| Topic: |
Science > Physics |
| User: |
"Richard777" |
| Date: |
15 Nov 2007 01:37:10 PM |
| Object: |
Viewpoint Matters |
Observational Perspectives
Observation and measurement of a natural event may result in data
which is summarized and normalized to a physical constant. It may be
beneficial to generalize or disassociate the data summary from any
normalization constant. This generalization may be achieved by the use
of =E2=80=9Cobservational perspectives=E2=80=9D. These perspectives may be i=
ncluded in
a definition of the uncertainties associated with the observation.
Two perspectives (=E2=88=86,=E2=88=82) shall be identified;
- a delta perspective associated with a delta time operator (=E2=88=86 /=E2=
=88=86t)
- a differential perspective associated with a differential time
operator (=E2=88=82 /=E2=88=82t)
It is simplifying (and possibly misleading) to call the differential
operator a =E2=80=9Csubjective perspective=E2=80=9D and also to name the del=
ta
operator as an =E2=80=9Cobjective perspective=E2=80=9D.
It is also possible to associate the differential perspective with
momentum (p) and assume the delta operator acts upon position (x).
These assumptions are arbitrary (also convenient) and are not required
by nature.
The perspectives may be illustrated by a hypothetical observation of
the motion of an airplane. A passenger inside the airplane will
experience a force (F) acting upon him due to a change in the momentum
of the aircraft (and of the passenger). This will be identified as the
subjective perspective (differential perspective).
F =3D =E2=88=82p /=E2=88=82t
A person observing the same airplane from the ground will be unaware
of the forces acting upon the passenger. He will notice a spatial
displacement of the airplane with respect to time . He may infer a
velocity (v) and this will be assumed to be the objective perspective
(delta perspective).
v =3D =E2=88=86x /=E2=88=86t
The uncertainties of momentum (=E2=88=82p) and position (=E2=88=86x) are *****=
ociated
with the two perspectives of observation (=E2=88=86,=E2=88=82) and combined =
as an
increment of angular momentum (U) called the =E2=80=9Cuncertainty product=E2=
=80=9D.
=E2=88=86x=E2=88=82p =3D U =3D P=E2=88=86t=E2=88=82t (E1)
Where power (P) is; P =3D Fv
Heisenberg=E2=80=99s =E2=80=9CPrinciple of Uncertainty=E2=80=9D with respect=
to position and
momentum may be represented as;
=E2=88=86x=E2=88=86p =3D nh (E2)
Where;
=E2=80=98h=E2=80=99 is Plank=E2=80=99s constant, which is a fundamental unit=
of angular
momentum.
=E2=80=98n=E2=80=99 represents a ratio dependant upon the event being obser=
ved
=E2=88=86x represents an uncertainty of position
=E2=88=86p represents an uncertainty of momentum
Please note the similarities and the differences between the two
equations E1 and E2. Both represent the product of uncertainties as
some type of angular momentum (U,nh). Heisenberg=E2=80=99s uncertainties are=
both delta uncertainties and do not include a differential
uncertainty. For photo-electro-magnetic events the Heisenberg
relationship is appropriate, however there may be other observations
that require a generalization as represented by E1.
Observational Reference System;
It is necessary to define some type of observational reference system
to serve as a benchmark for experimental observations. The system
shall be a set of ratios which relate observed characteristics to
benchmark (or infered) characteristics. The benchmark characteristics
shall be identified as follows.
Benchmark force (Fb) and momentum (pb) are related by the differential
time operator;
Fb =3D =E2=88=82pb /=E2=88=82t
An experimental observation of force (F) may be referenced to the
benchmark force as a =E2=80=9Cforce ratio=E2=80=9D (RF).
RF =3D F/Fb
Benchmark velocity (vb) and position (xb) are related by the delta
time operator;
vb =3D =E2=88=86xb /=E2=88=86t
An experimental observation of velocity (v) may be referenced to
benchmark velocity as a =E2=80=9Cvelocity ratio=E2=80=9D (RV).
RV =3D v/vb
The benchmark uncertainty product (Ub) is; Ub =3D =E2=88=86xb=E2=88=82pb=
An experimental uncertainty product (U) may be referenced to the
benchmark uncertainty product as an =E2=80=9Cuncertainty ratio=E2=80=9D (RU)=
..
RU =3D U/ Ub =3D RVRF =3D Tan(=EF=81=B1)
Where the angle (=EF=81=B1) is called the =E2=80=9Cevent angle=E2=80=9D.
The power (P) associated with an observed event is; P =3D Fv
A benchmark power (Pb) is; Pb =3D Fbvb
The power ratio (RP) is; RP =3D P/ Pb =3D RVRF =3D RU (E3)
The ratio of uncertainty is equal to the power ratio; RU =3D RP
This does not imply that the uncertainty product is a magnitude of
power.
The ratios of force and power are assumed to combine as follows; RF2
- RP2 =3D 1 (E4)
This does not imply that power is a vector magnitude. Power is scalar
magnitude.
An unobservable ratio is represented by the complex multiplier (i).
The power ratio is unobservable;
iRP =3D (1 - RF2 )=C2=BD
Substitution for RP (from E3) in E4 gives; RF-2 + RV2 =3D 1 (E5)
The ratios in E5 are ratios of vector magnitudes.
Mass Ratio;
A mass ratio (Rm) is; Rm =3D m/mb
It may be determined if the following assumptions are true.
Benchmark momentum; pb =3D mbv (this assumption is not necessarily
true)
Event momentum; p =3D mv
Giving; Fb =3D =E2=88=82pb /=E2=88=82t =3D mb=E2=88=82v/=E2=88=82t
F =3D =E2=88=82p/=E2=88=82t =3D m=E2=88=82v/=E2=88=82t
RF =3D F/Fb =3D m/mb =3D Rm (E6)
=46rom equation 5; RF-2 + RV2 =3D 1
Substitution for RF (from E6) in E5 gives;
Rm-2 + RV2 =3D 1
(mb/m)2 + (v/vb)2 =3D 1
Relativistic mass is obtained if; mb =3D m0 (rest mass)
vb =3D c (speed of light in vacuum)
Giving; (m0/m)2 + (v/c)2 =3D 1
Motion;
A moving object may have two possible types of motion, discontinuous
motion or continuous (cyclical) motion. An object in cyclical motion
may have a circular or an elliptical trajectory. An object in
discontinuous motion, such as a ball thrown into the air will follow a
segment of a parabolic trajectory and will have a beginning limit and
an ending limit. If both perspective ratios are known, the trajectory
of an observed object and its uncertainty product may be obtained.
Discontinuous Motion;
If the discontinuous motion of an object is assumed to limit it=E2=80=99s
center to a spatial plane, then the definition of the trajectory will
be simplified. This is =E2=80=9Cplane restricted motion=E2=80=9D. The defini=
tion of a
=E2=80=9Ctrajectory ratio=E2=80=9D (RT) is a ratio of perspective ratios.
RT =3D RF/RV
A parabolic trajectory is; RT =3D =C2=BD
RF =3D =C2=BD RV
It shall be assumed that observed momentum is; p =3D m=EF=81=B7x
Where; m is the dynamic mass of an observed object
=EF=81=B7 is frequency
x is location
Observed force (F) is; F =3D =E2=88=82p/=E2=88=82t =3D =E2=88=82m=EF=81=
=B7x/=E2=88=82t =3D m=EF=81=B7=E2=88=82x/=E2=88=82t
Benchmark force (Fb) is; Fb =3D m=EF=81=B7=E2=88=82xb/=E2=88=82t
The force ratio is; RF =3D F/Fb =3D =E2=88=82x/=E2=88=82xb
Observed velocity (v) is; v =3D =E2=88=86x/=E2=88=86t
Benchmark velocity (vb) is; vb =3D =E2=88=86xb/=E2=88=86t
The velocity ratio is; RV =3D v/vb =3D =E2=88=86x/=E2=88=86xb
A parabolic trajectory is; RF =3D =C2=BD RV
=E2=88=82x/=E2=88=82xb =3D =C2=BD =E2=88=86x/=E2=88=86xb
=E2=88=86xb/=E2=88=86x =3D =C2=BD =E2=88=82xb/=E2=88=82x
Let; =E2=88=86x =3D x - x0
=E2=88=86xb =3D xb - xb0
Giving a differential equation; (xb - xb0) / (x - x0) =3D =C2=BD =E2=88=82=
xb/=E2=88=82x
(E7)
The solution of E7 is; (xb - xb0) =3D -k(x - x0)2
Where; =C2=BD =E2=88=82xb/=E2=88=82x =3D -k(x - x0)
This is a parabolic trajectory with plane co-ordinates (x, xb) and
maxima (x0 ,xb0).
The start limit is; (0, xb0 - kx02)
The end limit is; (x0 + [xb0/k]=C2=BD , 0)
The product of uncertainty is; U =3D m=EF=81=B7(x - x0)=E2=88=82x =3D =E2=
=88=86p=E2=88=82x
In this example; =E2=88=86p=E2=88=82x =3D =E2=88=86x=E2=88=82p
Continuous motion can also be represented by perspective ratios.
Conclusion;
Observational perspectives (=E2=88=86,=E2=88=82) are associated with time op=
erators
and they generalize observational uncertainties.
Uncertainties may commute with respect to perspective.
Observed characteristics (F,v) are vector magnitudes derived from time
operators acting upon fundamental characteristics (p,x).
An observational reference system is a set of ratios (RF ,RV) which
relate observed characteristics (F,v) to inferred characteristics
(Fb,vb).
Unobservable characteristics are complex (i).
If a reference system includes perspectives then a trajectory ratio
(RT) and an uncertainty product (U) can be defined.
.
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| User: "Uncle Al" |
|
| Title: Re: Viewpoint Matters |
15 Nov 2007 03:57:58 PM |
|
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Richard777 wrote:
Observational Perspectives
Observation and measurement of a natural event may result in data
which is summarized and normalized to a physical constant.
http://www.mazepath.com/uncleal/horse.htm
It may be
beneficial to generalize or disassociate the data summary from any
normalization constant.
Engineering seeks dimensionless constants. Physics sets Planck units
to 1.
This generalization may be achieved by the use
of “observational perspectives”. These perspectives may be included in
a definition of the uncertainties associated with the observation.
The universe is covariant.
Two perspectives (∆,∂) shall be identified;
- a delta perspective associated with a delta time operator (∆ /∆t)
- a differential perspective associated with a differential time
operator (∂ /∂t)
It is simplifying (and possibly misleading) to call the differential
operator a “subjective perspective” and also to name the delta
operator as an “objective perspective”.
Was there some destination targeted by your 276 lines posted?
[snip]
Unobservable characteristics are complex (i).
as are unknown hazards. Doesn't hinder economics, social advocacy,
climatology, Enviro-whinerism, and religion.
1)That which supports it is supportive.
2)That which ignores it is supportive.
3)That which contradicts it is supportive - test of faith!
4)Anybody who criticizes is thereby proven unqualified to comment -
and must be destroyed lest god(s) or the Officially Sad take offense.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
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| User: "Richard777" |
|
| Title: Re: Viewpoint Matters |
15 Nov 2007 01:46:48 PM |
|
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sorry about the corrupted fonts, this is my first posting.
.
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| User: "Neil Bates" |
|
| Title: Re: Viewpoint Matters |
15 Nov 2007 02:55:53 PM |
|
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This is a multi-part message in MIME format.
------=_NextPart_000_0092_01C827A0.0041EBF0
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
"Richard777" <rickingstone07@aol.com> wrote in message =
news:660411d8-3d93-4ef2-8e2c-55db852670d0@b40g2000prf.googlegroups.com...=
sorry about the corrupted fonts, this is my first posting.
Most of them looked good, especially the nice partial diff ( =B6 ) =
symbols. Actually, I wish more people would post in RTF - then we could =
see symbols. I'll pass on the content, it looks like Foundations of =
Physics or Physics Essays stuff. One thing that goes wrong IIUC: you =
make the symbols in Word using insert object, and they are actually =
embedded in the original font like TNR and not as "symbol." Use Wordpad =
to copy to OE, or compose in OE with correct font turned on, or =
otherwise ensure that the actual symbol font characters are used =
directly.
Hope this helps.
------=_NextPart_000_0092_01C827A0.0041EBF0
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 6.00.2745.2800" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY>
<DIV><FONT face=3D"Courier New" size=3D2></FONT> </DIV>
<DIV><FONT size=3D2>"Richard777" <</FONT><A=20
href=3D"mailto:rickingstone07@aol.com"><FONT=20
size=3D2>rickingstone07@aol.com</FONT></A><FONT size=3D2>> wrote in =
message=20
</FONT><A=20
href=3D"news:660411d8-3d93-4ef2-8e2c-55db852670d0@b40g2000prf.googlegroup=
s.com"><FONT=20
size=3D2>news:660411d8-3d93-4ef2-8e2c-55db852670d0@b40g2000prf.googlegrou=
ps.com</FONT></A><FONT=20
size=3D2>...</FONT></DIV>
<DIV><FONT size=3D2>> sorry about the corrupted fonts, this is my =
first=20
posting.</FONT></DIV>
<DIV><FONT size=3D2></FONT> </DIV>
<DIV><FONT size=3D2>Most of them looked good, especially the nice =
partial diff=20
( <FONT face=3DSymbol>=B6 </FONT> ) symbols. =
Actually, I wish=20
more people would post in RTF - then we could see symbols. I'll =
pass on=20
the content, it looks like <EM>Foundations of Physics</EM> or =
<EM>Physics=20
Essays</EM> stuff. One thing that goes wrong IIUC: you make the =
symbols in=20
Word using insert object, and they are actually embedded in the original =
font=20
like TNR and not as "symbol." Use Wordpad to copy to OE, or =
compose in OE=20
with correct font turned on, or otherwise ensure that the actual symbol =
font=20
characters are used directly.</FONT></DIV>
<DIV><FONT size=3D2>Hope this helps.</FONT></DIV></BODY></HTML>
------=_NextPart_000_0092_01C827A0.0041EBF0--
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