Hi, I wrote this some time ago- does it explain the puzzle?
1. Consider a bicycle wheel. Looking at the wheel, there are
pairs of spokes emanating from arond the hub, that cross over
each other, all lying on the near side of the wheel. On the far
side of the wheel we see a similar pattern.
2. Looking at the wheel from a slight angle, I notice something.
The effect of perspective makes it appear that the crossing-point
of a pair of spokes on the near side, coincides with the crossing
point of a pair of spokes on the far side. A particular angle of
view to two pairs of spokes gives this impression. So it looks as
if four spokes enter and depart from one cross-over point.
3. Further around the wheel, a far pair, and a near pair, are
visually separated to create an impression of the far-pair
crossing-point being alongside the near-pair crossing point.
4. I think: imagine the apparant "side-by-side" crossing-points
as representing the "side-by-side" slits in the well-known
physics "double slit" experiment.
5. But just as the crossing-points within two separate pairs of
spokes can appear side-by-side; I notice that a particular angle
of view can make those crossing-points appear to be a single
crossing point. Thus a way to see how the double-slits they
represent can appear as one slit.
6. Actually, if you look at the double slits on a plane from the
top-edge of the plane, you also collapse the slits into a linear
sequence (or superposition) by virtue of your angle of view.
7. Returning to the double slits in a plane: two slits yes, but
the question is "What is a rigid object?". How do we know they
are in the same plane? Or rather, what is a "rigid plane"?
Richard Stafford has, I understand, already caught the
significance of these questions.
8. I scan my eyes from right to left across a plane. I see light
from the left. A little later I see light from the right. So the
"plane" is actually not a plane from the light-point-of-view; but
a line that moves from left to right into the future!
9. One might thus say it forms a plane of sorts, tilting from the
past into the future. This looks like the"Argand" plane, on which
"complex numbers" are mapped. You get the "real" part of the
number from the "line" aspect, whatever moment-of-time you
choose. And the "imaginary" part from the fact that your "chosen
line" is "in the future" of the "line" you scanned before
(beside) it. (Or a mid-point on your line is in the light-travel-
future of each end of your line). I'm talking here of scanning
the plane as a series of lines.
10. Of course. I could have scanned the plane from right to left;
so that the left-side line-section of the plane would be in the
future of the earlier-scanned right-side line-section.
11. Note also: if I describe seeing the whole " ordinary plane"
at once (could call it: "proper plane"), then: light from the
left and right sides of the plane has longer to travel to get to
me than light from the center. Light from the top and base takes
longer to get to me than light from the center. So when I see a
whole plane at once; I am seeing a "past-future" spherical
object! Of course it still looks flat, because I don't notice
that the light from the corners is older than the light from the
center.
12. The speed of sound is much slower than the speed of light.
Suppose I hovered in a ballon-basket low over a flat field much
larger than a sports-ground; and people all over the field fired
athletics-starting guns at the same time by their synchronized
watches.
13. I would hear the sounds of the guns directly below me before
I progressively heard the guns further away. I would not hear the
sounds all at once. My experience of the "sound object" as a
whole would be an experience of nearness and farness, like a
'sound-sphere'.
14. Actually a flat object has a 'near-ness' and 'far-ness' about
it; just hold a flat sheet of paper up close! It's a bit like a
bump. In skiing,as you turn from going stright down-hill to
coming increasingly more across a steep planar slope; you
increasingly are like you are encountering the up-side of a bump.
15. There is a technique (pivot-retraction) for skiing a steep
planar slope by "absorbing" the steep in the turn as if it were a
bump on a more gentle slope.
16. Also, if you cycle over a judder-bar bump in the road; you
can avoid a big vertical deflection in the plane of your wheel;
by not cycling directly at the bump. Cycle at a shallow angle to
the bump and you spread the deflection over a longer path.
17. By tilting the bicycle at an angle and taking the bump as
part of a big turn with the bike strongly inclined, you also
reduce the component of deflection through the wheel-plane by
placing more of its component out to the side of the wheel plane.
This technique is useful for an easier trip through bumps on a
ski slope.
18. Returning to the double-slit experiment: Take slit "A": From
the point-of-view of a photon at slit "A"; the instantaneous-
matching 'now' that 'B' has, as 'A' has its 'now', is in "A's"
"light-past".
19. This is because: by the time 'A' could learn about that
instant at 'B' from a photon that visited it from 'B'; time has
gone by.
20. Just as by the time 'A' knew eventually (!), via light, about
'B's' instantaneous-match 'now'; that match-now was already
history; so to this scenario applies to 'B' receiving information
about 'A'. Or you can swap 'A' and 'B'.
21. Slit 'B' is in the "light past" of 'A' because by the time
you travelled at c from 'A' to 'B' you've got a 'new' 'B'. And
'B' would be in the "light past" of 'A'.
22. From the point of view of a "light-photon-in-the-present",
the two slits are not in a plane but are in "light 3-D".
23. In other words, one slit is in the other slit's future, from
the perspective of light!
24. So the photon CAN go through "both slits at once"; because
the two slits do not appear in a rigid plane from a light-point-
of-view!
25. Referring to the bicycle wheel analogy; this is just like: my
eyes can 'go through' two spoke-intersections at once (that
appeared side-by-side in a plane from one perspective), by
viewing the spoke-intersections as a linear superposition caused
by a viewing angle that places one intersection behind the other.
26. From a certain view-angle, the spoke-intersections on the
near and far side of the wheel appear super-imposed in linear
sequence directly away from me.
27. If a photon "sees" the world from a "photon perspective";
then the two slits can be seen as displaced out of the usual
assumed plane (whose 'rigidity' now comes under question), with
one slit in the future of the other slit. The light can travel in
this "light 3-D" in a straight diagonal path, through both slits
one after the other, in "light-3-D".
28. Of course, when you take a measurement, you find the whole
photon travelled through one slit! But it actually travelled
through both, only you assumed that the slits were in a rigid
plane which was a concept not properly analysed. That plane was
really a line diagonally sloping across time to make an imaginary
plane. Actually, more exactly, each point on the line must be a
dot sloping through time.
29. After all, take a line-shaped object, say a pencil. It takes
light longer to get to you from the near end, than the far end.
So you could view the "instantaneous match-points" along the
pencil as being in a linear sequence through time! So the pencil
can be regarded from a photon-point-of-view as a line through
time!
30. Of course, we don't mind that parts of the pencil we see are
in the "light past" of other parts. So we just see it as a
"rigid" object with hardly-noticed past-future dimensions!
31. If you look at the pencil from across from the middle of it;
the ends of the pencil effectively slope away into the past at
each end (because the light from the ends is older).
32. Having considered that a plane actually curves away into the
past from a light-travel-time point-of-view, so looks like a
sphere, consider an ordinary 3-D cube. Each face will slope-away
in accordance with the age of the light coming from it (as
compared to an instaneous match-points view of the cube).
33. A "light travel-time" view of the world gives us a pencil
that is curved away at each end, making 2D from 1D. A sheet of
paper was found to curve away into the light-past, the further
from the center of the sheet you consider. The 2-D sheet became 3-
D (or many 2-D lines). |