doug@arizona.UUCP (11/08/83)
I thought these questions might be of interest. Before I answer them,
let me set up a hypothetical case. Since we are talking about a vehical
in motion, let's designate the x-axis as the direction of travel, i.e.
the NJ turnpike. We are also talking about two angles, the angle that an
object appears to be at when we are in motion, let's call it A, and when
we are at rest, let's call that angle B. Let's measure them with respect
to the x-axis. So if we are stopped at some point O, then a star that
appears to be B degrees away from the x-axis will appear to be A degrees
away when we pass over the same point, traveling along the x-axis at
velocity v. Now for your questions.
1) When does the panorama split into two disks? There will be a separation
of two degrees between the edges of the two disks when v = .0175 c .
2) Where is the dividing line and which stars appear in each disk? The
dividing line is the y-z plane, and any stars with angle B < 90 degrees
will be in the forward disk, and B > 90 degrees will be in the aft disk.
3) What does a passing star look like? Let's assume that we start observing
this star while still quite aways off, it's reasonably close to the direction
of travel, and it emits predominantly yellow light. It will appear bluish
in color, and will be close to the center of the forward disk. As we
approach the star it will move away from the center and as it does, its
color will become more yellow. When we pass the star, it will be on the
edge of the disk and it will be yellow. If it is too far away to discern
as a disk, then it will appear to become a tiny cresent and at the same
time it will appear as a cresent on the aft disk. It will remain in the
same position on the aft disk as on the forward disk. If it's at 3:00 on
one disk, it will be at 9:00 on the other (9:00 touches 3:00 when they
wrap around). As we move away from the star it moves to the center of
the aft disk and becomes reddish.
Relation: star at rest
v * * star when
cos B + - d|\ | /| in motion v = .5c
c i| \ | / | o
cos A = --------- s| \ | / | A = 60
v k| \ | / | o
1 + - cos B | \ | / | B = 90
c o| \|/ A |
red shifted -> ----f+------+------+----> x-axis <- blue shifted
| /|\ |
v| / | \ |
i| / | \ |
e| / | \ |
w| / | \ |
|/ | \| <- normal color
y-axis
Pasedoug@arizona.UUCP (Doug Pase) (11/08/83)
This is a continuation of the saga of the NJ Turnpike. As you recall
from the last episode, our hero had just reached near-light speed and
noticed that somebody had constructed an incredibly long tunnel. In
actual fact it was his own relativistic perspective...
I had several (well maybe one or two...) people ask me to be a little more
specific in my description of what actually happens in New Jersey. As I
have not recently travelled to that fair state, I'll have to satisfy them
with a description of what happens to your vision. Recall that an other-
wise continuous panorama divides into two 'disks' centered on the direction
of travel. The view through a disk greatly resembles looking through a
fish-eye lens with a focal length of about 9mm.
Let me set up a hypothetical case. Since we are talking about a vehical
in motion, let's designate the x-axis as the direction of travel, i.e.
the NJ turnpike. We are also talking about two angles, the angle that an
object appears to be at when we are in motion, let's call it A, and when
we are at rest, let's call that angle B. Let's measure them with respect
to the x-axis. So if we are stopped at some point O, then a star that
appears to be B degrees away from the x-axis will appear to be A degrees
away when we pass over the same point, traveling along the x-axis at
velocity v. Now for your questions.
1) When does the panorama split into two disks? There will be a separation
of two degrees between the edges of the two disks when v = .0175 c .
2) Where is the dividing line and which stars appear in each disk? The
dividing line is the y-z plane, and any stars with angle B < 90 degrees
will be in the forward disk, and B > 90 degrees will be in the aft disk.
3) What does a passing star look like? Let's assume that we start observing
this star while still quite aways off, it's reasonably close to the direction
of travel, and it emits predominantly yellow light. It will appear bluish
in color, and will be close to the center of the forward disk. As we
approach the star it will move away from the center and as it does, its
color will become more yellow. When we pass the star, it will be on the
edge of the disk and it will be yellow. If it is too far away to discern
as a disk, then it will appear to become a tiny cresent and at the same
time it will appear as a cresent on the aft disk. It will remain in the
same position on the aft disk as on the forward disk. If it's at 3:00 on
one disk, it will be at 9:00 on the other (9:00 touches 3:00 when they
wrap around). As we move away from the star it moves to the center of
the aft disk and becomes reddish.
Relation: star at rest
v * * star when
cos B + - d|\ | /| in motion v = .5c
c i| \ | / | o
cos A = --------- s| \ | / | A = 60
v k| \ | / | o
1 + - cos B | \ | / | B = 90
c o| \|/ A |
red shifted -> ----f+------+------+----> x-axis <- blue shifted
| /|\ |
v| / | \ |
i| / | \ |
e| / | \ |
w| / | \ |
|/ | \| <- normal color
y-axis
Pasestekas@houxy.UUCP (11/09/83)
" 1) When does the panorama split into two disks? There will be a separation
of two degrees between the edges of the two disks when v = .0175 c .
2) Where is the dividing line and which stars appear in each disk? The
dividing line is the y-z plane, and any stars with angle B < 90 degrees
will be in the forward disk, and B > 90 degrees will be in the aft disk."
Doug Pase seems to contend that a moving observer can stars only within forward
and aft disks, and that some area at 90 degrees to his direction of motion
is black. It just ain't so.
Doug's results would imply that there is some point of transition at which
an object moves from the forward to the aft disk. But such a transition
is discontinuous and could not possibly be derived from special relativity
because relativistic transformations are *continuous*! Such results are
usually a tipoff of a mathematical mistake, not a breakthrough. Most of
the "paradoxes" of relativity can be traced to similar origins.
Jim
Unfortunately,