A Space-time Map of the Universe
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On a summer morning in 1981 I sat at my kitchen table in
upstate New York and drew a space-time map of the cosmos, such as we see in
Fig. 1. It has remained unchanged in all essential details since that time.
(See: Space-time Map Fig. 1).
The map shows a universe that is 14 billion years old, with
billion-year intervals represented by circles concentric on a central ÒBig
BangÓ (http://www.johnagowan.org/spacemapnew.pdf).
Obviously, a map of this type will only work for a ÒBig BangÓ universe, one
which has a discreet, small, and sudden beginning. As we will see, the map
works for our universe, which suggests that we do indeed live in a ÒBig BangÓ
cosmos (an origin similar to the Genesis story).
Notice first that only the upper left quadrant of this map
is ÒrealÓ. If the universe contained only light, then the whole circular form
would be appropriate; but when we add a material observer, the spherical
symmetry of the light universe is broken due to the one-way character of time,
the unique perspective of the observer, and the consequent need to avoid
mapping ÒnegativeÓ space. Hence, we must arbitrarily choose a single quadrant
of the circle to represent our observational position (Òmapping artifactÓ
– the map is not simply a scale model of the universe).
There are two critical features of the map which must claim
our immediate attention: first, we have collapsed all three spatial dimensions
into a single line, with increasing space running vertically from the central
ÒBig BangÓ. This allows us to construct the time line horizontally, at right
angles to all three spatial dimensions simultaneously, giving space and time
equal importance as mapping parameters. The time dimension is one-way,
increasing from the central Big Bang to the left-hand margin of the map, where
it ends in earthÕs present position, our Òhere and nowÓ. Whereas the space line
is marked off in units of billion light years, the time line is marked off in
units of billion years. This correspondence between time and space is the
essence of EinsteinÕs and MinkowskiÕs space-time metric; notice that both space
and time are increasing in lockstep as metric equivalents. Both expansions are primordial
expressions of entropy in free vs bound electromagnetic energy. The intrinsic
motion of light drives the spatial expansion while the intrinsic motion of time
drives the historical expansion, with gravity mediating between them,
converting one into the other. (See: http://www.johnagowan.org/thermo.html ÒEntropy, Gravity, and
Thermodynamics).
We connect the equivalent units of time and space via
circles representing space-time volumes of equal age: since all points on a
given circle are equidistant from the central Big Bang, all the space
represented by that circle is of exactly the same age. Thus the spatial circles
represent Ò3-spheresÓ of a specific age as indicated by their intersection with
the time line. The first circle represents the spatial volume of the universe
(and all material objects within it) when the cosmos was precisely one billion
years old; and so on for each succeeding circle. The final circle represents
the present spatial volume of the universe, including all the galaxies, as it
exists now in the Òuniversal present momentÓ, about 14 billion years after the
ÒBig BangÓ.
Secondly, because we are trying to understand how we
see our universe, we must indicate the path of all light rays coming to planet
earth from the cosmos. Any observer stands at the center of a nested,
concentric set of observational shells –- two-dimensional spherical
surfaces that get larger as they recede into spacetime. These 2-D spherical
observational shells intersect the 3-D spatial circles of the map at some
specific point on their arc, but how to identify this point? Since the mapÕs
spatial lines already represent 3 dimensions, a 2-dimensional intersection of
their volumes would have to be represented as a point, and points on a circle
can be designated by a tangent line -- in this case drawn from earthÕs
location. We act upon this hunch and construct tangent lines from earthÕs
position to all the spatial circles in the real quadrant of the map (I show only
one), and then connect the tangent points. We discover that all such points lie
on another circle which has earthÕs time line as its diameter.
If
this (one-way) Òlight lineÓ is a valid representation of the path of (all)
light rays coming to earth from the cosmos, then we should be able to use the
same principle of construction to indicate the position and Òlight lineÓ of a
second observer who is looking at earth while we are looking at him, and note
if this reciprocal exchange of observerÕs perspectives maps properly. We have
indicated this second observer at ÒBÓ, 4 billion light years distant, and we
have constructed BÕs time line from the Big Bang through the position where we
see him (4 billion years in his past), extending the time line to his present
position on the outermost spatial circle. We draw BÕs light line, which is a
circle with BÕs time line as a diameter, finding that BÕs light line indeed
intersects earthÕs time line 4 billion years in our past, validating our
mapping procedure for these Òlight linesÓ.
Consider
next a demonstration of the mapÕs validity. Because the cosmological ÒredshiftÓ
is caused (according to Steven WeinbergÕs The
First Three Minutes, Basic Books,
1977) by the difference in the size between the observerÕs universe as compared
to the size of the observed universe (since we look backward in time to always
smaller and younger historical eras of our universe as we look outward in any
direction in space), we can calculate directly from the map what we expect the
redshift should be for any galaxy at a given distance: simply substitute the
mapÕs radius in years for the wavelength of light. The formula is: wavelength
observed minus wavelength emitted (or age of our universe minus age of observed
universe), divided by wavelength emitted (divided by age of observed universe).
Thus the redshift of a galaxy seen at a distance of 7 billion light years is
14-7 divided by 7 = 1 (redshift 1 is therefore halfway to the Big Bang). These
calculations are for a universe expanding uniformly at velocity c, as indicated
by our flat map. We would like to know what this map would yield in terms of
redshift calculations if gravity were added, bending the map. Accordingly, I
made another (approximate) calculation from this same map, but with gravity
sufficient to halt its expansion in 300 billion years. These two sets of
numbers gave me an upper and a lower bound (expansion with gravity vs expansion
without gravity) to compare with real-world observations (taken mostly from Sky and Telescope and Science). (See: Space-time Graph Fig. 2.)
The graph shows three lines: the lower line is the
Òno gravityÓ curve, the upper line is the Òwith gravityÓ curve, both calculated
from the raw parameters of the map, flat in one case and spherical in the other
(http://www.johnagowan.org/14gyr.gif).
Redshift values increase toward the right on the horizontal axis, distance
increases toward the top on the vertical axis. The third line is the
observational data line, which falls just between the top and bottom calculated
lines, as we must expect if the map is a valid representation of space-time.
This is the ÒhardÓ observational evidence that the map actually ÒworksÓ as
constructed.
Explaining
the ÒhorizonÓ paradox to myself was the original motivation for drawing the
map, and we will turn to it now. Most people, apparently including some
professional astronomers, think the Òedge of the universeÓ is somewhere Òout
thereÓ in deep space, whereas the map clearly shows that Òhere and nowÓ is the
true edge of the universe. What is Òout thereÓ in deep space is the Big Bang,
the center of the universe in the sense of its beginning in space-time. We are
poised on the edge of space-time, looking backward in time (along our
lightline) toward ever-smaller and younger historical eras of our universe as
we look outward in space – in every direction. The common failure to
appreciate this point has led to the perceived paradox of the Òhorizon problemÓ
(among others) –- in which hard data (from the cosmic microwave
background radiation) shows the universe to be a causally unified whole, but
that evidence is at odds with what we think we see in the sky.
An
example of the Òhorizon problemÓ (as commonly misconceived) is found in an
article in ÒScientific AmericanÓ in a
special issue on cosmology and the theory of ÒinflationÓ (Jan 1999, pages
63-69). In this article, the authors claim that two galaxies, both seen at 12
billion light years distance, but 180 degrees apart as we see them in the sky
(one east and the other west), must be separated by 24 billion light years of
space and therefore cannot have exchanged light signals in the lifetime of our
cosmos, which is only 14 billion years old (they are therefore beyond each
otherÕs visual ÒhorizonÓ). A glance at the map reveals the fallacy of this
argument: at 12 billion light years distance, both these galaxies occupy a
universe which is only 2 billion light years in diameter. Their maximum
separation in space-time is therefore 2 billion light years, not 24, and they
have had ample time to exchange light signals. Similar arguments apply to the
ÒsmoothnessÓ and ÒflatnessÓ problems (the background radiation is too
homogenous, and the overall geometry of space-time is not gravitationally
warped). Because the theory of inflation was developed specifically to address
such problems, we have to wonder about the motivational and theoretical
foundations of ÒinflationÓ. It seems it is our view of the universe that is
ÒinflatedÓ rather than the universe itself. The cosmic microwave background
radiation, for example, is thought to be redshifted (or ÒinflatedÓ) by a factor
of about 1100. (An ÒinflatedÓ view comes about because as our observational shells
increase in size with increasing distance, the historical universe we are
observing grows always smaller and younger – and yet visually, continues
to surround us completely.)
In summary, we look at several types of reality represented
in the map. Almost the entire universe is invisible to us; we cannot see our
historical past, which is fully ½ of the ÒbulkÓ universe, the area
between our time line and our light line. Also, we cannot see the other half of
the universe, the area above our light line, which is a sort of Òmanifest
futureÓ consisting of light signals from the universe which are Òin the
pipelineÓ but which have not yet reached us. Our light line is our only view of
the cosmos, which neatly separates these two areas into equal halves of past and
future (as required by the reciprocal perspectives of observers everywhere),
both unseen (by us) but both perfectly real (insofar as light and space-time
are real), and both currently visible to observers elsewhere in the cosmos. All
the galaxies that occupy the Òuniversal present momentÓ are likewise invisible
to us, as they all lie in the outermost spatial circle, the Òuniversal present
momentÓ (which we contact only by touch). We donÕt see objects where they are,
we see them where they were at various times in the past, depending on their
distance from us. We see only as and what the space-time metric allows us to
see (as the phenomenon of gravitational lensing demonstrates). The advantage of
our map is that it shows us what we do see as well as what we donÕt see. The
unseen universe represents an extra, large, spacetime dimension, encompassing
past, present, and Òmanifest futureÓ, a
vast dimension consisting of causal or ÒkarmicÓ information, not only our own,
but that of all other observers in the cosmos, real or potential.
The special significance of our ÒobserverÕs positionÓ
is that it is the 4-way intersection of space, time, light, and matter, the
only point in our personal universe where two-way interactions are possible.
From Òhere and nowÓ we receive and send light signals from and to the universe,
and mould our future with a mixture of karmic influence from the past, physical
contact with present matter, and free-will action embedded in the ever-moving
entropic flow of time and space. Note finally that our light line directly
connects our position, which represents the center of creative energy in our
personal universe, with the ÒBig BangÓ, which represents the center of creative
energy in the macro-universe.
This is the view from the flightdeck of ÒSpaceship
EarthÓ: looking out into space in every direction we see the galaxies receding
into space and history, the more distant they are the faster they recede. This
progressive recession is how we perceive the entropic expansion of historical
spacetime. In front of us we see nothing but the blank void of the unformed
future; and of the present, we actually perceive only what we touch. The vast
bulk of the cosmos we do not see at all, including our own historical past, the
universal present moment, and the Òmanifest futureÓ of light Òin the pipelineÓ
which has not yet reached us.
Cosmology
Section
V: Introduction to Cosmology
A Spacetime Map of the
Universe (text - updated copy)
A Spacetime Map of the
Universe (updated pdf
diagram)
The "Spacetime Map" as a
Model of a 5-Dimensional Holographic Universe
Commentary on the Physical
Parameters of the "Spacetime Map"
A Graph of the 14 Gyr Cosmos
Expanding with and without Gravity
Table of Data Inputs to
"13.7 Gyr Graph" of Cosmic Expansion
Dr. Richard D. Stafford's
Spacetime Map (text)
Dr. Richard D. Stafford's
Spacetime Map (diagram)
