Download THE CURSE OF THE PLANCK LENGTH

MULTIPLE DIMENSIONS
THE CURSE OF THE PLANCK LENGTH AND
THE DIGITAL INFORMATION CATASTROPHE
ABSTRACT :
It is the ultimate dream of physicists to forge a hypothetical single, allencompassing, coherent theoretical framework of physics that fully explains
and links together all physical aspects of the universe, a single mathematical
framework in which all fundamental forces and units of matter can be
described together in a manner that is logical and coherent with current and
future observation. Having extra dimensions of space makes it possible to
substantiate such a theory … five-dimensional anti-de Sitter space, 26dimensional spacetime in bosonic string theory, 10-dimensional spacetime in
superstring theory, and 11-dimensional spacetime in supergravity theory …
Starting with the exploration of the fourth dimension envisioning why it is not
possible to physically explore a higher dimension a surprisingly simple
deduction will have a significant impact on the quest and research of ndimensional spaces with repercussions in those fields of science where extra
spatial dimensions, if they really exist, are thought to be curled-up, or
compactified.
KEYWORDS :
string theory, fourth dimension, compactified dimensions, m-theory, f-theory,
bosonic string theory, Planck length, graviton, perceptron, neural network,
prefrontal cortex, basal ganglia, higher intelligence
A satire of science and mathematical fiction, the work of Edwin A.
Abbott. It takes the reader into the journeys of A. Square, a
mathematician and resident of the two-dimensional Flatland. Through
strange occurrences that bring him into contact with a host of geometric
forms, Square has adventures in three dimensions (Space land), one
dimension (Line land) and no dimensions (Point land ) and ultimately
dreams of visiting a land of four dimensions ….
…. One day this world is visited by a three dimensional object, a sphere,
to introduce the idea of a third dimension to the square, in hopes of
educating the inhabitants of Flatland on the third dimensional reality.
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The sphere tries to convince him by example of the existence of a third
dimension, “look at me magically passing through your world” and
as it passes through, all that the square will see is a growing 2
dimensional circle until the sphere is half way through. As it moves
further through, all the confused square (!) will see is a shrinking circle,
until it is no more” ….. so the story goes !!!
The Flatlander - those who introduced this fictional world into the
world of physics and turned it in a thought experiment did so to have a
stepping stone to a world with multiple dimensions.
The fictitious two-dimensional realm as a link to another world beyond
the three-dimensional reality, an unrealistic assumption to create a
realistic representation of an impossible world in order to give another
speculative world legitimacy.
If the two-dimensional world would already exist and assuming that a
sphere is passing through a certain area of that world the square as an
inhabitant of that world has not the ability to perceive the passing as a
circle, he is a two-dimensional entity NOT a three-dimensional
inhabitant of the world of the sphere, a three dimensional space with
three spatial dimensions and one temporal dimension, the only thing he
sees is a (short) curved line .... Nothing else. He has to shuffle around
to find out that the line is closed unaware of the final shape.
The sphere an inhabitant of the three dimensional world is not restricted
to only two dimensions, a third dimension "height" frees him from
living on that flat two-dimensional world and enables him to rise above
that level … literally.
And so we arrive in a reality where an object, a space is described …
with three numbers width, depth and height, numbers that can vary
independently from one another, for an exact location on his world are
longitude, latitude and elevation above sea/ground level the most
important numbers, and in mathematics and physics it is about
dimensions, a number of independent coordinates to specify any point
in a given space.
And the story continues …
Flabbergasted the square asks the sphere what exists beyond the 3-D
world; the sphere is startled because he as the square before him can't
comprehend a world beyond his, and in this way, stands in for the
reader. Our brains are not set up to detect a higher dimension other than
2
our three dimensional world, and there has to be something more to
make that possible.
And that other world the square is referring to is the four dimensional
world. (drop the time part completely and consider a four dimensional
space, a space just like our three dimensional space, but with one extra
dimension)
So the question is “ what would happen when (!!!) a four dimensional
sphere would pass through the three dimensional world”? The first
thing the three dimensional inhabitant would see is a point and then a
curved circle growing bigger and bigger into a sphere, slowly sliding
towards a point to disappear.
THE DIGITAL CONNECTION
If the square in Flatland is to observe something, it must be able to
process information (data) in some kind of neural network.
Neural because one considers the square in this story as a primitive life
form with eyesight and the ability to move … name the constituent part
of that neural system a “perceptron”, invented in 1957 by Frank
Rosenblatt at the Cornell Aeronautical Laboratory. A perceptron being
the simplest neural network possible: a computational model of a single
neuron.
A perceptron consists of one or more inputs, a processor, and a single
output.
This simplified neural network by the nature of its environment is a two
dimensional one and individual perceptron’s have the ability to receive
an input, process it and generate an output. a [0] OR a [1] (the Heaviside
Step function).
The sphere on the other hand in his 3-dimensional world, will make use
of a more sophisticated type of neural network, where the processing
of data (information) will result in a TWO digit answer, and with a [0]
AND a [1] or [ON] AND [OFF] there are an infinite ways to understand
and describe the world.
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So why is it that the three dimensional sphere is unable to perceive or
even enter a higher dimensions” ???
The answer is that there is a layer of information missing: in the 2dimensional world a second layer of information is missing to enter the
3th dimension (only [0] OR [1]), and in the 3th dimension a third layer
of information is missing to enter the 4th dimension (only [0] AND [1]),
meaning that the fourth dimension is a three digit [0] AND [1] AND [?]
system that has not yet been deciphered, until then ….
( perceptron with n inputs, weights and bias are initialized with random
values between -1 and 1. Working with values -1 and 1 in essence does
not differ from using 0 or 1)
So there we have it, the sphere being the personification of real beings,
us, living in the reality of a 3-D world, endowed with a neural network,
a brain.
The question is if those neural computation are (part) digital and
whether the brain is a computer or not?
The perceptron (artificial neuron) has a number of input channels, a
processing stage, and one output that can fan out to multiple other
perceptron’s, it simulates a biological neuron with dendrites that
receives signals, have a cell body to process them, and axons to send
signals out to other neurons.
THE BRAIN CONNECTION
A region of the human brain that scientists believe is critical to human
intellectual abilities surprisingly functions much like a digital
computer. Digital computers operate by turning electrical signals into
binary "on and off states" and flexibly manipulating these states by
using switches. The neurons in the prefrontal cortex are binary, they
have two states, either active or inactive and the basal ganglia is
essentially a big switch that allows you to dynamically turn on and off
different parts of the prefrontal cortex. (1)
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Physicists have developed a technique that can tell which part of the
brain rely on analog signals and which rely on digital signals.
The approach of Mochizuki and Shinomoto (…. empirical Bayes
modelling designed to simulate analog signals, hidden Markov
modelling designed at capturing properties of digital codes to
determine whether a neuronal signal is digital or analog) indicated that
parts of the brain rely on different forms of encoding. Fractions of
neurons exhibiting analog and digital coding patterns differ between
the three brain regions. (2)
It all points to the fact that neurons in specific areas of the brain exhibit
digital characteristics and have a similar working as the perceptron in a
layered feed forward neural network and once the result of those
neuron’s calculations is turned into an output signal, that signal travels
to an activation function in (one, both or ..) the three brain regions
where things become analog by turning that digital signal into an
internal electrical signal.
Speaking of neurons “calculating” is a matter of speech, neurons
receive signals from the synapses and will react accordingly,
active/inactive (on/off, 0/1, 1/-1) …. a binary response.
It is not difficult to make the connection with the world of the sphere
“the personification of real beings, us, living in the reality of a 3-D
world, endowed with a neural network, a brain …” and missing an extra
layer of information to enter the 4th dimension, being a three digit [0] [1] and [?] system that has not yet been deciphered.
It is this organic restriction in our brain that is responsible for certain
information being unavailable and thus obscuring the n-dimensional
image, and why only a mathematical approach gives a limited insight
into the fourth dimension.
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THE CURSE OF THE PLANCK LENGTH
Is the universe concealing dimensions that are too small to see ?
String theory posits that the world is made of incredibly small strings
vibrating in n-dimensional spacetime, and extra “compactified, curled
up” dimensions existing only on the microscopic level of strings, a
concept introduced to support super string theories with 10 dimensions,
m-theory with 11dimensions, f-theory with 12 dimensions, and even
bosonic string theory saying that our world is 26 dimensional ……
In string theory, oscillating strings are in the order of magnitude of the
Planck length.
The bosonic string theory is the length scale at which the structure of
space becomes dominated by quantum effects, and it is impossible to
determine the difference between two locations less than one Planck
length apart as a shorter length does not make physical sense.
Based on this argument, the limitation imposed by the Planck length
invalidates most, if not all theories of compactified and curled up
dimensions. It literally undermines the foundation of the existence of
extra dimensions in the world of strings.
“Closed strings or branes the size of the Planck length have diagonals
smaller than the Planck length and therefore mathematical and
logically cannot exist”
This argument was further elaborated in “Time The Elusive Factor - A
3D Time Structure - Orthogonal Scalar Time”(3) and “Addendum To
Time The Elusive Factor - A 3D Time Structure - Orthogonal Scalar
Time”(4). It is strongly advised to take a look at reference 3 and 4 to
estimate its importance.
Furthermore in physics the definition of a closed string is a string that
has no endpoints, and therefore is topologically equivalent to a circle,
but as proven a single string is unable to curl up and if that “closed
string” refers to a single string with the assumption that one of the
vibrational modes of a closed string can be identified as the graviton,
there is a problem.
….. the curse of the Planck length.
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CONCLUSION
Whether or not higher dimensions actually exist and mathematics
shows that they should exist, does their existence in mathematical
models actually translate to something that occurs in reality, or is it just
that a mathematical construct?
Speaking of hypothetical 4-ball’s, 4-sphere’s, hyperspheres, tesseracts,
hexadecachorons,
hecatonicosachorons,
dodecacontachorons,
hecatonicosahedroids in the non-compactified “n” dimensional world
some kind of deciphering needs to open up that world and if that
happens then there is no stopping, then all non-compactified
dimensions are available for exploration, but until then …. math rules
the imagination.
The answer on the question if the universe is concealing dimensions
that are too small to see we must accept that it is impossible that a string
with Planck length can be closed in the shape of a circle, to put it in the
correct context, even under any circumstance it is impossible to bring
two ends of a single string (in physics) together one way or another
ruling out compactified and curled up dimensions in string theory.
So does this argument debunk string theory? I do not think that there is
any reason to be pessimistic, new insights and approaches will come
forward and will reveal a universe that is built on “1-dimensional
fundamental constituents” …. the true beauty of string theory.
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References :
(1) Psychology Professor Randall O'Reilly of the University of
Colorado at Boulder
(2) Cornell University Library “Analog And Digital Codes In The
Brain” Yasuhiro Mochizuki, Shigeru Shinomoto
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(3) Time the elusive factor - A 3D time structure - Orthogonal scalar
time
https://doi.org/10.5281/zenodo.264258
(4) Addendum To Time The Elusive Factor - A 3D Time Structure Orthogonal Scalar Time
https://doi.org/10.5281/zenodo.268652
Hoc est proprium intellectualis G. KINET. Cum in aliis disputationibus
scriptorum citanda vel ut.
Paginae constans octo
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