In the graph, relative, local Past-Entropy and future-information, | and 0 combine for any system finite in space and time duration, into infinite fractal Ø-beings with a body-wave ‘momentum’; integrated along the whole world cycle of its exi=st¡ence into energy, which is conserved as a zero sum, when the cycle is closed.
This simple conceptual sentence resumes the interaction of the 3 arrows of time in physics, upgrading conceptually the conservation principles and Noether’s theorem (awesome math, blurred thought, as usual in humans without the right understanding of the 3 arrows of time).
The word speed would define the simplex present that of a mere ratio between frequency of motion and distance, v=s/t=λ x ƒ. But to fully grasp the being its particle-field, mass-speed or charge-speed momentum is preferred as it will represent the being in its past to future configuration, giving us an e (speed) x i (charge, mass) =st-being power to move in the outer world. It is this present momentum when integrated through a long world cycle path, what we call then energy, related to the whole trajectory of the being.
Momentum of existence.
The best way to measure a quanta of time-space is to measure its momentum. We define in that sense the momentum of a being as a quanta of present, product of the relative past and future, entropy and information which flux into a quanta.
This in physical systems gives us a p=m (t) x v (s) natural measure of a quanta of present momentum as the product of the mass and speed of the system, the derivative of momentum then gives us a quanta of present, while its integral gives us the whole ‘world cycle’ in terms of energy, and a wholes are inverse to infinitesimals, we can say that the operation of integral and derivative are Inverse (taking the word inverse in its most logical widen concept: entropy = 1/form.)
If we consider then more than mass a ratio (density=mass/volume) of density of information as the best way to measure the momentum of a physical system a loose concept of a ‘top predator’ as the species with maximal information/brain speed and maximal body force, will give us the non-quantitative, but qualitative and quite exact (top predators both in physical and biological systems always win in collisions), concept for a biological system of maximal momentum:
‘mens sana in corpore sanum’, body x brain = biological momentum
We shall call the fundamental parameter of energy in each scale, momentum of existence, and it will be the measure of its particle-field limb-head strength, force or power. For example in biology a top predator can be considered to have a momentum of existence, product of its ‘rough’ intelligence and brute force. We naturally regard such being with top head and top muscle a top predator. In physics the mass with maximal momentum wins in collisions, more momentum from the other species so it somehow ‘provokes its entropy and destruction’ and feed on it.
Present ‘momentums’ will thus have also an organic value. While this might not be so ‘precise’, let us remember once more than GST is not about precise measures but homological laws, the inverse concept of modern instrumental science, more akin to Greek science. Yet indeed, even if most quantitive scientists will shun off the idea, there is A LOGIC ORGANIC SURVIVAL, TEMPORAL GAME IN THE UNIVERSE THAT RULES ABOVE MATHEMATIC, A ‘MANIFESTATION’ OF THIS GAME, of three time arrows playing through its organisms and momentums of existence.
The Universe conserves the present, but the way the present appears different in detail and latitude. Iteration is thus the true meaning of present which conserves itself because it iterates a world cycle zero sum, restarting the game of existence, which could not happen without iteration.
The conservation of energy and its derivative, or true ‘present instant’, momentum, and its ‘second derivative’ or ‘past’ mass, and vice-versa, the integration of a single present momentum into a worldcyle conserved in as much as it closes itself, is thus as in classic physics, the fundamental starting point for a derivation of the infinite, immortal Universe, departing from a single principle:
PRESENT exists, and it conserves itself in a finite world of time cycles, by iterating its moments and actions in fixed ordered causal patterns of time-space.
Momentum is the as the name indicates (this eerie equality between english verbal expressions and gst meanings, as in exi = st-1 (balance of two scales, between the present wave e x i and its past field, st-1 found in so many equations of space-time events) is a good mnemonic resource. MOMENTUM IS THE FUNCTION OF PRESENT, simplified to one dimension in the equation of speed, v=s/t, which uses only ‘frequency’ t¯¹ but in more complex dimension ads mass, which is basically an accelerated vortex of time, t¯²
Once the equivalence principle of mass-acceleration is understood,then we can consider mass, the singularity Tiƒ state of a physical system (so goes for charge in the ∆-1 scale), which multipled by its present speed forms an mv present>future system, which the Universe conserves, and who integral full path will be despite ‘smaller worldlines’, when integrated a full zero-sum/conservative energy world cycle.
energies and world cycles are thus closely related, and the conservation principle of both is the same. This is expressed in classic physics in the noether theorem, which essentially ascribes energy conservation to the fact that the multiple cycles of time of the Universe close into themselves (forming Lagrangian zero sums along its paths of least time.)
The simplest appearance of present is an instantaneous derivative, ∂s / ∂t, which reduces a world cycle of time to a single simultaneous point of space-time. This present v however must ad the mass, m, which the system is bringing from the past as an accelerated vortex of time, thus we have momentum. And this is what the present conserves in a more complex way, p.
p =mv can then be studied with the three arrows of time. m, is an accelerated mass vortex (strong principle of equivalence, mass is acceleration – not only the gravitational force is acceleration (einstein). So we talk then of two waves:
One in which a number of ps, mvs move extending itself as a point (motion lineal steady state), or dissolves as it moves, its information (wave dissolution), or reproduces its mv species as it expands (density reproductive wave). This final way will leave a surface of energy, it will be a reproductive wave of density of energy, and it will be the most complex of them.
Present then integrates p, as ½ p², and we conclude that the energy of a system is the total momentum of its world cycle.
energy is the integral so to speak of speed, or momentum. Speed is a present instant, ∂s/dt, the fourth dimension of time. As we discuss speed = s/t = s x ƒ(t) = K, and its integral along an entire worldcycle of existence or total sum of present actions = 0, we shall disentangle the meaning of mathematical, physical, biological and topological concepts of present speed and energy potential and factual world cycles.
A speed is thus an instantaneous derivative of present which allow us to perceive a system in an instant. This might mean to see it spread in a wave region of simultaneous present. Often this results in the perception of the entity in its point of balance or mass, reason why it is also useful to measure presents, the function of momentum, though one could also consider its decomposition in its relative past field – the motion and future form the particle. So present would be more the body wave of speed future, the scalar particle, present-future the momentum and energy by increasing the momentum with its integral of various solutions, will map out the whole field of the system, where the speed respect to the larger whole in a way is mediated by the membrane.
In that regard indefinite integrals of first order mapping out all the constants, give us a field, which in the case of complex numbers as in maldebrot can extend through the i-factor across scales of size but normally map out in a single ∆-scale, all the possible configurations of the field, while the F(x)=0 solution give us the likely point of the particle.
ENERGY IN TIME, SPACE AND ∆-SCALES
To put some order in the complex universe of ∆º±ST systems, the best procedure is to define first its 3 terms ‘ceteris paribus:
Its ‘space-entropy’, ‘time-information’ & space-time=energy components across its different ∆- stientific scales.
Those 3 ‘fundamental concepts’ are ternary since the trinity principle also applies to dimensions. Important to notice though that present energy combines dimensions of space and time – so it is by definition bi-dimensional or 4-Dimensional in a more complex view, when we define the singularity point adding to it a height dimension along the scalar Universe where it hides its information and when we ad to the cyclical time membrane, the dimension of curvature≈speed of time cycles to complete its description.
So we have a simplified version:
1 Tiƒ singularity + 1 π-dimension of the membrane perimeter = 2 Dimensional space-time energy open ball.
2 Tiƒ singularity dimensions (point and 5D scalar existence as a whole) + 2 dimensions of membrane =4D vital space-time energy
In that regard, MOMENTUM is the vital iterative inner volume of the being or Present Space≈time put together:
‘MOMENTUM=PRESENT=ST=Ø=MOTION WITH FORM=BODY-WAVE-WORKING CLASS (3 sub-stientific fields).
Body-waves-working classes are thus the 3 st-present ‘energetic components of an organic system.
Lagrangians of present-action vs. energy world cycles.
There is then the formulation of those laws in terms of energy. And so we shall make a Huge statement that responds to the whys of most physics:
‘A Lagrangian function is a an action of time and its Integral a full zero-sum world cycle of time of a physical motion-system; a Hamiltonian is its configuration as a ternary system of 3 organic topologies in Space’.
We have explained that energy is essentially a measure of the space-time content of the system in terms of present – that is, in a single space-time plane, between pure information seed ∆-1 to which the system returns, as pure entropy ∆-1 at the end of the cycle, the word cycle or ‘the conservative energy cycle’ becoming thus a zero sum and so ‘conservative Energy cycles and world cycles must equal to zero’.
And that is precisely the formulation of a motion in physical systems in terms of energy:
So we have through lagrangians and hamiltonians an easy understanding of what is a world cycle in physics.
What is their difference? One of derivatives; which represent for any quantity its ‘finitesimal quanta in a lower ∆-1 dimension’, in the case of motion a finitesimal step of the whorls cycle (and inversely an integral represents its total path, or sum of steps to reach the whole zero sum of the world cycle).
It follows that the Hamiltonian is the definition of a worldcycle of a physical system, time independent in as much as it covers the whole world cycle, as in the case of the Schrodinger time independent equation, shown above, and it must therefore enclose the past-present-future states of the system, as a whole:
But a ‘quantum system’ does have a world cycle much faster than one of our scale (5D metrics: Min. Spe = Max. Tif). Thus we must find a way to express it for multiple consecutive world cycles and that is where the ‘imaginary’ function, of eˆi comes so handy, if H is independent of time, (meaning we represent whole world cycles from ‘here to eternity’:
Hamiltonian and lagrangian mechanics.
It also follows that Hamiltonians, being whole cycle analysis (often a vibration between the potential, future and kinetic, past state, through a point of present balance) will be simpler to resolve in terms of differentials, and indeed, Hamilton’s equations consist of 2n first-order differential equations, while Lagrange’s equations consist of n second-order equations (As a second derivative will gives us a ‘minimal action’ of the system.)
If we define speed as v=s/t= λ ƒ in terms of lineal and cyclical time, as the minimal quantity of present information of a system, it follows that Hamiltonians will ad a new dimension to calculate the whole world cycle in ∆º±1, being that dimension in physical systems the accelerated vortex or ‘gravitational potential sink’ of time≈mass, which the system possess ‘perpendicularly’ across its ∆±1 dimension. And so instead of v, speed (the minimal present parameter in one ∆-scale) we have mv, momentum.
Hamiltonian mechanics thus aim to replace the generalized velocity variables of the Lagrangian, with generalized momentum variables, also known as conjugate momenta, giving more information about the total ∆º±1 world cycle of the physical system.
So instead of forces, Lagrangian mechanics uses the energies in the system. The non-relativistic Lagrangian for a system of particles can be defined by:
And if we apply the principle of ‘balance’ according to which a world cycle or an action tends to balance past (kinetic energy here) and future (potential energy) such as T-V->0, which is call an stationary action. So the Lagrangian follows immediately:
As the system evolves, q traces a path through configuration space. The path taken by the system has a stationary action (δS = 0) under small changes in the configuration of the system (δq). So we obtain, equaling T-V to 0 at each instant of time:
Which obviously only works for ‘present-worldcycle paths’, or ‘conservative ones’ in the jargon of classic physics.
And this will be of course a rule for all kind of physical equations, which become regular, ordered, deterministic when they represent a full world cycle through its 3 stationary points of ‘ages’, constrained to the finite space-time domain of existence of the being.
This can be summarized by Hamilton’s principle:
Which is the definition of a minimal step of motion of a physical system, also called principle of least action, which simply means, we try to conserve our energy=total time duration of existence, minimising our expenditure of it, and so it applies to all beings of all scales of reality.
In that regard while Newton’s laws can be also derived from the ternary structure of the Universe, the Lagrangian and Hamiltonians give us a more clear connection with the meaning of a zero-sum worldcycle.
Indeed, in Lagrangians we talk more on TERMS Of past Kinetic Energy transforming back and forth into future, Potential energy, which IS a TIME-STORAGE OF FORM:
Potential energy trans/forms kinetic energy into fixed form/position, as a FORM OF cyclical TIME.
Noether’s theorem is now more clear, as it states that every differentiable=present symmetry of the action of a physical system has a corresponding conservation law. That is, the integral over time of a Lagrangian function (which may have a space-symmetry as an integral over space of a Lagrangian density function), from which the system’s behavior can be determined by the principle of least action (minimal time used on it) is zero and as such the total momentum action and energy of the Universe is conserved in an eternal present of different ‘durations’ – larger for the total energy of the world cycle, minimal for the action of least time, with its tail of past accelerated mass added in momentum
Yet, constants of motion do not apply to systems that cannot be modeled with a Lagrangian: that is, entropic, Spe dissipative systems do not have a corresponding conservation law, as they erase information, increasing the disorder of the Universe, compensated though by the growth of order effected by singularities, which ad on (or multiply depending on event studied and law of balance considered) to maintain its sum/product, a present, unchanged.
The case of least time: Fermat light principle>Broglie>Bohm>entanglement>relativity
And it was first expressed by fellow countryman Fermat: “light travels between two given points along the path of shortest time,” which is known as the principle of least time. And ultimately shows that the Universe is about time world cycles, not space distances. Since systems choose the ‘time-distance’ between two points, as you would rather take a highway with longer space if it takes you faster than a straight, 3rd class slow road.
How do then light ‘knows’ the shorter time distance? This means as you can ‘see’ and judge the path, light MUST have an ‘action at distance’ form to obtain from the photon-particle p.o.v. information to guide it, and this is the neutrino theory of light, analysed in our cosmological articles, by De broglie with enormous consequence to reformulate general relativity and quantum physics in terms of ‘classic reality’:
A particle connects through a neutrino with another particle, entangling itself with it at the ∆-i gravitational scale that we do not see (hence v=s/t=s/o information = ∞) to which it directs after locking a second neutrino back and forth, giving origin to Broglie’s neutrino theory of light, which emerges from the entropy of the ∆-1 quantum field (hence it explains also Bohm’s theory).
And it follows next that as both particles are entangled, they do NOT ad speeds of c-light, so we do NOT need relativity (we do from the human non-entangled perception of that scale, but from the 2 electrons or human electronic measure machine, there is 0 relative speed between both entangled particles).
Thus we can offer a realist explanation of all the measure quantum and relativity ‘spooky effects’, if we just want to know how at the electron scale, the world will seem for the electron – no spooky, no relativity effects at all.
We are not electrons though so for measure at this scale we do see spooky effects and time dilations, space shortenings etc.