as you have to
>>> admit.
>> Actually, it is the simplest possible Lagrangian that satisfies the
>> clear and obvious symmetries.
>
> I don't see the simplicity in Hilbert Lagrangian. Simplicity is
> awefully subjective.
Consider all possible scalar functions of all of the the curvature
tensors. The simplest is clearly R+L, where R is the Ricci curvature
scalar and L is a constant. That is the Lagrangian density for GR.
> What guarantees it being the valid one?
Comparison with experiment. This is, of course, no "guarantee".
> What
> does the Hilbert-Einstein Action have to be minimized?
The action itself is to be extremized. This is the whole basis of
Lagrangian methods in physics. <shrug>
Tom Roberts
Tom Roberts
> Tensors have to do with parallel transport of vectors along an
> n-dimensional subspace of a greater than n dimensional space.
You are confused. The affine connection is what determines the parallel
transport of vectors along a 1-d path. I have no idea what "parallel
transport of vectors along an n-dimensional subspace" means. Transport
inherently means from here to there along a 1-d path.
The affine connection is not a tensor.
> The
> questions which are answered by tensors have to do with objects falling
> in gravity, light bending in gravity, and time slowing in gravity, and
> (maybe) space expanding in gravity.
You use language that implies _FAR_ more generality than is actually the
case. The metric tensor of spacetime can be used to determine "time
slowing in gravity" and "space expanding"; all the others need the
affine connection, not any tensor. Note, however, that given a metric
tensor on the manifold there is a unique affine connection that is
consistent with it, and in GR it is always used.
> I don't actually know what these questions are... only that they have
> to do with gravitational potential fields and gradients. In
> particular, non-zero gradients and non-constant fields.
Your word salad dos not apply to GR.
> I have no idea what Einstein "thought" but it seems to me, he may have
> gone off the deep end for a little while. I've read two books now that
> pointed out that Einstein tried to fit his theory in with the Machian
> principles, which claimed such things as "rotation and acceleration do
> not exist without outside reference."
GR conforms loosely to Mach's principle, but not completely.
Specifically, the class of locally-inertial frames at a given point
depends in some sense on all the mass-energy in its past lightcone. But
the mass of an object is intrinsic and does not come from interactions
with "all the mass in the universe".
> Martin Gardner even used the
> notion of "the average motion of all objects in the universe" in his
> description of the twin paradox.
I would not quote him as an expert on GR. His audience is clearly not an
expert one, and his writing is rather loose (bordering on being wrong).
> If you assume the universe is finite, then there is an average
> momentum. Also, there is a center of gravity, and thus a nonzero
> gravitational gradient at every point except the center.
Not necessarily. The universe could be finite and compact, and it could
be that the "center of mass" is no specific point, but rather mass is
equally distributed around each and every point. Similarly for "average
momentum". For instance, an analogy is to find the intrinsic "center of
mass" of a uniform spherical shell (i.e. restricted to its 2-d surface).
> [... further wild speculations omitted]
Tom Roberts
Spoonfed
> Spoonfed wrote:
> > Tensors have to do with parallel transport of vectors along an
> > n-dimensional subspace of a greater than n dimensional space.
>
> You are confused.
Quite!
"...in particular the so-called Ricci tensor tells us how vectors turn
as you parallel transport in a curved space. This is exactly what
Einstein had been looking for. From the Ricci tensor, Einstein then
constructed the field equations. These all-important equations tell us
all we need to know about the properties of space-time in a
gravitational field."
-Relativity and Cosmology, William J. Kauffman, III
Now, are you saying that I am wrong, (that tensors have nothing to do
with parallel transport of vectors) or that I am correct, but confused?
> The affine connection is what determines the parallel
> transport of vectors along a 1-d path. I have no idea what "parallel
> transport of vectors along an n-dimensional subspace" means. Transport
> inherently means from here to there along a 1-d path.
The orbit of mercury is a more-or-less 2-D path in exactly 3-D space,
or perhaps 4-D spacetime, which turns out not to be elliptical, and I
am indeed confused, because I don't know what tensors say about the
problem... I only know the problem can be approached using them.
And I did not know that "transport" inherently meant a straight line.
Once again tripped up by the redefining of common words.
>
> The affine connection is not a tensor.
>
>
> > The
> > questions which are answered by tensors have to do with objects falling
> > in gravity, light bending in gravity, and time slowing in gravity, and
> > (maybe) space expanding in gravity.
>
> You use language that implies _FAR_ more generality than is actually the
> case. The metric tensor of spacetime can be used to determine "time
> slowing in gravity" and "space expanding"; all the others need the
> affine connection, not any tensor. Note, however, that given a metric
> tensor on the manifold there is a unique affine connection that is
> consistent with it, and in GR it is always used.
>
metric tensor-time slowing and space expanding
affine connection-objects falling in gravity, light bending in gravity
Now, from what you say here, it sounds as though the Lorentz
transformation could be an example of a metric tensor.
It also sounds like the affine connection might describe the sequence
of events of an object moving through space?
>
> > I don't actually know what these questions are... only that they have
> > to do with gravitational potential fields and gradients. In
> > particular, non-zero gradients and non-constant fields.
>
> Your word salad dos not apply to GR.
>
Yes it does.
I'm trying to be very clear, so for you to call this a word salad, it
seems we have very different backgrounds.
Gravitational potential is a scalar quantity which has a value at every
point in space, analogous to electric potential, but caused by mass
instead of charge.
If that quantity is constant through a region of space then an object
will not be attracted one way or another. If the gravitational
potential is different through the region, that means that the object
must be attracted to the region of lower gravitational potential.
The gradient of a scalar field F is a vector field determined by
dF/dx i_x + dF/dy i_y + dF/dz i_z
and it is quite a neat little vector because it points straight toward
the highest increase of the field. Of course, since gravitational
potential is made negative by the presence of mass, you have to take
the negative of the gradient of the gravitational scalar field to get
the direction of pull.
Aside: What's interesting is that you can have a region of zero scalar
gravitational potential and another region with a lower scalar
gravitational potential but have no gradient in either area. By the
equivalence principle, gravity is equivalent to acceleration. Is the
slowing of time in GR based on the local gradient of gravitational
field or the absolute scalar field? Standing on earth we are in a
frame equivalent to one accelerating 9.8 m/s^2 straight up. What if
there were two earth's held apart and we were floating between them?
We are in the same or lower scalar gravitational potential but the
gravitational gradient pulling us down is gone. If acceleration is
equivalent to gravity, we've almost eliminated it.
And back to the main point, it is very clear that GR applies to nonzero
gravitational gradients. It is not so clear (to me) whether it applies
to zero gravitational gradients.
>
> > I have no idea what Einstein "thought" but it seems to me, he may have
> > gone off the deep end for a little while. I've read two books now that
> > pointed out that Einstein tried to fit his theory in with the Machian
> > principles, which claimed such things as "rotation and acceleration do
> > not exist without outside reference."
>
> GR conforms loosely to Mach's principle, but not completely.
> Specifically, the class of locally-inertial frames at a given point
> depends in some sense on all the mass-energy in its past lightcone. But
> the mass of an object is intrinsic and does not come from interactions
> with "all the mass in the universe".
>
>
> > Martin Gardner even used the
> > notion of "the average motion of all objects in the universe" in his
> > description of the twin paradox.
>
> I would not quote him as an expert on GR. His audience is clearly not an
> expert one, and his writing is rather loose (bordering on being wrong).
>
I am glad that this is not an element of GR. It is also not an element
in SR. Also Boltzmann had some pretty choice words about Mach here and
there.
>
> > If you assume the universe is finite, then there is an average
> > momentum. Also, there is a center of gravity, and thus a nonzero
> > gravitational gradient at every point except the center.
>
> Not necessarily. The universe could be finite and compact, and it could
> be that the "center of mass" is no specific point, but rather mass is
> equally distributed around each and every point. Similarly for "average
> momentum". For instance, an analogy is to find the intrinsic "center of
> mass" of a uniform spherical shell (i.e. restricted to its 2-d surface).
>
Are you referring to a 3-D shaped universe curved in a 4-D universe? I
suppose this might seem less speculative than my idea of an infinite
mass perfectly symmetrical universe in 3-D.
>
> > [... further wild speculations omitted]
>
>
> Tom Roberts
Not wild and speculative--more just lucky, I think. Actually, most
everything fits together the way it does because it has to be a
particular way within the framework. For instance, I never even
thought of considering extra global spatial dimensions, I was merely
looking for a good explanation for the CBR, then when I hit upon it, I
found that I was in total disagreement with everybody. My insistence
on an infinite mass comes from trying to figure out what the density
map would look like. When I did the calculation, my units were off. I
popped in a fudge factor and realized I'd just accounted properly for
HUP. When I did that, I found out I couldn't get an initial zero size.
Could make it arbitrarily small, but never zero. Was it an infinite
number of arbitrary size particles or an arbitrary number of infinite
size particles? Who knows? But I'm going to insist on a singularity
or it all falls apart, so it can't be arbitrarily small, it has to be
zero. Thus infinite mass. I think you won't find a wild speculation.
You'll find the only possible answer to the question within those
guidelines.
If you want to say that there are other dimensions in which this
universe is blowing up like a balloon, that is something you can feel
free to do, but I've traced that idea back to several sources, and it
appears to be speculation of considerably wilder flavor than mine.
Ken S. Tucker
Spoonfed wrote:
...
> Now, from what you say here, it sounds as though the Lorentz
> transformation could be an example of a metric tensor.
Yes, I think so too, have a quick glance at
Tetrads.
Ken
Koobee Wublee
> Koobee Wublee wrote:
>> Do you have an example of whatever not covariantly divergenceless?
>
> The Einstein tensor and the metric tensor.
I am not sure if you know what you are talking about.
>> Try the following spacetime.
>>
>> ds^2 = c^2 (1 - 2 U) dt^2 - dr^2 - r^2 dH^2 ...
>>
>> It has a flat space but with gavitational time dilation. It explains
>> gravity just as good as the Schwarzschild spacetime. Thus, the cause
>> of gravitation is not and none other than gravitational time dilation
>> regardless if space is curved or not.
>
> But this is not a solution of the weak field equations. The Ricci
> tensor won't vanish for this "solution", so it's not a good example..
Who cares about Ricci tensor if dealing with a general metric in
spacetime? The above metric is a solution to the field equations which
in term are the solution to a certain Lagrangian. The above equation
indicates gravitational time dilation but no curvature in space and
adequately explains gravity. You have given very weak and handwaving
arguments so far. Please be more convincing that gravitational time
dilation plus a curvature in space is the definitely the only solution
to explain the nature of gravitation. Again, please try to avoid
handwaving this time.
>> Since the metric is indirectly derived from the Hilbert Lagrangian
>> through the calculus of variations, you still have to justify the
>> reason behind that. What is extremizing the Hilbert-Einstein Action
>> necessary for a particular metric to exist?
>
> No. The metric is already part of the Lagrangian in the more general
> sense. It's not derived. The functional shape of the metric
> components is determined by the field equations, which are based on
> the variational principle. Classical mechanics is also derived using
> variational principles. There are metrics there also. Note the metric
> tensors for flat spaces described by polar and speherical coordinates.
> But notice there is no talk of curvature there at all.
If you cannot justify the reason to apply the Calculus of Variations,
you have no right to apply the Calculus of Variations to a scalar which
you claim is a Lagrangian. You cannot violate the basic principle of
mathematics.
You also are talking gibberish by claiming the metric is not derived at
all. The metric is a solution to the set of field equations which are
merely the Euler-Lagrange Equations to a certain Lagrangian. In the
case of Einstein Field Equations, the Schwarzschild metric is one such
possible solution.
Why don't you try to answer my questions instead of making more
outrageous claims please?
Koobee Wublee
> Koobee Wublee wrote:
>>
>> What is this integral you are referring to? EFE are the results of
>> differentiation.
>
> It is an _example_ of a similar phenomenon -- where the usual
> mathematical "derivation" does not necessarily provide the complete
> solution.
Your example implies an integration while the actual EFE represent
differentiation. Your suuport of the Cosmological Constant still does
not have any support.
>>>> Let's say instead of the Hilbert Lagrangian. I find another one
>>>> resulted in the field equations that yield a metric similar to the
>>>> Schwarzschild metric except with unity term (1) associated with dr^2
>>>> (instead of (1 -2 U)^-1). Can this new metric explain gravity? Yes,
>>>> it does. Does this new metric indicate a curvature in space? No.
>>>> Space is flat described by this new metric. So, how can you claim
>>>> gravitation can only be modeled by a curvature in spacetime?
>>> Because the underlying manifold is spacetime, not simply space. The
>>> foliation of spacetime into space and time is of no physical
>>> significance, because it is the same symmetry as changing coordinates.
>>
>> I don't understand what you are saying.
>
> That's quite clear. You do not understand much about GR at all. This is
> very basic.
GR is governed by a shell of mathematics in which I understand.
However, I tend to get lost in your word salad, and this is not the
first time.
> And I don't claim that gravitation can _only_ be modeled by curvature in
> spacetime. Such curvature has proven to be an excellent model of
> gravitation. But of course that does not rule out the possibility that
> other models can be found; indeed, Newtonian gravitation is also a
> pretty good model.
In the simple mathematics I showed, gravitation is merely adequate to
be modeled by gravitational time dilation regardless if space is curved
or not. So, I still don't see why space has to be curved. A
self-proclaimed Lagrangian is not enough to decide if space is curved
or not.
>> Again, foliation? There is not even such a word in the English
>> language. Please stop talking in riddles to justify your points.
>
> Clearly you do not know the standard vocabulary, so how can you expect
> to be taken seriously?
It is up to you if you take me seriously. Do you ever take anyone
seriously? My Random House Webster Dictionary published in August of
1993 does not have this word 'foliation' in it. Please do not try to
deify GR by using tall words or fancy vocabularies which no one
understands.
> Foliation is the word used to indicate the separating of an N
> dimensional manifold into submanifolds whose dimensions add up to N. It
> is a normal part of the standard vocabulary of differential geometry and
> GR. <shrug>
What you are saying still does not make any sense. First of all, you
try to separate something which is not a fluid or a fabric but a
manifold into N dimensions and add up the sub-manifolds you get N
dimensions back again. In analogy, you can separate a cube into tiny
cubes and the add up the tiny cubes back into the original cube with 3
dimensions. I can see that. It only takes 1st grade intuition to do
so. <shrug>
>> I don't see the simplicity in Hilbert Lagrangian. Simplicity is
>> awefully subjective.
>
> Consider all possible scalar functions of all of the the curvature
> tensors. The simplest is clearly R+L, where R is the Ricci curvature
> scalar and L is a constant. That is the Lagrangian density for GR.
And what justifies adding the determinant of a metric? What justifies
even the curvatue tensor at all?
>> What guarantees it being the valid one?
>
> Comparison with experiment. This is, of course, no "guarantee".
That says a lot about the Lagrangian you (plural) worship, don't you?
>> What
>> does the Hilbert-Einstein Action have to be minimized?
>
> The action itself is to be extremized. This is the whole basis of
> Lagrangian methods in physics. <shrug>
Let me correct my question again. Hopefully, this time won't result in
another answer that is totally obvious.
Why does the Hilbert-Einstein Action have to be extremized to dictate
gravitation?
Koobee Wublee
> GR, as a tensor theory, is based on the equivalence principle, which
> states that, gravitational acceleration cannot be locally distinguished
> from any arbitrary acceleration.
That is a total lie. GR is based on the Lagrangian which Hilbert came
up with. The Equivalence Principle has nothing to do with GR. In
fact, the Equivalence Principle has nothing to do with physics anyway.
It is merely a decoy to hide the origin of the field equations.
> Well, there was a period where he certainly was obsessed with Mach and
> tried very hard to make Mach's ideas fit into the theory. He
> eventually gave up when solutions to his GR equations were found that
> completely disagreed with all of Mach's concepts.
It is the case because GR is built from a scalar called a Lagrangian to
the Hilbert-Einstein Action.
> A lot of people miss the point that has been done to death in the last
> hundred years. Whether or not the aether exists in some form is
> irrelevant. So far as we have been able to observe, not only have we
> not been able to find any aether, it doesn't even seem to be necessary.
The existence of the Aether is perceived as irrelevant only because the
Aether is not well understood.
> Actually, the notion of geodesic is a generalization of the concept of
> a straight line and in most cases, as in GR, geodesics are never
> straight lines. But they are the path of least effort for a body to
> move through the geometry. In GR, planetary orbits become elliptical
> geodesics and the path of light is bent when it nears a massive object
> like the sun. No one pretends that these are straight lines. They are
> merely geodesics for the curved spacetime generated by the sun.
In GR, the geodesics follow the path with the highest value of
spacetime squared. For a photon, the spacetime is always zero. Thus,
it is absurd for any specific geodesics for a photon in GR to happen at
all.
generated by the sun.
Tom Roberts
> "Tom Roberts" <tjrobe...@sbcglobal.net> wrote in message
> news:2u2jg.114073$dW3....@newssvr21.news.prodigy.com...
>> dimensional manifold into submanifolds whose dimensions add up to N. It
>> is a normal part of the standard vocabulary of differential geometry and
>> GR. <shrug>
>
> What you are saying still does not make any sense.
Your problem, not mine.
Here is an example: a 3-d Euclidean space can be foliated into a series
of 2-d planes and a 1-d line: apply Cartesian coordinates and consider
the XY planes and the Z coordinate. It can also be foliated into a
series of concentric spheres: apply spherical coordinates and consider
the theta-phi planes and the r coordinate. The 3-d manifold has zero
curvature; the first foliation has flat 2-d surfaces; the second
foliation has curved 2-d surfaces.
How you choose to foliate the manifold will determine the curvatures of
the submanifolds; while there are restrictions, there is no simple
relationship between the curvature of the manifold and of the
submanifolds -- the curvature of the submanifolds depends on an
_arbitrary_ choice of foliation, and is therefore not of any physical
importance.
In the spacetime manifolds of GR the same holds, and the curvature of
the spatial submanifold is of no physical significance. But it takes
nonzero curvature in the spacetime manifold to model gravitation. <shrug>
> First of all, you
> try to separate something which is not a fluid or a fabric
This is _geometry_, not fluids.
> Why does the Hilbert-Einstein Action have to be extremized to dictate
> gravitation?
That is how science operates -- postulate a theory and compare it to
experiments. choosing the Hilbert-Einstein action and computing the
consequences compares extremely well with a multitude of experiments.
<shrug>
Tom Roberts
surrealis...@hotmail.com
> > > > gu...@hotmail.com wrote:
> > > > > I think long ago I read (anyone have the link and Einstein's words on
> > > > > it) that Einstein believed there was an Aether (is there any
> > > > > relationship of the Aether with his cosmological constant mistake)?
> > > > >
> > > > > *****When**** Einstein wrote his GR theory, did he still believe in an
> > > > > Aether?
> > > > >
> > > > > If so then it seems his warped space, rubber sheet model and Einstein's
> > > > > math for tensors could have based on an Aether (or space as a fabric),
> > > > > if no then why not?
> > > >
> > > > It's not warped space, it's curved spacetime. The rubber sheet model
> > > > is a poor analogy used in popular treatments and can lead to tremendous
> > > > misunderstandings. Tensors already existed as mathematical objects
> > > > prior to Einstein, and they are just generalizations of vectors. And
> > > > no, Einstein never believed in an aether after his first papers on
> > > > relativity were published.
> > >
> > > Check my other post, in 1920 Einstein said he based his GR on the
> > > Ether.
> >
> > No he did not. I think you must have your wires crossed and are taking
> > him out of context.
>
>
>
> Tom Roberts wrote:
> > Igor wrote:
> > > gu...@hotmail.com wrote:
> > >> Check my other post, in 1920 Einstein said he based his GR on the
> > >> Ether.
> > >
> > > No he did not. I think you must have your wires crossed and are taking
> > > him out of context.
> >
> > This is indeed out of context. In 1920 Einstein attended a conference on
> > the aether, and made remarks that essentially say that the "aether" of
> > GR is utterly unlike any other aether, in that it has no physical
> > properties (density, temperature, pressure, etc.), and no state of rest
> > can be ascribed to it.
> >
> > To consider GR as an "aether theory" requires an incredible PUN on the
> > word that robs it of all meaning. Einstein knew this. But he spoke in
> > the style of his time, not ours. <shrug>
> >
>
> IS UNTHINKABLE"
>
> His further claims that the Ether is not a tangeable substance (perhaps
> the same way photon has no mass or not a particle,etc...) is to cover
>
Roberts is wrong on that. Einstein spoke, as ever, in term acceptable
to Einstein. Einstein's views on ether may not be liked by the modern
view, but that may mean that the modern view is wrong. But to give a
glib rejection of Einstein on his views on ether is to restart an
arguement that cannot succeed on this NG. In the end, I argue that
Einstein is entitled to HIS viewpoint, no matter how
out-of-the-mainstream it seems today! In any case, both sides on this
NG make too much out of Einstein's notion of ether in 1920. By neither
the relativistic nor Mechanistic viewpoint is his view on ether as
espoused in his 1920 essay a big deal.
The physics community today is no better than the lay community in
reading Einstein's physics essays to learn precisely what Einstein felt
about ether and many other things of a philosophical nature relating to
his interests in physics. Read Ideas and Opinions to find out what
Einstein really thought about these things. I can't understand how
anyone interested in relativity would not read it. Read it many times.
Get your highlighter out and use it!
On the other hand, Einstein was not "covering his ass," either. He
simply adopted a different definition of "ether" than you have. To
Einstein, it seems, an ether is any hypothetical space-filling thing
that is used in some physical theory. I sometimes leave out the word
"hypothetical" when defining "ether." I really shouldn't because
physics is not metaphysics and the truth of such a hypothetical thing
is irrelevant in physics. Under this definition, a space-filling field
is an ether, though Einstein might have thought of a narrower
definition of ether to accomodate the metric field alone. I see no need
to tailor the definition so restrictively.
I posted the following article recently but it seems to have gotten
lost in the shuffle. It explains exactly how Einstein regarded ether in
the post 1905 world of physics.
Ether, Mechanics, the Laws of Physics, and Relativity
Question: Did Einstein discover general relativity?
Well, invented is more like it. Einstein set about the intensional task
of explaining gravity from a field-theoretic viewpoint by
1) making the field equations for gravity and the equations of motion
generally covariant and
2) by intensionally generalizing the concept of the "laws of physics"
as behavioral constraints which do not give any intrinsic preference to
description from within inertial frames of reference. In other words,
Einstein set about the task of demoting the inertial frame of reference
relative to the concept of "law of physics" to just another frame;
accelerated frames of reference, in this viewpoint, are just as valid
for the discovery of the "laws of physics" as are the inertial frames.
And this generalization necessitated the generalization of what was
meant by a "law of physics" in SR.
Thus, each time the principle of relativity is generalized the notion
of "law of physics" is generalized. Einstein revealed this clearly in
the following quote:
H. A. Lorentz even discovered the "Lorentz transformation," later
called after him, though without recognizing its group character.
To him Maxwell's equations in empty space held only for a particular
coordinate system distinguished from all other coordinate systems by
its state of rest. This was a truly paradoxical situation because
the theory seemed to restrict the inertial system more strongly than
did classical mechanics. This circumstance, which from the empirical
point of view appeared completely unmotivated, was bound to lead
to the theory of special relativity.
---- Einstein, "H. A. Lorentz, Creator and Personality,"
Ideas and Opinions, p. 75.
To understand what Einstein meant by the "group character" of the
transformation, we can go back to Newton's mechanics. That formal
system had a set of "laws" that were covariant under Galilean
transformation of the equations between any two inertial frames. (The
compositon of these transformations form a mathematical group, which
may not be a familiar term to physics laymen.) Thus, in Newton's
mechanics, all inertial frames are equivalent for the discovery of the
laws of physics, because the simplest interpretation of the covariance
of the equations of that system, consistent with empirical data, demand
that "law of physics" be conceptualized as "in their covariant forms
they are true of all inertial frames." (Of course, definitions don't
give us physical content, but a good definition can be of heuristic
use.)
Now, Lorentz invented a theory of electrodynamics that showed that one
does not have to conceptualize the "laws of physics" as tied to all
inertial frames by a covariance group connecting all inertial frames.
Ironically, his attempt to generalize Newton's mechanics to include
electrodynamics with a mechanical explanation of E&M built into it, led
to the demotion of the concept of "laws of physics" to mere
"regularities true only in the rest frame of the ether." So, from this
formal point of view, Lorentz was not motivated to investigate the
"group nature" of Maxwell's equations. (Einstein referred to the
"synthesis" Lorentz obtained of Newton's mechanics and Maxwell's field
theory, Physics and Reality, Ideas and Opinions, p. 306.)
What Einstein meant by "restrict the inertial system more strongly than
did classical mechanics" is that Newton's mechanics had no concept of a
"special" inertial frame because in that theory the laws of physics are
the same in all inertial systems (frames) --the PoR. But in Lorentz's
theory, one claims that: there exists a special frame (system of
coordinates) in which in that frame alone the "laws of physics" hold.
What could have led Lorentz to adopt this bizarre viewpoint, which was
discordant with classical mechanics? I can think of only one hypothesis
to proffer: Besides the imperative implicit in the mechanical program,
Lorentz additionally took the view that the laws of physics are
SUPPOSED to tell us about what is really, truly happening in nature,
whereas to Einstein, the laws of physics were merely faithful
descriptions of the behavior of phenomena (though admittedly Einstein
equivocated from that simple doctrine with respect to his views on QM).
To Lorentz, the true behavior was only knowable in the rest frame of
the ether because in that frame alone stationary rods and clocks give
"true" values.
But to Einstein, once the operational definitions that connect the
measurements of variables to the theoretical variables have been made,
then the "laws of physics" are covariant manifestations of the
variable-relationship regularities true of the behavior of phenomena as
seen in any inertial system. (For example: F= ma is a
variable-relationship regularity, covariant under a Galilean
transformation of coordinates.) This is the same viewpoint as in
classical mechanics with only one important generalization (neglecting
gravity): whereas classical mechanics was about the (covariant) laws of
the description of the behavior of uncharged particles, SR is about the
(covariant) laws of the local description of the behavior of particles,
uncharged or charged. And in the latter case, that brings in
electrodynamics for the 1905 version of SR. Now, however, SR is about
the local laws for all phenomena, not just electrodynamics.
There are two profound differences between classical mechanics and
relativistic mechanics: The former does not allow field to be treated
as an irreducible of the theory and the latter does not allow for
action-at-a-distance, or effects traveling 'through space' faster than
the speed of light (in flat spacetime, of course).
Finally, Einstein said, "This circumstance, which from the empirical
point of view appeared completely unmotivated, was bound to lead to the
theory of special relativity." What did he mean? He told us in his 1905
SR paper. He said that the description of the behavior of
electrodynamics is dependent only on the relative velocities among the
interacting parts, and not on their absolute velocities in any way, and
also that all experiments designed and implemented to detect the
earth's absolute velocity through "space" (if there really is such a
thing) had failed. I.e., no empirical justification!
It's as if Einstein were saying: "In our efforts to generalize Newton's
mechanics to include electrodynamics, do we really have to drag along
this dead horse of the mechanical ether with its unique, but
unobservable, rest frame, given that 1) there is no empirical mandate
to do so, and 2) the formal equations of electrodynamics, being Lorentz
covariant (the "group nature"), makes this unique frame undetectible
even if it exists? So, even if it does exist, it's superfluous to a
minimalist mind frame.
To Einstein, the answer was an obvoiusly no. To Einstein, Lorentz's
theory wasn't so much "being wrong" as "being unsimple and
disharmonious." It was unsimple formally because it postulated the
existence of a special frame which SR shows to be superfluous (which is
a violation of parsimony). It was disharmonious because it purported to
be a generalization of Newton's physics, yet it contradicted the
classical mechanical notion of a "law of physics," which is implicit in
the classical theory. Ironically, instead of the notion of "law of
physics" generalizing going from Newton to Lorentz, the notion actual
became narrower!
Einstein wrote much about what led him to SR. The quote above says a
lot about that in a succinct but cryptic way. Let's add to that from
what he and Infeld wrote in "The Evolution of Physics":
There seems to be only one way out of all these
difficulties. In the attempt to understand the phenomena
of nature from the mechanical point of view,
throughout the whole development of science up to the
twentieth century, it was necessary to introduce artificial
substances like electric and magnetic fluids, light corpuscles,
or ether. The result was merely the concentration of all
the difficulties in a few essential points, such as ether
in the case of optical phenomena. Here all the fruitless
attempts to construct an ether in some simple way,
as well as the other objections, seem to indicate that the
fault lies in the fundamental assumption that it is possible to
explain all events in nature from a mechanical
point of view. Science did not succeed in carrying
out the mechanical program convincingly,
and today no physicist believes in the possibility of its
fulfillment.
--- Evolution of Physics, p. 120-121.
Both SR and early QM contributed to the demise of the philosophical
viewpoint held up to the end of the nineteenth century that all
phenomena HAVE to be explained in terms of particles in motion
influenced by forces acting at-a-distance (i.e., in terms of classical
mechanics). And thus physics evolved not only by adding new empirical
information to its corpus, but also by adding new modes (i.e.,
non-mechanical modes) of physical explanation.
If you missed the subtle point relative to Lorentz's theory and 1905
SR, I'll explain. In Lorentz's theory you have the irreducible concepts
of mass (material) particles and forces acting-at-a distance. The EM
field was "explained" as emergent properties of states in the
mechanical ether. In SR you have mass/energy particles and forces
derived from fields, which are held to be irreducible; that is, they
are not treated as "explainable" in terms of a mechanical states of
some material ether.
Einstein said:
Since the special theory of relativity revealed the physical
equivalence of all inertial systems, it proved the untenability
of the hypothesis of an ether at rest. It was therefore necessary
to renounce the idea that the electromagnetic field is to be
regarded as a state of a material carrier. The field thus
becomes an irreducible element of physical description,
irreducible in the same sense as the concept of matter in the
theory of Newton.
--- Relativity and the Problem of Space, Ideas and Opinions,
p. 371.
So, when the mechanical program fell, the field program was initiated.
In other place Einstein said:
For several decades most physicists clung to the conviction
that a mechanical substructure would be found for Maxwell's
theory. But the unsatisfactory results of their efforts led to the
gradual acceptance of the new field concepts as irreducible
fundamentals---in other words, physicists resigned themselves
to giving up the idea of a mechanical foundation.
---- The Fundaments of Theoretical Physics, Ideas and
Opinions, p. 328.
Einstein went on to say that the beginnings of a new program of field
research was instituted. In other words, physics had evolved to a new
paradigm for theoretical research.
Another quote in which Einstein argued clearly, solely on the principle
of parsimony (no unnecessary hypotheses!) and irrespective of his or
his generation's intuitions of deep reality, to a theoretic ontology
without an underlying ether to explain Maxwell's field equations:
Now a question arose: Since the field exists even in a
vacuum, should one conceive of the field as a state of a
"carrier," or should it rather be endowed with an independent
existence not reducible to anything else? In other words,
is there an "ether" which carries the field; the ether being
considered in the undulatory state, for example, when it
carries light waves.
The question has a natural answer: Because one cannot
dispense with the field concept, it is preferable not to introduce
in addition a carrier with hypothetical properties. However, the
pathfinders who first recognized the indispensibility of the field
concept were still too strongly imbued with the mechanistic
tradition of thought to accept unhesitatingly this simple point of
view. But in the course of the following decades this view
imperceptibly took hold.
--- On the Generalized Theory of Gravitation, Ideas and Opinions,
p. 344.
Finally, Einstein seems to suggest in the first quote that SR was
inevitable in the face of all this supporting evidence of the
superfluous nature of the mechanical ether. Yet, I sometimes wonder if
we'd still be without special relativity were it not for Einstein.
And to those who would jump to the name of Poincare or someone else, I
say: Even holding a comittment to the Einstein (SR) version of the PoR
does not forbid one to also hold a belief in the use of an underlying
mechanical ether. This is precisely what Einstein said in the last
quote! It's a free choice and part of one's elective formal point of
view.
And one last quote in which Einstein expounded this notion of the
formal point of view:
In order to construct a theory, it is not enough to have a
clear conception of the goal. One must also have a formal
point of view which will sufficiently restrict the unlimited
variety of possibilities.
--- The Fundaments of Theoretical Physics, Ideas and Opinions,
p. 328.
There seems to be a common incredulity of laymen in physics who cannot
grasp why today's physicist cannot just "see the necessity of having a
mechanical ether underlying phenomena." And modern physicists are not
very good at explaining their lack of attraction to this mechanical
model. I have given some of the reasons why physicists over the long
decades had left the old bandwagon of support for a mechanical ether,
but something more needs to be emphasized.
It's a question of freedom of choice! Prior to the general acceptance
of SR, physicists had only one choice for a foundation to physics:
Mechanics. Therefore in those dogmatic days it was a matter of course
that if you dealt in electrodynamics, you needed some mechanical
interpretation for Maxwell's fields that appeared in his field
equations. But today, it's wide open. One can invent any foundation one
wants, so long as it produces a theory that works. Therefore, the
physicist of today, who has been educated in such a liberal school of
foundations, is hardly automatically impressed by the claimed
"obviousness of the existence of an underlying mechanical ether to
explain electrodynamical phenomena."
The answer is that there is nothing obvious about what goes on beneath
the "visible to the naked eye." Physical concepts are free creations of
the human mind. Any time a modern physicist desires to reduce the EM
field to something "more primitive," he or she has the virtual infinite
freedom of choice by which to do so, and to do so by the mode of
classical mechanics is only one of those many choices by which it could
be done. On the other hand, the long history of the failed attempts of
physicists to invent an elegant mechanical explanation of
electrodynamics is why they are so skeptical of such a claim, and
deservedly so.
One last question to answer: What explains the huge gap between the
typical layman and the professional physicist in their philosophical
outlook on foundational issues in physics? The obvious answer is
education. But that is a mere truism at this point.
The next question is: Exactly what is it about their differences in
physics education accounts for this philosophical divergence? Okay,
let's start with what they probably have in common: university or
college physics. Aaah, university physics! That unabashed dogmatic
promotion of the efficacy of the Mechanical Progam to answer all
questions in physics -- or so it seems to the naive physics student!
Physics education at this level seems to create the same misconceptions
in physics students that had dominated the thinking of early modern
physicists, which put blinders on their eyes to the possibility of any
explanation in physics other than in term of classical mechanics. (I'm
speaking in generalities, of course. By the leadership of a few
individuals over the centuries since Newton, ending in Einstein, they
led physics away from that dogma.) Unwittingly, we're doing it all over
again. We're allowing the Mystery of Mechanics to deceive people who
take lower-division physics classes. And this is an explanation why so
many engineers come to this NG so resistant to the philosophy of modern
physics. Modern physics got to where it is by a long and hard process
of evolution away from classical mechanics.
Every introductory physics textbook should report as it develops the
material, not only where the theory of mechanics succeeds, but also
were it fails. We all tend to come out of such a class "strongly imbued
with the mechanistic" philosophy or outlook or prejudice, as Einstein
put it. However, the layman's formal education in physics is likely to
end there or with some other mechanical subject at the lower-division
level. But the professional physicist will of necessity take those
classes, such as special relativity and QM, in which it becomes obvious
that mechanics is not the foundation for all of physics! Hence the
philosophical divide and the layman can't fathom why the divide even
exists. Well, maybe now he or she can a little better.
Koobee Wublee
> Here is an example: a 3-d Euclidean space can be foliated into a series
> of 2-d planes and a 1-d line: apply Cartesian coordinates and consider
> the XY planes and the Z coordinate. It can also be foliated into a
> series of concentric spheres: apply spherical coordinates and consider
> the theta-phi planes and the r coordinate. The 3-d manifold has zero
> curvature; the first foliation has flat 2-d surfaces; the second
> foliation has curved 2-d surfaces.
What is the big deal about foliation? Any object can be foliated into
smaller building blocks. Some perfect cubes. Some distorted.
> How you choose to foliate the manifold will determine the curvatures of
> the submanifolds; while there are restrictions, there is no simple
> relationship between the curvature of the manifold and of the
> submanifolds -- the curvature of the submanifolds depends on an
> _arbitrary_ choice of foliation, and is therefore not of any physical
> importance.
>
> In the spacetime manifolds of GR the same holds, and the curvature of
> the spatial submanifold is of no physical significance. But it takes
> nonzero curvature in the spacetime manifold to model gravitation. <shrug>
Why is the foliation of an observer's choosing? In Riemannian space,
the curvature is independent of observers, no? However, I still have a
tough time of grasping your manifolds and submanifolds. I know it is
my problem and will remain so. GR is best explained with math even the
geometric curvature in both space and time.
I have presented the following spacetime that does explain graviation
even without a curvature in space.
ds^2 = c^2 (1 - 2 U) dt^2 - dr^2 - r^2 dH^2 ...
Please try to refute it without invoking the Frankenstein (Hilbert's
Lagrangian).
>> Why does the Hilbert-Einstein Action have to be extremized to dictate
>> gravitation?
>
> That is how science operates -- postulate a theory and compare it to
> experiments. choosing the Hilbert-Einstein action and computing the
> consequences compares extremely well with a multitude of experiments.
> <shrug>
No, this is not science. You don't guess at a number and apply a
series of operator to claim the validity of a hypothesis. Your method
is not scientific. It is alchemy. Modern alchemy. GR is the
by-product of alchemy in action.
Spoonfed
Thanks, but what is a tetrad, and is the Lorentz transformation a
tetrad, and is a tetrad a tensor?
Spoonfed
Koobee Wublee wrote:
> "Igor" <thoo...@excite.com> wrote in message
> news:1150048641.2...@m38g2000cwc.googlegroups.com...
>
> > GR, as a tensor theory, is based on the equivalence principle, which
> > states that, gravitational acceleration cannot be locally distinguished
> > from any arbitrary acceleration.
>
> That is a total lie. GR is based on the Lagrangian which Hilbert came
> up with.
What's the Lagrangian that Hilbert came up with?
> The Equivalence Principle has nothing to do with GR. In
> fact, the Equivalence Principle has nothing to do with physics anyway.
It sure makes a good first approximation in gravity.
> It is merely a decoy to hide the origin of the field equations.
Which field equations?
>
> > Well, there was a period where he certainly was obsessed with Mach and
> > tried very hard to make Mach's ideas fit into the theory. He
> > eventually gave up when solutions to his GR equations were found that
> > completely disagreed with all of Mach's concepts.
>
> It is the case because GR is built from a scalar called a Lagrangian to
> the Hilbert-Einstein Action.
>
Have you got a good source on this? Lagrangian, if I understand my
classical mechanics and statistical thermodynamics correctly, is a
calculation of Kinetic minus Potential energy that can be put to good
use by Noether's theorem. It would create a scalar quantity mapped
over a set of generalized coordinates (including time). The set's
dimension would be equal to the degrees of freedom of all of the motion
in the system.
So if I understand you, correctly, the Hilbert-Einstein Action can
determine the kinetic and potential energy of *something* over a set of
convenient coordinates established over that same *something*.
So what is that something? Is it an arbitrary number of gravitating
particles? What sort of constraints are brought into play by the
Hilbert-Einstein Action?
> > A lot of people miss the point that has been done to death in the last
> > hundred years. Whether or not the aether exists in some form is
> > irrelevant. So far as we have been able to observe, not only have we
> > not been able to find any aether, it doesn't even seem to be necessary.
>
> The existence of the Aether is perceived as irrelevant only because the
> Aether is not well understood.
>
Well, you won't find Aether in a Lagrangian. Instead you'll find a set
of dimensions which are peculiarto whatever problem you're trying to
solve. Now, I suppose you could set up an infinite dimensional
Lagrangian to set up a problem for an infinite number of particles, but
you would still need to know the current locations of all of those
infinite particles.
And I have read enough to know that many, including Einstein, made the
unfounded assumption that the universe has constant density across
space at a given time. But from talking to people, I've found they
think that is the only geometry possible which maintains the
cosmological principle. This would be true if we went back to Galilean
relativity where the speed of light was infinite.
But with SR, the only geometry which maintains the cosmological
principle is where the density over constant f(t,x,y,z)=(c^2 t^2 - x^2
-y^2 -z^2) is constant. For example, at f(1,0.866c,0,0)=f(0.25, 0,
0,0). So the density of the universe at a point 86.6% of the way to
the edge of the universe should be the same density as it was here 75%
of the age of the universe ago.
I don't don't think Einstein ever realized his error, and I don't know
how deep his incorrect assumption is buried in cosmological theory.
Is it in the setup of the Lagrangian of the Hilbert-Einstein Action?
> > Actually, the notion of geodesic is a generalization of the concept of
> > a straight line and in most cases, as in GR, geodesics are never
> > straight lines. But they are the path of least effort for a body to
> > move through the geometry. In GR, planetary orbits become elliptical
> > geodesics and the path of light is bent when it nears a massive object
> > like the sun. No one pretends that these are straight lines. They are
> > merely geodesics for the curved spacetime generated by the sun.
>
> In GR, the geodesics follow the path with the highest value of
> spacetime squared. For a photon, the spacetime is always zero. Thus,
> it is absurd for any specific geodesics for a photon in GR to happen at
> all.
> generated by the sun.
I don't think spacetime has a scalar value. Are you referring to
spacetime interval?
Ken S. Tucker
Sorta of...
http://en.wikipedia.org/wiki/Teleparallelism
Also see "vierbein" which is another word for
a tetrad.
Ken
Bilge
>news:1150048641.2...@m38g2000cwc.googlegroups.com...
>
>> GR, as a tensor theory, is based on the equivalence principle, which
>> states that, gravitational acceleration cannot be locally distinguished
>> from any arbitrary acceleration.
>
>That is a total lie. GR is based on the Lagrangian which Hilbert came
>up with. The Equivalence Principle has nothing to do with GR. In
>fact, the Equivalence Principle has nothing to do with physics anyway.
>It is merely a decoy to hide the origin of the field equations.
You are a complete idiot. How can you manage to make so many
completely wrong statements in so few sentences?
Eric Gisse
Koobee Wublee wrote:
> "Tom Roberts" <tjrobe...@sbcglobal.net> wrote in message
> news:90gjg.43922$fb2....@newssvr27.news.prodigy.net...
>
> > Here is an example: a 3-d Euclidean space can be foliated into a series
> > of 2-d planes and a 1-d line: apply Cartesian coordinates and consider
> > the XY planes and the Z coordinate. It can also be foliated into a
> > series of concentric spheres: apply spherical coordinates and consider
> > the theta-phi planes and the r coordinate. The 3-d manifold has zero
> > curvature; the first foliation has flat 2-d surfaces; the second
> > foliation has curved 2-d surfaces.
>
> What is the big deal about foliation? Any object can be foliated into
> smaller building blocks. Some perfect cubes. Some distorted.
"Again, foliation? There is not even such a word in the English
language. Please stop talking in riddles to justify your points. "
>
> > How you choose to foliate the manifold will determine the curvatures of
> > the submanifolds; while there are restrictions, there is no simple
> > relationship between the curvature of the manifold and of the
> > submanifolds -- the curvature of the submanifolds depends on an
> > _arbitrary_ choice of foliation, and is therefore not of any physical
> > importance.
> >
> > In the spacetime manifolds of GR the same holds, and the curvature of
> > the spatial submanifold is of no physical significance. But it takes
> > nonzero curvature in the spacetime manifold to model gravitation. <shrug>
>
> Why is the foliation of an observer's choosing?
"Again, foliation? There is not even such a word in the English
language. Please stop talking in riddles to justify your points. "
> In Riemannian space,
> the curvature is independent of observers, no? However, I still have a
> tough time of grasping your manifolds and submanifolds. I know it is
> my problem and will remain so. GR is best explained with math even the
> geometric curvature in both space and time.
>
> I have presented the following spacetime that does explain graviation
> even without a curvature in space.
>
> ds^2 = c^2 (1 - 2 U) dt^2 - dr^2 - r^2 dH^2 ...
So....this metric has a null curvature scalar? Or do you simply have no
idea what you are talking about?
>
> Please try to refute it without invoking the Frankenstein (Hilbert's
> Lagrangian).
>
> >> Why does the Hilbert-Einstein Action have to be extremized to dictate
> >> gravitation?
> >
> > That is how science operates -- postulate a theory and compare it to
> > experiments. choosing the Hilbert-Einstein action and computing the
> > consequences compares extremely well with a multitude of experiments.
> > <shrug>
>
> No, this is not science. You don't guess at a number and apply a
> series of operator to claim the validity of a hypothesis. Your method
> is not scientific. It is alchemy. Modern alchemy. GR is the
> by-product of alchemy in action.
Thats why GR models all known gravitational phenomena?
shuba
> The gradient of a scalar field F is a vector field determined by
>
> dF/dx i_x + dF/dy i_y + dF/dz i_z
>
> and it is quite a neat little vector
But that's NOT a vector, at least not a "normal" vector (pun
intended). The gradient is a dual vector, also known by other
names, my favorite is a one-form. Since you are asking questions
about tensors within the context of relativity and you seem to have
a penchant and the ability for mathematical formulae and the
associated discussions, why don't you study this stuff from a
reliable source? The following notes will answer many of your
questions about tensors and hopefully allow to see where some of
your speculations and ideas are completely off the mark.
http://nedwww.ipac.caltech.edu/level5/March01/Carroll3/Carroll1.html
Click on "Contents" button at the top to see the complete notes for
this GR course, but the material in the linked page explains
tensors clearly and concisely.
---Tim Shuba---
Tom Roberts
> "Tom Roberts" <tjrobe...@sbcglobal.net> wrote in message
> news:90gjg.43922$fb2....@newssvr27.news.prodigy.net...
>> In the spacetime manifolds of GR the same holds, and the curvature of
>> the spatial submanifold is of no physical significance. But it takes
>> nonzero curvature in the spacetime manifold to model gravitation. <shrug>
>
> Why is the foliation of an observer's choosing?
Because it is _arbitrary_ -- there are infinitely many ways to foliate
spacetime into space and time. That's why the curvature of space is not
of physical relevance. <shrug>
> In Riemannian space,
> the curvature is independent of observers, no?
Yes. That's why the curvature of the manifold is physically relevant,
but the curvature of submanifolds is not: if you foliate that space into
submanifolds the curvatures of those submanifolds are NOT independent of
the method of foliation, which is arbitrary. That's what I have been
saying repeatedly. <shrug>
> I have presented the following spacetime that does explain graviation
> even without a curvature in space. [...]
Sure -- for U(r)=kM/r your metric is equivalent to Schwarzschild
spacetime to lowest order, and for many applications that is good enough
(indeed it is often better than Newtonian gravitation). But the absence
of curvature in space is _IRRELEVANT_. See above. <shrug>
>> That is how science operates -- postulate a theory and compare it to
>> experiments. choosing the Hilbert-Einstein action and computing the
>> consequences compares extremely well with a multitude of experiments.
>> <shrug>
>
> No, this is not science.
Yes it is. Formulating theories and testing them experimentally is the
essence of science. You just don't have a clue. <shrug>
Tom Roberts
alanm...@yahoo.com
gu...@hotmail.com wrote:
> I think long ago I read (anyone have the link and Einstein's words on
> it) that Einstein believed there was an Aether (is there any
> relationship of the Aether with his cosmological constant mistake)?
No, when he plugged in his equations, they indicated the universe
had to be either expanding or contracting. Everyone thought the
universe was static at that time; his fudge factor was to allow for a
static universe. When soon afterwards Hubble discovered the receding
galaxies and expanding universe, Einstein stated that his cosmological
constant was the stupidest mistake he ever made- A. McIntire
Koobee Wublee
news:1150214303.0...@u72g2000cwu.googlegroups.com...
> Koobee Wublee wrote:
>> The Equivalence Principle has nothing to do with GR. In
>> fact, the Equivalence Principle has nothing to do with physics anyway.
>
> It sure makes a good first approximation in gravity.
>
>> It is merely a decoy to hide the origin of the field equations.
>
> Which field equations?
http://en.wikipedia.org/wiki/Einstein_field_equation
How do you figure the Equivalence Principle has anything to do with GR?
When Einstein finally understood Newtonian law of gravity, he
celebrated this achievement by giving the Newtonian law of gravity
another name, the Equivalence Principle. Unlike Newton who studied
gravity by observing an apple falling from a tree, Einstein tried to
picutre himself as the falling apple. Of course, it did not get
anywhere. He then enlisted his classmate Grossmann's help and still
did not get anywhere. Unitl Hilbert came along...
>> GR is based on the Lagrangian which Hilbert came up with.
>
> What's the Lagrangian that Hilbert came up with?
This Lagrangian is the density to the Einstein-Hilbert Action.
http://en.wikipedia.org/wiki/Einstein-Hilbert_action
You can do wonderful things with this Lagrangian through the
mathematical tool called the Calculus of Variations or the Lagrangian
Method.
http://en.wikipedia.org/wiki/Calculus_of_variations
However, you still have to justify using this mathematical tool.
Hilbert did not.
> Have you got a good source on this? Lagrangian, if I understand my
> classical mechanics and statistical thermodynamics correctly, is a
> calculation of Kinetic minus Potential energy that can be put to good
> use by Noether's theorem. It would create a scalar quantity mapped
> over a set of generalized coordinates (including time). The set's
> dimension would be equal to the degrees of freedom of all of the motion
> in the system.
The classical Lagrangian must represent the density to a meaningful
action. As early as the first half of the 19th century, Hamilton did
speculate this action being the elapsed time of the event where an
event is an evolution of an instance (a snap shot) according to time.
This action being the elapsed time is the integral of the Lagrangian
with the initial instance and the final instance as the integration
limit. From the ridiculous concept of spacetime, if the geodesics
following the principle of least time, you can derive this classical
Lagrangian. However, the physics communities have dictated the
geodesics to follow the false principle of maximal spacetime. Why is
this false? Just take a look at any photon where the spacetime is
always zero.
> So if I understand you, correctly, the Hilbert-Einstein Action can
> determine the kinetic and potential energy of *something* over a set of
> convenient coordinates established over that same *something*.
There is no such thing as potential energy nor kinetic energy. They
are parts of the overall energy very simply described by the famous (E
= m c^2).
> So what is that something? Is it an arbitrary number of gravitating
> particles? What sort of constraints are brought into play by the
> Hilbert-Einstein Action?
I don't understand what you are talking about.
> Well, you won't find Aether in a Lagrangian. Instead you'll find a set
> of dimensions which are peculiarto whatever problem you're trying to
> solve. Now, I suppose you could set up an infinite dimensional
> Lagrangian to set up a problem for an infinite number of particles, but
> you would still need to know the current locations of all of those
> infinite particles.
As you have expressed without knowing what Lagrangian is, a Lagrangian
is the density to an action while the Aether is a substance.
> And I have read enough to know that many, including Einstein, made the
> unfounded assumption that the universe has constant density across
> space at a given time. But from talking to people, I've found they
> think that is the only geometry possible which maintains the
> cosmological principle. This would be true if we went back to Galilean
> relativity where the speed of light was infinite.
Forget about Einstein, every piece of his work has another author
behind it. At least, Einstein's source was correct to say speed of
light has a finite limit.
> But with SR, the only geometry which maintains the cosmological
> principle is where the density over constant f(t,x,y,z)=(c^2 t^2 - x^2
> -y^2 -z^2) is constant. For example, at f(1,0.866c,0,0)=f(0.25, 0,
> 0,0). So the density of the universe at a point 86.6% of the way to
> the edge of the universe should be the same density as it was here 75%
> of the age of the universe ago.
You are covering something I don't know and care not to know.
>> In GR, the geodesics follow the path with the highest value of
>> spacetime squared. For a photon, the spacetime is always zero. Thus,
>> it is absurd for any specific geodesics for a photon in GR to happen at
>> all.
>> generated by the sun.
>
> I don't think spacetime has a scalar value. Are you referring to
> spacetime interval?
I don't think there is such a quantity called spacetime. According to
Dr. Draper, the concept of spacetime is a solid guess. That implies a
lot of BSing. According to Lorentz Transform, you can come up with
this spacetime in an ad hoc way. This I believe was what Minkowski
discovered.
Ilja Schmelzer
"Eric Gisse" <jow...@gmail.com> schrieb
> "Again, foliation? There is not even such a word in the English
> language. Please stop talking in riddles to justify your points. "
"Foliation" is a word in scientific English which is often used in
physics (general relativity), and math (diff. geometry).
Especially important for discussions "ether vs. relativity", because
"preferred foliation" describes a generalization to GR of
"preferred frame" in SR, which is another word for the Lorentz ether.
Ilja
Eric Gisse
Mabey I was being too subtle.
http://groups.google.com/group/sci.physics.relativity/msg/5fe41c249cf017a6?dmode=source
>
> Ilja
Tom Roberts
> Tom Roberts wrote:
>> Spoonfed wrote:
>>> Tensors have to do with parallel transport of vectors along an
>>> n-dimensional subspace of a greater than n dimensional space.
>> You are confused.
>
> Quite!
> Now, are you saying that I am wrong, (that tensors have nothing to do
> with parallel transport of vectors) or that I am correct, but confused?
As usual, the answer cannot be phrased in a sound bite. As I said, the
affine connection _determines_ how vectors are parallel transported.
This does not mean parallel transport is completely disconnected from
"tensors" (which tensors??). For instance, by considering how a vector
is parallel-transported around an infinitesimal loop, and considering
all possible loops, one can obtain the Riemann curvature tensor. And
from that one can obtain all the other curvature tensors.
But given a metric tensor on the manifold, it uniquely determines the
affine connection. The metric tensor also determines the Riemann
curvature tensor. And all the others.
> The orbit of mercury is a more-or-less 2-D path in exactly 3-D space,
> or perhaps 4-D spacetime, which turns out not to be elliptical, and I
> am indeed confused, because I don't know what tensors say about the
> problem... I only know the problem can be approached using them.
What you call the "orbit" of Mercury in 3-space is not a trajectory at
all, in the context of modern physics -- it is a _projection_ of the
trajectory onto the 3-space submanifold of spacetime. If I neglect the
precession and the eccentricity, the trajectory of mercury is a helix
with axis along the sun's time coordinate axis. Obviously this is not a
closed trajectory (as indeed no timelike trajectory can ever be closed
in a sensible spacetime manifold -- that would necessarily include time
travel into the past).
> And I did not know that "transport" inherently meant a straight line.
It doesn't. But it does mean along a 1-d path, as I said.
> Now, from what you say here, it sounds as though the Lorentz
> transformation could be an example of a metric tensor.
I have no idea how you got that.
There is a sense in which the Lorentz transform between
a specified pair of inertial frames is a tensor. But it
is unusual to think of it that way, and I in no way
discussed it.
> It also sounds like the affine connection might describe the sequence
> of events of an object moving through space?
No. Not even close. The _trajectory_ of the object does that.
Trying to continue via this "20 questions" mode is useless. Get a book
and _STUDY_.
Tom Roberts