I haven't done any maths since I was 16, so I'm talking from
ignorance (and I've probably missed the point anyway) - but would a
line around a sphere be straight, but also could be viewed as curved
at the same time - isn't is relative?
nb. anyone want to know how faster than light travel is possible?
If you consider the sphere as a solid, three-dimensional object, then its surface is curved annd
so are any lines on it.
If instead you consider the surface of a sphere as a two-dimensional entity in its own right,
then you can see it as being 'flat' and having straight lines on it: but its geometry is different
to that of an infinite plane, known as Euclidean geometry, which is the geometry we usually
use. For example: in Euclidean geometry, the angles in a triangle add up to 180°. In
spherical geometry they add up to AT LEAST 180°. Also, parallel lines don't exist in spherical
geometry - all lines cross at some point.
Go on then - how is faster than light travel possible? Does it involve warping space and
time?
no, and it depends on your view point. Boffins reckon they've
identified stars moving away from us at greater than the speed of
light. But it could be said that we're moving away from them at 5/8 the
speed of light and they're moving away from us at 5/8 speed of light,
so it depends on what you take as your referance point for 0.
Actually, it depends on your reference point, but not in the way you
think. The speed of light is a constant. Starts moving away from us
(due to the current expansion of the universe) still give off light that
reaches us traveling the same speed as in would if they were moving
towards us. However, the Dopler effect works to lower the wavelength
of the light waves reaching us (much like a train passing us) so that
light frmo stars receeding from us looks redder (longer wavelength).
This is what the red shift is all about. If a star (that is really far away
from us and therefor is moving faster) receeds on us at a speed
approaching the speed of light, the wavelength of light emmitted frmo
the star (and, correspondingly, the energy of the photons) becomes
less and less. If a start were receeding from us at 99% of the speed
of light, the light that we receive, while still traveling at the speed of
light, would be so low in wavelength/energy as to be undetectable by
our currect technology.
So the point is that starts moving away from us at greater than the
speed of light would have light shifted infinitely (and a bit more!) far
to the red and with infinitely low energy. I don't see how they could
then be detected.
Incidentally, there is a much simpler way to witness time travel (or at
least its effects.) Any takers?
--Rein