From Newsgroup: rec.aviation.military
Stephen Harding wrote:
I recall reading "somewhere"
"The Science of 'Interstellar'"? 8-)
that space travel in the future (very, very, very* future) won't involve actually traveling gazillions of light years away but instead, "punching through" the space-time fabric as a sort of short cut.
_Spacetime_ is not a fabric, but a way to assign coordinates to events.
You mean a wormhole, an additional path between events that is spatially shorter than the one along the spacetime manifold.
I suppose it would be like a great circle route on a
globe is shorter than the apparent straight line route
It is the other way around, of course. With a positively curved spatial manifold, the Euclidean (straight-line) distance between points on it is the shortest. This can be seen by considering the corresponding metrics.
Euclidean metric:
ds^2 = dx^2 + dy^2 + dz^2.
Spherical coordinates:
x = r sin(theta) cos(phi)
y = r sin(theta) sin(phi)
z = r cos(theta)
dx = dr sin(theta) cos(phi)
+ r cos(theta) (d theta) cos(phi)
- r sin(theta) sin(phi) (d phi)
dy = dr sin(theta) sin(phi)
+ r cos(theta) (d theta) sin(phi)
+ r sin(theta) cos(phi) (d phi)
dz = dr cos(theta) - r sin(theta) (d theta)
ds^2 = dr^2 + r^2 (d theta)^2 + r^2 sin^2(theta) (d phi)^2.
A path P along the equator, dr = 0, theta = pi/2 ==> (d theta) = 0:
ds = r (d phi) ==> s = int_P ds = r int_0^phi d phi' = r (Delta phi).
[Due to the spherical symmetry, we can rotate the coordinate system
such that any geodesic lies on the equator.]
Suppose, for example, the first point on a sphere with radius r has coordinates
(r, theta = pi/2, phi = 0) <--> (x = r, y = 0, z = 0),
and the second point has coordinates
(r, theta = pi/2, phi = pi/2) <--> (x = 0, y = r, z = 0)
then the Euclidean distance between them is
s_2 = sqrt[(0 - r)^2 + (r - 0)^2 + (0 - 0)^2]
= sqrt(2 r^2)
= r sqrt(2) =~ r * 1.41
but the geodesic distance (along the equator) is
s = r (pi/2 - 0) = r pi/2 =~ r * 1.57 > s.
You are maybe confusing this with the *apparent* straight-line path if the curved surface is being projected on a flat surface.
or as we think of SciFi wormholes and such.
But without that sort of mechanism, there is no way we'll see other life forms,
Not true. We might see lifeforms on Mars, and possibly Europa and Enceladus (there are oceans under the frozen surfaces of those moons).
let alone intelligent ones.
There are intelligent lifeforms on Earth, not counting humans :-p
As far as we know, even with exoplanet systems that we have now found,
the odds are scarce that a planet will have the requirements for life
(as we know it) let alone the roll of the dice evolutionary process
to produce intelligence.
Humans know too little about the conditions for life to make even educated guesses. Currently they are in a position similar to that of person who
knows a hammer as the only tool.
That's a primary reason I don't believe in UFOs and extraterrestrial incidents. Some weird stuff no doubt, but explainable at some point,
now or in the future with more knowledge.
There are much better reasons for not believing that UFOs are of extra-terrestrial origin.
--
PointedEars
Twitter: @PointedEars2
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