Re: Gravity, space-time, and black holes?
- From: NoEinstein <noeinstein@xxxxxxxxxxxxx>
- Date: Fri, 07 Sep 2007 16:07:05 -0700
On Sep 7, 6:15 am, Jim Black <trams...@xxxxxxxxx> wrote:
On Fri, 07 Sep 2007 04:30:00 -0000, thomat65 wrote:
Hello all.
Just wondering if anyone could clear up my confusion about gravity and
other jazz.
I understand that gravity is the result of relative "distortion" of
space-time,
If by "distortion," you mean that there are normal distances and times
between events which have been stretched and/or compressed by gravitation,
then no, that is not how general relativity, Einstein's theory of
gravitation, describes space-time. It is often described that way in the
popular press because it's easier than teaching the readers general
relativity.
but I'm not quite sure how that ends up making things
(matter, light, w/e) change their paths in space as they travel
through space-time.
Relativity models time as a fourth dimension of an modified version of the
concept of space that we call spacetime. In this spacetime, nothing is
changing. Your birth, every event in your life, and your death all exist
at different points along a line in spacetime, which we call your
worldline.
Newton's first law states that when no external forces on an object, then
if it is at rest, it will remain at rest, and if it is in motion, it will
continue to move along a straight line with constant velocity. We need to
reformulate this law as a statement about the worldlines of objects that
have no external forces acting on them. So let's start with a simple case,
a train car that can move forward and backward along a straight railroad.
To simplify things, we'll put the railroad in space, where there is no
gravity. We can draw on a piece of paper the two-dimensional cross-section
of spacetime that contains the railroad. This type of diagram is called a
spacetime diagram. We can draw the train's worldline by plotting the
distance the train has gone down the track as the x coordinate, and the
time as the y coordinate. If the net external force on the train is zero,
the x and y coordinates will satisfy the equation
x = v*y + x0
where x0 is the train's position at time zero, and v is the constant
velocity of the train. If you plot this equation, you get a straight line.
So the spacetime version of Newton's first law is that where there are no
external forces on an object, the worldline of the object is straight.
In highschool we learn a system of axioms about points, lines, and planes
called Euclidean geometry. But Euclidean geometry is not the only possible
geometry. For example, one of the theorems you can prove from the axioms
of Euclidean geometry is that the sum of the angles in a triangle is 180
degrees. But we can construct geometries in which this theorem isn't true.
For example, we can construct an alternate version of plane geometry by
using the points on a sphere as our points, and the great circles on the
same sphere as our lines. Then in the triangle formed by drawing a line
from the north pole down to the equator, going east 90 degrees, and coming
back up to the north pole, the angles add up to 270 degrees. We can
formulate this geometry without ever referring to a third dimension; we
just have to accept that the lines follow different rules than the ones
we're used to.
In general relativity, gravity is not modelled as a force. A freely
falling object has no external forces acting on it, and by the spacetime
version of Newton's first law, its worldline is straight. It is the
objects lying on the ground that have curved worldlines; their worldlines
are curved, concave upwards, because of the upward force on them from the
ground.
What general relativity has to explain is: If a falling object's worldline
is straight, and if the worldline of the center of the earth is straight,
then why does the distance between them decrease at an increasing rate as
one moves forward in time along the worldlines? General relativity
explains this by postulating a non-Euclidean geometry. To see how this can
work, consider two longitude lines on the surface of the earth. As one
moves from the equator to the north pole, the distance between them
decreases at an increasing rate. But both longitude lines are parts of
great circles, and one can construct a geometry in which straight lines
behave like the great circles on a sphere.
Is the distortion in space-time comparable to a change in "density" of
space-time
No. There is no distortion of spacetime, and there is no concept analogous
to density for spacetime in general relativity.
(from the same POV of all those bowling-ball-on-a-blanket
analogies)?
Those are only analogies, and one should be careful not to draw more out of
them than the point they're trying to get across, which is that the
presence of the bowling ball is affecting the behavior of the "straight"
lines along the blanket (which are not actually straight, but they
represent straight lines in spacetime).
Also, I, like so many others, have some questions about black-holes. I
agree that from the POV of someone watching from just beyond the event-
horizon, someone else entering the black hole would never actually
pass the event-horizon,
If by "from the POV" you mean that this is what the outside observer will
see by means of light rays coming to his eyes, then this is correct so far,
because light at or below the event horizon will never reach the outside
world.
and that the daring astronaut that went black-
hole diving would appear to be squeezed as he approaches the
singularity after an infinite amount of time.
I think this would be true for someone looking at it from the side, but
what an observer sees by means of light isn't really important; it's just
an illusion. But I doubt that was what the person who described it to you
had in mind. It sounds an awful lot like they were pretending that the
Schwarzschild coordinates were actual distances and times, which is a lot
like pretending latitude and longitude differences are actual distances
along the earth's surface.
What will actually happen to the infalling astronaut, assuming a limited
strength for his body, is that he will be ripped apart along the up-down
direction (where down here means toward the black hole) and squeezed in the
horizontal directions. This is of course from his perspective; other
people might see something different, but their perspectives can only come
from light and other signals that come out to them from the astronaut, and
sensors getting those signals can be fooled, particularly if they evolved
in a nearly Euclidean geometry.
I also accept that from
the POV of the daring astronaut, it would only take him a few minutes
to reach the singularity
This is correct.
while time in the outside world appears to be
going infinitely fast.
But this last statement is wrong. The infalling observer only sees a few
minutes of the remaining history of the outside world before reaching the
singularity.
Am I right so far?
But what I don't understand is that from the POV of the daring
astronaut, he would feel any side-effects of actually reaching the
singularity. (Please correct me in my misunderstanding) to an outside
observer, the daring astronaut is getting squeezed into nothing
because the outside observer's units of measuring distance would have
increased infinitely compared to the daring astronaut's ruler.
The explanation you have apparently read is analogous to someone saying
that the reason planes from Los Angeles to Beijing fly over Alaska is that
metersticks get longer in the east-west direction when you take them to the
polar regions, so a path through Alaska has a shorter subjective length as
measured by the metersticks along the plane's path. This is something you
might say if you were pretending that latitude and longitude differences
were actual distances, and weren't willing to explain that the earth isn't
actually flat. Analogously, spacetime is not Euclidean, and units of
distance no more change when you bring them close to a black hole than they
change when you take them to Alaska.
There will be effects on the astronaut, but they have nothing to do with
this imaginary squeezing. Assuming the feet of the astronaut are pointed
toward the black hole, the worldlines of the astronauts head and feet, in
the absense of a very strong force to make them do otherwise, will each
follow a straight worldline. But since the geometry near the black hole is
highly non-Euclidean, these straight worldlines rapidly diverge from each
other, ripping the astronaut in two.
So the
astronaut's space has decreased (compared to the observer), but so did
everything inside of it including the astronaut and his unit of
distance and all his composing molecules, thus looking at himself, the
daring astronaut would not see or feel any change. Does this make
sense?
You are right in concluding that the Schwarzschild coordinate system will
cause the same effects on the astronaut that the latitude-longitude
coordinate system has on an Alaskan, i.e., none whatsoever. In addition,
the astronaut will be ripped apart as his head and feet both follow
straight worldlines.
Now assuming that at least the astronaut's camcorder survives, what
would be recorded after it reached the singularity? Would it do
something cool like pass through some wormhole and come out a white-
hole somewhere? Or would it simply pass the singularity and launch out
the other side of the black-hole with the same velocity that it
entered with (of course after several infinite amounts of the outside
observer's time)? Or is it all guesswork after that, and I don't need
to worry about it because I'll never see anybody black-hole diving
anyway?
Nobody knows.
I'm also wondering how can there even be a singularity when to an
outside observer, no matter ever actually reaches that point, so a
point of infinite density is never actually created?
The description that you have heard called the "outside observer's POV" not
only is a highly ...
read more »
Dear Jim Black: The standard definition of a triangle is a three-sided
polygon whose angles add up to 180 degrees. Curves aren't segments of
a polygon. Explaining "space-time" is a waste of your time, and the
readers' time, because: I have invalidated the Michelson-Morley
experiment. Haven't heard? Such experiment doesn't have an
unchanging CONTROL light course, just two identically changing (with
respect to TIME, not speed and distance) TEST light courses. Data
comparisons can only be made if one set of data remains unchanging, or
is at least different. Interference is just a comparison of two light
beams traveling different courses. If each quantum (or photon, if you
wish) always requires the same amount of TIME to circuit its course
regardless of the orientation of the apparatus relative to Earth's
velocity vector, then there will be no interference fringe shifts.
My "NoEinstein" Interferometer Type 1 has an unchanging CONTROL light
course, and a changing TEST light course that detects Earth's movement
in the cosmos quite well. Einstein said no Earth based experiment
could do that. But he was wrong, again^100 Power.
Lorentz's laughable idea that all matter (and rulers) contracts in the
direction of motion was just his botched attempt to explain the nil
results of M-M. Since I have invalidated M-M, as explained above,
then there is no contraction factor Beta that is so basic to both of
Einstein's theories. No valid M-M-no valid contraction factor Beta!
No valid contraction factor beta-no valid space-time, and all of its
mishmash! - NoEinstein -
.
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- Gravity, space-time, and black holes?
- From: thomat65
- Re: Gravity, space-time, and black holes?
- From: Jim Black
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