In physics we make use of a number of physical dimensions or units. The Prime examples are Length, Mass and Time. The so-called rationalized MKS system (now SI) uses the Meter, Kilogram and Second for the units of length, mass and time. All three of these units have arbitrary measures. The Meter was originally defined as one ten-millionth of the distance from the equator to the North Pole. The Kilogram was conceived as equal to the amount of mass in 1/1000 of a cubic meter of water. The Second was defined as 1/60th of a minute, which is 1/60th of an hour, which is 1/24 of a mean solar day. Despite the common Earth-Centric origins of the units of the metric system, we now have better and more precise definitions of these units. Obviously, if one takes a universal view as opposed to an Earth-Centric view then these new definitions are still arbitrary. Sometimes physicists like to simplify things by giving some units or combinations of units the measure 1. This is most commonly done by setting Planck’s constant and the speed of light to 1. This has the convenient consequence that mass and energy become equal, and e2 (the electron charge squared) equals the fine structure constant (approximately 1/137). In DM, it makes perfect sense for c and ħ to equal 1.
What is amazing is that given just the SI physical-mathematical definitions of the Second, the Meter and Planck’s constant, the relationships of the DP units of Length and Time (L and T) to the Meter and Second can, in theory, be calculated from within the DM model with no need for any additional physical experiments! This is because, in theory, the number of T units in one second could be calculated within a successful DM theory by modeling the atomic system that defines the second. [1] In the DM model, the speed of light is L/T. Once we know T in seconds, it is trivial to calculate the number of L units in the Meter.
The way that this DM model of physics has evolved has nothing in common with rolling dice, pulling rabbits out of a hat, or having a flight of fancy. There is a consistent logic that guided the selection of possibilities that have been incorporated into the DM model. This involved the rejection of a very large number of other constructs. DM models must have emergent properties that make physical sense. What might be unusual is the selection of the order of importance of properties of physics. What follows is a short list of properties of physics in the order of importance with regard to the development of a DM model:
1. Finite Nature – the assumption that all is discrete and finite
2. Computational Universality
3. Reversibility and Conservation of Information
4. CPT symmetry
5. Discrete
6. Allowing for particles and their properties
If this DM model incorporates something as bizarre as 6-phase time, it is not an idle whim; it allows for a simple way to have CPT and conservation of charge. So try to bear with all the surprises in this description of a DM model. Each aspect of this model is part of an attempt to have a number of properties of physics simultaneously emerge from the dynamical behavior of the DM system.
One must, at all times, keep in mind the nature of everything in this paper. The point is to convey the general concepts and to illustrate the possibilities. This is done by giving examples as to how things might work. This should enable the reader to get a glimpse of what is emerging from the horizon; a truly new concept of physics.
In DM, there are three basic dimensions or units. However unlike conventional physics there is no need for assigning arbitrary values to these units because for all three, their actual value is exactly 1. Further these are not just units; each of them is a constant of nature. While it may seem unusual for a constant of nature to have the exact value 1 that is indeed the case in the DM theory. The three Units are B, L and T. B stands for the Bit, which is the unit of information, L is the unit of length and T is the unit of time. These three units replace the Mass, Length and Time dimensions of conventional physics. Associated with the three units are three constants with the same names. These constants and their values are: B=1, L=1, and T=1. In the SI system of units, B has the same dimensions as angular momentum or action, ML2T-1. The value of B is the same as the value of ħ, Planck’s constant Reduced. Because the constant B has angular momentum, when the direction of time is reversed, the angular momentum of B must change handedness (from right handed to left handed and visa versa. We represent this by the sign of B which is for time going in one direction and – for time going in the opposite direction. Also, the sign of B at even micro-time steps is the opposite of the sign of B at odd micro-time steps.
The reason that the Bit has angular momentum has to do with the nature of the Rule. In DM all microscopic angular momentum (spin) is orbital. The motion of bits always has an orbital component superimposed on possible translational motion. One might now ask, “Why call it ‘Bit’? Why not call it ‘Spin’?” The reason is that the Bit is a 2 state system and configurations of Bits represent every kind of information in physics. The information can be quantitative i.e. information representing a vector such as velocity or a scalar such as energy. The information can be procedural i.e. defining the processes that result in the behaviors and properties of all the various particles of physics. The information can be structural; implementing the machinery of a particle. The reason the 2 states of the bit are 1 and –1 instead of 1 and 0 has to do with the fact that the atom of B can be ħ or –ħ but not zero.
The unit of length, L, is related to the dimensions of the cellular array in a simple way. However, we do not yet have a method of defining both L & T directly from the RUCA lattice parameters. On the other hand, we define T as one cycle of micro-time steps. This means that T/P represents one micro-time step. We use the Greek letter “τ” to signify the time for one micro-time step. Given an independent definition of T, we define L as Tc (T times the speed of light).
Both T and P are related to the Automata time. Each time cycle, T, consists of a number of phases (P phases consisting of P micro-time steps). In this DM model P=6. Nothing happens between micro-time ticks as microscopically, there is no continuous motion in an automaton. An automaton is in some state at time τ, and is in a different state at time τ 1. It makes no sense to think about the amount of time that passes between ticks of the automaton clock. Time is defined by the sequence of states. In the DM model, time is not quite as simple as the ordinary time of physics. For a number of reasons it appears that it is logical to consider time to repeatedly cycle through a number of phases. While this paper is basically about a DM model with P=6, we will first, briefly, describe a model where P=2. The rule that is, in effect, the fundamental law of physics, can either be thought of as a rule that has P as a parameter and the micro-time as an argument or it can be thought of as P micro-rules applied over and over again in rotation. The state of any region of space-time is always made up of 2 adjacent time states, in that DM is a 2nd order system. When time is reversed, we replace T with –T and a consequence is that B becomes –B. Thus B and T both change signs under time reversal while L remains the same.
Amazingly, the DM, P=6 model has perfect T symmetry. When T is changed to –T the consequences in DM are exactly the same as changing CPT to –C –P –T in ordinary physics.
The fourth constant of the DM theory is the number of space dimensions -- D = 3. Of course it seems obvious that space is three-dimensional. While it is conventional in physics to consider ordinary space-time as a simple 4 dimensional manifold, this does not appear to be most appropriate in DM. We call the space of the DM model that we will be describing “Salt”. The lattice of the RUCA is a lattice made up of 2 sub-lattices. This is similar to a salt crystal (NaCl) where there is a regular Cartesian lattice of ions; half are sodium ions and the other half are chloride ions. Both of the sub-lattices are Face Centered Cubic structures. An FCC crystal is similar to the stacking of cannon balls where each ball (inside the array) is in contact 12 nearest neighbors; six on the same level, 3 below and 3 above. A simple way to think about it is to give each cell in the salt lattice 3 integer Cartesian coordinates; x, y and z. If x y z is odd, we have a chloride ion, and if x y z is even, we have a Sodium ion. In DM, when the micro-time, τ, is even the even cells (Sodium) represent the present state and the odd cells represent the past state. Thus x y z τ is always an even number for every cell, past, present and future.
The presence of 2 time states in the Salt array (the past and the present), allowing DM to be defined as a 2nd order system, facilitates reversibility and the static representation of dynamical information. A requirement of all DM systems is inherent CPT symmetry and the Salt Array facilitates the incorporation of such features into a DM model.
One can consider DM to be a 10 dimensional model of physics. It has a 4 dimensional space-time and 6 extra time dimensions.
The next constant of the DM theory is R. R is the Rule defined by an algorithm. The algorithm for R is best defined by a table, as is done in Automata Theory for a Finite State Machine, or more precisely, as is done for a Cellular Automaton. R is not a normal number where the magnitude of the number has significance. The bits in R represent the rule table of a Cellular Automaton; they are like the digits in a multiplication table. The meaning of R requires the definition of a standard, canonical way to represent CA rules. We all know and understand the concept of number so well that when we use a number we normally don’t have to worry about defining what it means. In DP this is not the case, as numbers are sometimes used in ways where the magnitudes of the numbers have no meaning. We give an example of a definite rule on page 38.
Computer programs, algorithms and automata are something new and there are no accepted canonical ways of expressing their representations . However what we know for sure is that any algorithm or CA can be represented by a transition table or by a string of instructions for any Universal computer and that each representation can be made exactly equivalent to an integer. Thus every computational algorithm can be represented by a set of integers (computer words) or it can be represented of as one very large integer (a block of computer words). Such integers are concatenated sets of instructions for some canonical computer model. In the DM model, a simple, short table gives the definition of the Rule. R defines the process that converts the present state of the Universe into the next state. This is done every unit of micro-time, τ. τ = T/P. At micro-time, t=1, R1 is simultaneously applied to all neighborhoods to convert the CA to the next state; micro-time t=2. R is defined as P sub-rules, for P=6 there is R0, R1…, R5.
The last 2 are the cosmological constants. A is the age of the Universe in T time units, and I is the initial condition. A is quite unique in that it has the character of a cosmological constant of nature yet its value is always changing. A is the number of units of time, T, from the beginning of the universe until the present moment. We currently do not know A very accurately. Its value is the equivalent of approximately 15 billion years. If T equaled 10-30 Seconds then A would be approximately 5x1047 and counting at a rate of 1030 per second. α equals the age of the Universe in micro-time steps. A is equal to the integer part of α/P. Each successive integer value for A is subdivided into P micro-time steps (we are assuming that P=6):
α0=6A, α1 =6A 1, α2 =6A 2, α3 =6A 3, α4 =6A 4, α5 =6A 5,
α6 =6(A 1), α7 =6(A 1) 1, α8 =6(A 1) 2…
a modulo 6 is the space-time phase and that determines which of the 6 Rules is used at that time.
I is the Initial Condition of the Salt Array when α =1. I is defined by means of an algorithm. Unlike R, I is defined by a conventional computer program. We do not know whether the initial state of the universe was something complex or simple. We already know enough about RUCAs to be certain that the level of total complexity that we see in this universe could be the result of an extraordinarily simple initial condition! If I were very simple, then a short algorithm would be able to compute the initial state. If I was extraordinarily complex then it would take a much longer algorithm to describe it exactly. While it's difficult for us to imagine what the initial conditions were, it's easy for us to imagine that within the concept of DM an algorithm exists that will produce that state. I is the last of the eight constants of the DM theory and is the one that we’re least likely to be able to figure out. The initial condition, I, is defined by an algorithm because of the fact that we need an algorithm to specify the state of every bit in the entire RUCA. In DP empty space is filled up with bits just as are matter and energy. What we know is that defining I by means of an algorithm means that if I is simple, the algorithm will be short and simple, even if the initial conditions defined a repetitive pattern that fills all of space.
While within ordinary physics the Fine Structure constant, Planck's constant, and other fundamental constants of ordinary physics are usually expressed as a decimal number with as many digits as we can measure, there are some constants of nature that we know exactly. For example, the number of charge states of an electron is 2; Plus and Minus ( e and –e). The number of lepton species is 3: (e.g., electron, muon and tau). We don't normally consider these simple numbers like 2 and 3 to be constants of ordinary physics. We often associate the idea of a physical constant with experimental measurements wherein we try to make ever more accurate measurements. In DM, it should be possible to computationally derive all such numbers from the first 6 constants.
Physical Dimensions: Ordinary Physics vs. DM
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Mass, L and T
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Bit, L and T
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Mass
Angular Momentum -- Action
Energy
Momentum
Force
Power
Pressure
Rotational Inertia
Charge2
Viscosity
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M
ML2T-1
ML2T-2
MLT-1
MLT-2
ML2T-3
ML-1T-2
ML2
ML3T-2
ML-1T-1
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BL-2T (BT-1)
B
BT-1
BL-1
BL-1T-1
BT-2
BL-3T-1
BT
BLT-1
BL-3
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–3 (–1)
3
3
1
1
3
3
1
3
–1
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Mass, as a fundamental unit is replaced by the Bit, which has the same dimensions as Angular Momentum. While any choice of units is somewhat arbitrary, the BLT system has several esthetic advantages over the MLT system insofar as fundamental physics is concerned. First of all, there is a natural unit of B (Planck’s Constant, ħ) while there is no known natural unit of Mass. Second, the number of units needed to represent useful physical quantities is generally less in the BLT system. For example, the MLT representation for energy is ML2T-2 or MLL/(TT), 5 instances of a unit. In the BLT system, it is BT-1 or 2 instances of a unit so for Energy, the BLT system has a 3 unit advantage as indicated above. Third, for energy, momentum and viscosity, in the chart above, the BLT system makes particular intuitive sense versus the MLT system. B/T as energy is the temporal frequency of bits, while B/L is the spatial frequency of bits. This corresponds to the Quantum Mechanical viewpoint associating energy with temporal frequency and momentum with spatial frequency. BL-3 for viscosity is charming from an intuitive point of view.
Since in DM, the speed of light, c, is L/T, c is the unit of velocity. That means that c2=c so that in DM, energy and mass can have the same units, B/T. Under time reversal, B and T both change signs. Therefore all physical quantities (in DM) that have an odd number of occurrences of B and T combined (computed by taking the sum of the absolute values of the exponents of B and of T), change sign under time reversal. Those that have an even number of occurrences of B and T combined do not change signs. Thus, angular momentum (B), momentum (BL-1), power (BT-2), and dynamic viscosity (BL-3) all change sign under time reversal, as does velocity (LT-1). Charge, B½L½T-½, actually has an odd number of B and T units, one half of each makes 1 unit total so charge changes sign under time reversal. Mass (BL-2T), energy (BT‑1), force (BL-1T-1), pressure (BL-3T-1), rotational inertia (BT), acceleration (LT-2) and charge squared or q2, (BLT-1) do not reverse sign under time reversal. Under the MLT system it is simpler; units with an odd power of T change sign under time reversal. In DM as in physics, charge certainly does reverse sign and all particles become their conjugates under time reversal. The DM mechanisms that cause proper CPT symmetry are discussed on page 38.
Fundamental Units: Ordinary Physics (SI) vs. DM
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m meter
kg kilogram second
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SI
Units
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B, L, T
Units
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Definitions
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Length
Mass
Time
Angular Momentum
Energy
Momentum
Force
Power
Pressure
Moment of Inertia
Charge
Viscosity
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m
kg
s
m2 kg s-1
m2 kg s-2
m kg s-1
m kg s-2
m2 kg s-3
m-1 kg s-2
m2 kg
Q
m2 s-1
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Meter
Kilogram
Second
Newton Meter
Joule
p
Newton
Watt
Pascal
I, J
Coulomb
Pascal Sec
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L
BL-2T or BT-1
T
B
BT-1
BL-1
BL-1T-1
BT-2
BL-3T-1
BT
±a1B1L1T-1
BL-3
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For SI
m is how far light travels in
1/299792458 seconds.
kg is the mass of a standard from 1901
s is 9,192,631,770 cycles of Cesium 133 hyperfine transition.
For DM
B is ħ, Planck’s Constant Reduced
L is c times T
T is the natural unit of time.
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The point of the previous units table is to illustrate that in DM, B, L and T each stand for a fundamental physical dimension (such as length) but at the same time, each is the fundamental unit of that dimension. Thus L stands for the dimension of length and L stands for the fundamental unit of length. Except for charge, which involves the Fine Structure Constant, there is no need to have meetings to update or revise these constants. The value of all the other constants is exactly 1.
The following narrative on the quantities of physics looks like a throwback to ancient Greece. In some ways it is. However, what we are trying to describe are precise and exact representations that are similar to what might eventually be the exact underpinnings of physics. If you can get through them all – the ideas begin to take shape. Our advise is to tell your mind to hold its tongue until the end.