Straight line?

Imagine you are on a flight and suddenly pushed out into the open
[atmosphere]

You tend to fall like this under gravitational free fall : shown by path
etc.

*
*
*
*
*
*
*

If you have the guts and energy you can dictate your path to take the * * *
route which is an Euclidean straight line.

You cannot now say that space is curved [well the free fall is curved under
gravity : I won't accuse earth of causing the space to warp]
I will not call the curved path the shortest [though it spent least energy]

I am sure I will reach the destination faster traversing path * * * etc.
[any footballer or sportsman knows this]

What does this mean?

To us : trying to understand

Researcher

PS : Spare me of spurious, self-boasting and filthy replies

"Researcher" wrote in message
.. .
If straight line is curved,
what did you mean by straight line?

Researcher



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"Researcher" wrote in message
.. .
| Imagine you are on a flight and suddenly pushed out into the open
| [atmosphere]
|
| You tend to fall like this under gravitational free fall : shown by path

| etc.
|
| *
| *
| *
| *
|
| If you have the guts and energy you can dictate your path to take the * *
*
| route which is an Euclidean straight line.

Wrong.

*
*
(2 lines between)
*

(4 lines between)

*



(8 lines between)


*
(16 lines between)

Androcles

Researcher wrote:
Imagine you are on a flight and suddenly pushed out into the open
[atmosphere]
You tend to fall like this under gravitational free fall : shown by path
etc.
*
*
*
*
*
*
*
If you have the guts and energy you can dictate your path to take the * * *
route which is an Euclidean straight line.

"guts and energy" are not enough for you to follow the * line, you need
a rocket engine or some equivalent method to throw material down (to
cancel the Newtonian force of gravity).

It is not "curvature of space" that matters, it is curvature of spaceTIME.

As a simple example, drop a rock from rest relative to the earth, and
plot its height vs time -- that is a parabola (ignoring air), and is
inherently curved -- THAT is curvature in spaceTIME. But if you dropped
a rocket with a thrust 9.8 m/s^2 upward then it could follow a straight
line in that spacetime plot -- accelerated motion does not follow
geodesics (that parabola is a geodesic in spaceTIME near earth).


Tom Roberts

Dear Researcher:

"Researcher" wrote in message
.. .
Imagine you are on a flight and suddenly pushed out
into the open [atmosphere]

You tend to fall like this under gravitational free fall :
shown by path
etc.

*
*
*
*
*
*
*

If you have the guts and energy you can dictate
your path to take the * * * route which is an
Euclidean straight line.

Yes, and far from any massive object, that is the path everyone
would expect... and get.

You cannot now say that space is curved [well
the free fall is curved under gravity : I won't
accuse earth of causing the space to warp]

It doesn't care either way.

I will not call the curved path the shortest [though
it spent least energy]

I am sure I will reach the destination faster
traversing path * * * etc.
[any footballer or sportsman knows this]

Not necessarily. Besides railing at Nature for how She behaves,
how did you plan to maintain this artificial path? Your method
may have side effects...

What does this mean?

To us : trying to understand

A boy throws a ball into the air, and away from him. He sees a
parabolic path, as it moves up and then down. He imagines that
there is some force acting on the ball. Yet he ignores the very
strong force constantly acting on the soles of his *own feet*.
Why imagine a mystical force for someone / something else, when
he is very aware of a force acting on him? The ball was simply
describing a highly elliptical orbit, as much as atmospheric and
lithospheric friction would allow...

David A. Smith

Researcher wrote:
Imagine you are on a flight and suddenly pushed out into the open
[atmosphere]

You tend to fall like this under gravitational free fall : shown by path
etc.

*
*
*
*
*
*
*

If you have the guts and energy you can dictate your path to take the * * *
route which is an Euclidean straight line.

Have a horizontal ruler dropped along with you at the same time you
jump from the plane. If atmospheric forces are negligible, then the
ruler says path is a straight line, following the ruler.

.... It means that if you wanted to take a straight path (***) to the ground,
you must jump from a balloon rather than a jet. The curved path in this case
is a resultant of adding a horizontal force vector, to the gravitational
vector. A good pilot realizing that you had fallen out, I mean pushed out of
the jet could take a sudden nose dive and take path (***) without much added
energy. Full flaps and let wind resistance do the work. Will E.


"Researcher" wrote in message
.. .
Imagine you are on a flight and suddenly pushed out into the open
[atmosphere]

You tend to fall like this under gravitational free fall : shown by path

etc.

*
*
*
*
*
*
*

If you have the guts and energy you can dictate your path to take the * *
*
route which is an Euclidean straight line.

You cannot now say that space is curved [well the free fall is curved
under
gravity : I won't accuse earth of causing the space to warp]
I will not call the curved path the shortest [though it spent least
energy]

I am sure I will reach the destination faster traversing path * * * etc.
[any footballer or sportsman knows this]

What does this mean?

To us : trying to understand

Researcher

PS : Spare me of spurious, self-boasting and filthy replies

"Researcher" wrote in message
.. .
If straight line is curved,
what did you mean by straight line?

Researcher



--
Posted via a free Usenet account from http://www.teranews.com




--
Posted via a free Usenet account from http://www.teranews.com

Hi,

Thanks.
Why I talked about reaching the same spot where otherwise the object would
have free-fallen is to show the shortest route to it and the extra effort
[in whatever way it can be imparted to or derived from] involved.
Not really to save myself or reach the ground by the shortest.

Researcher

"will1" wrote in message
...
... It means that if you wanted to take a straight path (***) to the
ground,
you must jump from a balloon rather than a jet. The curved path in this
case
is a resultant of adding a horizontal force vector, to the gravitational
vector. A good pilot realizing that you had fallen out, I mean pushed out
of
the jet could take a sudden nose dive and take path (***) without much
added
energy. Full flaps and let wind resistance do the work. Will E.


"Researcher" wrote in message
.. .
Imagine you are on a flight and suddenly pushed out into the open
[atmosphere]

You tend to fall like this under gravitational free fall : shown by
path

etc.

*
*
*
*
*
*
*

If you have the guts and energy you can dictate your path to take the *
*
*
route which is an Euclidean straight line.

You cannot now say that space is curved [well the free fall is curved
under
gravity : I won't accuse earth of causing the space to warp]
I will not call the curved path the shortest [though it spent least
energy]

I am sure I will reach the destination faster traversing path * * * etc.
[any footballer or sportsman knows this]

What does this mean?

To us : trying to understand

Researcher

PS : Spare me of spurious, self-boasting and filthy replies

"Researcher" wrote in message
.. .
If straight line is curved,
what did you mean by straight line?

Researcher



--
Posted via a free Usenet account from http://www.teranews.com




--
Posted via a free Usenet account from http://www.teranews.com






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Posted via a free Usenet account from http://www.teranews.com

Researcher wrote:
Hi,

Thanks.
Why I talked about reaching the same spot where otherwise the object would
have free-fallen is to show the shortest route to it

Are you sure it is the shortest route? From the falling person's
perspective, he never went anywhere at all, and the guy with "guts and
energy" and rocket thrusters moved down, then back up to where he
started.

From the horizontally moving plane's perspective, it's possible they
both took straight lines, and the distance they travelled was equal.

The point here is that a concept of "the shortest route" that only
considers the falling object's motion through space isn't a
well-defined concept unless you pick out someone's perspective as
special. We must remember that the beginning and end of the
free-faller's journey aren't just two places; they're also two times.

General relativity says that the freely falling person takes a straight
path through space-time, provided we define a "straight path" in
space-time to mean the path that maximizes the time experienced by the
falling object.

Good insight.

Researcher

"Jim Black" wrote in message
ups.com...
Researcher wrote:
Hi,

Thanks.
Why I talked about reaching the same spot where otherwise the object
would
have free-fallen is to show the shortest route to it

Are you sure it is the shortest route? From the falling person's
perspective, he never went anywhere at all, and the guy with "guts and
energy" and rocket thrusters moved down, then back up to where he
started.

From the horizontally moving plane's perspective, it's possible they
both took straight lines, and the distance they travelled was equal.

The point here is that a concept of "the shortest route" that only
considers the falling object's motion through space isn't a
well-defined concept unless you pick out someone's perspective as
special. We must remember that the beginning and end of the
free-faller's journey aren't just two places; they're also two times.

General relativity says that the freely falling person takes a straight
path through space-time, provided we define a "straight path" in
space-time to mean the path that maximizes the time experienced by the
falling object.




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On Thu, 19 Oct 2006 20:53:41 -0700, will1 wrote:

... It means that if you wanted to take a straight path (***) to the
ground, you must jump from a balloon rather than a jet.

Not really following this but just picking a nit:

If you jump from a balloon anywhere except one of the poles, you won't
fall straight either, because the Earth is rotating. Viewed from the
ground, it will appear that the Coriolis force pushes you off course and
your path curves to the east. OTOH, viewed from a "stationary" point above
the pole, since the balloon was comoving with the surface of the Earth,
you'll be observed to follow a parabolic path, just like the case with the
jet.

If, instead, you jump from a jet moving west at about mach 1 (exact value
depending on your latitude), just fast enough to cancel the velocity of
the surface of the Earth (from the POV of a "stationary" observer looking
down from somewhere over the pole), you'll follow a path that would appear
to the stationary observer to be straight ... _except_ the 1000 MPH breeze
will blow you off course, and in any case an observer on the surface of
the Earth still won't think you're falling straight down.

So again, to take an unambiguously straight, unpowered path from a high
point to the Earth's surface, you should jump from a balloon over one of
the poles. Wear warm clothes.


The curved path in
this case is a resultant of adding a horizontal force vector, to the
gravitational vector. A good pilot realizing that you had fallen out, I
mean pushed out of the jet could take a sudden nose dive and take path
(***) without much added energy. Full flaps and let wind resistance do
the work. Will E.


"Researcher" wrote in message
.. .
Imagine you are on a flight and suddenly pushed out into the open
[atmosphere]

You tend to fall like this under gravitational free fall : shown by
path

etc.

*
*
*
*
*
*
*

If you have the guts and energy you can dictate your path to take the *
* *
route which is an Euclidean straight line.

You cannot now say that space is curved [well the free fall is curved
under
gravity : I won't accuse earth of causing the space to warp] I will not
call the curved path the shortest [though it spent least energy]

I am sure I will reach the destination faster traversing path * * *
etc. [any footballer or sportsman knows this]

What does this mean?

To us : trying to understand

Researcher

PS : Spare me of spurious, self-boasting and filthy replies

"Researcher" wrote in message
.. .
If straight line is curved,
what did you mean by straight line?

Researcher


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