About frames moving at constant velocity with respect to inertial ones

On Aug 11, 12:25 am, wrote:
[....]
The problem is that in 1905R an empty Inertial System (without bodies)
can't exist at all. That "constant velocity" must be necessarily only
an approximated one. Between any pair of bodies exist always at least
a gravitational attraction that implies an acceleration (no matter how
tiny). Then, to determine an inertial system we have only one option:
to consider the centre of mass (CM) inertial system associated to some
body set (an atom, Earth and satellites, Solar System, Galaxy, etc.).
Let me denote that inertial system as a Hierarchical Inertial System
(HIS). When you determine the CM, only the bodies belonging to the
selected set are taking into account, what implies that no other body
exist. As a result, the CM must be considered at "absolute" rest (do
not exist any other thing to move with respect to it). For any
selected body set, we have then a unique HIS that modelled it. The HIS
correspond to the "Stationary System", and any body of the set as the
"Moving System". A HIS can be used only to describe movements of
bodies belonging to it. Try to describe the movement of the Sun using
the Earth's system!(ask Galileo).
Resuming, 1905 Principle of Relativity states that for all Inertial
Systems (sufficiently separated HIS moving with approximately constant
relative velocities) Physics laws are the same. LT applies from a
"Stationary System"(HIS) to a "Moving System" (some of its bodies,
lower hierarchy HIS). Newton's laws hold good in any HIS. To describe
its bodies "absolute" attributes a HIS is at "rest"; to be described
as a whole body, a HIS has "absolute" attributes in the higher
hierarchy HIS where it belong.


Dear Rafael, I highly appreciate your point of view regarding 'HIS' or
Center of Mass (CoM) reference frames and the questionable validity of
the so called 'Inertial Reference Frames'. Let me elaborate these
points in some detail.

Valid Coordinate Reference Frames
---------------------------------
Ideally, a reference frame is a set of space coordinates, which is
fixed in some defined way. Let us consider a closed volume V of space
containing a system of N particles of matter in all possible physical
states. We consider the closed volume of space in the sense that
there is no transfer of mass or energy across the boundary surface of
this volume and the enclosed particles do not experience any
significant force or interaction from outside this volume. Let point
A be the center of mass of these N particles and let K be a non-
rotating Cartesian coordinate reference frame with its origin located
at point A. In this reference frame K, let the positions of all N
particles be defined to be certain function of time (x_i(t), y_i(t),
z_i(t)), provided they remain bounded within the closed volume V.
Since K is a reference frame with origin at the center of mass of the
enclosed N particles, it is generally referred as a Center of Mass
(CoM) Reference Frame. In a CoM reference frame total momentum of all
of its domain particles is zero.

Obviously within the closed volume V under consideration, the total
momentum and the total mass-energy content of the given N particles
will be conserved. We may refer this set of N particles to any
coordinate reference frame for quantifying or assigning certain
measure numbers to the relative positions of these particles, but that
must not alter the physical state (e.g. pressure and temperature
distribution) or content of matter (e.g. mass-energy content) within
the closed volume (or the domain volume) V under consideration. This
requirement may be treated as a physical constraint on the choice of
valid coordinate reference frames.

Out of all other inertial reference frames, which could be constructed
for referring the positions and velocities of given N particles within
the closed volume V, the total mass-energy content measured in a CoM
reference frame is the minimum. Hence a CoM reference frame may be
considered as an absolute or fixed or the preferred reference frame
for the given N particles contained within a closed volume V. This is
the fundamental notion of an absolute reference frame in relation to
matter contained within a closed volume of space. Since the domain
particles of the reference frame K do not experience any significant
force or interaction from outside its domain volume, the center of
mass and hence the origin A of reference frame K will continue to
remain in its state of rest or of uniform motion in the external space
outside its domain volume. Hence the reference frame K can also be
regarded as a unique, fixed Inertial Reference frame for the closed
volume under consideration.

As an example of such a valid reference frame we may consider the
International Celestial Reference System (ICRS), which consists of the
Barycentric Celestial Reference Frame (BCRF) and the Geocentric
Celestial Reference Frame (GCRF), both kinematically defined by the
position of same extragalactic radio sources. The origin of space
coordinates defining BCRF is located at the barycenter or the CoM of
our solar system. The task of establishing and maintaining the ICRS
and its components has been assigned to the International Earth
Rotation and Reference Systems Service (IERS).

http://www.iers.org/iers/earth/icrs/icrs.html
http://www.iers.org/iers/about/tor/

Critical Observations on Relativity Principle
---------------------------------------------
Whereas the principle of relativity gave us the impression that
infinitely many inertial reference frames (IRF) are available to the
user for use as per convenience; the elaborate arrangements required
for establishing just one reference frame, the BCRF, must be a bit
perplexing. Probably the notion of inertial reference frames, in
relative uniform motion, is too simplistic, vague and misconstrued.
Let us examine this notion critically.

Why should reference frames be required to move at all?
Logically it is the particles of matter that are expected to move in a
reference frame. Primarily the reference frames are required for
quantifying the positions of various particles located in a given
region of space. A reference frame with its origin fixed at the CoM
of all the particles in the given region of space, is sufficient to
quantify the positions of all such particles. We just don't need a
large number of reference frames in relative uniform motion to
quantify the positions of given set of particles. Imagine how stupid
it will look if the IERS created 10 more celestial reference frames in
relative uniform motion with respect to the BCRF.

Why do we need very many reference frames?
For studying the kinematic motion and dynamic interactions of an
infinitely large number of particles located in a given region of
space (of closed volume V), we need to reference their positions to a
single CoM reference frame (like BCRF for the solar system). If we
create a separate reference frame for each particle (with its origin
located at the center of that particle) the very objective of creating
a reference frame will be lost. However, some local reference frames
(like GCRF in the solar system) could always be created for the
convenience of practical measurements of positions and velocities,
provided such local measurements could ultimately be transformed to
the fixed CoM reference frame.

Can many IRF in relative motion be under acceleration in BCRF?
As per the Relativity Principle all non-rotating reference frames that
move with uniform velocity with respect to one another, are defined as
Inertial Reference Frames. Let us consider three space ships
S1,S2,S3, moving within our solar system with relative uniform
velocity with respect to one another. Further let us associate
reference frames K1, K2, K3 with these space ships so that these
reference frames also move with relative uniform velocity with respect
to one another. Therefore, in accordance with relativity principle,
these reference frames K1, K2, K3 will be defined as inertial
reference frames. But apart from relative uniform velocity between
S1S2, S2S3, S1S3, all three space ships S1,S2,S3, could also be
moving under common gravitational acceleration in BCRF towards the
barycenter of the solar system. Hence we find that inertial reference
frames defined as per relativity principle could actually be moving
under accelerated motion in a CoM or fixed reference frame. As such
the very notion of inertial reference frames under uniform relative
motion is ambiguous, vague, impractical and misleading. Apparently
this notion was introduced just for conducting hypothetical thought
experiments.

Why do we need to locate fictitious observers on each IRF?
Actually the notion of fictitious observers is as ambiguous and
misleading as the notion of IRF. Modern advancements in technology
have replaced the fictitious observers with advanced electronic
instrumentation while the real observers watch the computer displays
to observe the process. For example the position and velocity
measurements of a spacecraft are first recorded in the local reference
frame of instrumentation and then transformed to the CoM fixed frame
of the solar system, the BCRF.

Can relative measurements alone yield correct information?
No, the relative measurements alone cannot yield true information
regarding position and velocity measurements of particles in the
relevant region of space under consideration. To illustrate this
point let us consider two space ships S1 and S2 moving in the solar
system. Let their position vectors in BCRF be R1 and R2 and their
velocity vectors be V1 and V2 respectively. The dynamic motion of
these space ships will obviously be governed by the parameters R1, R2
and V1, V2 . Now the relative separation between S1 and S2 will be
given by R_12 = R2 - R1 and the relative velocity between them will
be given by V_12 = V2 - V1. If we use only relative coordinates
and measure only the relative parameters R_12 and V_12 (without
using BCRF) we find that the dynamic motion of the two space ships is
not governed by the relative parameters R_12 and V_12 . Hence it is
quite obvious that the relative measurements alone do not provide the
complete information as required.

Finally we may conclude that a CoM reference frame may be considered
as an absolute or fixed or the preferred reference frame for the given
N particles contained within a closed volume of space. The
measurements in a convenient local reference frame constitute a
necessary step for establishing the absolute measurements in a
relevant CoM fixed reference frame. Relative measurements alone,
without reference to a CoM fixed reference frame can give misleading
results. For example, relative measurement of position and velocity
of a uniformly moving spacecraft, from the DSN stations may indicate
as if the spacecraft is periodically accelerating towards or away from
the DSN stations, which is highly misleading. Purely relative
reference frames, popularly known as inertial reference frames in SR
parlance, are only useful for conducting hypothetical thought
experiments and hence constitute a practically redundant notion.

All laws of Nature are practically valid in all closed spaces 'V' and
are not influenced by the arbitrary human choice of reference frames.

GSS

On 12 ago, 04:12, GSS wrote:
On Aug 11, 12:25 am, wrote:
[....]

The problem is that in 1905R an empty Inertial System (without bodies)
can't exist at all. That "constant velocity" must be necessarily only
an approximated one. Between any pair of bodies exist always at least
a gravitational attraction that implies an acceleration (no matter how
tiny). Then, to determine an inertial system we have only one option:
to consider the centre of mass (CM) inertial system associated to some
body set (an atom, Earth and satellites, Solar System, Galaxy, etc.).
Let me denote that inertial system as a Hierarchical Inertial System
(HIS). When you determine the CM, only the bodies belonging to the
selected set are taking into account, what implies that no other body
exist. As a result, the CM must be considered at "absolute" rest (do
not exist any other thing to move with respect to it). For any
selected body set, we have then a unique HIS that modelled it. The HIS
correspond to the "Stationary System", and any body of the set as the
"Moving System". A HIS can be used only to describe movements of
bodies belonging to it. Try to describe the movement of the Sun using
the Earth's system!(ask Galileo).
Resuming, 1905 Principle of Relativity states that for all Inertial
Systems (sufficiently separated HIS moving with approximately constant
relative velocities) Physics laws are the same. LT applies from a
"Stationary System"(HIS) to a "Moving System" (some of its bodies,
lower hierarchy HIS). Newton's laws hold good in any HIS. To describe
its bodies "absolute" attributes a HIS is at "rest"; to be described
as a whole body, a HIS has "absolute" attributes in the higher
hierarchy HIS where it belong.

Dear Rafael, I highly appreciate your point of view regarding 'HIS' or
Center of Mass (CoM) reference frames and the questionable validity of
the so called 'Inertial Reference Frames'. Let me elaborate these
points in some detail.

Valid Coordinate Reference Frames
---------------------------------
Ideally, a reference frame is a set of space coordinates, which is
fixed in some defined way.
I derived the HIS concept from 1905 Relativity. Einstein identifies
systems of coordinates with rigid bodies. Absolute space doesn't
exist, ether is "superfluous". Then, the starting point must be the
bodies themselves. Any body set determine his own and unique HIS, and
they are considered the unique existing bodies in the model. The
centre of mass must be at rest, because doesn't exist any other thing
to move with respect to it.
Let us consider a closed volume V of space
containing a system of N particles of matter in all possible physical
states. We consider the closed volume of space in the sense that
there is no transfer of mass or energy across the boundary surface of
this volume and the enclosed particles do not experience any
significant force or interaction from outside this volume.
No, the bodies themselves determine the space (and also the time). No
other body is considered existing, the HIS is a closed system by
definition. A HIS model some selected part of the universe. As any
model, it reflects Nature in an approximated way. You can model the
Earth-Moon system with a HIS, but it is not necessary to suppose null
interaction with the exterior, it is sufficient to suppose that the
HIS interact with its exterior as a whole entity (all the bodies of
its associated set experimenting approximate equal acceleration owed
to external interaction). The lower hierarchy HIS of Earth and Moon
belongs to the higher hierarchy HIS of the Solar System, having in it
a definite velocity and acceleration (or any other higher derivative
of space with respect to time). To describe its associated body set
the HIS is at rest, as part of a higher hierarchy HIS, its centre of
mass considered a material point can has any movement.
Let point
A be the center of mass of these N particles and let K be a non-
rotating Cartesian coordinate reference frame with its origin located
at point A. In this reference frame K, let the positions of all N
particles be defined to be certain function of time (x_i(t), y_i(t),
z_i(t)), provided they remain bounded within the closed volume V.
Since K is a reference frame with origin at the center of mass of the
enclosed N particles, it is generally referred as a Center of Mass
(CoM) Reference Frame. In a CoM reference frame total momentum of all
of its domain particles is zero.

You don't need any volume V as a limit. Remember 1913 N.Bohr's
Hydrogen atom model (the best reference to understand what a HIS is).
The consider Universe is only the proton and the electron, with the
complete infinite Euclidean space.
Obviously within the closed volume V under consideration, the total
momentum and the total mass-energy content of the given N particles
will be conserved. We may refer this set of N particles to any
coordinate reference frame for quantifying or assigning certain
measure numbers to the relative positions of these particles, but that
must not alter the physical state (e.g. pressure and temperature
distribution) or content of matter (e.g. mass-energy content) within
the closed volume (or the domain volume) V under consideration. This
requirement may be treated as a physical constraint on the choice of
valid coordinate reference frames.

Of course that we must take into account the attributes of the part of
Nature that we want to model with a hierarchical net of HIS. But after
the adequate selection of the body sets, the valid reference frames
are unique. The coordinate reference frames are always derived from
the bodies, and these bodies are the unique ones that can be described
in the corresponding coordinate reference frame.
Out of all other inertial reference frames, which could be constructed
for referring the positions and velocities of given N particles within
the closed volume V, the total mass-energy content measured in a CoM
reference frame is the minimum. Hence a CoM reference frame may be
considered as an absolute or fixed or the preferred reference frame
for the given N particles contained within a closed volume V. This is
the fundamental notion of an absolute reference frame in relation to
matter contained within a closed volume of space.
We have no minimum (or maximum) because we have a UNIQUE HIS to
describe the body set. It is not a preferred frame, it is the UNIQUE
frame. You can denote is as "absolute" when used to describe the
interior of the HIS.
Since the domain
particles of the reference frame K do not experience any significant
force or interaction from outside its domain volume, the center of
mass and hence the origin A of reference frame K will continue to
remain in its state of rest or of uniform motion in the external space
outside its domain volume. Hence the reference frame K can also be
regarded as a unique, fixed Inertial Reference frame for the closed
volume under consideration.

No, the origin A can be only at rest. I can't have a single entity
moving at constant velocity, because absolute space an time (or ether)
doesn't exist. For the interior A is at rest, for the exterior can
have any movement corresponding to its interaction as a whole with
other external bodies (A is a material point modelling the HIS). We
have NEVER a constant velocity movement for A. The indeterminate
constant velocity of an inertial body disappears completely in the HIS
approach. Of course, if a body belonging to some HIS has null
resultant force over it, then it is moving with some determinate
constant velocity, but NEVER with an indeterminate constant velocity.
In the real world this is only an approximate condition, even if a
good one.
As an example of such a valid reference frame we may consider the
International Celestial Reference System (ICRS), which consists of the
Barycentric Celestial Reference Frame (BCRF) and the Geocentric
Celestial Reference Frame (GCRF), both kinematically defined by the
position of same extragalactic radio sources. The origin of space
coordinates defining BCRF is located at the barycenter or the CoM of
our solar system. The task of establishing and maintaining the ICRS
and its components has been assigned to the International Earth
Rotation and Reference Systems Service (IERS).

I have not too much knowledge about real world time systems. But I
know that the ECI time of GPS is delayed about 5 nanoseconds with
respect to the Solar System time, owed to the "absolute" Earth's speed
of about 30Km/s in the Solar System.
http://www.iers.org/iers/earth/icrs/...ers/about/tor/

Critical Observations on Relativity Principle
---------------------------------------------
Whereas the principle of relativity gave us the impression that
infinitely many inertial reference frames (IRF) are available to the
user for use as per convenience; the elaborate arrangements required
for establishing just one reference frame, the BCRF, must be a bit
perplexing. Probably the notion of inertial reference frames, in
relative uniform motion, is too simplistic, vague and misconstrued.
Let us examine this notion critically.

Surely you are referring to Special Relativity, but not to 1905
Relativity (1905R). Yes, they are not the same. I am claiming this
here for some years.
Why should reference frames be required to move at all?
Logically it is the particles of matter that are expected to move in a
reference frame. Primarily the reference frames are required for
quantifying the positions of various particles located in a given
region of space. A reference frame with its origin fixed at the CoM
of all the particles in the given region of space, is sufficient to
quantify the positions of all such particles. We just don't need a
large number of reference frames in relative uniform motion to
quantify the positions of given set of particles. Imagine how stupid
it will look if the IERS created 10 more celestial reference frames in
relative uniform motion with respect to the BCRF.

Total agreement.
Why do we need very many reference frames?
For studying the kinematic motion and dynamic interactions of an
infinitely large number of particles located in a given region of
space (of closed volume V), we need to reference their positions to a
single CoM reference frame (like BCRF for the solar system). If we
create a separate reference frame for each particle (with its origin
located at the center of that particle) the very objective of creating
a reference frame will be lost. However, some local reference frames
(like GCRF in the solar system) could always be created for the
convenience of practical measurements of positions and velocities,
provided such local measurements could ultimately be transformed to
the fixed CoM reference frame.

We have a UNIQUE inertial system once we select the body set to
describe.

I consider redundant to make comments to the rest.
[skipping the rest]

GSS

RVHG (Rafael Valls Hidalgo-Gato)