My 125th midi composition, done on 20th March 2002. Yes, that was a decade ago...
Adrian Wonoto
Random Ideas, Disjointed Thoughts, and Meaningless Rants.
Tuesday, July 31, 2012
Monday, July 30, 2012
FLATLAND UNIVERSE
I know I am being preposterous in writing this small "essay" of a blog post. Somehow, an idea got stuck in my mind that I simply had to put it out in order for someone to explain to me where I got it wrong, in logic or observation.
The idea came suddenly to me as I watched Sagan's Cosmos episode ten, “The Edge of Forever.” The basic premise of the idea is to
consider the Flatland of Sagan’s presentation as having the same natural laws
and the same observations as our own three dimensional universe, minus one
space dimension as I imagine the flatlanders would observe, and to speculate
how that would work.
I’m not a scientist. I’m a
layman with only a very rudimentary understanding of science. I don’t know much
about neutrinos, quasars, or photons. To be honest, everything I learned was
from only a select few of readings – Wikipedia articles, A Short History of
Nearly Everything, and the Cosmos series by Carl Sagan. Therefore, all the observational evidence and physics that I understand are limited to how they are explained to the layman.
Of course, I naturally am expecting that
most of the ideas I have to be completely in error. I'm quite embarrassed to have written this at all. It is just that the idea is latched on to my
mind without any understanding on how to test the speculations that my embarrassment
is not enough to stop me in writing out the ideas.
In case you have figured out where I am in total error, I would very
much appreciate it if you could point it out to me. I wonder, even maybe wish, that there’s a tiny smidgen of merit in
any of the idea, but I’m not wishing much.
FLATLAND UNIVERSE
How a Two Dimensional Representation of Our Universe Should Look Like
Gravity, as Einstein explained in his theory of Relativity, is the result of the bending of space time caused by mass. Space time is explained as a three-dimensional space that we occupy, plus a dimension called Time. Of course, we don’t have much problem with conceptualizing a three dimensional space, but not so for the additional time dimension. We’re usually asked to imagine a matter on top of a mattress with a significant mass to bend the mattress. Things moving in straight line would “fall” towards the object with mass due to the bending of this mattress.
Carl Sagan in Cosmos episode ten, The Edge of Forever, explained about the fourth dimension by asking us to envision how a two dimensional creature would experience the additional third dimension. He asked us to imagine a ‘flatland,’ a universe of two dimensions (The idea of flatland itself was derived from a novel by Edwin Abbott). He then asked us to imagine a third dimensional creature descending on the flatland to meet with a two dimensional creature, appearing before the flatlanders as if magically inside an enclosed space. The three dimensional being then whisked the flatlanders to the third dimension where it could see the innards of everything, and returning to the flat universe where it was unable to point to the third dimension when prodded by its friends. From there, he explained how we as three dimensional beings are trapped in our own three dimensionality, just like the flatlander is trapped in its two dimensionality.
However, there are two flaws in the
presentation. First of all, the two dimensional universe, which I will call the
“Flatland universe” from now for brevity and clarity’s sake, wouldn’t look like
how Sagan presents it. The flatlanders in Sagan’s thought experiment is
enclosed on a wall and is assumed to be standing on something. That something,
the floor, is an extra dimension of height that should not have existed in the
true two-dimensional universe.
Any wall in this universe, which is a
construct of height that is relative to the center of gravity, would become a
formidable barrier to any beings to move in the forward and backwards direction
– they would not have the concept of left and right, although we can change the
terms used between left right and back forward and it would make no difference to
the flatlanders. Or, in terms familiar to gamers, the universe would look more
like a “side-scroller” like Super Mario Bros rather than a top-down game like
Zelda, only that there is no background sky and cloud in such a world (I
apologize for this analogy, it just seems like a perfect analogy to me).
The Third Dimension in Flatland?
Another aspect in Sagan’s presentation of
Flatland that I consider to be flawed is that the three dimensional being that
looks like an apple is moving freely within the third dimension as if it is
another spatial dimension. If the fourth dimension of space time is a time
dimension, then the third dimension in the flatland universe should also be a
time dimension. I do not think that the time dimension should be a dimension
where matter can freely move back and forth. Matter should only travel through
the dimension of time in one direction only. It should have come from the past
in the dimension and is travelling towards the future.
Let us expand the exercise of imagining
flatland further, while keeping in mind that the third dimension is the
dimension of time. Now, the citizen of flatland can point forward and
backwards, and up and down (down being the direction of where gravity pulls
relatively). But the flatlanders has no concept of left and right and they
would be unable to point to the direction of the third dimension in space,
which in this exercise is the time dimension.
If we, as a three dimensional creature, can
see the two dimensional universe with the additional of time dimension, we
could see that the movement of a flatland object as a column. If the flatland
object splits in half, we would see parts of the being splitting from the being
into two separate columns. The edge of the column, the “top,” would constitute
the present, which continually grows. However, this assumes that we are beings
who can see through time, and that there is something to be seen in the spacetime of the past, which may not be the case as we speculate further.
The Shape of Flatland Universe
Now I will continue the assumption that the
laws of physics and observed state of nature apply equally to the Flatland
universe as it is in our three dimensional universe. One observed phenomena of
our universe is that of an expanding space, with galaxies moving away from us
and faster the further away they are. The conclusion of such observation is
that there was once a point in time where all space and matter that ever exist
were once a singularity, and the point where it ceased from being a singularity
has been known as the moment of Big Bang.
Now suppose the Flatland universe also has
a moment where everything was a singularity. That moment lies in the past – we
will say 13.7 billion years in the past just like our universe. The point has
been made that as a three dimensional creature, we say that the past in the
time dimension of the flatland is down. Now following that everything that ever
was, and all space that ever exists, were once a singularity in the beginning,
it would mean that all down direction of all space where time is 0 is a single point
in the down direction. An area where all the downwards (or inwards) direction
is a singular point would describe an area of a sphere, or something close to a
sphere depending on the distance between a point in the area to the central
point downwards.
This goes to show that our flatland
universe would have its space curved into something like a sphere. How apt
then, that Sagan in the Cosmos episode The Edge of Forever, shows a
visualization of a sphere to explain the expansion of space and the apparent
movement of galaxies accelerating away from any one point. If time could serves
as measurement, then the radius of such sphere would be 13.7 billion years as
observed by the acceleration rate of galaxies.
As we know it in our universe, the basis of
the big bang theory is the observation that the universe is expanding, and that
galaxies are racing away from us, and faster the further they are from us.
However, there is not enough force to explain what drives the expansion. As I
understand it, it has been theorized that the force that drives this expansion is
dark energy.
Now imagine again the visualization that
Sagan gave us through the expanding sphere in a flatland universe. I am struck
by how similar it looks to an expanding beach ball, or any kind of ball that
uses air pressure to maintain its form for that matter. What drives the
expansion of the beach ball, of course, is the air that we are pumping into it.
But there is no cosmic pump from outside of the sphere plugged into the fabric
of cosmos to drive the expansion. It should have come somewhere from the inside
of the sphere. As we have established,
we are calling the inside of the sphere as the “down” direction of time
dimension, or in other words, the past.
So there is something from the past, some
force that is driving the expansion of space itself. This hypothetical force,
aside from driving the expansion of time, is also driving the two dimensional
space towards the “up” direction, or towards the future. Without this force, there
would be no expansion of space and there would be no sense of time progressing.
The citizens of flatland, being trapped in two dimensions, would not be able to
point to the direction of this force.
So this force would be coming from past and
drives both the expansion of space and the progress of time itself. For
brevity’s sake, I will call it “Time force” or Ft in my illustrations. So what
Dark Energy is, is actually the Time force itself that is pushing the fabric of
space time, which is space as it is in a given moment, outwards. This time
force would be pushing space everywhere, in all of space, presumably in equal
force.
Mass and Black Holes in This Understanding of Flatland
Mass is understood to have created the
force of gravity, but the explanation of what mass actually is, is still being
debated (or has it been clarified by the findings in Quantum Theory?).
Regretfully, my understanding of quantum theory and the study of the seat of
mass is woefully inadequate. But from what little I know, that gravity is the
result of the bending of space time by mass, I would like to make a leap in
speculation that is based solely on my own thought and not based on any
observations.
I speculate that mass is the manifestation
of interaction between the Time force and some subatomic substance that tugs
the fabric of space time at towards the direction of the past. Dark Energy is
simply Time force that does not interact with such subatomic substance. What we
perceive as mass then is truly a construct of the bending of space; a warp in
the “fabric” of space time at the present. This means that somehow, in Flatland
universe, gravity works not only on the traditional spatial dimensions, but
also on the time dimension where there’s an actual “down” direction.
Let’s take all these speculations further
to consider the phenomenon of black holes, where the force of gravity is so
great that even light cannot escape. Considering that in flatland we use the
direction of “down” as the past, assuming that black holes form wormholes that
connect to another opening of black holes in some exotic dimension or another
universe or another point of space and time would be incorrect. Instead, in a
black hole, the fabric of space time at present bends towards the “down”
direction or the past.
It is said of black holes that they occupy
a singularity of space. Also, there are many possibilities of the fate of a
black hole theorized. As the gravitational pull of a black hole is too strong
even for light to escape, then can matter and information be truly destroyed
from the universe? Could the amount of radiation released by a black hole
account for all the matters and energy that is consumed by a black hole? And
then, could we one day detect evidence of black hole evaporation events when
enough energy escapes the black hole until the mass of a black hole is reduced
until light can finally escape?
Back in the flatland universe, if we accept
that the black hole occupies a singularity of space, this would mean that the
flatland space time has a curvature that is infinite, and the curvature goes
infinitely “down,” or rather, it would bend only to the point of the original
singularity of t=0.
Considering this, I speculate that the matter and information
trapped by the black hole go “down” through the curved fabric of space time of
present to reach t=0, or at least t=certain point in the past, where in a
process beyond my understanding and is admittedly just pure speculation, is
processed to become the energy that fuel the Time force that expands space and
time. In a sense, physical information is not lost, but processed to become the
Time force (since mass and energy is equivalent – E = mc2).
How the End and Beginning of Flatland Might Look Like
I will now speculate on the ultimate fate
of the flatland universe as space expands further away into the future. Space
would one day expand so greatly that matters began to disintegrate. The
universe would be empty of matter, with only black holes scattered throughout
space. At that point, there would be no more matter that black holes can
devour. If Time force is dependent on mass to become energy, then one day there
would be no source of energy to expand space time. Perhaps this would be the
start of the evaporation event of black holes.
I imagine that such event would happen more
or less at the same moment. There would be no more bending of the fabric of
space time. There would be no interaction between Time force and the subatomic
substance that created the illusion of mass and gravity.
Let me wildly speculate further on the fate
of flatland universe after there’s no more Time force and no more bending of
the fabric of space time. Just like a star that has exhausted its Hydrogen fuel
and starts to consume Helium instead, the singularity would begin to consume
back Time force that it has produced. At this moment, the fabric of space time
would lose its meaning, both as a concept of space and a concept of time. There
would be no more time force to expand space and move time forward (“outward” in
the three dimensional map of flatland), and there would be no more matter also.
It’s not difficult to imagine the absence of expansion of space – we are well
aware on the limitations of space around us. However, without matter and
forward movement of time, then truly there would be nothing left to define an
existence of anything.
So in the end, even all the energy of Time
force is consumed back to the singularity of t=0, the exact same condition as
the big bang. This would mean that the end of our universe would be exactly the
beginning of the next reincarnation of the same universe, which would mean that
the flatland universe is an oscillating universe. However, the oscillating
universe doesn’t have the fabric of space time crunching back through the past
to become a singularity. It would simply create a new fabric of space time,
completely separate from the previous fabric of space and time which, to
repeat, would have lost its meaning.
Explaining the Distribution of Galaxies Using Assumptions
and Speculations of the Flatland Universe
It has been noted that the distribution ofgalaxy is not evenly scattered throughout space and time, but clumped together
and is distributed almost “like on the surface of bubbles” as Sagan noted. There are amazingly large areas of complete emptiness
between the strings of galaxies, which was noted as being similar to “the
inside of the bubbles.”
How would the Flatland universe look like
if the distribution of galaxies is anything like the observation made in our
universe? If we visualize the sphere of flat land universe, we would see it
more like a standard soccer ball, with lumps on the ball and galaxies
distributed on the crevasses of the ball (this analogy doesn’t work on some
soccer ball designs like the Jabulani). Or, to make a simpler analogy, we can
imagine it like bubbles on a flat surface, while keeping in mind that only
where the surface of the bubbles touch the flat surface do the galaxies are
distributed.
Considering mass as a manifestation of the
warping of space and time, in the flat land universe, this would push mass
towards the bent space. Meanwhile, Time force keeps on acting to expand the
fabric of space time outwards. As a
result, bulges form on spaces where there is no mass that warp the fabric of
space time. These bulges in Flatland universe would become the empty space
where no galaxies with enough mass could venture into. These bulges would, in
our three dimensional universe, be the inside of bubbles where there is no concentration
of galaxies.
If this is true, then in the flatland
universe, it would appear that there are some imaginary central lanes forming
between the bulges. Then galaxies, following the bending of space time, would
be pulled towards it and then move past the central lane, only to stop and move
back. The apparent movement of the galaxies in the Flatland universe as
observed by three dimensional being would be like a pendulum. Perhaps then,
like the pendulum, we can see that a galaxy that moves towards the central lane
would be accelerating relative to the central lane and a galaxy that moves away
from the central lane would be decelerating relative to the central lane.
The Apparent Flatness of Space in Our Universe
According to observations from WilkinsonMicrowave Anisotropy Probe, it has been observed that “the observable universe
is flat with only a margin of error of 0.5%.” Unfortunately, again, my
understanding of the nature of observation is woefully inadequate to fully
comprehend it. I could only infer that my assumption about our universe being like
the Flatland universe I have been conjecturing is flat out wrong.
The only way this observation could be
reconciled is to take the margin of error and surmise that the universe as a
whole is amazingly large that the apparent flatness is such that the observable
universe follows a local geometry.
So let’s say that a flatland observer
observed that that the observable universe is flat with only a margin of error
of 0.5%. I know that the margin of error of 0.5% does not mean that it is
curved to a 0.5% of a full circle, but for simplicity’s sake and absent further
understanding I will assume that 0.5% is the curve of the flatland universe.
This means that far as the observable flatland universe is concerned, which is
27.4 billion light year in radius (or 13.7? Should we account for the space
that has moved away from us since 13.7 billion years ago?), the local geometry
of the observable universe is 99.5% flat and 0.5% curved.
Considering that, could we then surmise
that 0.5% of the sphere of the flatland universe (figure 4) is 54.8 billion
light years long? We take a point of the event horizon in the flatland universe
(edge of the observable universe) and take the opposite point, then we make
imaginary lines from those points towards t=0 in the third dimension of time.
Then I just wonder if with the assumptions made, the two intersecting lines
would make an angle of 1.8 degrees, which is 0.5% of 360 degrees of a full
circle.
If, and it’s a very big if, all these
assumptions are near correct, then we can roughly calculate the size of the
flatland universe! The full circumference of the sphere would be 54.8 billion
light years times 360 degrees divided by 1.8 degrees, which would be 10,960
billion light years. This means that the
radius of the sphere in terms of distance (not time) is 1.745 trillion light
years. The area of the sphere then would be 3.82 x 1025 Light years2.
I wonder then if we could use the radius of
the sphere to infer the volume of space in our three dimensional universe. What
is a four dimensional sphere? There is a concept of spheres in higher dimensions,
called the n-Sphere where the n denotes the number of dimensions of the sphere.
For example, in flatland universe, the area of the universe is a two
dimensional area on a three dimensional sphere (the third dimension being the
time dimension). This is understood as the sphere being 3-Sphere, and the area being
in n-1 dimension.
In our universe then, with the fourth dimension
being the direction of time and accepting the assumption that the shape is spherical,
then it would be 4-Sphere where the volume of the universe would be the three
dimensional “area” of the 4 sphere. The formula for the three dimensional space
of the 4-Sphere is 2Π2R3 (since the area of a
3-Sphere is 4ΠR2, then
the additional dimensional space is the 2D area of 3-Sphere times (2Π2R3 / 4ΠR2 = ½ ΠR). If these were all true, then the
total volume of the universe would be approximately 1.046 x 1038 Light
years3.
There Wouldn’t Be Time Travel in Flatland Universe
Many have speculated whether it is
physically possible to time travel in reality. In the hypothetical Flatland
universe with properties as I have presumed, I do not think that is the case.
The only space that exists at any given time would be the space at one certain
position at t=present. Some of the fabric of space time may be curved more
towards the past due to gravity, but they still represent the same point of
time t=present. This would be true even
on the extremes of space time bending like the black holes. In another sense, everything is travelling through the time dimension to the future, but not the past.
The only thing that exists in the past, or
t=past is only the Time force that is pushing space and the matter it contains
outwards. There would be neither space nor matter in the dimension of time
whether in the past or the future. In
the oscillating universe of flatland, matter and even Time force do not survive
to the next reincarnation of the universe.
So Many Questions Unanswered
Due to severe limitations of my
understanding, I haven’t discussed many aspects of physics in this flatland
universe model. Electromagnetism, nuclear force, quantum theory, Quasars, et
cetera are beyond what I can plausibly presume. Even the speculations I’ve made
are stretching what’s plausible. I couldn’t comprehend enough to offer any
method on how to test all these ideas (with a possible exception on the motion
of galaxies). I hope that someone who has a more thorough understanding of these subjects to point out to me where the logical or observational fallacies lie so I can properly correct, or even discard, some if not all of these ideas.
Appendix
Additional Random Considerations and Disjointed
Thoughts of the Flatland Universe
On 4th of July 2012, experiments
at the Large Hadron Collider have confirmed on the existence a subatomic
particle of Higgs Boson. I wonder if this could be considered the subatomic
particle that interacts with Time force to create mass, and that Higgs field could
be considered the fabric of space time itself?
I wonder about how to explain quantum
theory and string theory with this model of Flatland universe: how would
subatomic particles and quarks behave absent one spatial dimension? I wonder if
it’s realistic to presume that the behavior eludes observers because they move
about in that extra dimension of time. I'm suspicious that the way scientists are trying to describe the characteristic of elementary particles in the standard model as having flavors is due to the elementary particles moving about the fourth dimension of time. Imagine a flatlander trying to describe the elementary particles that move about the time dimension up and down, while only being able to observe the two dimension of space. The flatlanders would be hard-pressed to explain energy that strikes the two space dimension from differing angles within the time dimension. I wonder if the flatlanders would then describe the elementary particles as having flavors.
Any living creature on the flatland would
not be able to have a digestion tract which has the food intake at one side and
the excretion at the other side. That would split the creature in half, with no
extra dimension to put them together. So any predatory creature that eats of
“plants” or “animals” would either have a digestion system where the intake and
excretion at the same point, or it would have a completely exotic system yet to
be imagined. Perhaps evolutionary forces would produce many “flying” and
“jumping” creatures since relative horizontal movement would be difficult on
planets with bumps and valleys.
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