About Mechanics of Virtual Reality
BinGuang Ma
Email: bgMa@sdut.edu.cn
(written in 2005, published in: The General Science Journal, August 25, 2006)
Abstract
Developments
of computer science, especially the computer simulation technology, enable us
to create a vivid lifelike virtual world, which makes people have experiences
both in real and virtual worlds. We have entered a realvirtual mixed age and
need new physics to depict such a realvirtual mixed universe. In this article,
some personal views about the unification and the future of fundamental physics
are proposed. The article contains three parts: (1) Super Transformation. SpaceTime Transformation with Simulator
which describes the spacetime transformation between two bodies in two
different worlds; in this part, a new picture of nature is plotted to be
virtual world net, called Super Universe, on which information can flow from
one world to another. (2) Similarity
Mechanics. A conceptual framework for the unification of fundamental
interactions, relativity and quantum in the formulism of fractal geometry and
fluid dynamics; in this part, the long range interactions are unified as
inversesquare interaction and short range interactions can be regarded as the
combination and decomposition of “Rotons”. (3) Artificial Universe. The physical foundation of artificial reality;
in this part, we act as creators to create different kinds of virtual worlds in
the formulism of extended cellular automaton at microscopic level and
simulation dynamics at macroscopic level.
The
result shown here, as a physics theory, is just a beginning, while it greatly
deepens our understanding about nature, and provides a new viewpoint and a
novel methodology for physics study.
This
paper is dedicated to the World Year of Physics 2005 to commemorate the hundredth
anniversary of relativity theory and the 50^{th} anniversary of great physicist
Albert Einstein’s death.
Introduction
Developments
of computer science have not only changed our life but also changed our
thought. Thanks to the computer simulation technology, we have now been able to
create a vivid lifelike virtual world, via which scientists do their researches,
teachers do their educations and game players kill their time. All these people
have their experiences both in real and virtual worlds. Moreover, in some artworks,
especially in the film “Matrix”^{1},
the existence of our world which we call reality have been questioned to be a
virtual world controlled by computers; we face the difficulty to tell the world
we are living in is virtual or real. In sum, we have entered a realvirtual
mixed age and need new physics to depict such a realvirtual mixed universe. Now,
we begin our study with the following interesting hypothesis: “if the great physicist,
Albert Einstein, lived in our age and
saw the film ‘Matrix’ (Figure 1),
what should he tell us?”
Figure 1. Albert Einstein sees the film “Matrix”. The left half is real world and
the right half is virtual world. We shall give the spacetime transformation
between Einstein and Neo.
I. Super Transformation
(Super general relativity)
Contradiction
in Simulation
Suppose
a simulation experiment, in which we simulate the running of solar system. We
can set the form of the law of gravity at programming time. For example, we can
make the gravitational constant smaller than that in our world and we can make
it inversecube law instead of inversesquare law. Then the speed rate of
planet in the simulated solar system is smaller than that in our world. Suppose
there is a physicist living in that simulated world. Through longtime
observation, he can find the law of gravity of his world. It must be different
from the law of gravity of our world: the gravitational constant of the
simulated world is smaller and the form of it is inversecubed. That’s to say,
the forms of physical laws are not invariant between the simulated and
simulating worlds.
Here
we meet a contradiction between two statements: “the two worlds are the same
real” and “physical laws are invariant in the two worlds”. Which one is right?
Basic Principles
We
insist on the former and propose two principles as follows:
1
all the worlds are the same real.
2
simulated event and simulating event coexist.
The
former means if one has no enlightenments from other worlds, he cannot tell the
world he is living in is virtual or real just as one cannot tell he is moving
or resting if he has no reference system, i.e.,
reality is relative, which is the generalization of general relativity
principle, called Super General
Relativity Principle, and shows the Relativity
of Reality. For a world, we call it reality or virtuality depends on
whether we are living in it: we call the world we are living in reality, and
other worlds virtuality. For example, if we are living in world A, we call it
reality and another world B virtuality. While if we transfer our consciousness
from world A into world B, then, we shall call world B reality and world A
virtuality. Therefore, reality is relative, just as movement is relative; the
two worlds are equal in reality.
Generally, all the virtual worlds are equal in reality and there is no
absolutely real world just as there is no absolutely resting reference system. If
we insist on the first principle (Same Real
Principle), we have to give up the proposition that “the physical laws are
invariant in the two worlds”. Generally, physical laws for different worlds can
be different forms, which is a substantial advance of our view about nature
that reality doesn’t equal to physical
law.
The
second principle states a fact, called Coexistence
Principle. Nowadays, there are mainly two kinds of simulators available:
one is computers; the other is human brains. For computers, suppose there is a
glinting ball in the simulated world by a computer, the counterpart of it in
the simulating world is the combination of zeros and ones (high and low
electrical levels) of the running computer’s circuits. In fact, for anything in
the simulated world, there is its counterpart (combination of high and low
electrical levels of the running computer’s circuits) in the simulating world. For
human brains, suppose there is a beautiful girl in someone’s imagination, the
counterpart of it in the real world is the biochemical reactions in his brain.
In fact, for anything in one’s imagination, there is its counterpart
(biochemical reactions) in the real world. In sum, simulated events and
simulating events coexist. The second principle says “simulated events and
simulating events coexist”, which doesn’t mean that simulated events and
simulating events exist in the same form. Taking the beautiful girl in someone’s
imagination as an example, its existing form in the simulated world is a
beautiful girl, while the existing form of its counterpart in the simulating
world is biochemical reactions.
Super Transformation
Based
on these two principles, we deduce the SpaceTime Transformation with Simulator
(STTS) which is also called Super Transformation.
Let
the simulating world be world R (real world), and the simulated world be world
V (virtual world). Suppose there is a simulator B in world R which simulates
world V. Suppose a body A in R is on the left of B, and it is moving at speed _{}to right (towards B). In world V there is a body C’, which is
moving to right (from B) at speed _{}. It is illustrated in Figure 2. We shall give the spacetime
transformation between bodies A and C’.
Figure 2. Three
relatively moving bodies used to deduce super spacetime transformation. B is a
simulator. Body A is moving at velocity u
relative to B in the real world where B in; body C’ is moving at velocity u’ relative to B in the virtual world simulated
by B; The spacetime transformation between A and C’ will be deduced.
According
to the first principle, the body A in R and the body C’ in V are the same real;
therefore, the spacetime transformation between them is of meaning.
According
to the second principle, there must be a onetoone map between the simulated
events and simulating events, which can be taken as the “tunnel” of simulator
through which the two worlds R and V are connected. Suppose the tunnel is
symbolized by P. There must be two ends of P: one end is open in R, symbolized
by P_{R}; the other end is open in V, symbolized by P_{V}.
Thus, P_{R} and P_{V} are the proxies of simulator B in R and
V, respectively. Therefore, the speed _{} is defined as the
velocity of A relative to P_{R} in world R, and the speed _{} is defined as the
velocity of C’ relative to P_{V} in world V.
To
get the spacetime transformation between A and C’, we need know the
transformation through tunnel P first. Generally, suppose the transformation
through the tunnel P of the simulator B is _{} and the spacetime
transformation from A to B in world R is _{} and the
spacetime transformation from B to C’ in world V is _{}, then the transformation from A to C’ is:
_{},
(1)
where “_{}” is the composition of transformations. Equation (1) is the
general form of the SpaceTime Transformation with Simulator.
In
the following, we shall consider the concrete form of STTS under some simple
hypothesis. Firstly, consider the transformation between the two ends of the tunnel
P. Let the event at P_{R} be represented by _{} and the event at
P_{V} be represented by _{}, the length measured at P_{V} is _{} and it measured
at P_{R} is _{}. Generally, there is a space scale factor _{} which is the
scale between model and prototype. Suppose the length of tunnel P is 0, which
means P_{V} and P_{R} are superposed with each other (in “super
space”), thus _{}, then:
_{}.
(2)
Suppose
an event process. This process lasts _{} in V, and the
time for simulating it in R is _{}. Generally, there exists a time scale factor _{} which is
determined by the running frequency of simulator B. Suppose the time to cross
tunnel P is 0, which means, for a event process, the time to start simulating it
in R is the same time it starts in V, thus _{}, then:
_{} (3)
Merge
(2) and (3), we get the transformation through tunnel P:
_{}.
(4)
By
stipulating (if we can) the space unit and time unit of any one of the two
worlds, we can set the value of _{} and _{} to be 1 so as to
make _{} an identical
transformation:
_{} ,
(5)
then
_{} ,
(6)
which is the spacetime transformation between A and C’.
Parity Violation
Look
at an example. If the transformation in R is Lorentz transformation^{2},
then there must be the principle “the light speed is constant” tenable in R.
Suppose the light speed in R is _{}. Then the transformation from A to P_{R} is:
_{}.
(7)
If
the transformation in V is also Lorentz transformation, then there must be the
principle “the light speed is constant” tenable in V. Suppose the light speed
in V is _{}. Then the transformation from P_{V} to C’ is:
_{}.
(8)
Suppose
_{} can be set to identical
transformation:
_{}.
(9)
Substitute _{}, _{} and _{ }into _{}, we arrive at:
_{}, (10)
which is the spacetime transformation from A to C’.
Take
_{}, _{}, _{} and _{}as independent variables, and inversely solve the equations
in _{}, we can get the inverse transformation _{}. The formula _{} and _{} represent the
spacetime transformation between two bodies in two different worlds.
From
_{}, we can get the velocity transformation formula _{} in world R by
differential operation. Likewise, we can get the velocity transformation
formula _{} in world V from _{}.
Now
we consider the relative speeds between A and C’. Suppose the velocity of C’
relative to A obtained by _{} is _{}, the velocity of A relative to C’ obtained by _{} is _{}. Because the spacetime transformation in two different
worlds can be different forms, thus the velocity transformation _{} and _{} are also
different generally speaking. Therefore, _{} is not necessarily
equal to _{}.
For
example, from (7) and (8), we can get:
_{}
(11)
and
_{}.
(12)
If _{}, then _{}.
As
a general proposition:
_{},
(Prop. 1)
(for two relatively moving bodies, the velocity of A
relative to B and the velocity of B relative to A are equal in value and
opposite in direction.) is not always tenable in the transformation between two
bodies in two different worlds.
Noticing
this, we have to clarify our symbols. The above _{} is the velocity
of A relative to B and should be rewritten as _{}; the above _{} is the velocity
of C’ relative to B and should be rewritten as _{}.
World Classification
In
fact, even for two bodies in one world, we have no enough reason to believe (Prop. 1) tenable. In the existent
spacetime transformations, such as Galilean or Lorentz transformations, (Prop. 1) is merely regarded as a
priori presumption.
Generally,
suppose the spacetime transformation from body A to B in a world is _{} and the velocity of
B relative to A is _{}, that’s:
_{}.
(13)
There
are two ways to get _{}: one is to inversely solve the equations in _{}, the result is symbolized by _{}, i.e.,
_{}; (14)
the other is to swap the event symbols of _{} and substitute _{} for _{}, the result is symbolized by _{}, i.e.,
_{}.
(15)
Which
way is right? The former is the direct mathematical calculation and right. The later
depends on whether we can get _{} from _{}. In the existent spacetime transformations, such as Galilean
or Lorentz transformations, _{} is merely presumed
as _{} a priori, which
is selfconsistent that for Galilean or Lorentz transformations, _{} under the
condition _{}. But if _{} is of some form
different from Galilean or Lorentz transformations, _{} is not necessarily
equal to _{} under condition _{}.
According
to whether the following proposition:
_{}
(Prop. 2)
tenable, the worlds can be classified into two
classes: TransformationSymmetric world and TransformationAsymmetric world,
with the former being true of (Prop. 2) and
the later being false of (Prop. 2).
If our world keeps to Lorentz transformation, it is a TS world.
World Wind
Now
we consider the spacetime transformation between two bodies with one in TS
world and the other in TA world. Suppose another example:
_{}. (16)
Note _{} in _{} which is
different from Lorentz transformation, which makes the world keeps to it a TA
world.
From
(16) we can get the velocity transformations:
_{} . (17)
Let _{}, _{}, _{}, then from (17) we get
_{}. (18)
In (18), the velocity of C’ relative to A _{} means “from the
viewpoint of A, the body C’ runs faster than A, and the body A cannot chase up
C’ (in R)”, while the velocity of A relative to C’ _{} means “ from the
viewpoint of C’, the body A runs faster than C’ and the body A can chase up C’
(in V)”. Here, as for “whether A and C’ can meet with each other”, body A and
body C’ have different opinions. It sounds like a paradox but it is true.
Let
_{}, _{}, _{}, which means the velocity of C’ relative to B and the
velocity of A relative to B are reversed, then from (17) we get
_{}. (19)
In (19), the velocity of C’ relative to A _{} means “from the
viewpoint of A, the body C’ runs faster than A, and the body C’ can chase up A
(in R)”, while the velocity of A relative to C’ _{} means “ from the
viewpoint of C’, the body A runs faster than C’ and the body C’ cannot chase up
A (in V)”. Here, as for “whether A and C’ can meet with each other”, body A and
body C’ also have different opinions.
Considering
_{} in (18) and _{} in (19)
simultaneously, we will find a very interesting phenomenon that if all the
velocities are rightward, we will see the body A and the body C’ meeting with
each other in world V, and if all the velocities are leftward, we will see the
body A and the body C’ meeting with each other in world R, which means “if
rightward, A runs faster than C’, while if leftward, C’ runs faster than A”.
Figuratively,
it looks like a fat man and a thin man running in wind. If downwind, the fat
runs faster than the thin because of his larger volume benefiting more positive
wind force; if upwind, the thin runs faster than the fat because of his smaller
volume suffering less negative wind force. This windlike phenomenon
originating from the different forms of spacetime transformations of two
worlds is called “world wind”.
Super Universe
In
the above deduction, B is a simulator and C’ is a body in the simulated world
by B. If C’ is also a simulator and it simulates another virtual world V’. In V’,
there is a body D’’ moving to right (from C’). What is the transformation
between A and D’’? Here we generalize STTS to recursivevirtual worlds.
Now
consider a virtual world chain:
_{},
(20)
where “_{}” means “there is a simulator in the former world and it
simulates the latter world”. The arrow “_{}” is called “simulation arrow” and represents simulation
relation. The world on the left of simulation arrow is called “father world” and
the world on the right of simulation arrow is called “child world”. Suppose the
simulator in _{} is S_{1},
and the tunnel transformation of S_{1} is symbolized by _{}; the simulator in _{} is S_{2},
and the tunnel transformation of S_{2} is symbolized by _{}; and so on; until the simulator S_{n1} in _{}, it simulates the world _{}, and the tunnel transformation of S_{n1} is
symbolized by _{}. Then the transformation between a body A_{1} in _{} and a body A_{n}
in _{} is the
composition of transformations in these virtual worlds:
_{}.
(21)
If the transformations of simulators can be set to
identical transformation, then (21) is simplified as:
_{},
(22)
which is the spacetime transformation between two
bodies in recursivevirtual worlds.
There
are 3 logical states of virtual world chain:
_{}.
Here
we introduce a concept “super universe”. Three logical states of virtual world
chain correspond to 3 basic types of super universe structures. The 1^{st}
type is called “L” (line) type which is opened at two ends. The 2^{nd}
type is called “O” (circle) type which is a closed structure. The 3^{rd}
type is call “P” (polliwog) type which is opened at one end and closed at the
other end.
For
the 2^{nd} type of super universe, the virtual world chain begins at _{}, when it reaches _{}, there is a simulator S_{n} in _{}, and the world it simulates is just _{}.
According
to (22), there is
_{},
(23)
thus,
_{} (24)
and
_{}.
(25)
For
the 3^{rd} type of super universe, the virtual world chain begins at _{}, when it reaches _{}, there is a simulator in _{}, and the world it simulates is _{} where _{}.
According
to (22), there is
_{} (26)
and
_{}.
(27)
For
the 2^{nd} and 3^{rd} types of super universe, because of the
restrictions (24), (25), (26), (27), the transformations in virtual worlds
cannot be arbitrary forms.
The
existence of super universe structure implies the property of “self simulation”
of the nature which means that the running of the whole super universe can be
simulated by a part of one of its worlds. Selfsimulation property is the
selfsimilarity of existence. The restrictions (24), (25), (26), and (27) are
called “selfsimulation restriction”. In the above deduction, if V=R, which
means the simulated world by simulator B is just the same world B in, then _{} has the same form
as _{}. In this situation, the transformations between A, B, C’ are
just the same as transformations between 3 bodies in only one world.
Now
image there are more than one simulator in a world, we will get a picture of
super universe to be the virtual world net with simulators being edges, worlds
being vertexes, and three basic type “L”, “O”, “P” structures being leaves
(Figure 3), on which information can flow from one world to another. Our world
is only a node of super universe. The simulator that our world is running on is
called The Simulator.
Figure 3.
Illustration for (a part of) the structure of super universe. A rectangle
represents a simulator and an ellipse represents a world. Solid line represents
the relation “contain” which means there are simulators in that world and dotted
line represents the relation “simulate” which means the simulator simulates the
world. W_{n1}S_{n1}…W_{n}S_{n}…W_{n+1}S_{n+1}…W_{n+2}
is a sample of L type super universe; W_{n}S_{n}…W_{n+1}S_{n+1}…W_{n+2}S_{n+2}…W_{n}
is a sample of O type super universe; W_{n1}S_{n1}…W_{n}S_{n}…W_{n+1}S_{n+1}…W_{n+2}S_{n+2}…W_{n+3}S_{n+3}…W_{n}
is a sample of P type super universe. Super Universe is also called “simuverse”
(Simulational Multiverse), a world of which is also called “artiverse”
(Artificial Universe).
Test
Experiments
Here
we design two realvirtual mixed experiments to test this theory. One is
particle decay and the other is particles chase. Figure 4 is the sketch map for
these two experiments.
Figure 4. Sketch
map for two realvirtual mixed experiments. The red bar at OA is the place to
send real particles. The green bar at OC’ (on the computer screen) is the place
to receive (or send) virtual particles. P_{R} (red circle) is a target
to receive real particles which is connected with a computer on which a
simulating program is running to generate virtual particles. P_{R} is
also a device to send real particles triggered by the simulating program when a
virtual particle with leftward velocity reaches P_{V}. P_{V}
(green circle) is the middle point of the left edge of computer screen from
where the generated virtual particles begin to run rightward at some a speed.
1. Particle Decay
This
experiment is designed to test the rightness of composition of transformations
(formula 10). Suppose a particle is sent from OA (red bar in R) at a rightward
speed _{}, and the intrinsic life time of it is _{}. The distance between OA and OB is _{}, and the distance between
2. Particles
Chase
This
experiment is designed to test the rightness of the velocity transformation
formula. Let _{}.
Firstly,
we observe the rightward particle chase. Suppose a real particle is sent at
speed _{} from OA, and at
the same time (take
Secondly,
we observe the leftward particle chase. Suppose a virtual particle is sent from
OC’ at speed _{}, and at the same time (take
If
in the experiment, such phenomena are observed, the rightness of the velocity
transformation formula is verified.
Practical
Stories
Story 1. swimming fish and
flying bird — a story in nature
Suppose
there is a fish swimming in the lake and there is a bird flying in the sky. On
the surface of the lake, there is a swimmer (B) with his left eye in water and
his right eye in air. Through his left eye, he see the fish (A) swimming
towards him to right, and through his right eye, he see the bird (C’) flying
from him to right. By his left eye, he measured the velocity of the fish
relative to him is _{}, and by his right eye, he measured the velocity of bird
relative to him is _{}. Because the velocity in water and that in air all keep to
Lorentz transformations, but the light speed in water is not equal to that in
air, therefore, the swimmer will tell us that the velocity of the bird relative
to the fish is not the opposite number of the velocity of the fish relative to
the bird.
Story 2. policeman and thief — a
story in future
Suppose
in future, man can enter the virtual world simulated by computers owing to the
development of manmachine interface technology. Now consider a policeman (A)
and a thief (C’). The policeman holds a baton and the thief hold a pistol. There
has happened a fighting between them in world R. The thief’s pistol has been
damaged when they are fighting, but it is not a fatal damage. Any one able to
use pistol can fix it in 10 minutes (intrinsic time). Suppose the thief is
running to east, when he meets the simulator B, he enters the virtual world V. In
the virtual world, the thief begins to fix his pistol. When the policeman
arrives at simulator B, if the policeman is clever enough and knows Super
Transformation, he should do a calculation before his making decision whether
to enter the virtual world or not. Because if the time he runs to the simulator
in world R plus the time he runs after the thief until he gets him in world V
is longer than the time the thief used to fix his pistol, the policeman doesn’t
dare to enter the virtual world to catch the thief: Obviously, the baton is not
the match of pistol.
Story 3. a contemporary version
of story 2 — a story in game
Suppose
we hold a realvirtual mixed game. There are two players in this game. They are
all good game players and longdistance runners. But the game we let them play
is very ordinary: “policeman and thief”. The player A acts as policeman and the
player C acts as thief. We plot a game scene as follows:
There
are two racetracks in a playground. At the end of the racetracks, there is a
computer. The computer is equipped with a large screen which is in the sight of
the two players, and two keyboards, each one of which is used by one player. When
the players reach the finish line, they begin to contest with each other in
computer game: “policeman and thief” (a simple computer game in which the thief
runs ahead and the policeman runs after the thief in order to catch him).
The
player A (policeman) lets the player C (thief) run first. After a while, the
player A begins to run. When the player C reaches the finish line, he enters
the computer game by pressing the “Enter” key on his keyboard; at the same
time, there is a “thief” (a character in computer game) appearing at the middle
point of the left edge of the screen and he begins to run rightward along the
horizontal line (to the middle point of the right edge of the screen). When the
player A reaches the finish line, he also enters the computer game by pressing
the “Enter” key of his keyboard; at the same time, there is a “policeman”
appearing at the middle point of the left edge of the screen, and he begins to
run after the thief; simultaneously, a computer program starts to simulate the
process of “fix pistol”.
In
this game, the simulator is the computer, and the tunnel P of it is the electrocircuit
of the computer, and the end in the real world of tunnel P (P_{R}) is
the “Enter” key on the keyboard, and the end in the virtual world of tunnel P
(P_{V}) is the middle point of the left edge of the computer screen.
The spacetime transformation in virtual world V is defined as the
transformation between a moving body on the computer screen and the middle
point of the left edge of the screen.
We
make game rules as follows: if player A enters the computer game and catches
the thief, he wins; if the policeman is shot, player C wins; the winner will
win 1000 dollars, a half of which is paid by the sponsor (here us) and the
other half of which is paid by the loser. But before the player A enters the
computer game, if any one gives up, then, the one who gives up pays no money,
and the winner will get 500 dollars from the sponsor.
Under
such game rules, before the player A entering the computer game, any of the two
players should do a calculation and make his decision whether to give up to minimize
his loss. In this condition, the one who knows STTS can reduce his losing and
increase his winning.
Unification
of Three Worlds
Figure
5. Super
Transformations bridge three kinds of worlds: objective material world, human
mind world and computer simulation world. The three kinds of worlds are unified
as virtual realities.
Three
kinds of simulators are mentioned above: The Simulator, Human Brains, and
Computers. The Simulator is the simulator where our world is running on, which
is a “God”made one. Human brains are the evolution result of our world and
computers are manmade simulators. These three kinds of simulators simulate
three kinds of worlds: objective material world, human mind word, and computer
simulation world. The three kinds of worlds are bridged by super
transformations and unified as virtual realities, which makes it possible to
give a uniform description of nature.
Discussions
1.
Virtuality of Existence Same Real Principle can
also be called “ZhuangZi Principle”. In ancient
2.
Reality of Mind Conduct a thought experiment.
Imagine there is a metal ball moving around you. Firstly, imagine it moves
clockwise; after some loops, try to make it move anticlockwise as soon as
possible; meanwhile, you will feel exerting. Say, you feel clearly that the
metal ball in your imagination has inertia, which means it is massive just as a
real metal ball. In sum, things in your imagination are the same real as you
are.
3.
Reality and Physical Law Einstein believes that
people in different reference systems should feel the same “physical reality”,
while we beyond him believe that people in different worlds should feel the
same “reality”. Please note the difference between Einstein and us. Einstein use
the term “physical reality”, we use “reality”. That’s to say, the same reality
doesn’t means the same physical law, i.e., “reality” doesn’t equal to “physical
law”, which is a substantial advance of our view about nature. Einstein,
limited to his age, cannot realize the difference between reality and physical
law. But nowadays, thanks to the development of simulation technology, we can
create a virtual world with different physical laws from ours. We have been
playing the role of “God”, maybe only partially, but this fact will enable us
to greatly deepen our understanding about nature.
4.
Information Conservation
Law In
the picture of super universe, body’s translation from one world to another,
actually, is the representation of the body in different worlds. A
transformation action corresponds to a recreation procedure. “Body C transfers
from world A to world B” means the recreation of body C in world B (using the
elements of world B) according to the information carried by body C. Ensuring
body C to be body C must require the conservation of information.
5.
Consciousness Suppose in future, man can
enter the virtual world simulated by computers owing to the development of
manmachine interface technology. If consciousness can be transferred from one
world to another, its essence may be information. That is, the essence of
consciousness is information flow, is the running of human brain as a
simulator. Furthermore, simulation relation also joints the subjective world
and objective world, which enables a uniform description of nature.
6.
Free Will Free Will is the
correlation of two worlds with different physical laws. There are two necessary
factors for Free Will: Difference and Correlation. Owing to difference, the
physical laws in one world (typically the simulating world) cannot determine
all the phenomena in the other world (typically the simulated world), which
ensures that there is room to accommodate Free Will. If the two worlds have the
same physical laws, they can be taken as one bigger world, and therefore there
is no room to accommodate Free Will. Owing to correlation, Free Will can be
manifested. If there is no correlation between the two different worlds, one
can only lives in either this world or that world, which is just like there is
only one world, and therefore Free Will cannot be manifested. We have free will
just because we are living in a superposed state of two different worlds (here “different”
means the two worlds have different physical laws), i.e., we are living in both
reality and imagination. If we just live in one world, we won’t have free will;
and even we have, it cannot be manifested. Both the two factors are necessary
to ensure the existence of our free will.
7.
Super Universe Super universe is a kind of
vertical structure of multiverse (may be called “vertiverse”) in comparison to
the parallel structure of multiverse such as in the multiworld interpretation
of quantum mechanics.
(
II. Similarity Mechanics
(Special super general relativity)
Super
general relativity theory based on “same real principle” and “coexistence principle”
unifies conceptually three worlds: objective matter world, subjective mind
world and computer simulated world and gives a new plot of nature as virtual
world net called Super Universe. While as for a concrete node of super
universe, especially for the world we are living in, it does not unify its
physical laws, thus it is incomplete. Since physical laws in different worlds
can be different forms, the physical laws in one world should be in the same
form. Based on this idea, we proposed Special Super General Relativity Theory
as a special case of super general relativity in which same real principle and
coexistence principle are applied to one special node of super universe, i.e.,
our world. Special super general relativity theory aims at unifying the
physical laws of different existence scales, so it may also be called “Scale
Relativity Theory”.
Basic Principles
and Matter Structure
Relativity
of Measurement all of our knowledge about quantity are from measurement.
Measurement is a procedure of comparison where a measure unit is taken as a
standard to be compared with the object to be measured and the quantity of this
object is determined according to the number that this object contains the
measure unit. The property of measurement that a measure unit is always taken
as a reference is called the “relativity of measure”. Here measure includes the
measure of space, time, speed and energy. The relativity of measure means that
big or small (of space), short or long (of time), fast or slow (of speed), high
or low (of energy) are all relative. A human’s body is smaller than a mountain
but bigger than an ant; a human’s lifespan is shorter than a tortoise but
longer than a fly; a human runs slower than a leopard but faster than a snail;
a human has more power than a rabbit but cannot pull back an elephant. All the
above examples demonstrate that big or small, long or short, fast or slow and
high or low (of energy) are all relative. The key is to see the measure of the
object as standard (reference), or namely, the relative scales of the two
objects for comparison.
From
the “relativity of measure”, it can be deduced that the matter structure is
infinitely divisible. Proof is as follows: because measure is relative, there
is no absolute bigness or smallness; if the matter structure is not infinitely
divisible, there must exist absolute bigness or smallness, which contradicts
the “relativity of measure”; so the matter structure is infinitely divisible.
Basic
Principles
(Same Law principle and Statistics principle are special forms
of Same Real principle and Coexistence principle, respectively.)
According
to the above “relativity of measure”, an infinitely divisible matter structure
is obtained. While what is the relationship between matter structures at
different existence scales? And what is the relationship between the laws that
they keep to? Same law principle tells us that matter structures at different
existence scales are similar to each other because they keep to the same
physical laws. Then, we can know that if we take human beings’ existence scale
as the center, there are infinite numbers of “big human” worlds upward and among
them the one who takes solar system as an atom is the nearest world from ours
along the direction of big scale, and from now on, if we say the “big human
world” without otherwise statement, it is default as this world. Likewise,
there are infinite numbers of “small human” worlds downward and among them the
one who takes an atom as the solar system is the nearest world from ours along
the direction of small scale, and from now on, if we say the “small human world”
without otherwise statement, it is default as this world. Therefore, the matter
structure of our universe is an infinitely divisible fractal.
According
to the selfsimilarity of a fractal, we know that particles at any existence
scales have a structure like solar system or atom, i.e., the “nucleated revolving”
structure. At the same time of space scaling, the time is also scaling. That’s
to say, the time unit used in the small human world is shorter than that of our
world whilst the time unit used in the big human world is longer than that of our
world. But the scale for space scaling and that for time scaling is not the
same, therefore, the light speeds in different scale worlds are not the same. Suppose
the light speed in our world is _{}, then the light speed in the small human world is larger
than _{} (may be _{} ) called “fast light” and the light speed
in the big human world is less than _{} (may be _{}) called “slow light”.
However,
the human beings in big human world do not feel the socalled (by us) “slow
light” in their world is slow because all of the processes in their world are
slowed; and thus the speed of “slow light” is still the fastest speed in their
world. We say the speed of “slow light” slow just because we take the light
speed in our world as a reference. Likewise, the human beings in small human
world do not feel the socalled (by us) “fast light” is fast because all the
processes in their world are fasted. For an existence scale, the light speed of
that scale is the fastest signal speed for that scale which makes the
interactions local seen in that scale.
Special
coexistence principle (Statistics principle) indicates that there are two
scales for the description of physical phenomena: macroscopic and microscopic. And
there exists a scale transformation able to transform the description of
microstate to macrostate. Therefore, special super general relativity theory
can also be called “Scale Relativity”.
Unification
of “Fundamental” Interactions
Since
30’s of 20th century, human beings’ exploring frontier of micro world has been
boosted into the field of particle physics. At the beginning of 1960’s, thanks
to the development of the building technologies of big accelerators, a large
quantity of new “elementary particles” has been found. Till then, five forces
came into human sight, i.e., electrostatic, magnetic, gravitational, strong
nuclear and weak nuclear forces. Among them, electrostatic and magnetic forces
had already been unified by Faraday/Maxwell as electromagnetic force^{4};
the electromagnetic force and weak nuclear force were unified through QED, Feynman
rules, symmetry, group theory, gauge theory & renormalization etc.^{ }(by Glashow, Weinberg,
Salam, et al.) as electroweak force^{5};
on similar lines with quantumchromodynamics (QCD), the strong force is further
considered to be unified, leading to the socalled StandardModel^{68}.
Standard
Model believes that there exist four fundamental interactions in the nature:
strong, weak, electromagnetic and gravitation, and three kinds of elementary
particles: gaugebosons, fermions, and maybe higgs. Great Unification Theories
(GUT) are just those theories aiming at unifying the different particles and
interactions in different existence scales, and String/Membrane theory and its
variant Supergravity/quantumgravity theory are representatives of GUT^{8}.
However, can these interactions be unified? And how can it be done?
InverseSquare Law The form of
fundamental interaction is determined by the dimension of the space. The only
reasonable form of interaction in 3D space is inversesquare law. Proof is as
follows:
Figure 6. Inversesquare
force as a result of the decrease of meson flow areal density. The area of the spherical
surface _{}, therefore the areal density of meson flow _{}, which is the origin of inversesquare force.
As
shown in Figure 6, suppose the interaction between two bodies M and m are realized by exchanging meson flows; a body’s ability of
sending and receiving mesons proportions to its matter quantity; and the
interaction strength accepted by a body proportions to the meson numbers that
it receives.
Then
the meson flow sent by body M
uniformly diffuses to different directions in the 3D space, and then the
frontier of this flow is a sphere. Therefore, the area of the front sphere of this
meson flow increases with the increase of the square of propagation distance r, resulting in the areal density of the
meson flow on the front sphere decreases with the square of propagation
distance r. Then, the meson numbers
received by a unit quantity of matter decrease in proportion to the square of r. And thus there is:
_{}
(a)
This is just the form of inversesquare law where K is a constant to be measured by
experiment.
An
important view of special super general relativity is that the form of
fundamental interaction is determined by the dimension of the space. In the
above deduction, three principles are referred: (1) Locality principle. That is, the interactions are local ones and
realized by exchanging mesons with finite speeds. There is no instant
interaction acting at a distance. (2) Simplicity
principle. That is, the strength of interaction linearly proportions to the
matter quantity. (3) Symmetry principle.
That is, different directions of our space are symmetric with each other and
space is isotropic. In 3D space, the formula who keeps to the above three principles
is only inversesquare law (a). Similarly, the formula who keeps to the above
three principles in 2D space is only the inverselinear law while that for 4D
space must be inversecubic law. And so on.
Gravitation
and Electrostatic Force They are all inversesquare interactions and essentially the
same interaction but appearing at different scales, and thus they are relative.
The socalled “gravitation” by us is the electrostatic force for big human; and
the socalled electrostatic force by us is gravitation for small human.
Therefore, it can be predicted that there must exist antigravitation
(repulsive force). Galaxies composed of matter and those composed of antimatter
must be repulsive to each other so that our solar system is not attracted by
other solar systems composed of antimatter and collides and annihilates. For
big human, our solar system is just like an atom and sun is the nucleus and the
planets are just like electrons. When the planets jump between the orbits
running around the sun, slow light is emitted which is the light wave in the
big human world and the speed of it is less than c (suppose c is the light
speed of our world). Likewise, from the viewpoint of small human, our atom is
just like the solar system of their world and the nucleus is the sun and the
electrons are the planets. Communication between the nucleus and electrons are
like the process of the sun throwing light to the earth. Therefore, the
communication between nucleons and electrons is conducted by the “fast light”,
i.e., the light in small human world.
Strong and Weak
Forces
Essentially speaking, they are not interactions but reactions. Because strong
and weak interactions only manifest in nuclear reaction or particle decay
reaction, thus their essence are reactions just like chemical reactions. Because
there is only one fundamental interaction— inversesquare interaction —in 3D
space which is a long range interaction, the short range properties of strong
and weak interactions prove them to be reactions
not interactions. Thinking that
strong and weak interactions have equivalent positions to gravitation and
electricity to be the fundamental interactions of our world is a wrong
thinking. Their short range properties just prove that they are not
interactions but reactions just like chemical reactions. Like in chemical
reactions where two atoms must approach to each other very close so that the
electron orbits of the two reacting atoms are superposed with each other to
incur chemical combination, two nucleons can only react with each when they are
near enough so that the orbits of the nucleons’
electrons can superpose with each other (see Figure 7). Just as we do not regard
chemical reaction as fundamental interaction of our world, we should not regard
nuclear reaction and particle decay reaction as fundamental interaction. By the
analogy between particle table and chemical element table, we are convinced
that the essence of strong and weak interactions is reaction not interaction.
Figure 7.
Schematic illustration of “nucleus in nucleus” structure of particles.
In
a summary of the above, we know that there is only one fundamental interaction
in 3D space and that is inversesquare interaction which is a long range
interaction. Any short range “interaction” is essentially reaction. In the
fundamental interaction, fermions are the agents and bosons are the media. Higgs
particles do not exist.
Conciliation
of Relativity and Quantum
As
two cornerstones of the physics building of twenty century, Relativity Theory
and Quantum Mechanics have achieved glorious triumph in their own applicable
fields, respectively. But there are deep contradictions between them. The
contradictions between relativity and quantum mainly reflect at two points: (1)
certainty and uncertainty. Relativity is rigorously a theory of certainty.
Einstein persists stubbornly in that “God doesn’t play dice”, while quantum
shows some intrinsic uncertainty such as the Heisenberg’s uncertainty relation;
(2) locality and nonlocality. Relativity is rigorously a local theory and
believes that there is the maximum signal speed while quantum demonstrates some
nonlocal correlation such as in entanglement.
These
diametrically opposed contradictions disturb physicists deeply so that many
people believe that one of them must be wrong. However, is this really so? Here
we shall tell that the contradictions between relativity and quantum are phenomenological
although they seem profound, and relativity and quantum can be unified under
the framework of Scale Relativity.
We
shall begin with the uncertainty effect
of quantum. Here we say uncertainty effect instead of uncertainty principle is
aiming at emphasizing that the uncertainty is only a kind of effect rather than
a principle. Just as space contraction and time dilation in special relativity
are effects of motion relativity,
uncertainty is some kind of effect of scale
relativity. We cannot determine the position of an electron but we can
accurately measure the orbit of a planet. This fact tells us that whether or
not we can obtain a precise measure depends on the relative scale of the
observer and the object to be observed. From this fact, it can be deduced that
small human must be able to accurately measure the position of an electron
because an electron looks as big as a planet in their eyes. Likewise, the orbit
of our earth must be unable to be accurately measured by big human just like we
cannot do it to an electron. Therefore, whether or not an object can be
accurately measured is relative, thus, certainty and randomness (uncertainty)
is relative. There is no absolute certainty and randomness just as there is no
absolute motion and rest. So the uncertainty of quantum does not contradict the
certainty of relativity.
Now
see the locality and nonlocality. They are also relative. As aforementioned,
two particles (such as an electron and a proton) that rest relative to each
other communicate by “fast light”, viz.
the light in small human world. Therefore, the interaction between two
particles with nonlocal correlation seen from our world may be local one seen
from the small human world. We think the correlation is nonlocal because the
meson speed that connect the two particles surpasses the light speed of our
world while small human think the correlation is local because the meson speed
that connect them does not surpass the light speed of their world. Likewise,
the local interactions seen from our world may be nonlocal ones seen by big
human. Just because the maximum signal speeds at different existence scales are
different, the nonlocal interactions seen from a scale may be local ones when
seen from a smaller scale; likewise, the local interactions seen from a scale
may be nonlocal ones when seen from a bigger scale. Therefore, to be local or
nonlocal is relative. There is no absolute locality and nonlocality just as
there is no absolute motion and rest. So the nonlocality of quantum does not contradict
the locality of relativity and is just some kind of effect of Scale Relativity.
Now
we see another manifestation of quantum: Discreteness. “Discreteness” and “Continuity”
is a pair of relative concepts. That is, a discrete phenomenon seen from a
scale may be continuous seen from another scale and vice versa. For example,
asphalt road surface is rugged seen by ants but smooth for a van tire. Discreteness
is only observable at specific scale. For a bigger scale, it seems continuity
due to the rough resolution of the apparatus. For a smaller scale, it is
unobservable due to too large span of intervals (even longer than the human activity
scope and history of that scale). Therefore, there is no absolute discreteness
and continuity just as there is no absolute motion and rest. The difference
between discreteness and continuity is only a kind of effect of Scale Relativity.
About Superluminal
Speed
For every existence scale, there is a maximum signal speed which is the light speed
of that scale. For a scale, the light speed of that scale cannot be surpassed
whilst for a smaller scale, there is a faster light speed (the speed of “fast
light” seen from the former scale). The smaller the scale is, the faster the
light of it runs. Therefore, whether a light speed can be surpassed or not is
relative. For every existence scale, it cannot surpass the light speed of its
own scale, while for a smaller scale, the light speed of that scale is not a
limit. The existence of maximum signal speed is also a kind of effect of Scale Relativity.
About Minimum
Quantum of Action It is believed that Planck constant stipulates the minimum
quantum of action of our world. However, because of the relativity of measure, for a bigger or smaller existence scale, it
is not the minimum quantum of action. The smaller the scale is, the higher the
energy density. Therefore, the minimum quantum of action only has a relative
meaning; it is only meaningful at a specific existence scale; the existence of
it cannot be taken as a reason for denying the infinitely divisible nature of
matter structure.
The Essence
of Matter Wave
What
is matter wave? And what is wave function. Making a clear comprehension for
matter wave and wave function in quantum mechanics is another difficult problem
disturbing physicists deeply. Here we shall give the answers. The essence of
matter wave is the motion trajectory of the position center of a “nucleatedrevolving”
system in 3D space, i.e., a wavelike motion of position center; and meanwhile
it is also the wavelike character of the systematic action of a “nucleatedrevolving”
system. While the wave function in quantum mechanics is an artificial
(manmade) description of the systematic action of the “nucleatedrevolving” system
as an empirical formula and essentially is an approximation of the wave character
of the systematic action in Hilbert space. The module square of wave function
reflects the distance between some position in the space (at some time) and the
position center of the “nucleatedrevolving” system and proportions to the
probability to find the “nucleatedrevolving” system at that position. Proofs
are as follows:
Figure 8.
The trajectory of the position center of a moving “nucleatedrevolving” system
is wave.
As
illustrated in Figure 8, suppose there is a free “nucleatedrevolving” system
(a free particle) with a mass center velocity of _{}. Here “free” means there is only the interaction between the
nucleus and the peripheral particle (internal force) and no external forces
acting on the “nucleatedrevolving” system. Under such a condition, the system
should rotate around their common mass center and the momentum and energy and
the angular momentum of this system all conserve in the moving. Suppose the
distance between the nucleus and the mass center is d_{p} and the distance between the peripheral particle and
mass center is d_{e}, then
the distance between the nucleus and the peripheral particle is d = d_{p}
+ d_{e}. Suppose the angular
velocity of the system revolving around their mass center is _{}, the linear velocity of the nucleus running around the mass
center is _{} and the linear
velocity of the peripheral particle running around the mass center is _{}, then there is _{}. Taking the direction of the velocity of the mass center as
the positive direction, the coordinate frame is established, and then the vertical
coordinate _{} of the mass
center is always zero. The position center of the “nucleatedrevolving” system
is defined as the middle point of the line between the nucleus and the
peripheral particle. Suppose the distance between the position center and the
mass center of the system is _{}, then _{}. Suppose the mass of the peripheral particle is _{} and that of the
nucleus is _{} and there is _{}. Now we deduce the trajectory of the position center of this
“nucleatedrevolving” system.
Suppose
the coordinates of the peripheral particle are _{} and _{}. Because the velocity of the mass center _{} is along the
positive direction of _{} coordinate, the
trajectory of the peripheral particle is:
_{}.
(28)
Suppose the coordinates of the nucleus are _{} and _{}, then there is:
_{}.
(29)
From (28) and (29), the coordinates of the position
center of this system is:
_{}.
(30)
Substitute _{} into (30), we
get:
_{}.
(31)
This is the parameter equation of the trajectory of
the position center of the “nucleatedrevolving” system.
From
(31), we know that if the mass of the two parts of the “nucleatedrevolving”
system (i.e. the nucleus and the peripheral particle) equals, then the position
center and the mass center of the system are superposed with each other and _{}, and thus there shows no wave character of this system;
otherwise, if the mass of the two parts of the “nucleatedrevolving” system
does not equal to each other, then the position center and the mass center of
the system do not superpose with each other and _{}, and thus the trajectory of the position center is a wave. Generally
speaking, the mass of the “nucleatedrevolving” system is largely centralized
on the nucleus. So the position center does not superpose with the mass center
and there shows the wave character of the system.
Uncertainty Relation The distance _{}between the two parts of the “nucleatedrevolving” system is
the span of the system in the position space and represents the uncertainty
degree of the position of the system; the relative speed _{} is the span of
the system in the velocity space and represents the uncertainty degree of the
velocity of the system. When the uncertainty degree of the velocity is
multiplied by the mass of the system, it represents the uncertainty degree of
the momentum of this system. According to the definition and conservation of
angular momentum, we get:
_{}.
(32)
From (32), we know that the uncertainty of position
and the uncertainty of momentum have a relation of one growing and the other
declining. That is, the smaller the uncertainty of position, the bigger the uncertainty
of momentum; and vice versa. This is just the meaning of Heisenberg’s
uncertainty relation. Therefore, the uncertainty relation is a result of angular
momentum conservation.
Seen
from another viewpoint, it is also a result of energy conservation of the “nucleatedrevolving”
system. Because the inner force of the system is a conservative attractive force,
the longer the distance between the two parts of the system (namely, the bigger
the uncertainty of position), the higher the percentage of the system’s
potential energy and the lower the percentage of the system’s kinetic energy
(namely, the smaller the uncertainty of the momentum); on the contrary, the
shorter the distance between the two parts of the system (namely, the smaller
the uncertainty of the position), the lower the percentage of the system’s
potential energy and the higher the system’s kinetic energy (namely, the bigger
uncertainty of the momentum). In one word, the system’s position uncertainty
and momentum uncertainty have a relationship that one grows and the other
declines.
Readers
who are familiar with the deduction procedure of the uncertainty relation from
the wave function of quantum mechanics^{9} should feel the conciseness
of the deduction here. To obtain the uncertainty relation from the wave
function of quantum mechanics needs a long and tedious deduction procedure, and
the explanations for this relation are even more strange and elusive^{10}.
Taking the orthodox explanation given by Heisenberg himself as an example, he
thinks that uncertainty comes from the disturbance from the instruments to the
system to be measured. Later, his this idea has been developed to the function
of human’s consciousness, sinking into subjective idealism.
From
the above deduction, we know that the uncertainty relation is a necessary
result of the conservation of the angular momentum (or energy) of a free “nucleatedrevolving”
system. The deduction procedure is simple and the physical meaning is clear.
The Wave
Character of Action By differential operation on
equation (31), the velocity of position center is obtained:
_{}.
(33)
Then the action of position center is:
_{}where _{} is the total mass
of the whole system.
From
(34) it can be seen that the action of the system waves with time t. Comparing (34) with Schrödinger’s
wave function for a free particle:
_{},
(35)
it can be found that the wave in Schrödinger’s
equation is an approximation of the wave of the action of a “nucleatedrevolving”
system in Hilbert space. The original intention of Schrödinger’s establishing
wave equation is to study the atom structures with a new idea of wave motion.
He made an analogy between free particle and plane wave and introduced
artificially an imaginary exponential function to make the action of a free
particle wave so that the stability of atom structure can be explained by the
aid of a concept similar to standing wave. While the cost for this doing is dragging
the wave in 3D real space into a mysterious complex space. As for the Planck
constant in wave function (35), it is a reflection of the precision of our
apparatus under the present ability of measurement. Now we have known the
essence and origin of matter wave, we do not need Schrödinger’s wave equation
any longer in principle. Nevertheless, as a set of empirical formulas, the
formulism of quantum mechanics is still valuable in dealing with some practical
problems.
Distance Function Equation (31) is the
parameter equation of the trajectory of position center of a “nucleatedrevolving”
system. For a given time t, it gives
the average position of the “nucleatedrevolving” system in the space. Therefore,
we can define a distance function:
_{}.
(36)
It represents the distance between the position (x, y)
and the position center of the “nucleatedrevolving” system and reflects the
probability to find the system at position (x,
y) and approximately proportions to
the module
The
position center of a “nucleatedrevolving” system represents the position of
the whole of this system. Equation (31) shows that there is a certain position
of the position center of the system at time t and the probability of finding this system at position (x, y)
negatively proportions to the distance from the point (x, y) to the position
center of the “nucleatedrevolving” system. Because the nearness or farness of
the distance is relative, the probability to find the position center of the “nucleatedrevolving”
system at some position does not change when the distance function multiplied
by a constant (it is equivalent to changing the measure unit of the distance). So
the wave function can be normalized.
By
now, we know that the relativity of farness or nearness of distance is the foundation
that the wave function of quantum mechanics can be normalized and we also know
that the distance function is the essence of the target of Born’s
interpretation for wave function. In addition, we need notice that the position
center is just the position center; it only gives the position of the whole of
the “nucleatedrevolving” system in an average (statistical) sense. In fact,
there is neither the nucleus nor the peripheral particle at the position center
of the “nucleated revolving” system. Therefore, by detecting the motion of the
whole system via the position center (just as what we do at our existence scale
to conduct microscopic experiments), we can only attain a statistical result in
the end.
Take hydrogen atom as an example. We can
detect the wave character of a hydrogen atom in experiment just because we
probe the motion of the position center as the proxy of the whole hydrogen atom.
For small humans, they do not probe the position center of a hydrogen atom to
describe its motion because in their eyes, a hydrogen atom is as big as a solar
system and they can directly determine the position of proton and electron just
as we directly probe the position of sun and earth. So what they get is not a
statistical result. In a word, that’s to say, whether or not obtaining a
statistical result is relative. We get the statistical result is some kind of
effect of Scale Relativity.
De Broglie Relation,
Schrödinger Equation and Born Interpretation The concept of matter wave was given
by de Broglie in 1924^{11}. He was enlightened by the waveparticle
duality of photon and guessed that matter particles may also have wave character.
His idea was verified by Davisson and Germer in an experiment of electron
diffraction in 1927^{12}. The proposition of the concept of matter wave
by de Broglie is a muchtold tale by physicists as a successful example of
using analogy. By analogy, de Broglie established the famous relation:
_{}. (37)
Comparing (37) with (32), we will find that de Broglie
relation is another expression of uncertainty relation actually. In other
words, they are the same thing in essence. They are all results of the
conservation of angular momentum and energy of the “nucleatedrevolving”
system.
Schrödinger
equation was established by Schrödinger in 1926^{13}. It is also a
result of analogy. Schrödinger analogized the moving free particle with the
propagation of plane wave and established the wave equation named by his name.
The concept of wave function originates from his work. While seen in the direct
meaning, the wave in Schrödinger’s equation and the wave in de Broglie’s
relation are not the same “wave”. For example, the wave length in de Broglie
relation has a dimension of length and a direct physical meaning. While the
wave length for the wave in Schrödinger equation has no direct meaning because
it is a wave in complex space. Therefore, the wave in de Broglie relation and
the wave in Schrödinger equation are not the same wave seen from a direct
meaning. The essence of the wave in Schrödinger equation is an artificial
empirical formula reflecting the wave character of the action of a “nucleatedrevolving”
system.
Born’s
interpretation for wave function^{14} is called the “
Summarizing
the above, we know that seen from the direct meaning, the wave in de Broglie
relation and the wave in Schrödinger equation and the wave in Born interpretation
have different meaning, respectively. However, they are also reflections from
different aspects for the same underlying wave: the wavelike trajectory of the
position center of the “nucleatedrevolving” structure of micro particles. De Broglie
relation reflects the conservation of the angularmomentum (or energy) of the “nucleatedrevolving”
system; Schrödinger equation reflects the wave character of the action of the “nucleatedrevolving”
system; while the Born interpretation reflects the distance from some point of
the space to the position center of the “nucleatedrevolving” system.
WaveParticle
Duality From the above deduction, we know that the motion of a “nucleatedrevolving”
system spontaneously demonstrates the wave character (of the position center)
as a whole (the essence of wave is just the propagation of periodicity). On the
other hand, the object who can spontaneously demonstrates the wave character
must be a “nucleatedrevolving” system. Electrons show some
stationarywavelike character on the orbits around the nucleus of an atom;
therefore they must have “nucleatedrevolving” structures. Generally speaking,
any micro particles (except bosons, see explanation later) are “nucleatedrevolving”
systems.
Now
make a comparison with solar system. Earth is running around the sun and the
moon is running around the earth. The mass ratio between earth and moon is
80:1, and then the position center of earthmoon system and the mass center of
this system do not superpose with each other, and then the trajectory of the
position center of the earthmoon system must be a standing wave surrounding at
the orbit of the mass center of this system (Figure 9). In addition, our solar
system is composed of about ten planets, from which it can be speculated that
the sun may be also not a unitary solid ball and that it may be a composite
ball made up of about teen ~ twenty small balls as parts of it seeming like an
atom nucleus. If really so, some characters of the composite ball may demonstrate
in the activities of the sun, for example, the sunspots may be the seams
between these part balls, and the precession of perihelion of the planets may
originates from the nonuniformity of the gravitation due to the non
uniformity of the density of sun as a composite ball.
Figure
9. Illustration for the trajectory of the
position center of earthmoon system.
The
essence of matter wave is the wavelike motion of the position center of a “nucleatedrevolving”
system which embodies the waveparticle duality very well: On one hand,
position center demonstrates spontaneously the wave character in the moving; on
the other hand, at a specific time, the position center has a specific position
so that it also demonstrates the particle character as a whole. However, as aforementioned,
position center is just position center; it only represents the position of the
whole system in an average (statistical) sense. Therefore, the whole particle
only has certain position in a statistical meaning and the results of our
experiments remains statistical.
After
knowing the essence of matter wave, we can then evaluate different sorts of
interpretations for wave function. The following is the evaluation of two
representative standpoints. One is Schrödinger’s wave package interpretation
which emphasizes the wave character too much to face the problem of diffusion
of wave package. In fact, from the wavelike motion of the position center, we
know that the “nucleatedrevolving” system does not diffuse because the
attractive inner force between the two parts (nucleus and the peripheral
particle). The other interpretation is the ensemble interpretation from
Einstein which thinks that the wave character is a collective property of a
large quantity of particles which originates from their aggregation. This interpretation
emphasizes the particle character too much. In fact, as what we know now, the
essence of matter wave is a kind of composite motion (the compound of
revolution and translation), and an intrinsic property of “nucleated revolving”
system which can be demonstrated by a single particle and does not rely on the
aggregation of many particles. Therefore, the above two interpretations for
wave function are all biased in meaning and lose the key point of the truth.
Just
as what is said above, because of the relativity
of measure, whether the wave character is significant or not is also
relative. For small human, electrons seem as big as planets, and thus they do
not care the wave character of electrons. Likewise, for big human, our earth is
as small as an electron, and our solar system is not more than an atom.
Therefore, if big humans make a big grating and take a beam of solar systems to
throw on it, they will also detect the diffraction phenomenon of solar systems.
Hereby, we know that the wave character and particle character are relative,
and they are only some kind of effect of Scale
Relativity.
Scale Transformation,
Symmetry Breaking, Randomness and the Time Arrow With the above discussion
about matter wave, we can now discuss “Scale Transformation” in more details. “Scale
transformation” is actually a simple averaging (summarizing) procedure. Because
summarizing operation is a manytoone map, it is an irreversible procedure
which is the origin of symmetry breaking and randomness. The reason is simple:
we know 1 + 1 = 2, but if it is asked that 2 equals what? The answer is not necessarily
to be 1 + 1, because 1.5 + 0.5 or 0.8+1.2 also equals to 2. That is to say, if
knowing the two addends, we can uniquely determine the sum while if knowing the
sum, we cannot uniquely determine the two addends. The essence of matter wave
may serve as an excellent example to explain that the randomness just
originates from “Scale Transformation”.
According
to “Statistical principle” (special coexistence principle), we know that there
are two scales for the description of the state of matter motion: microscopic
and macroscopic. At microscopic scale, we can directly describe the motion of
the two parts of the “nucleatedrevolving” system and need not describe the
whole of the system in a manner of position center approximation, therefore uncertainty
does not appear. While if because of the limitation of scale, we have to
describe the whole of the “nucleatedrevolving” system in a manner of position
center approximation, then we have to perform a statistical averaging to get
the position center of the whole system (usually, this is automatically done by
our apparatus which is used for measurement and so we need not do it
explicitly) which is an irreversible single direction physical procedure
because knowing the positions of the two parts of the “nucleatedrevolving”
system we can uniquely determine its position center while knowing the position
center of the system, we cannot uniquely determine the positions of the two
parts, which is the origin of randomness.
The
concept of Time Arrow is extensively
discussed in recently years such as by Stephen Hawking in his “A Brief History of
Time”^{6} or by Ilya Prigogine in his “The End of Certainty”^{15}.
The time arrow is just a simple fact: every one of us (except some patients
suffering mind diseases) can feel the single direction of time as it is always
going from yesterday to today to tomorrow. But why the time is single
directional? This problem is not a simple one. To know the answer of this
question, we have to refer to the reversibility of physical process. Yet the
reversibility of a physical process relies on the determinacy of the physical
law that dominates the process. If the physical law is of certainty, just like
Here,
we shall tell that the increase of entropy and the arrow of time just come from
“Scale Transformation”. It is generally acknowledged that entropy is a measure
of the microstate number of a system and the application of entropy increase principle
relies on the adequate randomness of the system, i.e., ergodicity must be
satisfied. As aforementioned, randomness just originates from the “Scale Transformation”
and this is the precondition of the application of
entropy increase principle and the entropy increase principle is only useful
for a description of microstates at a macroscopic level. If we can directly
measure and control the system at microscopic level (as if we have the ability
of Maxwell’s demon), then entropy is a useless concept for us (Note: if we do
not care a more microscopic existence scale) and every process is reversible
for us and thus there is no single directional time in our eyes.
Summarizing
the above, we know that there is no absolute reversibility or irreversibility
for a physical process and that there is no absolute certainty or randomness of
physical phenomenon. Whether a physical process reversible or not and whether a
physical phenomenon certain or random rely on the measure scale. We detect the
motion of an electron to be random but for small human, the motion of an
electron is completely certain no matter for position or momentum. So whether
or not time is reversible are relative and the time arrow is a kind of effect
of Scale Relativity.
The Essence
of Field
What is Field? Field is meson flow. And
the force lines are intuitive description of field.
What is Magnetic
Field?
Magnetic field is a kind of measure effect of “Motion Relativity” (Einstein’s
special relativity) coming from the space contraction.
As
shown in Figure 10, suppose the interactions between the protons in A_{1}
and the protons in A_{2} is _{} and the
interactions between the electrons of A_{1} and those of A_{2}
is _{} and the
interactions between the protons in A_{1} and the electrons in A_{2}
is _{} and the
interaction between the electrons in A_{1} and the protons in A_{2}
is _{}. Then,
_{}, _{} (38)
Figure 10. Schematic
illustration for the generation of magnetic filed. When the electric currents
in the two conductors A_{1} and A_{2} are in the same
direction, the two conductors attract each other and when the electric currents
in them are in the opposite direction, they repulse each other.
Before
adding voltage, because there are equal positive and negative charges in the
two conductors, there is
_{},
(39)
and thus
_{}.
(40)
After
charging, the electrons in the two conductors begin directional movements
(without losing generality, suppose the magnitudes of the two currents in the
two conductors are equal to each other).
Firstly,
we see the situation where the two currents in the two conductors are in the
same direction. In this case, the protons in the two conductors are resting
relative to each other and the electrons in the two conductors are resting
relative to each other too. Therefore, _{} and _{} do not change,
and thus the repulsive force between the conductors _{} also does not
change, i.e.,
_{}
(41)
where _{} is the repulsive
force after charging.
The
electrons in A_{2} have a directional speed _{} relative to the
protons in A_{1}, and then because of the conservation of the quantity
of electricity (i.e., the quantity of electricity is an invariant of “motion
relativity”) and the contraction effect of length (of the “motion relativity”),
the areal number density of meson flow emitted from the protons in A_{1} and
received by the electrons in conductor A_{2} seems increased and as a consequence
_{} increased. The
following is a concise deduction procedure.
According
to length contraction formula of “motion relativity”,
_{}
(42)
there is
_{}.
(43)
Let
_{}.
(44)
Then “_{}” is the decrease factor of length.
According
to the definition of the areal number density of meson flow, there is
_{}
(45)
where “_{}” is the increase factor of the areal number density of meson
flow.
Therefore,
_{} (46)
and then
_{}.
(47)
As a result,
_{} (48)
where the _{} is the attractive
force after charging. Then we detect the phenomenon of a net attraction between
the two conductors which looks like there is magnetic field between the two
conductors.
Secondly,
we see the situation where the two currents in the two conductors are in the
opposite direction. In this case, the protons in the two conductors are resting
relative to each other and then, _{} does not change. The
relative speeds of electrons in the two conductors are _{} (Here Galileo velocity
addition law is used because the speeds of the directional motion of electrons
in conductors are not very high), then the length contraction factor is
_{}
(49)
Then, there is _{}.
Therefore,
_{}.
Consider
_{}
and
_{},
we arrive at
_{} (50)
Then we shall detect a net repulsion between the two
conductors which are explained as the magnetic field between the two conductors.
From
the above, we know that the magnetic field is a kind of effect of “motion
relativity” (special relativity) of electric field, namely, the motion of
electricity generates the magnetism. There is never magnetism without
electricity. So, magnetic charge and magnetic monopole do not exist.
What is Gravitation?
Gravitation
is the most common force around us. According to Einstein’s General Relativity,
it can be regarded as the curvature of spacetime^{16, 17}. In 2005, Prof.
R. C. Gupta (I.E.T.,
Figure 11.
Schematic illustrations for the generation of gravitational field. Suppose two
bodies (body I and body II) contain Heliumlike atoms; the distance d between the two bodies is far larger
than the radius of the atoms R. For
simplicity, suppose two atoms (each one in each body) are arranged as shown
where A1 & B1 are electrons in Body I and A2 & B2 are electrons in body
II; the two protons in body I are grouped as P1 and the two protons in body II
are grouped as P2. The net Attraction (+) and Repulsion () factors between
electrons and protons of the two atoms in the two bodies due to length
contraction are listed in the following Table.
Table
1 Net Attraction (+) and
Repulsion () factors between electrons and protons of the two atoms in the two
bodies due to length contraction
Observations 

Net Attraction (+) or repulsion factor due
to length contraction 



Without relativistic velocity addition (first order effect) 

With relativistic Velocity addition (second order effect) 
A1 as
observer sees A2 

0
= 0 

0
=
0 
A1 as
observer sees P2 

+2x(1/2)v^{2}/c^{2} = +β^{2} 

+2x(1/2)v^{2}/c^{2}
= +β^{2} 
A1 as
observer sees B2 

(1/2)x(2v)^{2}/c^{2}= 2β^{2} 

(1/2)x(2v)^{2}/c^{2} 





B1 as
observer sees A2 

(1/2)x(2v)^{2}/c^{2}= 2β^{2} 

(1/2)x(2v)^{2}/c^{2} 
B1 as
observer sees P2 

+2x(1/2)v^{2}/c^{2} = +β^{2} 

+2x(1/2)v^{2}/c^{2}
= +β^{2} 
B1 as
observer sees B2 

0
= 0 

0
= 0 





P1 as
observer sees A2 

+2x(1/2)v^{2}/c^{2} = +β^{2} 

+2x(1/2)v^{2}/c^{2}
= +β^{2} 
P1 as
observer sees P2 

0
=0 

0
=
0 
P1 as
observer sees B2 

+2x(1/2)v^{2}/c^{2} = +β^{2} 

+2x(1/2)v^{2}/c^{2}
= +β^{2} 
atomI as observer sees atomII 

Total = 0 

Total ≈ + 8β^{4} 
As
shown in Figure 11 and Table 1, the net attraction will appear when the Lorentz
velocity addition law is used in the length contraction formula and
_{} (51)
and the gravitationalconstant G can be theoretically estimated as:
_{}.
(52)
The detailed procedure for the deduction and
estimation of these formulas are presented in Gupta’s paper^{18}.
According
to Prof. Gupta, the “Van der Waals” force between two mesoscopic bodies such as
two molecules, which are due to charge distribution, can be regarded as the “zerothorder”
relativistic effect of electrostatic force, meaning with “no” relativistic
effect at all; the magnetism can be regarded as “firstorder” relativistic
manifestation of electrostatic force because it considers the length
contraction of special relativity; and the interactions between two macroscopic
bodies can be regarded as the “secondorder” relativistic manifestation of electrostatic
force of special relativity because it considers the relativistic velocity
addition (Lorentz velocity addition law). This view can conceptually unify the
(long range) interactions as electrostatic force and its relativistic effects. But
there are residual problem of this view because the gravitation between two
neutrons cannot be explained in the way of two atoms unless that neutrons can
also be regarded as a nucleated structure like atoms. According to special
super general relativity, we know that all the (real) particles have a “nucleatedrevolving”
structure. Then the forces can be unified as the inversesquare interaction and
its relativistic effects, which fulfills the unification of long range interactions.
Does the
mass really increase? The mass of a body will increase with the increase of the
body’s speed is an important inference of special relativity (motion
relativity). But is this the truth? Up to now, our evidence about the increase
of mass mainly comes from the acceleration experiments where it is found that
it becomes more and more difficult to accelerate particles and when it is calculated
using the formula of chargemass ratio and seems as if the mass has increased. However,
what about the truth? This should be started from the mechanism of
acceleration. When a particle is accelerated in the external field, the
increase of its momentum comes from the impulsive force of meson flow. Figuratively,
it seems like a cobble is pushed rolling by the flow of a brook. The rolling
speed of the cobble cannot surpass the speed of the stream. And when the speed
of the cobble becomes faster and faster, the difference between the speeds of
the cobble and the stream becomes smaller and smaller, and then the impulsive
force the cobble received becomes less and less, and as a result, it seems that
the cobble becomes more and more difficult to be accelerated. If we take the
impulsive force as an invariant, we will think that the mass of the cobble is
increased. While in fact, the mass of the cobble does not change, and just the
impulsive force becomes less and less. Similar situation appears for particles
to be accelerated. Therefore, we know that mass just like electricity is also
an invariant of “motion relativity”. Previously, thinking the increase of the
mass with the speed is a misunderstanding.
Electricity
and Mass Essentially, mass and electricity are the same physical quantity: inversesquare
quantity. They are the same physical quantity manifested at different existence
scales. If the matter is not infinitely divisible, then if electricity is discrete,
mass is discrete. In fact, as aforementioned, the matter is infinitely
divisible, so discreteness and continuity is relative, just a kind of effect of
Scale Relativity. The discreteness
of charge originates from our observation scale and the inadequate resolution
of our apparatus. In fact, fractional charge has been suggested in QCD. This
has already challenged the traditional view of integral discreteness of
electricity. It can be reasonably expected that the relativity of discreteness
and continuity will be recognized with the development of the resolution of our
apparatus.
What is Spin? Spin is the
selfrotation of a particle and at the same time, is the revolution of the
peripheral particle on its orbit around the nucleus. Therefore, the angular
momentum of spin and the angular momentum of orbit of peripheral particle are
relative and up to our observation scale. What is spin (the angular momentum of
selfrotation) seen from the macroscopic scale where the nucleated structure of
the particle is out of sight may be the angular momentum of orbit of the peripheral
particle when seen from microscopic scale where the nucleated structure of the
particle is in sight; and vice versa. This is why they keep to the same commutation
relation. Spin, as a kind of angular momentum, reflects the polarity of a
particle or more accurately speaking, the directional property of a particle. Why
we always get two values of spin (a positive one and a negative one) when we detect
the spin of fermions? The reason is as follows. Although, as angular momentum,
the spin of a particle can have many directions, but when coupling with each
other as magnetic moment, there are only two arrangement states of equilibrium:
upmagnetic (paramagnetic) and downmagnetic (diamagnetic). The former is a stable
equilibrium and has lower energy; and the latter is an unstable equilibrium and
has higher energy. That is why we can only detect two values of spin.
What is
isospin? It is a wrong concept introduced in a wrong way. It has its historical
meaning in a phenomenological theory staying in an empirical stage, but it
cannot be taken as a concept with the meaning of truth. Once we have recognized
the true structure of matter, we should abandon it in time.
Does light “really”
exist?
This
is an advanced topic. According to the first chapter of bible, the first thing
that the creator created is the light. God said: “Let there be light”, and
there was light. But does light really exist? We’ll begin the topic from the
difference between fermions and bosons.
Fermions and
Bosons
In quantum mechanics, the particles with half spin are called fermions and the
particles with integer spin are called bosons because they keep to different
statistical laws: bosons keep to BosonEinstein statistics and fermions keep to
FermiDirac statistics. An import difference between bosons and fermions is
whether they keep to Pauli’s exclusion principle. This difference is an
essential one which differentiates the “real” and “virtual” of a particle. Fermions
are real particles because only real particles occupy the space and have an
exclusive property but virtual particles have not. Therefore, standing on a
point of substantialism, bosons do not exist. Bosons are always emitted from
one fermion and absorbed by another fermion and serve as the media between two
fermions. Bosons reflect the relationship between two fermions and have no
position in substantialism. Figuratively, if the two fermions interacting with
each other can be analogized as man and women, the bosons can be analogized as
the love between them. Love is virtual and has no position in substantialism. It
does not occupy our 3D space and merely reflect the relationship between two
persons.
Therefore,
we say that bosons as the media particles are not real particles. They have no
position in substantialism and do not occupy the volume of 3D space. In this
sense, light does not exist because photons are bosons. All the fermions are “nucleatedrevolving”
system while bosons are not. However, if so, why light also has a wave character?
As mentioned above, the wave character is a reflection of “nucleatedrevolving”
structure. If photons are bosons without a “nucleatedrevolving” structure, why
do they also wave as the fermions do such as in a diffraction experiment?
Why light
waves?
The reason is as follows. Photons as a kind of meson reflect the relationship
between fermions. No matter in double slits interference experiments or in
single slit diffraction experiments, appearing of the bright and dark intervals
is a result of the interaction between the fermions on the slits and the
fermions on the screen (of course, it also includes the fermions in the light
source and in our eyes if we observe). Therefore, the wave character of light
(as shown in the above mentioned experiments) is not the wave character of
photons essentially speaking, but reflects the wave character of the fermions
in the slits and on the screen. The wave character of light is only a kind of
phenomenological appearance not the essence. It is only a convenient way for
understanding and not the truth. On the other hand, light as the mesons between
fermions, can propagate of the wave character of one fermion to another leading
to interference between fermions. Likewise, electromagnetic wave, as an equivalence
of light, its wave character is also a reflection of the wave character of
fermions that interact with each other.
The Essence
of Light Usually, we cannot recognize
the truth of some things just because we and they exist in the same level. To recognize
the truth of light, we need outgo the world we are living in to the simulator
(running in our super world) which our world is running on to play a role of “God”.
In fact, super general relativity theory has given us the viewpoint of it. Our
world is running on a simulator that works like a cellular automaton and the
light is the neighbororiented updating rules made by the creator i.e., the rules
on how to update the state of the current cell according to the states of its neighbors.
Why the
light speed is the maximum and does not change? After having known the truth of the
light, we can now explain why the light speed does not change. Because the
simulator which our world is running on, as a computational system, needs time
to execute instructions, and to judge the states of the neighbors of the
present cell to make an update of the state of the present cell needs a fixed
number of clocks; and at the same time, the distance between the present cell
and the neighbors whose states can affect the state of the present cell is
preset to a fixed number. Therefore, the quotient of the former divided by the
latter is also fixed and that is the light speed. Therefore, the light speed
does not change. On the other hand, because all the things in the conformation
space are made up of cells and their motions are driven by the
neighbororiented updating rules. So the light speed is also the maximum. Because
the essence of light is only the updating rules and does not occupy the
conformation space, how does it exist? This should consult the following “SuperSymmetry”.
SuperSymmetry
Supersymmetry
is a great concept. It is proposed originally for the unification of the
socalled fundamental interactions. It aims to construct a bigger group to accommodate
both bosons and fermions, i.e., letting them be the representation of this
group. Regarding particles as representations of groups is a beautiful idea and
a model of symmetry guiding physical research. But symmetry is a sward with two
sharp edges: It can guide physical research in the right way and also can
misguide it. Which result appears depends on whether it is used correctly. If
someone wants to find a group to accommodate all the chemical molecules, i.e., rendering
them to be the representations of this group, his doing is reasonable or
unreasonable just as we render the socalled elementary particles to be the
representations of some group. Anyhow, the doing of correlating the group
representation with the law of fundamental interaction is unreasonable. The law
of fundamental interaction is determined by the dimension of space and has
nothing to do with group representation. But supersymmetry is indeed a great
concept if we can realize its essence.
The
essence of supersymmetry is the symmetry between the code and data of a
program. No matter the code or the data of a program occupies the storage space
of the computational system. Seen from this point, they are equivalent and show
some symmetry relation. Because our world is running on a simulator built up
according to the principles of cellular automaton, supersymmetry here means
the symmetry between the rules and the conformations and it is essential for creating
a selfexistence evolution system.
Supersymmetry
is weird but profound. The weirdness of supersymmetry is not less than that of
adding two quantities with the different physical dimensions while the
profoundness of it can be rated as a revolution of physical thoughts. Supersymmetry
dose not only exist in the field of particles, but also plays important roles
in the field of life. It is the fundamental elements for the existence and
reproduction of living beings. As we know, genetic materials are DNA which is
in a structure of double helix in our cell. DNA strands contain at least two
aspects of information: the information for the living being’s body’s
construction and the information for its function. Early before Watson and
Crick found the double helix structure of DNA, Van Neumann had posed an idea in
his selfreproduction machines according to logical analysis that the genetic
materials of life should contain two respects of information about body’s construction
and function, which is the beginning of the idea of supersymmetry. We shall
discuss it in more detail in the third part of this article: Artificial
Universe.
String and Roton Representing
particles as the different vibration model of strings is a beautiful idea in
string theories^{19} and can be appreciated as a piece of artwork but
cannot be regarded as the truth because there is no solid foundation of this
idea. In contrast, “nucleatedrevolving” system (called “Roton” for short) is a
model with solid foundation that at least the structures of atom and solar
system are all this kind of structures. The idea that all the real particles
(namely fermions) are Rotons satisfies the invariance of scale transformation
and can unify interactions. Logically speaking, there are no more than two
forms of interaction: “direct contact” or “via media”. In 3D space, the sole reasonable
interaction in the form of “via media” (long range interaction) is the inversesquare
interaction whose formula has been proved above to be determined by the
dimension of the space, and Rotons are the nucleated revolving structures naturally
formed under such an interaction. While all the interactions in the form of “direct
contact” can be regarded as the combination and decomposition of Rotons.
Roton and
Mass Point Roton, as a concept, represents the ubiquitous “nucleated revolving”
structure of particles. It differs from
(
III. Artificial Universe
(An upgrade from creature to creator)
According
to the record of “Old Testament”, The Creator created our world in six days. He
created the light, firmament, plants and so on successively. But the Bible does
not tell us that where The Creator comes from and also it does not tell us the
details of the creation procedure. In this section, we shall give some clues on
the details of the creation procedure according to the new picture of nature
provided by super general relativity. Here we shall play the rule of “God” to
create different sorts of virtual worlds. In fact, everyone can be a “God” and
the creation of a world is also not very difficult. What we need is just an
automaton and some programming skills. Let’s begin our topic from the structure
of the simulator which our world is running on.
Micro Scale:
Extended Cellular Automaton
Cellular
Automaton and Grid Universe For an introductory definition of cellular automaton,
see Ref. 20. Here, Cellular
Automaton is defined as an eightelement set,
_{}, (53)
where S is a
space, P is some kind of partition of
the space S, S and P are called Cellular
Space; each part of S (element of P) is called a cell; Q is the set of cellular state; C is the boundary condition of cellular
space; I is the initial configuration
of the cellular space; D is the configuration,
viz., the distribution of cellular
states at a step n; N is the neighbor rules and U is the update rules.
The Extension
of Cellular Automaton To create a lifelike
world, we extend the above ordinary cellular automaton in three aspects: SuperSymmetric,
Position Weighted and MultiLeveled & Bidirectional Causality (Figure 12). Therefore
an extended cellular automaton is defined as a nineelement set,
_{}
(54)
where _{} is the configuration
of the grid universe observed at level l
and _{} is the position
weighted neighbor rules and _{} is a relation
(supersymmetry relation) between the configuration D and update rules _{}.
Figure
12. Schematic representation of Extended
Cellular Automaton.
(a)
SuperSymmetric: the symmetry between states and rules. In a
super space, the states and rules can be unified, i.e., they can exist in the
same existence level so as to interact with each other.
(b)
PositionWeighted: different positions are endued with different
weights to weight the ability of the neighbors to affect the current cell,
which can increase/decrease the symmetry degree of the system such as to make a
square configuration have the symmetry degree of a circular one, or vice versa.
(c)
MultiLeveled & Bidirectional Causality: selfsimilarity
of the cellular space manifested in multilevels. Bidirectional Causality is different
from the reductionism in that not only the underlying microstates can determine
the apparent macrostates but also the apparent macrostates can inversely act on
the underlying microstates. Bicausality makes macrostates change from a pure passive
model to an active one.
Light Speed
and Special Relativity In the cellular automaton
game, for a finite body, if it moves one cell per iteration step, then the
object have the maximum speed. It has been proved that nothing can move faster
than such a speed in cellular space. Therefore, this speed is called light
speed, the being maximum and invariant property of which is the foundation of special
relativity^{16}.
Macro Scale:
Simulation Dynamics
In
accordance with the recursive simulation structure of super universe, simulation
dynamics is the simulation of physical phenomena in an iteration way, which is
the kinetics of artificial universe. In simulation dynamics, evolution of a system
is an iteration process and structure of a system is a resultant attractor of
iteration process.
Interaction
and Transformation
Now
consider the “interaction” between body A in world R and body C’ in world V. As
what we know by far, the sole correlation between them is super transformation,
that’s, if there exists “interaction” between them, it must be represented by
some kind of transformation. In fact, the effect of interaction is leading to
motion or changing motion state of a particle/object, which can be fulfilled by
a transformation as what to be done in computer graphics^{21}. Therefore,
an “interaction” is equivalent to a “transformation”.
Origin of Inertia
“Interaction”,
in Aristotle’s age, is known as “force”, which is regarded as the “cause” of
motion. Galileo may firstly notice the inertia of object^{22} and
Descartes point out that motion of an object needn’t a constant “push force”^{23}.
Subsequently, the great physicist Isaac Newton gives his three laws of motion,
and in his first law, he makes it clear that “force” is not the “cause” of
motion but the “cause” of changing an object’s motion state^{24}. Say,
if there is no such a “cause”, an object will preserve the motion state owing
to its inertia.
As
to the origin of inertia, it’s still an enigma. Via his famous pail experiment,
Simulation
Representation
Now
consider the simulation of a physical world. The first question we meet is how
to represent particles in the simulated world. A natural idea is to represent a
particle by a point in that space. But if so, we have nowhere to place physical
properties of the particle, because a point has only one property, namely, its
position in the simulated space. Of course, we can assign some physical
property artificially at programming time, i.e., we define a variable to assign
a physical quantity to it and then correlate this variable to the point. But
this doing will result in another defect, singularity, such as in Newtonian mass point model. In Newtonian mass
point model, because the “volume” of a point is zero, any finite mass assigned
to it will lead to infinite density, i.e., singularity.
Considering
the above defects, we represent a particle by a point set in the simulated
space. Point set representation of particles/objects unified the nuclei and
field pictures. A particle is represented by a point set and the filed is
represented by a partial point flow under a transformation. And the motion of a
particle/object is represented by the whole point set flow under another
transformation. The partial transformation makes a fast (high speed) flow of
some points of the point set and the whole transformation makes a slow (low
speed) flow of the whole point set.
Each
point in the point set, if observed at a smaller scale, will be a point set. That
is, there is selfsimilarity of the point set. The two kinds of charges are
represented by two directions of point flow: centrifugal and centripetal.
Referring to fractal geometrics, a particle can be represented by a Burel set^{27}
in the simulated space, and thus, an object as a collection of particles can be
represented by a union of particle sets. Thus, the physical property can be
represented by some kind of “measure” on it. Through different measure definitions,
different kinds of physical quantities are simulated.
Motion
of a particle/object is represented by a transformation on it just as what to
be done in computer graphics^{21}. Correlation between
particles/objects is represented by the Hausdorff distance between them defined
on a fractal space _{} which is defined
on the simulated distance space_{}. In simulation dynamics, the time dimension has been
occupied by the running of the simulator, thus, only space is explicit variables
in the kinetic equations and time is implicit appearing as subscript.
Iteration
Formulism
One particle/object. Suppose a particle/object
is represented by a point set _{} (Burel set) in a
simulated space S, then the motion
equation of it is:
_{}, (55)
where _{} is the state
(i.e. the position in S) of particle/object _{} in step _{} of the iteration
process and _{} is the state of _{} in step _{}; _{} is a transformation
on _{} which is a
function with respect to variable _{} which is the
Hausdorff qdimensional measure of
point set _{}; “_{}” represents the operation of transformation _{} on point set _{}. The motion of a particle is illustrated in Figure 13.
a).
Two particles/objects. Suppose two
particles/objects are represented by point set A and B (Burel sets) in the
simulated space S, respectively, then
the kinetic equation for them is:
_{}, (56)
where _{} is the state
(positions) of the two particles/objects _{} and _{} in step _{} of the iteration
process and _{} is the state of _{} and _{} in step _{}; _{} is a transformation
on _{} which is a
function with respect to variable _{}, _{} and _{} where _{}, _{}are the Hausdorff qdimensional
measures of point set _{} and _{}, and _{} is the Hausdorff
distance defined on the fractal space _{} where _{} is a distance
defined on the simulated space S; “_{}” represents the operation of transformation _{} on the union of
point set _{} and _{}. The Hausdorff
distance between particle A and B is illustrated in Figure 13. b).
Multiple particles/objects. Suppose these
particles/objects are represented by_{},_{},_{}, respectively, then the kinetic equation for them is:
_{}, (57)
where
_{} is the state
(positions) of these particles/objects in step _{} of the iteration
process and _{} is the state of
these particles/objects in step _{}; _{} is a transformation
on _{} which is a
function with respect to variable _{},_{},_{} and _{} where _{},_{},_{} are the Hausdorff qdimensional
measures of point sets _{}, _{}, _{}, and _{}, _{} are the Hausdorff
distances between them defined on the fractal space _{} where _{} is a metric
defined on the simulated space S; “_{}” represents the operation of transformation _{} on the union of
point sets _{},_{},_{}.
For
multiple body problems, to avoid the combinatorial explosion of the number of
distances for an efficient calculation, we can define a proper “global” measure
on the whole system, so that the kinetic equation can be rewritten as:
_{}, (58)
where _{} is the _{} dimensional
Hausdorff measure on the whole system _{}.
Equations
(55), (56), (57) and (58) are the kinetic equations of simulation dynamics for
one body, two bodies and multiple bodies, respectively.
Collision: Measure
Conservation Law
Particle
A occupies some of the space S and
particle B too. When they meet with each other, the point sets for them are
superposed somewhat. The result is that they are annihilated and the union of
them is generated as a new particle, and meanwhile, the intersection of them is
released as another new particle (Figure 13. c)). In this process, the total
size of point sets is conservational, which lead to the conservation of
Hausdorff measure. Because physical quantities are represented by some kinds of
Hausdorff measure, they are also conserved in this process. Therefore, the
conservation laws of physical world are simulated. When a collection of
particles assembles to form a body, the body is the union of the point sets for
these particles and the intersection of these point sets is released, some kind
of measure on which may be called (as what in our world): the binding energy.
Figure 13.
Illustration of simulation dynamics in space S. a) particle P moves
from P to P’ by the transformation T in space S; b) the Hausdorff distance h(A,B) between particle A and particle B
in fractal space (F(S),h(d)); c)
particle A collides with particle B, annihilated, and particle C and particle D
are generated. Some of the space originally occupied by A and B are released
because the superposition of them, and the released part is D, thus there is,
D=A∩B.
Correspondingly, the Hausdorff qdimensional measure is conserved in this
process.
Three Kinds
of Structures
Now
we consider system structures in the simulated world. As what we know in our
world, there are mainly three kinds of structures: static structure, periodic
motion structure and dissipative structure. They can be simulated by the three
kinds of attractors of the iterated process (dynamic system), respectively. As
shown in Figure 14, the static structure (Figure 14. a)), such as crystals, is
simulated by the fixed point attractor; the periodic motion structure (Figure 14.
b)), such as atoms, is simulated by the limit circle attractor; the dissipative
structure (Figure 14. c)), such as flames, is simulated by the chaotic
attractor. Of course, there are some kinds of mixtures of these basic
structures, such as a clock (Figure 14. d)) (mixture of static and periodic
motion structure), with which people living in the simulated world can tell
time just as we do in our world: watching a clock.
Figure 14.
System structures in simulation Dynamics. a)
Static structure, simulated by the fixed point attractor; b) periodic motion structure, simulated by the limit circle
attractor; c) dissipative structure,
simulated by the chaotic attractor; d)
a mixture of static and periodic motion structure which can be used as a timer.
The Levels
and Evolution of Artificial Reality
Artificial Universe: Selfexistence system, the
physical foundation of artificial reality. Artificial universe is a piece of
artwork of the super beings of that universe.
Artificial Life: selfproducing system, the
active agents that can interact with environments. Artificial life is an
evolutionary result of artificial universe.
Artificial Intelligence: selfreflection system. Selfreflection
is a kind of ability to form a second level reality (mind world) in comparison
to the first level reality (material world) where the body of this system lives
in. Three points are necessary for a being to be of intelligence: (1) possessing
of a first level reality (body world) and a second level reality (mind world);
(2) living in the superposed state of the two realities; (3) the ability of
doing super transformations, i.e., the ability of jumping between the two
worlds. Artificial Intelligence is an evolutionary result of artificial life.
Artificial Society: selforganization system
of intelligent active agents. The interdependent relationship of the agents
makes it a lifelike being. Artificial society is an evolutionary result of
artificial universe.
Unification
of Science and Religion
1.
Science and Religion Super General Relativity
Theory may uniform Science and Religion. The Creator is the maker of The
Simulator. For Godmade world where we are living in, we are creatures, while
for manmade world where virtual creatures are living in, we are creators.
Future may be an age where Creators (gods), Creatures (human beings), and
Robots (and virtual creatures) live together.
2.
The Origin of Universe and
Life
Three kinds of simulators are mentioned in this paper: The Simulator, Human
Brains, and Computers. The Simulator is the simulator where our world is
running on, which is a Godmade one. Human brains are the evolutionary result of
our world and computers are manmade simulators. These three kinds of
simulators simulate three kinds of worlds: our world, human imagination, and
computer virtual reality. Considering all these three kinds of worlds and the
creatures living in them, we know that the origin of the universe and life is
neither a simple Creation, nor a simple Evolution, but some kind of mixture of
them. Therefore, Super General Relativity unifies the Creation and Evolution.
(The unified theory can be called “Crevolution” theory.)
3.
Unomniscience and
Unomnipotence of Creators Creator is the maker of simulator. Because simulator is automaton,
maker of it can create a world by making some simple laws/rules, but he cannot
completely know and completely determine the running results of the simulator
due to its automation property. But creator has ability to break the laws he
made to bring some changes directly to the world that he creates, which his
creatures may call miracles. Creator as a super being to his creature has more
power when he is in his super position. But if he gets involved in the world he
created, he must keep to the game rules he himself made. Therefore, creators
and creatures are relative, and they have equal rights as beings.
Discussions and Conclusions
Discussions
1.
Quantization of Reality Since reality is not
absolute but relative, the realities of events are comparable in some degree which
leads to the quantization of reality.
2.
Physics and Mathematics The invention of infinitesimal calculus supports the establishment
of classical mechanics, and the development of complex analysis supports the establishment
of quantum mechanics. Now the emergence of nonlinear science, especially the
fractal geometrics and dynamics system theory, will support the establishment
of simulation dynamics. The formulism of classical mechanics is real differential
equation, and the formulism of quantum mechanics is complex partial
differential equation, while the formulism of simulation dynamics is iteration
equation. A remarkable difference of formulism between simulation dynamics and
the classical & quantum mechanics is that there is no time variable in its
kinetic equations.
3.
Tow Viewpoints: Wherein
and Whereout In the picture of super universe, there are two viewpoints of physics
study: “wherein viewpoint” and “whereout viewpoint”. The wherein viewpoint is
the viewpoint from the simulated
world, and the whereout viewpoint is the viewpoint from the simulating world. In Similarity
Mechanics, the two viewpoints are microscopic
and macroscopic; In Motion
Relativity, the two viewpoints are moverside
and spectatorside. The kinetic
equations of simulation dynamics is established at the whereout viewpoint. It
may degenerate to the form of classical mechanics or quantum mechanics when the
viewpoint changing from “whereout” to “wherein”. From now on, physics study,
especially the fundamental physics study, has an alternative choice of
viewpoint to establish physical equations. From the “wherein viewpoint”,
mechanics is relative, while from the “whereout viewpoint”, mechanics is
absolute.
4.
Super Physics Super Physics may be the
unification of Physics, Metaphysics, and Philosophy. Super Physics mainly has
two branches: Super Cosmology and Psychophysics. Super cosmology is the
development of virtual reality, and intends to give a uniform description of recursive
virtual worlds. Psychophysics is a redefinition of parapsychology, and intends
to give a uniform description of matter world and mind world.
5.
Paradox and Existence Paradox doesn’t mean
nonexistence. Paradox often occurs in a selfreflection situation, such as
Russell’s set paradox. Paradox only exists when talking from the “wherein”
viewpoint, while for a spectator from “whereout” viewpoint, many paradoxes do
not exist at all.
6.
Why exist? Existing is just a simple
fact for every one. We have no choice on whether or not, when and where we are
born. So most people accept the fact of being existence. But there are some
people who love to ask why. These
people are usually rationalist and believe logic. Here is an answer for them.
Try to answer the following question: does nonexistence exist? If nonexistence
exists, it’s not nonexistence, say, there is only existence; if nonexistence
doesn’t exist, and then there is also only existence. So existence is a necessary
result of logic.
Conclusions
Reality
is relative and doesn’t equal to physical law. Universe may have many existence
levels. Super universe is a big fractal as virtual world net. Our world may be
running on a simulator. Simulation is a methodology for universe modeling. Super
transformations bridge the three worlds: objective matter world, human mind
world and computer simulation world, which makes it possible to give a uniform
description of nature. Our world is a big fractal composed of recursive “nucleatedrevolving”
structures (Rotons). The form the law of fundamental interaction of our world is
determined by the dimension of the space. The sole long range interaction of
our world is the inversesquare interaction and short range interactions can be
regarded as the combination and decomposition of Rotons at different existence
scales. The creation of artificial universe can be done in the formulism of
extended cellular automaton at microscopic level and simulation dynamics at
macroscopic level. There are two viewpoints for physics research: “wherein” and
“whereout”. In super general relativity, two viewpoints are: “simulated” and “simulating”;
in special super general relativity, they are: “microscopic” and “macroscopic”;
while in special relativity, they are “moverside” and “spectatorside”. The
existence of two viewpoints is a reflection of the relativity of reality.
(
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Acknowledgement
Many Thanks to HongYu Zhang, WuSheng Dai and Gang Lv
for valued discussions.
BinGuang
Ma
Email: bgMa@sdut.edu.cn
or kylin.ma@gmail.com