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Ideas; Includes: Why Clocks Give "Proper Time"

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Posted by Alan on January 3, 2002 06:27:18 UTC

Here are some ideas; including "Why clocks give
"proper time". I think I have found much of
the key to Richard Stafford's paper, and
demonstrated some of his results to be correct.
What he discovered is quite awesome; maybe
it's like what happened with the Hubble Space
Telescope. It was the world's most perfect mirror; but the wrong shape! A test used by amateur telescope-makers would have revealed
what had happened.

Maybe Dr. Stafford did the homework others
didn't do? There wasn't time to tidy up the
unclear bits below, and some of it is
speculative. But I just wanted to get something
typed up for now.

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). What about a cube?

34. A cube's left-side face which slopes ("proper slope") away
anyway; will be more curved-into-the-present over its near line-
section; than is the case over a line-section further away (where
the differences among light-travel-distances-to-you, from points
along the line, is not as large). The same affect occurs for the
other sides around the cube.

35. Also: the near-face will be sloping away like a sphere from a
light-distance point-of-view; the far side will be curved away
such that the middle is "light-distance" nearer than the edges
(as it is in real distance)(like that far face was concave, but
bulging spherically towards our view through the
near face).

36. So a cube, from a light-perspective, has how many dimensions?
Probably 6 extra curvature dimensions, one for each face! Thus
the "6 missing dimensions" in our space have been found?

37. Add the regular-3-D and the match-point-instantaneous-now
dimension (true time or "jump" time, will explain) and you have
10 dimensions. But "jump"-time gives you a jump from one 10-D to
the next 10-D, so can look like 11 dimensions (10 + CHOICE).(When
you jump you get a new choice, or virtual 11th-D). Thus M-theory
revealed? As apparantly the supposed superstrings imply a
phenomenon that sometimes look like 10-D, sometimes look like 11-
D!

38. O.K., so what we think of as a rigid-plane with two slits in
it; appears from a light-travel-time photon perspective as not
even just a plane sloping from past into future; but a sphere
where the two slits are just points on either side! And that
looks like Riemann geometry!

39. To exit that imaginary sphere, the light has to go through
both slits at once! But we don't notice that the slits are
linearly superposed; so we think the photon all went through one
slit on a supposedly rigid plane without analysing "what is a
rigid object?"

40. From the photon point of view, you took a reading at both
slits without realising how you did that. You didn't notice how
the slits were in line from a certain "photon" or "light travel
time" perspective". Apparantly there was a mistaken assumption
of the visible plane being a rigid "instantaneous match-points"
perspective, when the visible plane is actually tilted through
genuine instantaneous-match-points 'space'.

41. One could talk of instant-match-space versus photon-c-space
versus our visible space (proper space). In genuine instantaneous-
match-points-space, the photon saw photon-3-D view of things,and
the photon superposed the slits for you, like threading two
needles!

42. What is a rigid object? An agreement. A contract. A jump.
I saw an interesting lightning pattern. There was a bolt roughly
vertical, cloud-to-ground; and another, from the same point in
the cloud, that went a long way to the left at cloud-level; all
apparantly roughly at once. But the slower speed of sound of the
thunder gave away what was happening.

43. One can follow the location of the source of a high-flying
jet's sound as the source travels high above; even though the
sound-source lags behind the visible jet, or light-source.

44. Similarly, I could follow the sound-source of the thunder. It
started low, travelled up the vertical lightning path, was the
loudest 'bang' at the origin in the cloud, then rippled along
from right to left along the horizontal cloud lightning path.
This confirms the textbooks, that say that the brightest visible
bolt of the lightning (not the faint stepped leader) is usually a
ground-to-cloud surge of current (heating a channel of air and
making thunder as it goes).

45. So from the perspective of "thunder"; I saw that lightning
bolt as a "past-future object"; not an all-at-once pattern of
light; but a sequence in time.

46. The whole lightning bolt rather looked like just an instant-
drawing on a plane surface from a light perspective of course.
But since light takes time to travel; then strictly the light-
version must be like the thunder-version I sound-tracked: a
linear time-sequence, not a planar-type object!

47. Consider a cube. Take one line-edge of the cube; call that
the present. The rest of the cube you see, because it takes
increasingly long for its light to get to you, is effectively
ROTATED away from you into the past.

48. Actually, take just one point on the cube; that point is all
the "instantaneous-all-there-now" cube has in common with the
cube you see visibly, in that the rest of the cube is rotated
into the past. (As the light from the rest of the cube took
longer to reach you so is older).

49. You can rotate your present corner of the cube into the light-
past by looking at a different corner. Thus a kind of relativity
here. From the point-of-view of photons on one side of the cube;
the other side is in the future. The side near you could learn
about the INSTANTLY-matching other-side from photons setting off
from it. But it would not receive that information till the
future.

50. At this stage it would be possible to obtain results like
those already obtained by Richard Stafford in I think chapter 5
of his paper (on rotations, n-rotations, and on 'events' having
dimensions, not objects). These ideas of Richard Stafford's seem
to be relevant to Roger Penrose's work on 'spinors' and
'twistors'.

51. Note this: you can look at a cube from say either side. Each
of these views of the cube rotates the other view-side into the
past. So each view contains an element of the other view. An
exchange of views? Kind of like "in two places/times at once?"

52.The symmetry tables I drew up, of interchanges between two 10-
dimensional objects, "ABC" and "YPR", seem to be relevant here
Inter-dimensional DNA? I found 11 ways to rotate a table of four
triplets, such that no rows or columns contained an item more
than once. Starting pattern: 10A-10P-10C
10B-10Y-10R
10Y-10C-10B
10P-10R-10A
Actually there may be 120 tables like this that are related
through 11 rotational transformations (incuding split
rotations) into groups of 11 (so 121 tables?; 11 x 11).

53. The 10-dimensions are because there are ten ways of
describing two states of eg. "A" using B,C,Y.P,R as states but
not including mirror images like if have A,C states of B, I left
out C,A states of B.

54. When I listed other symmetries including mirror images, I had
found also six groups each containing five subgroups; eg.
subgroups AB, AC, AY, AP, and AR were in the group ABC, ABY, ABP,
ABR, ACB, ACY, ACP, ACR, AYB, AYC, AYP, AYR, APB, APC, APY, APR,
ARB, ARC, ARY, ARP. Twenty "amino acids"? Made from combinations
from the six groups of 20, not just this "A" group of 20?

55. It appears that the "twenty amino acids" can be split into
mirror images; one for one helix, one for another? With bridges
connecting the two, made from the four triplets? Maybe as DNA
involves a ladder with bases paired in complementary mirror
images, maybe the forces of nature do likewise? 10 pairs,
dimensions? per revolution? Maybe fermions are like DNA, and
bosons like messenger RNA?

56. Looking at the explanation of DNA in the book "Godel, Escher,
Bach, An Eternal Golden Braid" by Douglas R. Hofstadter; I note
the table on page 520. This gives the genetic code, by which each
triplet in a strand of messenger RNA (bosons?) codes for one of
twenty amino acids (or a punctuation mark). He talks on page 19
of mRNA as like recording tape, a ribosome as like a tape
recorder. As mRNA "tape" passes ribosome "playing head", "notes"
of amino acids are made; "pieces of music" of proteins are
produced. Could genetic transcription and translation have a
close corolary in quantum physics?

57. Considering the square root of minus 1; this is a
vector that when multiplied by "itself" (multiplication is
effectively "imaginary addition") gives a vector in a "negative"
direction (the past?).

58. You define a 'rigid object' by rotations? Self-reference? What
if rigid objects are constructed by two rotating helixes, building
space-time structural "proteins" by exchanges of views that via
the 4 triplets of inter-dimensional DNA give fixed reference-
points (pasts) from which new future-choices evolve? The splitting
of DNA strands is reminiscent of the state-vector? Of Everett's
many worlds? Of the inherent freedom in nature, of alternative
options? (See Roger Penrose page 243 "The Emperor's New Mind".)

59. Roger Penrose appears to recognise a "putting up options" in
nature, a requirement that there be alternative possibilities.
Karl Popper recognised that humans make choices from many
hypotheses available. I noticed that language sub-conscious
patterns can be many and varied; one seems to "sort the wheat
from the chaff" and match up patterns as seems best.

60. When one looks around a room, one frames and matches patterns.
One's eyes hop one's attention about the place. Making pattern
matches, "rigid" MATCH objects that are new foundations, stepping
stones, for new dimensions of pattern-matching. Make a MATCH, and
have freedom to make NEW MATCHES!

61. Consider: The Hubble Space telescope had the most perfect
mirror ever built; but to the wrong shape! A test used by amateur
telescope-makers would have revealed the flaw. Maybe Dr.Stafford
has done with physics something like the amateur-telescope-makers
test? I have obtained what appears to be validation of some of
his results.

62. Take a cube. Say one edge is regarded as "now". Looking along the
edge at right angles to the edge facing me, it "rotates into the
past" as part of the back-in-time REAL position of the timeless
imstantaneous-points-all-match version of the cube.

63. Looking at the line we see; the real-position becomes
increasingly uncertain as you go along that line. Because the
REAL instant-match edge is rotated more and more into the past!
It seems to me that the REAL (instant-match) position of the cube
is not just uncertain along the visible (say "proper") line of
the cube (a line-edge 'properly'-going away from me). There is an
'amplitude' to that uncertainty that is the extent of rotation
into the past of that line the further you travel it away from
yourself in space.

64. One can talk not just of the probability of finding a particle
along that line, but the probability amplitude, as in Roger
Penrose's book "The Emperor's New mind", of finding the particle
on that line.

65. To measure something: what happens?
Within the boundary of rough guesswork based on comparing
previously compared patterns; a length of a table could be
anything. (This can substitute for Richard Stafford's "undefined
object").

66. O.K., as I see it, what we call "time" is "reference distance".
Example, the distance a clock-hand moves, or a caesium atom
vibrates. (Though a harmonic vibration of an atom may give us
something more than that, at least, a unit of true-jump-time as a
multiple, relative to other-jump-time (quantised time) units of
harmonic oscillators).

67. Now, take a line AB (A is one end, B is the other). Line AB
could be the unknown length of the table. Call "A" the past, and "B"
the future. If I bring a similar "past-future" ruler, say CD, up
to AB, it doesn't solve anything as I'm still stuck with how to
measure CD as surely as stuck with AB. I may though find out how
many CDs fit into an AB.

68. What if I placed the "C" end of my "past-future" ruler at "A"
("A" being a "past" end, of past-future AB), but have the CD past-
future ruler angling away from AB (as if CD was rotated away from
AB by increasing amounts away from common origin A matching C?

69. Now I have a shared "past" "A' and "C", but two futures, one
heading towards "B", the other heading towards "D".
Note also that whichever of these two futures turns out to be the
one selected, with no real way of measuring, we simply jump to
the new future which becomes a new origin from which two new
futures can be viewed.

70. Returning to where we have a shared past, and two futures.
Suppose I place another past-future ruler from 'D" to "B' thus
completing an equilateral triangle? I just connected two futures,
but futures 'repel' (you have to have one or the other).
What if I regarded each of those two futures as a 'new past'?
Then I could draw two new equilateral triangles. Each of these
would take a future-point on the old triangle as a 'new past', an
origin to make a new triangle with two futures. So the old two
futures become two new pasts, give two lots of two new futures.
And so on, one may take those four new futures as another level
of new pasts; and obtain eight new futures, and so on. Looks like
Everett's "many worlds" hypothesis!

71. Also this reminds me of Benoit Mandelbrot's discussion of "How
Long Is The Coast of Britain?". It's as if the first triangle is
the whole coast seen at once, as ONE JUMP, not measured. And the
next two-view is a subdivision using smaller jump-yardsticks.
Then using smaller, and smaller yardsticks; yet the "length" of
the "past-future" "Object" keeps getting longer in terms of its
"jump number" or "event-scale". This suggests that complex events
are fractal patterns when measured by a "dimensionless" "quantum
ruler".

72. Note that with one triangle I can make interchanges all around
its three points; I can hop around it. The triangle: line AB
being past-A to future-B; line CD being shared-past C superposed
at A but alternative future angled over to B; line DB being
future D that could be a new-past from which to approach future
B. But B could be a past; you can't go future-to-future so to hop
around the triangle you would have to keep jumping past to future
which becomes new-past so jump to new-future etc.

73. The jump from A to B can be a quantum. How can you measure a past-
future 'ruler' with another past-future ruler?

74. Problem: A bus stops at a bus stop. It then starts moving.
So far "then" is undefined. It might as well be a quantum jump
from "stops" to "starts", you might suppose.
But I walk say twenty paces during the INTERVAL "bus stops" to
"bus starts". O.K., so I matched these two patterns: quantum "bus
stops" "bus starts"; with quantum "twenty paces" (or twenty
little quanta). The problem seems to remain: I still don't seem
to be able to measure time!

75. Each of my paces is like a jump-interval as surely as the "bus
stops, bus starts" jump-interval. My whole twenty paces is like
one jump interval superposed on the "bus stops/starts" interval!
It's like I couldn't measure time. I still had to JUMP!

76. The reference distance of my "20-paces" is effectively the same
as the reference-distance of a clock's moving hand. Neither
measures time! The reference distance may be made of smaller
jumps; so you will get a relativity in jump-number between the
INTERVAL "bus stops, bus starts" and the interval "my pace
starts, my pace stops" or the interval "clock hand starts, clock
hand stops". (Actually; 'time' looks like an illusion? Jump-creation
the reality. Measurement involves comparing jump-numbers.)

77. I think this may be what Richard Stafford is talking about when
he says about a problem, that f(x) = 0. How do you know 'past'
and 'future' on a past-future ruler; to measure 'past-future' on
the ruler you are trying to measure?

78. Roger Penrose, in "The Emperor's New Mind", seems to almost ask
this question on page 448 in the last few sentences of the main
text of the book.

79. Generalising; we have discovered Richard Stafford's question:
"HOW DO YOU KNOW ANYTHING AT ALL?"

80. The answer: Freedom is the measurement-ruler! The glass is not
empty, but full to overflowing! We can't tell the difference
between our universe and any other; because our universe runs at
maximum freedom. We COULD be in any other universe!

81. Take the two rulers. Line AB is a past-future ruler. Line CD
starts also with C at origin A; but it angles away giving a
different future. How do you really measure the first ruler? The
difference between the two rulers is how; the difference is
FREEDOM. Two options, two futures! Make a CHOICE, and you JUMP!
The two rulers are measured by the very fact there are two of
them, two options, two views! If one ruler is 3 jumps, with the
other 3 jumps; you have a "phase space" of all possible views
of the options.

82. Apparantly there are 27 different ways to fit 3 different
coloured beans spread over a set of 3 boxes. There are 18 ways of
having 2 items in a box (18 quarks?); 3 different pairs of beans
(quark colours?); and 6 ways of having each pair in a box
(6 quark flavours?). If the boxes and beans swap roles; you would
get your 18 mirror-quarks (anti-matter)(going backwards in time?).

83. Note that Roger Penrose asks on page 281 of his "...Mind" book
as to what's all the alleged jumping? Reality looks like being all
about CHOICES; freedom everywhere.

84. It looks as if Richard Stafford's finding holds true: that
EVENTS have dimensions. You can model this by rotations, which he
does I think in chapter 5. Also; Two lines from a shared past to two
possible futures; choose a future, it becomes a new past, with a
new divergence into two possible futures; choose one, get a newer
past and a new range of futures, and so on.

85. It is possible to represent a straight line movement of a
particle from 'A' to 'B' by imagining: The particle is a cube, with
a red top, blue base. a hole drilled through the middle of the top
down through the base allows the particle to ride on an axle. A giant
semicircle axle allows the particle to go from A to B in a big arc,
but of course it lands upside-down at B. So a half-rotation on the
spot at B, via an axle through the middle of the cube-side (having
disconnected the big curved axle first) will restore the red-surface
to the top.

86. A fractional rotation about a vertical axis would allow
the cube to get its relative direction oriented correctly compared to
other horizontal directions it could have taken from its journey start.
Two small other rotations would allow to take account of any out-of-
square aspects if you wanted to fully map one random cube to another
across space; only by rotations (including the big space-hopping arc.).

87. Consider a particle moving from A to B, from the past to the
future. It has a probability of being somewhere along that line;
but if that line is just a "light-view" of things then its REAL
location (instantaneous, not the 'slow' light-speed location) is
increasingly in the instant-match-past compared to the visible-
line of its movement (if moving away). Just as that lightning bolt
was in the past of its thunder-description in space viewed from a
distance.

88. Need to keep in mind that I am now talking about a world where
"time" is a very real dimension like space (actually is 'reference
space'). With the lightning; I could sense the "momentum" thanks to the
thunder-source 'slowly' travelling along it; where its position was
known independently. The two measurements can be made in the absence of
each other.

89. Replace the slow sound speed of thunder, and the "instant"
appearance of the lightning before; with the "slow" speed of
light and the concept of "instantaneous match points" of an object
(true-rigid object).

90. Suppose I take an event: AB. A is the past-end, B is the future-
end. I take a ruler, CD, (C is past, D is future) and place it
parallel. So I can connect the two rulers to form a square with
new rulers past-past (AC) and future-future (BD). If my ruler CD,
which is effectively a clock; is separate from event AB; the
problem is that there is now a past-future between my clock-ruler
past and the event past. Past-past between the rulers is
effectively a past-future at right angles. So is future-future
between the rulers.

91. These new "at right anles" rulers occupy "space" between the past-
future line AB and my "clock" past-future line CD.
It seems as if when I use a clock in real life; I am doing what
is described here. So I've got intervals between the clock-ruler
and the past-future being measured; intervals that take account
of the space between the two. So I am measuring the space-time
interval between the past and future of the event AB?

92. Must be, because I can not measure AB other than in a multiple of
jumps; and by incuding jumps at right angles across space I am
measuring the Lorentz invariance between the two via a square set-
up. I have locked in the event AB by jumps: AB is a past-future
jump; CD my ruler/clock is a past-future jump; the distance of my
ruler from AB gives jumps: across-space (time) AC, forwards-in-
time diagonal AD, across-space jump BD, backwards in time-
diagonal BC, forwards-in-time diagonal CB, backwards-in-time-
diagonal DA. Eight jumps there.

93. So have obtained same result as Richard Stafford: clock's measure
the space-time interval; called "proper time". Note: Freedom
measures true time; as CHOICES.

94. One can apply similar logic further. Apparantly one can talk of
"freedom mass" and "proper mass"; "freedom momentum" and "proper
momentum", "freedom energy" and "proper energy", "freedom space" and
"proper space", even "freedom gravity and "proper gravity",
"freedom n" and "proper n"?

95. Since this issue can apparantly be generalised; measure-ruler-n
measures proper-n of n; and freedom is the true measure-ruler;
one might suppose now is a way to show how classical mechanics is
"tautological" or circular in the way quantum physics may appear.
Actually, its kind of circular and not circular. By comparing and
matching numbers of jumps (so that's why Richard Stafford thinks
of reality as a set of numbers!), numbers of jumps relative to
other numbers of jumps; you can get somewhere in exploring the
fractal dimensions of reality, it would seem.

96. This tallies with Roger Penrose's comments about why does
Newtonian Mechanics succede? Answer: effectively big particles
(Earth, sun, etc.) few numbers of particles, generalisation rules.

97. Consider: an electromagnetic field can be seen as two clocks; a
magnetic clock and an electric clock. One may suppose that as the
two waves diverge, they are viewing options, as they come
together, they are narrowing down their choice. The decision is
made as they cross over and diverge again, viewing new options.
From the perspective of a "probability ruler", light thus appears
as probability waves?

98. The cross-over points may be a kind of "mass" of light. There is
more to write; haven't time now to tidy up the muddly bits above.
I figured out something to do with mass; seems connected to the
"Fresnel lense" and refraction. Richard Stafford saw there may be
be a connection between gravity and refraction I seem to recall.

99. How do you measure mass? Proper mass versus quantum mass?
The issue of Bose-Einstein condensates arises too. I figured out some
diagrams that seem to correlate with Roger Penrose's probability
amplitudes. No time to explain; but one can figure out situations
involving concepts: two clocks; momentum states, Dirac delta function,
ratios, velocity and jump velocity, inverse square law, relativity,
apparant circularity of Schrodinger equation, 3-way jumps, freedom.

-Alan

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