Euclidean Geometry, Flatness, And Gravity.
John Bell (Change John to Liberty for email)
to spatial curvature whereas Einsteinian gravity equates to spacetime
curvature.
My problem with this is that Newton's inverse square law of gravity
requires Euclidean space to ensure that the surface area of a sphere
is precisely proportional to the square of its radius, which, afaict
implies spatial flatness.
Can anyone clarify here?
======================================= MODERATOR'S COMMENT:
Sure :-)
Oh No
<john...@accelerators.co.uk>
>I recall a comment at SPR to the effect that Newtonian gravity equates
>to spatial curvature whereas Einsteinian gravity equates to spacetime
>curvature.
I am a bit hazy about the details (as it is many years since I read the
relevant passage), but I think this refers to a treatment due to Cartan
and described in MTW.
>My problem with this is that Newton's inverse square law of gravity
>requires Euclidean space to ensure that the surface area of a sphere
>is precisely proportional to the square of its radius, which, afaict
>implies spatial flatness.
>
This is something a bit different. To find the Newtonian correspondence
for general relativity we define a tangent space - i.e. a space which is
flat by definition. Then the perturbation of the metric is reinterpreted
as a potential field.
Regards
--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and
braces)
John Bell (Change John to Liberty for email)
> Thus spake "John Bell (Change John to Liberty for email)"
> >My problem with this is that Newton's inverse square law of gravity
> >requires Euclidean space to ensure that the surface area of a sphere
> >is precisely proportional to the square of its radius, which, afaict
> >implies spatial flatness.
>
> This is something a bit different. To find the Newtonian correspondence
> for general relativity we define a tangent space - i.e. a space which is
> flat by definition. Then the perturbation of the metric is reinterpreted
> as a potential field.
Hmm,... This would seem to imply that, if the universe is flat (on the
large scale), Newtonian gravity will be zero, on average. Such a
conclusion would also appear to follow naturally (for Newtonian
gravity) from the assumptions of homogeneity and isotropy...wouldn't
it?
Oh No
universe with zero cosmological constant. It has decelerating expansion
(which never stops) ) which intuitively follows from the effect of
gravity.
The place this breaks down is that we can only use the tangent space to
model Newtonian gravity within a region. Outside of that region the
terms in the metric become too large to treat gravity as a perturbation
to flat space.
Ken S. Tucker
On Apr 20, 4:36 am, "John Bell (Change John to Liberty for email)"
<john.b...@accelerators.co.uk> wrote:
> I recall a comment at SPR to the effect that Newtonian gravity equates
> to spatial curvature whereas Einsteinian gravity equates to spacetime
> curvature.
In Newtonians gravitation field, light rays are NOT subject
to gravitational effects. The effects of space and spacetime
curvature use light rays as a surveying tool, therefore there
is NO gravitational curvature in Newton's theory.
Newton's gravitation applied only to mass and NOT to energy,
as the conservation of mass and conservation of energy were
separate then.
The derivation of E=mc^2 (and it's theoretical basis) unified
those into the conservation of mass-energy.
> My problem with this is that Newton's inverse square law of gravity
> requires Euclidean space to ensure that the surface area of a sphere
> is precisely proportional to the square of its radius, which, afaict
> implies spatial flatness.
John, you are correct. Once SR predicted "radiant energy"
is subject to gravitational effects as a result of the unified
conservation of mass and energy law, the light-rays used
to survey the gravity field were understood to be affected
by the field, leading to the need of GR applied to gravity
rendering a "red-shift" when light is vertically directed and
"light deflection" such that the mass-energy law holds in
g-fields.
After some effort (1905-1916) it was found to be a very
complicated problem, that necessitated a thorough
understanding of tensor analysis because the clocks
and measurement lengths were variables dependant
upon the gravitational potential, (these are termed
unitary base vectors, or "basis" for short), and GToR
(General Theory of Relativity) used a simplified
continuum as a 1st approximation, that is termed
"classical GToR".
> Can anyone clarify here?
IMO, start with how E=mc^2 relates to gravitation.
Regards
Ken S. Tucker
Eric Gisse
<john.b...@accelerators.co.uk> wrote:
> I recall a comment at SPR to the effect that Newtonian gravity equates
> to spatial curvature whereas Einsteinian gravity equates to spacetime
> curvature.
Pretty much.
> My problem with this is that Newton's inverse square law of gravity
> requires Euclidean space to ensure that the surface area of a sphere
> is precisely proportional to the square of its radius, which, afaict
> implies spatial flatness.
It took me a while to understand this, but the Cartan reformulation of
Newton (which is what was referred to) is not a metric theory of
gravitation.
What that means, in practice, is that means is that there is no metric
to determine distances. There is a connection chosen such that it
reproduces Newton, but that's about as interesting as it gets.
John Bell (Change John to Liberty for email)
> In Newtonians gravitation field, light rays are NOT subject
> to gravitational effects.
This is not strictly true. Newtonian physics and GR both predicted
bending of starlight grazing the Sun. GR was confirmed because it
predicted twice the bending
> The effects of space and spacetime
> curvature use light rays as a surveying tool,
Yes, this can be a very useful way of looking at things. (However, I
find it can also become tricky and confusing within a metric theory
such as GR, since the length of the metric element ds for light,
becomes zero)
John Bell (Change John to Liberty for email)
> Once SR predicted "radiant energy"
> is subject to gravitational effects as a result of the unified
> conservation of mass and energy law, the light-rays used
> to survey the gravity field were understood to be affected
> by the field, leading to the need of GR applied to gravity
> rendering a "red-shift" when light is vertically directed
IIRC from MTW, the gravitational redshift of light is also directly
derivable from Newtonian physics and energy conservation, given the PD
between higher and lower points.
I do like the way you tend to interpret things simply, but sometimes
(like now), this does not quite seem to cut the mustard.
However, I do appreciate the comments of all respondents. In
combination, these have helped to clarify the situation here for me.
======================================= MODERATOR'S COMMENT:
You're welcome - this NG has 4 moderators, and its members, too, exhibit quite widely spread views on certain topics...
Juan R.
> Thus spake "John Bell (Change John to Liberty for email)"
> <john...@accelerators.co.uk>
>>I recall a comment at SPR to the effect that Newtonian gravity equates
>>to spatial curvature whereas Einsteinian gravity equates to spacetime
>>curvature.
>
> I am a bit hazy about the details (as it is many years since I read the
> relevant passage), but I think this refers to a treatment due to Cartan
> and described in MTW.
Newton-Cartan theory and Newtonian gravity are two very different beast.
The former is a metric theory formulated after general relativity, the
latter is an AAAD theory formulated before general relativity and even
before field theories.
>>My problem with this is that Newton's inverse square law of gravity
>>requires Euclidean space to ensure that the surface area of a sphere is
>>precisely proportional to the square of its radius, which, afaict
>>implies spatial flatness.
>>
> This is something a bit different.
The original poster is noticing the difference between Newtonian gravity,
where gravity is not related to curvature, from metric theories as GR or
Newton-Cartan, where gravitation is related to curvature.
> To find the Newtonian correspondence
> for general relativity we define a tangent space - i.e. a space which is
> flat by definition. Then the perturbation of the metric is reinterpreted
> as a potential field.
But that "Newtonian correspondence" does not hold upon close inspection.
(i)
As showed in my work [#] and confirmed by GR expertise Eric Poisson, it is
not possible to find a regime in GR giving (a) flat geometry plus (b)
non-zero acceleration plus (c) linear 'field' equations, all at once. You
just ignore this.
(ii)
As showed in my work [#] and confirmed by non-linear field theory
expertise Yurij Barishev, a 'perturbation' of the metric is not a
potential field, because violates the mathematical and physical
propoerties associated to a true gravitational field. You are confounding
the GR 'perturbation' tensors h_ab utilized in the geodesic equations with
the field potentials \Psi_ab used in Kalman equations. You just ignore
this also.
(iii)
As showed in my work [#] and confirmed by GR expertise Norbert Straumann,
both the 'perturbation' h_ab and the background \eta_ab are not observable
in GR. Strautmann calls to \eta_ab an "kind of unobservable aether" and I
completely agree. You are defining a perturbation over an unphysical
"space which is flat by definition". Finally, you also ignore this
important point.
P.S: Your confusion between metric potentials and field potentials (you
denote both concepts with the same symbol) is only one of reason which
your claimed "unification of GR with quantum mechanics" [$] has not
mathematical or physical basis.
Regards.
[#] http://www.canonicalscience.org/en/publicationzone/drafts.html
[$] http://www.teleconnection.info/rqg/GeneralRelativity
http://www.teleconnection.info/rqg/ParticlesOrFields
http://www.teleconnection.info/rqg/SpacetimeStructure
--
http://www.canonicalscience.org/
Usenet Guidelines:
http://www.canonicalscience.org/en/miscellaneouszone/guidelines.html
======================================= MODERATOR'S COMMENT:
Stay friendly ;-)
harry
"Juan R. González-Álvarez" <juanR...@canonicalscience.com> wrote in
message news:pan.2009.04...@canonicalscience.com...
> Oh No wrote on Mon, 20 Apr 2009 06:32:23 -0600:
>
>> Thus spake "John Bell (Change John to Liberty for email)"
>> <john...@accelerators.co.uk>
>>>I recall a comment at SPR to the effect that Newtonian gravity equates
>>>to spatial curvature whereas Einsteinian gravity equates to spacetime
>>>curvature.
>>
>> I am a bit hazy about the details (as it is many years since I read the
>> relevant passage), but I think this refers to a treatment due to Cartan
>> and described in MTW.
>
> Newton-Cartan theory and Newtonian gravity are two very different beast.
> The former is a metric theory formulated after general relativity, the
> latter is an AAAD theory formulated before general relativity and even
> before field theories.
Why do you regard Newtonian physics as not a field theory? If his "Absolute
space" relative to which physical acceleration is defined is not a kind of
field, then what is it?
[..]
Regards,
Harald
======================================= MODERATOR'S COMMENT:
Container only
Juan R.
(...)
>> My problem with this is that Newton's inverse square law of gravity
>> requires Euclidean space to ensure that the surface area of a sphere is
>> precisely proportional to the square of its radius, which, afaict
>> implies spatial flatness.
>
> It took me a while to understand this, but the Cartan reformulation of
> Newton (which is what was referred to) is not a metric theory of
> gravitation.
>
> What that means, in practice, is that means is that there is no metric
> to determine distances. There is a connection chosen such that it
> reproduces Newton, but that's about as interesting as it gets.
It would took you "a while" but all you say above violates any known
presentation [1-3] of Newton-Cartan (NC) theory!
First, as even noticed at Wikipedia basic level [1] NC is a (geo)metric
theory.
Second, as is well-known [2,3], NC is a metric theory built over a
structure (h^ab, t_a, D_a, rho), where rho is a scalar field mass density,
D_a is the derivative operator associated to the connection, h^ab is the
degenerate spatial *metric* and t_a the orthogonal degenerate temporal
*metric* associated to NC spacetime.
Evidently, the spatial *metric* is needed to make sense of the distances
for computing the potentials phi_NC used in the 'gauge' decomposition of
the connection.
REFERENCES
[1] http://en.wikipedia.org/wiki/Newton-Cartan_theory
[2] Section II in Exactly Soluble Sector of Quantum Gravity 1997:
Phys. Rev. D 56, 4844-4877, Christian, J.
[3] Section 3 in http://arxiv.org/abs/gr-qc/9604054
Oh No
>Oh No wrote on Mon, 20 Apr 2009 06:32:23 -0600:
>
>
>> To find the Newtonian correspondence
>> for general relativity we define a tangent space - i.e. a space which is
>> flat by definition. Then the perturbation of the metric is reinterpreted
>> as a potential field.
>
>But that "Newtonian correspondence" does not hold upon close inspection.
>
>(i)
>As showed in my work [#] and confirmed by GR expertise Eric Poisson, it is
>not possible to find a regime in GR giving (a) flat geometry plus (b)
>non-zero acceleration plus (c) linear 'field' equations, all at once. You
>just ignore this.
This is because this is not the way the Newtonian correspondence works.
Also, his is not your work. It is well known, and discussed in major
textbooks.
(incidentally expertise is what an expert has, not what an expert is)
>(ii)
>As showed in my work [#] and confirmed by non-linear field theory
>expertise Yurij Barishev, a 'perturbation' of the metric is not a
>potential field, because violates the mathematical and physical
>propoerties associated to a true gravitational field. You are confounding
>the GR 'perturbation' tensors h_ab utilized in the geodesic equations with
>the field potentials \Psi_ab used in Kalman equations. You just ignore
>this also.
There is a difference between saying that something is a potential
field, and saying that it is treated or interpreted as a field. What I
stated is also well treated in major textbooks.
>(iii)
>As showed in my work [#] and confirmed by GR expertise Norbert Straumann,
>both the 'perturbation' h_ab and the background \eta_ab are not observable
>in GR. Strautmann calls to \eta_ab an "kind of unobservable aether" and I
>completely agree. You are defining a perturbation over an unphysical
>"space which is flat by definition". Finally, you also ignore this
>important point.
By the same token, and as recognised by Newton himself, Newtonian
absolute space is not observable. Your point is not important, but
rather irrelevant.
>P.S: Your confusion between metric potentials and field potentials (you
>denote both concepts with the same symbol) is only one of reason which
>your claimed "unification of GR with quantum mechanics" [$] has not
>mathematical or physical basis.
>
The use of the same symbol for the same quantity should not confuse any
competent theoretical scientist when only interpretation is different.
Note that (e.g. for the reasons you have given) there is no classical
gravitational potential in GR. Any discussion of equivalent field
potentials is thus completely irrelevant to my treatment of relational
quantum gravity.
harry
"harry" <harald.NOTT...@epfl.ch> wrote in message
news:1240325...@sicinfo3.epfl.ch...
Newton's absolute space defines what physically a "straight" trajectory is,
in contrast to for example a "straight" trajectory that is traced over a
merry-go-round (and which in Newton's description is a curved trajectory).
Mere containers do *not* (cannot!) define uniform motion; thus the moderator
is certainly wrong!
Regards,
Harald
Juan R.
> "Juan R. González-Álvarez" <juanR...@canonicalscience.com> wrote in
> message news:pan.2009.04...@canonicalscience.com...
>> Oh No wrote on Mon, 20 Apr 2009 06:32:23 -0600:
>>
>>> Thus spake "John Bell (Change John to Liberty for email)"
>>> <john...@accelerators.co.uk>
>>>>I recall a comment at SPR to the effect that Newtonian gravity equates
>>>>to spatial curvature whereas Einsteinian gravity equates to spacetime
>>>>curvature.
>>>
>>> I am a bit hazy about the details (as it is many years since I read
>>> the relevant passage), but I think this refers to a treatment due to
>>> Cartan and described in MTW.
>>
>> Newton-Cartan theory and Newtonian gravity are two very different
>> beast. The former is a metric theory formulated after general
>> relativity, the latter is an AAAD theory formulated before general
>> relativity and even before field theories.
>
> Why do you regard Newtonian physics as not a field theory?
As is well-known, there exists two basic approaches to interaction
mechanisms. One is the model of action-at-a-distance initially formulated
by Newton and after copied by Coulomb. From the Wikipedia entry on AAAD:
"In physics, action at a distance is the interaction of two objects
which are separated in space with no known mediator of the interaction.
This term was used most often with early theories of gravity and
electromagnetism to describe how an object could "know" the mass (in the
case of gravity) or charge (in electromagnetism) of another distant
object."
The other approach is the contact-like model formulated much more latter.
Contact-like models are the field and metric models. The mediator of
interaction is the field (e.g. EM field) or a dinamical spacetime (e.g. GR
spacetime), respectively.
Moreover, being better versed than me in the history of physics, Harry,
you would know that the concept of field was introduced in physics by
Faraday, Maxwell, and other great researchers, many many years after
Newton passed away.
Juan R.
> Thus spake Juan R. González-à lvarez
> <juanR...@canonicalscience.com>
>>Oh No wrote on Mon, 20 Apr 2009 06:32:23 -0600:
>>
>>
>>> To find the Newtonian correspondence
>>> for general relativity we define a tangent space - i.e. a space which
>>> is flat by definition. Then the perturbation of the metric is
>>> reinterpreted as a potential field.
>>
>>But that "Newtonian correspondence" does not hold upon close inspection.
>>
>>(i)
>>As showed in my work [#] and confirmed by GR expertise Eric Poisson, it
>>is not possible to find a regime in GR giving (a) flat geometry plus (b)
>>non-zero acceleration plus (c) linear 'field' equations, all at once.
>>You just ignore this.
>
> This is because this is not the way the Newtonian correspondence works.
> Also, his is not your work. It is well known, and discussed in major
> textbooks.
Some major textbooks (Carroll, Weinberg) pretend to give (b) and (c) at
once, and they force this result with 'derivations' that explicitely
violate the Bianchi identity.
The textbook by Ivanenko pretends to obtain also exactly (a) in presence
of gravitation and choses a metric is not solution of the metric
equations.
> (incidentally expertise is what an expert has, not what an expert is)
Thanks by this useful and important correction.
>>(ii)
>>As showed in my work [#] and confirmed by non-linear field theory
>>expertise Yurij Barishev, a 'perturbation' of the metric is not a
>>potential field, because violates the mathematical and physical
>>propoerties associated to a true gravitational field. You are
>>confounding the GR 'perturbation' tensors h_ab utilized in the geodesic
>>equations with the field potentials \Psi_ab used in Kalman equations.
>>You just ignore this also.
>
> There is a difference between saying that something is a potential
> field, and saying that it is treated or interpreted as a field. What I
> stated is also well treated in major textbooks.
Your exact words were "Then the perturbation of the metric is
reinterpreted as a potential field."
But neither the "perturbation of the metric" can be reinterpreted as a
potential field neither can be "treated" as one, because the math is
different.
Unfortunately, major textbooks (Carroll, Weinberg, MTW, Ivanenko, Wald)
treat the perturbation as a true field and this is the source of the
misguided claim that general relativity has both a field and geometrical
formulation.
A relevant example of the confusion is Weinberg book. He presents his book
like a non-geometrical formulation of GR, when he is really presenting
just another geometrical formulation of gravity, *not* a field
formulation.
>>(iii)
>>As showed in my work [#] and confirmed by GR expertise Norbert
>>Straumann, both the 'perturbation' h_ab and the background \eta_ab are
>>not observable in GR. Strautmann calls to \eta_ab an "kind of
>>unobservable aether" and I completely agree. You are defining a
>>perturbation over an unphysical "space which is flat by definition".
>>Finally, you also ignore this important point.
>
> By the same token, and as recognised by Newton himself, Newtonian
> absolute space is not observable. Your point is not important, but
> rather irrelevant.
Newton did not considered the subtleties of the posterior Riemanian
geometry; your remark looks irrelevant.
A rigorous understanding of the metric approach of general relativity
reveals that your above words "the perturbation of the metric" makes no
sense, because \eta_ab is not a physical metric.
>>P.S: Your confusion between metric potentials and field potentials (you
>>denote both concepts with the same symbol) is only one of reason which
>>your claimed "unification of GR with quantum mechanics" [$] has not
>>mathematical or physical basis.
>>
> The use of the same symbol for the same quantity should not confuse any
> competent theoretical scientist when only interpretation is different.
Unfortunately, with statements as this you are again showing your complete
confusion.
The symbols h_ab utilized in the geodesic equations and the symbol \Psi_ab
used in Kalman equations denote completey *different* objects, with
*different* mathematics and *different* physics.
You may believe, as you state above, that "competent theoretical
scientists" use the same symbol for completely different objects when
developing their own theories mixing geometric and field formulations [$],
but this only gives inconsistent theories without interest.
Regards
Ken S. Tucker
On Apr 21, 1:09 am, "John Bell (Change John to Liberty for email)"
<john.b...@accelerators.co.uk> wrote:
> On Apr 20, 9:35 pm, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
>
> > In Newtonians gravitation field, light rays are NOT subject
> > to gravitational effects.
>
> This is not strictly true. Newtonian physics and GR both predicted
> bending of starlight grazing the Sun. GR was confirmed because it
> predicted twice the bending
What you would need to do is use Newton's
F=GMm / r^2
and calculate the deflection of light, (without E=mc^2,
or the Equivalence Principle), how?
Back in 1911 AE used the EP to predict a deflection,
but that's old history, why dwell on it, it was wrong.
(as you say 1/2 the value).
> > The effects of space and spacetime
> > curvature use light rays as a surveying tool,
>
> Yes, this can be a very useful way of looking at things. (However, I
> find it can also become tricky and confusing within a metric theory
> such as GR, since the length of the metric element ds for light,
> becomes zero)
ds=0 makes things easy, from that one can readily
calculate the dx/dt, dy/dt for the velocity of light.
We can do that if you want.
Regards
Ken
Juan R.
> "Juan R. González-Álvarez" <juanR...@canonicalscience.com> wrote in
> message news:pan.2009.04...@canonicalscience.com...
>> Oh No wrote on Mon, 20 Apr 2009 06:32:23 -0600:
>>
>>> Thus spake "John Bell (Change John to Liberty for email)"
>>> <john...@accelerators.co.uk>
>>>>I recall a comment at SPR to the effect that Newtonian gravity equates
>>>>to spatial curvature whereas Einsteinian gravity equates to spacetime
>>>>curvature.
>>>
>>> I am a bit hazy about the details (as it is many years since I read
>>> the relevant passage), but I think this refers to a treatment due to
>>> Cartan and described in MTW.
>>
>> Newton-Cartan theory and Newtonian gravity are two very different
>> beast. The former is a metric theory formulated after general
>> relativity, the latter is an AAAD theory formulated before general
>> relativity and even before field theories.
>
> Why do you regard Newtonian physics as not a field theory?
As is well-known, there exists two basic approaches to interaction
mechanisms. One is the model of action-at-a-distance initially formulated
by Newton and after copied by Coulomb. From the Wikipedia entry on AAAD:
"In physics, action at a distance is the interaction of two objects
which are separated in space with no known mediator of the interaction.
This term was used most often with early theories of gravity and
electromagnetism to describe how an object could "know" the mass (in the
case of gravity) or charge (in electromagnetism) of another distant
object."
The other approach is the contact-like model formulated much more latter.
Contact-like models are the field and metric models. The mediator of
interaction is the field (e.g. EM field) or a dinamical spacetime (e.g. GR
spacetime), respectively.
Moreover, being better versed than me in the history of physics Harry, you
would know the concept of field was introduced in physics by Faraday,
Maxwell, and other great researchers, many many years after Newton passed
away!
--
http://www.canonicalscience.org/
Usenet Guidelines:
http://www.canonicalscience.org/en/miscellaneouszone/guidelines.html
======================================= MODERATOR'S COMMENT:
Descartes' interaction is contact interaction, CEM is "field interaction" (Sommerfeld)
Oh No
>Oh No wrote on Tue, 21 Apr 2009 10:20:45 -0600:
>
>> <juanR...@canonicalscience.com>
>>>Oh No wrote on Mon, 20 Apr 2009 06:32:23 -0600:
>>>
>>>
>>>> To find the Newtonian correspondence
>>>> for general relativity we define a tangent space - i.e. a space which
>>>> is flat by definition. Then the perturbation of the metric is
>>>> reinterpreted as a potential field.
>>>
>>>But that "Newtonian correspondence" does not hold upon close inspection.
>>>
>>>(i)
>>>As showed in my work [#] and confirmed by GR expertise Eric Poisson, it
>>>is not possible to find a regime in GR giving (a) flat geometry plus (b)
>>>non-zero acceleration plus (c) linear 'field' equations, all at once.
>>>You just ignore this.
>>
>> This is because this is not the way the Newtonian correspondence works.
>> Also, his is not your work. It is well known, and discussed in major
>> textbooks.
>
>Some major textbooks (Carroll, Weinberg) pretend to give (b) and (c) at
>once, and they force this result with 'derivations' that explicitely
>violate the Bianchi identity.
I cannot comment on Carroll or Weinberg's treatments, since I have not
read either.
>
>The textbook by Ivanenko pretends to obtain also exactly (a) in presence
>of gravitation and choses a metric is not solution of the metric
>equations.
>
>> (incidentally expertise is what an expert has, not what an expert is)
>
>Thanks by this useful and important correction.
>
>>>(ii)
>>>As showed in my work [#] and confirmed by non-linear field theory
>>>expertise Yurij Barishev, a 'perturbation' of the metric is not a
>>>potential field, because violates the mathematical and physical
>>>propoerties associated to a true gravitational field. You are
>>>confounding the GR 'perturbation' tensors h_ab utilized in the geodesic
>>>equations with the field potentials \Psi_ab used in Kalman equations.
>>>You just ignore this also.
>>
>> There is a difference between saying that something is a potential
>> field, and saying that it is treated or interpreted as a field. What I
>> stated is also well treated in major textbooks.
>
>Your exact words were "Then the perturbation of the metric is
>reinterpreted as a potential field."
>
>But neither the "perturbation of the metric" can be reinterpreted as a
>potential field neither can be "treated" as one, because the math is
>different.
The maths is the same in the correct approximation. Mathematically a
potential field is simply a function on R^n such that its derivative
gives the acceleration.
>
>Unfortunately, major textbooks (Carroll, Weinberg, MTW, Ivanenko, Wald)
>treat the perturbation as a true field and this is the source of the
>misguided claim that general relativity has both a field and geometrical
>formulation.
I tend to agree that the field formulation is misleading.
>A relevant example of the confusion is Weinberg book. He presents his book
>like a non-geometrical formulation of GR, when he is really presenting
>just another geometrical formulation of gravity, *not* a field
>formulation.
This has put me off Weingberg's book. I agree that his introduction is
extremely misguided.
>
>>>(iii)
>>>As showed in my work [#] and confirmed by GR expertise Norbert
>>>Straumann, both the 'perturbation' h_ab and the background \eta_ab are
>>>not observable in GR. Strautmann calls to \eta_ab an "kind of
>>>unobservable aether" and I completely agree. You are defining a
>>>perturbation over an unphysical "space which is flat by definition".
>>>Finally, you also ignore this important point.
>>
>> By the same token, and as recognised by Newton himself, Newtonian
>> absolute space is not observable. Your point is not important, but
>> rather irrelevant.
>
>Newton did not considered the subtleties of the posterior Riemanian
>geometry; your remark looks irrelevant.
>
>A rigorous understanding of the metric approach of general relativity
>reveals that your above words "the perturbation of the metric" makes no
>sense, because \eta_ab is not a physical metric.
And nor should it be. Absolute space is an idealisation, not a reality.
>
>>>P.S: Your confusion between metric potentials and field potentials (you
>>>denote both concepts with the same symbol) is only one of reason which
>>>your claimed "unification of GR with quantum mechanics" [$] has not
>>>mathematical or physical basis.
>>>
>> The use of the same symbol for the same quantity should not confuse any
>> competent theoretical scientist when only interpretation is different.
>
>Unfortunately, with statements as this you are again showing your complete
>confusion.
I have no confusion.
>The symbols h_ab utilized in the geodesic equations and the symbol \Psi_ab
>used in Kalman equations denote completey *different* objects, with
>*different* mathematics and *different* physics.
I have googled Kalman equations and find nothing of any relevance.
>
>You may believe, as you state above, that "competent theoretical
>scientists" use the same symbol for completely different objects when
>developing their own theories mixing geometric and field formulations [$],
>but this only gives inconsistent theories without interest.
The very fact that you think geometric and field formulations are mixed
is indication of your own confusion - you cannot be blamed for this,
because the confusion is present in other treatments, and in other areas
of physics.. The only sense in which "field" means anything is the
mathematical one I have given above. The very notion of a "field
quantity" meaning something physically substantive indicates confusion
about the use of mathematics in physics.
Ken S. Tucker
<john.b...@accelerators.co.uk> wrote:
> On Apr 20, 9:35 pm, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
>
> > Once SR predicted "radiant energy"
> > is subject to gravitational effects as a result of the unified
> > conservation of mass and energy law, the light-rays used
> > to survey the gravity field were understood to be affected
> > by the field, leading to the need of GR applied to gravity
> > rendering a "red-shift" when light is vertically directed
>
> IIRC from MTW, the gravitational redshift of light is also directly
> derivable from Newtonian physics and energy conservation, given the PD
> between higher and lower points.
Sorry, I don't use MTW anymore, but I invite you to
provide a brief explanation of how they do that, or an
online ref.
I find one can use Newtonian Physics in adhoc ways
to explain some GR predictions *after the fact*, but
one has difficulties explaining light deflection and
the correction to the orbits of planets, and other things.
GR is respected because it does all of those.
> I do like the way you tend to interpret things simply,
Thanks we try :-).
> but sometimes (like now), this does not quite seem to
> cut the mustard.
LOL, "cut the mustard", GR is more complicated than
garnishing a hot-dog, that's certainly true.
GR is often regarded as the greatest and most difficult
intellectual achievement to understand, and has many
depths, including it's relation to EM and QT, it all
depends on how much detail one wants?
Regards
Ken
John Bell (Change John to Liberty for email)
> On Apr 21, 5:45 am, "John Bell (Change John to Liberty for email)"
>
> <john.b...@accelerators.co.uk> wrote:
> > On Apr 20, 9:35 pm, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
>
> > > Once SR predicted "radiant energy"
> > > is subject to gravitational effects as a result of the unified
> > > conservation of mass and energy law, the light-rays used
> > > to survey the gravity field were understood to be affected
> > > by the field, leading to the need of GR applied to gravity
> > > rendering a "red-shift" when light is vertically directed
>
> > IIRC from MTW, the gravitational redshift of light is also directly
> > derivable from Newtonian physics and energy conservation, given the PD
> > between higher and lower points.
>
> Sorry, I don't use MTW anymore, but I invite you to
> provide a brief explanation of how they do that, or an
> online ref.
Loss in gravitational potential energy (del phi) = gain in photon
actual energy (h del f)
Reverse for light travelling up potential well
Couldn't be simpler
: - )
John Bell (Change John to Liberty for email)
PS Admittedly, you do have to assume that effective mass of photon =
momentum/speed (which IS Newtonian physics), to give
h(f + del f) = hf + gdhf/c^2
hence f'/f = 1 + gd/c^2
(IIRC MTW did not actually spell this out, explicitly)
Ken S. Tucker
On Apr 22, 3:42 pm, "John Bell (Change John to Liberty for email)"
Yes, that's part of it.
(What follows is my opinion).
I did an article on that, that subsequently appeared, see
Weinberg's "Grav&Cosmo" pg.84, (a classic) following
"Incidentally" on that pg.
It's one of the rare times Weinberg didn't provide a ref.
(I didn't publish the essay, only circulated it).
John, your above analysis is based on E=hf.
What you have done is employed "h" as a universal
invariant, to your credit.
Now John, if you did not have Plancks E=hf, could
you have arrived at the same conclusion?
IMHO, SR uses the local invariant "c" but GR uses
the universal invariant "h", based also on charges,
such as the product of fundamental charges to
provide an action, (Fred the moderator is an expert
on that).
Suppose there are two aspects in our universe,
Change, and Stability.
Change is locally defined by "c" being a constant
using ds=0, and "h" defines a static stability.
Regards
Ken S. Tucker
John Bell (Change John to Liberty for email)
> Hi John.
>
> On Apr 22, 3:42 pm, "John Bell (Change John to Liberty for email)"
> > Loss in gravitational potential energy (del phi) = gain in photon
> > actual energy (h del f)
> > Reverse for light travelling up potential well
> > Couldn't be simpler
> > : - )
>
> Yes, that's part of it.
> (What follows is my opinion).
> I did an article on that, that subsequently appeared, see
> Weinberg's "Grav&Cosmo" pg.84, (a classic) following
> "Incidentally" on that pg.
Unfortunately, I do not have that to hand, having only read it once
years ago, by ordering it from local library
> It's one of the rare times Weinberg didn't provide a ref.
> (I didn't publish the essay, only circulated it).
> John, your above analysis is based on E=hf.
Which is the founding step of QM, circa 1900 (pre-dating relativity)
> What you have done is employed "h" as a universal
> invariant, to your credit.
Yes and no. Since it cancels out, I could arguably have instead used
the action of a custard pie :-)
> Now John, if you did not have Plancks E=hf, could
> you have arrived at the same conclusion?
Difficult to say. Don't forget Newton's theory of light was
corpuscular, and who knows where that would have gone if Huygen's wave
theory had not become more fashionable, for a while.
Juan R.
> Thus spake Juan R. González-Álvarez <juanR...@canonicalscience.com>
(...)
>>Your exact words were "Then the perturbation of the metric is
>>reinterpreted as a potential field."
>>
>>But neither the "perturbation of the metric" can be reinterpreted as a
>>potential field neither can be "treated" as one, because the math is
>>different.
>
> The maths is the same in the correct approximation. Mathematically a
> potential field is simply a function on R^n such that its derivative
> gives the acceleration.
And once again, you confound the metric-like function h_ab = h_ab(x,t)
used by general relativists and geometers with the field-like function
Psi_ab = Psi_ab (x,t) used by field theorists.
NOTE: The symbol Psi_ab for denoting the true field potential is standard
in the field-theoretic literature I have studied.
(...)
>>The symbols h_ab utilized in the geodesic equations and the symbol
>>\Psi_ab used in Kalman equations denote completey *different* objects,
>>with *different* mathematics and *different* physics.
>
> I have googled Kalman equations and find nothing of any relevance.
Kalman wrote his relevant paper in Phys. Rev. 123, 384 in the year 1961,
where he corrected an error in the derivation of field theoretic equations
of motion in previous Thirring's paper "An alternative approach to the
theory of gravitation".
In the draft announced in spf and updated on Abr 21 [#], I include a
introduction to Kalman field-theoretic equations used today by astronomers
and astrophysicists to explain observations. I also compute the Newtonian
limit of Kalman equations with detail.
Regards
LINK
[#] http://www.canonicalscience.org/en/publicationzone/drafts.html
Oh No
>Oh No wrote on Tue, 21 Apr 2009 16:00:46 -0600:
>
>
>(...)
>
>>>Your exact words were "Then the perturbation of the metric is
>>>reinterpreted as a potential field."
>>>
>>>But neither the "perturbation of the metric" can be reinterpreted as a
>>>potential field neither can be "treated" as one, because the math is
>>>different.
>>
>> The maths is the same in the correct approximation. Mathematically a
>> potential field is simply a function on R^n such that its derivative
>> gives the acceleration.
>
>And once again, you confound the metric-like function h_ab = h_ab(x,t)
>used by general relativists and geometers with the field-like function
>Psi_ab = Psi_ab (x,t) used by field theorists.
On the contrary, you confound a mathematical function with
interpretation. You are making a distinction without a difference.
Mathematically, both h_ab and Psi_ab are fields.
>NOTE: The symbol Psi_ab for denoting the true field potential is standard
> in the field-theoretic literature I have studied.
Notational differences are of no importance.
>>>The symbols h_ab utilized in the geodesic equations and the symbol
>>>\Psi_ab used in Kalman equations denote completey *different* objects,
>>>with *different* mathematics and *different* physics.
>>
>> I have googled Kalman equations and find nothing of any relevance.
>
>Kalman wrote his relevant paper in Phys. Rev. 123, 384 in the year 1961,
>where he corrected an error in the derivation of field theoretic equations
>of motion in previous Thirring's paper "An alternative approach to the
>theory of gravitation".
>
>In the draft announced in spf and updated on Abr 21 [#], I include a
>introduction to Kalman field-theoretic equations used today by astronomers
>and astrophysicists to explain observations. I also compute the Newtonian
>limit of Kalman equations with detail.
>
This is hardly mainstream. You say it is used by astronomers and
astrophysicists, and in may be used by one or two, but it is certainly
not generally used, and it inappropriate to refer to it as such.
Juan R.
(...)
>>> The maths is the same in the correct approximation. Mathematically a
>>> potential field is simply a function on R^n such that its derivative
>>> gives the acceleration.
>>
>>And once again, you confound the metric-like function h_ab = h_ab(x,t)
>>used by general relativists and geometers with the field-like function
>>Psi_ab = Psi_ab (x,t) used by field theorists.
>
> On the contrary, you confound a mathematical function with
> interpretation. You are making a distinction without a difference.
> Mathematically, both h_ab and Psi_ab are fields.
Mathematically, the functions h_ab and Psi_ab are different.
In my draft [#], the physical difference is done clear and the entire
section 14 is devoted to review some of the mathematical differences
between both functions. The draft includes additional field-theoretic
literature in the topic of similarities and differences between both.
I do not know how many general relativists read this newsgroup, but if
they read your above assertion that h_ab in general relativity is "simply
a function on R^n such that its derivative gives the acceleration" they
may be mailing you now a copy of some GR basic textbook.
(...)
>>Kalman wrote his relevant paper in Phys. Rev. 123, 384 in the year 1961,
>>where he corrected an error in the derivation of field theoretic
>>equations of motion in previous Thirring's paper "An alternative
>>approach to the theory of gravitation".
>>
>>In the draft announced in spf and updated on Abr 21 [#], I include a
>>introduction to Kalman field-theoretic equations used today by
>>astronomers and astrophysicists to explain observations. I also compute
>>the Newtonian limit of Kalman equations with detail.
>>
> This is hardly mainstream. You say it is used by astronomers and
> astrophysicists, and in may be used by one or two, but it is certainly
> not generally used, and it inappropriate to refer to it as such.
(i)
Several relevant astrophysical predictions were first predicted by field
theorists.
For instance, the typical GR textbook formulae for Lense-Thirring effect
is inapplicable when the gyroscope can no longer be treated as a test
particle being as massive as the companion.
N.D. Hari Dass and C.F. Cho derived the correct formula in 1975 using
field theory methods. As Dass reports: "GR people derived the same much
later."
V. Radhakrishnan predicted, again using field theory, observable effects
in binary pulsars 30 years before Hotan, Bailes, and Ord reported
observing these effects in PSR J1141-6545.
(ii)
The general relativist N. Straumann writes:
An obstacle for a full understanding of GR has always been the necessity
of absorbing first a considerable amount of mathematical machinery. This
is, of course, no problem for theoreticians, but experimentalists and
astronomers often do not find the time for this. (This is at least true
for many people I know.) To some extend, this hurdle can be postponed in
an ungeometrical approach to GR, which has been advocated in the course
of time by a number of authors, in particular by R.P. Feynman in his
Caltech lectures [1]. One may call it the flat spacetime - or the field
theoretic approach. I first learned about it in my youth from
discussions with M. Fierz. That was shortly after he left CERN as theory
director and came to Zurich as Pauli's successor. His ideas were
partially worked out in the thesis of W. Wyss [2]. At about the same
time W. Thirring was advocating this approach with different emphasis in
talks and some publications [3]. S. Weinberg had a related paper [4], in
which he made an attempt to develop a quantum theory of a
selfinteracting spin-2 field on flat spacetime. (We now know that such
theories are unrenormalizable, also for supersymmetric extensions.) The
theme was taken up later by S. Deser [5], R.M. Wald [6], and others.
The idea of this alternative approach is to describe gravity - in close
analogy to electrodynamics - by a field theory on flat Minkowski
spacetime. I shall spend much of my time in showing you how this can be
done without much effort.
[...]
One of the advantages of this field theoretic approach is that it
follows the patterns of well understood field theories and may thus be
closer to what many of you are used to. Other pros and cons will be
discussed later.
Unfortunately, Straumann's mathematical treatment of the field theoretic
approach is incorrect. E.g. I prove in my draft [#] that his
renormalization procedure of spacetime gives final geometrical equations
of motion are incompatible with Kalman equations of motion.
The misguided claim of identity of field and geometric formulations that
one finds in GR textbooks and some papers has two ironic consequences.
The first that some astronomers and astrophysicists, *using* a field-
theoretic approach to gravitation, *believe* are using the geometric
approach of GR!
The second that authors, *using* a geometric approach to gravitation,
*believe* are using a non-geometrical one! Weinberg book on gravitation
is a relevant example.
Finally, there exists another group of authors (one or two) that neither
understand general relativity nor field theory [$$].
Regards.
LINKS
[#] http://www.canonicalscience.org/en/publicationzone/drafts.html
[$$] http://www.teleconnection.info/rqg/GeneralRelativity
http://www.teleconnection.info/rqg/ParticlesOrFields
http://www.teleconnection.info/rqg/SpacetimeStructure
--
Oh No
>
>(...)
>
>>>> The maths is the same in the correct approximation. Mathematically a
>>>> potential field is simply a function on R^n such that its derivative
>>>> gives the acceleration.
>>>
>>>And once again, you confound the metric-like function h_ab = h_ab(x,t)
>>>used by general relativists and geometers with the field-like function
>>>Psi_ab = Psi_ab (x,t) used by field theorists.
>>
>> On the contrary, you confound a mathematical function with
>> interpretation. You are making a distinction without a difference.
>> Mathematically, both h_ab and Psi_ab are fields.
>
>Mathematically, the functions h_ab and Psi_ab are different.
This is not interesting. Only one component is important in the weak
field limit of gtr, and the field theoretic approach is unsound
metaphysics and not interesting at all.
>
>I do not know how many general relativists read this newsgroup, but if
>they read your above assertion that h_ab in general relativity is "simply
>a function on R^n such that its derivative gives the acceleration" they
>may be mailing you now a copy of some GR basic textbook.
I already have at least five on my shelves.
Juan R.
> Thus spake Juan R. González-Álvarez <juanR...@canonicalscience.com>
>>Oh No wrote on Thu, 23 Apr 2009 08:05:15 -0600:
>>
>>(...)
>>
>>>>> The maths is the same in the correct approximation. Mathematically a
>>>>> potential field is simply a function on R^n such that its derivative
>>>>> gives the acceleration.
>>>>
>>>>And once again, you confound the metric-like function h_ab = h_ab(x,t)
>>>>used by general relativists and geometers with the field-like function
>>>>Psi_ab = Psi_ab (x,t) used by field theorists.
>>>
>>> On the contrary, you confound a mathematical function with
>>> interpretation. You are making a distinction without a difference.
>>> Mathematically, both h_ab and Psi_ab are fields.
>>
>>Mathematically, the functions h_ab and Psi_ab are different.
>
> This is not interesting. Only one component is important in the weak
> field limit of gtr, and the field theoretic approach is unsound
> metaphysics and not interesting at all.
Do you mean the same field theoretic approach you never studied and could
not write the (Kalman) equations of motion here and now [@]?
Or the same field theoretic approach you said would be used "by one or
two" but is routinely taught and utilized [@]?
Or the same field theoretic approach has given many non-trivial
predictions after confirmed [@]?
>>I do not know how many general relativists read this newsgroup, but if
>>they read your above assertion that h_ab in general relativity is
>>"simply a function on R^n such that its derivative gives the
>>acceleration" they may be mailing you now a copy of some GR basic
>>textbook.
>
> I already have at least five on my shelves.
Don't surprise if you receive another five.
Regards
[@] Data, quotes, and links deleted by Charles in his reply but available
in my previous messages in this thread.
--
http://www.canonicalscience.org/
Usenet Guidelines:
http://www.canonicalscience.org/en/miscellaneouszone/guidelines.html
======================================= MODERATOR'S COMMENT:
Snipping is encouraged
Oh No
>Oh No wrote on Thu, 23 Apr 2009 16:49:25 -0600:
>
>>>Oh No wrote on Thu, 23 Apr 2009 08:05:15 -0600:
>>>
>>>(...)
>>>
>>>>>> The maths is the same in the correct approximation. Mathematically a
>>>>>> potential field is simply a function on R^n such that its derivative
>>>>>> gives the acceleration.
>>>>>
>>>>>And once again, you confound the metric-like function h_ab = h_ab(x,t)
>>>>>used by general relativists and geometers with the field-like function
>>>>>Psi_ab = Psi_ab (x,t) used by field theorists.
>>>>
>>>> On the contrary, you confound a mathematical function with
>>>> interpretation. You are making a distinction without a difference.
>>>> Mathematically, both h_ab and Psi_ab are fields.
>>>
>>>Mathematically, the functions h_ab and Psi_ab are different.
>>
>> This is not interesting. Only one component is important in the weak
>> field limit of gtr, and the field theoretic approach is unsound
>> metaphysics and not interesting at all.
>
>Do you mean the same field theoretic approach you never studied and could
>not write the (Kalman) equations of motion here and now [@]?
The equations of motion in general relativity were given by Einstein. I
have no interest in your obscure approach.
>
>Or the same field theoretic approach you said would be used "by one or
>two" but is routinely taught and utilized [@]?
Clearly the approach referred to is not routinely taught or used.
>
>Or the same field theoretic approach has given many non-trivial
>predictions after confirmed [@]?
I think you have made it quite clear that you do not understand the
difference between the mathematical definition of a field, which can be
used to get correct predictions, and the metaphysical definition, which
indicates only confusion about the reason those predictions are correct.
John Bell (Change John to Liberty for email)
> Thus spake "John Bell (Change John to Liberty for email)"
> <john.b...@accelerators.co.uk>
>
> >I recall a comment at SPR to the effect that Newtonian gravity equates
> >to spatial curvature whereas Einsteinian gravity equates to spacetime
> >curvature.
>
> I am a bit hazy about the details (as it is many years since I read the
> relevant passage), but I think this refers to a treatment due to Cartan
> and described in MTW.
See
for Steve Carlip's further clarification.
(Wonderful!)
Juan R.
(...)
> I have no interest in your obscure approach.
Is not mine!
The field theoretic approach was developed by other authors: Feynman,
Thirring, Deser, Kalman... You would know this if you had read the
references and relevant quotes of my previous messages.
(...)
>>Or the same field theoretic approach has given many non-trivial
>>predictions after confirmed [@]?
>
> I think you have made it quite clear that you do not understand the
> difference between the mathematical definition of a field, which can be
> used to get correct predictions, and the metaphysical definition, which
> indicates only confusion about the reason those predictions are correct.
I think you have been made clear that you ignore the "mathematical
definition" of field associated to the field theoretic approach; approach
wich you never studied, could not google, believed was not taught and
used, and that so proudly you claim to be not interested in.
But after re-reading this thread, it is not so clear, at least for me, if
you finally understand that your confusion between the mathematics of h_ab
(x,t) and the mathematics of \Psi_ab(x,t) is one of basis for your
"metaphysical definition" of field and your unfounded claims of
unification of physics.
Regards
[@] Data, quotes, and links available in my previous messages in this
Oh No
>
>(...)
>
>> I have no interest in your obscure approach.
>
>Is not mine!
>
>The field theoretic approach was developed by other authors: Feynman,
>Thirring, Deser, Kalman... You would know this if you had read the
>references and relevant quotes of my previous messages.
I have ascertained only that you links references to your own
unpublished papers for which open access is not given, so that they
cannot be viewed.
>
>(...)
>
>>>Or the same field theoretic approach has given many non-trivial
>>>predictions after confirmed [@]?
>>
>> I think you have made it quite clear that you do not understand the
>> difference between the mathematical definition of a field, which can be
>> used to get correct predictions, and the metaphysical definition, which
>> indicates only confusion about the reason those predictions are correct.
>
>I think you have been made clear that you ignore the "mathematical
>definition" of field associated to the field theoretic approach;
I am sorry, but this appears to be an oxymoron. If the definition is
mathematical, then it is as I have given it. It says nothing about the
metaphysical existence of fields, and there is no big deal.
>But after re-reading this thread, it is not so clear, at least for me, if
>you finally understand that your confusion between the mathematics of h_ab
>(x,t) and the mathematics of \Psi_ab(x,t) is one of basis for your
>"metaphysical definition" of field and your unfounded claims of
>unification of physics.
>
I make no metaphysical definition, but when an author talks of a field
theoretical approach, it is usually implicit that the author intends a
metaphysical definition. So that we are clear what you are talking
about, can you provide a definition of a field theoretic approach.
John Bell (Change John to Liberty for email)
<juanREM...@canonicalscience.com> wrote:
> (i)
> As showed in my work [#]
[...]
> (ii)
> As showed in my work [#]
[...]
> (iii)
> As showed in my work [#]
[...]
> Regards.
>
> [#]http://www.canonicalscience.org/en/publicationzone/drafts.html
Very funny
This draft is dated in the future.
Its portal is secret password protected, with no means provided to
obtain such a password.
Additionally, the server reports a 404 Not Found error was encountered
while trying to use an ErrorDocument to handle the request.
Juan R.
> Thus spake Juan R. González-Álvarez <juanR...@canonicalscience.com>
>>Oh No wrote on Fri, 24 Apr 2009 06:25:21 -0600:
>>
>>(...)
>>
>>> I have no interest in your obscure approach.
>>
>>Is not mine!
>>
>>The field theoretic approach was developed by other authors: Feynman,
>>Thirring, Deser, Kalman... You would know this if you had read the
>>references and relevant quotes of my previous messages.
>
> I have ascertained only that you links references to your own
> unpublished papers for which open access is not given, so that they
> cannot be viewed.
This is a new misconception.
If you had read my messages in this thread, you would see that I cited
Kalman paper (Phys. Rev. 123, 384) published in 1961. And also named
several other authors who contributed and/or used the field theoretic
approach.
I cited Thirring's paper "An alternative approach to the theory of
gravitation". It may be easy to find this.
I named the authors N.D. Hari Dass, C.F. Cho, and V. Radhakrishnan. It
may be easy to find their works in field theory.
I reproduced a large quote from N. Straumann, who has taught the field
theoretic approach to many physicists and astronomers.
In the quote, Straumann cites the works of Weinberg, Deser, Wald, and
others. All those works are well-known and may be easy to find.
Straumann also cites the very very famous Caltech lectures on gravitation
by R.P. Feynman. They are still used in clasroom, reedited in 2002 by
Westview Press Inc.
(...)
Regards.
harry
"Juan R. Gonz�lez-�lvarez" <juanR...@canonicalscience.com> wrote in
Right.
> The other approach is the contact-like model formulated much more latter.
> Contact-like models are the field and metric models. The mediator of
> interaction is the field (e.g. EM field) or a dinamical spacetime (e.g. GR
> spacetime), respectively.
>
> Moreover, being better versed than me in the history of physics Harry, you
> would know the concept of field was introduced in physics by Faraday,
> Maxwell, and other great researchers, many many years after Newton passed
> away!
I have not researched the development of the field concept. As discussed in
a parallel message, Newton assumed some kind of a medium that serves for
transmitting the action at a distance. I can imagine that Newton (as well as
Coulomb?) did think that the action was direct, through the medium (direct
action at a distance), and not indirect, by means of the medium (the essence
of fields).
> ======================================= MODERATOR'S COMMENT:
> Descartes' interaction is contact interaction, CEM is "field interaction"
> (Sommerfeld)
Regards,
Harald