What is it that curves?
Mark Hendy
specifically what is it that gets curved?
kenseto
"Mark Hendy" <mt...@bigpond.com> wrote in message
news:5PZ6b.89005$bo1....@news-server.bigpond.net.au...
> If space is a vacuum and space is curved by the presence of matter then
> specifically what is it that gets curved?
>
>
GR does not say that space is curved. It says that matter follows a curved
path in space-time and space-time is not a physical entity but rather it is
a math construct.
dlzc@aol.com (formerly)
"Mark Hendy" <mt...@bigpond.com> wrote in message
news:5PZ6b.89005$bo1....@news-server.bigpond.net.au...
> specifically what is it that gets curved?
The straight line between points A and B gets curved in spacetime. Also
known as "geodesic" if you want to look it up on a search. It is the path
a light signal would travel, and is known as a null geodesic. Material
bodies will travel similar paths, in that no energy transfer occurs, but
their paths are always more curved. Material bodies always travel at less
than c (so they spend more time in any given curvature), and they carry
some curvature with them (so they get to affect neighbors).
Have you visited the FAQ site? Here is one link:
http://www.math.ucr.edu/home/baez/physics/
then to:
http://math.ucr.edu/home/baez/relativity.html
David A. Smith
Bonnie Granat
"Mark Hendy" <mt...@bigpond.com> wrote in message
news:5PZ6b.89005$bo1....@news-server.bigpond.net.au...
> specifically what is it that gets curved?
>
>
Worldlines?
--
___________________________
Bonnie Granat
GRANAT EDITORIAL SERVICES
http://www.editors-writers.info
Overnight service available
Bill Hobba
> If space is a vacuum and space is curved by the presence of matter then
> specifically what is it that gets curved?
Well while space is curved by the presence of matter more than that occurs.
Space-time is curved. Rally you need to have a read. Have a look at
http://www.math.ucr.edu/home/baez/physics/. It is maintained by John Baez
whose opinion you can trust.
Thanks
Bill
Danny McCarty
>From: "kenseto" ken...@erinet.com
>Date: 9/8/2003 8:38 AM Central Standard Time
>Message-id: <vlp1ek1...@corp.supernews.com>
Yes, space IS curved. What is "straight"? When we sight along an arrow to
see if it is "straight", we are defining "straight" as the path of a light ray,
of a photon. Light travels on a "curved" path in a gravitational space, but
that curved path fits the definition of straight, so it is straight. It
appears curved because the vacuum it travels in has been curved by nearby mass.
The curvature is only apparent to us when the light passes close to a large
mass like the sun.
Igor
wrote:
>If space is a vacuum and space is curved by the presence of matter then
>specifically what is it that gets curved?
>
It's highly technical mathematically, but alot of it has to do with
the notion of vector transplantation. If I have two vectors and move
one away from the other such that any given point on the second vector
is moved along a line perpendicular to the first vector, then two
things can eventually occur. Either the two vectors will still remain
parallel (flat space), or they will no longer be parallel (curved
space). This is exactly what happens with lines normal to the
longitude and latitude on the surface of a globe, a fairly good
example of a two dimensional curved space.
Robert J. Kolker
Igor wrote:
> On Mon, 08 Sep 2003 11:34:25 GMT, "Mark Hendy" <mt...@bigpond.com>
> wrote:
>
>
>>If space is a vacuum and space is curved by the presence of matter then
>>specifically what is it that gets curved?
>>
>
>
> It's highly technical mathematically, but alot of it has to do with
> the notion of vector transplantation.
Also known as transport.
Bob Kolker
Igor
And sometimes called parallel displacement...
Ken S. Tucker
>On Wed, 10 Sep 2003 05:08:45 -0400, "Robert J. Kolker"
><bobk...@attbi.com> wrote:
>>Igor wrote:
>>> On Mon, 08 Sep 2003 11:34:25 GMT, "Mark Hendy" <mt...@bigpond.com>
>>> wrote:
>>>
>>>>If space is a vacuum and space is curved by the presence of matter then
>>>>specifically what is it that gets curved?
Light rays.
Before relativity, it was imagined that objects in space
could always be described by three coordinates, x,y,z
and the axes X,Y,Z were everywhere at right angles.
But these axes are completely imaginary.
Relativity ruled light rays must be used to coordinate
x,y,z much as lasers are used in surveying.
But light must obey the rules of mass-energy conservation,
just as masses do in gravitational fields, so they must also
bend.
>>> It's highly technical mathematically, but alot of it has to do with
>>> the notion of vector transplantation.
>>
>>Also known as transport.
>>Bob Kolker
>
>And sometimes called parallel displacement...
Yeah, to make everything add up correctly using light-rays
to survey with, a branch of math called tensor analysis was
required. This math deals with axes that cannot be set to right
angles.
Regards
Ken S. Tucker
Mitchell
The directions in space are curved.
If time is a flowing medium it then has a speed. This same speed is light
speed. And it moves forward in every possible "curved" direction.
What I mean to say here is that a moving time is what carries light around.
And a moving time is what bends around mass. so a bending time carries
light around.
If you wish to see time's movement think of a light bubble in which
light is moving in every direction - not just outward.
Mitch Inc.
John Anderson
Mark Hendy wrote:
> If space is a vacuum and space is curved by the presence of matter then
> specifically what is it that gets curved?
You measure intrinsic curvature using geodesic deviation. Two
initiallyparallel geodesic curves have divergent world lines. This is an
operational
definition that doesn't really answer your question because, unless you
have a meta-theory that subsumes general relativity, you can't really
explain "what" is happening, only what the effects are on things that you
can measure.
Physics is like that. It correlates observations and doesn't really
explain
them. Explanations are the domain of metaphysics.
John Anderson
John Anderson
Bonnie Granat wrote:
> "Mark Hendy" <mt...@bigpond.com> wrote in message
> news:5PZ6b.89005$bo1....@news-server.bigpond.net.au...
> > If space is a vacuum and space is curved by the presence of matter then
> > specifically what is it that gets curved?
> >
> >
>
> Worldlines?
>
The ? is (sort of) unnecessary. Geodesic world lines that are initially
parallel
and move towards or away from each other tell you that there is
intrinsic spacetime curvature.
This is an operational definition. That is all that physics is ever
going to give you.
Physics explains how observations are related, not "why" they occur.
John Anderson
Mark Hendy
"Ken S. Tucker" <dyna...@vianet.on.ca> wrote in message
news:2202379a.03091...@posting.google.com...
Thanks Ken, this was the kind of answer I was looking for. So if I
paraphrase you, am I correct in saying that it is light that bends and not
space-time? Also, can I question your last sentence (no disrespect
intended), is tensor analysis math for axes that cannot be set to right
angles or inclusive of axes that can or cannot be set to right angles?
David McAnally
>Dear Mark Hendy:
>"Mark Hendy" <mt...@bigpond.com> wrote in message
>news:5PZ6b.89005$bo1....@news-server.bigpond.net.au...
>> If space is a vacuum and space is curved by the presence of matter then
>> specifically what is it that gets curved?
>The straight line between points A and B gets curved in spacetime. Also
>known as "geodesic" if you want to look it up on a search. It is the path
>a light signal would travel, and is known as a null geodesic. Material
>bodies will travel similar paths, in that no energy transfer occurs, but
>their paths are always more curved.
This is true in that material bodies follow geodesic paths, which
are not null.
David McAnally
--------------
David McAnally
Is Ken still on about this idea that he was promoting ages ago about
tensor analysis being very specific to non-orthogonal axes? You
look like you've been left with the wrong impression, a state of
affairs which is unavoidable if you listen to certain people. Yes,
tensor analysis is applicable in the case when the axes are not
orthogonal and, in fact, there is a distinction between the two types
of vectors (covariant and contravariant, or 1-form and tangent),
specifically their components, if the axes are not orthogonal. I
recall Ken claiming that there was no such distinction between components
when the axes are orthogonal, but he was wrong. It is very easy to come
up with examples of orthogonal axes where there is a distinction between
the components of covariant vectors and the components of contravariant
vectors (e.g. cylindrical polar coordinates and spherical polar
coordinates). Further, it is possible to discuss the two different kinds
of vectors (covariant and contravariant), even if you can't discuss
distances, magnitudes or angles.
As for your original question, curvature is an intrinsic property of
spacetime, and the geodesics appear as they do as a consequence of
the curvature (and the related property: the connection).
David McAnally
--------------
Jim Jastrzebski
>
> [...] am I correct in saying that it is light that bends and not
>space-time?
No, it is not correct. It is assumed that there is
something independent of light that bends and it is
called figuratively "spacetime". It can be called this way
since space and time can be described together by
a single equation (with tensors).
Physically it is of course "space" and "time" that are
qualitatively different things. Out of those two, space
is bent, and time is "dilated" (runs at various rates
and various points in space). Only the time dilation
causes light rays to bend (and also orbits of planets
to bend and look like conical curves).
Space itself is bent but light rays would follow this
curvature (the same way as "straight" railway tracks
follow the curvature of the earth surface) if not for
the time dilation. The reason is of course that light
necessarily follows the paths of extremal time and
when time is dilated this path can't be straight. So the
light rays are bent by time dilation (and not by the
curvature of space nor by the curvature of "spacetime"):
in a curved space there is no other standard of
"straightness" as geodesics, e,g, "straightness" of
a railway track on the earth) and without time dilation
the light would follow geodesics in space (as straight
railway tracks do).
With the time dilated, it turns out that light (as
anything that is in free fall) follows geodesics in this
mathematical construct called "spacetime". But this
is a mathematical feature not physical one since
physically we have only "space" and "time" related
to each other in this interesting way that makes free
falling objects following geodesics in spacetime.
Why it has to be so is an interesting thing too but
too complex for short message.
> [...] is tensor analysis math for axes that cannot be
>set to right angles or inclusive of axes that can or
>cannot be set to right angles?
Inclusive. Tensor analysis doesn't care about angles
of axes, it is physical world in which you can't have
right angles for axes, except at one point. If you pull
your axes far enough they start crossing each other
at strange angles since the space of our universe
happen to be curved, and for a very good reason,
but it is quite another story.
-- Jim
Ken S. Tucker
Good, but as Bob and Igor wrote (above) the math is usually
regarded as highly technical. I figure you wouldn't be interested
in a highly technical response.
>So if I
>paraphrase you, am I correct in saying that it is light that bends and not
>space-time?
I think it would be better to say, space-time is defined
by light-rays paths, and light-ray paths are defined by
space-time. These cannot be separated, essentially
relativity insists *seeing is believing*, and seeing uses light-
rays. Of course we're talking about light-rays moving in
the vacuum of space.
Our most accurate survey tool is the laser, there is no
known way to create a straighter line than that in reality,
and relativity deals with this reality of measurement.
>Also, can I question your last sentence, is tensor analysis
>math for axes that cannot be set to right
>angles or inclusive of axes that can or cannot be set to right angles?
Tensor analysis permits every concievable coordinate system
that can be related to one another, from cartesian to polar to
lines on a globe. It can even be extended to function logically
in any number of dimensions.
Your questions are welcome,
Ken S. Tucker
Ken S. Tucker
[snip inappropriate technical BS and misquotes]
>As for your original question, curvature is an intrinsic property of
>spacetime, and the geodesics appear as they do as a consequence of
>the curvature (and the related property: the connection).
>David McAnally
David, read Mark Hendy's question,
Mark asked, "If space is a vacuum and space is curved
by the presence of matter then specifically what is it that
gets curved?"
Does "specifically" mean imaginary to you?
In order to specifically confirm any imaginary notion of
"curvature" real objects are used, *specifically* light-rays.
Ken S. Tucker
ghytrfvbnmju7654
> paraphrase you, am I correct in saying that it is light that bends and not
> space-time? Also, can I question your last sentence (no disrespect
> intended), is tensor analysis math for axes that cannot be set to right
> angles or inclusive of axes that can or cannot be set to right angles?
It is space-time that is curved. The curvature is difficult
to visualize, so it helps to start out simple and work up.
Imagine a two-dimensional surface. We all know what it means when
such a surface is curved. But how would creatures who live in
the surface know about a third dimension?
The answer is that they very well might not. Imagine the surface
was a sheet of paper, and someone bent it. The relationships
between the things on the paper would not be affected.
But some surfaces are not be flattenable. Spheres, for example,
can't be flattened without ripping the material, which certainly
changes the relationships between things on the paper. One might
then guess that creatures living in such a curved surface could
tell that it was curved.
And they could tell it was curved. Let's use a cube with rounded
corners for an example. If a creature went around one of those
corners, and tried to keep his face in the same direction, he
would find that when he got back to the place he started, he was
facing in a different direction, 90 degrees from the direction
he was facing when he started.
If you were to flatten the cube, you would find that at a corner,
there would be 90 degrees "missing":
+-------+
| | 90 degrees
| |-+ "missing"
| | |
+-------+-------+-------+
| | | |
| | | |
| | | |
+-------+-------+-------+
| |
| |
| |
+-------+
| |
| |
| |
+-------+
If the creature made his trek around two corners of the cube,
he would find himself 180 degrees from where he started.
So the creature would realize that his universe had something
called intrinsic curvature, which could be quantified in
degrees per area.
The creatures would have no way of deducing the exact shape
of their universe, and in fact, they might come up with
alternate explanations for the curvature. So these creatures
would regard talk of a third dimension as "metaphysics."
They would much rather talk about the intrinsic curvature
they could measure.
We can extend the idea to a three-dimensional world. Since
it's difficult to visualize an extra dimension, we would
have to find another way to think about it. One way would
be to imagine the curvature was concentrated in small places,
even though it really wasn't. This would be like imagining
a uniformly curved sphere as a soccerball with corners. In
the three-dimensional case, we would concentrate the curvature
not at points, but at lines -- lines that extended forever or
until they met another such line. If we walked around such a
line (imagining it oriented up+down), we would get the same
result the cube-dweller did. We would see that there was
a missing or extra angle. Would we want to speculate about
extra dimensions? It wouldn't help us if we did.
Now our world, which possesses intrinsic curvature, is
four-dimensional, with three dimensions of space and one
of time. To extend the visualization technique to four
dimensions, let the lines be allowed to move at a constant
speed in a constant direction. Of course, in the real
world, the curvature is uniform, not concentrated at lines,
but this can help to visualize things, like field lines
in electrodynamics, especially in situations where the
curvature is small.
Imagine one of the lines rushed between two people.
The problem of what happens is more conveniently
handled from the perspective of the line, with the
people rushing toward the line. If there was a
"missing angle," the two people would end up colliding:
|
|
<---| "missing"
^ | angle
| +---------
| ^
| |
| |
The two people might therefore conclude that a
"force" pulled them together. But what happened
was really the result of spacetime curvature.
This is how the apparent "force" of gravity can
be explained by spacetime curvature. Realistic
situations, of course, are a bit more complicated,
but this is the general idea.
G=EMC^2 Glazier
is an illusion. This illusion is created by attraction at a
distance by a massive object. This massive object such as the sun has a
gravity field that wants everything to fall to it. The earth's angular
motion(energy) is equal to this gravity field and makes a complete
circle,and goes round and round. A light ray has to much speed,and can
only be slightly curved,and away it goes. A BH is the
only gravitational object that can put light in orbit. Einstien had to
curve space to show attraction at a distance. Its still a problem today.
He did not like quantum gravity. He did not like quantum gravity's
graviton(messenger particle for gravity. He did not like QM because he
was smart enough to know it was a better theory to use in the micro
realm. Bert
ghytrfvbnmju7654
> The Curving of the vacuum of space,and photons following that curvature
> is an illusion.
a) It's not just photons that are affected by the curvature.
b) If you say space-time curvature is an illusion, but that
everything acts exactly as if space-time was curved, you're
just talking meta-physics.
> This illusion is created by attraction at a
> distance by a massive object.
Information that could be used to communicate does not travel faster
than light.
> This massive object such as the sun has a
> gravity field that wants everything to fall to it.
Fields do not have desires; only people do.
> The earth's angular
> motion(energy)
Angular motion and energy are not the same thing.
> is equal to this gravity field
The earth's energy is only one number; a field consists of a number,
or vector, or tensor, or spinor, at each and every point in space-time.
> and makes a complete
> circle,and goes round and round.
What are you saying goes in circles? The earth's energy? Yes, it does,
but only once a year. Technically it goes in an ellipse.
> A light ray has to much speed,and can
> only be slightly curved,and away it goes. A BH is the
> only gravitational object that can put light in orbit.
No, a black hole is an object that can keep light, on the event horizon
or closer, moving straight outward, from escaping further outward than
the escape horizon. You don't quite need a black hole to put light in
an (unstable) orbit.
> Einstien
Einstein
> had to
> curve space to show attraction at a distance. Its still a problem today.
> He did not like quantum gravity. He did not like quantum gravity's
> graviton(messenger particle for gravity.
Quantum gravity did not exist in Einstein's day. A good quantum
theory of gravity still does not exist.
Mark Hendy
matter and that it is the bending of light rays that are the observable
phenomenon.
Didn't Einstein say that space consists of a collection of points and that
each point is surrounded by a collection of other points and so on and that
there is no "space" between those points and thats what puts the "continuum"
into space time continuum? Then presumably the curvature of spacetime by
mass is really the squishing up of these points around the mass.
But there seems a contradiction here. If there were no "space" between the
points and they moved out of the way in the presence of mass then you would
expect them to instantly push each other all the way to the edge of the
Universe. But then they would be travelling faster than light. But if
instead they squish up, they create a geodesic, then surely they were
compressable and had some space between then.
"Jim Jastrzebski" <jim...@aol.com> wrote in message
news:20030913101847...@mb-m01.aol.com...
Mark Hendy
> Good, but as Bob and Igor wrote (above) the math is usually
> regarded as highly technical. I figure you wouldn't be interested
> in a highly technical response.
> Ken S. Tucker
Precisely! :) I find that people who understand their subjects well can
explain their knowledge conceptually. And that even though their
descriptions dont contain specific details that support the concepts (these
may confuse or discourage novices) they speak "truthfully" about the subject
they're referring to. It is my goal to find out more about our modern
conceptual understanding of the Universe, and specifically about space-time.
Jim Jastrzebski
>
>Ok so let's say that it is spacetime that is curved by the presence of
>matter and that it is the bending of light rays that are the observable
>phenomenon.
>
>Didn't Einstein say that space consists of a collection of points
>and that each point is surrounded by a collection of other points
>and so on and that there is no "space" between those points and
>thats what puts the "continuum" into space time continuum?
>Then presumably the curvature of spacetime by mass is really
>the squishing up of these points around the mass.
>
>But there seems a contradiction here. If there were no "spa
>ce" between the points and they moved out of the way in the
>presence of mass then you would expect them to instantly push
>each other all the way to the edge of the Universe. But then they
>would be travelling faster than light. But if instead they squish up,
>they create a geodesic, then surely they were compressable and
>had some space between then.
"Point" is a figure of speech and not a physical thing that can
get squished. Physically it is a piece of empty space of zero
size in every direction. It can't be squished to anything smaller.
But since it is just nothing it can't prevent the space from being
squished so if you mark two points in space you may see them
getting closer to each other, or getting farther away from each
other which would mean that the space between them is getting
smaller or bigger respectively. No contradiction. A separate
problem is how to mark empty space, but if you solve this
problem you are all set.
-- Jim
Ken S. Tucker
>> Good, but as Bob and Igor wrote (above) the math is usually
>> regarded as highly technical. I figure you wouldn't be interested
>> in a highly technical response.
>
>explain their knowledge conceptually. And that even though their
>descriptions dont contain specific details that support the concepts (these
>may confuse or discourage novices) they speak "truthfully" about the subject
>they're referring to. It is my goal to find out more about our modern
>conceptual understanding of the Universe, and specifically about space-time.
There are limits to explaining physics "conceptually", ie,
using words. At a point the exactitude is blunted by using
analogies - but analogies can be useful for introducing
concepts - it's a craft I admire in skilled teachers.
About space-time, it's difficult to avoid a bit of math.
Here's why, you want to stay as realistic as possible,
and employ abstract concepts as necessary. But some-
times abstract concepts require a *leap of faith* and too
many of those, and the next thing you know, the subject
gets religious.
For example, if you want to understand space-time
you need to know the International Standard of Units
definition of length and time and how the
speed of light *inter-defines* these units,
Length = (speed of light) x Time
as you probably know, although it would be difficult
(for me) to describe conceptually.
Regards
Ken S. Tucker
Robert J. Kolker
Ken S. Tucker wrote:
>
> There are limits to explaining physics "conceptually", ie,
> using words. At a point the exactitude is blunted by using
> analogies - but analogies can be useful for introducing
> concepts - it's a craft I admire in skilled teachers.
All physical theories are analogies and metaphors.
Bob Kolker
Thor
attraction of massive objects such as planets, stars, etc.
Mike Helland
> If space is a vacuum and space is curved by the presence of matter then
> specifically what is it that gets curved?
I think I have an innovative answer for this question.
If you had a cube whose length was Planck's Length, this cube would be
unobservable. Because we see zero dimensions of this 3d object, it
appears to us as a point.
Our space is just all these points, and what hides behind these points
is more space. Because this subspace within Planck's Cube (I might
have just coined that but I'm not sture) has dimensions, even if they
are not observable, these cubes can be shaped.
The collective effect of these shaped cubes is a larger space that can
be curved in the shape of its shaped sub-space cubes, even if those
cubes appear as points to us.
Mike Helland
Ken S. Tucker
Hi Bob,
A theory: Grab your nose and pull hard,
predicted result= you sense pain.
This is a theory that can be confirmed by
repeating the experiment.
For reference see Michael Jackson.
How would this Theory be an analogy or a metaphor?
Ken S. Tucker
Jim Jastrzebski
<2202379a.03091...@posting.google.com>
>
>"Robert J. Kolker" <bobk...@attbi.com> wrote in message
>news:<bk3n8q$odeet$1...@ID-76471.news.uni-berlin.de>...
>>Bob Kolker
>
>A theory: Grab your nose and pull hard,
>predicted result= you sense pain.
>
>This is a theory that can be confirmed by
>repeating the experiment.
>
>For reference see Michael Jackson.
>
>How would this Theory be an analogy or a metaphor?
>Ken S. Tucker
Bob must have meant a "mathematical theory" not
"physical theory" (like yours).
Mathematical theories are just metaphors since they
replace real stuff by other stuff (metaphors) and operate
on them according to some special rules.
E.g. in Newtonian gravity "gravitational potential" is a
metaphor for time dilation. When you divide the first
one by c^2 you get exactly the second one. Yet
Newtonian gravity knows nothing about time dilation
and is quite happy with physically non existent
"gravitational potential" (and its derivative "gravitational
acceleration"). In this sense Newtonian gravity being
a mathematical theory (as opposed to GR which might
be a physical as far as we know) operates on metaphors
like "gravitational attraction" etc. only. Which doesn't
prevent it from being as much useful a theory as yours
with the nose.
-- Jim
David McAnally
>Ok so let's say that it is spacetime that is curved by the presence of
>matter and that it is the bending of light rays that are the observable
>phenomenon.
Take a tangent vector (represent it by something physical, like a
horizontal arrow) at the North Pole, and pointing in the direction of the
Greenwich Meridian. Now, parallel transport that vector as you travel
down the Meridian to the Equator (i.e. travel south along the Meridian,
keeping the arrow pointing in the same direction as much as possible WHILE
KEEPING IT HORIZONTAL), then parallel transport the vector as you travel
east to 90 degrees longitude along the Equator (i.e. travel east along the
Equator, keeping the arrow pointing in the same direction as much as
possible while keeping it horizontal), and then parallel transport the
vector north along the new Meridian to the North Pole (i.e. travel north
to the North Pole, keeping the arrow pointing in the same direction as
much as possible while keeping it horizontal). We are now back where we
started (the North Pole). What has happened to the vector (arrow) in the
meantime? The vector starts by moving along the same Meridian along which
it is pointing, so it remains pointing south. Then it moves along the
Equator, and all south pointing vectors along the Equator point in the
same direction in three-dimensional space, so the vector remains pointing
south. Finally, the vector moves north to the North Pole, and since it is
moving along a Meridian, it remains pointing south. And so it reaches the
North Pole pointing south along the 90 degree East Meridian, in other
words, the vector has turned 90 degrees counterclockwise. This change in
the vector may seem surprising when one remembers that at all times, the
vector was transported parallel to itself, and the explanation lies in the
fact that the surface of the Earth is curved (and in fact, it is
demonstrable that any vector which is parallel transported around a closed
loop on a sphere turns in the same direction as the loop sweeps out about
its enclosed area, and that the angle of turn (in radians) is equal to the
area enclosed by the loop divided by the square of the radius of the
sphere). In other words, there is a quantity, called curvature, which is
evenly distributed about the surface of the sphere, and parallel transport
around any closed loop on the sphere yields a turn of any vector by an
amount equal to the nett enclosed curvature.
This gives the main contrast between a flat space and a curved space. If
a vector is parallel transported about a closed curve in a flat space,
then the vector remains unchanged, but if a vector is parallel transported
about a closed curve in a curved space, then the generic vector will
change after being parallel transported on the generic closed path (i.e.
the set of vectors and closed paths such that the vector remains unchanged
after the parallel transport is a set of measure zero, i.e. almost all
vectors will, after parallel transport on almost all closed paths, change
value). This allows us to define when a space (or spacetime) has an
intrinsic curvature. A closed path in spacetime finishes when and where
it starts, so a closed path in spacetime is generally not a path which can
be followed by a material body, or by a light ray (either part of the path
must be backwards in time or the path must be spacelike, unless the
universe has a weird geometry like that of Goedel's universe).
There is not an additional assumption required by accounting for the
possibility of a curved spacetime. On the other hand, if one
requires spacetime to be flat, then that IS an additional assumption.
As far as "what is curved" is concerned, one can imagine isometrically
embedding (embedding so that the metric is preserved, i.e. the magnitudes
of vectors, and the distances, are preserved) the universe in a flat
spacetime manifold of higher dimension (i.e. p+q, where p is at least 3, q
is at least 1, and p+q > 4). Then the embedded manifold will be obviously
curved in the same way that a 2-sphere is obviously curved when embedded
in Euclidean 3-space.
David McAnally
--------------
ghytrfvbnmju7654
misunderstandings:
> No, a black hole is an object that can keep light, on the event horizon
> or closer, moving straight outward, from escaping further outward than
> the escape
This should be "event."
> horizon. You don't quite need a black hole to put light in
> an (unstable) orbit.
> Quantum gravity did not exist in Einstein's day. A good quantum
> theory of gravity still does not exist.
To be clearer, it did not exist as a human theory.
tran...@gmail.com
> "Mark Hendy" <mt...@bigpond.com> wrote in message
> > specifically what is it that gets curved?
> >
> >
>
> path in space-time and space-time is not a physical entity but rather it is
> a math construct.
Absolutely Vertical
> On Monday, September 8, 2003 9:36:22 AM UTC-4, kenseto wrote:
>> "Mark Hendy" <mt...@bigpond.com> wrote in message
>> news:5PZ6b.89005$bo1....@news-server.bigpond.net.au...
>>> If space is a vacuum and space is curved by the presence of matter then
>>> specifically what is it that gets curved?
>>>
>>>
>>
>> GR does not say that space is curved. It says that matter follows a curved
>> path in space-time and space-time is not a physical entity but rather it is
>> a math construct.
in spacetime, but that is not what gr says. gr says the direct opposite.
>
> I agree. Space "curving" is used here in a metaphorical way to describe the behaviour of matter,
> which in the presence of matter acts AS IF it were on a dented kind of space. But space itself
> cannot curve because it is not a physical thing. Space is a mental (or at best mathematical) construct.
> Mental is fine. It's strictly euclidian in the mind, throuhg and through. And Euclidian geometry does
> not disappear out of non-Eucledian geometry. It's still there, playing peekaboo all the time, now you
> seeme, now you don't. What I mean is, the geodesic does not take the secant out of existence. The
> straight line is still very much under it. The fact that sometimes it can't be used (by matter) does
> not matter. It's still there. Because if it werent, it would not make sense to say something is "curved".
> Curved with respect to what? Well, to the straight line, of course. What else? So that line is still
> in the system.
>
saying that just because we have the _words_ straight and curved and
there is a distinction between them, then these words apply to reality.
and that a 'straight line' _must_ exist in reality otherwise we would
not have a word for it. i also have a word and a clear concept for a
four-legged whale. does this mean that such a thing exists? but let's
suppose you are right and there is such a thing as a euclidean straight
line. how would you define straightness? be as clear and precise as
possible, because i want to use your definition to test whether some
things are straight or not. if you can't define straightness in
unambiguous terms, then why are you using a word that you don't know the
meaning of, and furthermore why would you insist that such a description
applies to reality if you can't even clearly say what it means?
tran...@gmail.com
You can’t.
The best we can do is define straighness as absence of curvature, and curvature as absence of straightness. Both are readily understood concepts in eucledian geometry. They need no corroboration because they are mental entities. My mental lines are perfectly straight by definition. Concpts established by definition need no physical corroboration. The fact I cannot prove the edge of this table is straight is irrelevant. Eucledian geometry does not deal with physical objects.
I’ve already said that I consider space an inherent mental faculty. Not a tangible part of reality, and maybe not a part of reality at all except to the extent that mental intuitions are part of reality.
You seem to accept without problem the existence of curvature, but you doubt the existence of straigthness. That’s very odd. Just as odd as accepting the existence of lowness, but rejecting highness out of principle, or endless similar pairs.
More fruitful would be for you to offer a definition of space so we know what you understand by it. Once we know that, explain how you can conceive of a space where straighness has been ejected, if it ever existed, and curvature is the only tenant.
If straightness is out, then the curvature is curved with respect to what exactly? The memory of straightess as a former tenant? What else?
Absolutely Vertical
> On Thursday, February 14, 2013 3:17:41 PM UTC-5, Absolutely Vertical wrote:
>> On 2/14/2013 1:52 PM, tran...@gmail.com wrote:
>
>> and in your case, i'd like to probe your thinking here. you seem to be
>> saying that just because we have the _words_ straight and curved and
>> there is a distinction between them, then these words apply to reality.
>> and that a 'straight line' _must_ exist in reality otherwise we would
>> not have a word for it. i also have a word and a clear concept for a
>> four-legged whale. does this mean that such a thing exists? but let's
>> suppose you are right and there is such a thing as a euclidean straight
>> line. how would you define straightness? be as clear and precise as
>> possible, because i want to use your definition to test whether some
>> things are straight or not. if you can't define straightness in
>> unambiguous terms, then why are you using a word that you don't know the
>> meaning of, and furthermore why would you insist that such a description
>> applies to reality if you can't even clearly say what it means?
>
>
> OK, you want definitions. How do you define curvature without recourse to straightness?
> The best we can do is define straighness as absence of curvature, and curvature as absence of straightness.
pair of words that only refer to each other in a circular loop, because
then you can't really distinguish one from the other. if i gave you some
object x and asked you whether it were straight or curved, you'd have to
apply some criteria to decide, other than some arbitrary statement like
'well, it's not curved so it must be straight.'
this points precisely to the problem. you are using a word that you
cannot define, except in terms of not being something else which you
also cannot define. so you don't even have a clear understanding of the
mental concept of 'straight', and yet you want to say that 'straight'
things exist in reality. how do you _know_ unless you can say what the
concept even means?
> Both are readily understood concepts in eucledian geometry. They need no corroboration because they are
> mental entities. My mental lines are perfectly straight by definition. Concpts established by definition
> need no physical corroboration. The fact I cannot prove the edge of this table is straight is irrelevant.
> Eucledian geometry does not deal with physical objects.
that _you_ have called straight should also be called straight by
someone else. otherwise the word 'straight' is private to you and you
only and has no meaning. you might as well say that you have a concept
of 'blaubility' which is the property of lacking 'corrificeness'.
>
> I�ve already said that I consider space an inherent mental faculty. Not a tangible part of reality, and maybe
>
> You seem to accept without problem the existence of curvature, but you doubt the existence of straigthness.
definition of that, so that then we could discern curvature from it on
the basis of those criteria. but it seems you have no criteria for
straightness, and so you also don't have any criteria for curvature.
about the only thing you have said is, 'what i say is straight, is
straight' or 'i know it when i see it', neither of which is terribly useful.
> That�s very odd. Just as odd as accepting the existence of lowness, but rejecting highness out of principle,
>
> More fruitful would be for you to offer a definition of space so we know what you understand by it. Once we
> know that, explain how you can conceive of a space where straighness has been ejected, if it ever existed,
> and curvature is the only tenant.
straight and which things should be labeled curved, even the idealized
versions? and you have no criteria for that, other than capricious
labeling 'i say this is straight because i have _named_ it straight' and
'this other thing is not labeled straight and so it is curved.'
ultimately the problem is that you are invoking reality to _words_ which
is not a problem in itself, if you know what the word means and can
define it or describe the criteria for having that property. but if you
can't even describe the criteria for applying the word, then what have
you done other than arbitrary gibberish.
i say this with respect, in the hopes that you can see the problem and
then ask yourself, 'well, heck, what _do_ i mean by the word straight
when i use it?'
Ryan Scott
>> "Mark Hendy" <mt...@bigpond.com> wrote in message
>> news:5PZ6b.89005$bo1....@news-server.bigpond.net.au...
>> > If space is a vacuum and space is curved by the presence of matter
>> > then specifically what is it that gets curved?
tran...@gmail.com
> On 2/14/2013 2:46 PM, tran...@gmail.com wrote:
well, clearly that's an untenable situation. one should never have a
pair of words that only refer to each other in a circular loop, because
then you can't really distinguish one from the other.
>
Well, since you apparently know the definition of curvature without recourse to straightness, go ahead and offer it.
Speaking of a “curved space” may be useful in a metaphorical sense to describe the behavior of matter in certain situations. It may be convenient to describe its behaviour AS IF it took place a “deformed” space. I am okay with that. The fact that something is convenient does not make it conceptually tenable. You may say that it’s wrong that the sun revolves around the earth, and right that the earth revolves around the sun. But in fact both statements are equally true depending on your point of reference. It is certainly much more convenient, however, to adopt a sun-centered position, that’s all.
Conceptually, to me, a “curved space” is about as true or as meanignless a phrase as a “straight space” would be. Space is neither curved nor straight, but rather a kind of mental container to both curvature and straightness. The concepts of point, line (straight or curved) plane (straight or curved), volume, and the shapes and the solids and so on are NOT material objects, nor is space itself a material object at all, but all these concepts are essential to geometry and to all the hard sciences, which could not exist without them. And these concepts and objects are Eucledian. The sphere is an often-used object in metaphorical explanations of non-Eucledian geometries, but the sphere is still a Eucledian object, and it revolves in the mind with a perfectly straight diameter and a perfectly curved surface. Other geometries can be and have been superimposed on Eucledian geometry. But they haven’t replaced it. It’s still under them. At the very core of them. You could do nothing without those concepts. Taking out Eucledian geometry would be the equivalent of shutting down the human mind.
Absolutely Vertical
> On Thursday, February 14, 2013 4:03:34 PM UTC-5, Absolutely Vertical wrote:
>> On 2/14/2013 2:46 PM, tran...@gmail.com wrote:
> well, clearly that's an untenable situation. one should never have a
> pair of words that only refer to each other in a circular loop, because
> then you can't really distinguish one from the other.
>>
> =================================
> Well, since you apparently know the definition of curvature without recourse to straightness, go ahead and offer it.
even straightness that you're aware of. this is where education can
help, even if your mind cannot reproduce it in itself. (that's not a
slam. one should not expect every intelligent person to replicate all by
himself hundreds of years of thinking by very smart and dedicated
people. that's what education is for -- to provide guidance over ground
already conquered by hard fighting.)
if i might suggest some things to consider, just to seed your head.
let's consider some line in a plane which we don't know whether is
curved or straight, and we want to find a way to test which it is.
1. the metric approach: you might consider two points on the line and
ask: if i wiggle the line at all, does the distance between the points
as walked _along_ the line increase or decrease? if it always increases,
then i know the line was straight. if it sometimes increases or
sometimes decreases, depending on which way i wiggle it, then it is curved.
2. the reflection approach: if i take the line and make a copy of it and
flip the plane over that contains it and overlay it over the first, then
do the two lines completely overlap? if yes, then the line is straight.
3. the parallel transport approach: if i am on the line, then i can
certainly distinguish between a direction along the line at the point
where i'm standing and a direction perpendicular to it. i can then say
(in the case of a line in a plane) there is 'ahead' and 'left' and
'right'. then a line is straight if the trajectory of the line has no
displacement to the left or to the right after movement in the 'ahead'
direction, even infinitesimally.
there are others. the point is, there are concrete criteria available to
determine straightness which are much more usable and meaningful than
'not curved'. you just were never made aware of them, and so your
understanding of the concept of 'straight' is vague and shallow and
without much usable meaning. hopefully, i've at least given you a
launching point on how to think about it a little more deeply and clearly.
>
> Speaking of a �curved space� may be useful in a metaphorical sense to describe the behavior of matter in certain
> situations. It may be convenient to describe its behaviour AS IF it took place a �deformed� space. I am okay with
> that. The fact that something is convenient does not make it conceptually tenable. You may say that it�s wrong that
> are equally true depending on your point of reference. It is certainly much more convenient, however, to adopt a
actually, there is a difference. in the sun-centered view, then you can
account for all the motions of the bodies using a central-force law of
gravity like what newton proposed. in the earth-centered view, there is
no law that accounts for the orbits observed in that framework. this is
not a small difference.
>
> Conceptually, to me, a �curved space� is about as true or as meanignless a phrase as a �straight space� would be.
> The concepts of point, line (straight or curved) plane (straight or curved), volume, and the shapes and the solids
> and so on are NOT material objects, nor is space itself a material object at all, but all these concepts are essential
> to geometry and to all the hard sciences, which could not exist without them. And these concepts and objects are
> Eucledian. The sphere is an often-used object in metaphorical explanations of non-Eucledian geometries, but the sphere
> is still a Eucledian object, and it revolves in the mind with a perfectly straight diameter and a perfectly curved
> would be the equivalent of shutting down the human mind.
human mind. your statement is saying that if one removes euclidean
geometry, then understanding is hopeless. riemann would strenuously
disagree, as would thousands who followed. he showed that it is
perfectly possible to have real spaces where even the axioms of
euclidean geometry (in particular the fifth postulate) do not apply, and
yet there is a very sensible geometry that comes out of that that is not
euclidean.
the problem is, you only know of euclidean spaces and euclidean rules,
so the prospect of abandoning euclidean concepts leaves you with nothing
to hang on to. this is solved by finding out that you have more than one
option, even if you didn't know it.
you mention the surface of a ball being curved, which is something you
can visualize. but you embed that in a flat euclidean 3d space. and i
ask you if you can stretch your mind to visualize what would happen if
that 3d space were as curved as the 2d surface of the ball? riemann
certainly could, and i can. surprisingly, the universe doesn't go to
hell in a handbasket.
tran...@gmail.com
>
> > situations. It may be convenient to describe its behaviour AS IF it took place a “deformed” space. I am okay with
>
> > that. The fact that something is convenient does not make it conceptually tenable. You may say that it’s wrong that
> > the sun revolves around the earth, and right that the earth revolves around the sun. But in fact both statements
>
> > are equally true depending on your point of reference. It is certainly much more convenient, however, to adopt a
>
>
>
> actually, there is a difference. in the sun-centered view, then you can
>
> account for all the motions of the bodies using a central-force law of
>
> gravity like what newton proposed. in the earth-centered view, there is
>
> no law that accounts for the orbits observed in that framework. this is
>
> not a small difference.
>
>
>
> >
>
> > Space is neither curved nor straight, but rather a kind of mental container to both curvature and straightness.
>
> > The concepts of point, line (straight or curved) plane (straight or curved), volume, and the shapes and the solids
>
>
> can visualize. but you embed that in a flat euclidean 3d space. and i
>
> ask you if you can stretch your mind to visualize what would happen if
>
> that 3d space were as curved as the 2d surface of the ball? riemann
>
> certainly could, and i can. surprisingly, the universe doesn't go to
>
> hell in a handbasket.
Define space, explain what it is, or what it's made of. Then explain what exactly it is that "curves" in it. And with respect to what.
Absolutely Vertical
>
> You still haven't defined curvature. Nor have you defined space for that matter, but have no
> problem pontificating on your ability to see curved spaces embeded on more curved spaces
> apparently endlessly without saying with respect to what they are curved.
concept of 'straight', i offered you three common tests that would help
clarify it. i also pointed out that there are other criteria, also
interesting and useful. this should have prompted you to say to
yourself, 'well, i clearly have some things to learn, and perhaps i
should pause to find out how to learn more about them.' instead, you
grumbled about what did not come on the rubber-coated spoon.
and since you are having difficulty seizing on that opportunity, i will
mention a search term 'intrinsic curvature' that you can use to find out
how curvature can be defined without respect to anything else, let alone
straight.
to guide your eye, let me point out just three ways you can test for the
intrinsic curvature of a 2d space without stepping out of the surface to
see it in the embedding space at all.
first, now that we have a definition of straight, make three line
segments _in_ the surface that satisfy any of the operational
definitions of straight (the metric approach, the reflection approach,
the parallel transport approach) and have them be arranged so they meet
at three corners. (in a flat surface, we would call that a triangle.) if
there is no intrinsic curvature to the surface, the sum of the interior
angles will be 180 degrees. if there is intrinsic curvature the sum will
be something other than 180 degrees.
second, choose a point on the surface and then make a figure consisting
of all points equidistant (as measured on the surface) from the point.
call that distance r. on a surface with no intrinsic curvature, the
ratio of the circumference of that circle to the radius will be 2*pi. if
there is intrinsic curvature, then the ratio will be something else.
third, choose a straight line and point not on the line, both in the
surface. if the surface has no curvature, then there will be one and
only one straight line in the surface through the point that also never
intersects the first line. (this is euclid's fifth axiom.) if the
surface has curvature, then there may be more than one such line or no
lines at all.
you'll find that the geometry that describes intrinsic curvature is
quite interesting, if only you will have some courage and motivation to
pursue it.
mpc755
> On Monday, September 8, 2003 9:36:22 AM UTC-4, kenseto wrote:
nature as the state of displacement of the aether.
Tom Roberts
> What is referred to as the curvature of spacetime physically exists in
> nature as the state of displacement of the aether.
freedom per point in the manifold, while curvature is specified by the Riemann
tensor with 20 degrees of freedom per point. Those are wildly incommensurate.
Find another hobby. One you have some hope of understanding, as physics
certainly isn't working for you.
Tom Roberts
mpc755
has mass.
'Galactic Pile-Up May Point to Mysterious New Dark Force in the
Universe'
http://www.wired.com/wiredscience/2013/01/musket-ball-dark-force/
"The reason this is strange is that dark matter is thought to barely
interact with itself. The dark matter should just coast through itself
and move at the same speed as the hardly interacting galaxies.
Instead, it looks like the dark matter is crashing into something —
perhaps itself – and slowing down faster than the galaxies are. But
this would require the dark matter to be able to interact with itself
in a completely new an unexpected way, a “dark force” that affects
only dark matter."
It's not a new force. It's the aether displaced by each of the galaxy
clusters interacting analogous to the bow waves of two boats which
pass by each other.
There is no such thing as non-baryonic dark matter anchored to matter.
Matter moves through and displaces the aether.
The Milky Way's halo is what is referred to as the curvature of
spacetime.
The Milky Way's halo is the state of displacement of the aether.
Tom Roberts
> How do you define curvature without recourse to straightness?
opposite is not "straight", but rather is FLAT -- a zero Riemann tensor. because
"curvature" applies to the manifold, not to lines or trajectories.
> The best we can do is define straighness as absence of curvature,
apply to everybody. A little STUDY would teach you that.
> Both [curvature and straicht] are readily understood concepts in
> eucledian geometry.
But that applies to LINES, not to MANIFOLDS, which is really the subject of this
thread. And curved manifolds are by definition NON-Euclidean geometry. You need
to expand your imagination and horizons.
> They need no corroboration because they are mental
> entities. My mental lines are perfectly straight by definition. Concpts
> established by definition need no physical corroboration. The fact I cannot
> prove the edge of this table is straight is irrelevant. Eucledian geometry
> does not deal with physical objects.
distinction clearly in mind. It avoids the confusion you display here.
> I’ve already said that I consider space an inherent mental faculty. Not a
> tangible part of reality, and maybe not a part of reality at all except to
> the extent that mental intuitions are part of reality.
> More fruitful would be for you to offer a definition of space so we know what
> you understand by it.
objects in the world.
More to the point, spaceTIME is a model of the spatio-temporal relationships
among all possible locations at all possible times, for all objects in the
world. It is curvature of spaceTIME that is important in GR.
> Once we know that, explain how you can conceive of a
> space where straighness has been ejected, if it ever existed, and curvature
> is the only tenant.
line. Note the difference in concepts to which "curved" and "straight" apply
here -- manifold and line.
> If straightness is out, then the curvature is curved with respect to what
> exactly?
and definitive statement without reference to anything else.
Tom Roberts
Tom Roberts
> Speaking of a “curved space” may be useful in a metaphorical sense to
> describe the behavior of matter in certain situations.
"metaphorical" at all, this is from the technical vocabulary and has a very
specific meaning: the Riemann curvature tensor is not zero.
> It may be convenient
> to describe its behaviour AS IF it took place a “deformed” space.
"deformed", CURVED. Not "as if", actual.
> Conceptually, to me, a “curved space” is about as true or as meanignless a
> phrase as a “straight space” would be.
try to understand GR without it.
> Space is neither curved nor straight,
> but rather a kind of mental container to both curvature and straightness.
of the model, not the world. The entire model is a mental construct. And a given
manifold is indeed either curved or straight (Riemann != 0 or Riemann == 0).
Tom Roberts
mpc755
http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html
"According to the general theory of relativity space without ether is
unthinkable"
"the state of the [ether] is at every place determined by connections
with the matter and the state of the ether in neighbouring places"
The PHYSICAL state of the aether at every place determined by its
PHYSICAL connections with the matter and the PHYSICAL state of the
aether in neighboring places is the state of displacement of the
aether.
Curved spacetime is the state of displacement of the aether.
Tom Roberts
> Curved spacetime is the state of displacement of the aether.
understanding the devastating implications this has on any theory claiming that
aether is the cause of gravitational phenomena.
In GR, the curvature of spacetime is described by the Riemann curvature tensor,
which has 20 degrees of freedom at every point in the manifold. An "aether
displacement" would be a vector field with only 4 degrees of freedom per point.
That is insufficient to describe basic gravitational phenomena, such as tidal
forces, not to mention more subtle phenomena such as frame dragging.
So your "theory" is DEAD -- solidly refuted by basic observations.
Rather than repeatedly posting nonsense to the 'net, you should STUDY and
actually LEARN something about the subject. You have no hope of formulating
anything useful about physics without understanding the experiments that have
been performed; IGNORANCE like yours is not a basis for science, and your
rantings and ravings are useless. Or, as I said before, find some other hobby
more suited to your abilities.
And quoting one paper he read at a conference DEDICATED TO AETHER
does not mean Einstein actually "believed" in an aether. Indeed,
NONE of his theories contain one, which is solid proof that he
did not.
Tom Roberts
mpc755
"It is ironic that Einstein's most creative work, the general theory
of relativity, should boil down to conceptualizing space as a medium
when his original premise [in special relativity] was that no such
medium existed [..] The word 'ether' has extremely negative
connotations in theoretical physics because of its past association
with opposition to relativity. This is unfortunate because, stripped
of these connotations, it rather nicely captures the way most
physicists actually think about the vacuum. . . . Relativity actually
says nothing about the existence or nonexistence of matter pervading
the universe, only that any such matter must have relativistic
symmetry. [..] It turns out that such matter exists. About the time
relativity was becoming accepted, studies of radioactivity began
showing that the empty vacuum of space had spectroscopic structure
similar to that of ordinary quantum solids and fluids. Subsequent
studies with large particle accelerators have now led us to understand
that space is more like a piece of window glass than ideal Newtonian
emptiness. It is filled with 'stuff' that is normally transparent but
can be made visible by hitting it sufficiently hard to knock out a
part. The modern concept of the vacuum of space, confirmed every day
by experiment, is a relativistic ether. But we do not call it this
because it is taboo." - Robert B. Laughlin, Nobel Laureate in Physics,
endowed chair in physics, Stanford University
"According to the general theory of relativity space without ether is
of light, but also no possibility of existence for standards of space
and time (measuring-rods and clocks), nor therefore any space-time
intervals in the physical sense." - Albert Einstein
The relativistic ether referred to by Laughlin is the ether which
propagates light referred to by Einstein
Ryan Scott
>> It may be convenient to describe its behaviour AS IF it took place a
>> “deformed” space.
>
> GR goes further and models the world as a curved spacetime manifold. Not
> "deformed", CURVED. Not "as if", actual.
curved;
actually deformed sounds more appropriate, since curved space(time)
sounds quite stoopid, just to say the least
Ryan Scott
> In a curved manifold (i.e. Riemann != 0), there is no such thing as a
> straight line. Note the difference in concepts to which "curved" and
> "straight" apply here -- manifold and line.
Ryan Scott
> Except that "displacement of the aether" is a vector field with 4
> degrees of freedom per point in the manifold, while curvature is
> specified by the Riemann tensor with 20 degrees of freedom per point.
> Those are wildly incommensurate.
your 20 !? are there indexes that not run from 0 to 3 (or 1 to 4)? are
they reduced, simplified??
regards
Ryan Scott
> Except that "displacement of the aether" is a vector field with 4
> degrees of freedom per point in the manifold, while curvature is
> specified by the Riemann tensor with 20 degrees of freedom per point.
> Those are wildly incommensurate.
are there indexes that do not run from 0 to 3 (or 1 to 4) ? reduced,
simplified, how??
regards
tran...@gmail.com
Ok, let me throw some thoughts at this notion of a curved space. If I read you right, a space where the Riemann tensor is different from zero, is said to be intrinsically curved, and this means no straight lines are possible. The straightest possible line in that space would still be an arc. A way to illustrate this might be to say that, in such a space, the shortest path for any physical entity to be displaced from any point A to any point B is still an arc.
Fine. I understand that matter is prevented from taking a straighter path than this arc. But how about we forget what matter can or cannot do, and ask ourselves what is the shortest path between two points, period. Would it still be the same arc?
If so, it would seem that this arc has no chord. Or this arc is simultaneously its own chord.
In what sense can a line form an arc that lacks a chord? Can an arc be its own chord and still be thought of as an arc?
This is where my mind gets stuck and where the question “with respect to what” inevitably pops up. You insist that if a space is “intrinsically” curved, this curviness needs no reference or comparison to straightness or flatness in order to be declared curved. But then how the hell do you know it is curved? What is the meaning of “curved” in this sense. Again, forget about what matter can or cannot do in that environment. How is it that the arc is somehow flattened into its own chord and yet retains its archness? Its archness without a chord.
I consider this notion of chordless arcs to be semantic nonsense. Waving the word “intrinsically” does not help. The surface of a sphere is intrinsically curved, but points along it can still be linked by secants. In your model, the surface allows no such secants under itself because the surface is simultaneously flat but yet curved. And its curviness needs no reference to any flatness in order to call itself curved.
Really? It seems to me the reference is needed, else the word “curved” is devoid of meaning. At the very least, you need to mentally smuggle the notion of flatness into your model to keep calling it “curved”. And you do smuggle it in there, though you maintain you don’t.
altergnostic
sense in stating that the shortest path between two points is not a
straight line. This may be the case when describing tge possible routes on
the surface of a sphere, but the chord is still there.
To get rid of the chord is not to get rid of straight lines, it is to get
rid of curvature so that the chord has no place left to exist - the arc
replaces it completely by becoming the straight line itself.
If the frame is curved, one may say that there's no reason that the arc
described by AB demands a chord, but the curvature of the frame itself
does. If the axis are curved with no reference to straight lines, you can't
reproduce them accurately. To reproduce a circle we need to know the
radius, which is a straight line. If one defined the radius as a curved
entity, with no reference to straight lines, you can't reproduce the same
curvature accurately.
In conclusion, straight lines are more fundamental then curves because of
their dimensions. You can't represent a curve in one dimension. If one
defines a dimension as already curved, then one can always decompose the
curvature of such dimension into an euclidean set if coordinates in 2D and
no less. It is only impossible to do so by defining the operation as
forbidden, which is proof by itself that such operation is fundamentally
allowed.
Dirk Van de moortel
> On Friday, February 15, 2013 1:16:25 AM UTC-5, tjrob137 wrote:
>> On 2/14/13 2/14/13 2:46 PM, tran...@gmail.com wrote:
>>
>> It is intrinsic, and not "with respect to" anything. "Riemann != 0"
>> is a clear and definitive statement without reference to anything
>> else.
>>
>> Tom Roberts
> ------------------------------------
> Ok, let me throw some thoughts at this notion of a curved space. If I
> read you right, a space where the Riemann tensor is different from
> zero, is said to be intrinsically curved, and this means no straight
> lines are possible.
> The straightest possible line in that space would
> still be an arc.
"straight line". It is a just name. No reason to be afraid of names.
> A way to illustrate this might be to say that, in
> such a space, the shortest path for any physical entity to be
> displaced from any point A to any point B is still an arc.
>
> Fine. I understand that matter is prevented from taking a straighter
> path than this arc.
> But how about we forget what matter can or cannot
> do, and ask ourselves what is the shortest path between two points,
> period.
> Would it still be the same arc?
>
> If so, it would seem that this arc has no chord. Or this arc is
> simultaneously its own chord.
not coincide with the straight line, is longer than the straight line.
>
> In what sense can a line form an arc that lacks a chord? Can an arc
> be its own chord and still be thought of as an arc?
>
> This is where my mind gets stuck and where the question “with respect
> to what” inevitably pops up.
measuring rod.
> You insist that if a space is
> “intrinsically” curved, this curviness needs no reference or
> comparison to straightness or flatness in order to be declared
> curved. But then how the hell do you know it is curved?
they sum to 180 degrees, or less, or more.
> What is the
> meaning of “curved” in this sense.
curved.
> Again, forget about what matter
> can or cannot do in that environment. How is it that the arc is
> somehow flattened into its own chord and yet retains its archness?
> Its archness without a chord.
>
> I consider this notion of chordless arcs to be semantic nonsense.
> Waving the word “intrinsically” does not help. The surface of a
> sphere is intrinsically curved, but points along it can still be
> linked by secants. In your model, the surface allows no such secants
> under itself because the surface is simultaneously flat but yet
> curved. And its curviness needs no reference to any flatness in order
> to call itself curved.
>
> Really? It seems to me the reference is needed, else the word
> “curved” is devoid of meaning. At the very least, you need to
> mentally smuggle the notion of flatness into your model to keep
> calling it “curved”. And you do smuggle it in there, though you
> maintain you don’t.
degrees for their angles. No smuggling involved.
Dirk Vdm
Giovano di Bacco
> "Straight lines" are defined as lines with the shortest measured length.
the path along a light beam???
lets say is true, where would you go ahead to measure with your
meterstick, since you dont know it just by following the path of light
tran...@gmail.com
-----------------------
I like the way you put it. Particularly your conclusion:
"You can't represent a curve in one dimension. If one defines a dimension as already curved, then one can always decompose the curvature of such dimension into an euclidean set if coordinates in 2D and no less. It is only impossible to do so by defining the operation as forbidden, which is proof by itself that such operation is fundamentally allowed."
Dirk Van de moortel
with your meter stick. The shortest path you can find, is CALLED
the "straight path". That is the path light would follow.
Dirk Vdm
mpc755
The question is what curves? The question is what do particles of
matter physically curve?
There should be a place in physics for discussing what actually occurs
physically in nature beyond the geometrical representation of curved
spacetime.
Physics is now trying to invent a 'new dark force' in order to not
understand space itself has mass.
'Galactic Pile-Up May Point to Mysterious New Dark Force in the
Universe'
http://www.wired.com/wiredscience/2013/01/musket-ball-dark-force/
"The reason this is strange is that dark matter is thought to barely
interact with itself. The dark matter should just coast through itself
and move at the same speed as the hardly interacting galaxies.
Instead, it looks like the dark matter is crashing into something —
perhaps itself – and slowing down faster than the galaxies are. But
this would require the dark matter to be able to interact with itself
in a completely new an unexpected way, a “dark force” that affects
only dark matter."
with space itself which is displaced by each of the galaxy clusters
other.
particles of matter which exist in it and move through it.
The geometrical representation of curved spacetime actually physically
exists in nature as the state of displacement of the aether.
There is no such thing as non-baryonic dark matter traveling with
The Milky Way's halo is what is referred to as the curvature of
spacetime.
A moving particle physically displaces the mass associated with space
itself. A moving particle has an associated wave in space. In a double
slit experiment the particle travels through a single slit and the
associated wave in space passes through both.
Giovano di Bacco
mpc755
"a "field" in physics may be envisioned as if space were filled with
interconnected vibrating balls and springs, and the strength of the
field can be visualized as the displacement of a ball from its rest
position"
A 'field' in physics is space filled with aether and the strength of
the field is the displacement of the aether from its rest position.
Each of the plates in the Casimir effect displace the aether. The
displaced aether which exists between the plates is pushing back
toward each of the plates which causes the force associated with the
aether displaced by each of the plates which exists between the plates
to offset. This aether is more at rest than the aether which is
displaced by the plates which encompasses the plates. The reduced
force associated with the aether which exists between the plates along
with the displaced aether which encompasses the plates which is
pushing back and exerting inward pressure toward the plates causes the
plates to be forced together.
What occurs physically in nature in the Casimir effect is the same
phenomenon as gravity.
Photons from distant stars which curve as the pass by the Sun as the
head toward the Earth are following the path of least resistance.
The aether connected to and neighboring the Sun is displaced by Sun.
The strength of the field is the displacement of the aether from its
rest position. The closer to the Sun the greater the displacement the
stronger the field.
Photons don't 'fly off' because the aether which is further away from
the Sun than the path the photon travels is pushing back and exerting
inward pressure toward the Sun.
So, to answer your question, there is a straighter line from the
distant star to the Earth than the path the photon travels but the
strength of the field associated with the aether displaced by the Sun
keeps the photon from traveling this path.
Giovano di Bacco
> On Feb 16, 8:47 am, Giovano di Bacco <gdb...@gmail.com> wrote:
>> Dirk Van de moortel wrote:
>>
>> > "Straight lines" are defined as lines with the shortest measured
>> > length.
>>
>> are you just telling that i can get a shorter distance by NOT following
>> the path along a light beam???
>>
>> lets say is true, where would you go ahead to measure with your
>> meterstick, since you dont know it just by following the path of light
>
> http://en.wikipedia.org/wiki/Casimir_effect#Vacuum_energy
mpc755
paparios
T.M. Sommers
> On Friday, February 15, 2013 1:16:25 AM UTC-5, tjrob137 wrote:
>> On 2/14/13 2/14/13 2:46 PM, tran...@gmail.com wrote:
>>
>> It is intrinsic, and not "with respect to" anything. "Riemann != 0"
>> is a clear and definitive statement without reference to anything
>> else.
>>
>> Tom Roberts
> ------------------------------------
> Ok, let me throw some thoughts
> at this notion of a curved space. If I read you right, a space where
> the Riemann tensor is different from zero, is said to be
> intrinsically curved, and this means no straight lines are possible.
> The straightest possible line in that space would still be an arc. A
> way to illustrate this might be to say that, in such a space, the
> shortest path for any physical entity to be displaced from any point
> A to any point B is still an arc.
>
> Fine. I understand that matter is prevented from taking a straighter
> path than this arc. But how about we forget what matter can or cannot
> do, and ask ourselves what is the shortest path between two points,
> period. Would it still be the same arc?
>
> If so, it would seem that this arc has no chord. Or this arc is
> simultaneously its own chord.
>
> In what sense can a line form an arc that lacks a chord? Can an arc
> be its own chord and still be thought of as an arc?
higher-dimension flat space. That is not so.
--
T.M. Sommers -- ab2sb
Dirk Van de moortel
so what? He must stick to the rules and stay -- and think -- within the
space under discussion.
Dirk Vdm
mpc755
<dirkvandemoor...@hotspam.not> wrote:
> T.M. Sommers <tmsomme...@gmail.com> wrote:
> >> On Friday, February 15, 2013 1:16:25 AM UTC-5, tjrob137 wrote:
Tom Roberts
In particular, in regions with only weak gravity, such as in the solar system,
background Minkowski coordinates are possible, and straight lines are well
defined with respect to them -- a light beam does NOT follow such a straight
line. That is, in such a situation the null geodesics that light follows are NOT
uniform straight lines with speed c relative to the background coordinates. And
we can measure the difference (Pound & Rebka, Shapiro delay, light bent by the sun).
But in general in GR, "straight lines" are not well defined.
IOW: your GUESSES are wrong.
Tom Roberts
Tom Roberts
When projected onto a coordinate system, the Riemann curvature tensor has 4
indexes, and thus 4^4 = 256 components. But it satisfies several symmetries
among its various components that reduce the number of independent components to
20. For instance, it is anti-symmetric on two different pairs of indices, and
there are additional more subtle symmetries as well.
For the details, get a textbook and STUDY. Attempting to learn physics via "20
questions" is hopeless....
Tom Roberts
Giovano di Bacco
>> a light beam would define the straightness
>
> No, it doesn't. It defines a null GEODESIC, which is not really
> "straight".
and your answer seems wrong as well, since the GEODESIC is the geodesic
light ONLY, a rock would have another geodesic, yes?
>
> In particular, in regions with only weak gravity, such as in the solar
> system, background Minkowski coordinates are possible, and straight
> lines are well defined with respect to them -- a light beam does NOT
> follow such a straight line. That is, in such a situation the null
> geodesics that light follows are NOT uniform straight lines with speed c
> relative to the background coordinates. And we can measure the
> difference (Pound & Rebka, Shapiro delay, light bent by the sun).
that is finite and ovoid shaped
> But in general in GR, "straight lines" are not well defined.
>
> IOW: your GUESSES are wrong.
not my fault!
kenseto
> On 2/15/13 2/15/13 2:00 PM, Ryan Scott wrote:
>
> > Tom Roberts wrote:
> >> In a curved manifold (i.e. Riemann != 0), there is no such thing as a
> >> straight line. Note the difference in concepts to which "curved" and
> >> "straight" apply here -- manifold and line.
>
> > a light beam would define the straightness
>
> No, it doesn't. It defines a null GEODESIC, which is not really "straight".
Because different planets will have different curvature and thus
different speed of light.....right?
Ryan Scott
>> how come 20? a two indexes gives 4², three 4³, four gives 4⁴ etc are
>> there indexes that do not run from 0 to 3 (or 1 to 4) ? reduced,
>> simplified, how??
>
> I said "degrees of freedom", not "components".
> When projected onto a coordinate system, the Riemann curvature tensor
> has 4 indexes, and thus 4^4 = 256 components. But it satisfies several
physically, i cant visualize, can anybody??
> symmetries among its various components that reduce the number of
> independent components to 20. For instance, it is anti-symmetric on two
> different pairs of indices, and there are additional more subtle
> symmetries as well.
>
> For the details, get a textbook and STUDY. Attempting to learn physics
> via "20 questions" is hopeless....
should i buy such a book for free?
regards
Ryan Scott
>> > a light beam would define the straightness
>>
>> No, it doesn't. It defines a null GEODESIC, which is not really
>> "straight".
>
> In that case the speed of light is not a universal constant....why?
> Because different planets will have different curvature and thus
> different speed of light.....right?
Tom Roberts
> On Friday, February 15, 2013 1:16:25 AM UTC-5, tjrob137 wrote:
>> On 2/14/13 2/14/13 2:46 PM, tran...@gmail.com wrote:
>> It is intrinsic, and not "with respect to" anything. "Riemann != 0" is a
> notion of a curved space. If I read you right, a space where the Riemann
> tensor is different from zero, is said to be intrinsically curved, and this
> means no straight lines are possible.
> The straightest possible line in that
> space would still be an arc. A way to illustrate this might be to say that,
> in such a space, the shortest path for any physical entity to be displaced
> from any point A to any point B is still an arc.
is a geodesic. In Euclidean space, all geodesics are straight lines, and people
who don't know better confuse the two.
> Fine. I understand that matter is prevented from taking a straighter path
> than this arc.
> But how about we forget what matter can or cannot do, and ask
> ourselves what is the shortest path between two points, period. Would it
> still be the same arc?
But in relativity, the manifold is 4-d spaceTIME, and a massive object follows a
timelike path through spacetime; lines, on the other hand, are spacelike paths,
and no object can follow such a path. For a timelike geodesic, pairs of points
are separated by a timelike interval. For a line drawn on the floor, pairs of
points are separated by a spacelike interval.
A timelike interval can be measured by a clock present at both
events. A spacelike interval is measured by a ruler, not a clock.
> If so, it would seem that this arc has no chord. Or this arc is
> simultaneously its own chord.
connecting the two points with a straight line -- a chord. But in a curved
manifold, when the "arc" is a geodesic, the arc itself is the shortest distance
between the points; it is not really a "chord" for the same reason it is not a
"straight line" -- those concepts include aspects that simply are not possible
in a curved manifold.
> This is where my mind gets stuck and where the question “with respect to
> what” inevitably pops up. You insist that if a space is “intrinsically”
> curved, this curviness needs no reference or comparison to straightness or
> flatness in order to be declared curved. But then how the hell do you know it
> is curved? What is the meaning of “curved” in this sense.
it. That is a HUGE difference.
In Riemannian geometry, the special case is flat, not curved. In general there
are infinitely many possible manifolds, and only a subset of measure zero are flat.
> Again, forget about
> what matter can or cannot do in that environment. How is it that the arc is
> somehow flattened into its own chord and yet retains its archness? Its
> archness without a chord.
terminology.
> I consider this notion of chordless arcs to be semantic nonsense.
non-Euclidean geometry. Ditto for "straight line".
You need to learn how to generalize your Euclidean concepts to non-Euclidean
geometry.
> The surface of a sphere is intrinsically
> curved, but points along it can still be linked by secants.
there are no such "secants". In GR, the model of the universe is a curved
manifold, and you CANNOT "leave the universe" to draw such "secants".
> In your model,
> the surface allows no such secants under itself because the surface is
> simultaneously flat but yet curved. And its curviness needs no reference to
> any flatness in order to call itself curved.
non-Euclidean manifold. That is inappropriate. The problem is YOURS.
> Really? It seems to me the reference is needed, else the word “curved” is
> devoid of meaning. At the very least, you need to mentally smuggle the notion
> of flatness into your model to keep calling it “curved”. And you do smuggle
> it in there, though you maintain you don’t.
non-Euclidean manifolds.
Tom Roberts
Tom Roberts
> "Straight lines" are defined as lines with the shortest measured length.
are no straight lines, but there are geodesics.
>> The straightest possible line in that space would
>> still be an arc.
>
> Sure, an arc if you like, but this particular arc gets *called* the
> "straight line". It is a just name. No reason to be afraid of names.
word is geodesic. I have never before heard "arc" used in this context.
"Straight line" has connotations and implications that cannot
be met in a curved manifold. "Geodesic" avoids them.
>> A way to illustrate this might be to say that, in
>> such a space, the shortest path for any physical entity to be
>> displaced from any point A to any point B is still an arc.
>
> No, it is a staight line, by definition.
that's so ONLY in Euclidean manifolds. All Euclidean manifolds are flat, but not
all flat manifolds are Euclidean.
And in a SEMI-Riemannian manifold, such as those used in
relativity, even if the manifold is flat there are timelike
and null geodesics which do not meet the requirements of
"straight line"; they are not the shortest path between a
given pair of points, they are an EXTREMAL path, and in for
timelike paths they are the longest path (the inertial twin
ages the most between meetings). In some manifolds for some
pairs of points there can even be multiple geodesics between
the points.
> [... more of the same]
Tom Roberts
altergnostic
dimensions, why would you need excessive dimensions?
Furthermore, a curve is not 1D, no matter how you define it. If you say a
curve is one dimensional in a curved spacetime, like a geodesic, what you
have done is push the two or more dimensions necessary to describe it below
the frame of reference - which is itself curved. Then you can describe that
curved framework within euclidean space.
There's no way around this. You can only keep someone from performing this
operation by defining it as illegal for one reason or another, but
fundamentally, the geometry of any curve must be referenced to straight
axes, else the curvature remains undefined. Even if that curvature is the
curvature of the coordinate system being employed - you will need straight
one dimensional lines to define the curvature of such system of coordinates
just the same.
altergnostic
The question IS fundamentally mathematical, because there is not a single
measurement if curved space, of course. We have a model of spacetime that
operates on curved geometry to perform calculations, which predictions
agree with observations, but the model is purely geometrical. There is no
mechanism for curvature, nor a good definition of how matter curves the
field, and how is this curvature physically described in vacuo. What curves
is the math, not the aether.
Space(time) is not curved nor straight, it simply is. We describe it with
geometry, and a one dimensional line is more fundamental than a two
dimensional curve, and any curve can be decomposed into straight
(euclidean) lines. A curve with no chord is undefined. A curved frame with
no reference to straight axes has undefined curvature. You may assign
curvature to magnitudes of any chosen parameters, but geometrically a curve
can only be reproduced if you know how it relates to a straight line.
altergnostic
imagining a plane describing that chord, you can imagine a drill doing so.
Can you see it now?
There is no possible curve you can develop that can't be decomposed into
straight lines. More important, maybe, is the fact that there is no way you
can decompose a straight line into constituent curves, since there are
none. A line is 1D, a curve is 2D, that should be enough.
Dirk Van de moortel
> On 2/16/13 2/16/13 7:27 AM, Dirk Van de moortel wrote:
>> "Straight lines" are defined as lines with the shortest measured
>> length.
>
> That's in general a geodesic, not a "straight line". In a curved
> manifold there are no straight lines, but there are geodesics.
>
>
>>> The straightest possible line in that space would
>>> still be an arc.
>>
>> Sure, an arc if you like, but this particular arc gets *called* the
>> "straight line". It is a just name. No reason to be afraid of names.
>
> Only people who don't know better would call it a "straight line";
extension of the definition in Euclidean space.
> the correct word is geodesic.
> I have never before heard "arc" used in
> this context.
It's just silly a way of "transpan" to find something to mutter about.
> "Straight line" has connotations and implications that cannot
> be met in a curved manifold. "Geodesic" avoids them.
But for the nkind of dummies we have here, "straight" as a kitchen
table ersatz for "extremal" should do :--)
[...more of same]
Cheers,
Dirk Vdm
Giovano di Bacco
>> The straightest possible line in that space would still be an arc. A
>> way to illustrate this might be to say that,
>> in such a space, the shortest path for any physical entity to be
>> displaced from any point A to any point B is still an arc.
>
> The correct word is "geodesic": the shortest path between a given pair
> of points is a geodesic. In Euclidean space, all geodesics are straight
> lines, and people who don't know better confuse the two.
geodesic, while a photon its own as well
i suppose you choose the the photon geodesic as the standard geodesic,
yes?
Dirk Van de moortel
> paparios <papa...@gmail.com> wrote:
>> El sábado, 16 de febrero de 2013 10:16:05
>>
>> Try to fly a 747 through the chord of the New York to London arc!!
>
> Ridiculous. The point is that you can DRAW that chord. If you have
> trouble imagining a plane describing that chord, you can imagine a
> drill doing so. Can you see it now?
If the space is defined as the surface of a sphere, the shortest
possible line between two points is *called* a straight line.
Don't mutter about going from one point to the other through the
"body of the sphere". It is not allowed by the definition of the
space. Stay within the defined space.
How hard is it to listen to the definitions and stick with the rules?
When you have to find a checkmate in four moves in a chess problem,
you are supposed to stay within the space of the chess rules. Don't
mutter about checkmating in one move by smashing the black king
with a hammer.
How hard is it to listen to the definitions and stick with the rules?
How hard is it to stop being afraid?
How hard is it to stop muttering like a James Driscoll?
Dirk Vdm
Giovano di Bacco
>> The straightest possible line in that space would still be an arc. A
>> way to illustrate this might be to say that,
>> in such a space, the shortest path for any physical entity to be
>> displaced from any point A to any point B is still an arc.
>
> The correct word is "geodesic": the shortest path between a given pair
> of points is a geodesic. In Euclidean space, all geodesics are straight
> lines, and people who don't know better confuse the two.
then decrease exponentially;
arcs are parts of perfect circles, this is the reason why tensors are
used in relativity, yes?
T.M. Sommers
>>
>> You seem to be assuming that curved space must be embedded in a
>> higher-dimension flat space. That is not so.
>
> Quite the opposite. Curved space is embedded in a flat space of equal
> dimensions,
> why would you need excessive dimensions?
> Furthermore, a curve is not 1D, no matter how you define it.
curved space in a flat space.
> fundamentally, the geometry of any curve must be referenced to straight
> axes, else the curvature remains undefined.
Giovano di Bacco
> possible line between two points is *called* a straight line. Don't
> mutter about going from one point to the other through the "body of the
> sphere". It is not allowed by the definition of the space. Stay within
> the defined space.
user would know that since the surface is curved, by definition cant be
the shortest path, the principle of least action should apply
Tom Roberts
> Tom Roberts wrote:
>>> a light beam would define the straightness
>> No, it doesn't. It defines a null GEODESIC, which is not really
>> "straight".
>
> well, that was kinda question;
> and your answer seems wrong as well, since the GEODESIC is the geodesic
> light ONLY, a rock would have another geodesic, yes?
connotations that simply cannot be met in a curved manifold. So we say
"geodesic" instead of "straight line", to avoid them.
In the 4-d spacetime manifolds of relativity, there are three types of
geodesics: timelike, spacelike, and null; they are labeled by the type of
interval between pairs of points. Light follows a null geodesic, and massive
objects in freefall follow timelike geodesics. Different types of geodesics are
necessarily different; for example, a timelike geodesic and a spacelike geodesic
can intersect in at most a countable number of points.
>> In particular, in regions with only weak gravity, such as in the solar
>> system, background Minkowski coordinates are possible, and straight
>> lines are well defined with respect to them -- a light beam does NOT
>> follow such a straight line. That is, in such a situation the null
>> geodesics that light follows are NOT uniform straight lines with speed c
>> relative to the background coordinates. And we can measure the
>> difference (Pound & Rebka, Shapiro delay, light bent by the sun).
>
> this sounds like you admit a universal coordinate system, for an universe
> that is finite and ovoid shaped
you attempted to apply it outside that restriction.
Tom Roberts
mpc755
itself which has mass.
'Galactic Pile-Up May Point to Mysterious New Dark Force in the
Universe'
http://www.wired.com/wiredscience/2013/01/musket-ball-dark-force/
"The reason this is strange is that dark matter is thought to barely
interact with itself. The dark matter should just coast through itself
and move at the same speed as the hardly interacting galaxies.
Instead, it looks like the dark matter is crashing into something —
perhaps itself – and slowing down faster than the galaxies are. But
this would require the dark matter to be able to interact with itself
in a completely new an unexpected way, a “dark force” that affects
only dark matter."
pass by each other.
http://www.universetoday.com/95094/surprise-ibex-finds-no-bow-shock-outside-our-solar-system/
'“While bow shocks certainly exist ahead of many other stars, we’re
finding that our Sun’s interaction doesn’t reach the critical
threshold to form a shock,” said Dr. David McComas, principal
investigator of the IBEX mission, “so a wave is a more accurate
depiction of what’s happening ahead of our heliosphere — much like the
wave made by the bow of a boat as it glides through the water.”'
The wave ahead of our heliosphere is an aether displacement wave. This
is evidence of a moving 'particle', the solar system, having an
associated aether wave.
'Hubble Finds Ghostly Ring of Dark Matter'
http://www.nasa.gov/mission_pages/hubble/news/dark_matter_ring_feature.html
"Astronomers using NASA's Hubble Space Telescope got a first-hand view
of how dark matter behaves during a titanic collision between two
galaxy clusters. The wreck created a ripple of dark mater, which is
somewhat similar to a ripple formed in a pond when a rock hits the
water."
The 'pond' consists of aether. The moving 'particles' are the galaxy
clusters. The ripple is an aether displacement wave. The ripple is a
gravitational wave. This is also evidence of a moving 'particle', the
galaxy clusters, having an associated aether wave.
'Offset between dark matter and ordinary matter: evidence from a
sample of 38 lensing clusters of galaxies'
http://arxiv.org/PS_cache/arxiv/pdf/1004/1004.1475v1.pdf
"Our data strongly support the idea that the gravitational potential
in clusters is mainly due to a non-baryonic fluid, and any exotic
field in gravitational theory must resemble that of CDM fields very
closely."
The offset is due to the galaxy clusters moving through the aether.
The analogy is a submarine moving through the water. You are under
water. Two miles away from you are many lights. Moving between you and
the lights one mile away is a submarine. The submarine displaces the
water. The state of displacement of the water causes the center of the
lensing of the light propagating through the water to be offset from
the center of the submarine itself. The offset between the center of
the lensing of the light propagating through the water displaced by
the submarine and the center of the submarine itself is going to
remain the same as the submarine moves through the water. The
submarine continually displaces different regions of the water. The
state of the water connected to and neighboring the submarine remains
the same as the submarine moves through the water even though it is
not the same water the submarine continually displaces. This is what
is occurring physically in nature as the galaxy clusters move through
and displace the aether.
'Milky Way's halo more squished than spherical'
http://www.msnbc.msn.com/id/34735679/ns/technology_and_science-space/t/milky-ways-halo-more-squished-spherical/#.TjkpbmDmE2c
The Milky Way's halo is the state of displacement of the aether. The
matter which would form the Milky Way was moving as it displaced the
aether. The aether displaced perpendicular to the major direction of
motion became the majority force of the displaced aether and forced
the matter into the disk. This resulted in the angular momentum of the
matter. It is the aether which is displaced outward relative to the
plane of the angular momentum which exerts force toward the center of
the Milky Way. This force, along with the state of displacement of the
aether as determined by the angular momentum of the Milky Way, forced
the matter closer together which resulted in the displaced aether
looking like a squished beach ball. Aether displacement explains how
the Milky Way was created, how the disk and halo formed and why the
rotational speed can not be accounted for by the mass of the matter of
the Milky Way itself.
'NASA's Voyager Hits New Region at Solar System Edge'
http://www.nasa.gov/home/hqnews/2011/dec/HQ_11-402_AGU_Voyager.html
"Voyager is showing that what is outside is pushing back. ... Like
cars piling up at a clogged freeway off-ramp, the increased intensity
of the magnetic field shows that inward pressure from interstellar
space is compacting it."
It is not the particles of matter which exist in quantities less than
in any vacuum artifically created on Earth which are pushing back and
exerting inward pressure toward the solar system.
It is the aether, which the particles of matter exist in, which is the
interstellar medium. It is the aether which is displaced by the matter
the solar system consists of which is pushing back and exerting inward
pressure toward the solar system.
Dirk Van de moortel
Sharpen your mind by finding the mate in four.
Failing that, you're either a lazy bum, or a stupid git.
Dirk Vdm
altergnostic
euclidean one. All that is necessary is to redefine space as flat and apply
the curvature to any fundamental field upon it (such as an aether field, if
it didn't bother us so much). Actually, Einstein himself said that he could
not fully conceive GR without some notion of aether, since empty space was
always defined as having no properties, and a field that can be curved by
matter (experience change) is surely not devoid of physical properties,
with curvature being a property in itself, and maybe implying stretching,
shearing, motion, stress, etc.
In any case, you can't define the geometry of any specific curvature
without resorting to at least two straight axes.
T.M. Sommers
>
> a sphere surface implies 3d
Only if the 2-d surface is embedded in a 3-d space. It may be hard to
visualize such a surface not being so embedded, but that is a limit
imposed by our brains, not by mathematics.
Giovano di Bacco
>> this sounds like you admit a universal coordinate system, for an
>> universe that is finite and ovoid shaped
>
> READ WHAT I WROTE! I explicitly said "in regions with only weak
> gravity",
> and you attempted to apply it outside that restriction.
most of the universe has weak gravity anyway;
galaxies are rare points in that ovoid, and would not make much
difference anyway, also, the most of a galaxy contain weak regions as
well, yes?
mpc755
>
> A 'new dark force' is more speculative than understanding it is space
> itself which has mass.
>
> 'Galactic Pile-Up May Point to Mysterious New Dark Force in the
> Universe'http://www.wired.com/wiredscience/2013/01/musket-ball-dark-force/
>
> "The reason this is strange is that dark matter is thought to barely
> interact with itself. The dark matter should just coast through itself
> and move at the same speed as the hardly interacting galaxies.
> Instead, it looks like the dark matter is crashing into something —
> perhaps itself – and slowing down faster than the galaxies are. But
> this would require the dark matter to be able to interact with itself
> in a completely new an unexpected way, a “dark force” that affects
> only dark matter."
>
> It's not a new force. It's the aether displaced by each of the galaxy
> clusters interacting analogous to the bow waves of two boats which
> pass by each other.
>
> '“While bow shocks certainly exist ahead of many other stars, we’re
> finding that our Sun’s interaction doesn’t reach the critical
> threshold to form a shock,” said Dr. David McComas, principal
> investigator of the IBEX mission, “so a wave is a more accurate
> depiction of what’s happening ahead of our heliosphere — much like the
> wave made by the bow of a boat as it glides through the water.”'
>
> The wave ahead of our heliosphere is an aether displacement wave. This
> is evidence of a moving 'particle', the solar system, having an
> associated aether wave.
>
itself has mass.
It's what waves.
Giovano di Bacco
>> a sphere surface implies 3d
>
> Only if the 2-d surface is embedded in a 3-d space. It may be hard to
> visualize such a surface not being so embedded, but that is a limit
> imposed by our brains, not by mathematics.
Giovano di Bacco
path he know it must exist; he just put two and two together, yes?
Dirk Van de moortel
Giovano di Bacco
are you tryen to evade mistakes mister Dirk, yes?
altergnostic
analysing a curve.
But I understand your point. If a geodesic is defined as the shortest path
along curved space, there is no point in arguing otherwise... But I argue
against the validity of such definition, when applied to the physical
universe - and not restricted to the specific model at hand.
What I mean is that we have many flat and curved models of the universe,
which are problem-specific descriptions of the physics involved, but no
evidence that "the fabric of reality" (as is pop to say) is curved.
Actually, it can't be either curved or flat. It just is. We describe it as
we want. So, to answer "what curves", it is the geometry used in a model
that do the curving, not nature, and the definitions of such models forbid
us from looking at a geodesic from outside the curved system of coordinates
and from finding the chord, for instance.
But my point is that it isn't FUNDAMENTALLY impossible to describe the same
events in flat 3D space plus time. It may be practically or experimentally
impossible or not, as seems so far, but any curve IMPLIES a chord - even if
you are not allowed to find it. The chord would only be an impossibility if
the geodesic is not a curve - and I know that inside the model, it isn't,
the metric is - but one may always desire to look into the metric from
outside and try to describe the same phenomena without curved space. It
could be done with universal vector reversal, for example. As an example,
instead of defining gravity as an acceleration of bodies towards a central
mass, defining it as a 3D accelerating expansion of the central mass
(equivalence principle) - and do so for every other body and particle of
the universe, so all the scales and proportions remain the same. Then you
could revert back to euclidean space and all the interactions would be the
same.
Of course this is simplistic in the extreme, I am just pointing out that
curvature is not fundamental and not necessarily a true configuration of
the universe, but only an abstraction. So, again, what curves is the math,
and a purist can always leave the model and find the chord in flatland (be
it useful or not).
tran...@gmail.com
> If the space is defined as the surface of a sphere, the shortest
> possible line between two points is *called* a straight line.
> Don't mutter about going from one point to the other through the
> "body of the sphere". It is not allowed by the definition of the
> space. Stay within the defined space.
>