D  e  n  s  i  t  y                            R  e  l  a  t  i  v  i  t  y

            

The misconception that requires clarification before physics can enter another paradigm shift, is that Galilean and Einsteinian relativity is not just relativity of motion or velocity, it is relativity of space and time, and relativity of space and time can be magnitude of motion but also magnitude of non-motion, the former a vector quantity involving inertial causality, the latter a scalar quantity involving scalar fields of temporal density.

The premises behind density relativity (DR) are, one: if there is a finite limit and relativistic effects to space-over-time-spacetime – causality, as established by Einstein, there is a finite limit and relativistic effects to time-over-space-spacetime – temporal density; and two, that time is limited to an emergent effect of causality. DR reasons that quantum mechanics is emergent from relativity rather than commonly believed macroscopic from quantum mechanics. Quantum mechanics’ proposed emergent nature described here as coming from a fundamental causality superimposed with virtual relativistic density.

DR rests on the following: 

1. If there is a finite limit to space-over-time-spacetime leading to relativistic effects of motion, there is a finite limit to time-over-space-spacetime leading to relativistic effects of temporal density. 

2. However, time is not an observable, it is proposed as being limited to an emergent effect of causality. From spacetime first principles, time is proposed as an intrinsic rate effect of causal spatial reference frames, of motion, and not absolute, nor a phenomenon in itself, as consistently indicated by Einstein’s relativity and Minkowski spacetime. Furthermore, the inverse of space over time motion, time over space density, is proposed as not a phenomenon in itself either if time is an emergent parameter within causation. 

Although time is suggested limited to an emergent effect of causality, it has a virtual conglomerate scalar reference frame capacity, separate to its role in causality, from which non-local DR effects are derived, and, because time is limited to a relation, from which superimposed inverse localised effects transpose to. 

Let time t be limited to emergence from causality such that time in rate of change of spatial reference frames has no direct DR effect (indirect yes). Therefore, relativity of time over space, or time density, t/s - rate of non-movement – has DR effects that are, because time is limited to an emergent effect from causality, naturally virtual that are made real by exponentially inverse translation external to each centre of t/s - or ρ/P. 

Due to time only being a relation, time-over-space-density’s equivalent, mass-density-over-energy-density, is proposed to have this virtual reference frame property, yet only have discernible DR effects by scalar DR field effects instantly supplanting with ‘external’ exponential opposite vector-reaction-Hilbert-space-equivalent. 

Time contraction DR effect equivalence with mass 

A side equivalence principle that shows reality can be explained with just space and time and relativistic principles, is the DR effect of time contraction’s equivalence with mass. Mass is universally equivalent to DR effect, time contraction, and/or its perpetual creation which can look classically as conservation. 

If there is only space and time, using energy of a system as an example, mass is a temporal phenomenon, albeit not the forward passing time as there is no pertinent motion but less time per space. It cannot be a spatial phenomenon because there is no observable spatial difference. 

Mass as a DR time contraction effect, and its ‘conservation’, are relative to conglomerate-time (CT). CT can seem an approximation of absolute time, an approximation because the temporal effect of innate vibration, or oscillation, underlying all phenomena would resemble absolute time but for extremes of velocity and density creating spacetime glitches to absolute time. Separately, the innate vibration underlying all phenomena is reasoned as a DR effect of any small enough spacetime energy, that is, relative high energy/mass density. The conglomeration of the emergent time effect of all particles’ vibrations that are not in extremes of spacetime velocity and/or density, resembles time as we experience it, as if time was universal, whereas, as presented in second premise here, is intrinsically not universal. 

Time-over-space – in Minkowski spacetime context – is proposed to have a virtual limit and relativistic effects. Although time is fundamentally relational and non-global here, it is integral to spacetime, still adhering to a virtual spacetime scalar limit and having relativistic effects to an observer; that is, mass-density-over-energy-density (ρ/P) is proposed to have a virtual scalar spacetime density maximum limit that incurs virtual non-local unstable relativistic effects that, though virtual (due to time not existing per se), instantly stabilise and localise to emergent time by superimposed inverse action of external exponential energy-density-over-mass-density (P/ρ). As the density limit is virtual due to time not existing per se, means there is no literal limit to mass density in our Hilbert space, just the limit’s DR effects. 

One of the fundamental DR effects is time contraction of the ρ/P virtual field. It flips instantly into time dilation of the P/ρ field, though that time dilation is not instant but causally bound and not a direct DR effect per se. Close to mass density maximum and energy density minimum, to an observer, there is virtual mass density decrease and virtual energy density increase; however, due to time being limited to an emergent effect, those virtual DR effects turn instantly into exponentially decreasing mass density increase and energy density decrease, of which time dilation is part. Temporal-wise, there is virtual time contraction and exponential real time dilation. The DR time contraction, in Hilbert space, is equivalent to what we would call mass. 

This leads to superposition of DR effects and DR reciprocal effects observable at hyper-dense parameters, such as hadron phenomena at the quantum level, and gravity and electromagnetism at non-hyper-dense macroscopic systems – Einstein’s description of gravity is a macroscopic DR reciprocal effect only. The superposition of ‘virtual’ ρ/P DR effects and reciprocal ‘real’ P/ρ DR effects display innate symmetries and conservations that physics laws derive from yet are not completely symmetric or conserved due to the latter’s spread-out time-dependent focal point and former’s central focal point. This is reflected by nucleonic processes – up quark the virtual ρ/P DR effect with perfect symmetry whereas reciprocal ‘real’ P/ρ DR down quark effect more influenced by Coulomb and colour charge interactions. This has direct correlation with time asymmetry with particle decays of different quark flavours via weak interaction. 

DR effects are disparate because time is not a thing in itself. They may come from one DR source but are dependent on the operator used, or measurement. Although disparate, there are only, fundamentally, space and time operators. Important secondary operators, due to initial DR effects, are mass and energy operators. As we shall see, DR spatial operator effects give us electromagnetic phenomena which has an indirect temporal source whereas DR temporal operator effects give us quantum phenomena. 

DR effect for time-over-space's fundamental yet virtual time-contraction is exemplified by up quark mass, as will be explained – all other stable particle rest masses are conserved quantities, including the down quark mass. Masses of the electron and neutrino, as will be explained, are conserved masses in the P/ρ field coming from virtual DR effects of up quark creation. 

The reason DR has eluded us thus far is because, ostensibly, macroscopic pressure of a system does not inordinately increase and mass density decrease to an observer the closer a system gets to a hypothetical finite maximum limit of non-causal density – as space-over-time's spatial contraction and time dilation does for motion’s observer in Einstein’s relativity. In fact, mass and energy are scaled equivalent in nature, as per Einstein’s famous equation. It is proposed here, though, that the scaled equivalence is exactly that because time is not a thing in itself, which promotes the proposition to more than just a philosophical abstract debate to fundamental physics tenet. Furthermore, that a DR finite limit and relativistic effects applies, yet, because time is only an emergent relational property, is a virtual action necessitating external inverse-to-centre-of-mass-density opposite effects, of which are not subject to the density limit, from spatial reference frames. 

DR does not stop black holes from existing. As can be seen from above, even though there is a virtual finite limit and relativistic effects for time-over-space, or ρ/P, there is no mass density limit for the P/ρ field and Hilbert space that ρ/P DR effects reciprocate to. There can be close to infinite density spacetime from an observer because time is emergent. Thus, even though the density limit does not limit densities in our localised Hilbert space, it does not stop incurring DR effects, spatial reference frame to spatial reference frame. 

ρ/P and its gamma density relativistic factor γρ effect are not in spacetime. Because time is emergent, γρ DR effect of ρ/P is a necessary action, moment to moment, on spacetime, as operators acting on spacetime Lagrangian densities. Just like mass/energy is conserved in all systems translating in time, operators acting on spacetime Lagrangian densities are conserved because time is emergent. Obvious example is the Schrödinger equation, the equivalence of the operator of energy’s Hamiltonian H to change in field coordinates through time.

$$ iℏ {dΨ\over dt} = H ̂Ψ $$

P/ρ and its gamma density relativistic factor reciprocal DR effect, however, only exists in Hilbert space and, localised moment to moment, is directly influenced by DR effects of γρ ρ/P action on spacetime, the latter’s effect no different to virtual particles acting on particle/waves in quantum field theory. In Dirac’s equation the complex aspect of the equation is the ρ/P aspect and real is P/ρ DR reciprocal effect. All DR effect operators of ρ/P are proposed to transpose instantly, each instant within localised causation, to geometrically-temporally-bound P/ρ effects, dependent on the observer/measurement and subject system and Einstein’s causal limit. 

It is this perpetual γρ ρ/P action on spacetime that propels conglomerate time forward in one direction and facilitates entropy. Low entropy is high density that inexorably moves to high entropy and low density via incessant DR effects, with conglomerate non-local time (CT) moving forward as a byproduct. From first principles, mass is localised DR effect time contraction relative to, and only relative to, non-absolute CT. 

The scaling velocity limit squared always stays the same in the external P/ρ field Hilbert space due to time not being an entity in itself, yet DR effects of energy density or mass density change into each other and the scaling velocity limit squared is contextual, as in nuclear fusion/fission, from ρ/P DR actions on the external P/ρ field. The change’s facilitating bosons – weak interactions bosons, are suggested as having direct DR cause. If time is emergent, DR effects of mass changes cancel, leaving spacetime effects, conserving mass, and by externalised reciprocal, energy. The c2 scaling factor is necessary as a translation factor for P/ρ communicating back to ρ/P the mass density relations of spacetime for γρρ/P relativity to act upon next ‘moment’. ‘Directions’ of measuring DR effects of ρ/P or reciprocal P/ρ effects are suggested as what is defined as quantum ‘spin’ measurement yet can have actual angular momentum after ‘measurement’. 

It is proposed by DR that forces are not involved, no different to how there is no ‘force’ in Einstein’s general relativity (GR) – the illusion of ‘force’ being time dilation and spatial curvature in the presence of energy density. At high energy densities it is not just increases in temporal and spatial change that give the illusion of force, that it is also, suggested here, transpositions of decreases in temporal change and spatial curvature due to DR effects. DR effects that change spacetime yet conserve energy, are attributed to fundamental interactions – standard model’s electromagnetism, weak and strong interactions, and separately, gravity. It is suggested here that Einstein’s GR outcome of spatial curvature comes from non-force-acceleration-dynamic reference frames sourced from DR effects. It is not based directly on GR’s core assumption that spacetime is fundamentally curved, but that temporal curvature is a DR effect, and that spacetime is fundamentally flat, as evidence suggests, curved only from DR effects.  

For spatial charge effects from DR, the initial gamma

γ 𝛾 

  DR factor on ρ/P, or mst2/ms3, working on spatial DR effects in 3 dimensions with background CT and particle’s DR contracted time – or mass, gives t2C2/ms3, permittivity constant

ε 

0 - where C is Coulomb spatial charge, leaves inverse scaling strength of ms/C2, or

μ 

0, permeability constant, but the latter is only for motion P/ρ Hilbert space field. 

For temporal charge effects from DR, the initial gamma

γ 𝛾 

DR factor on ρ/P, or mst2/ms3, working on temporal DR effects, CT and DR time contraction effect, or mass, that is,

γ 

mt. The side constants of mst2/ms3, the spatial operators, are not polar as far as temporal charges are concerned, thus cancel to 2 spatial dimensions, gives ms2/t, Planck constant units. 

Gravity is a secondary effect. It is the direct inverse P/ρ field reciprocal catalysed from ρ/P DR effects of time contraction effect, or mass. 

Gravity 

It is presented here that gravity as we know it is emergent from DR effects between densities that are not hyper-densities. Macroscopically, anything with mass density is proposed to have DR effects of less mass density and more energy density, but because ρ/P cannot exist as an entity in itself, its effects are reciprocated as exterior – to each scalar centre of mass –  opposite DR effects of exponentially weaker energy density decrease and mass density increase. Macroscopic DR effects of such, for a spherical matter object, have negative and positive mass DR effect components balance out leaving mass invariant, and DR effects around each ‘point’ mass density reference frame of time dilation, and, after one maximum positive divergent spatial radial dimension is slightly cancelled out by the radial component of three negative convergent spatial dimensions, leaves two remaining convergent spatial dimensions of spatial curvature, one radial divergent spatial dimension, and time dilation squared. This creates the illusion of attraction between masses reflecting Einstein/Minkowski spacetime curvature’s metric tensors to energy density/momentum tensors of general relativity. For macroscopic systems of hyper-densities or hypo-dense reference frames of hyper-dense phenomena, however, greater DR effects would be evident, anomalous to the general macroscopic effects just described. At present the standard model of cosmology’s successful gravitational theory is based on P/ρ fields whereas large anomalies such as dark matter and dark energy are proposed here as also including DR factors of ρ/P from hyper-dense phenomena and hypo-dense reference frames of hyper-dense phenomena respectively. 

DR gravitational effects are from overall macroscopic mass density point to point. For example, a man named Bob has the same density as Alice, however after eating fast food is denser than Alice. Bob and Alice are events in Minkowski spacetime. From Alice’s perspective, assuming constant pressure, Bob’s greater mass density creates an ‘internal’ DR effect of lessening mass density and increasing energy density, but because time is not a thing in itself, translates to ‘external’ environment reaction of more mass density and less energy density, which means more time (∆t) than Alice (∆t0). It is as if something around Bob has slowed down although Bob’s time to himself would be no different. Alice would experience this on a physiological level and would likely not cognise it. The DR time dilation/spatial curvature warps the spacetime around Bob more than before, creating a physical attraction between them. 

A right angle triangle represents different scalar reference frames of density in DR. The hypotenuse of the triangle is the time between the fundamental density of Alice and Bob from Alice’s perspective g∆t – with g being the density constant – maximum mass density over minimum pressure. Another side is the time between Alice and Bob from Alice’s perspective ρg∆t of Bob’s density – where ρg is the mass density over energy density. And another side is the time between the fundamental density of Alice and Bob from Bob’s physical perspective g∆t0. Obviously the effect is not discernible unless their densities are close to the density limit, nevertheless the effect is there.

g²∆t²  = ρ_g²∆t²  +  g²∆t₀²

g²∆t₀²   =  g²∆t²  -   ρ_g²∆t²

g²∆t₀²  =  ∆t² (g²  -   ρ_g²)

$$\Delta t^2 = {g^2\Delta {t_0}^2\over{(g^2 - ⍴^2)}}$$

$$\Delta t^2 = {\Delta {t_0}^2\over{(1 - {⍴^2\over g^2})}}$$

$$\Delta t = {\Delta t_0\over\sqrt{1 - {⍴^2\over g^2}}}$$

Although P/ρ matter is intrinsically acted on by the ρ/P maximum limit, it is not beholden to it from localised space’s perspective, due to time being limited to an emergent factor. External P/ρ reciprocal effects can create the illusion that ρ/P maximum limit is surpassed for macroscopic phenomena, such as in black holes. DR effects are in between spacetime systems in a relational manner, increasing mass density and decreasing pressure outside systems thereby homogenising density of the inner system to the greater system, lessening mass density of the greater system. It is why neutrons can be at the density limit and neutron stars can be just under and over the density limit. How does DR of ρ/P act on macroscopic densities when the P/ρ evident reality we are familiar with has densities over the ρ/P limit, such as in black holes? It does exactly what the macroscopic gravitational reciprocal DR reaction does, observes the interacting ρ/P limit and reciprocates; in the case of super massive black holes (SMBHs) next to but never at local ρ/P infinite density at event horizon core, DR effects flatten the galactic acceleration curve, recognising ever widening radii events of density that only the ρ/P limit can act on – ρ/P limit can only act on the density limit. Baryon and star densities under the ρ/P limit in ever-widening radii reciprocate with time dilation and spatial curvature. In the case of modest black holes, recognises incremental smaller radii of densities under the ρ/P limit, implying black holes that are not SMBHs are over the density limit, ρ/P-wise, yet not too much more than neutron stars are, on the whole, just under, in macroscopic reference frames. That is for scalar mass density reference frames; for vector energy density reference frames, the positive and negative divergent and convergent respective vectors create charge field effects. The ρ/P maximum density limit, to itself, is inviolate, and virtual reality operators on spacetime are definitively bound by ρ/P limit and gluon saturation reflects this, yet P/ρ fields have densities over the ρ/P limit because time is emergent. 

Expansion in flat universe if curvature emergent, and dark matter 

DR observational effects to an observer are exponentially apparent hyper-dense particle to far far distant hyper-dense particle/observer in ever greater volumes of space – the further back in cosmological time, the less and less density observed. Remembering, there is no DR effect of ρ/P per se except that its reciprocal, electron for example, makes the DR effect locally real. The DR effect responsible for the expansion effect is only possible with plasma proton to observer, with balancing to the density limit electron at a plasma-haze of electron energy-density distance. In the vast expanses of galaxies, the further away two proton nucleons are, one of them in plasma, the less evident are interfering localised electromagnetic time and spatial DR effects to the ρ/P time contraction red-shift expansion – the ρ/P action from plasma protons in intergalactic space. A far less evident DR time contraction effect may be ascertained in interstellar space. DR direct effects from internal mass density maximum are immeasurably small in the macroscopic world, observer to observer, until observed lack of density gets so large, volume-wise, that DR reaction effects eventually are far far more evident than exceptionally weak localised exterior electromagnetic DR reciprocal effects. Ostensibly it could be eternal/infinite time, yet due to the density limit, the further back in time between an observer and plasma proton in empty space observed, the less mass density between, with ‘internal’ DR effects of time contraction. This density effect is tempered by scaling relative time getting larger the larger the density scale. 

ρ/P macroscopic phenomena have time contraction DR effects in relative vacuum of exponential less-and-less-density-field from each ‘observer’, which, with spatial expansion of two non-radial spatial dimensions, looks like spatial expansion, or redshift, with time contracting and volume increasing to an observer. Eventually time contracts until there is no time left to the observer. Time contraction also creates DR effect of greater frequency observed in the cosmic microwave background, faster the further back in time observed. 

Each matter observer in the universe experiences the same time-contraction effect no matter where in the universe, or when. Just as in Einstein’s special relativity, an observer sees a rocket ship travelling slower than it actually is whilst the rocket ship’s astronaut experiences ordinary time, yet both observations are real. Similarly, the universe is literally expanding as a DR effect yet expansion is from every single point in space and in time. If an observer existed 400,000 years after the currently accepted big bang, they would still experience a past measuring cH0 behind them. This implies that the big bang and an initial infinite density did not and cannot occur. Unlike most DR effects, these DR effects are apparent, they cannot disguise the population of fully formed galaxies close to where time contracts to nothing as an observational DR effect, or what is presently understood, classically, as the big bang infinite density. The closer to big bang time zero, the rarer the sighting of galaxies. The variation in the cosmic microwave background (CMB) density is the difference in the observed DR proton plasmas and their reciprocal DR electrons. 

Time contraction is measured by spatial expansion/redshift. The speed of light c coupled with the inverse Hubble constant, cH0-1 is proposed to equate the averaged macroscopic density dynamic limit g, or ρ/P at constant pressure, multiplied by the time-contraction/‘external’-spatial-warp speed of light c, (cg)-1, giving the same time-contraction/volume-increase effect. 

Further acceleration/expansion correlating with dark energy occurs, from reasoning here, with greater time contraction and spatial curvature pressure between hyper-dense systems. The spatial curvature, a smaller radial dimension and two longer – longer than radial contraction – y,z dimensions, is an order of magnitude smaller effect than time contraction effect. Dark energy is attributed here to this DR effect. 

As per Einstein’s GR, the further out from a central mass the time dilation/volume curvature is less. However, nearly all galaxies display a flat rotation curve. The sphere of conventional dark matter around galaxies has maximum entropy, suggesting particle disbursement. However, galaxies have been modelled by Mond, a modification of Newtonian gravity, with stars’ acceleration around hyper dense phenomena slowing to an approximate acceleration minimum 1.2 x 10-10 m.s-2, then flattening the rotation curve, defying our understanding of galactic gravity and/or we are yet to find an elusive massive particle to explain the extra gravity. 

After stars burn their fuel, white dwarfs are kept from further gravitational collapse by Pauli’s exclusion principle maintaining degeneracy pressure between electrons, balancing gravity. There is also degeneracy pressure between neutrons in neutron stars balancing gravity, but also nucleon repulsion energy at hyper-densities. DR has neutrons having two waves of P/ρ balanced by ρ/P catalyst, stabilised by external mass density. If the integrity of neutrons’ degeneracy pressure and nucleon repulsion is not enough to stave off further collapse, it is suggested that collapse to a black hole close to infinite density in the P/ρ realm occurs. As mentioned, densities over the ρ/P maximum limit, such as in black holes, can occur in P/ρ ‘exterior’ reality, yet ρ/P only recognises the- ρ/P-maximum-density-limit. 

The close to infinite mass DR effect of the galactic centre beyond the event horizon of SMBHs is spatially recognised as far away from the core as to be under the ρ/P-maximum density limit, reciprocating flat rotational time dilation and spatial curvature. The immediate volume around the galactic centre is attuned to the time dilation and spatial curvature of the mass density of the SMBH, yet the further out a mass density body is, the more the ρ/P-maximum density limit is recognised. Even though P/ρ spacetime can entertain near infinite densities, ρ/P-maximum density limit can only recognise the density limit, thus the ever-widening density radii around SMBHs. Because the spread out time dilation/spatial curvature DR effect is catalysed to all baryonic density from the mass density DR effects, then correlation exists with baryonic densities and galaxies’ radial accelerations of individual galaxies. Empirical data indicates such a baryonic mass proportional to velocity correlation by Tully, Fisher et al (McGaugh, 2014). Diversity of rotation curves correlate with density/surface brightness. 

Although individual galaxies have their galactic core as the hyper-dense catalyst for raising accelerations of its starry contents at points that GR gravity peters out, galaxy clusters have every galaxy as an active hyper-dense core player with ever-widening initiations of ρ/P-maximum density limit recognition interacting in waves. Singular galaxies’ DR flattened curves of gravitational acceleration due to DR reciprocal effects of ρ/P recognising ever widening parameters, is shared with other galaxies’ SMBH’s density catalysts, the gravitational waves mixing with others, watering down collective ‘dark matter’ effect. 

Bullet clusters have been scrutinised as evidence for cold dark matter particles yet are also explained by DR. If galaxies collide then gross gas mass of galaxies’ nebulae are affected by the collision, but the galactic core density of stellar collapsed stars passes through, creating gravitational lensing from their localised passed-through core densities, not the gases. 

Standard model 

DR effects are reasoned to have two fundamental areas, both stemming self-consistently from one parameter, the density limit field dynamic. One is the macroscopic mentioned, the other is DR of the gluon field to itself. Standard model’s empirical description of hadronic phenomena is implied through data. Even though, as mentioned, there is no substantial ρ/P phenomenon in spacetime per se, its existence is inferred by data of perpetual P/ρ translation from ρ/P. 

‘Internal’ of ‘internal’ density limit phenomena terminology does not refer to within anything spatially, but that ρ/P has no form per se without ‘external’ P/ρ housing each scalar point of mass and reciprocal DR effect from ρ/P’s operators. Although time-over-space is not a thing it is necessary for spacetime to exist. Yet its non-individuated existence means it needs to exist as a perpetual dynamic of DR effects of the scalar reference frames of Hilbert space and then reciprocal DR effects. Nucleons represent such a dynamic. The proton’s positive charge is proposed as an example of direct ‘internal’ density DR effect which, by definition of ‘internal’ and ‘external’, means the proton charge does not and cannot exist in spacetime except for exterior reaction-phenomena inferring it, such as electrons or other nucleons or energy. The electron field excitation and its charge is an example of ‘external’ DR reaction to ‘internal’ catalyst, and why electron charge matches the proton’s quarks' sum charges perfectly, and why there is, on the whole, balance of protons and electrons in the universe. The relationship of ‘internal’ and ‘external’ direction is proposed to represent quantum spin, the unitary symmetry. The external classically reacts to internal’s scalar DR change, the scalar DR change interpreted by exterior P/ρ field as vector jumps of angular momentum and/or motion and/or energy. 

The fundamental density limit field incurs a superposition of opposite mass density and energy density DR effects, the latter having intrinsic geometric and temporal properties. DR effects of non-local-per-se ρ/P are made local by externalisation into P/ρ waves, and P/ρ waves are not real unless observed/perceived, their DR spatial effects collapsing ‘initial’ probability-density waves from energy density’s momentum or mass density’s position operators, or, energy density’s energy or mass density’s time operators. Within the DR dynamic, a dual determinism is conserved, affirming Einstein’s heuristic description of quantum mechanics and entailing predictability, potentially too many lie group variable spacetime predictability, but predictability nevertheless. Predictability is based on non-spatial-locality of ρ/P yet obeys gauge symmetry. 

Entanglement between interacting particles is proposed to operate within non-locality of DR effects of ‘inner’ ρ/P. Classically spin comes from magnetic effects, yet spin on the quantum level is proposed to represent a superposition of DR directions from ‘inner’ ρ/P acting on ‘exterior’ P/ρ, such as W boson action on particular fermions interpreted as left-hand spin delineating chirality; or P/ρ relaying time-ful least action information to ρ/P, which has no direct DR effect on fermions. Hypercharge relates the DR electric charge effect less DR isospin effect. Weak isospin and weak hypercharge take into account P/ρ density causes between moments. 

The fundamental density limit field is a P/ρ reaction to ρ/P instigator of DR effects. The strong interaction is stronger the greater the distance that quark DR effects are from gluon fields’ mass density focal points, yet are asymptotically free within, representing DR effects of less mass density and more pressure translating to and becoming physical by ‘external’ to scalar mass point-centred less energy density and more mass density. 

For the standard model, DR effects of less mass density and more energy density become physical by ‘external’ to scalar mass point-centred less pressure and more mass density – the internal and external dynamic responsible for fermionic partons and bosons. Being dynamics of densities of energy and mass relativistic effects means fields are fundamental, and, due to superposition of DR effects of ρ/P and P/ρ, are particles and fields at the same time. From first principles, effects, combinations of scalar, vector and tensor, of DR of the gluon field density waves are proposed as colour charge, electric charge and the weak interaction, based on observable Lagrangian density least-action fields catalysed by unobservable Hamiltonian density maximums. After the DR gamma factor acts on the Hamiltonian density maximums of each moment of P/ρ in an energy density lattice manner, DR effects instantly affect the causal-limited P/ρ field. 

A boson field exists in itself for the P/ρ reaction field in the guise of the photon field residing at the space-over-time limit, yet a boson interaction field must exist from the ρ/P density limit but cannot exist as an entity in itself because time is not an entity in itself. This means that the boson interaction field from the ρ/P density limit has to have its own charge, as it does with the gluon.

$${ c^2 ∂P \over { ∂⍴}} + {∂Ψ\over ∂t } + { ∂Ψ\over ∂x } = c^2 γ_⍴ ({∂⍴\over ∂P}) $$

where γ⍴ is the DR gamma factor, detailed further on, and ψ is the P/ρ wave field of DR effects. Translation of internal phenomena also put bounds on symmetries of external phenomena, reflected by Pauli exclusions that fermion fields are limited by relative to boson fields. 

Charge being time-dependent emergent, moment to moment, from DR effects, and spacetime and charge being conserved in Hilbert space, there is a moment to moment ratio of charge to the velocity limit and density limit through Hilbert space. The fine structure constant (FSC) represents this. The FSC was initially thought to be an electromagnetic interaction strength adjustment yet has since been found to be also integral to quantum field theory. It is the difference in strength between the strong interaction and weaker electromagnetic interaction, difference in velocity of the electron and photon. Strength of the strong interaction is the direct DR effect of ρ/P of ‘external’ to scalar mass point-centred less energy density and more mass density. The electromagnetic interaction’s Coulomb strength is the P/ρ spacetime field reaction to the ρ/P catalyst and less weak by geometric and temporal field effects, approximately 137 times weaker. 

The ‘observable’ least action and timefulness is ascertained by setting a system’s Euler-Lagrange density to zero, representing local minimum that P/ρ DR effects emanate, as mentioned, catalysed by ρ/P DR effect. The unobservable ρ/P maximum limit means its observable P/ρ reciprocal cannot be a smooth zero minimum action in spacetime. If it could be observed as a point particle, it implies ‘initial initiating’ infinite maximum mass density. Thus a direct DR effect of the ρ/P maximum limit is discretisation at energy density minimum. 

Ostensibly, the gluon field is a density limit field just as the electromagnetic field is the velocity limit field, both fields unattainable by everyday matter – the electromagnetic field by movement and the gluon field by density. There is a difference though. The velocity-limit field is charge-less because it is only a velocity-limit field; nothing under the velocity limit, that is, all particles with mass, can ever reach the velocity limit. However, the density-dynamic limit field, which is a ρ/P field, cannot exist in itself – because time is not a thing in itself – and must have external inverse action fields that have DR charges; so there are charged bosons from the density-dynamic field. Gluon bosons represent the non-linear density limit by having DR ‘colour’ charge effects, whereas linear photon bosons are charge-less. 

DR effects and are a lessening in mass density and increase in energy density the closer to maximum mass density, however cannot exist in themselves, requiring balance from DR effects spatially external to mass density reference points. DR reference frames and dominate quantum phenomena and hyper dense star effects with dark energy and matter phenomena, and not evident in everyday macroscopic phenomena. 

DR reciprocal effects and are an increase in ‘external’ to mass points of mass density and decrease in energy density. This extends to macroscopic phenomena with DR reciprocal effects behind the electromagnetic field and gravitational field. It is also behind the strong and weak interactions at femtometer density scales. 

Mass 

Masses of weak interaction bosons and different masses of hadrons and fermions are proposed as DR effects originating from the gluon density field. It will be shown that the constant mass of DR’s gluon field is equivalent to the Higgs field excitation boson mass. Again, the gluon density field’s ρ/P-catalysing-wave is dependent on P/ρ-wave in an unseparated ‘chromodynamically white’ manner, and mass/energy differences can be DR effects. 

Nearly all baryonic mass comes from the gluon field, of which is a massless boson energy density field with maximum pressure on either side of the density limit, yet minimum pressure at approximately a femtometer, the locale of maximum scalar mass density. DR effects of pressures come from the density limit dynamic and the Coulomb interaction. Mass-density limit must have the energy density maximum directly ‘outside’ centre of mass density maximum, as it is for the measured proton (Vayenas C.G. et al, 2019). 

Protons 

Protons represent the fundamental ρ/P’s interaction with itself. By itself, ρ/P has no dimension, it is not an external field, does not obey locality per se, thus the proton baryon represents the density limit field of ρ/P’s interaction with itself, ρ/P field, made into physical reality by the locality-dependent P/ρ wave-interaction. The nucleons’ two waves of ρ/P are greater than the wave of P/ρ, creating DR effect balance of positive spatial charge, balanced by exponentially weaker external energy density either by electron/s and/or kinetic ionised behaviour. It has DR effects of internal less ρ/P, external less P/ρ and external less ρ/P. External P/ρ reaction to positive balance of ρ/P field is the electron negative charge and minimum mass. 

As mentioned, DR effect of the gluon field gives off DR spatial charge effects, with, for the proton, a balance of ρ/P DR effects of sum positive elementary charge that has no reality unless interacted with ‘external’ phenomena. P/ρ time-dependent reference frames also incur external negative reciprocal charge of the electron as a direct response to the P/ρ maximum DR effects of the proton. 

The proton’s spatial charges are DR effects of the balance of positive 4/3 up quark effects. Pauli’s exclusion principle is satisfied because the two up quarks have different sources, internal ρ/P’s mass density positive charge and external P/ρ’s energy density positive charge. Balancing it to the density field is the external P/ρ DR decrease effect, represented by the electron. 

Neutrons 

Neutron’s mass/energy density waves are proposed as being at the ρ/P density limit, yet only stable with necessary exterior ρ/P connection, such as other nucleons, because at the nucleonic gluon field level, because time-over-space, or ρ/P, cannot exist as a thing in itself, the ‘purpose’ is for ρ/P to connect to ρ/P via P/ρ, as in protons. A core of less ρ/P is matched by two less P/ρ reactions. The neutron has external DR effects of less P/ρ, internal ρ/P decrease effect, and external less P/ρ. External mass density DR effects come via proton and/or neutron exterior environments, stabilising the neutron to the density limit with no excess DR effects. 

The neutron’s spatial charges are DR effects of the balance of positive ⅔ up quark effect and two negative ⅓ down quark effects. Pauli’s exclusion principle is satisfied because the two down quarks have different sources, external ρ/P’s mass density charge and external P/ρ’s energy density charge. Balancing it to the density field is the ‘internal’ ρ/P external to the nucleus. When ‘external’ mass density is not there, for a free neutron, an antineutrino is released in decay, being the missing confined energy of mass to mass DR effects. 

Lorentz Density Transformation 

Lorentz transformations pertain to inertial reference frames that involve positions and velocities, that is, to reference frames where at least one reference frame is moving relative to another. Mass is Lorentz invariant. 

However, from static inertial scalar field reference frames, the Lorentz transformation dynamic is proposed to also apply to density reference frames that resist force relative to another, across space. Underlying these density reference frames is a fundamental field density dynamic limit. 

Mass changes of pressure and mass density cancel out, leaving spatial and time variables. From first principles, disregarding gravity, in the context of spacetime two dimensional Cartesian planes, mass density reference frames are holonomic where nothing actually moves and each reference frame is a measure of scalar mass/energy – unobservable ρ/P replaces observable spatial reference frames of all-space-over-time relativistic fields, whilst the time dimension is replaced by energy density action, or pressure. In these static lattice reference frames, time is infinite in the same manner massless particles are time-less – in light of everything being at the density limit in much the same way that everything travels at lightspeed in spacetime. 

Internally, the density field is purported to transform with ρ/P catalysing the drive to energy density. The present standard model would be the limit if transformations are limited to a Galilean energy-field-density transformation. In the following, ρ is mass density, ρg is a system’s proper ρ/P, and P is pressure or energy density. 

ρ’ = ρ – ⍴_g P

to

⍴ = ⍴’ + ⍴_g P’

However if there is an assumed density constant g then a gamma relativistic scaling factor γ⍴ would apply. 

⍴’ = γ_⍴ (⍴ – ⍴_g P)

with transformation 

⍴ = γ_⍴ (⍴’ + ⍴_g P’)

For density field Cartesian coordinates, the x axis is the mass density ⍴ and the y axis is the product of energy density P and density constant g. On these coordinates, g = ⍴’/ P’ and g = ⍴/P, or ⍴’ = gP’ and ⍴ = gP. 

Against intuition, pressure is imaginary in DR calculations, just as time is imaginary in special relativity, with implications for quantum mechanics and antimatter, yet as far as Hilbert space that we reside in, it is ⍴/P that is imaginary. 

Multiplying the above transformations together and replacing ⍴ with gP and ⍴’ with gP’ 

g²PP’  = γ_⍴² (g²PP’ + gP ⍴_gP’ – gP ⍴_gP’ – ⍴_g²PP’)

g²  = γ_⍴² (g²  – ⍴_g ²)

which becomes 

$$γ_⍴ = {1\over\sqrt{1 - {{⍴_g}^2\over g^2}}}$$

Density Gamma Factor Application 

Least action of the P/ρ vector field – by integrating the Lagrangian – is the meeting point of the minimum action S P/ρ field and the ρ/P catalyst. 

$$ S = \int d^4 \times \mathscr{L} dt $$

Gamma factor γρ is indirectly evident due to time-over-space not existing as a phenomenon in itself. It acts on the previous moment’s static scalar ρ/P ‘field’ component 

$$ {∂Φ \over ∂t} (d^3, t) $$

of P/ρ continuous field effects, then instantly transforms into time-dependent ‘external’ P/ρ indirect separate DR effects, which can be found by using either mass density or energy density operators.

Summary 

This work introduced density relativity as a work-in-progress explanation for gaps in the standard model and standard model of cosmology. A field dynamic of observer-dependent-discretisation from a virtual density limit using a DR temporal operator is described correlating with the Planck constant and quantum properties; a DR spatial operator correlating with permittivity and permeability constants and electromagnetic field. Mass operator is a secondary operator based on amount of conserved time contraction DR effect. 

Experiment in the field of high density quantum chromodynamics may uncover further supporting candidates of evidence. An area of study to explore is determinism in quantum field theory that takes into account the sum of observed and observer’s density relativities, moment to moment. In summary, when density reference frames and relativity of those densities to the density limit are accounted for, the standard model becomes affirmed in its completeness with interactive forces having greater reasoning for existence, whilst giving reason to the dark sector in the standard model of cosmology. 

References 

Bazavov A. et al, 2018, Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD, website accessed 19/ 1/19, https://web.physics.wustl.edu/cb/1802.04248.pdf 

Carlson C.E., 2015, The Proton Radius Puzzle, website accessed 14/6/17, https://arxiv.org/pdf/1502.05314.pdf 

Gao H., 2021, The proton charge radius, website accessed 11/09/21, https://arxiv.org/pdf/2105.00571.pdf 

McGaugh S.S., 2014, The Third Law of Galactic Rotation, website accessed 4/7/17, https://arxiv.org/pdf/1412.3767.pdf 

McNeile C. et al, 2010, High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD, website accessed 3/11/19, https://arxiv.org/pdf/1004.4285.pdf 

Schmidt A, et al, 2020, Probing the core of the strong nuclear interaction, website accessed 31/7/20, 

https://www.nature.com/articles/s41586-020-2021-6 

Vayenas C.G., Grigoriou D, Martino E, 2019, Proton internal pressure distribution suggests a simple proton structure, website accessed 17/2/22, https://www.proquest.com/openview/a4bd338bb38de67b9614f41a16679916/1?pq-origsite=gscholar&cbl=2038891 

Witze A, 2019, How long do neutrons live, website accessed 5/12/21, https://www.nature.com/articles/d41586-019-01203-9