Some add-on and finalization on my series of economy-related blogs, which I did to understand this economy I was born into and is so much not my kind of economy.

currency_control for control_currency

Depending on the location, around 5000 BP control gangs formed: regimes. Regime money schemes to control wage_slaves (control_currency) have their roots in those first empires. The modern state is an institutionalized entity owned by those in control, the elite. Democracy is facade, because central/remote valuation of labor fundamentally conflicts with equality. “Democracy” has a process called “election” that relinquishes individual control, and thus democracy. Companies rent wage_slaves from the regime, growing ad infinitum due to control, thus collecting control at a few, giving the few more value, more interest. Money accumulation is control accumulation, leaving most with 0 control and thus 0 democracy.

Valuation by power makes most worthless to the point of revolt. A historic fact. The Roman Empire had several slave revolts. More recently, the French revolution (1789-1799), which was also driven by the realization that they were programmed far too long by silly stories from religion and the claim of god-chosen emperors. Actual slavery in the colonies made wage_slaves systemic in Europe (Industrial Revolution).

slave

slave is property of a private power

wage_slave

slave is property of the regime, where the rich can rent it from, having less maintenance costs

Wage_slavery produced the buildup to

• WWI (1914-1918)
• the communist Revolution (1917- in Russia, 1927- in China)
• fascist regimes and WWII

In hindsight, of course, by all those people agreeing to be close to 0 value, they allowed the valuation of some grow to unbearable arrogance.

Right-wing, those in control, the regime, the rich, know how to program the masses: by relinquishing all your power and value to me you become valuable via me. Seize to exist. Identify yourself with me. “me” would be a country/regime name. Those people valued down to 0, daring to voice their existence (left-wing), are declared terrorists, a danger to all. Communistic regimes have shown that left-wing behave the same when getting control: they become right-wing. It is not about right-wing vs left-wing, it is about remote control vs local control.

It is human nature not to give up what is conquered, basically founded in the locality principle, one’s own little world. If this own little brain has accumulated immense power, it will act as if there were no other brain out there, it will wreak chaos. On the other hand those little brain out there have their little world to care about – also locality principle – and will not protest. They can even be programmed to die for the fascist elite: “My subjects! I valued you 0. You agreed. Now die to actually be gone. I will declare you martyr to convince some others to do the same.”

Regimes made several adjustments to keep their control_currency more stable, but did never touch wages_slavery itself, because that is the whole idea of the control_currency in the first place. They have realized that the accumulation associated with wages_slavery, when let loose untethered buys up all essential assets, land, houses, raw materials, energy, …, cornering the market, making the prices, rent-seeking, creating inflation. Their solution is to bind/tether that accumulated capital:

• regimes provide bonds with interest to allow that capital an escape from the regime-wanted inflation
• they have also regulated stock as a way to bind that capital for wage_slave usage

But since wage_slavery is harvesting by design, accumulated wealth at one company is used to buy the competition, to optimize harvesting and to have more prize control on the market ( Microsoft , Meta , Alphabet , Apple , Nvidia ). Why not counteract this accumulation? Why not a progressive taxation on the company profit? That would tax automation and AI and wage_slave exploitation, … But, of course, why even allow wage_slave contracts in the first place. Regarding bonds: Since regime bond interest is financed by taxes on the general population, the exploited wage_slaves need to pay interest to their exploiters. In short, currency stabilization does not avoid control accumulation, but rather intensifies it.

More control speeds up control accumulation ($\frac{dC}{dt} = kC$), money being a measure of control. The exponential dynamics leaves very little time to react to avoid a collapse: But how to muster a reaction, if the majority has no control and is mostly programmed. And indeed those with money have social media power, propagate right-wing as the best for the poor, because for them the 0-value people dying is a lot better than them loosing some of their wealth and control. The logic of the personal interest is not wrong per se, it is just wrong, if the interest of some has global collateral damage.

Since the regime valuation of labor is the root cause of many problems, the key is to avoid the regime valuation of labor and move to a market valuation of labor, which I call same_market_valuation, meaning the same market where one also buys products. A legal entity company needs to be found that represents the link to the market, but does not use labor/wage_slavery. Rather one accumulates ownership (shares) on the market link legal entity by working (together). There is no pre-valuation of labor at all. The valuation is via the profit (sharing).

Interest In Pareto Freezing

Continuation of control_currency musings: monopoly_of_violence, regime_chaos, fiat_money, wage_slave, control_principle cooling reflected by pareto-distribution. With some reference to physics: control_principle between layers.

The central concept in economics is valuation.

An organizational structure that allows a central valuation leads to wealth accumulation. The regimes central valuation of labor reflects its intention to control people for bureaucracy, military, policing, infrastructure, … That is how money came into existence in the first place: control_currency. Companies take the regime valuation and add their central valuation for the products and services of the company.

Debtors create money. Regime money_creation has shifted from money printing to bonds, making them bank debtors. Interest rate represent motivation, like force as gradient of change in physics. The foundational force was and is monopoly_of_violence, but it is encoded in the centralization of valuation by the interest rate imposed by banks. Interest rate is a pressure to optimize, a pressure towards technological development. Efficient extraction of energy is freezing the society into big pareto chunks: big regimes, big companies. The current technological jump, AI, means more centralized surveillance, centralized judging and decisions. Like every new force is a new existence, a new layer, having no force due to the centralization also means non-existence.

Valuation and Interest

Energy is change. In the Lagrangian T-U split

• $U(q)$ is the remote influence at the current location $q$
• resulting in an local time (local change) $T$ to be added to the geodesic (the local changes without that $U(q)$)

If the force/gradient $F = - \frac{dU}{dq} = - \frac{dH}{dq} = \dot{p}$ is not zero we have a new existence, a new layer, a new local change, a new local time.

• As comparison to AI deep networks the loss gradient is the relevant direction to follow per learning step to reach a state of less energy. For example, in input classification random activation of final neurons would be high energy, while recognizing the object would activate just one neuron and thus be minimal energy. The gradient is backpropagated to internal layers until the structure relevant for classification is fixed/memorized.
• As comparison to economy the profit gradient is the relevant direction a factory/company follows to maximize profit. Work $F\Delta q$ is the little extra money you earn making a change $\Delta q$. This can be applied to lowest layer employment, where $\Delta q$ is given by the employer, or structural, a change in the method of production of profit.

— Physics: Force as Gradient Of Change

People’s time is their energy.

As the regime’s currency by decree (fiat_money) is to control (control_currency), the valuation of the time of individuals is by the regime. Companies are extensions of the regime and use the same metric. All more local valuations are compared with this wage baseline valuation.

The need to survive is quite constant (subsistence). But the valuation of this need is not, meaning the prices of food, clothing, … do change. Regime valuation tends to miss that. Therefore it is paramount that the decisions, which profit relevant steps $\Delta q$ to take are local, especially whether structural or not.

The intelligence of a system is by mutation (creativity, producing alternatives) and selection (choosing or being chosen). This produces many paths one can take. The gradient is the direction of the largest profit. In this picture, with more alternatives, steps can be taken in more directions at the same time (components). $\Delta q$ consists of more components, and can include money investments, time investments, structural changes.

The interest compares the future to the present valuation to decide about the next steps.

$$\text{ Interest } = \frac{\text{revenue } - \text{ cost}}{\text{cost }}$$

Interest is a measure of profit or loss relative to cost. Interest as a quantification of motivation.

— Interest

The own valuation of time depends the own creativity on producing alternatives, how to use the time. So ideas like oportunity cost depend much on what you see as exclusive alternatives. A product has more components and more uses. A person meets more skills and joins more uses (formal concept jargon). It is not absolutely necessary to take the regime valuation of time for personal decisions, but the pressure is high due to the use of regime valuation (money) in all activities.

For example

• If I build a house by myself I need X hours to build the house.
• If I build a house with the wage I need Y hours of my time for the job.

If building a house is not a pleasurable activity for me (loss),

• then, if X < Y, I build the house myself, because my loss is less in this case.

If building a house is a very pleasurable activity for me (a profit),

• then, if X > Y, I build the house myself, because it is more profit for me.

Every valuation has an associated interest, positive or negative. A step consists of smaller steps with costs and profits with associated interests. So to make a decision can become complicated. This additional effort is always compared to the baseline valuation by the regime. The effort can pay off via structural improvements, or maybe just by gaining valuation power. But most accept the central valuation, because it is easier, and get locked-in against local valuation.

Banking

A central bank does the bookkeeping for the regime control_currency, defined by regime valuation of labor in order to use that labor.

The logic of economy is via valuation and interest, which applies to banks as well. But banking license is just for fiat_money. For other financial products an investment license is needed. The bank operates via interest alone, as valuation is done by the regime’s labor valuation.

Bank clients are

• Debtors take loans from banks.
• Creditors deposit money at the bank.

money_creation

Every loan is a money creation. I owe you. IOU.

money_deletion

Paying back the loan, deletes the money.

Debtors create money.

• Horizontal money creation is by private debtors.
• Vertical money creation (meaning by power) is by regime.

The bank interest on the loan is the interest in economic activity. The bank interest includes the regime interest.

Bank balance:

• Liabilities are the deposits
• Assets are the loans
• Equity = Asset - Liability

Commercial banks demand high interests on their private assets (the loans). and offer 0-interest on their private liabilities (the deposits). When competing with other banks the 0-interest on deposits should make loan interest low, too. Here the central bank steps in: The central bank offers a key interest on deposits from commecial banks. Also loans from central banks to commercial banks relate to the key interest. With 0-interest on deposits, banks could become profitable just due to the key interest from the central bank. This is why private money creation is always above key interest, and usually quite a bit above. Commercial bank assets are mostly private (55% to 70%), then regime bonds (10% to 25%) and parking at the central bank (10%).

Regime

The central bank is a money faucet by regime autority. Basically central banks and regimes are on the control layer, with different interests than for the private/commercial sector.

Regimes also create money via loans (bonds) (vertical money creation).

• While normal debtors are checked for credit-worthiness, and not necessarily get the right to create money,
• the regime can always create money.

The regime is a money faucet by its monopoly_of_violence. New bonds are the regime’s promise to tax its subjects more than spending on them, in order to pay the interest.

Why would a regime pay interest for its money creation (bonds) just like any other debtor? The regime has the monopoly_of_violence and surely has no obligation to pay interest. The regime extracts taxes here to spend it there already, completely on its own devices. The regime with its monopoly_of_violence is completely unrestricted in its decisions. This makes the regime a money faucet. It can fulfill every financial obligations. It always will be able to pay back on maturity of bond – by creating other bonds, unlimited. To use bonds, pay interest, for its money creation is a deliberate choice. Moderated wanted inflation can be achieved with money printing, so why the bonds?

• The regime acknowledges the idea that interest encodes motivation.
• The central bank has been commissioned by the regime and can be considered part of the regime. It has to keep its balance according control layer interests.
• Bonds produce moderate wanted inflation, just like money printing, just like any new money_creation.
• Moderate inflation is targeted at the commercial layer, to make the wage_slaves spend their money.
• But the moderate inflation should not jeopardize certain wealth (of the rich, of purpose-bound regime bonds like pension).
• If the wealthy spent all their money because of the regime-wanted inflation, the inflation would get out of control. Bond interests compete with other financial products to bind money.

Why the financial products in general: The regime realized that its central wage_slave valuation, when clashing with decentralized market valuation via companies, leads to wealth accumulation, which can jeopardize the regime’s control on its currency, if the accumulated money is not bound by financial products.

Valuation of labor and product in the same market (same_market_valuation), meaning sharing of profit between work mates, would be a different currency not fitting to the regime’s intention to control wage_slaves.

Extraction Efficiency

Wage_slaves are not supposed to take loans. The idea of the control_currency is to use money to keep them working, but keep them poor.

To keep them poor, it helps, though, if occasionally some become debtors to create value for themselves, because then they also need to create

• value for the bank by the bank’s interest
• value for the regime by the taxes associated with the spending of the borrowed money
• value for the inherent valuation asymmetry to produce accumulation of wealth somewhere
• value to balance inflation loss

What we get is an devaluation of labor time, meaning low income.

• For one, this makes them work a lot to survive.
• For two, they can not buy anything with the money other than the essential.

The drive to extreme misery has happened throughout history, several times. And from those instances it can be observed that it was also associated with technological jumps. Those in control have time and resources to optimize extraction. When the extraction reached a natural limit, structural changes allowed for more extraction, i.e. better use of wage_slaves.

How did it get to systematic wage_slavery beyond regime use of subjects in the first place? For Europe and America the reason was actual slavery in the Americas and the exploitation of the colonies in general. Massive raw material needed massive processing. At the time of the industrial revolution in Britain, the rich and their government took land from self-sufficient people (enclosure acts), to force them into factories, making them dependent on wages. But then more and more machines were used for mass production and the wage_slaves were not needed any more. Back than there were still escape routes, though. They could go to America and claim land.

With machines the labor shifted from simple physical work to more intelligent work, machine construction, factory planning. Electricity came. Computers came. All these needed more and more qualification and also a lot of labor to build new infrastructure. The tech people had to do overtime, because they worked for many. But they were becoming also super-super-efficient. A few could produce for millions, using the machines, basically in all industries.

What became of those not needed anymore due the super-efficiency of a few. They became cannon fodder in World Ware I and World War II. These were civilization collapses, as was the french revolution before, already.

From history we can learn:

• slow extraction produces optimization and technological jumps
• fast extraction produces collapses

This is also how biological evolution works.

• The cooling produces higher collaboration, higher organisms, to cope with the energy loss.
• But it also can produce extinction, if the environment changes to quickly.

The cooling is characterized by a pareto distribution. In the pareto distribution a population (of molecules, people, …) is distributed to chunks (organisms) of low energy. This freezing pattern is seen in many systems

• chunk-forming in freezing water
• magnetized chunks in iron (ising model)
• species body size
• empires, emperor survival in empires
• economy with no limit in company size

Organization/organism/structural_complexity/chunking is related to energy extraction, induced freezing. Human energy is the local time of individuals (compared to clock time). Wage to survive using almost full wake time is the lower wage limit. That is where most wage_slaves are kept in the big chunks called companies. With all the optimization so far, this would not be necessary. But it is wanted by those who control to get yet some more freedom. Think of what some can do already:

• Hey, let’s go to the moon.
• Hey, let’s take over control of those 90 million people there.
• Hey, let’s shake world economy a bit and collect the falling fruits
• …

Learn and control. Use your intelligence to control. Intelligence is to control. The regimes monopoly_of_violence can override that natural logic from evolution by brute force. Regimes impose their valuation by their title categorization, meaning especially “wage_slave/employee” vs “company owner”. Regimes using brains for bureaucracy is state-of-the-art since first empires, leading to writing and mathematics, and money. Since the era of systematic flat wage_slavery valuation, making up current control_currency/fiat_money, pareto-cooling, chunk sizes, have grown immensely.

The spacetime/change of a physical system is its action, which compared to our clock time becomes energy. For mind coordination, energies are often split into their own times and spaces,

• like $E = TS$ (temperature, entropy)
• like $Fs$ (force, space)
• like $PV$ (pressure, volume)
• like $\mu N$ (chemical potential, particle number)
• like $\gamma A$ (surface tension, area)
• like $Vq$ (voltage, charge)
• like $EP$ (electric field, polarization)
• like $HM$ (magnetic field, magnetization)
• like $h\nu$ (action, time), the comparison of local time with our clock t

In information theory information is defined by space: $\log(\text{count})$ or $I = - \Sigma p\log(p)$. The latter actually has indirectly time in it, via $p$, but normalized away. Physically, though, due to locality principle, information is inseparable from time. I call it spacetime or just time, and it is local, an own universe unaware of a neighboring equal ones. Counting the parallel particles is a mind thing, not physical. In information science, programs or languages have a space-time complexity trade-off. More structural or space complexity can reduce the energy consumption (time complexity). Structural complexity: Organizations/organism have little freedom for their components, low entropy.

— Physics: Structural complexity (space)

between layers

Understanding and consciousness is to compare. And I like to start with physics when placing something in the information space of my mind. That might look a bit out of context for some topics, but I don’t see physics only as the study of relations between measurements, but rather a philosophical approach, a method of epistemology. The following thoughts were starting points for musings on economy, a topic of current interest to me.

I’ve realized since quite some time that not seeing the bigger picture makes physics dogmatic. For example when saying “the kinetic energy is $\frac{1}{2}mv^{2}$”: It is wrong as a general statement. It is practical in the sense that if a body is stopped to a halt, that energy is transmitted. But as a state: an inertial frame moving with $v$ has no distinction from a body at rest, and therefore has no energy.

Here I place the

• split of energy into kinetic and potential energy

as a

• connection between layers.

Spacetime

energy

Energy is the rate of change of something, the frequency.

space

The something that is changed with the frequency.

Space is physically not existing without a change, without a time. Therefore also “spacetime”.

Space is not the vacuum, not the space with nothing in it. Space is something that changes or cycles in a lower layer. Space is energy at a lower layer. Space is associated with matter and matter has mass and mass is energy. So space is also energy. We make the distinction in the mind, but physics comes with equations that uncover them as one. The method makes sense, to coordinate our mind variables with reality, but this description and the reality as such are different things.

From the macroscopic viewpoint, not looking at the nucleus, not looking at the strong force, all matter is electromangetic. A photon can be considered matter. A photon is the change of electric and magnetic components in the electromagnetic field. We live in an electromagnetic world.

Field is a mapping from our $\mu = t,x,y,z$ to reality. We cannot assume the space in our mind is reality. No, the field is the real space. We coordinate it to our mind space via the equations of motion, plus further restrictions (guage: which potential $A_{\mu}$ with same $E$ and $B$). A coordinate whose mapping stays constant (symmetry) is like saying that it maps to a property intrinsic to the object, like $t$ to Hamiltonian $H$, or $x$ to momentum $p$. (Noether).

So what is a field? The field is the real space, well spacetime of course, because it is an evolving system and does not exist without the changes of it. The field is the reality, and that is local. The field can be $E$ or $B$, but it can as well be a biological system, in the more general idea that changes happen locally and form the system. In our mind we can say: Oh, see that star, as if we would see something that existed now, when saying it. We can look at the road while driving, see nobody, look at the phone, and have killed somebody.

T-U split

work

Work is the additional rate of change due to some influence from a another/remote/below system.

Work is change on this layer, extracting energy from layers below. “Below” shall define the source of energy, not actually below. The sun is above, but would be below in the layer idea, being a source of energy, to make changes in this layer, the layer of interest. Work can be seen as extraction process to produce change “here”. But intentions in “extracting” is of course judging and very much a mind thing.

force - potential energy

We start with the energy source, corresponding to a change “there”. This is also called potential energy $V$. In the context here I might call it remote/below energy. Then we map this to a change “here” ($dq$). $dq$ is a local change and as such a local time step. A force is a local change due to an remote energy source, the influence depending on the location $q$: $F = \frac{dU}{dq}$.

momentum - local energy

We start with the local change without the external influence. I call this the local energy $T$, but is also called kinetic energy. In classical physics there was the idea of something ($m$) moving in a straight line $p = mv = m\frac{dq}{dt}$ (uniform motion, momentum). But we have to generalize this, because we realize there is no actual uniform motion to be found. It was just a local mental simplification due to the limited observation space. By comparing $dq$ to a clock change $dt$ we had left physics already – which is fundamentally local, and had gone to a mental comparison process. Both $q$ and $t$ have by chance units or our choice, but $t$ is detached, a different system, we compare to. Rather we should think of $p$ as a (cycling) trajectory (geodesic) without the energy extracted from another source ($V$). Uniform motion and inertial frame becomes a local simplification on the geodesic, a linear coordinate system for our mind. Seeing change/energy as fundamental, one would fix the mental unit of change $dt$ and see $p$ as the size of the according local change $dq$ (local space). The linear $\dot{q}$ projection from remote mental $t$ to local reality $q$ would change along the geodesic. The more general momentum is this change of spacetime projection $p = \frac{dT}{d\dot{q}}$.

time - energy

$\frac{dp}{dt} = F$ (Euler-Lagrange), $p = \frac{dL}{d\dot{q}}$, $F = \frac{dL}{dq}$, $L\left( \dot{q},q \right) = T\left( \dot{q} \right) - U(q)$. The idea is that energy is change, be it of remote origin $V$ or of local $T$, and therefore additive, with total constant Hamiltonian $H = T + V$, while the Lagrangian $L$ denotes local rate change $T$, represented by the change of the mapping $dt \rightarrow dq$, due to the remote $V$ influence at $q$: $L = T\left( \dot{q} \right) - U(q)$. The closed system has constant total action $S = \int Ldt$. The action can be seen as information of the system (the local chain of time steps). The energy or Hamiltonian $H$ is the local time steps compared to our clock $\frac{\partial S}{\partial t} = - H\left( q,\frac{\partial S}{\partial q} \right)$ (Hamilton-Jakobi equations), a rephrasing of Hamiltonian $H = p\dot{q} - L$ as the Legendre transform, using $\frac{\partial S}{\partial q} = p$. Hamilton equations show this H as timing of the system: $\dot{p} = - \frac{\partial H}{\partial q}$, $\dot{q} = \frac{\partial H}{\partial p}$.

Seeing the time and space physically inseparable (spacetime), I prefer to start from time, i.e. the local rate of change, i.e. from energy, saying: The source energy $V$ is more fundamental physically, than the force $F$. But if you want to overlay human intention, you could say: exert force $F$ along $q$ to extract energy $V$, which kind of fits to a mind trained by evolution to control. Work can be defined as extracting energy from lower layers, not meaning necessarily physical work, moving things, by seeing $dq$ as any local change in $dU = Fdq$, not a change of space coordinates. We can also say work is the energy lost from layers below. Wording does matter socially but the physical system is “unaware” of them.

Every new force is a new layer that cycles, if not stopping the layer below, where the potential energy $V$ comes from, but rather adding a new dimension to which lower layers are bent.

• The T-U split is the link between layers
  • U: energy of layer one
  • T: and energy of layer two

In the energy bill actually only $U$ is mentioned. That is what you pay for, be it food, be it electricity.

Physics of control

Close systems do not exist, other than as a mental approximation. The T-U split is between two layers already. Such systems last for a long time, think of an atom or of a star system. In reality of course more than two systems interact. But the two-system is the minimal interface, a great starting point for a description, like the bit to describe all kinds of information. Minor other interactions can be practically handled as a direct time dependence of a change, i.e. not associated to an actual localized spacetime change. This of course is a mind method, a mathematical method, not a reality.

In higher layer systems, in biological systems, in economic systems,

• the extractable energy $V$ varies along $q$, the local spacetime
• On the expense side the systems have a rather constant energy dissipation.

Such systems harvest more than needed at any point in spacetime and save it in more local buffers, like in glycogen and fat for animals or equity/ownership in economy. That makes interactions more localized between the one cell or a few cells and the energy buffer, between an individual or a family and the assets under control (control = ownership).

Loss of energy at “lower” layers creates layers “above”. The layer above is sometimes called Maxwell demon. I also name this control_principle, when intending dissipation of energy, really lost energy, not a back-and-forth interaction that will cycle forever.

Action as spacetime

The T-U split is the Lagrangian $L = T - U$ On can see the Lagrangian $L$ as the local spacetime step, meaning both space and time, inseparable, but of course with our time as something to relate to. Action $S = \int Ldt$ is accumulated Lagrangian ($L = d\frac{S}{d}t$). If a closed system, as an approximation, $S$ can be seen as the information of the system.

Energy (Hamiltonian $H$) is the comparison to our remote time $H = \partial\frac{S}{\partial}t$

In our electromangetic_world a constant $c$ says “space and time are the same” and a constant $h$ says “there is not infinity”, there is a smallest step. Most steps sizes of change are much larger than $h$, though.

Here some synonyms of action:

spacetime

spacetime conveys that space (what changes) and time (the change) are physically one. Splitting spacetime into space and time is a mind thing and not physical.

variable

The values of the variable are changing, implying both the exclusive states and their change. A mind variable is physically happening/real in the mind but might not be mappable to an external world physical equivalent even if intended.

particle

Particle refers to one spacetime localization (the particle) among many similar ones (a layer). “This spacetime consists of lower layer spacetimes” is to say “This particle consists by lower layer particles”.

Between layer’s: The lower layer’s action change is this layer’s step/quantum (Hamiltonian $H$) by which this layer’s spacetime emerges (Lagrangian). The Lagrangian is a 2D variable, the components being called potential energy $U$ and kinetic energy $T$.

While there are more $q_{i}$ changes observable (collectively named just $q$), they are components of one change in a 2D deterministic spacetime $L = T - U$ line. Nature does not do a $q_{i}$ projecting to 2D, but rather relation between the many lowest layer 2D spacetimes produce the mental 3D world. With many independent localizations, layers of changes, the actual world around us is high-dimensional, with a 3D substrate.

The action $S = \int Ldt$ is the full spacetime extension of a potential-kinetic-cycle. In an independent cycle the action is constant. Constant action leads to the equation of motion (Euler-Lagrange Equation):

$$F = \frac{dp}{dt}$$

$$F ≔ \frac{\partial L}{\partial q}$$

$$p ≔ \frac{\partial L}{\partial\dot{q}}$$

Every spacetime particle is curved by $F \neq 0$. $F = 0$ corresponds to no change, which is synonymous to non-existence. Note the correspondence between change, existence, spacetime curvature, limited size and locality.

In the real world of layers, $S$ is not stationary. It changes in $H$-steps lost to the layer above: $\frac{\partial S}{\partial t} = - H$. The local Lagrangian becomes part of another change (dependent on another time) and its 2D curve is not a cycle any more, a spiral possibly, unless the loss is compensated by an equivalent gain from yet further down, keeping a particle busy with turnover from below to above.

The layer above has the same description, but with

• different action $S$
• different time extension $\tau = \frac{S}{H}$
• different space extension $\lambda = \frac{S}{p}$

Hamiltonian $H$ is the layer’s time unit. Momentum $p$ is the layer’s space unit. It follows a layer-specific speed $v = \frac{\lambda}{\tau}$ linking space and time via layer specific $\lambda = v\tau$.

Special relativity is basically the relationship between layers, totalling lowest layer spacetime creation speed to $c$: $\left( \frac{E}{c^{2}} \right)^{2} = \left( \frac{p}{c} \right)^{2} + \left( m_{0} \right)^{2}$. Total mass is $m = \frac{E}{c^{2}}$. $m_{0}$ is the masses from layers below.

A potential is an energy gradient $\partial_{i}U$. It compare mind space $i = x,y,z$ with actual spacetime energy. For electric we would have written $qE = \partial_{i}qU$, and $B$ vertical to that.

In 4D $\mu = t,x,y,z$ the Euler-Lagrangian equation is

$$\partial_{\mu}\left( \frac{\partial L}{\partial\left( \partial_{\mu}A_{\mu} \right)} \right) = \frac{\partial L}{\partial A_{\mu}}$$

$$L = - \frac{1}{4}F_{\mu\nu}F^{\mu\nu} - J^{\mu}A_{\mu}$$

The space $q,t$ above have become $A_{\mu}$. I like that. More closer to reality. The mapping to our mind variable $\mu = t,x,y,z$ happens via $A_{\mu}$ To coordinate with our mind variables is an essential step for a description.