| Topic: |
Science > Physics |
| User: |
"GSS" |
| Date: |
07 May 2006 07:13:08 PM |
| Object: |
Experimental Measurement of Space Metric |
Very many scientists, including the ardent followers of GR, believe
that the metric of space is a physical property of space. As per GR
the gravitational field of a material body of mass M influences the
metric of the physical space through EFE. As such the metric of
gravitational field free space must be quite different from the metric
of space containing a significant strength of gravitational field.
Logically therefore, measurement of the metric of space in any
particular region will immediately indicate whether any gravitational
field exists in that region.
Another parameter, the intrinsic impedance Z0 of vacuum or free space,
representing an important physical property of space, is routinely
measured and its value is about 377 ohms. Therefore, if the metric of
space represents a physical property of space, it should be possible to
routinely measure it. The metric of space is identified with the metric
tensor g_ij. Since a tensor is an invariant entity, we can measure it
in any convenient coordinate system.
Readers are therefore requested to share their views on the following
pertinent questions on the metric tensor of space.
(a) Just as the intrinsic impedance Z0 of space is routinely measured
as 377 ohms, whether the metric of space is also routinely measured by
working scientists and engineers? If so, what are the units in which
the metric coefficients of space are measured (in any convenient
coordinate system)?
(b) If the working scientists and engineers have not felt any necessity
of measuring the metric coefficients of space, is it in principle
possible and feasible to measure these metric coefficients? If so, how
and in what units?
(c) If it is just not possible to measure the metric coefficients of
space, then could it be that the metric tensor does not represent any
physical property of space? Could be that the metric tensor just
represents the scaling characteristics of an arbitrarily defined
reference coordinate system?
GSS
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| User: "Bill Hobba" |
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| Title: Re: Experimental Measurement of Space Metric |
08 May 2006 12:29:51 AM |
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"GSS" <gurcharn_sandhu@yahoo.com> wrote in message
news:1147047188.542591.51310@g10g2000cwb.googlegroups.com...
Very many scientists, including the ardent followers of GR, believe
that the metric of space is a physical property of space.
It sure is.
As per GR
the gravitational field of a material body of mass M influences the
metric of the physical space through EFE. As such the metric of
gravitational field free space must be quite different from the metric
of space containing a significant strength of gravitational field.
The metric of an inertial frame (which by definition is gravitational free)
is the Lorentzian metric.
Logically therefore, measurement of the metric of space in any
particular region will immediately indicate whether any gravitational
field exists in that region.
You bet it would.
Another parameter, the intrinsic impedance Z0 of vacuum or free space,
representing an important physical property of space, is routinely
measured and its value is about 377 ohms.
Purely an artifact of the units used - of no fundamental importance at all.
Therefore, if the metric of
space represents a physical property of space, it should be possible to
routinely measure it. The metric of space is identified with the metric
tensor g_ij. Since a tensor is an invariant entity, we can measure it
in any convenient coordinate system.
Readers are therefore requested to share their views on the following
pertinent questions on the metric tensor of space.
(a) Just as the intrinsic impedance Z0 of space is routinely measured
as 377 ohms, whether the metric of space is also routinely measured by
working scientists and engineers? If so, what are the units in which
the metric coefficients of space are measured (in any convenient
coordinate system)?
Nope - it is not directly measured - it is inferred. Although it can in
principle be measured it would not be trivial. For small curvature it is
well known the metric reduces to a simple function of the gravitational
potential and that has been used in for example the Pound and Rebka
experiment to verify that space-time is curved by gravity.
(b) If the working scientists and engineers have not felt any necessity
of measuring the metric coefficients of space, is it in principle
possible and feasible to measure these metric coefficients? If so, how
and in what units?
The metric is a dimensionless object - it gives the coefficients used to
determine infinitesimal lengths from infinitesimal coordinate lengths.
(c) If it is just not possible to measure the metric coefficients of
space, then could it be that the metric tensor does not represent any
physical property of space?
It can in principle be measured from for example accurate measurements of
the validity of 'Pythagoras theorem' for each axis of your coordinate
system. The quotes is for the fact it would need to be altered when using
time as a coordinate with its - sign. Probably beyond our current
technological capability but still in principle possible. Gauss for example
tried to do it and failed (ie to the accuracy of the equipment he used space
had the Euclidian metric). I have not heard of any modern attempts.
Bill
Could be that the metric tensor just
represents the scaling characteristics of an arbitrarily defined
reference coordinate system?
GSS
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| User: "Ken S. Tucker" |
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| Title: Re: Experimental Measurement of Space Metric |
08 May 2006 01:38:40 AM |
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Bill Hobba wrote:
.......
The metric is a dimensionless object - it gives the coefficients used to
determine infinitesimal lengths from infinitesimal coordinate lengths.
Oh yeah, in 2D transfrom from METrick (centimeter's)
to imperial inches...
Invariant = g_11 x^1 x^1 = g'_11 x'1^x'^1
x^1 =2.54 , x'1 = 1 (inch)
The metric "g_11" is NOT dimensionless !!!!
It's an area.
The metric is a purposeful co-efficient to relate
invariants as demo'd, nothing is mysterious.
Ken S. Tucker
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| User: "sal" |
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| Title: Re: Experimental Measurement of Space Metric |
10 May 2006 02:16:33 PM |
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On Sun, 07 May 2006 23:38:40 -0700, Ken S. Tucker wrote:
Bill Hobba wrote:
......
The metric is a dimensionless object - it gives the coefficients
used to determine infinitesimal lengths from infinitesimal
coordinate lengths.
Oh yeah, in 2D transfrom from METrick (centimeter's) to imperial
inches...
Invariant = g_11 x^1 x^1 = g'_11 x'1^x'^1
x^1 =2.54 , x'1 = 1 (inch)
The metric "g_11" is NOT dimensionless !!!! It's an area.
Then, in flat space, with relativistic units, suppose we look at the
position vector
V = (0,1,0,0).
In other words, measuring everything in seconds, V's coordinates are
V = (0 second, 1 light-second, 0 light-seconds, 0 light-seconds)
With a metric of diag(-1,1,1,1), then the proper length of V will be
sqrt(g_ab V^a V^b) = sqrt(g_11 V^1 V^1)
Now, V^1 has units of light-seconds (a length). If, as you say, g_11
has units of _area_, then our expression for proper length must be
sqrt(g_abV^aV^b) = sqrt(1 light-second ^ 4)
= 1 light-second^2
So, proper length is apparently measured in light-seconds _squared_.
Strange.
The metric is a purposeful co-efficient to relate invariants as
demo'd, nothing is mysterious. Ken S. Tucker
--
Nospam becomes physicsinsights to fix the email
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| User: "Bill Hobba" |
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| Title: Re: Experimental Measurement of Space Metric |
08 May 2006 12:42:01 AM |
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"GSS" <gurcharn_sandhu@yahoo.com> wrote in message
news:1147047188.542591.51310@g10g2000cwb.googlegroups.com...
Very many scientists, including the ardent followers of GR, believe
that the metric of space is a physical property of space. As per GR
the gravitational field of a material body of mass M influences the
metric of the physical space through EFE. As such the metric of
gravitational field free space must be quite different from the metric
of space containing a significant strength of gravitational field.
Logically therefore, measurement of the metric of space in any
particular region will immediately indicate whether any gravitational
field exists in that region.
BTW just to check you have actually applied yourself mind telling us what
the metric of a Riemanian space is? If you don't know then have you thought
about finding out before asking such questions?
Thanks
Bill
Another parameter, the intrinsic impedance Z0 of vacuum or free space,
representing an important physical property of space, is routinely
measured and its value is about 377 ohms. Therefore, if the metric of
space represents a physical property of space, it should be possible to
routinely measure it. The metric of space is identified with the metric
tensor g_ij. Since a tensor is an invariant entity, we can measure it
in any convenient coordinate system.
Readers are therefore requested to share their views on the following
pertinent questions on the metric tensor of space.
(a) Just as the intrinsic impedance Z0 of space is routinely measured
as 377 ohms, whether the metric of space is also routinely measured by
working scientists and engineers? If so, what are the units in which
the metric coefficients of space are measured (in any convenient
coordinate system)?
(b) If the working scientists and engineers have not felt any necessity
of measuring the metric coefficients of space, is it in principle
possible and feasible to measure these metric coefficients? If so, how
and in what units?
(c) If it is just not possible to measure the metric coefficients of
space, then could it be that the metric tensor does not represent any
physical property of space? Could be that the metric tensor just
represents the scaling characteristics of an arbitrarily defined
reference coordinate system?
GSS
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| User: "Bill Hobba" |
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| Title: Re: Experimental Measurement of Space Metric |
08 May 2006 12:46:30 AM |
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"Bill Hobba" <rubbish@junk.com> wrote in message
news:JSA7g.24884$vy1.13281@news-server.bigpond.net.au...
"GSS" <gurcharn_sandhu@yahoo.com> wrote in message
news:1147047188.542591.51310@g10g2000cwb.googlegroups.com...
Very many scientists, including the ardent followers of GR, believe
that the metric of space is a physical property of space. As per GR
the gravitational field of a material body of mass M influences the
metric of the physical space through EFE. As such the metric of
gravitational field free space must be quite different from the metric
of space containing a significant strength of gravitational field.
Logically therefore, measurement of the metric of space in any
particular region will immediately indicate whether any gravitational
field exists in that region.
BTW just to check you have actually applied yourself mind telling us what
the metric of a Riemanian space is? If you don't know then have you
thought about finding out before asking such questions?
For simplicity the 2 dimensional case will do. Once you actually understand
it I am certain you will see your questions are very trivial.
Thanks
Bill
Thanks
Bill
Another parameter, the intrinsic impedance Z0 of vacuum or free space,
representing an important physical property of space, is routinely
measured and its value is about 377 ohms. Therefore, if the metric of
space represents a physical property of space, it should be possible to
routinely measure it. The metric of space is identified with the metric
tensor g_ij. Since a tensor is an invariant entity, we can measure it
in any convenient coordinate system.
Readers are therefore requested to share their views on the following
pertinent questions on the metric tensor of space.
(a) Just as the intrinsic impedance Z0 of space is routinely measured
as 377 ohms, whether the metric of space is also routinely measured by
working scientists and engineers? If so, what are the units in which
the metric coefficients of space are measured (in any convenient
coordinate system)?
(b) If the working scientists and engineers have not felt any necessity
of measuring the metric coefficients of space, is it in principle
possible and feasible to measure these metric coefficients? If so, how
and in what units?
(c) If it is just not possible to measure the metric coefficients of
space, then could it be that the metric tensor does not represent any
physical property of space? Could be that the metric tensor just
represents the scaling characteristics of an arbitrarily defined
reference coordinate system?
GSS
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| User: "Tom Roberts" |
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| Title: Re: Experimental Measurement of Space Metric |
08 May 2006 07:23:34 PM |
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GSS wrote:
Very many scientists, including the ardent followers of GR, believe
that the metric of space is a physical property of space.
No. Physicists know that GR is an accurate _model_ of the world we
inhabit. But careful writers do not ascribe the properties of the model
to the world.
In GR (qua model), spacetime is a manifold that has no properties other
than continuity, a suitable topology, and a local differential structure
suitable to support various tensor fields. "Space" does not even appear
in the theory itself, though one can foliate spacetime into space and
time if one wishes -- how to do that is an arbitrary human choice that
has no effect whatsoever on the predictions of the model for physical
measurements.
And in any case, the metric is a _geometrical_ property of a manifold,
not a "physical" one.
Logically therefore, measurement of the metric of space in any
particular region will immediately indicate whether any gravitational
field exists in that region.
You need to measure the metric of spaceTIME to do this. As I said above,
doing it for space alone involves an arbitrary human choice of
foliation. For instance, flat Euclidean 3-space can be foliated as a
concentric series of spheres and a radius; those spheres have nonzero
curvature even though the full space does not. _Exactly_ the same thing
can happen when you foliate spacetime into space and time.
Another parameter, the intrinsic impedance Z0 of vacuum or free space,
representing an important physical property of space, is routinely
measured and its value is about 377 ohms.
This is merely a choice of units.
The metric of space is identified with the metric
tensor g_ij. Since a tensor is an invariant entity, we can measure it
in any convenient coordinate system.
The tensor itself is invariant; the set of its components relative to a
given basis {g_ij} is most definitely not invariant. While older
textbooks called g_ij a "tensor", the correct terminology is that the
set {g_ij} are the components of the tensor g (notated in bold) -- this
avoids the confusion you are making.
(a) Just as the intrinsic impedance Z0 of space is routinely measured
as 377 ohms, whether the metric of space is also routinely measured by
working scientists and engineers?
Certainly. Surveyors do it all the time. That is, they measure distances
and angles of triangles and verify that the angles sum to 180 degrees
and the length obey the Pythagorean theorem. They don't actually write
down the metric coefficients, but what they do is equivalent to that.
If so, what are the units in which
the metric coefficients of space are measured (in any convenient
coordinate system)?
The units of the {g_ij} depend on the units of your coordinates. This
should be obvious from the line element
ds^2 = g_ij dx^i dx^j
because ds^2 must have units (length)^2. If, for instance, dx^0 has
units (seconds) and dx^1,dx^2,dx^3 have units (meters), then g_12 is
unitless and g_01 must have units (meters/sec); etc. But if on the other
hand one simply assigned numbers as coordinate values to space and time,
without ascribing any units to them, then {g_ij} all have units (meters)^2.
(b) If the working scientists and engineers have not felt any necessity
of measuring the metric coefficients of space, is it in principle
possible and feasible to measure these metric coefficients? If so, how
and in what units?
See above, and the introduction to MTW. By measuring the distances
between a sufficient number of points, the metric coefficients can be
determined. For instance, on the surface of the earth the metric
coefficients of the 2-d surface can be determined by measuring all
pairwise distances among 4 points; if you assume it is a sphere, 3
points is enough.
(c) If it is just not possible to measure the metric coefficients of
space, then could it be that the metric tensor does not represent any
physical property of space? Could be that the metric tensor just
represents the scaling characteristics of an arbitrarily defined
reference coordinate system?
See above. The metric tensor describes the geometrical properties of the
manifold. Its components are an admixture of that and the vagaries of
the coordinates used.
Tom Roberts
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| User: "Mike" |
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| Title: Re: Experimental Measurement of Space Metric |
12 May 2006 04:27:20 PM |
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Tom Roberts wrote:
GSS wrote:
Very many scientists, including the ardent followers of GR, believe
that the metric of space is a physical property of space.
No. Physicists know that GR is an accurate _model_ of the world we
inhabit. But careful writers do not ascribe the properties of the model
to the world.
Accurate?
failure 1: GR predicts an order of magnitude less for the energy of
cosmic rays
failure 2: gravitomagnetic effects measurements are million billion
times more than GR predicts
failure 3: For GR the two-body problem has no solution unless it is
restricted so one of the masses is a test particle. Even there, only
numerical solutions exist.
failure 4: gravity waves never detected
failure 5: frame dragging never detected
failure 6: any deviations from geodesic paths must be referenced
absolutely although the theory is named "General Relativity". This is
serious from a philosophical viewpoint.
failure 7: for GR to survive cosmological measurements most of the mass
of the universe must be unobservable.
and the list can go on for ever
So the correct way to put it is that GR is a crackpot theory.
In GR (qua model), spacetime is a manifold that has no properties other
than continuity, a suitable topology, and a local differential structure
suitable to support various tensor fields. "Space" does not even appear
in the theory itself, though one can foliate spacetime into space and
time if one wishes -- how to do that is an arbitrary human choice that
has no effect whatsoever on the predictions of the model for physical
measurements.
And in any case, the metric is a _geometrical_ property of a manifold,
not a "physical" one.
I see you and Hobba have different ideas about it. No surprise.
Logically therefore, measurement of the metric of space in any
particular region will immediately indicate whether any gravitational
field exists in that region.
You need to measure the metric of spaceTIME to do this. As I said above,
doing it for space alone involves an arbitrary human choice of
foliation. For instance, flat Euclidean 3-space can be foliated as a
concentric series of spheres and a radius; those spheres have nonzero
curvature even though the full space does not. _Exactly_ the same thing
can happen when you foliate spacetime into space and time.
Another parameter, the intrinsic impedance Z0 of vacuum or free space,
representing an important physical property of space, is routinely
measured and its value is about 377 ohms.
This is merely a choice of units.
The metric of space is identified with the metric
tensor g_ij. Since a tensor is an invariant entity, we can measure it
in any convenient coordinate system.
The tensor itself is invariant; the set of its components relative to a
given basis {g_ij} is most definitely not invariant. While older
textbooks called g_ij a "tensor", the correct terminology is that the
set {g_ij} are the components of the tensor g (notated in bold) -- this
avoids the confusion you are making.
(a) Just as the intrinsic impedance Z0 of space is routinely measured
as 377 ohms, whether the metric of space is also routinely measured by
working scientists and engineers?
Certainly. Surveyors do it all the time. That is, they measure distances
and angles of triangles and verify that the angles sum to 180 degrees
and the length obey the Pythagorean theorem. They don't actually write
down the metric coefficients, but what they do is equivalent to that.
If so, what are the units in which
the metric coefficients of space are measured (in any convenient
coordinate system)?
The units of the {g_ij} depend on the units of your coordinates. This
should be obvious from the line element
ds^2 = g_ij dx^i dx^j
because ds^2 must have units (length)^2. If, for instance, dx^0 has
units (seconds) and dx^1,dx^2,dx^3 have units (meters), then g_12 is
unitless and g_01 must have units (meters/sec); etc. But if on the other
hand one simply assigned numbers as coordinate values to space and time,
without ascribing any units to them, then {g_ij} all have units (meters)^2.
I see you and Hobba have different ideas about it. No surprise.
(b) If the working scientists and engineers have not felt any necessity
of measuring the metric coefficients of space, is it in principle
possible and feasible to measure these metric coefficients? If so, how
and in what units?
See above, and the introduction to MTW. By measuring the distances
between a sufficient number of points, the metric coefficients can be
determined. For instance, on the surface of the earth the metric
coefficients of the 2-d surface can be determined by measuring all
pairwise distances among 4 points; if you assume it is a sphere, 3
points is enough.
(c) If it is just not possible to measure the metric coefficients of
space, then could it be that the metric tensor does not represent any
physical property of space? Could be that the metric tensor just
represents the scaling characteristics of an arbitrarily defined
reference coordinate system?
See above. The metric tensor describes the geometrical properties of the
manifold. Its components are an admixture of that and the vagaries of
the coordinates used.
Let's have a party. I bring the coordinates and you bring the metric
tensor.
hahahahahahahahahahahahahaha
The funny thing is that most students pay to learn this crackpot stuff.
Mike
Tom Roberts
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| User: "Tom Roberts" |
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| Title: Re: Experimental Measurement of Space Metric |
12 May 2006 06:39:41 PM |
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Mike wrote:
Tom Roberts wrote:
Physicists know that GR is an accurate _model_ of the world we
inhabit. But careful writers do not ascribe the properties of the model
to the world.
Accurate?
Yes. This is extremely well established for scales between ~1mm and the
solar system. There are puzzles for scales outside that range, but at
present there are no definitive refutations of GR.
failure 1: GR predicts an order of magnitude less for the energy of
cosmic rays
The GZK limit is based on some questionable assumptions about how far
the cosmic rays have traveled. This is one of the puzzles.
failure 2: gravitomagnetic effects measurements are million billion
times more than GR predicts
There's _one_ experiment that claims that, and there are numerous
possible systematic effects that could explain it (in particular, spin
polarization of their materials). Don't believe everything you read,
_especially_ when it does not include errorbars, as all the web pages I
have seen omit.
failure 3: For GR the two-body problem has no solution unless it is
restricted so one of the masses is a test particle. Even there, only
numerical solutions exist.
This is not a "failure", this is merely a reflection of the fact that GR
is complicated and subtle. <shrug>
failure 4: gravity waves never detected
That's one of the puzzles. Perhaps LIGO and friends will soon shed some
light on this.
failure 5: frame dragging never detected
The LAGEOS satellites were used to measure it, and obtained a value of
1+-0.5 times the GR prediction. They were not launched with this in
mind. GP-B should soon have a definitive answer (it was launched
specifically to test this).
failure 6: any deviations from geodesic paths must be referenced
absolutely although the theory is named "General Relativity". This is
serious from a philosophical viewpoint.
That is merely a failure in YOUR personal lack of understanding of the
theory. <shrug>
failure 7: for GR to survive cosmological measurements most of the mass
of the universe must be unobservable.
This is one of the puzzles. Perhaps the biggest. It is also an active
area of research.
You forgot the Pioneer anomaly, the anomalous rotations of spiral
galaxies, and the incompatibility with QM (or rather, all the
experiments that validate QM).
and the list can go on for ever
Actually not. Except, perhaps, in your imagination. <shrug>
Yes, there are puzzles. They are _opportunities_for_research_, not
refutations of GR. Any of them have the potential to become refutations,
but are not yet solid enough to be considered such.
BTW major fraction of the physics community considers GR to be an
approximation to some as-yet-unknown deeper theory. There are _LOTS_ of
people trying to think up ways to refute GR, and to thus obtain glimpses
of that deeper theory....
You were told in the past that you confuse units with what is being
measured.
Being told something does not make it true.
No choice of units can effect the properties of a measurable
quantity. What is affected is the value obtained. Physical properties
exist independently of the values assigned to them.
Yes, of course, as long as by "properties" you mean something
independent of the system of units. For instance, the fact that this
ball fits through that hoop is such a property; its radius being 10 cm
is not. So is the fact that this muon is traveling at 0.999999 times the
speed of light, and there's no particular reason why that 0.999999
cannot be used as the value of its speed (in an appropriate system of
units, of course).
Tom Roberts
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| User: "Schoenfeld" |
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| Title: Re: Experimental Measurement of Space Metric |
13 May 2006 09:58:22 PM |
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Tom Roberts wrote:
Mike wrote:
Tom Roberts wrote:
Physicists know that GR is an accurate _model_ of the world we
inhabit. But careful writers do not ascribe the properties of the model
to the world.
Accurate?
Yes. This is extremely well established for scales between ~1mm and the
solar system. There are puzzles for scales outside that range, but at
present there are no definitive refutations of GR.
failure 1: GR predicts an order of magnitude less for the energy of
cosmic rays
The GZK limit is based on some questionable assumptions about how far
the cosmic rays have traveled. This is one of the puzzles.
failure 2: gravitomagnetic effects measurements are million billion
times more than GR predicts
There's _one_ experiment that claims that, and there are numerous
possible systematic effects that could explain it (in particular, spin
polarization of their materials). Don't believe everything you read,
_especially_ when it does not include errorbars, as all the web pages I
have seen omit.
failure 3: For GR the two-body problem has no solution unless it is
restricted so one of the masses is a test particle. Even there, only
numerical solutions exist.
This is not a "failure", this is merely a reflection of the fact that GR
is complicated and subtle. <shrug>
failure 4: gravity waves never detected
That's one of the puzzles. Perhaps LIGO and friends will soon shed some
light on this.
failure 5: frame dragging never detected
The LAGEOS satellites were used to measure it, and obtained a value of
1+-0.5 times the GR prediction. They were not launched with this in
mind. GP-B should soon have a definitive answer (it was launched
specifically to test this).
failure 6: any deviations from geodesic paths must be referenced
absolutely although the theory is named "General Relativity". This is
serious from a philosophical viewpoint.
That is merely a failure in YOUR personal lack of understanding of the
theory. <shrug>
failure 7: for GR to survive cosmological measurements most of the mass
of the universe must be unobservable.
This is one of the puzzles. Perhaps the biggest. It is also an active
area of research.
You forgot the Pioneer anomaly, the anomalous rotations of spiral
galaxies, and the incompatibility with QM (or rather, all the
experiments that validate QM).
and the list can go on for ever
Actually not. Except, perhaps, in your imagination. <shrug>
Yes, there are puzzles. They are _opportunities_for_research_, not
refutations of GR. Any of them have the potential to become refutations,
but are not yet solid enough to be considered such.
UNTIL YOU SOLVE ALL THE PUZZLES, you must say that 'GR is wrong'.
You have no basis to favour an _inference from the evidence_ over the
_evidence_ itself, and this is exactly what you are doing.
The simplest choice between "the theory is correct but new phenomenon
exist" and "the theory is incorrect" is the latter. It doesn't mean
it's the correct choice, it just means that it is the simplest choice
and this is what scientists are supposed to do (Occam's razor).
Otherwise, I can say Newtonian physics is absolutely true, simultaneity
is absolute, and use like lorentz ether's, exotic matter, etc to
account for almost everything - then I can dismiss every other
experimental result as 'a puzzle which needs to be solved' and
'opportunity for reasearch'.
But that's what it is really about - rather than ADMIT failure with the
theory, it's spinned into the form 'opporunity for research' because
this means the funding still flows, and the percetion legitmacy that
academia's physicists carry remains in tact - never mind the truth, the
objective progress.
The simple truth is that you guys have no better idea than ordinary
'laymen'.
BTW major fraction of the physics community considers GR to be an
approximation to some as-yet-unknown deeper theory. There are _LOTS_ of
people trying to think up ways to refute GR, and to thus obtain glimpses
of that deeper theory....
You were told in the past that you confuse units with what is being
measured.
Being told something does not make it true.
No choice of units can effect the properties of a measurable
quantity. What is affected is the value obtained. Physical properties
exist independently of the values assigned to them.
Yes, of course, as long as by "properties" you mean something
independent of the system of units. For instance, the fact that this
ball fits through that hoop is such a property; its radius being 10 cm
is not. So is the fact that this muon is traveling at 0.999999 times the
speed of light, and there's no particular reason why that 0.999999
cannot be used as the value of its speed (in an appropriate system of
units, of course).
Tom Roberts
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| User: "Tom Roberts" |
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| Title: Re: Experimental Measurement of Space Metric |
14 May 2006 07:39:17 PM |
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Schoenfeld wrote:
UNTIL YOU SOLVE ALL THE PUZZLES, you must say that 'GR is wrong'.
That is not science. No possible theory constructed by humans can be
completely correct. You are advocating the approach of theology, not
science.
The simplest choice between "the theory is correct but new phenomenon
exist" and "the theory is incorrect" is the latter.
Not when the theory has a large number of successes, as GR does.
Otherwise, I can say Newtonian physics is absolutely true,
That's your problem -- attempting to claim some physical theory is
"true" or "wrong". The choice is _NOT_ between "true" and "wrong", but
rather is an assessment of what the domain of applicability of the
theory is. As I said, for GR it is pretty clear that scales between ~1mm
and the solar system are within its domain of applicability. Outside
those bounds there are indeed puzzles related to applying GR. <shrug>
But that's what it is really about - rather than ADMIT failure with the
theory, it's spinned into the form 'opporunity for research'
Obviously you don't understand how science is actually performed. Is GR
"perfect"? No. But it is the best theory within its domain of
applicability that we have. The puzzles I mentioned are indeed
opportunities for research, with several possibilities: a) further
experiments might refute GR, b) they might suggest a better theory, c)
they might discover something new.
Tom Roberts
.
|
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| User: "Schoenfeld" |
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| Title: Re: Experimental Measurement of Space Metric |
14 May 2006 11:03:04 PM |
|
|
Tom Roberts wrote:
Schoenfeld wrote:
UNTIL YOU SOLVE ALL THE PUZZLES, you must say that 'GR is wrong'.
That is not science. No possible theory constructed by humans can be
completely correct. You are advocating the approach of theology, not
science.
I never said that the theory had to be correct, I just said that it had
to predict all experimental outcomes, and GR does not do that. And I'm
not talking about outcomes outside it's own domain, but inside. GR
predicts the distribution of cosmlogical bodies wildly out from what is
observed. Therefore, until you actually solve all the 'exotic matter'
problems (which may indeed be the case), you must, by default, assume
that 'GR has been falsified according to the evidence relevant in GR's
domain'.
The simplest choice between "the theory is correct but new phenomenon
exist" and "the theory is incorrect" is the latter.
Not when the theory has a large number of successes, as GR does.
It does not matter how many successes it has, it requires only 1
failure within domain A , for the theory to be falsified in domain A.
Since GR cannot account for the distribution and composition of
galaxies and clusters of galaxies, GR has been falsified within, at the
minimum, the domain of cosmology. You can save the theory by
_inferring_ the existence of exotic matter, but until that _inference_
becomes a _measurement_ then you must say 'GR has been falsified within
the domain of cosmology'. If you do not say that then you are no
different than an ether theorist.
Otherwise, I can say Newtonian physics is absolutely true,
That's your problem -- attempting to claim some physical theory is
"true" or "wrong". The choice is _NOT_ between "true" and "wrong", but
rather is an assessment of what the domain of applicability of the
theory is. As I said, for GR it is pretty clear that scales between ~1mm
and the solar system are within its domain of applicability. Outside
those bounds there are indeed puzzles related to applying GR. <shrug>
If you are stating that GR is valid within only those domains (~1mm to
solar system), there is no problem with that statement and it is, as
far as the best observation and experiment outcomes availble, true.
Unfortunately, that is not the impression people are getting from
physics lectures and the pop-sci industry. It is the impression that GR
somehow accounts for all observations and suffers no empirical
contradiction.
But that's what it is really about - rather than ADMIT failure with the
theory, it's spinned into the form 'opporunity for research'
Obviously you don't understand how science is actually performed. Is GR
"perfect"? No. But it is the best theory within its domain of
applicability that we have. The puzzles I mentioned are indeed
opportunities for research, with several possibilities: a) further
experiments might refute GR, b) they might suggest a better theory, c)
they might discover something new.
In your delusions of authority, you have forgotten how science is
_supposed_ to be performed. If a scientific theory suffers 1 empirical
contradiction, that theory has been 'falsified'. That's all it takes.
You admit that GR fails outside of the solar system and yet you
_give_the_impression_ to the unwary that GR is 'the correct approach'
and, due to perceived notions of professionalism from the same unwary,
you indirectly help guide research and funding resources into a
direction you know suffers empirical contradiction. The problem is that
the whole pop-sci industry and academia-squatters have become an
obstacle to objective progress, which is what 'science' was supposed to
provide.
Tom Roberts
.
|
|
|
| User: "" |
|
| Title: Re: Experimental Measurement of Space Metric |
15 May 2006 09:06:43 AM |
|
|
Schoenfeld wrote:
Tom Roberts wrote:
Schoenfeld wrote:
UNTIL YOU SOLVE ALL THE PUZZLES, you must say that 'GR is wrong'.
That is not science. No possible theory constructed by humans can be
completely correct. You are advocating the approach of theology, not
science.
I never said that the theory had to be correct, I just said that it had
to predict all experimental outcomes, and GR does not do that.
This what I meant to say, rather.
[snip here]
And I'm
not talking about outcomes outside it's own domain, but inside. GR
predicts the distribution of cosmlogical bodies wildly out from what is
observed. Therefore, until you actually solve all the 'exotic matter'
problems (which may indeed be the case), you must, by default, assume
that 'GR has been falsified according to the evidence relevant in GR's
domain'.
The simplest choice between "the theory is correct but new phenomenon
exist" and "the theory is incorrect" is the latter.
Not when the theory has a large number of successes, as GR does.
It does not matter how many successes it has, it requires only 1
failure within domain A , for the theory to be falsified in domain A.
Since GR cannot account for the distribution and composition of
galaxies and clusters of galaxies, GR has been falsified within, at the
minimum, the domain of cosmology. You can save the theory by
_inferring_ the existence of exotic matter, but until that _inference_
becomes a _measurement_ then you must say 'GR has been falsified within
the domain of cosmology'. If you do not say that then you are no
different than an ether theorist.
Otherwise, I can say Newtonian physics is absolutely true,
That's your problem -- attempting to claim some physical theory is
"true" or "wrong". The choice is _NOT_ between "true" and "wrong", but
rather is an assessment of what the domain of applicability of the
theory is. As I said, for GR it is pretty clear that scales between ~1mm
and the solar system are within its domain of applicability. Outside
those bounds there are indeed puzzles related to applying GR. <shrug>
If you are stating that GR is valid within only those domains (~1mm to
solar system), there is no problem with that statement and it is, as
far as the best observation and experiment outcomes availble, true.
Unfortunately, that is not the impression people are getting from
physics lectures and the pop-sci industry. It is the impression that GR
somehow accounts for all observations and suffers no empirical
contradiction.
But that's what it is really about - rather than ADMIT failure with the
theory, it's spinned into the form 'opporunity for research'
Obviously you don't understand how science is actually performed. Is GR
"perfect"? No. But it is the best theory within its domain of
applicability that we have. The puzzles I mentioned are indeed
opportunities for research, with several possibilities: a) further
experiments might refute GR, b) they might suggest a better theory, c)
they might discover something new.
In your delusions of authority, you have forgotten how science is
_supposed_ to be performed. If a scientific theory suffers 1 empirical
contradiction, that theory has been 'falsified'. That's all it takes.
You admit that GR fails outside of the solar system and yet you
_give_the_impression_ to the unwary that GR is 'the correct approach'
and, due to perceived notions of professionalism from the same unwary,
you indirectly help guide research and funding resources into a
direction you know suffers empirical contradiction. The problem is that
the whole pop-sci industry and academia-squatters have become an
obstacle to objective progress, which is what 'science' was supposed to
provide.
Tom Roberts
.
|
|
|
|
|
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|
| User: "Schoenfeld" |
|
| Title: Re: Experimental Measurement of Space Metric |
09 May 2006 09:37:32 PM |
|
|
Tom Roberts wrote:
GSS wrote:
Very many scientists, including the ardent followers of GR, believe
that the metric of space is a physical property of space.
No. Physicists know that GR is an accurate _model_ of the world we
inhabit. But careful writers do not ascribe the properties of the model
to the world.
The same physicists also believe that buildings can in-place freefall
due to a couple of hours of minor fire damage.
In GR (qua model), spacetime is a manifold that has no properties other
than continuity, a suitable topology, and a local differential structure
suitable to support various tensor fields. "Space" does not even appear
in the theory itself, though one can foliate spacetime into space and
time if one wishes -- how to do that is an arbitrary human choice that
has no effect whatsoever on the predictions of the model for physical
measurements.
And in any case, the metric is a _geometrical_ property of a manifold,
not a "physical" one.
It's all in your head Roberts, the evidence clearly shows GR is a
miserable failure at accounting for the distribution of large scale
astronomical bodies.
Logically therefore, measurement of the metric of space in any
particular region will immediately indicate whether any gravitational
field exists in that region.
You need to measure the metric of spaceTIME to do this. As I said above,
doing it for space alone involves an arbitrary human choice of
foliation. For instance, flat Euclidean 3-space can be foliated as a
concentric series of spheres and a radius; those spheres have nonzero
curvature even though the full space does not. _Exactly_ the same thing
can happen when you foliate spacetime into space and time.
Another parameter, the intrinsic impedance Z0 of vacuum or free space,
representing an important physical property of space, is routinely
measured and its value is about 377 ohms.
This is merely a choice of units.
The metric of space is identified with the metric
tensor g_ij. Since a tensor is an invariant entity, we can measure it
in any convenient coordinate system.
The tensor itself is invariant; the set of its components relative to a
given basis {g_ij} is most definitely not invariant. While older
textbooks called g_ij a "tensor", the correct terminology is that the
set {g_ij} are the components of the tensor g (notated in bold) -- this
avoids the confusion you are making.
(a) Just as the intrinsic impedance Z0 of space is routinely measured
as 377 ohms, whether the metric of space is also routinely measured by
working scientists and engineers?
Certainly. Surveyors do it all the time. That is, they measure distances
and angles of triangles and verify that the angles sum to 180 degrees
and the length obey the Pythagorean theorem. They don't actually write
down the metric coefficients, but what they do is equivalent to that.
If so, what are the units in which
the metric coefficients of space are measured (in any convenient
coordinate system)?
The units of the {g_ij} depend on the units of your coordinates. This
should be obvious from the line element
ds^2 = g_ij dx^i dx^j
because ds^2 must have units (length)^2. If, for instance, dx^0 has
units (seconds) and dx^1,dx^2,dx^3 have units (meters), then g_12 is
unitless and g_01 must have units (meters/sec); etc. But if on the other
hand one simply assigned numbers as coordinate values to space and time,
without ascribing any units to them, then {g_ij} all have units (meters)^2.
(b) If the working scientists and engineers have not felt any necessity
of measuring the metric coefficients of space, is it in principle
possible and feasible to measure these metric coefficients? If so, how
and in what units?
See above, and the introduction to MTW. By measuring the distances
between a sufficient number of points, the metric coefficients can be
determined. For instance, on the surface of the earth the metric
coefficients of the 2-d surface can be determined by measuring all
pairwise distances among 4 points; if you assume it is a sphere, 3
points is enough.
(c) If it is just not possible to measure the metric coefficients of
space, then could it be that the metric tensor does not represent any
physical property of space? Could be that the metric tensor just
represents the scaling characteristics of an arbitrarily defined
reference coordinate system?
See above. The metric tensor describes the geometrical properties of the
manifold. Its components are an admixture of that and the vagaries of
the coordinates used.
Tom Roberts
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| User: "GSS" |
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| Title: Re: Experimental Measurement of Space Metric |
09 May 2006 12:13:48 PM |
|
|
Tom Roberts wrote:
GSS wrote:
Very many scientists, including the ardent followers of GR, believe
that the metric of space is a physical property of space.
No. Physicists know that GR is an accurate _model_ of the world we
inhabit. But careful writers do not ascribe the properties of the model
to the world.
Yes I agree that the metric of space is not a physical property of
space. Yet very many scientists do believe it to be a physical property
of space. How else would you view the LIGOs type of experiments being
planned to detect the variations in the space metric?
In GR (qua model), spacetime is a manifold that has no properties other
than continuity, a suitable topology, and a local differential structure
suitable to support various tensor fields. "Space" does not even appear
in the theory itself, though one can foliate spacetime into space and
time if one wishes -- how to do that is an arbitrary human choice that
has no effect whatsoever on the predictions of the model for physical
measurements.
And in any case, the metric is a _geometrical_ property of a manifold,
not a "physical" one.
Yes I agree. Spacetime itself is only a model, a manifold and not a
physical entity. Naturally therefore, its metric cannot be a physical
entity.
Logically therefore, measurement of the metric of space in any
particular region will immediately indicate whether any gravitational
field exists in that region.
You need to measure the metric of spaceTIME to do this.
But how to measure something which is not physical?
......
Another parameter, the intrinsic impedance Z0 of vacuum or free space,
representing an important physical property of space, is routinely
measured and its value is about 377 ohms.
This is merely a choice of units.
Kindly elaborate this point.
Do you think the intrinsic impedance Z0 is not a propeerty of space?
Or do you think its value could be different from 377 ohms in some
other unit system? If so kindly point out its value in some other unit
systems that you know of.
GSS
.
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| User: "Tom Roberts" |
|
| Title: Re: Experimental Measurement of Space Metric |
09 May 2006 09:22:08 PM |
|
|
GSS wrote:
Tom Roberts wrote:
Physicists know that GR is an accurate _model_ of the world we
inhabit. But careful writers do not ascribe the properties of the model
to the world.
Yes I agree that the metric of space is not a physical property of
space. Yet very many scientists do believe it to be a physical property
of space.
Only ones who have not thought about the issue. Admittedly that is not
the empty set.
How else would you view the LIGOs type of experiments being
planned to detect the variations in the space metric?
LIGO is an experiment to test the predictions of GR. And also to perform
a whole new type of astronomy.
What LIGO actually measures is the _difference_ in the geodesic path
length between two points (the mirrors of one arm) for a spacelike and a
null path, measured as a difference between two such pairs at right
angles. This can be _interpreted_ as "variations in the spatial metric",
and also as "variations in the speed of light"; these are both
coordinate dependent statements, while my description is not.
Yes I agree. Spacetime itself is only a model, a manifold and not a
physical entity. Naturally therefore, its metric cannot be a physical
entity.
But it might well be a _model_ of a physical entity. Or, perhaps more
likely, an _approximation_ to one....
But how to measure something which is not physical?
_All_ measurements are ultimately geometrical. No problem. As I said
before, by simply measuring the pairwise distances between a sufficient
number of points one can determine all components of the metric.
Another parameter, the intrinsic impedance Z0 of vacuum or free space,
representing an important physical property of space, is routinely
measured and its value is about 377 ohms.
This is merely a choice of units.
Kindly elaborate this point.
Do you think the intrinsic impedance Z0 is not a propeerty of space?
I think you can get any value you might want by choice of units. Any
property that is affected like that by an arbitrary human choice cannot
be a physical property of anything.
This is an unacknowledged pun on the word "impedance". Normally that
word implies 1/conductance, but in vacuum conductance=0 identically.
Or do you think its value could be different from 377 ohms in some
other unit system? If so kindly point out its value in some other unit
systems that you know of.
I believe its value is 1 in the usual geometrical units. But there might
be a factor of 4pi (or somesuch) in there.
Tom Roberts
.
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| User: "GSS" |
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| Title: Re: Experimental Measurement of Space Metric |
10 May 2006 12:04:14 PM |
|
|
Tom Roberts wrote:
GSS wrote:
......
Yes I agree. Spacetime itself is only a model, a manifold and not a
physical entity. Naturally therefore, its metric cannot be a physical
entity.
But it might well be a _model_ of a physical entity. Or, perhaps more
likely, an _approximation_ to one....
But how to measure something which is not physical?
_All_ measurements are ultimately geometrical.
Wrong!! Think it over.
No problem. As I said
before, by simply measuring the pairwise distances between a sufficient
number of points one can determine all components of the metric.
Euclidean metric can be measured that way. In fact there is no need to
measure the Euclidean metric of space. Main question was about the
measurement of space and time components of Schw. metric in a strong
gravitational field. You can not measure the distances by measuring
rods and compute the Schw. metric coefficients. If you still believe it
can be done, then kindly explain.
Another parameter, the intrinsic impedance Z0 of vacuum or free space,
representing an important physical property of space, is routinely
measured and its value is about 377 ohms.
This is merely a choice of units.
Kindly elaborate this point.
Do you think the intrinsic impedance Z0 is not a property of space?
I think you can get any value you might want by choice of units. Any
property that is affected like that by an arbitrary human choice cannot
be a physical property of anything.
Again wrong!! If you don't understand why you are wrong then kindly
get me a value zero for the intrinsic impedance of free space by
choosing any units which you know of. It appears you are not familiar
with dimensional analysis which is an essential link between
mathematical abstraction and the physical reality. Can you distinguish
between fundamental dimensions and units as used in physics?
This is an unacknowledged pun on the word "impedance". Normally that
word implies 1/conductance, but in vacuum conductance=0 identically.
Again wrong!!! Robert what happened to you today? Too many mistakes!
Impedance does not imply 1/conductance. For your information note the
following relations.
Z = R + j X
where Z is the impedance, R the resistance, j is the square root of
minus one and indicates the phase relationship. X is the reactance. An
ideal capacitor will have only reactance and no resistance.
Y = G + j B
where Y is the admittance, G is conductance, and B the susceptance.
Admittance is the inverse of impedance. For free space resistance and
conductance do not come in the picture. Instead the inductance and
capacitance per unit length are important notions. Of course I do not
expect you to be familiar with the transmission line theory but then
you must not bluff about things which you are not familiar with.
Or do you think its value could be different from 377 ohms in some
other unit system? If so kindly point out its value in some other unit
systems that you know of.
I believe its value is 1 in the usual geometrical units. But there might
be a factor of 4pi (or somesuch) in there.
Again wrong!!! There is no 'usual' geometrical unit of impedance.
Why don't you come out of your geometrical shell and study physics that
applies to physical reality? Perhaps GR has already done too much
damage to the scientific community. When are we going to get rid of
this geometrical farce??
GSS
.
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|
| User: "FrediFizzx" |
|
| Title: Re: Experimental Measurement of Space Metric |
10 May 2006 06:40:55 PM |
|
|
"GSS" <gurcharn_sandhu@yahoo.com> wrote in message
news:1147280654.394697.207620@i40g2000cwc.googlegroups.com...
|
| Tom Roberts wrote:
| > GSS wrote:
| .....
|
[snip]
| > >>> Another parameter, the intrinsic impedance Z0 of vacuum or free
space,
| > >>> representing an important physical property of space, is
routinely
| > >>> measured and its value is about 377 ohms.
|
| > >> This is merely a choice of units.
|
| > > Kindly elaborate this point.
| > > Do you think the intrinsic impedance Z0 is not a property of
space?
|
| > I think you can get any value you might want by choice of units. Any
| > property that is affected like that by an arbitrary human choice
cannot
| > be a physical property of anything.
|
| Again wrong!! If you don't understand why you are wrong then kindly
| get me a value zero for the intrinsic impedance of free space by
| choosing any units which you know of. It appears you are not familiar
| with dimensional analysis which is an essential link between
| mathematical abstraction and the physical reality. Can you distinguish
| between fundamental dimensions and units as used in physics?
In gaussian cgs units, free space impedance is 4pi/c ~= 377 ohms. The
4pi is EXTREMELY important. It is 1/eps0 in SI units and is really a
ratio of length/length = 4pi. Even in natural units of hbar = c = 1, it
DOES NOT disappear. In that unit system, free space impedance is 4pi.
So what properties does free space have that gives us this 4pi ratio of
lengths?
[snip]
| > > Or do you think its value could be different from 377 ohms in some
| > > other unit system? If so kindly point out its value in some other
unit
| > > systems that you know of.
| >
| > I believe its value is 1 in the usual geometrical units. But there
might
| > be a factor of 4pi (or somesuch) in there.
|
| Again wrong!!! There is no 'usual' geometrical unit of impedance.
| Why don't you come out of your geometrical shell and study physics
that
| applies to physical reality? Perhaps GR has already done too much
| damage to the scientific community. When are we going to get rid of
| this geometrical farce??
Yes there is. As you see above, free space impedance in natural units
is simply 4pi.
FrediFizzx
http://www.vacuum-physics.com
.
|
|
|
| User: "GSS" |
|
| Title: Re: Experimental Measurement of Space Metric |
11 May 2006 01:09:16 PM |
|
|
FrediFizzx wrote:
"GSS" <gurcharn_sandhu@yahoo.com> wrote in message
news:1147280654.394697.207620@i40g2000cwc.googlegroups.com...
|
| Tom Roberts wrote:
| > GSS wrote:
| .....
|>>>> Another parameter, the intrinsic impedance Z0 of vacuum or free
|>>>> space, representing an important physical property of space, is
|>>>>routinely measured and its value is about 377 ohms.
|>>> This is merely a choice of units.
|>> Kindly elaborate this point.
|>> Do you think the intrinsic impedance Z0 is not a property of
|>> space?
|> I think you can get any value you might want by choice of units. Any
|> property that is affected like that by an arbitrary human choice
|>cannot be a physical property of anything.
| Again wrong!! If you don't understand why you are wrong then kindly
| get me a value zero for the intrinsic impedance of free space by
| choosing any units which you know of. It appears you are not familiar
| with dimensional analysis which is an essential link between
| mathematical abstraction and the physical reality. Can you distinguish
| between fundamental dimensions and units as used in physics?
In gaussian cgs units, free space impedance is 4pi/c ~= 377 ohms. The
4pi is EXTREMELY important. It is 1/eps0 in SI units and is really a
ratio of length/length = 4pi. Even in natural units of hbar = c = 1, it
DOES NOT disappear. In that unit system, free space impedance is 4pi.
So what properties does free space have that gives us this 4pi ratio of
lengths?
At least I can hope that you are familiar with dimensional analysis and
you can distinguish between fundamental dimensions and units as used in
physics. May I therefore request you to kindly clarify why the
dimensions of charge in SI system (Coulomb) and in cgs system (esu or
statcoulomb) are not the same. Consider any other parameter in physics,
say force, energy, power, density, acceleration, momentum etc.etc. the
dimensions of all these parameters are always the same, regardless of
the units employed to quantify them. Then why the dimensions of charge
not the same in SI and the cgs unit systems. Naturally therefore, if
the dimensions of charge (and hence current) in the two systems is
different, the dimensions of the proportionality constants in the
corresponding force relations will also be different and they will
represent different aspect of the physical reality.
In this regard kindly see a detailed note appended below on
Permittivity and Permeability Constants of Vacuum.
.....
|>> Or do you think its value could be different from 377 ohms in some
|>> other unit system? If so kindly point out its value in some other
|>> unit systems that you know of.
|> I believe its value is 1 in the usual geometrical units. But there
|> might be a factor of 4pi (or somesuch) in there.
| Again wrong!!! There is no 'usual' geometrical unit of impedance.
| Why don't you come out of your geometrical shell and study physics
|that applies to physical reality? Perhaps GR has already done too much
| damage to the scientific community. When are we going to get rid of
| this geometrical farce??
Yes there is. As you see above, free space impedance in natural units
is simply 4pi.
The use of so called natural units where hbar=G=c=1 is invalid in
physics on the grounds of dimensional inequality in physical relations.
Use of such shortcut methods is permissible only in the realm of pure
and abstract mathematics (not in applied mathematics) . It is a pity
that very many mathematicians keep advocating the use of such 'units'
to the physicists and engineers though of course, engineers never pay
any heed to that.
GSS
---------------------------------------------------------------------------------------------
Permittivity and Permeability Constants of Vacuum
-------------------------------------------------
Many Scientists believe that the proportionality constants of
permittivity 'eps0' and permeability 'mu0' associated with free space
or vacuum, depend entirely on the choice of units of the main
parameters and that they do not characterize any property of free space
or the vacuum. Hence it is contended that mere 'existence' of these
constants should not imply physical properties of the free space.
Further, it has also been asserted that there is some sort of
arbitrariness in the choice of units and physical dimensions of many
universal constants like eps0 and mu0.
For detailed study of this problem, let us first consider a general
system with inter-related parameters A1, A2, A3, A4 ... etc. Let a
typical (physically observed) relationship of these parameters be
written as
(A1^a1).(A2^a2).(A3^a3)= constant ............(1)
where a1,a2,a3 etc. may be +ve or -ve digits or fractions. If the
dimensions of parameters A1, A2, A3 are well defined, then through
dimensional analysis we can ascertain whether the constant in equation
(1) is a dimensional number or a dimensionless number. Only if this
constant is a dimensionless number, we can declare with certainty that
this constant does not characterize the system, that is, it does not
represent any physical property of the system in addition to the ones
already represented by A1, A2, and A3. The magnitude of such a
dimensionless constant may depend on the choice of units of the
parameters A1, A2, and A3. The choice of units here essentially implies
the choice of scale and not a choice of dimensions of various
parameters.
On the other hand, if the constant in equation (1) is a dimensional
number, we can replace it with a dimensional parameter say B1, so that
equation (1) can be rewritten as
(A1^a1).(A2^a2).(A3^a3)= B1 .........(2)
In this case the parameter B1 will certainly characterize the system,
that is, it will represent a physical property of the system; even
though under given observational environment this parameter may remain
constant in magnitude. The magnitude of such a dimensional parameter
too is governed by the choice of scale in the units of the parameters
A1, A2, and A3. But the 'essence' of parameter B1 and its dimensions
cannot be arbitrarily changed without simultaneously tampering with the
essence and dimensions of parameters A1, A2 etc. On the whole, a unit
system is highly inter-related and dimensions of any one parameter
cannot be arbitrarily changed without affecting all other dependent
parameters. It is, however, possible that parameter B1 may be a
'lumped' parameter, that is, it may consist of two or more physical
parameters which remain constant under given observational environment.
As a typical example, let us consider the case of Boyle's Law for an
ideal gas at constant temperature. The relation between pressure p and
volume V is written as
p.V = Constant ........... (3)
It can be easily seen through dimensional analysis that this constant
is a dimensional constant. Therefore, we can replace it with a
dimensional parameter or with a group of dimensional parameters R.T
that characterize the gas in its current state. This leads us to the
perfect gas law or the equation of state.
p.V/T = R ............ (4)
where T is the absolute temperature and R is the 'characteristic gas
constant'. Here again, R is a dimensional constant, which can be
further split into m(mass of the given quantity of gas in moles) and
R0(the universal gas constant). Therefore, equation (4) reduces to
p.V/(m.T) = R0 ......... (5)
Here too, R0 is a dimensional parameter that characterizes some most
fundamental features of an ideal gas. Magnitude of R0 varies in
different unit systems but it does not imply that units of R0 can be
chosen arbitrarily. The essence of R0 does not change with the change
in unit system. However, we cannot extract the true essence of R0 from
the perfect gas law or all the associated experimental data. To fully
understand as to how R0 characterizes an ideal gas system, we need a
kinetic theory of gases, which tells us that R0 is a composite
parameter consisting of N_0 (Avogadro's number) and kB (Boltzmann's
constant).
Let us take up the specific case of permittivity eps0 and permeability
mu0. We have following three relations involving parameters eps0, mu0
and the charge Q (or I) to enable us fix their units.
F = [1/(4.pi.eps0)].(Q^2/r^2)
Or eps0 = [1/(4.pi.F)].(Q^2/r^2) ............ (7)
where F is the force between two equal charges Q separated by distance
r.
F/L = (mu0/2pi). (I^2/d)
Or mu0 = 2pi.(F/L ).(d/I^2) ............ (8)
where F/L is the force per unit length of two parallel conductors
separated by distance d and carrying current I. Since the units of time
are well established, we need to establish the units of only one of the
two parameters Q and I, the other will get fixed automatically.
Sqrt(eps0.mu0) = 1/c ........... (9)
where c is the speed of light in vacuum, with well-established units.
On the basis of these three equations (7), (8) and (9), the units of
three parameters eps0, mu0 and Q (or I) can be fixed satisfactorily.
The units thus established, will be self-consistent and mutually
compatible. We cannot arbitrarily change the units of any one of these
parameters without affecting the units of other two. In MKSA system,
units of parameters eps0, mu0 and I (hence Q) have been fixed this way
and they satisfy all of the above mentioned three equations. We may
once again highlight the fact that the proportionality constants in
equations (7), (8) and (9), being dimensional parameters, play an
extremely important role in characterizing the system, in
characterizing the entity called 'free space, or 'vacuum'. In addition
there is one more parameter called the intrinsic impedance of free
space that is given by the relation,
Z0 = sqrt(mu0/eps0) ............ (10)
From equations (9) and (10) we can see that mu0 can be replaced by Z0/c
and 1/eps0 can be replaced by c.Z0 . Hence the intrinsic impedance Z0
also represents a physical property of free space or vacuum.
It will not be out of place to mention here that in Gaussian CGS system
of units, a bold attempt had been made to fix the proportionality
constant in equation (7) to unity, apparently to give a simpler look to
various equations. It is very interesting to find out how exactly it
was done. Essentially the two parameters Q and 'eps0' in equation (7)
are lumped into one new parameter (say) Qg with units of 'statCoulomb'.
Correspondingly the unit of current in this system is also named
'statamp'. Replacing (1/(4.pi.eps0)).Q^2 with Qg^2 in equation (7) and
(1/(4.pi.eps0)).I^2 with Ig^2 in equation (8) we get
F = (Qg^2/r^2)or (1/F).(Qg^2/r^2) = 1 ............. (11)
and F/L = (mu0/2pi).(Ig^2/d).(4.pi.eps0) = 2.(mu0.eps0).(Ig^2/d)
= (2/c2).(Ig^2/d)
Or (F/2L). (d/Ig^2) = 1/c^2 ............. (12)
Units of various other parameters in Gaussian CGS system are then fixed
such that they are consistent with equations (11) and (12) and mutually
compatible. Here it is very important to note that the dimensions of
charge Q in MKSA system are entirely different from the dimensions of
charge Qg (=Q/sqrt(4.pi.eps0)) in Gaussian system and hence they do not
represent the same physical quantity. Essentially in cgs system, the
dimensions of the charge Coulomb and that of sqrt(1/eps0) have been
'lumped' together to define a new parameter of esu or statCoulomb.
Naturally therefore the dimensions of the proportionality constants in
equations (11) and (12) also get adjusted accordingly and these
'constants' no longer represent the same physical properties as were
represented by the dimensional constants appearing in equations (7) and
(8) above. This fact is often overlooked by many scientists and they
keep harping about arbitrariness of proportionality constants.
GSS
.
|
|
|
| User: "FrediFizzx" |
|
| Title: Re: Experimental Measurement of Space Metric |
11 May 2006 03:45:03 PM |
|
|
"GSS" <gurcharn_sandhu@yahoo.com> wrote in message
news:1147370956.643506.299400@y43g2000cwc.googlegroups.com...
| FrediFizzx wrote:
| > "GSS" <gurcharn_sandhu@yahoo.com> wrote in message
| > news:1147280654.394697.207620@i40g2000cwc.googlegroups.com...
| > |
| > | Tom Roberts wrote:
| > | > GSS wrote:
| > | .....
|
| >|>>>> Another parameter, the intrinsic impedance Z0 of vacuum or free
| >|>>>> space, representing an important physical property of space,
is
| >|>>>>routinely measured and its value is about 377 ohms.
|
| >|>>> This is merely a choice of units.
|
| >|>> Kindly elaborate this point.
| >|>> Do you think the intrinsic impedance Z0 is not a property of
| >|>> space?
|
| >|> I think you can get any value you might want by choice of units.
Any
| >|> property that is affected like that by an arbitrary human choice
| >|>cannot be a physical property of anything.
|
| >| Again wrong!! If you don't understand why you are wrong then
kindly
| >| get me a value zero for the intrinsic impedance of free space by
| >| choosing any units which you know of. It appears you are not
familiar
| >| with dimensional analysis which is an essential link between
| >| mathematical abstraction and the physical reality. Can you
distinguish
| >| between fundamental dimensions and units as used in physics?
|
| > In gaussian cgs units, free space impedance is 4pi/c ~= 377 ohms.
The
| > 4pi is EXTREMELY important. It is 1/eps0 in SI units and is really
a
| > ratio of length/length = 4pi. Even in natural units of hbar = c =
1, it
| > DOES NOT disappear. In that unit system, free space impedance is
4pi.
| > So what properties does free space have that gives us this 4pi ratio
of
| > lengths?
|
| At least I can hope that you are familiar with dimensional analysis
and
| you can distinguish between fundamental dimensions and units as used
in
| physics. May I therefore request you to kindly clarify why the
| dimensions of charge in SI system (Coulomb) and in cgs system (esu or
| statcoulomb) are not the same.
Why would they be the same? They are different unit systems. Amperes
are not defined as a fundamental dimension in gaussian cgs units like it
is in SI. What is there to clarify?
Consider any other parameter in physics,
| say force, energy, power, density, acceleration, momentum etc.etc. the
| dimensions of all these parameters are always the same, regardless of
| the units employed to quantify them.
Hmm... Why do you suppose energy is equal to the units of mass and mass
is equal to the units of energy in natural units? So you are clearly
wrong here.
| Then why the dimensions of charge
| not the same in SI and the cgs unit systems. Naturally therefore, if
| the dimensions of charge (and hence current) in the two systems is
| different, the dimensions of the proportionality constants in the
| corresponding force relations will also be different and they will
| represent different aspect of the physical reality.
It is impossible for man-made unit systems to change physics. Anyone
that thinks it can is a dolt. Any aspect of physics can be represented
in any system of units if that system of units doesn't have any
inconsistencies. For sure, some unit systems are more handy for
applying to a particular problem. As John points out constantly, it is
easier to order capacitors in farads than in length. ;-)
| In this regard kindly see a detailed note appended below on
| Permittivity and Permeability Constants of Vacuum.
OK.
| >|>> Or do you think its value could be different from 377 ohms in
some
| >|>> other unit system? If so kindly point out its value in some other
| >|>> unit systems that you know of.
|
| >|> I believe its value is 1 in the usual geometrical units. But there
| >|> might be a factor of 4pi (or somesuch) in there.
|
| >| Again wrong!!! There is no 'usual' geometrical unit of impedance.
| >| Why don't you come out of your geometrical shell and study physics
| >|that applies to physical reality? Perhaps GR has already done too
much
| >| damage to the scientific community. When are we going to get rid of
| >| this geometrical farce??
|
| > Yes there is. As you see above, free space impedance in natural
units
| > is simply 4pi.
|
| The use of so called natural units where hbar=G=c=1 is invalid in
| physics on the grounds of dimensional inequality in physical
relations.
Don't be a maroon. You just don't know how to convert or use them.
However, I am holding a reservation that Newton's G is not a true
fundamental constant. The speed c is definitely a fundamental constant
because it is now defined that way in SI units.
| Use of such shortcut methods is permissible only in the realm of pure
| and abstract mathematics (not in applied mathematics) . It is a pity
| that very many mathematicians keep advocating the use of such 'units'
| to the physicists and engineers though of course, engineers never pay
| any heed to that.
Because you don't know how to use different unit systems and convert
between them is not the fault of others. ;-) Absolutely no physics
disappears in natural units of hbar = c = 1.
| GSS
| ----------------------------------------------------------------------
-----------------------
| Permittivity and Permeability Constants of Vacuum
| -------------------------------------------------
|
| Many Scientists believe that the proportionality constants of
| permittivity 'eps0' and permeability 'mu0' associated with free space
| or vacuum, depend entirely on the choice of units of the main
| parameters and that they do not characterize any property of free
space
| or the vacuum. Hence it is contended that mere 'existence' of these
| constants should not imply physical properties of the free space.
| Further, it has also been asserted that there is some sort of
| arbitrariness in the choice of units and physical dimensions of many
| universal constants like eps0 and mu0.
Granted that there are some physicists that are equally confused as you
are by different unit systems. It is impossible for eps0 and mu0 to
disappear in any system of units. They simple become represented by
other dimensions. For example; in gaussian cgs and natural units, eps0
is simply 1/4pi and is dimensionless.
| For detailed study of this problem, let us first consider a general
| system with inter-related parameters A1, A2, A3, A4 ... etc. Let a
| typical (physically observed) relationship of these parameters be
| written as
|
| (A1^a1).(A2^a2).(A3^a3)= constant ............(1)
|
| where a1,a2,a3 etc. may be +ve or -ve digits or fractions. If the
| dimensions of parameters A1, A2, A3 are well defined, then through
| dimensional analysis we can ascertain whether the constant in equation
| (1) is a dimensional number or a dimensionless number. Only if this
| constant is a dimensionless number, we can declare with certainty that
| this constant does not characterize the system, that is, it does not
| represent any physical property of the system in addition to the ones
| already represented by A1, A2, and A3. The magnitude of such a
| dimensionless constant may depend on the choice of units of the
| parameters A1, A2, and A3. The choice of units here essentially
implies
| the choice of scale and not a choice of dimensions of various
| parameters.
|
| On the other hand, if the constant in equation (1) is a dimensional
| number, we can replace it with a dimensional parameter say B1, so that
| equation (1) can be rewritten as
|
| (A1^a1).(A2^a2).(A3^a3)= B1 .........(2)
|
| In this case the parameter B1 will certainly characterize the system,
| that is, it will represent a physical property of the system; even
| though under given observational environment this parameter may remain
| constant in magnitude. The magnitude of such a dimensional parameter
| too is governed by the choice of scale in the units of the parameters
| A1, A2, and A3. But the 'essence' of parameter B1 and its dimensions
| cannot be arbitrarily changed without simultaneously tampering with
the
| essence and dimensions of parameters A1, A2 etc. On the whole, a unit
| system is highly inter-related and dimensions of any one parameter
| cannot be arbitrarily changed without affecting all other dependent
| parameters. It is, however, possible that parameter B1 may be a
| 'lumped' parameter, that is, it may consist of two or more physical
| parameters which remain constant under given observational
environment.
|
|
| As a typical example, let us consider the case of Boyle's Law for an
| ideal gas at constant temperature. The relation between pressure p and
| volume V is written as
|
| p.V = Constant ........... (3)
|
| It can be easily seen through dimensional analysis that this constant
| is a dimensional constant. Therefore, we can replace it with a
| dimensional parameter or with a group of dimensional parameters R.T
| that characterize the gas in its current state. This leads us to the
| perfect gas law or the equation of state.
|
| p.V/T = R ............ (4)
|
| where T is the absolute temperature and R is the 'characteristic gas
| constant'. Here again, R is a dimensional constant, which can be
| further split into m(mass of the given quantity of gas in moles) and
| R0(the universal gas constant). Therefore, equation (4) reduces to
|
| p.V/(m.T) = R0 ......... (5)
|
| Here too, R0 is a dimensional parameter that characterizes some most
| fundamental features of an ideal gas. Magnitude of R0 varies in
| different unit systems but it does not imply that units of R0 can be
| chosen arbitrarily. The essence of R0 does not change with the change
| in unit system. However, we cannot extract the true essence of R0 from
| the perfect gas law or all the associated experimental data. To fully
| understand as to how R0 characterizes an ideal gas system, we need a
| kinetic theory of gases, which tells us that R0 is a composite
| parameter consisting of N_0 (Avogadro's number) and kB (Boltzmann's
| constant).
|
| Let us take up the specific case of permittivity eps0 and permeability
| mu0. We have following three relations involving parameters eps0, mu0
| and the charge Q (or I) to enable us fix their units.
|
| F = [1/(4.pi.eps0)].(Q^2/r^2)
|
| Or eps0 = [1/(4.pi.F)].(Q^2/r^2) ............ (7)
|
| where F is the force between two equal charges Q separated by distance
| r.
|
| F/L = (mu0/2pi). (I^2/d)
| Or mu0 = 2pi.(F/L ).(d/I^2) ............ (8)
|
| where F/L is the force per unit length of two parallel conductors
| separated by distance d and carrying current I. Since the units of
time
| are well established, we need to establish the units of only one of
the
| two parameters Q and I, the other will get fixed automatically.
|
| Sqrt(eps0.mu0) = 1/c ........... (9)
|
| where c is the speed of light in vacuum, with well-established units.
| On the basis of these three equations (7), (8) and (9), the units of
| three parameters eps0, mu0 and Q (or I) can be fixed satisfactorily.
| The units thus established, will be self-consistent and mutually
| compatible. We cannot arbitrarily change the units of any one of these
| parameters without affecting the units of other two. In MKSA system,
| units of parameters eps0, mu0 and I (hence Q) have been fixed this way
| and they satisfy all of the above mentioned three equations. We may
| once again highlight the fact that the proportionality constants in
| equations (7), (8) and (9), being dimensional parameters, play an
| extremely important role in characterizing the system, in
| characterizing the entity called 'free space, or 'vacuum'. In
addition
| there is one more parameter called the intrinsic impedance of free
| space that is given by the relation,
|
| Z0 = sqrt(mu0/eps0) ............ (10)
|
| >From equations (9) and (10) we can see that mu0 can be replaced by
Z0/c
| and 1/eps0 can be replaced by c.Z0 . Hence the intrinsic impedance Z0
| also represents a physical property of free space or vacuum.
|
| It will not be out of place to mention here that in Gaussian CGS
system
| of units, a bold attempt had been made to fix the proportionality
| constant in equation (7) to unity, apparently to give a simpler look
to
| various equations. It is very interesting to find out how exactly it
| was done. Essentially the two parameters Q and 'eps0' in equation (7)
| are lumped into one new parameter (say) Qg with units of
'statCoulomb'.
| Correspondingly the unit of current in this system is also named
| 'statamp'. Replacing (1/(4.pi.eps0)).Q^2 with Qg^2 in equation (7) and
| (1/(4.pi.eps0)).I^2 with Ig^2 in equation (8) we get
|
| F = (Qg^2/r^2)or (1/F).(Qg^2/r^2) = 1 ............. (11)
|
| and F/L = (mu0/2pi).(Ig^2/d).(4.pi.eps0) = 2.(mu0.eps0).(Ig^2/d)
| = (2/c2).(Ig^2/d)
| Or (F/2L). (d/Ig^2) = 1/c^2 ............. (12)
|
| Units of various other parameters in Gaussian CGS system are then
fixed
| such that they are consistent with equations (11) and (12) and
mutually
| compatible. Here it is very important to note that the dimensions of
| charge Q in MKSA system are entirely different from the dimensions of
| charge Qg (=Q/sqrt(4.pi.eps0)) in Gaussian system and hence they do
not
| represent the same physical quantity. Essentially in cgs system, the
| dimensions of the charge Coulomb and that of sqrt(1/eps0) have been
| 'lumped' together to define a new parameter of esu or statCoulomb.
This is wrong. eps0 is 1/4pi in gaussian cgs units. It just becomes
dimensionless.
| Naturally therefore the dimensions of the proportionality constants in
| equations (11) and (12) also get adjusted accordingly and these
| 'constants' no longer represent the same physical properties as were
| represented by the dimensional constants appearing in equations (7)
and
| (8) above. This fact is often overlooked by many scientists and they
| keep harping about arbitrariness of proportionality constants.
All we know for certain is that k_e/k_m = c^2/2. If you pick k_e to be
a certain value, then k_m is automatically fixed by this relationship.
Or if you pick k_m to be a certain value, then k_e is fixed. See
Jackson, the appendix on unit systems.
Our concept of quantum vacuum charge = +,- sqrt(hbar*c), in cgs units,
fully eliminates any "conflicts" between unit systems.
FrediFizzx
http://www.vacuum-physics.com
.
|
|
|
| User: "GSS" |
|
| Title: Re: Experimental Measurement of Space Metric |
12 May 2006 02:17:24 PM |
|
|
FrediFizzx wrote:
"GSS" <gurcharn_sandhu@yahoo.com> wrote in message
news:1147370956.643506.299400@y43g2000cwc.googlegroups.com...
......
| At least I can hope that you are familiar with dimensional analysis and
| you can distinguish between fundamental dimensions and units as used
| in physics. May I therefore request you to kindly clarify why the
| dimensions of charge in SI system (Coulomb) and in cgs system (esu or
| statcoulomb) are not the same.
Why would they be the same? They are different unit systems. Amperes
are not defined as a fundamental dimension in Gaussian cgs units like it
is in SI. What is there to clarify?
| Consider any other parameter in physics,
| say force, energy, power, density, acceleration, momentum etc.etc. the
| dimensions of all these parameters are always the same, regardless of
| the units employed to quantify them.
Hmm... Why do you suppose energy is equal to the units of mass and mass
is equal to the units of energy in natural units? So you are clearly
wrong here.
Dear sir, you must understand it very clearly that the so called
'natural units' with hbar=c=1 are the most un-natural 'units' and are
strictly meant for and valid in purely mathematics domain. These are
totally invalid in the domain of physics where all mathematical
equations expressing physical phenomenon or relationship between
physical parameters, must be *dimensionally balanced*. The moment you
write hbar=c=1 and call it a natural unit, you have 'killed' the
dimensions of physical parameters and thereby committed a *crime*
against physics. Hence you will no longer be entitled to call yourself
a physicist even though you may still claim to be a great
mathematician.
| Then why the dimensions of charge
| not the same in SI and the cgs unit systems. Naturally therefore, if
| the dimensions of charge (and hence current) in the two systems is
| different, the dimensions of the proportionality constants in the
| corresponding force relations will also be different and they will
| represent different aspect of the physical reality.
It is impossible for man-made unit systems to change physics. Anyone
that thinks it can is a dolt. Any aspect of physics ca | | | | | | | | |
