I was reading a book about physics and it states the following:

"What we consider to be a planet with its own gravitational field
moving around the sun in an orbit created by the gravitational
attraction of the sun, is actually a pronounced curvature of the
space-time continuum finding its easiest path through the continuum in
the vicinity of a more pronounced curvature of the continuum."

My question: is this correct? It sounds wrong to me. I thought that
the space-time continuum is only slightly curved near the sun, and
that this only slightly affects the orbit of the planets. The basic
classical physics/Newton's law of gravity approximates the orbits of
the planets and the effects of the curved space-time continuum is a
small correction, right? This explains why Mercury's perihelion moves
slightly, right?

"SynthDude" wrote in message
om...
I was reading a book about physics and it states the following:

"What we consider to be a planet with its own gravitational field
moving around the sun in an orbit created by the gravitational
attraction of the sun, is actually a pronounced curvature of the
space-time continuum finding its easiest path through the continuum in
the vicinity of a more pronounced curvature of the continuum."

My question: is this correct? It sounds wrong to me. I thought that
the space-time continuum is only slightly curved near the sun, and
that this only slightly affects the orbit of the planets. The basic
classical physics/Newton's law of gravity approximates the orbits of
the planets and the effects of the curved space-time continuum is a
small correction, right? This explains why Mercury's perihelion moves
slightly, right?

It is the curvature of spacetime that dictates the world line of an object.
"Mass tells spacetime how to curve. Spacetime tells mass how to move."
Kip Thorn

I was reading a book about physics and it states the following:

"What we consider to be a planet with its own gravitational field
moving around the sun in an orbit created by the gravitational
attraction of the sun, is actually a pronounced curvature of the
space-time continuum finding its easiest path through the continuum in
the vicinity of a more pronounced curvature of the continuum."

My question: is this correct? It sounds wrong to me. I thought that
the space-time continuum is only slightly curved near the sun, and
that this only slightly affects the orbit of the planets. The basic
classical physics/Newton's law of gravity approximates the orbits of
the planets and the effects of the curved space-time continuum is a
small correction, right? This explains why Mercury's perihelion moves
slightly, right?

In general relativity the curvature of space-time dictates the movement
of bodies like planets. So it leads to BOTH the elliptical orbits AND
the small perihelion correction. If you think that the perihelion
correction is caused by the space-time curvature, but the 'ellipticity'
of the orbits is caused by some Newtonian field, then you are mistaken
(and that is what I understand from your question). In the general
theory of relativity there is no longer any classical physics/Newton's
law of gravity.
So the curvature has to be large to make a planet move along a
non-straight curve, and not just small to cause only the tiny perihelion
movement.

--
M.vr.gr.
Dave
("d-dot-langers-at-wxs-dot-nl")

SynthDude wrote:

I was reading a book about physics and it states the following:

"What we consider to be a planet with its own gravitational field
moving around the sun in an orbit created by the gravitational
attraction of the sun, is actually a pronounced curvature of the
space-time continuum finding its easiest path through the continuum in
the vicinity of a more pronounced curvature of the continuum."

My question: is this correct? It sounds wrong to me. I thought that
the space-time continuum is only slightly curved near the sun, and
that this only slightly affects the orbit of the planets. The basic
classical physics/Newton's law of gravity approximates the orbits of
the planets and the effects of the curved space-time continuum is a
small correction, right? This explains why Mercury's perihelion moves
slightly, right?

Newtonian physics tacitly assumes lightspeed is infinite, which is
usually a pretty good approximation and wonderfully simplifies the
equations. General Relativity assumes lightspeed is finite, which is
a better approximation - though it does cause nasty computational
complexities.

The deformed rubber membrane model of gravitation is quite inadequate
except as a very gross approximation. If you accept the Equivalence
Principle as postulate then derive metric theories of gravitation with
spacetime curvaure, objects in gravitational fields pursue geodesic
trajetories in curved spacetime. Viewed in space this looks like the
orbits you see, complete with perihelion rotation and other minor
effects like frame dragging.

If you ignore the Equivalence Principle then drive affine theories of
gravitation and spacetime torsion, there are no geodesic paths.
Objects in gravitational fields are still predicted to give their
observed motions plus the elegant tweaks.

Metric and affine theories of gravitation, despite their huge
disparity in origin and mechanism, have an all but identical set of
predictions. Affine theoriess can be slightly richer than metric
theories. Affine theories as a class predict anomalies vs. metric
theories with

1) Physically spinning masses. Alas, tensile strength limits the
surface velocity of real world masses to about 100 miles/second for
micron-diameter single crystal diamond spheres in vacuum. This is
nowhere near 186,500 miles/second in whose neighborhood things would
be measurably interesting: For 100 miles/second, sqrt[1-(v^2/c^2)]=
0.9999999, which is to say "no effect above noise."

2) Spin-polarized masses (magnets). Alas, even if one couldo
create 100% manganese metal undecatuplet - the largest fraction of
electron spin to total mass in the Periodic Table, spin mass would
only be 0.00005 of total mass. Real world spin masses are ppm or
less, and would at best have a caclculated immeasureably small
associated anomaly.

3) Geometric parity test masses (identical composition;
non-superposable mirror image atomic structure along all three
coordinate axes; e.g., enantiomorphic single crystals of tellurium or
alpha-quartz). This experiment is doable on the cheap in existing
apparatus and is expected to have an easily measured anomaly.
Somebody should look.

http://www.mazepath.com/uncleal/qz.pdf
terse summary
http://www.mazepath.com/uncleal/eotvos.htm
the whole nine yards.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!

Dave Langers wrote in message ...
I was reading a book about physics and it states the following:

"What we consider to be a planet with its own gravitational field
moving around the sun in an orbit created by the gravitational
attraction of the sun, is actually a pronounced curvature of the
space-time continuum finding its easiest path through the continuum in
the vicinity of a more pronounced curvature of the continuum."

My question: is this correct? It sounds wrong to me. I thought that
the space-time continuum is only slightly curved near the sun, and
that this only slightly affects the orbit of the planets. The basic
classical physics/Newton's law of gravity approximates the orbits of
the planets and the effects of the curved space-time continuum is a
small correction, right? This explains why Mercury's perihelion moves
slightly, right?

In general relativity the curvature of space-time dictates the movement
of bodies like planets. So it leads to BOTH the elliptical orbits AND
the small perihelion correction. If you think that the perihelion
correction is caused by the space-time curvature, but the 'ellipticity'
of the orbits is caused by some Newtonian field, then you are mistaken
(and that is what I understand from your question). In the general
theory of relativity there is no longer any classical physics/Newton's
law of gravity.
So the curvature has to be large to make a planet move along a
non-straight curve, and not just small to cause only the tiny perihelion
movement.

Ok. I think I can accept that the orbit of the earth is simply caused
by the curvature of space-time. But could you please verify/refute
the following statements/lines of reasoning:

1. From my understanding, we can describe the orbit of the earth
around the sun by saying that the earth is freely falling through
space, following the curvature of space-time, which happens to be
caused by the sun. The planets in the solar system also cause some
curvature, but these curvature effects are minimal compared to the
curvature caused by the sun's mass.

2. If the earth was moving at its current speed through the middle of
empty space instead of its current position in our solar system, then
there would be (approximately) no curvature of space-time near the
earth, and therefore the earth would be falling through FLAT space in
a STRAIGHT line. It would NOT be in any sort of orbit, and therefore
it would NEVER be in the same place twice. However, we know that the
earth falls through CURVED space. It DOES orbit the sun, and it DOES
come back to the same place each year (approximately).

3. Isn't it true that light also follows the curvature of space-time?
If that were true, then wouldn't it follow logically that a light
emitted from earth in the direction of the earth's orbital path would
follow the same exact path of the earth's orbit around the sun? And
if that were the case, wouldn't it be possible, in theory, to shine a
REALLY bright light from earth in the direction of the earth's orbital
path, and this light would be seen by people on the other side of the
earth, once the light completed its orbit around the sun?!?!

Mike

SynthDude wrote:

1. From my understanding, we can describe the orbit of the earth
around the sun by saying that the earth is freely falling through
space, following the curvature of space-time, which happens to be
caused by the sun. The planets in the solar system also cause some
curvature, but these curvature effects are minimal compared to the
curvature caused by the sun's mass.

Right. (It's important that you wrote ``curvature of space-time''
and not just ``curvature of space.'')

2. If the earth was moving at its current speed through the middle of
empty space instead of its current position in our solar system, then
there would be (approximately) no curvature of space-time near the
earth, and therefore the earth would be falling through FLAT space in
a STRAIGHT line. It would NOT be in any sort of orbit, and therefore
it would NEVER be in the same place twice. However, we know that the
earth falls through CURVED space. It DOES orbit the sun, and it DOES
come back to the same place each year (approximately).

Not quite as right -- the earth moves through curved spacetime, not
just curved space.

3. Isn't it true that light also follows the curvature of space-time?

Yes.

If that were true, then wouldn't it follow logically that a light
emitted from earth in the direction of the earth's orbital path would
follow the same exact path of the earth's orbit around the sun?

No. Earth and the light may have the same initial directions in
space, but they have different initial directions in spacetime,
because they have different velocities. Two lines in a curved
spacetime that start out in different directions won't trace out the
same path, just as two great circles on the surface of the earth won't
coincide if they start out from the same point in different directions.

If it's not obvious that different initial velocities mean different
directions in spacetime, just draw an ordinary flat spacetime
diagram. An object at rest will be described by a straight line
perpendicular to the x axis and parallel to the t axis. An object
moving at the speed of light will be described by a straight line
at 45 degrees to the axes (assuming you're using units c=1). The
two lines are both straight -- they're both ``shortest lines'' in the
spacetime geometry -- but they are clearly different.

Your mistake comes from confusing ``following the curvature of
spacetime'' and ``following the curvature of space.'' If only the
curvature of space mattered, you might argue that light and the
earth should follow the same path through space, just at different
speeds. But general relativity requires you to think about paths
in spacetime, not just paths in space.

Steve Carlip

(SynthDude) wrote:
I was reading a book about physics and it states the following:

"What we consider to be a planet with its own gravitational field
moving around the sun in an orbit created by the gravitational
attraction of the sun, is actually a pronounced curvature of the
space-time continuum finding its easiest path through the continuum in
the vicinity of a more pronounced curvature of the continuum."

My question: is this correct?

Misleading. Gravitation is mostly a curvature in time, not space.
Curved time, in 3-dimensional language, means spontaneous
acceleration.

If it were Newtonian Physics, it would be entirely a matter of
curvature in time, not just mostly. The 3-dimensional equal-time
cross sections are still flat 3-D Euclidean spaces.

the effects of the curved space-time continuum is a small correction,
right? This explains why Mercury's perihelion moves slightly, right?

The curvature in space is negligible and has only minor effects
and is rightly considered as a Relativistic correction over
what the corresponding Newtonian gravity theory would say. The
curvature in space only has significant bearing for things moving
fast or in strong gravity fields.

You can answer the question easily for yourself. The equations
of motion for an object of mass m (ignoring its backreaction on
spacetime) is given by:
m c^2 d(x^a)/ds = sum g^{ab} p_b
d(p_a)/ds = @U/@x^a
@ is ASCII for the curly partial d operator
p_0,p_1,p_2,p_3 = components of particle's 4-momentum (E,-p)
U = 1/2 sum (g^{ab} p_a p_b/m) = gravitational potential
where
s = particle's clock time
x^0 = t, (x^1,x^2,x^3) = spatial coordinates

The dominant component of p is p_0 = E; the dominant contribution
to the gravitational potential U at ordinary speeds is therefore
from g^{00}, the purely temporal component of the gravitational
field. The rest is just minor corrections.

wrote:
Not quite as right -- the earth moves through curved spacetime, not
just curved space.

Things don't move through spacetime. They ARE in spacetime;
particularly: they are worldlines.

Motion is 3-dimensional language. There is no motion in 4
dimensions.

Alfred Einstead wrote:

wrote:
Not quite as right -- the earth moves through curved spacetime, not
just curved space.

Things don't move through spacetime. They ARE in spacetime;
particularly: they are worldlines.

Motion is 3-dimensional language. There is no motion in 4
dimensions.



Thank you for saying that. I never thought that I'd see the day when I
wanted to tell Carlip to get a real concept.

wrote in message ...
SynthDude wrote:

1. From my understanding, we can describe the orbit of the earth
around the sun by saying that the earth is freely falling through
space, following the curvature of space-time, which happens to be
caused by the sun. The planets in the solar system also cause some
curvature, but these curvature effects are minimal compared to the
curvature caused by the sun's mass.

Right. (It's important that you wrote ``curvature of space-time''
and not just ``curvature of space.'')

2. If the earth was moving at its current speed through the middle of
empty space instead of its current position in our solar system, then
there would be (approximately) no curvature of space-time near the
earth, and therefore the earth would be falling through FLAT space in
a STRAIGHT line. It would NOT be in any sort of orbit, and therefore
it would NEVER be in the same place twice. However, we know that the
earth falls through CURVED space. It DOES orbit the sun, and it DOES
come back to the same place each year (approximately).

Not quite as right -- the earth moves through curved spacetime, not
just curved space.

3. Isn't it true that light also follows the curvature of space-time?

Yes.

If that were true, then wouldn't it follow logically that a light
emitted from earth in the direction of the earth's orbital path would
follow the same exact path of the earth's orbit around the sun?

No. Earth and the light may have the same initial directions in
space, but they have different initial directions in spacetime,
because they have different velocities. Two lines in a curved
spacetime that start out in different directions won't trace out the
same path, just as two great circles on the surface of the earth won't
coincide if they start out from the same point in different directions.

If it's not obvious that different initial velocities mean different
directions in spacetime, just draw an ordinary flat spacetime
diagram. An object at rest will be described by a straight line
perpendicular to the x axis and parallel to the t axis. An object
moving at the speed of light will be described by a straight line
at 45 degrees to the axes (assuming you're using units c=1). The
two lines are both straight -- they're both ``shortest lines'' in the
spacetime geometry -- but they are clearly different.

Your mistake comes from confusing ``following the curvature of
spacetime'' and ``following the curvature of space.'' If only the
curvature of space mattered, you might argue that light and the
earth should follow the same path through space, just at different
speeds. But general relativity requires you to think about paths
in spacetime, not just paths in space.

Steve Carlip


A-HA! I think get it now.

Ok, to wrap things up (hopefully!), can somebody verify/refute THESE
statements?:

Special Relativity: When an object is moving close to the speed of
light (e.g. theoretical spaceship crusing at 99% speed of light, built
by a highly advanced alien civilization?), we must use special
relativity/lorentz transformations in order to make accurate
calculations of its motion. However, for an object that is moving at
a slow speed (e.g. a car going 55 mph), we can use classical physics
(i.e. distance = velocity x time) to make good approximate
calculations.

General Relativity: When an object is orbiting another object with a
huge mass (e.g. an earth-like object orbiting around a massive black
hole), we must use general relativity in order to make accurate
calculations of its motion. However, for an object that is orbiting
another object that is not too big (e.g. our earth orbiting the sun),
we can use classical physics (i.e. Newton's law of gravity) to make
good approximate calculations.

In both cases, the classical physics model was REPLACED by a new
theory (special relativity/general relativity) that covers ALL
scenarios. But in both cases, we can still use classical physics to
make calculations for "non-extreme" scenarios (e.g. car going 55 mph,
earth orbiting the sun).

Mike