Translated Fredkin Draft at www.digitalphilosophy.org
Lord of Chaos(Suresh Devanathan)
wording of the site www.digitalphilosophy.org, and content "Introduction to
Digital Philosophy". I make such claim to attract an advanced audience,
example Dr. Gill, Dr. Minsky, Dr. T Hooft and the like. I will post it both
on Usenet sci.physics, sci.physics.discrete and other yahoo groups The
Preface Digital Philosophy (DP) is fundamental to Nature. Philosophy of
Digital Physics, Digital Philosophy is a transcendental to everyday
intuition. We claim that all natural quantities are finite and occur in
discrete amounts. Theoretically, it implies every natural quantity can be
stored/manipulated/transformed as a finite integer variable. DP gets rid of
infinities, infinitesimals, continuities or any other naturally occurring
local random variables. Premises and consequences of a DP model will be
explained further. It is proposed that at the most fundamental levels of
physics, DP implies a totally discrete process called Digital Mechanics.
Digital Mechanics [1] (DM) forms a substrate for Quantum Mechanics. The
most fundamental assumptions of DP Universe Model are: a) All
fundamental quantities in the universe are integral. For example, the number
of neutrons in an atom can always be stored by an integer. An oversimplified
and attractive model is binary in the most microscopic storage of
information b) All fundamental processes can be modeled by a Turing
machine or an equivalent, for example, a modern day computer. A computer is
a useful tool for modeling the universe. A computer would keep track of
exact states of the universe. For example, given a reaction where a neutron
decays into a proton, an electron and a neutrino, a computer will tabulate
the number of neutrons, protons, electrons, neutrino with a formula, neutron
number = neutron number -1, proton number = proton number + 1, electron
number = electron number + 1, neutrino number = neutrino number + 1.
Although this paper focuses primarily on Digital Physics models, the
philosophy of DP applies to various sciences, like biology, chemistry. Our
work in progress "Introduction to Digital Philosophy", will be revised from
time to time. [1] This paper can be viewed as a continuation of my work
reported in a 1990 paper on Digital Mechanics, published in Physica D 45
(1990) 254 270 North-Holland." Comment I,Suresh kumar Devanathan, find
professor Fredkin, condescending to a superior reader. I only find him
shutting down avenues, not opening new ones. For that matter, the document
at http://www.digitalphilosophy.org/digital_philosophy/01_what_is_dp.htm can
be compared to the following Chapter 1: What Is DP? Mathematics of
continuous variables is useful in describing the real world. Digital
Philosophy (philosophy of Digital Mechanics), on the other hand, replaces
the most fundamental microscopic processes by binary automata. We will
explore the reasons behind the following: a) Why mathematics is good at
modeling processes in the physical sciences? b) Natural occurrence of
binary systems, 2 state systems,in physics, like electrical charges (+ and
¨C) and 2 sexes (¡â and ¡á), in biology and c) Various wonderful
symmetries of the real world Digital Mechanics (DM) and its philosophy (DP),
is easy to understand, even by the commoner. Since, Digital Philosophy is
new, and in development, faults and inconsistencies are expected with our DP
models. Currently, our models are purely conjectures, seeking experimental
confirmation. In this paper, we will deal with both verified experimental
data and mathematical models that fit that data, and conclusions, concepts,
models, pictures, etc drawn from that data. Our ideas may sounds in
contradiction to pre-established principles. We rather take the risk of
sounding wrong, than sounding right. CommentI, Suresh kumar Devanathan
will eliminate the Fredkin jargon and make Fredkin understand by an above
average reader. Chapter 2: Basic Principles
Occam's Razor[1] is a useful tool in guiding the development of Digital
Philosophy. Digital Mechanics is an atomic theory. Everything at the
fundamental level is discrete, especially, binary in description.
Development of Physics has promised us quantization and discretisation of
fundamental quantities like charge, angular momentum, etc. In DM, space and
time become discrete quantities themselves. We will later see reasons in
chapter Units.
Discrete variables are easily represented as finite integers. Even time,
flows as a series of steps, instead of continually. Where as, calculus is
very useful in modeling physical systems, calculus is a mere tool in
generating accurate approximations to the universe. DM mechanics is founded
on
a) Diophantine analysis; the mathematics of the integers
b) Automata Theory; the mathematics of discrete processes
Automata Theory is central to our analysis. Tremendous advances were made in
science following the discovery of the calculus (and partial differential
equations.) We claim DP will have the same effect. DP models are more
fundamental than modern day continuous models. Conway's game of Life [2] is
a great example of a simple digital system with emergent properties.
Digital Mechanics stores its information state in binary format, as modern
day computers do. Operations of computers are described by Discrete
Mathematics. Just as computers use 0 or 1s, to represent state of
information, a DM model may choose -1 or 1 to represent the bit of
information at a point. Matter, exists in Space-time lattice in digital
format. Automata Theory describes the behavior of matter at these points in
space-time.
--------------------------------------------------------------------------------
[1] Occam's, Razor (From Encyclopedia Britannica) also called LAW OF
ECONOMY, or LAW OF PARSIMONY, principle stated by William of Occam
(1285-1347/49), a scholastic, that Pluralitas non est ponenda sine
necessitate; "Plurality should not be posited without necessity." The
principle gives precedence to simplicity; of two competing theories, the
simplest explanation of an entity is to be preferred. The principle is also
expressed "Entities are not to be multiplied beyond necessity."
[2] Conway's Game of Life. See M. Gardner, The fantastic combinations of
John Conway's new solitaire game of 'Life', Scientific American 223 (April
1970) pgs 120-123.
Comment I will translate the Fredkin jargon
athttp://www.digitalphilosophy.org/digital_philosophy/03_the_purpose_of_dp.htm
written for an amateur to a document, understandable and meaningful for
experts. Professor Fredkin, if you do not sound confident about your ideas,
ask yourself why an experimentalist should bother proving your ideas. You
are not allowed to sound uncertain. You have to take the risk and
liabilities for your ideas. Otherwise, your ideas are provable only within a
closed system, like a computer or mathematics. Chapter 3: The Purpose of DP
Digital Physics describes the behavior of microscopic systems. DP can go
further, and even explain the process of life and aspects like behavior,
consciousness, and thought. The possibilities are endless. DP is
revolutionary, in its mode of thought. DP does not replace mathematics, but
lives in a domain of its own. DP is anotherform of mathematics. Mathematical
properties of physical world must be analytically derivable from the basic
rules of DM. We claim that even children will be fond of DM models. DP
claims: a) All information is digital. Any state of information is
ultimately stored in binary format. b) Information undergoes transforms
called digital informational processes.
Digital informational processes change data from one format into another.
Comment
I, Suresh kumar Devanathan, will eliminate the roundabout explanations and
redundancy of Fredkin's jargon. Fredkin is a theoretician, and as such, he
constantly reasserts his ideas in a closed system. I m only translating
Fredkin. I claim not to modify Fredkin's original intent or content.
Discontinuity in the layout of following ideas, reveal to me, that Fredkin's
ideas are scattered and is more worried about being grammatically correct
than sounding sane. My understanding of biology is not as solid as my
understanding of Physics or Computer Science. So, i have not been able to
preserve all information, dispensed by Fredkin's brain matter.
Chapter 4: DP and Biology
DP is related to Biology. The DNA contains discrete information. It
describes a complicated life form. If DP had existed 60 years ago, it would
have predicted the existence of the DNA. Take Mendel's law. Continuous
variables would be at disadvantage, explaining the interaction of binary
integer variables, like male or female, (True or False), or simple ratios
like ¼ or ½.
The following three key issue, bring to mind, the possibility of a digital
model:
a) The appearance of small integers in biological systems.
b) Hierarchical structures among the same species like leaders, servants or
group structures among the same species, like male-female pair.
c) Inherent information and information processing systems.
In chemistry, atoms of different elements are functionally identical to each
other. Nevertheless, chemistry also describes isotopes, but isotopes
normally do not have chemical properties, different from their counterparts.
Life forms are built from small structures: atoms, molecules, proteins, DNA,
cells etc. Information describing a life form, for example: a Guanine is
stored in the DNA, by the placement of G and C plus A and T atoms.
Structures similar to the DNA exist at all levels; take the functional
structure of a given species, where a species' behaviour is
delineated by the DNA and take distinct functions of the members of the same
species, for example, male-female distinctions, also described by the DNA.
Biologists would agree to Digital Philosophy. DP predicts the existence of
digital informational processes that govern growth and development of living
things.
Comment
My goal here is to cut the chase and get to the point. Fredkin has to
understand that his conclusions are trivial in the modern age. For example,
a statement, such as "Computers and their software are the complex things
ever made by man", is not astounding. Today, everybody uses a computer and
understands that computers are complicated. Professor Fredkin, everybody
understands clearly that it's not 1950's right now, and you do not have to
constantly remind us that. For example, your fascination with the
universality of a NAND gate is eagerly understood, by quite a few. Just
because others fail to understand your fascination, does not mean that they
do not want to be your friends, or they are against you. You have to be
careful not to alienate an expert. You cannot sound smarter than an expert.
If you do, you are the expert, not them. To attract other experts, you have
to compromise. You have be careful how you verbalize your intuition. There
are 2 kinds of worries, for a successful man: worrying about being right or
wrong, or worrying about winning or losing. If you worry about winning or
losing, you are an experimentalist. If you worry about being right or wrong,
you are a theoretician.
Chapter 5: The Ultimate Simplicity
Computers and software are complex. On the other hand, a unit of computation
is a simple 2-input NAND gate [1]. A simple circuit can be built by wiring,
a set of NAND gates. A complicated computer can be built by wiring many
identical simple circuits. Most complex processors and memories are built
this way.
Fundamental physics is complex, yet it is possible to find simple
fundamental automata that model physics. By Turing's argument [2], every
computer is a universal computer. And the simplest of computers is binary.
For simplicity offered, by binary state machines, our DP/DM models are
binary instead of having 3 states or 4 states.
[1] A 2 input NAND gate is a circuit where the output is a zero, if and only
if both inputs are 1. In all other cases the output is 1. The name "NAND"
is a reversed contraction of "AND" and "NOT". The output of an AND gate is
a 1, if and only if both inputs are 1. So a NAND gate is the same as an AND
gate whose output is complemented by a NOT gate. (A NOT gate is a gate with
a single input and a single output. If the input is 1 the output is 0, if
the input is 0 the output is 1).
[2] Turing's thesis, generalized and paraphrased: Once a computer has the
capabilities that enable it to be universal (which is true of every PC) then
it is capable of carrying out any computation or procedure, provided it has
enough memory.
Comment
Pay attention, the keyword is "DP Model". Your summary is that "DM" is a
more fundamental model.
Chapter 6: Digital Philosophy and Physics
We apply Digital Philosophy (DP) to physics. Our tasks are:
1. Finding binary representations for microscopic physical states
2. Defining physical laws in terms of informational processes (DM).
Our goal with this paper is to achieve the first step. To convince the
reader that the fundamental properties of physics are binary and that such a
binary representation is consistent with physics. Here's the list of topics,
we will explore
· 3+1 dimensional space-time (position, orientation and velocity)
· CPT [1] theorem and symmetries
· Necessity of Planck's constant
· Constancy of the speed of light
· Description of Momentum and angular momentum in a DM model
· Basis of Force
· Relationship between Mass and Energy
· Necessity of property of Charge
· Necessity of property of Color charge
· Natural requirement for Conservation laws
· Properties of particles
· Static representation of dynamic systems
In a DM model, bits store the properties of particles at the most
microscopic level.
[1] In CPT symmetry, the "C" stands for charge, the "P" stands for parity
and the "T" stands for time. See Chapter 10 on Symmetry.
Chapter 7: Methodology
Digital Mechanics (DM) and its relevant philosophy Digital Philosophy are
consistent with modern physics. Our analysis is rather trivial; a more
complete theory deserves intuition along these lines. Physics, itself is
inconsistent. Physicists have been unable to reconcile General Relativity
(GR, physics at large distances) with Quantum Mechanics (QM, physics at
small distances). The ideas presented here are new, and thus are open to
criticism. Conventional physics is well tested, and thus is more mature. DM
models have only slowly progressed over the last 40 years.
DM stores energy, linear momentum, angular momentum, electric charge, and
color charges in a series of bits. DM is not primarily consistent with all
of physics. Physics of fields, waves cannot be easily reconciled by the
complex physics of vacuum. Our model is rather simple. We claim that the
interaction of fundamental particles and their motion give rise to complex
behavior consistent with modern physics.
DM models are interesting and simple. Complex physical behavior is emergent
from these models. Our models are not mathematical equations, instead,
simple pattern match behavior or gate behavior that can be successfully
emulated on a computer.
Comment
Learn to use "our", "us", "you and me", since you are paying me. I am part
of your team. Professor Fredkin, you are not alone. Or eliminate "us", or
"our" completely. An advanced reader may not take your side. "Our" is
disparaging to him. Choose your audience.
Chapter 8: Cellular Automata
Useful DM models are Cellular Automata (CA) in nature. We restrict our
physical model analysis to Reversible, Universal Cellular Automata (RUCAs).
Cellular automata are a class computer with a regular structure, for
example: Cartesian lattice of cells. A checkered board is an example of
simple binary Cartesian cellular automata space. Universal CA(UCA) is a CA
that is universal. Reversible UCAs(RUCAs) are reversible and Universal. It
implies that RUCA can emulate a reversible computer operation. RUCAs can be
run, both forward and backward in time. The most useful DM Models are RUCAs.
Given the discrete nature of space-time, the most relevant RUCA [1] models
are Discrete Second Order System(DSOS). A DSOS RUCAs take into account,
neighboring time states and they are consistent with reversibility of CPT
symmetry.
Our system is quite foreign to a physicist. Charge, angular momentum, linear
momentum and energy can be modeled successfully by DP. Further more, DP
violates angular isotropy above the scale of quantization. DP demands the
existence of an independent unaccelerated reference frame. Both these ideas
are incongruent to a physicist version of mechanics.
There exists a lattice structure of DM RUCA. This lattice may not correspond
to physical ideas of space-time. The DM RUCA is an informational process
that translates particles, like Muons, in space-time. When DM models are
completed, they will be able to explain all kind of experimental
observation, like interference, symmetry breaking. Both special relativity
and general relativity will be consistent with DM.
The lattice structure of DM does not exist in the physical domain. We claim
that Relativity is consistent with our models. Our DM models will explain
the geodesics motion of particles through gravitational fields.
--------------------------------------------------------------------------------
[1] In this paper the following abbreviations are commonly used: CA for
"Cellular Automaton", UCA for "Universal CA", RUCA for "Reversible UCA", DP
for "Digital Physics", DM for "Digital Mechanics and QM for "Quantum
Mechanics".
[2] For insight into how a CA model can be relativistic, see "Universal CA's
Based on the Collision of Soft Spheres." Norman Margolus, Boston
University Center for Computational Science and MIT Artificial Intelligence
Laboratory. A PDF version is available at:
http://www.im.lcs.mit.edu/nhm/cca.pdf
Chapter 9: History
DP is an interesting cosmogony principle. The DM lattice exists in the
"Other", wherever the other is. God or God-like being is running the DM
model in his plane.
DP, dating back the early 1950's, explained three central properties of
physical law: process, universality and cosmogony. Universality of Physical
law implies that any physically universal system can emulate another
universal physical system.
Professor Fredkin elaborates the history of his ideas:
These were and are important concepts and problems which were not generally
recognized in the 1950's and which are not generally recognized today. Once
DP included computational universality it was obvious that theoretically
every and any kind of discrete physics could be modeled exactly by any
Universal Computational DP model. The only question was whether the model
would be direct and simple, or baroque and contrived. Those three early
results, on Process, Universality and Cosmogony provided impetus for the
further development of Digital Philosophy, despite the fact that the
earliest DM models had nothing else to recommend them.
It was a great advance to go to Cellular Automata as a basis for DM models.
The author's first CA model, the XOR rule, was a step forward in being a
direct model of a space-time that was locally Cartesian. It replicated
patterns and had a wonderful form of superposition, but it was a step
backwards in that, at the time, we could not see how such simple rules could
model universality, be reversible or be consistent with any other aspects of
physics.
After being shown early DM cellular automata models and understanding the
concept of Digital Philosophy, Marvin Minsky issued a challenge: "Find a
simple CA rule that propagates with asymptotic spherical symmetry as opposed
to the typical 4 fold symmetries produced by rules like 2D XOR. This was a
brilliant insight, combining a known property of physics with what might be
possible within the then primitive understanding of CA models. Minsky's
challenge took years to get done but it was an important step in the
evolution of DP. The early CA models of DP faced seemingly insuperable
obstacles. No simple CA was known to be computationally universal [4] , and
it was common knowledge that all simple universal models of computation were
known to be irreversible. Those 2 facts alone were enough to cause almost
any rational person to abandon DP as a sensible model for physics.
It was ridiculous to assume that something as arcane as a Turing Machine or
a commercial computer could be a substrate for physics. The idea of an
irreversible computer modeling the reversible laws of physics was obnoxious.
Progress on DP was put on hold in order to solve those two problems:
inventing simple universal cellular automata and inventing simple models of
reversible computation. Finally, a third problem emerged; we had to do more
than discover a model of reversible computing, we had to gain understanding
and familiarity with every aspect of reversible computing. After completing
the first of these 3 tasks, there appeared, out of the blue, Conway's
remarkable "Game of Life." It was a CA and it had stable particles that
moved! This was another fantastic step that arrived unexpectedly. Gosper
was able to demonstrate that the Game of Life was actually a UCA [5] . We
then discovered Konrad Zuse, who in the late 1960's, came up with a similar
general concept of Digital Philosophy, and published a book called
"Rechnender Raum". We invited him to come to MIT where he found the ideas
in his book appreciated for the first and only time during his life.
(According to Zuse.) In 1974 the author invented Conservative Logic, as a
physically correct model of reversible computation [6] . Following that
invention, the author and his students developed a great and complete
understanding of issues related to reversible computation. Along the way,
the author invented the Billiard Ball Model of computation which served as
the model for the first RUCA developed by Norman Margolus. Finally all of
these tasks were accomplished by the mid 70's by the author who, with his
students and colleagues, including Roger Banks, Norman Margolus and Tommaso
Toffoli [7] expanded and elaborated these concepts. Charles Bennett had
independently discovered a Turing Machine model of reversible computation,
but his motivation and methodology were unrelated to Digital Philosophy.
Gaining a thorough understanding of reversible processes took a number of
years. The development of Digital Physics and Digital Mechanics has been a
strange process but we have no shame.
To summarize, Digital Philosophy carries atomism to an extreme in that we
assume that everything is based on some very simple discrete process, with
space, time and state all being discrete. The workings of DM are like the
workings of a hypothetical computer processor: there are bits of
information, there are discrete instants of time and there are rules that
govern how the state at one instant is time is translated into the state at
the next instant of time. Today, our understanding of how to simultaneously
incorporate Universality and Reversibility into CA models (RUCAs) is so
advanced, that we take it as a matter of course that all our DM models
incorporate these 2 principles. 30 years ago there was considerable doubt
as to whether or not a RUCA was possible. Most of those who thought about
the problem had assumed that reversibility and universality were
incompatible concepts.
[1] The idea of representing physics as a computer program occurred to the
author in the mid 1950's. The earliest form of Digital Philosophy involved
little more than the concept that underlying physics there might be some
kind of computational process.
[2] Early works on Automata Theory defined "Universal Computer" as a system
with an infinite memory that could emulate the behavior of any other
computer. A more modern definition (and the one used in this paper) defines
"Universal Computer" as one with enough memory to hold an emulation program
(which is usually very small) plus the contents of the memory of whatever
finite computer it will emulate. It's the nature of the computer, not the
infiniteness of its memory that determines whether or not it is Universal.
All modern computers (such as PC's) are Universal Computers.
[3] A New Cosmogony. The Physics of Computation Workshop, October 2-4,
1992, © IEEE 1992.
[4] The Universality of CA's was first established by von Neumann. See von
Neumann, John, Theory of Self-Reproducing Automata, edited and completed by
A.Burks, University of Illinois Press, Champaign, IL (1966). The problem
was that von Neumann's UCA was a 23 state machine with a 4 cell
neighborhood, totally ad hoc, designed to show that it could build a replica
of itself as a partial model of a living organism. Codd reduced the
complexity of a Universal CA with a von Neumann neighborhood to an 8 state
machine, and Roger Banks accomplished the ultimate in finding a 2 state
version.
[5] Ref to Gosper & Game of Life
[6] Reference to Conservative Logic
[7] Roger Banks showed how to create an extraordinarily simple UCA. This
followed the author's discovery of creating UCA's by using a CA to implement
digital logic circuitry as opposed to building a Turing Machine. Toffoli
was the first to invent a RUCA; Toffoli, T., 1977b, ``Cellular automata
mechanics,'' Ph.D. thesis, Logic of Computers Group, University of Michigan.
. His approach was to retain the past states in an added dimension.
Margolus invented the first RUCA that did not require an added dimension.
N. H. Margolus. Physics and Computation. PhD thesis, MIT Artificial
Intelligence Laboratory, 1988.
Chapter 10: Bits and DP
Physics is a complicated science. Physical systems deal with both particles
and atoms, with diverse properties. The proposed Digital Philosophy and the
like, deal with simple state machines that act on "bits". Only 2 states are
possible, +1 or -1, 0 or 1. Binary states machine process identical type of
information. A bit(logical variable) in 1 state machine is never different
from a bit in another state machine. In our proposed DP model, physical
attributes of the real world, like charge, spin, energy and momentum are
carried by a configuration of bits. In DP, both space and time are separate.
Our DP model is purely ad-hoc or made of simple digital constructs. Digital
Processes and geometrical arrangements are also very useful toolsin creating
a correct DM model. As a side note, Emeron's apology to a friend, for
writing a long letter instead of a short letter, brings to mind, our
dilemma, in describing our model. DP preserves information content.
Information is never created or destroyed. It is transformed from one form
to another. We will explore several DP alternatives, for representing
information. True or False(1 or 0) model is one such model. Physically
interesting models may use +1 and -1 for processing information. +i and -i
are also interesting values for phases. Description of the (+1, -1)
system: -1 * 1 = -1, 1 * 1 = 1, 1 * -1 = -1, -1 * -1= 1. Addition always
involves an odd number of addends. +1+1+1=-1, -1-1-1 =+1. Sum of (+1,-1) is
negative of their products. Description of the (+i, -i) system: Both sums
and products involve an odd number of arguments. Sum of (+i, -i) is same as
their products.Computational generality is not lost by such models. Physics
is derivable from the above numerical system.
Chapter 11: Conservation of Information
DM models transform digital information through digital information
processes. An effective DM model respects the established symmetries of
Physics, like CPT symmetry. Within our RUCA DM models, CPT symmetry implies,
a strong kind of Conservation of Information. Conservation of Information
should not be confused with Conservation of Momentum. Experimental data
support the theme of conservation of information. For example, a trajectory
of a particle is exactly reversible in our model. Inelastic collisions,
particle disintegrations have to be redefined within our DM model to suit
the information conservation requirement.
Conversation of information is as central as universality. Physical laws are
computationally universal. If physical laws were not computationally
universal, it would be impossible to construct a universal computer.
DM models are exact and it implies that the real world can be modeled
exactly.
DP time and space models are discrete and thus imply an atom of motion. A
simplest such operation of digital motion that conserves information is a
swap operation between spatial neighbors. Swap-based universal CAs form
perfect RUCAs. They are useful in describing physics.
Chapter 12: DP and Physics
DP is attractive to biology. Physical problems are also solved by DM models.
In a physical interaction, momentum is conserved, energy is conserved and
charge is conserved. A DM interaction conserves information. The totality of
the system stays constant.
We have a compelling story to tell and we will tell it, even though, we are
suffering limitations.
Information is digital. Properties of the physical universe are discrete.
For example:
· Number of spatial dimensions is exactly 3
· Number of different electrical charge states is exactly 2, +
and -
· Number of chiral parity states is exactly 2, left handed and
right handed
· Number of directions for time is exactly 2, forwards and
backwards
· Number of CPT modalities is exactly 2 out of 8, CPT & -C -P -T
· Number of spin state families is exactly 2, bosons and fermions
· Number of measurable spin states of an electron is exactly 2, up
or down
· Number of particle conjugates is exactly 2, particle and
anti-particle
· Number of different QCD color charge states is exactly 3, R, G
or B
· Number of Lepton and Quark generations is exactly 3
· Number of Leptons or Quarks per generation is exactly 2
· Spin of a boson is exactly n (n always a small integer)
· Spin of a fermion is exactly n + ½
· Maximum number of inner orbit electrons in an atom is exactly 2
That is a small list of naturally occurring integer phenomenon in physics.
DP is useful at explaining these discrete numbers.
During a particle-particle interaction, DM model transforms information of
both particles from one state into another. Such a computation, is a digital
information process. Elastic collisions are explained by DM models.
Inelastic collisions, on the other hand, are complex and are not considered
here.
Even though, physics of ordinary particles is reversible, a physically heavy
particle undergoing decay, looks irreversible, backward in time.
Nevertheless, DM predicts even decays are exactly reversible.
Chapter 13: Finite Nature
Physicists use discrete space-time models. Such models are usually digital
approximations of continuous models. Such models use real arithmetic to
compute successful approximations to reality.
We introduce the Finite Nature Hypothesis.
Finite Nature (FN) is the hypothesis that assumes space; time and all other
quantities of physics are ultimately discrete and finite. [1]
DP comes into vogue, once Finite Nature is understood. Given the finite
nature of the universe, DP is a natural phenomenon. Although one cannot
simulate a DM universe exactly, due to the need for tremendous resources, DM
models are exact.
DM models are not approximations to differential equations. Instead they are
based on the state of the state of the art, theory like Finite State Machine
[2] , Automata, Cellular Automata [3] , Universal Computer [4] and the
Speed-Up Theorem.
The Finite State Machine describes the behaviour of microscopic automata.
The FN assumption implies there are no infinities or infinitesimals. DM
models do not have infinities, infinitesimals, continuity or locally
determined random variables, but microscopic randomness is everywhere from
the continual inflow of information, orthogonal to any local process.
Research, to date, has addressed the following questions: are reasonable
models of physics, computationally reversible? Are Cellular Automata models
(DM) useful in describing physics? Is FN hypothesis verifiable? We have
discovered, many laws and characteristics of physics. We have been
encouraged by the progress, we have made, so far. We will explain, our
confidence in the models further.
--------------------------------------------------------------------------------
[1] Finite Nature, Edward Fredkin
[2] Consider time as a sequence of integers that are counting up. At
time=t, an FSM is in one of a number of states. The FSM has a number of
possible input states and can generate a number of possible output states.
The FSM is defined by a table. Each entry in the table consists of 4 items:
the FSM state, the input state, a new FSM state and the output state. The
way that an FSM transitions is by taking the FSM state and the input state
and looking them up in the table to find the new FSM state and the new
output state. The process is then repeated. See Marvin Minsky. Finite and
Infinite Machines. Prentice Hall, Englewood Cliffs, N.Y., 1967.
[3] An approximate definition of a CA as used in DM: A CA is a uniform,
basically 3-D Cartesian lattice. Two time states are always present (the
present and the past). A neighborhood is a small, local group of cells
identified by coordinates x, y, z, t. We consider every neighborhood as an
FSM where the FSM state and input state are both the state of the local
neighborhood, and the output state and the new FSM state are the state of
the local neighborhood for the next instant of time. The FSM table is the
CA rule. The rule is applied simultaneously to every x, y, z neighborhood
as one time step in the evolution of the CA.
[4] A Universal machine is basically some kind of computer that could, given
enough memory, exhibit behavior isomorphic to any other computer. In this
context, we require of all DM models that they are Universal.
Chapter 14: DM & QM
DP is in direct contradiction with the Copenhangen interpretation of QM. DM
universe is all there is. Observations are not irreversible actions.
Information is always conserved. And the classical world is not distinct
from the quantum world.
Quantum Mechanical behavior of uncertainty is emulated by DM models.
According to the speed-up theorem, it is not possible to predict the final
state of an arbitrary computation, with a shortcut. The speed-up theorem
requires that every action of computation, be performed, in order, to get
the final state. Even though a DM model is regular and involves simple
computation, such models have to simulated, to get the future state of the
DM universe.
Quoting Gerard't Hooft:
"Quantum Mechanics is not a theory about reality, it is a prescription for
making the best possible predictions about the future if we have certain
information about the past."
Taking 't Hooft's dictum that "Quantum Mechanics is not a theory about
reality.", DP expands on it, successfully. Digital Philosophy holds QM as a
set of analytical, mathematical methodologies for computing the
probabilities of future states of a DM process, from the limited
information, had from the possible initial states of that process. It is
reasonable to assume that a discrete, deterministic and reversible process
be the substrate for what Quantum Mechanics. Evolution of wave functions in
wave mechanics is deterministic and reversible.
DM models are not approximations of QM models. QM models are probabilistic
in nature. On the other hand, DM models are exact. For example, in a DM
model, a particle travels through a particular trajectory. In a QM model, a
particle travels through all possible trajectories with a given probability
for each. QM is an interesting theory of the moment. DM is continuing its
evolution as a successful theory. DM models are currently only Newtonian,
for example: the Billiard Ball model.
DM models are binary state machines. DM models do the same functions as a
differential equation, in physics. Accurate mapping of Cellular Automaton to
mathematical equations of physics has been successfully studied, for
example, in Computational Fluid Dynamics [2] .
DP research promises a fundamental theory of physics. Currently, DP research
is still at its inception. Even though, DP is not successful at explaining
all of modern physics, it will soon be, the next best theory. DM models have
the glory of predicting the evolution of the universe exactly.
We have the same problems as the person, who once tried to model physics
using algebra. For example, the relation, "T=H/M", the time it takes for an
object to fall to the ground be proportional to the height and inversely
proportional to the mass.
Even though, mathematical equations are wonderful, brilliant and correct,
the above equation, for example, holds only true in limited circumstances,
such as feathers falling through the air. We are modeling physics, not as
mathematical equation, rather as binary code. Our conclusions and
suppositions are elementary and are open to criticism. However, our
formulation will be self-consistent and importantly, adhere to established
physical law. DM is a work in progress, just as QM once was.
Correct DM models offer interesting possibilities. They will describe
physics exactly. Physical laws will be able to be laid on a short paragraph,
to be written exactly. Even an extraterrestrial would understand our
statement.
--------------------------------------------------------------------------------
[1] Starting in 1962, Richard Feynman never stopped advising the author to
think about nothing but using ideas about reversible logic and CA models to
do QM. His favorite admonition to the author was "QM is all there is!"
Feynman died in 1986 and others have taken up this chore.
[2] H. Chen, C. Teixeira, and K. Molvig, Digital Physics Approach to
Computational Fluid Dynamics, Int. J. of Mod. Phys. C, to appear.
Chapter 15: Symmetry
DP is consistent with symmetries of nature: Charge, Parity and Time. Take
Charge symmetry (C), it implies that the laws of physics are unchanged if
every particle is replaced by its anti-particle (charge conjugation). Take,
Parity (P), it refers to a mirror image of a process. Parity symmetry
implies that the physics of any process should be the same for the mirror
image of that process. Finally, take Time symmetry (T), it implies that for
dynamic systems, the fundamental laws of physics are the same for the
forwards system and the Time reversed system. Symmetry is an important
concept in physics.
CPT symmetry is one of the most important realizations of physicists.
Majority of experiments confirm T symmetry; physical laws do not change if
time is reversed. The same is true for P symmetry. In the mid 1950's,
Charge symmetry and Parity symmetry were violated in experiments. Then it
was believed that CP was symmetry of physics. CP symmetry holds that both
Charge and Parity be conjugated, for physical laws to remain exactly. Once
again, in the 1960's, CP symmetry was trashed. Kaon particles violated CP
symmetry. However, trust in CPT symmetry, became fundamental. It is crucial
to understand that CPT implies that C, P, T or other such symmetries
(involving combinations of Charge, Parity and Time) are inexact or
approximate under most circumstances. CP symmetry is correct for all of
physics except for situations where K0 (and perhaps B0) decays play a role.
The conclusion that physics has CPT symmetry is, philosophically, very
important. Preliminary conclusions cannot be made, based on number of
experiments that successfully verify a given law of physics. Instead,
experimental violations disprove a given law, as in the case with CP, C,P,T
symmetries. Our confidence in CPT symmetry lies in the fact that all other
permutation of symmetries were violated. Similarly, continuity would be
disproved, someday, with an amazing experiment. Until then, it does not
matter the number of experiments that verify translational symmetry and
rotational symmetry. Calculus is still an useful tool in describing physics.
Nevertheless, its successes and its merits should not hold ground against
DP.
Chapter 16: Noether's Theorem and Its Variant
Consider the Noether's Theorem [1] it states: "For every continuous
symmetry of the laws of physics, there must exist a conservation law". This
theorem is used in classroom physics to derive conservation laws from
symmetries, e.g. conservation of angular momentum from the symmetry of
angular isotropy. However, it is well known, that Noether's theorem itself,
is symmetrical! The converse of Noether's Theorem states, "for every
conservation law, there must exist a continuous symmetry." In the case of
angular momentum, the conserved quantity, spin, cannot vary continuously.
The angular momentum of a particle exists in integer multiple of h/2 (spin
½) [2] . DM models conserve angular momentum, exactly. RUCAs are designed to
conserve angular momentum. Angular momentum is neither created nor destroyed
by these models. Unfortunately, the existence of a cellular array implies
angular anisotropy, but only at a most microscopic level. A variant of
Noether's Theorem implies that exact conservation of discrete angular
momentum must enforce asymptotic continuous angular isotropy, if the process
is looked at, from a larger scale, than the cellular array. Similarly,
absolute microscopic conservation of discrete units of momentum must enforce
asymptotic continuous translational symmetry. Conservation of discrete
units of energy implies asymptotic continuous time symmetry. Experimental
violations of translational, angular and temporal isotropy will confirm our
RUCA DMs.
--------------------------------------------------------------------------------
[1] Emmy Noether "Invariante Variationsprobleme," Nachr. v. d. Ges. d. Wiss.
zu Göttingen 1918, pp 235-257
[2] All objects are either bosons (total spin is an integer multiple of h)
or fermions (an integer plus ½ multiple of h). Any object can be changed
from a boson to a fermion or visa versa by the addition of one electron.
Chapter 17: The Four Laws
I Information is Conserved.
II All fundamental processes of nature are computational universal.
III Every physical system has a Digital representation.
IV Changes are caused by Digital Informational Processes.
Laws III and IV require Finite Nature hypothesis to be true.
Conservation of Information is a consequence of Reversibility. If the laws
of nature are exactly reversible, then in principle, if time were reversed
in some physical system, its evolution would retrace its steps, exactly. It
implies that no information is lost. Information is lost whenever 2 or more
distinct states of a system lead to a common successor state, K. In
reverse, there would be no basis for choosing which state ought to follow
state K. The total number of distinct informational states of any closed
reversible system, S, is the same as the total number of states the system
will visit before it cycles and starts to repeat itself. The number S
always has the same value at any point in time; S is therefore a conserved
quantity. Finite irreversible systems must eventually cycle, but the cycle
does not include any of the states reached prior to the beginning of the
cycle. By having a counter and by saving the initial state, we can make any
irreversible system reversible. To get from state t to state t-1, the system
restores the initial state and then uses the counter to go forward t-1
steps. Even though it is a bit expensive, nevertheless mathematicians don't
mind it. Computers can also be made microscopically reversible by building
them out of reversible logic gates. Such computers are just as efficient as
ordinary computers (in terms of how much hardware and time are needed to do
a computation) and they hold the promise of being able to eliminate heat
dissipation during computation. The laws of physics make microscopic
reversibility an intrinsic part of all microscopic physical processes. It
must be believed that the cost of going forward from some state must be the
same as the cost of going backwards from that state. This means that
information is microscopically and locally conserved. We postulate that in
any volume of space-time, information that is gained or lost from that
volume must be lost to or gained from those regions that are space-time
neighbors of that volume. In this case, conservation of information is
similar to conservation of energy.