| Adapted for the Internet from: Why God Doesn't Exist |
1.0 What is the cone of light?
The Holy Cone of Light is an hourglass-shaped icon worshipped by relativists and an integral part of their religion:
- “ In relativity this cone plays a very important role and it is called the ‘light cone'.
It divides the universe into three different regions: the interior above, the interior
below, and the whole exterior.” (p. 66) [1]
[My God! I hope it doesn’t cut me in half!]
Relativists use this pseudo-analogy to describe to the layman how the top speed of light limits the spread of information in a
specified amount of time, a concept known as the cosmological horizon. For all practical purposes, the cosmological horizon
is the size of our Universe. In the language of the idiots of Mathematics, there is probably something beyond the ‘observable
universe,’ but it doesn’t concern science because it can’t affect us and because scientists can’t prove anything beyond this
boundary. Whatever lies beyond belongs exclusively to Philosophy.
Relativists believe that the cone analogy is also useful to illustrate the differences between time-like and space-like events.
What it really shows is that relativists have trouble understanding the difference between a picture and a movie.
In his book, Heidmann narrates how the sacred cone came to be and why it comes in handy to ‘understand’ space-time. He
begins his dissertation by proclaiming that Einstein:
- “ introduced the concept of the four dimensions of space-time, intimately interwoven,
which gave a new description of the real world.” [2]
This gives the misleading idea that Heidmann is going to talk about a physical object that has length, width, height, and some
other unspecified dimension which he will purportedly cover during the presentation. Instead, his entire speech is about
position (coordinates), motion (vectors), and time (number lines). Not once does he talk about the dimensions he advertised:
- “ A map traced on a transparent rectangle represents a small town…circles mark
the position of cars…Let us repeat this mapping operation for midday plus 10
seconds, plus 20 seconds, and so on. Within this transparent set of maps, the
positions of the Column define a vertical axis that is a reference for time…A
stationary car traces out a vertical line…a car clicking along First Avenue at 50
kmph traces out a sloping line” [3]
Oblivious to this, Heidmann continues to refer to the axes as ‘dimensions:’
- “ This transparent plan is a two-dimensional representation of the town…
Our imaginary town actually represents the three spatial dimensions of the
universe.” [4]
Heidmann utterly confuses spatial dimensions (length, width, and height) with coordinates (longitude, latitude, and altitude)
with number lines (parallel, meridian, and time) and with vectors (depth, breadth, and elevation). He describes the latter, but
implies the former and reaches a stunning conclusion: that we can stack a bunch of maps on top of each other and build a
cone. Think of a blot of ink that expands from frame to frame on a film. If we stack the frames vertically, we build a cone, from
the initial dot of ink to the last. But if the vertical axis is taken up by time (each frame in the film), we must surrender a spatial
dimension of the blot of ink (e.g., its height). Therefore, we are limited to seeing cross-sections of the blot of ink in every frame.
If we wanted to see the negligible yet greater-than-zero height of the ink blot we would have to get rid of time. We simply can’t
have height and time simultaneously on the same space-time diagram. Heidmann insinuates this when he asks rhetorically:
- “ Now how are we going to pile them up?” [5]
Heidmann is alluding to the fact that whether we aggregate squares or cubes we end up with the same rectangular box. In
other words, we can stack 3-D ink dots vertically (through the axis of time) and arrive at the same cone that we would build
with cross-sections. He insinuates that this inability to visualize 3 spatial dimensions moving through time is due to human
limitations:
- “ We need another dimension, in addition to the three we have already; but there
is no fourth spatial dimension in the real world. In relativity theory there are four
dimensions, however; three of space and one of time, but it is impossible four
our human senses fully to visualize what this means.” [6]
All prominent relativists more or less explain the Holy Cone in similar ways. (See for example Hawking, p. 24-30 [7] and
Penrose, pp. 193 – 221 [8] )
2.0 Integration: how Math comes into the picture
Relativists suggest a method – short of morphing into a 4-D monster – that enables a juror to construct the cone and by
extension ‘understand’ a 4-D object. This method is the mathematical process of integration, a technique that consists of
constructing an object gradually by aggregating subcomponents or cross-sections. This is how the cone analogy fits in
with General Relativity.
For example, assume that you have a cube that has 1 meter per side. If we have three such cubes in series, we can calculate
the volume of the resulting rectangular box (Fig. 1):
- “ Mathematically, volumes are defined by means of integral calculus, by
approximating the given body with a large amount of small cubes, and
adding the volumes of those cubes.” [9]
An alternative way to do integration is by moving the cube to three successive locations (Fig. 2). [10] The cube has effectively
scanned a volume the size of a rectangular box. We could also have constructed the box by scanning a square.
- “ the plane is derived affinely by sliding one straight line along another. If we
now displace the plane E along a straight line…the plane passes through all
space.” (pp. 18-19) [11]
Euclid was one who relied on integration to ‘construct’ his geometric figures. He peppered Elements with instructions on how
to draw planes and build solids:
- “ To construct an equilateral triangle…” (Bk. I, Prop. 1) [12]
“To draw a straight line…” (Bk. I, Prop. 12) [13]
“ When a semicircle with fixed diameter is carried round and restored again to
the same position from which it began to be moved, the figure so comprehended
is a sphere.” (Bk. XI, Def. 14) [14]
His breathtaking techniques have survived unscathed for 2000 years.
| Holy Cone! |
Following Euclid’s lead, the mathematicians continue to construct their solids dynamically. Some rotate, others translate,
and yet others integrate planes.
Shapiro tell us that:
- “ A sphere may be generated by revolving a semicircle through 360º about its
diameter as the axis.” [15]
[Let’s test Shapiro’s assertion. Take half a pizza. Rotate it once about itself. If you
did the experiment correctly, you should end up with half a pizza and not with a
ball! Likewise, if we perform a similar experiment in Geometry, we should end
up with a semicircle. A sphere is a solid and not the space scanned by a plane.
Shapiro confuses volume with solid. The word sphere doesn’t even belong in
an encyclopedia of Mathematics. A sphere cannot be calculated, believed in,
predicted, or proved. It can only be illustrated and named.]
However, it is obvious that whether you swing a pizza or a basketball around yourself, the doughnut-shaped volume either
scans in space is the same if they both have the same radius (Fig. 3). This has nothing to do with our limitations as 3-D beings
as the idiots of relativity like to say. This has to do with the fact that time is not a dimension – surely, not one comparable to
length, width, or height. This experiment conclusively shows that whether we include motion, time, temperature, or whatever
parameter relativists wish to factor, our physical universe is always 3-D, no more and no less.
Until the idiots of relativity can show a still image of a 4-D object they cannot talk about four ‘spatial’ dimensions. If they must
explain through analogy, it means that they are moving something. If they are moving something, this something does not
trace a dimension in Physics. It traces either a vector or a number line. Never should any of these axes be confused with the
others. Therefore, advocates of four ‘spatial’ dimensions need to show static objects if they want to talk about geometric
figures. If they ask you to watch a movie of cross-sections or dynamic slices, they are invoking time. In Physics, dimensions
are exclusively static concepts.
A. A still image of a cube. A. A still image of a cube B. A still image of a rectangular box B. A movie of a moving cube |
A routine misconception that relativists pass on to laymen is that a 2D plane moving through the ‘dimension’ of time scans
and thus ‘constructs’ a 3D object. In like manner, a 3D solid moving through or growing in time paints a 4D space-time.
Experiment refutes both these claims. I swung around a pizza at home to test whether I would end up with a doughnut. I
didn’t. I ended up with a pizza (which I ate afterwards). Crazy Al’s doughnut is not a still photograph, but a film! Whether
relativists factor in motion or time or temperature, our physical universe remains 3-D!
It is using dynamic ‘integration’ methods that relativists have inferred the large-scale structure of space-time and constructed
their Holy Cone. The mathematicians conceptualize our Universe as one of two: an integration of events or as a sphere
(i.e., a 3-D space-ball) expanding through time.
Some relativists integrate events:
- “ Space-time: The four-dimensional space whose points are events.” [16]
“ Space is the set of all points.” [17]
“ it is hard to believe that space-time is smooth at or below the Planck scale.
Space must be broken up and quantized.” [18]
- “ To find the distance Ds between two points a finite distance apart, we sum up
the differentials by integrating the metric along the geodesic connecting the
two points…By integrating this metric along the world line connecting two
events in flat spacetime, we can find the interval Ds between the events. Again,
there are easier ways to find the interval in flat spacetime, but in the curved
spacetime of GRT, finding the line integral of the metric is the only way that will
work, in general.” [19]
- The ‘block universe’ of relativity consists of every event that ever happened and is still to occur. [20]
Other relativists feel more comfortable translating or aggregating movie frames:
- “ Did you know that a four-dimensional sphere can be drawn on a web page?
This 4D-sphere actually complies with the relativistic geometry of our universe… [21]
a true 4D-sphere can only be shown properly in animation! No printed material
can possibly depict such an object appropriately…since time is the fourth
dimension, every object with four dimensions has to appear as moving… else
it is merely a familiar "static" 3D-object.” [22]
- “ Suppose that O is an enduring solid ball. What shape is O intrinsically? O’s
intrinsic shape is spherical. What shape is O extrinsically? Since O occupies
successive spherical regions of space-time, the region of space-time that O
fills is not spherical. Rather it is the four-dimensional analogue of a cylinder.
This is O’s extrinsic shape.”[23]
[Halleluiah! God has blessed these boys! Praise the Lord, they are saved! They
are among the few who realized that space-time is not a static geometric figure.
Now… is a video the same thing as a photograph? Is a shark moving through
the water the same as a shark? Is a shark moving through the water a four-
dimensional object? Unfortunately, most people seem to have brains for only
half the analysis. These gullible upstarts confuse a photograph with a movie!
The shape of a sphere doesn’t change because it moves (for else it would no
longer be called a sphere). Without memory, there is no ‘extrinsic’ shape of an
object except in the minds of deluded morons! A sphere that moves ‘in’ space
continues to be a sphere every step of the way. It becomes neither a cylinder
nor a thermos bottle. In every frame of this film that the idiots of relativity wish
to inspect they will only find a sphere! Once again, and for the benefit of mathe-
maticians only: (3D * 10 seconds ≠ 4D object) !!!]
The specific variant relativists use to ‘explain’ the Cone of Light is not the one where they aggregate solids (Fig. 1). Their
version consists of translating or aggregating planes (Fig. 2). In effect, what the idiots of mathematics do is remove the
dimension of height from a physical object and replace it with the seemingly equivalent ‘dimension’ of time while insinuating
that we still have a 3-D object:
- “ I shall generally use diagrams in which time increases upward and one of the
spatial dimensions is shown horizontally. The other two spatial dimensions
are ignored or, sometimes, one of them is indicated by perspective. These
are called space-time diagrams” (p. 24) [24]
“ To be able to represent conditions graphically we suppress one
space-co-ordinate, assuming space to be only two-dimensional, a Euclidean
plane.” (p. 150) [25]
With this innocent sleight of hand, relativists are now, after all these centuries, able to see what happens along the
forbidden temporal dimension, an ability heretofore reserved to 4-D beings. The cone is an analogy of our 4-D universe
and a momentous insight, comparable in significance to the striking 3-D revelations made by A Square to his fellow
Flatlanders. Relativists construct their cones with cross-sections of light emanating from an event as this light goes
from inception to the future.
Before we open the champagne bottles, however, it would behoove us to do a sanity check just to make sure that we
crossed all the t’s and dotted all the i’s. Perhaps relativists are doing something illegal. I submit three tests to verify
whether they can get away with their proposal.
3.0 Holy Cone: object or volume?
- The Holy Cone is an analogy that relativists use to persuade you that they can infer structural aspects of our Universe
(e.g., curvature of space, distribution of stars and galaxies, whether it is closed or infinite, etc.) through measurement
of parameters such as mass, density, and speed.
- “ In special relativity, a light cone is the pattern describing the temporal evolution
of a flash of light in Minkowski spacetime. This can be visualized in 3-space if the
two horizontal axes are chosen to be spatial dimensions, while the vertical axis
is time.” [26]
“ How is the universe organized on large scales? How did this structure evolve…
I review observational studies of large-scale structure, describe the peculiar
velocity field on large scales, and present the observational constraints placed
on cosmological models and the mass density of the universe.” [27]
[The universe is a structure? What contours and gives shape to the universe?]
“ We present a new method for calculating linear cosmic microwave background
(CMB) anisotropy spectra based on integration over sources along the photon
past light cone.” [28]
- The strategic word cone insinuates that the mathematicians are working on a physical object like a mechanic works on
a car. In the same way, the term space-time is supposed to convey the idea that we live inside an unfathomable 4-D
sphere of sorts. The Holy Cone is a geometric theory closely tied to General Relativity’s warped space theory. The liberal
use of words such as cone and object mislead jurors into believing that the dissertation is about Geometry and architecture
when in fact the theory has nothing to do with either.
The Holy Cone is, thus, stealthily insinuated as an object or perhaps as a volume. As an object, we can have hope that
the dissertation is about Physics. If the cone is a volume, the cone can conceivably belong to Mathematics. If neither,
then what is the Holy Cone of relativity? Why is it referred to as a cone and not as the trajectory or area or volume that
light covers in a given amount of time? Is the cone a metaphor? Is it a euphemism? What does it have to do with Physics
or, for that matter, with Mathematics? Let’s find out.
- 4.0 So, what then is the Holy Cone?
- The Holy Cone of Light is clearly not an object despite that this is what relativists insinuate. The everyday cone of Geometry
is a three-dimensional figure: a physical object. A cone is a solid, a still image or static sculpture that we visualize in a single
glance. All that the ET needs in order to ‘assimilate’ the earthly cone is his eyes. Therefore, the Holy Cone does not belong in
Physics if it is built piecemeal. We do not build cones with light wave fronts in Physics. Such surrealism is restricted to religion.
The Holy Cone is also not a volume. We deduce this by simply looking at the units. When we finish calculating the volume
of a cone, we should end up with units such as meter cubed (m³) or inches cubed (in³). By forcefully replacing height with
time, relativists replaced meters with seconds and predictably end up with a ‘volume’ stipulated in incongruous units (m²s).
These units stand in direct contradiction with the units specified in the definition of volume: ‘length’ cubed. This would
merely show, once again, just how careless and inconsistent mathematicians are with their own definitions. Therefore, the
cone doesn’t seem to have anything to do with Mathematics either.
The Holy Cone of relativity is neither a geometric cone nor a volume, but rather a movie of an expanding circle:
- “ The ripples spread out as a circle that gets bigger as time goes on. If one thinks
of a three-dimensional model consisting of the two-dimensional surface of the
pond and the one dimension of time, the expanding circle of ripples will mark
out a cone whose tip is at the place and time at which the stone hit the water”
(p. 25) [29]
Each frame in this film that relativists wish to inspect shows a single, 0-thickness slice: a circle. The Holy Cone is not a solid
or a volume because:
- • it is a movie
• in any frame of this film all you have is a shell of light surrounding the object
- that gave it origin
- • the alleged sculpture is perpetually under construction
But then, as always, we have a punch line:
“ The light-cone also has a particular shape that can only be adequately visualized
as a 4D object.” [30]
- [Visualized? You like to 'see' with your eyes?]
So after all is said and done, the Holy Cone of Relativity was actually another of those unimaginable 4-D objects, or volumes,
or whatever.
So Bill? Why is it that you say that relativists are a bunch of gullible idiots?
5.0 Conclusions
To summarize, the Holy Cone of relativity is neither an object nor a volume because it meets none of the foregoing criteria
for objects and volumes. It is neither static nor does it occupy space. It doesn’t have units of volume, and is actually a film
of an area moving through time, a light front so to speak. The cone of relativity is not a cone but, at best, a film of a dynamic
circle. (Or maybe of a sphere... who knows?)
My final comment is that the absurd notion relativists have that they can get away with replacing a static dimension such
as height with a dynamic number-line such as time originates in the forceful habit mathematicians have of arbitrarily
interchanging dimensions, coordinates, and vectors or suppressing them at will. To this day, not a single relativist can
justify why he does any of this. In Physics, we don't replace width with latitude or with breadth for fear of being treated
as idiots.
Fig. 3 Crazy Al’s dimensional doughnuts |
| The Holy Cone is the most sacred icon of our religion. |
- Module main page: Analogies are for laymen?
- Pages in this module:
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- Copyright © by Nila Gaede 2008