Inertia & Mach's principle & frame dragging & galaxy rotation
Wolfgang G. Gasser
> If inertia somehow depends on the other masses, shouldn't nearby
> masses have a bigger effect than more distant masses? A simple
> hypothesis is that the effect of a distant object on inertial
> motion of a test body is proportional to the mass of the
> distant object and inversely proportional to the distance, i.e.
> proportional to gravitational potential lost by the test body
> due to the distant object (what we can call the gravitational
> dependence on the distant object). This means that inertial
> motion of the test body is dragged by all these objects. The
> resulting drag can be calculated by weighted averages.
>
> Let us introduce a coordinate system where the mass center of
> a galaxy is at rest and define an 'inersis vector field' in the
> following way: the inersis velocity vector at any point is the
> average of the velocity vectors of all parts of the galaxy,
> weighted according to gravitational dependence.
>
> If the kinematics and the mass distribution of a galaxy is known
> then it is easy to calculate the inersis vector field. This vector
> field obviously rotates around the center of the galaxy. E.g. near
> earth, the weight of the stars in our neighbourhood is stronger
> than the weight of the stars on the other side of the Milky Way
> moving in the opposite direction. Therefore, the inersis vectors
> in our galactic region point roughly to the same direction as the
> movement of this region.
Maybe in this newsgroup somebody can answer these questions:
1) Is it clear what I mean by 'inersis velocity vector field'?
2) Is it easy to calculate this velocity vector field starting
with an already existing numerical simulation of a galaxy?
3) What is the rotation curve of the inersis vector field in
comparison with the rotation curve of the rotation speeds?
(see: http://en.wikipedia.org/wiki/Galaxy_rotation_problem)
4) Could the inersis vectors account for the discrepancy between
the observed rotation speeds and the predictions of Newtonian
dynamics?
Cheers, Wolfgang
Oh No
As a google search for inersis vector reveals only two hits, both
written by you, and those in terms of some theory based on ether unique
to you, I think you can safely assume no one knows what you mean or can
give answers to your question.
Regards
--
Charles Francis
moderator sci.physics.foundations.
substitute charles for NotI to email
Wolfgang G. Gasser
>> = Wolfgang G. Gasser in news:f8if8e$5uk$1...@atlas.ip-plus.net
>> Maybe in this newsgroup somebody can answer these questions:
>>
>> 1) Is it clear what I mean by 'inersis velocity vector field'?
>>
>> 2) Is it easy to calculate this velocity vector field starting
>> with an already existing numerical simulation of a galaxy?
>>
>> 3) What is the rotation curve of the inersis vector field in
>> comparison with the rotation curve of the rotation speeds?
>> (see: http://en.wikipedia.org/wiki/Galaxy_rotation_problem)
>>
>> 4) Could the inersis vectors account for the discrepancy between
>> the observed rotation speeds and the predictions of Newtonian
>> dynamics?
>
> As a google search for inersis vector reveals only two hits, both
> written by you, and those in terms of some theory based on ether
> unique to you, I think you can safely assume no one knows what
> you mean or can give answers to your question.
Please let me know if one of the following points concerning my
hypothesis is not clear:
P1: Inertial motion of a test body is influenced by the changes
in motion of all objects, due to which the test body has
lost gravitational potential. That means, velocity changes
of all these objects tend to induce an analogous velocity
change on the inertial movement of the test body.
P2: If there is only one massive object then any change in
velocity of this object leads to an idential change in
velocity of the test body's inertial movement.
P3: If there are n objects, then the n changes in velocity dV_1,
dV_2, ... dV_n affect the inertial movement of the test
particle. If the gravitational potential losses of the test
body due the n objects are respectively p_1, p_2, ... p_n, then
the resulting velocity change of the test body is the average
of the velocity change vectors dV_i weighted according to the
respective gravitational potential losses p_i:
dV = (p_1 * dV_1 + ... + p_n * dV_n) / (p_1 + ... + p_n)
In many cases, the approach of starting with the velocity vectors
V_i is more convenient than starting with the velocity changes dVi:
P4: We introduce a coordinate system with at its origin the mass
center of a galaxy. The galaxy is described at any given
time by n objects each having position vector X_i, velocity
vector V_i and mass m_i.
P5: The total loss in gravitational potential p(X) at point X of
the coordinate system is the sum of the gravitation potential
losses p_1, p_2, ... p_n due to the n objects:
p(X) = p_1(X) + p_2(X) + ... + p_n(X)
P6: At any point X, a velocity vector V(X) can be defined as
the average of the velocities V_i of the n objects, weighted
according to the corresponding potential energy losses p_i(X).
P7: We can call this vector field V(X) 'inersis', following the
'stasis' vector field of Bruce Harvey: "Taking a broader view
we find that stasis is a vector field existing throughout all
space and varying from point to point as we move around the
solar system, between the stars and from galaxy to galaxy."
(http://users.powernet.co.uk/bearsoft/Stsis.html)
P8: The inersis vector field rotates around a galaxy in a similar
way (but weaker) than the parts of the galaxy do.
Cheers, Wolfgang
Oh No
>>> = Wolfgang G. Gasser in news:f8if8e$5uk$1...@atlas.ip-plus.net
>
>>> Maybe in this newsgroup somebody can answer these questions:
>>>
>>> 1) Is it clear what I mean by 'inersis velocity vector field'?
>>>
>>> 2) Is it easy to calculate this velocity vector field starting
>>> with an already existing numerical simulation of a galaxy?
>>>
>>> 3) What is the rotation curve of the inersis vector field in
>>> comparison with the rotation curve of the rotation speeds?
>>> (see: http://en.wikipedia.org/wiki/Galaxy_rotation_problem)
>>>
>>> 4) Could the inersis vectors account for the discrepancy between
>>> the observed rotation speeds and the predictions of Newtonian
>>> dynamics?
>>
>> As a google search for inersis vector reveals only two hits, both
>> written by you, and those in terms of some theory based on ether
>> unique to you, I think you can safely assume no one knows what
>> you mean or can give answers to your question.
>
>Please let me know if one of the following points concerning my
>hypothesis is not clear:
>
>P1: Inertial motion of a test body is influenced by the changes
> in motion of all objects, due to which the test body has
> lost gravitational potential. That means, velocity changes
> of all these objects tend to induce an analogous velocity
> change on the inertial movement of the test body.
If this is clear, it is false. You would be better to start by studying
mechanics up to general relativity before thinking that you can create
laws from imagination.
Peter
...> Please let me know if one of the following points concerning my
> hypothesis is not clear:
Hello Wolfgang,
It is not clear to me which status these statements have got, are they
axioms, conclusions, requirements, definitions? You use some well-known
notions like 'inertial motion', but in the common sense? Are you assuming
background, absolute space and time? Are you tempting at a foundation of
classical mechanics or gravitation theory?
Please don't take my questions not as discouragement, but as help to make
your ideas better understandable to others.
> P1: Inertial motion of a test body is influenced by the changes
> in motion of all objects, due to which the test body has
> lost gravitational potential. That means, velocity changes
> of all these objects tend to induce an analogous velocity
> change on the inertial movement of the test body.
What is "loss of gravitation potential"?
> P2: If there is only one massive object then any change in
> velocity of this object leads to an idential change in
> velocity of the test body's inertial movement.
If there is only one massive object, what changes its velocity?
"change of velocity" and "inertial movement" contradict each another
> P3: If there are n objects, then the n changes in velocity dV_1,
> dV_2, ... dV_n affect the inertial movement of the test
> particle. If the gravitational potential losses of the test
> body due the n objects are respectively p_1, p_2, ... p_n, then
> the resulting velocity change of the test body is the average
> of the velocity change vectors dV_i weighted according to the
> respective gravitational potential losses p_i:
> dV = (p_1 * dV_1 + ... + p_n * dV_n) / (p_1 + ... + p_n)
>
> In many cases, the approach of starting with the velocity vectors V_i
> is more convenient than starting with the velocity changes dVi:
>
> P4: We introduce a coordinate system with at its origin the mass
> center of a galaxy. The galaxy is described at any given
> time by n objects each having position vector X_i, velocity
> vector V_i and mass m_i.
What for a coordinate system, how its axes are defined?
> P5: The total loss in gravitational potential p(X) at point X of
> the coordinate system is the sum of the gravitation potential
> losses p_1, p_2, ... p_n due to the n objects:
> p(X) = p_1(X) + p_2(X) + ... + p_n(X)
>
> P6: At any point X, a velocity vector V(X) can be defined as
> the average of the velocities V_i of the n objects, weighted
> according to the corresponding potential energy losses p_i(X).
>
> P7: We can call this vector field V(X) 'inersis', following the
> 'stasis' vector field of Bruce Harvey: "Taking a broader view
> we find that stasis is a vector field existing throughout all
> space and varying from point to point as we move around the
> solar system, between the stars and from galaxy to galaxy."
> (http://users.powernet.co.uk/bearsoft/Stsis.html)
Ok, you can do that. What is the meaning of it?
> P8: The inersis vector field rotates around a galaxy in a similar
> way (but weaker) than the parts of the galaxy do.
Looking forward,
Peter
Wolfgang G. Gasser
>> = Wolfgang G. Gasser in news:f8l3vo$brp$1...@atlas.ip-plus.net
> It is not clear to me which status these statements have got, are they
> axioms, conclusions, requirements, definitions?
The points P1 .. P8 only should clarify the hypothesis I'm dealing
with in this thread.
> You use some well-known notions like 'inertial motion', but in the
> common sense?
I start with this definition of 'inertial motion':
A test body's movement is inertial if all gravitational forces
acting on the test body are compensated by artificial forces
(ignoring other forces such as electromagnetic and contact forces).
Then we can ask for the properties of 'inertial motion'. The answer
according to the classical principle of inertia is: rectilinear
motion at constant speed.
I deal here with an alternative answer to this question, namely the
assumption that inertial motion of the test body is not completely
independent of the movements of the other objects (a variant of
Mach's principle).
If one defines 'inertial motion' apriori as 'rectilinear motion
at constant velocity' then my alternative hypothesis obviously
seems impossible.
See my posting starting this thread (but not on s.p.f.):
http://groups.google.com/group/sci.astro/msg/c0a5209e4f686adb
And maybe also this extract of a letter I wrote in 1988 could make
my point of view more understandable:
"Der Trägheitssatz sagt aus, dass sich ein kräftefreier Körper
exakt geradlinig gleichförmig bewegt. Dies ist aber insofern eine
leere Aussage, als es kräftefreie Körper im Weltall nicht gibt.
Eine andere Version lautet so: Ein Körper bewegt sich immer exakt
gerade aus mit gleichbleibender Geschwindigkeit, wenn keine
anderen Körper vorhanden sind, die auf ihn einwirken können. Aber
auch diese Aussage bleibt inhaltslos, solange man nicht einen
'absoluten Raum' postuliert.
Albert Einstein hat von der Bewegung eines Körpers gesprochen,
der genügend weit von allen anderen entfernt ist. Aber auch in
dieser Version, die der Realität am nächsten kommt, wird das
eigentliche Problem nicht aufgehoben, sondern nur verschoben.
Denn unter was für Umständen ist ein Körper von allen anderen
genügend weit entfernt, sodass man von einer exakt geradlinigen
Bewegung mit gleichbleibender Geschwindigkeit (bezogen auf den
absoluten Raum?) sprechen kann?
Man muss versuchen, dem Trägheitssatz eine zeitgemässe (realitäts-
bezogene) Form zu geben. Jeder Körper, der sich z.B. in unserer
Milchstrasse bewegt, erfährt von allen Seiten Gravitations-
beschleunigungen. Bei genauer Kenntniss der Massenverteilung
der Milchstrasse (und der übrigen Galaxien) lässt sich die
resultierende Gravitationsbeschleunigung berechnen. Beschleunigt
man den Körper zu jedem Zeitpunkt künstlich um den umgekehrten
Vektor, so bekommt die Frage nach dem Verlauf des Körpers einen
konkreten physikalischen Sinn.
Auf diese Frage gibt es zwei prinzipiell verschiedene Antworten:
Die erste ist analog dem Galileischen Relativitätsprinzip und
besagt, dass die Bewegung des Körpers komplett unabhängig von der
Bewegung aller übrigen Himmelskörper verläuft, also geradlinig
gleichförmig bezogen auf einen geometrischen (und damit absoluten)
Raum.
Gemäss der zweiten Antwort ist die Bewegung des Körpers immer
noch an die Bewegung der übrigen Himmelskörper gebunden."
> Are you assuming background, absolute space and time?
At least insofar as for dealing with the dark-matter problem
classical approximations are enough, I assume absolute space and
time.
> Are you tempting at a foundation of classical mechanics or
> gravitation theory?
Here I only want to find out whether this rather simple inersis
hypothesis (originally introduced for other reasons) can resolve
the dark matter problem.
>> P1: Inertial motion of a test body is influenced by the changes
>> in motion of all objects, due to which the test body has
>> lost gravitational potential. That means, velocity changes
>> of all these objects tend to induce an analogous velocity
>> change on the inertial movement of the test body.
>
> What is "loss of gravitation potential"?
We can also call it gravitational dependence. Gravitational
potential loss is simply 0.5 * v_escape^2. Our gravitational
dependence on earth is 0.5 * (11.2 km/s)^2 = 63 km^2/s^2. Our
loss due to the sun is around 900 km^2/s^2.
>> P2: If there is only one massive object then any change in
>> velocity of this object leads to an idential change in
>> velocity of the test body's inertial movement.
>
> If there is only one massive object, what changes its velocity?
This is only a thought experiment for didactical purpuses.
>> P4: We introduce a coordinate system with at its origin the mass
>> center of a galaxy. The galaxy is described at any given
>> time by n objects each having position vector X_i, velocity
>> vector V_i and mass m_i.
>
> What for a coordinate system, how its axes are defined?
A simple cartesian coordinate system with the galactic plane
preferably in the x-y-plane.
>> P7: We can call this vector field V(X) 'inersis', following the
>> 'stasis' vector field of Bruce Harvey: "Taking a broader view
>> we find that stasis is a vector field existing throughout all
>> space and varying from point to point as we move around the
>> solar system, between the stars and from galaxy to galaxy."
>> (http://users.powernet.co.uk/bearsoft/Stsis.html)
>
> Ok, you can do that. What is the meaning of it?
The sun has lost potential energy due to all objects of the milky
way (and also due to other galaxies). Ignoring the other galaxies
we can calculate for the sun the average velocity of all these
objects weighted according to the correspondig gravitational
dependence (i.e. proportional to the object's mass and inversely
proportional to its distance from the sun). We get a resulting
velocity vector roughly parallel to the the sun's movement in the
galaxy.
Let us assume that this inersis velocity is around 30 km/s for
the sun and that the sun's orbital speed is 220 km/s. In this case
we would have to subtract this 'inertial drag' of 30 km/s from the
220 km/s and use the remaining 190 km/s to test whether the sun
has a stable orbit at a rather constant distance from the galactic
center. (The 190 km/s and not the 220 km/s would also be relevant
to kinetic energy and to the virial theorem).
Cheers, Wolfgang
Peter
> > It is not clear to me which status these statements have got, are they
> > axioms, conclusions, requirements, definitions?
> The points P1 .. P8 only should clarify the hypothesis I'm dealing
> with in this thread.
> > You use some well-known notions like 'inertial motion', but in the
> > common sense?
> I start with this definition of 'inertial motion':
>
> A test body's movement is inertial if all gravitational forces
> acting on the test body are compensated by artificial forces
> (ignoring other forces such as electromagnetic and contact forces).
>
> Then we can ask for the properties of 'inertial motion'. The answer
> according to the classical principle of inertia is: rectilinear
> motion at constant speed.
>
> I deal here with an alternative answer to this question, namely the
> assumption that inertial motion of the test body is not completely
> independent of the movements of the other objects (a variant of
> Mach's principle).
If there are no forces on the test body (not a good concept, BTW), what makes
it changing its motion?
> If one defines 'inertial motion' apriori as 'rectilinear motion
> at constant velocity' then my alternative hypothesis obviously
> seems impossible.
>
> See my posting starting this thread (but not on s.p.f.):
> http://groups.google.com/group/sci.astro/msg/c0a5209e4f686adb
>
> And maybe also this extract of a letter I wrote in 1988 could make
> my point of view more understandable:
>
> "Der Trägheitssatz sagt aus, dass sich ein kräftefreier Körper
> exakt geradlinig gleichförmig bewegt. Dies ist aber insofern eine
> leere Aussage, als es kräftefreie Körper im Weltall nicht gibt.
Es ist eine Idealisierung. Es geht um den Unterschied zum Aristotelesschem
Trägheitssatz (F=0 => v=0) und darum, dass kein Körper von sich aus seinen
Zustand ändert.
> Eine andere Version lautet so: Ein Körper bewegt sich immer exakt
> gerade aus mit gleichbleibender Geschwindigkeit, wenn keine
> anderen Körper vorhanden sind, die auf ihn einwirken können. Aber
> auch diese Aussage bleibt inhaltslos, solange man nicht einen
> 'absoluten Raum' postuliert.
Letzteres hat Newton getan, und Sie tun es nach meinem Eindruck auch.
> Albert Einstein hat von der Bewegung eines Körpers gesprochen,
> der genügend weit von allen anderen entfernt ist. Aber auch in
> dieser Version, die der Realität am nächsten kommt, wird das
> eigentliche Problem nicht aufgehoben, sondern nur verschoben.
> Denn unter was für Umständen ist ein Körper von allen anderen
> genügend weit entfernt, sodass man von einer exakt geradlinigen
> Bewegung mit gleichbleibender Geschwindigkeit (bezogen auf den
> absoluten Raum?) sprechen kann?
> Man muss versuchen, dem Trägheitssatz eine zeitgemässe (realitäts-
> bezogene) Form zu geben.
nein, muss man nicht, s.o.
> Jeder Körper, der sich z.B. in unserer
> Milchstrasse bewegt, erfährt von allen Seiten Gravitations-
> beschleunigungen.
er erfährt ~kräfte, nicht ~beschleunigungen
> Bei genauer Kenntniss der Massenverteilung
> der Milchstrasse (und der übrigen Galaxien) lässt sich die
> resultierende Gravitationsbeschleunigung berechnen. Beschleunigt
> man den Körper zu jedem Zeitpunkt künstlich um den umgekehrten
> Vektor, so bekommt die Frage nach dem Verlauf des Körpers einen
> konkreten physikalischen Sinn.
dann bleibt der Körper stehen
> Auf diese Frage gibt es zwei prinzipiell verschiedene Antworten:
>
> Die erste ist analog dem Galileischen Relativitätsprinzip und
> besagt, dass die Bewegung des Körpers komplett unabhängig von der
> Bewegung aller übrigen Himmelskörper verläuft, also geradlinig
> gleichförmig bezogen auf einen geometrischen (und damit absoluten)
> Raum.
>
> Gemäss der zweiten Antwort ist die Bewegung des Körpers immer
> noch an die Bewegung der übrigen Himmelskörper gebunden."
Wodurch?
> > Are you assuming background, absolute space and time?
> At least insofar as for dealing with the dark-matter problem
> classical approximations are enough, I assume absolute space and
> time.
> > Are you tempting at a foundation of classical mechanics or
> > gravitation theory?
> Here I only want to find out whether this rather simple inersis
> hypothesis (originally introduced for other reasons) can resolve
> the dark matter problem.
I don't know enough about the latter, I'm afraid
> >> P1: Inertial motion of a test body is influenced by the changes
> >> in motion of all objects, due to which the test body has
> >> lost gravitational potential. That means, velocity changes
> >> of all these objects tend to induce an analogous velocity
> >> change on the inertial movement of the test body.
> > What is "loss of gravitation potential"?
> We can also call it gravitational dependence. Gravitational
> potential loss is simply 0.5 * v_escape^2.
Where does this come from?
How this is related to energy conservation? What exactly is lost?
> Our gravitational
> dependence on earth is 0.5 * (11.2 km/s)^2 = 63 km^2/s^2. Our
> loss due to the sun is around 900 km^2/s^2.
> >> P2: If there is only one massive object then any change in
> >> velocity of this object leads to an idential change in
> >> velocity of the test body's inertial movement.
> > If there is only one massive object, what changes its velocity?
> This is only a thought experiment for didactical purpuses.
I don't like test bodies ;-)
Anyway, how P2 complies with momentum and energy conservation?
> >> P4: We introduce a coordinate system with at its origin the mass
> >> center of a galaxy. The galaxy is described at any given
> >> time by n objects each having position vector X_i, velocity
> >> vector V_i and mass m_i.
> > What for a coordinate system, how its axes are defined?
> A simple cartesian coordinate system with the galactic plane
> preferably in the x-y-plane.
> >> P7: We can call this vector field V(X) 'inersis', following the
> >> 'stasis' vector field of Bruce Harvey: "Taking a broader view
> >> we find that stasis is a vector field existing throughout all
> >> space and varying from point to point as we move around the
> >> solar system, between the stars and from galaxy to galaxy."
> >> (http://users.powernet.co.uk/bearsoft/Stsis.html)
> > Ok, you can do that. What is the meaning of it?
> The sun has lost potential energy due to all objects of the milky
> way (and also due to other galaxies). Ignoring the other galaxies
> we can calculate for the sun the average velocity of all these
> objects weighted according to the correspondig gravitational
> dependence (i.e. proportional to the object's mass and inversely
> proportional to its distance from the sun). We get a resulting
> velocity vector roughly parallel to the the sun's movement in the
> galaxy.
Who has gained the energy lost by the sun?
> Let us assume that this inersis velocity is around 30 km/s for
> the sun and that the sun's orbital speed is 220 km/s. In this case
> we would have to subtract this 'inertial drag' of 30 km/s from the
> 220 km/s and use the remaining 190 km/s to test whether the sun
> has a stable orbit at a rather constant distance from the galactic
> center. (The 190 km/s and not the 220 km/s would also be relevant
> to kinetic energy and to the virial theorem).
This partition of energy looks rather strange, but first you have to
eliminate the dragging ghost from your representation ;-)
Best wishes,
Peter