Establishing Science of Pursuit

Deduce Basic Physics from Science of Pursuit

In a perfect pursuit system, there are the following concepts: pursued quantity, symmetrical and anti-symmetrical occupying, symmetrical and anti-symmetrical occupied, beginning choice and finishing choice. Their definitions are given at Basic Definitions. They satisfy the following axioms about pursuit. Quantum Electrodynamics is equivalent with "pursuit theory about how to choose occupied the best".

Axiom 1:

When just considering occupied exchange, occupying is not influenced.

Axiom 2:

For a pursuer in a single market, his pursued quantity from symmetrical occupying is product of symmetrical occupying and symmetrical experienced occupied. His experienced symmetrical occupied is product of beginning choice and finishing choice.

From axiom 1, symmetrical occupying(m) does not change in single market exchange, so -S/m is experienced occupied. In each pursuer's pursuit process, there must exist earlier beginning choice (B) and later finishing choice (F). There are both beginning choice and finishing choice. Realization of pursued quantity includes two stages: "finish an earlier state and begin the present state" and then "begin the present state and finish a later state". So, the experienced symmetrical occupied in a short pursuit process is

(1) -S/m=F(x_i+dx_i)B(x_i)

The mathematical expression for F and B will be decided when they satisfy the following axioms. They are wave function and its complex conjugate function. dx_i must satisfy space-time metric.

Experienced occupied can also be FⁿB^m, or even complex, but (1) is the simplest. Experienced occupied can be viewed as a flow from beginning choice to finishing choice. Pursued quantity is product of beginning choice and finishing choice, so it is linear function of both beginning choice and finishing choice.

Each pursuer has a lot of choices, But total choices at one moment is 1, and probability for pursuer to be at choice x_i is F(x_i)B(x_i). In economy, people tend to say "desire for a product", but it is average value of many desires, similar to average momentum in physics. So, desire cannot describe a person's pursuit process accurately. Economist should use beginning choice and finishing choice.

Axiom 3:

Pursued quantity with completely different occupying or occupied is called "independent pursued quantity". Total pursued quantity is the sum of all independent pursued quantity.

Total pursuit process can be resolved into many independent small pursuit processes. Independent pursuit processes do not share any pursued quantity. Total pursued quantity is sum of pursued quantity from all independent processes. Any independent pursued quantity should be counted in total pursued quantity, and only once. So the best methodology for the pursued quantity will lead to the largest benefit for all occupying and occupied.

So the experienced symmetrical occupied is

(2) (-S₀)/m = òF(x_i+dx_i)B(x_i)dW

Axiom 4:

For any intersection of a pursuer’s pursuit process, new pursuit process begins and old pursuit process finishes.

At an intersection of a pursuit process, there are two properties: it is both the finishing of earlier pursuit and the beginning of later pursuit. It is one of the most important properties for pursuit. If any intersection satisfies axiom 4, pursuit is a process without beginning or ending.

The experienced symmetrical occupied for the old pursuit is:

(3) òF(x_i) B(x_i-dx_i)=òF(x_i)B(x_i)-òF(x_i)(¶/¶ x_i)B(x_i)dx_i

Similarly, the experienced symmetrical occupied for the new pursuit is

(4) òF(x_i+dx_i)B(x_i)=òF(x_i) B(x_i)+ò¶F(x_i)/¶x_i B(x_i)dx_i

In a perfect pursuit system, choices are finishing and beginning simultaneously. At an intersection of a pursuit process, it includes half of the old pursued quantity and half of the new pursued quantity. So the pursued quantity from symmetrical pursuit is:

(5) (-S₀)=mòFBdx_i+m/2ò (¶F/¶x_i)Bdx_i-m/2òF(¶B/¶x_i)dx_i

At each intersection, there are three terms: FdB, -(dF)B, and FB. They represent three flows of occupied: from earlier to current, from current to future, and from current to current.

Axiom 5:

When beginning choices and finishing choices have several components, F_j and B_k, then there are cross flow from F_j to B_k, and from F_k to B_j.

So (1) ought to be F(x_i+dx_i)G_iB(x_i). Each "G_i" is a matrix. Each matrix represents an independent kind of flow style. F is a row vector, B is a column vector.

(6) (-S₀)=mòFBdx_i+m/2ò (¶F/¶x_i) G_i Bdx_i-m/2òFG_i (¶B/¶x_i)dx_i

G_i must satisfy some conditions, like unitary condition. G_i corresponds to g_i in Quantum Electrodynamics.

Axiom 6:

Pursued quantity from anti-symmetrical pursuit is the correction to that from symmetrical pursuit. It is product of anti-symmetrical occupying and experienced anti-symmetrical occupied.

Pursued quantity in different conditions ought be corrected. Worse pursuit condition ought to have a larger correction. Good pursuit condition helps to increase pursued quantity, so its correction for the pursued quantity is negative. Condition’s correction to pursued quantity is (-S_e), which is opposite to its influence. Experienced symmetrical occupied is similar to sales volume, but corrected pursued quantity is similar to sales revenue. In economy, lower price leads to larger sales volume, which would lead to larger profit if price were normal, but profit must be corrected downwards. Pursued quantity from anti-symmetrical pursuit corresponds to the correction to revenue.

Let A_i represents anti-symmetrical occupied in unit symmetrical occupied, then A_idx_i is anti-symmetrical occupied along a direction (similar to the revenue change). A_i is similar to price in economics, but zero point have freedom, which represents gauge invariance. In a perfect market, price system is gauge invariant. So, correction from pursuit condition is

(7) (-S_e)=iòqFG_kBA_kdx_k

iqFG_iB is the flow of anti-symmetrical occupying, which corresponds to current j_i in universe. Imaginary unit i is separated from G_k just for conveniece, to be more similar to Quantum Electromagnetics.

Axiom 7:

For both symmetrical and anti-symmetrical occupied, its expected pursued quantity is sum of all possible influence to pursued quantity.

An unoccupied state in market is possible to be occupied, so there is expected pursued quantity (-S_A). In economy, unsold goods also have value, representing the value of market. Expected pursued quantity for occupied is a statistical result.

Axiom 8:

In a perfect pursuit system, total pursued quantity is the sum of pursued quantity from symmetrical pursuit and pursued quantity from anti-symmetrical pursuit, plus expected pursued quantity. Total pursued quantity is the largest.

(8) (-S)= (-S₀)+(-S_e)+(-S_A)

It means the sum of realized pursued quantity and possible pursued quantity, plus the correction from pursuit condition. In economics, it represents realized revenue plus expected revenue. In (8), I just include expected pursued quantity of anti-symmetrical occupied, that of symmetrical occupied is a constant in a stable universe, but when studying the expansion of universe, it should be included.

Now I deduce the mathematical expression for (-S_A). Theorem 1:

Expected pursued quantity for anti-symmetrical occupied is

(9) (-S_A)=(1/2)ò(¶A_i/¶x_j)(¶A_i/¶x_j) dW

Proof:

If positive and negative anti-symmetrical occupying is symmetrical, (-S_A) is not function of A_i. By variating F_i and B_i in (8), there is:

(10) (mG_i¶/¶x_i+m-iG_iqA_i)B=0

(11) F(mG_i¶/¶x_i-m+iG_iqA_i)=0

In economy，(10) and (11) means sales volume and price drop reaches marginal equilibrium. In other words, (-S₀) and (-S_e) reaches marginal equilibrium. F´(10)+(11)´B, there is:

(12) ¶/¶x_i(iqFG_iB)=0

This corresponds to charge-current conservation law.

From (7), the first order influence of electromagnetic field opposite is proportional to q, so, for all possible particles, total contribution to expected pursued quantity is zero. So we need to calculate the second order influence:

(13)S₂=m/4[B(¶/¶x_j¶/¶x_i)F+(¶/¶x_j¶/¶x_iB)F]dx_jdx_i

Since

(14)mG_i¶B/¶x_i=-mB+iG_iqA_iB

(15)F(mG_i¶/¶x_i)=Fm+iFG_iqA_i

Calculating total sum of all possible states in dW, it means calculating integral on surface ds_ij (perpendicular to x_j and x_i).

(16)(-S_A)=òS₂ds_ij

=ò¶/¶x_i¶/¶x_j(S₂)dW

Replacing S₂ by (13)、(14)、(15)，in the results, terms without q representing expected pursued quantity for space-time, terms proportional to q will be zero when all charges are considered. Term proportional to q⁴/m³ is much smaller than term proportional to q²/m. If dW and test charge-current is small enough, ¶A_i/¶x_j will be constants. So, terms proportional to q² is (¶A_i/¶x_j)²，its coefficiency is 1/2ò(q²/m)PdW. P is surface density of particle q,m in the Universe, (probability to find q,m in unit ds). Since electron has smaller mass and higher percentage, m can be treated as m_e. Because we know e₀, we can deduce surface density of electron (3X10^-4/m²).

(End)

From theorem one, by variating A_i,there is

_jS¶²A_i/¶x_j²=j_i

This represents the marginal equilibrium between (-S_e) and (-S_A), which means there is microscopic equilibrium between expection and realization. So, expection equals to realization. In (16), there is A_i¶²A_i/¶x_j² term, but sum of all possible j_i is zero.

So the pursued quantity satisfying the above axioms has the same mathematical expression as negative action in Quantum Electrodynamics.

Axiom 9:

In a perfect pursuit system, there are ordered two-dimensional supply-quantity. Symmetrical occupied is substitution between supplies.

The substitution between supplies includes all possible changes of occupied. So pursuer has largest freedom (most choices) in a perfect pursuit system. Each substitution is a line (one-dimensional) in space. In society, the two-dimensional supply-quantity are various goods and their quantity. But goods dimension is not ordered. This makes social market difficult to be perfect.More precisely, because of the anti-symmetrical occupied, space-time and electromagnetic field comes from two-dimensional complex supply-quantity-price.

If substitution rates between supplies are fixed, it is defined as the same development degree. All possible substitutions under the same development degree form a Euclidean space. When there are substitutions between different development degree, the market is isomorphic with curved space-time.

Theorem 2:

Under the same development degree, all possible substitutions between different supplies form three-dimensional space, and invariant substitution forms one-dimensional time.

Proof: When substitution rate between two supplies are fixed, two-dimensional supply substitution plus quantity dimension will form three-dimensional ordered set. In society, if there are n kinds of goods, then there are n´n possible substitutions. When n becomes infinite, it forms a two-dimensional sphere. For each substitution, there is one-dimensional substitution quantity, corresponding to radius. So, there are three-dimensional different supply substitutions. There is only one direction of invariance: repeating the same combination of supplies. (End)

So, every perfect pursuit system has 3D space and 1D time.

Axiom 10:

For symmetrical pursuit, invariant substitution brings positive pursued quantity, different supply substitution brings negative pursued quantity.

Each independent set is called a "direction". The positive direction is called "time". The three negative directions are called "space". In society and research, change also means negative pursued quantity, cannot occur without compensation. In a perfect pursuit system with only one pursued quantity, there is only one positive direction, and whole system move toward the direction. Why remaining invariant means positive pursued quantity? Maybe because it leads to a stable system.

So, in any local area, any small substitution ds can be divided into four independent substitutions, dx_i.

Theorem 3:

Expected pursued quantity for symmetrical occupied will determine space-time metric (algebra for x_i). Locally, it will be

(17)ds²=dt²-dx²-dy²-dz²

Proof: In a small pursuit process dx_i, pursued quantity can be expanded as Sa_n(dx_i)ⁿ. Since pursued quantity should be zero when there is no pursuit, n cannot be negative. Since -dx_i ought to have the same expected pursued quantity, n cannot be odd. So for the lowest-order approximation, expected pursued quantity for space-time is a₂dx_i². If the pursued quantity is invariant with the way we divide occupied, then

(18)a₂dt²-a₂dx²-a₂dy²-a₂dz²=a₂ds²

ds is the total occupied, dx_i is its component in each set. If dx_i is defined as real number, From axiom 10, we must add "-" in front of spatial directions.

So geometry is result of pursued quantity calculation. So, ds is expected pursued quantity along a path. Area and volume of a region is total expected action in the region.Currently, calculation of action in physics and Euclidean geometry are independent knowledge. Notice that there is no new hypothesis in the proof. Logic simplicity, even without new experimental results, also means knowledge progress.

(End)

Axiom 11:

Whole pursuit system can be described as a large beginning choice and finishing choice. When two pursuit process are mutually conditional, total beginning function is the product of the two beginning function; when two pursuit process are mutually independent, total beginning function is the sum of the two beginning function. It is the same for finishing function.

When more processes included, it means higher purturbation order in Quantum Electrodynamics. Process I and H can be mutually independent and as a whole conditional to J, then the total beginning function is (B^H+B^I)B^J. The total function will be conditional or independent with other pursuit processes, until whole system is included. Modern physics showed that it is calculable for such complex pursuit, and particles proved their calculation speed is amazing.

Axiom 12:

When occupied is owned by occupying, it follows private ownership, which is Fermi-Dirac distribution. When occupied is not occupied, it follows public ownership, which is Einstein-Bose distribution.

Private ownership means any two pursuers cannot occupy the same state. All possible states that cannot be occupied simultaneously can be expanded as the superposition of anti-symmetrical wave functions. On the other hand, all public owned states can be expanded as the superposition of symmetrical wave functions. In a perfect pursuit system, realized pursuit follows private ownership, so they are fermions; unrealized pursuit follows public ownership, so they are bosons. If unoccupied occupied has expected pursued quantity, it is possible to treat them as pursuers, but they are bosons. It means scarce resources follow Fermi-Dirac distribution; abundant resources follow Einstein-Bose distribution..

Pursuers can be classified by pursuit orders. Pursuers in each group have the same pursuit order. The pursuit order can also be called "searching order". When pursued quantity is invariant with observer, there are only two possible pursuit orders in an independent set: the two directions. If one pursuer searches the set like a,b,c,d, all must search so or reversely. This means supply-quantity is orderly arranged.

Pursuer not only searches in each direction, but also between directions. For pursuers with different pursuit order between directions, like swapping dx with dy or with -dy, they have different "spin". So there are many components for a pursuer.

So all possible pursuit orders is equivalent with all possible directions and spins.

These axioms form a set of rules to calculate pursuers' pursued quantity. If a perfect pursuit system is uniquely decided by these axioms, it means knowledge about environment (space-time and field) can be deduced from mathematical expression of pursuer's action, so physics can be greatly simplified.

Gravity and Universe Expansion Come from System Development

In this part, I deduced classical physics as the first order approximation of quantum physics. I also deduced Hubble red-shift and gravitational field as system development and development difference. I proved that perfect pursuit system must expand, because particles will continuously absorb energy from electromagnetic field.

The first order approximation for (¶F/¶x_i)B-(¶B/¶x_i)F is u_i, because pursuit desire for dx_i must increase with dx_i/ds. It means occupying proportional to occupied. In society, it means desire for a supply be proportional to consumption ratio of the supply.

In the first order, pursued quantity in a perfect pursuit system has the following form:

(19) d(-S)=-mcu_idx_i-qA_idx_i+aF_ik²dW-bRdW

In the Universe, u_i, dx_i/ds, is explained as four-dimensional velocity, F_ik is explained as electromagnetic field tensor, R is explained as space-time curvature, dW is invariant space-time volume, a and b are positive constants. But (1) can be explained differently in other pursuit systems.

In science of pursuit, pursued quantity (like negative action) is unnecessary to explain, and other quantities (length and field) are explained by "negative action". For logic simplicity, it is better to explain all familiar concepts from one abstract concept, not to explain one by all. "Negative action" is abstract for human beings because they do not have the same feelings as particles, so they cannot understand particles' pursuit. Particles think "happiness" an abstract concept too. Pursued quantity can have other forms of mathematical expression, but in science of pursuit, those universes would be worse than the present universe. In "Truth Evolutionism", they would have smaller observation probability.

The first order approximation for (¶F/¶x_i)B-¶B/¶x_i)F is u_i, because pursuit desire for dx_i must increase with dx_i/ds. It means occupying proportional to occupied, which means desire proportional to supply in society.

In the first order, mu_i is apparent occupying; mcu_i+qA_i is its real occupying (P_i); particle's pursued quantity (-S_m) is product of real occupying and dx_i. So, the particle's pursued quantity is S(P_idx_i)

For anti-symmetrical occupied, its expected pursued quantity (-S_f) is total influence on pursued quantity for all possible particle states in the field. Since every state is possible to be occupied, the natural way to evaluate field is sum of all possible influences to pursued quantity. If the Universe pursues rationally, the expected pursued quantity in whole Universe will be equal to the actually realized change of pursued quantity in whole Universe.

Total negative action in Universe is:

(20) (-S)=(-S_m)+(-S_f)

It means the sum of realized pursued quantity and possible pursued quantity, plus the correction from pursuit condition.

Theorem 1 is easier to prove in the first order appoxiamation. A classical particle's best pursuit behaviour satisfies:

(21) mc(du_i/ds)=qF_iku_k

In (21),

(22) F_ik=¶A_i/¶x_k-¶A_k/¶x_i

If the field area is small enough, F_ik can be treated as constants. So, for all possible states on a closed three-dimensional hypersurface C, after moving unit ds, expected action is

(23)(-S_f)=-ò_Cmc(du_i/ds)dV_i

=-F_ikò_Cqu_kdV_i

=F_ik²ò_C(q²/mc)dW

Theorem 4:

Statistically, anti-symmetrical occupying always increases in anti-symmetrical occupied and increase pursuer's symmetrical occupying. The expected absorption rate is proportional to (E²+H²)/2, which is expected energy for electromagnetic field.

This can be deduced from (20). Since pursued quantity of field is expected pursued quantity, momentum-energy of field represents expected momentum-energy. In a perfect pursuit system, total desire, sum of realized desire and expected desire, is a conserved quantity.

Suppose charges enter an enough small region uniformly from all directions. After unit time, there are three net movements. Firstly, there is net current, which is proportional to E, toward E, because positive charges are accelerated toward E and negative charges toward -E. Secondly, there is net current, which is proportional to H, around H, because positive charges are accelerated clockwise and negative charges anti-clockwise (viewed along H). Their contribution to real energy is proportional to (E²+H²)/2. Thirdly, there is net momentum, which is proportional to ExH, toward ExH, because the current toward E will interact with H. (E²+H²) is always positive, so charges absorb energy from electromagnetic field statistically.

Kinetic energy of particles, including photons, is called unstable energy. Particle's static energy is called stable energy. From theorem 3, unstable energy is gradually absorbed by particles, so stable energy increases monotonously in electromagnetic interaction. Unstable energy will become part of static energy. If there were no new unstable energy, unstable energy would be exhausted.

In the Universe, ultimately speaking, all unstable energy is generated from stable energy through strong and weak interaction, and turns into stable energy through electromagnetic interaction. From theorem 3, this circulation is self-magnified. If particles have larger static energy, they have stronger ability to "invest": create more unstable energy in one fusion. So the universe will expand forever. Since electron's static energy increases monotonously, atom radius reduces monotonously.

Theorem 5:

Relative to particle’s growing stable energy, past unstable energy relatively depreciates with time.

Proof:

When measured with a fixed energy-momentum unit, static energy increases with time. Suppose the speed is uniform,

(24) d(mc²)/dt=Hmc²

So, in fixed unit,

(25) m(t)=m(0)exp(Ht)

Space-time geometry is decided by atom radius of rulers and clocks. When atom radius reduces, clock is slower and ruler is shorter,

(26) dxⁱ(t)=dxⁱ(0)exp(-Ht)

So ruler is shorter and clock is slower with time. In order to measure correctly, observer needs to appoint his development degree. From time component of (26), we can deduce

(27) dt/dt₀=1/(1+Ht₀)

From (27), for a pursuit system with uniform expanding velocity, no matter when you measure, its origin time is -1/H. Similarly, reciprocal of expanding velocity is nominal origin time. For example, if developing velocity is 1% per year, economy is 100 years old in present unit. But if we use local time unit to measure, there is no origin time. This is a property for exponential expansion.

Clock is very slow at the origin of universe. If measured by present time unit, evolution is very fast at the origin of the universe. If a film shows the expansion of current universe very fast (measured be future unit), it looks like an explosion. But it is just normal expansion when showing slowly (measured by local unit).

From (25), a small distance measured at the border of the universe will be a long distance when measured by observers at the center of universe. From (26), clock is also very slow around the "border" of the Universe. The "border" of a perfect pursuit system is defined as the part of the system that can exchange with every pursuer at any time (can be observed by every observer at any time). In perfect pursuit system, light velocity is the upper limit of pursuer's velocity, so any two pursuers can exchange with each other, but they are point-to-point exchange. At the "border", a long time shrinks into a time point, so border pursuer exchanges with other pursuers as point-to-line. When light is close to the border, it needs infinite long time to reach the border. A perfect pursuit system is infinite large because pursuers can never reach the border.

Atom's energy level is proportional to particle's mass, so energy level in the past is smaller than that at present, and light will have a red-shift. Maybe different particles can increase mass at different speed.

(28) df=f₀[exp(-Hdt)-1]

f is frequency of light. When Hdt is very small, the red-shift is f₀Hdt. This is Hubble red-shift.

From above, both mc and dx changes with development, but it is possible to introduce two other variables, dxⁱ and dx_i, and make mc invariant. Define

(29) dxⁱ=dx⁰exp(-Ht)

(30) dx_i=dx⁰exp(Ht)

Then

(31) ds²=h_iidxⁱdxⁱ

(32) h_ii=exp(2Ht)

Theorem 6:

Space-time curvature comes from the difference of development degree.

Proof:

Development is not necessary to be uniform, the only limitation is: pursued quantity must be invariant, which means the whole pursuit system has only one goal. General form for (30) is

(33) dx_i=h_ijdx^j

This is first order approximation. So, expected pursued quantity for space-time is

(34) ds²=dx_idxⁱ=h_ijdx^jdxⁱ

So distribution of development degree makes space-time curved.

Theorem 6:

For gravitational field, its expected action is proportional to space-time curvature R.

Proof:

By variation, particle's best acceleration is

(35) du_i/ds=G^k_ij (dx_k/ds)(dx^j/ds)

From definition of curvature tensor, for a vector along a close path L, there is

(36)ò_LG^k_ijA_kdx^j=(1/2)R^k_ijlA_kdf^jl

L is a close path. For the sum of all possible states with fixed u^k in (37), it is integral along a close path (corresponding to u^j increase from minimum to maximum and then from maximum to minimum), the expected negative action is:

(37)(-S_g)=-ò_Lmcdu_i

=-ò_LmcG^k_iju_kdx^j

=-(1/2)R^k_ijlòmcu_kdf^jl

If k is not equal to l or m, -u_k and u_k will have opposite contribution to action. When k is equal to l or m, df^jl will change sign together with u_k. So index k and l, or k and j, ought to contract, and (-S_g) becomes:

(38)(-S_g)=-(1/2)R_jlmcu_jdf^jl

The u_j will disappear when contributions from all possible u_j are added. A close hypersurface is composed of many close path. dS_g from a hypersurface is sum of all components of R_jl,

Statistical result of all possible mcu_j will become a constant, which decides the gravitational constant. The area of df^jl(du^jdu^l) is proportinal to h^jl。So，for all possible df^jl, expected negative action is proportional to h^jlR_jl, which is space-time curvature R.

(39) R=S(h^jlR_jl)

Since distribution of development changes pursued quantity, by variation, the best distribution of development is not uniform development and existence of gravitational field is unavoidable. From above, (-S_g) is result of absorbing unstable energy unevenly, so gravity is not an independent interaction.

Electromagnetic interaction decides how to distribute and absorb unstable energy the best. How to produce unstable energy the best ought to be decided by strong and weak interaction. All three interactions have the same aim: negative action pursuit. Matter and space-time are links in a close pursuit process, in which every link is expanding. If one link broke, the other links could not expand.

From above, theory about perfect pursuit system is formalized. Any pursuit system satisfying these axioms will have the same results. For example, imagine universe as a society and each particle is a person. Treat a particle's negative action as happiness. Thinking about every complex interaction between particles as happiness exchange between persons, then a particle choosing state to have largest negative action corresponds to a person choosing state to have largest happiness. So, the Universe can be logically reproduced in any pursuit system.

Cosmology from Resource Equality
p>Theory about exchange in single market is foundation for general pursuit behaviors. In the above definitions and axioms, occupying and occupied are symmetrical: occupied and occupying can exchange their roles and still be a perfect pursuit system. In a perfect pursuit system, scarce resources can become abundant; abundant resources can become scarce. So there is axiom 13:

Each feeling is mapping between two resources, one is abundant, the other is scarce. All resources follow the same law in a perfect pursuit system.

This is called "resource equality". In physics, it means mass-charge and space-field ought to follow the same laws. Mass-charge is mass and charge. Space-field is space and electromagnetic field. In perfect society, it means supply and demand ought to follow the same laws. In the viewpoint of pursuit, the difference just comes from the scarcity, and scarcity leads to different statistics. In market, there are relatively much more supplies than demands, so demands choose supplies and become pursuer. While in research, there are much more demands than supplies, and researchers try to use these supplies the best to have the largest pursued quantity, which means supplies choose demands and become pursuer. Economy is the market that demand is scarce relative to supplies; and research is the market that demand is sufficient relative to supplies. So economy and research can be unified into "pursuit system of happiness". Similarly, space-field market is the market that mass and charge is relatively scarce; mass-charge market is the market that mass and charge is relatively abundant, which is black hole.

Feeling is mutual relation of two resources. By proper combination, it is possible to construct a most scarce quantity and a most abundant quantity, which are called occupying and occupied respectively.

Resources ought to be treated as one-dimensional complex continuity. Feeling is mutual mapping between two one-dimensional complex continuity. One-dimensional complex occupying substituting with one-dimensional complex occupying will produce three-dimensional complex space, which has SU(3) symmetry. Abundant resources substituting abundant resources will be electromagnetic interaction; scarce resources substituting scarce resources will be strong interaction; abundant resources substituting scarce resources, or scarce resources substituting abundant resources, will be weak interaction. Gravity is development difference, existing in every market.

Each section can also substitute with the mapping section, which means SU(2). In weak interaction, realized occupied can only substitute its occupying, not all occupying, so it is two-dimensional, not three-dimensional.

There is another reason for axiom 13, maybe more important. Since electromagnetic interaction is the perfect mechanism to expand space, but what is the best mechanism to create particles and unstable energy? It is unnecessary to have another perfect mechanism to create particles and unstable energy. If there is a symmetrical mass-charge market and a conversion mechanism between space-field and mass-charge, the two spaces can mutually provide particles and unstable energy.

So generally speaking, both abundant resources and scarce resources are pursuit resources, and should be eually treated. They split into two markets. In both markets, the scarce resources will be occupying, and the excessively supplied resources will be occupied.

Axiom 13 ensures that the Universe will expand forever. From the axiom, there are the following theorems. Every theorem can be deduced simply by exchange occupying with occupied.

Theorem 7:

Space and electromagnetic field in space-field market becomes charge in mass-charge market. Mass and charge in space-field market becomes electromagnetic field in mass-charge market.

When all occupied in one market becomes occupying in the other market, they are called perpendicular markets, like space-field market and mass-charge market. The two markets are perpendicular to each other. One market is very small in the other market. Our observing space-field market is just half of the Universe, in which mass-charge is scarce relative to space-field. There is another space-field market, in which space-field is scarce relative to mass-charge. By weak interaction, space-field market and mass-charge market can be mixed. It is impossible to distinguish a mixed market and a pure market.

Mathematical expression for negative action in mass-charge market is similar to that in space-field market, just exchanging x(i) with k(i), A(i) with J(i). In mass-charge market, discrete A(k) is surrounded by continuous charge-current. A(k) exchanges current to interact with each other. Neutrino in space-field market will become photon in mass-charge market, and photon in space-field market will become neutrino in mass-charge market. Propagation of electromagnetic field in mass-charge market is observed as particles interacting with each other in space-field market. For example, neutrino interacting with neutron will generate proton and electron, similar to that photon is electromagnetic field undulation.

When density of occupying is high enough, k-space is not just a useful mathematical tool, it really exists. When there are much more mass-charge than space-field, mass-charge market is a much better description than space-field market. Black-hole is just the situation.

In both markets, the scarce quantity is more active. Their adaptive behaviors will weaken field difference and spread unstable energy into whole system uniformly. When energy is high enough in space-field market, there is no difference with mass-charge market.

Theorem 8:

The two markets exchange with each other through black-holes. Black-hole in one market is active galactic nucleus in the other market.

Black-holes in one market makes occupying more scarce in the market, and makes occupying less scarce in the other market.

A black hole in space-field market will be an active galactic nucleus in mass-charge market, then lead to the formation of a galaxy. After some time, there will exist stars and fanally black holes in mass-charge market, which means active galactic nucleus in space-field market. So young black holes are normally one-way, but old black holes will be two-way: looking as black hole and active galactic nucleus in both market.

Since there are black holes in each market, the two markets will exchange with each other. A black hole in mass-charge market will disassemble its space-time and produce particles and charges for space-field market. It will also produce unstable energy for space-field market by restructuring particles. In a space-field market black hole, there maybe many mass-charge market black holes and cannot be distinguished. So those mass-charge market black holes just output particles and energy in space-field market. Older black hole in space-field market will produce more black holes in mass-charge market, so the black hole can output more particles and energy to space-field market.

Theorem 9:

Strong interaction in space-field market is electromagnetic interaction and vector addition in mass-charge market; electromagnetic interaction and vector addition in space-field market is strong interaction in mass-charge market. Weak interaction is exchange between occupying and occupied.

Measurement is different in different markets. Occupying is always realized, their expected pursued quantity is proportional to resource, so charge and mass can be added linearly in space-field market, but cannot when they become occupied in mass-charge market. In mass-charge market, charge has expected pursued quantity F²_ik; mass has expected pursued quantity ds²=dt²-dx²-dy²-dz². Mass-charge is distributed the best to make negative action the largest. In mass-charge market, calculation of SU(3) can be simplified as vector and electromagnetic field addition, similar to the calculation of dx_i and A_i.

Statistics will also change. Space-field will have private ownership, which leads to Fermi statistics. So, fermions in our space-field market will become Bosons in mass-charge market; bosons will become fermions there.

Each space is measured by its occupied. When using occupied in space-field market to measure mass-charge market, mass-charge market is very small. But when using occupied in mass-charge market to measure, space-field market is very small too. In black holes, there is another world just like our observing space-field market.

If a pursuer is a mapping between occupying and occupied, then there are three possible interactions: exchanging occupied, exchanging occupying and exchanging occupying with occupied. They are electromagnetic and gravitational interaction, strong interaction and weak interaction. In the simplest market, the main exchange is always called electromagnetic and gravitational interaction, which exchanges the abundant resouces. The simplest market is similar to a tangent market.

Weak interaction leads to pursuer jumping between spaces. Particle in one space turns into particle in the other space through weak interaction.

Since human beings can origin inside the Universe, another astonishing experimental result is: new pursuit systems, even perfect pursuit systems can origin inside a perfect pursuit system. This means new perfect system can origin inside perfect society. Human beings can be the creator of new world.

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