International Journal of Theoretical and Mathematical Physics
p-ISSN: 2167-6844 e-ISSN: 2167-6852
2015; 5(5): 76-86
doi:10.5923/j.ijtmp.20150505.02

Kalyan Deb
Correspondence to: Kalyan Deb , .
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Fundamental laws of Physical science are based on Symmetry, Possibility and five Elementary principles. The concept of Lethargy, like energy, has been introduced by me as being equivalent of the rest mass of an elementary particle, which the particle assumes when it enters into the state of Nothingness, which is the absence of all matter and space. Whereas strong, weak and electromagnetic interactions are always mediated by particle exchange, gravitation is a phenomenon instead of an interaction, which is self-activated in view of the property of mass only when the amount of Quantum gravitational mass is present in space as a medium having the electromagnetic property. Elementary particles are produced by spontaneous generation out of nothingness while annihilation and decay of elementary particles occur along with their entering into and coming out of the state of nothingness. Our observable universe is an integral part of one greater universe having identical laws of physical science. Dark matter consists of an elementary matter particle with high spin angular momentum and low angular frequency, while the pressure factor in outer space having extremely low mass density contributes to creation of new space out of the state of nothingness, making up for the negative volume having lethargy resulting in the observed accelerating expansion of space.
Keywords: Symmetry, Lethargy, Nothingness, Quantum state, Gravitation
Cite this paper: Kalyan Deb , On Fundamentals of Physical Science with Quantum State and Gravitation, International Journal of Theoretical and Mathematical Physics, Vol. 5 No. 5, 2015, pp. 76-86. doi: 10.5923/j.ijtmp.20150505.02.
and define this as a physical quantity to be called as slowness
. This is the parameter that generates time coupled with space during any motion that takes place. Taking into account the theoretical limit of speed in nature
we define this parameter as Quantum slowness being the inverse of that speed
. This is the limiting slowness by which motion can take place in nature.Now starting with the mass-energy relationship with usual notations
we may observe by following the symmetry and then define a new parameter as Lethargy
. This is the property which mass acquires by being converted by the square of the quantum slowness factor. There is another way of looking at this as follows.Again by using usual notations, we have the Maxwell’s relation
and accordingly we may write lethargy as
and energy as
So we may infer that lethargy is produced when mass is coupled with the combined electric and magnetic constants of nature and similarly decoupling of mass transforms it into energy.Let us look at the following interaction relationships between two electric charges and combining them we arrive at the above Maxwell’s relation:• Coulomb’s relation
: Space rated interaction• Ampere’s relation
: Time rated interactionHowever, both the electric constant
and the magnetic constant
of nature are merely two constants of proportionality having defined numerical values only, and so by combining them we would like to arrive at a new-look property of space to be called as the Electromagnetic parameter
which is also the square of the quantum slowness factor, which is an intrinsic property of space, as defined herein by us earlier, that creates time as and when motion takes place in space. Accordingly, we may redefine both energy
and lethargy 
by using this property of space.We may note here that on an elementary level this quantum slowness factor of space which is intrinsically related to the electromagnetic parameter of space or that of any intervening medium between two electric charges is responsible for arriving at the magnitude of the strength of electromagnetic interaction, which depends on the motion of the interchanging photons causing the interaction in the first place.
, having the mathematical form defined hereinabove. When two elementary particles truly annihilate, they must get together into total disappearance from existence in any other form. This is possible only when they transform into nothingness having their entire mass-energy being turned into lethargy. Space occupied by them will become non-existent, and all motion will cease to exist and flow of time will therefore stop. All quantum numbers will also disappear. However, this does not mean to violate the dictum of no demise ad nihil because herewith they will only change into a state of nothingness without actually being destroyed permanently.This state of nothingness may exist from an infinite beginning to an infinite end without violating the corresponding principle that no finite being can become infinite and vice versa. On the other hand, if elementary particles may disappear into nothingness, they may also appear only out of nothingness without violating the principle of causality or time reversal. This also does not in any way mean creation ex nihilo because in nature nothingness is actually a state in existence in an absolute form.So we may consider that elementary particles are first created spontaneously out of nothingness, which being in motion then create space and time and the corresponding quantum field. More numbers and varieties of elementary particles are created which interact to produce composite particles, which then create matter objects. Particles may collide and annihilate going back into the state of nothingness and reappear as other particles. This process goes on and on over time with particles being always in motion in space both as elementary and composites.Now let us try to correlate the above state of nothingness to physical reality by looking at various physical phenomena and characteristics of nature by way of seeking a proof for the existence of nothingness.• Elementary particles of the same type are identical: This is possible when they are produced from the same source by the same process and with the same recipe, and at all times. Nothingness meets all these criteria and so at all times elementary particles are primarily created out of nothingness only.• Particles and anti-particles: Elementary particles are produced simultaneously as pairs of particles/ anti-particles spontaneously out of nothingness, which is a direct vindication of the existence of the state of nothingness.• Conservation of total energy: Since nothingness acts as the only primary source and the ultimate destination of all the mass-energy of elementary particles, while their motion-energy and position-energy are frame dependent; in every physical process that takes place total energy will remain unaltered, as is always the case.• Particle/anti-particle annihilation: With head on collision or starting from rest, the particle/anti-particle pair loses all its properties except mass-energy, which is converted into lethargy as both particles enter into nothingness and thereafter only new particles can come out of the state of nothingness.• Particle decay: A decaying elementary particle first enters into nothingness losing all its properties except mass-energy which is transformed into lethargy and then a new particle or particles may come out with mass-energy equivalent of respective amount of lethargy and in case the decaying particle has an electric charge then the field at the point where it enters into nothingness retains the charge which is carried away later by one of the new particles that emerge.• Quantum entanglement: The two entangled particles are separated by nothingness allowing information to travel between them instantaneously with simultaneity because the state of nothingness offers no medium separating the two entangled particles. Moreover, each particle may act as either the source or the destination for the other particle in reciprocity with only nothingness between them, so it may appear to influence the past through an action in the future.• Quantum tunneling: This becomes possible in a seemly situation due to the state of nothingness allowing a particle to enter into and reappear out of nothingness.• Constituent principle: This is compatible with the state of nothingness since all matter is composed of and must end up into elementary constituent particles only that may appear out of and disappear into nothingness. • Causality principle: This is compatible with the state of nothingness as there must be a cause for an elementary particle to primarily come into existence, which is the spontaneous production phenomenon out of nothingness.• Covariance principle: This is compatible with the state of nothingness, as it exists equally and uniformly anywhere and everywhere.• Invariance principle: This is compatible with nothingness as it exhibits symmetry.• Equiprobability principle: This is compatible with the state of nothingness, since it always exists as a possibility.
as the sole property of nothingness and mass
of a particle as the result of electric and magnetic energy being in oscillatory transition inside an amount of space thus forming the particle [1], we may unreservedly postulate that a spontaneous decoupling of lethargy simultaneously produces a particle with mass and the electromagnetic field along with space. This may be vindicated by the fact that every such creation results in a particle and anti-particle pair and in reciprocity the annihilation of the pair converts the energy into lethargy, needing no particle or medium, as the sole plausible property of nothingness.The concepts of both lethargy and nothingness are abstract in nature with no direct observation or physical measurement being possible. As regards nothingness we cannot devise an experiment to prove what does not exist. Similarly for lethargy we may only indirectly justify the property assuming that decoupling of it produces particle mass and energy. However, the postulate that elementary particles go in and out of nothingness during the process of transformation into other elementary particles due to annihilation or decay, may call for an experimental observation of the values of mass, momentum and energy before and after the transformation, perhaps through a controlled experiment and in a collider such as the LHC, which may be a too futuristic yet a worthy feasible trial. As an aside, the state of nothingness may be visualized as a black box in an open system where outputs may be obtained as spontaneous creations or as assisted creations due to stimuli (or inputs). So an observer may devise an experiment with a control input as a stimulus in order to observe and interpret the output.Another stimulating corollary may be derived out of the above. The quantum state of nature appears to be the direct consequence of un-assisted spontaneous creation of elementary particles out of nothingness, limiting the dimensions to the minimum only. Starting with the fundamental physical entities like quantum length, quantum action and quantum slowness, nature provides for each and every other physical quantity a quantum characteristic by virtue of its being related to the primary creation out of nothingness and precisely adhering to the constituent principle thereafter. So upon creation, an elementary particle is born free, undertakes a motion with quantum slowness going through all possible transformations and unions with other similar particles.Once created out of nothingness, the elementary particles of all equiprobable and possible characteristics, resulting in being both stable and unstable particles, continue through the processes of annihilation, decay etc. transforming into other elementary and composite particles as well, while obeying the principles of probability and permutation and combination only [1] [2]. This is the reason it takes billions of years to set into a formalism of its own, although every change that takes place is due to the effect of an exogenous cause in local proximity. Thus is created the fabric of matter and space and often unleashing the inherent energy due to high-energy collision and scattering.While spontaneous creation out of nothingness will always produce a pair of particle/anti-particle, there may be production of a single particle or anti-particle only, in case of assisted creation. At any time after creation a particle or an anti-particle, (from now on we will mention particle only for simplicity), may enter into nothingness, as a purely natural probabilistic affinity or before or after being a product of annihilation, decay, transmutation, radioactivity or any other particle-particle interaction causing a new particle or particles to emerge with equal or different mass value and other related attributes; which all are considered as cases of assisted creation, with causal relation between the particle and the state of nothingness, which may accommodate a differential mass value as well, without violating the conservation principle. However, any electric charge carried by a particle will be retained in the field at the point where it enters into nothingness and will thereafter be carried away by a new particle created out of nothingness. In this way, all elementary particles will continue to have an in-out relation with the state of nothingness, embracing each and every form of particle interaction at any stage after being created spontaneously. Moreover, when a particle, elementary or composite, undertakes motion in space it exchanges its position with a virtual particle coming out of nothingness, as an assisted creation by virtue of the motion of the particle, resulting in a dual wave-particle quantum motion [1].So we may summarize the above particle/anti-particle creation as follows noting that the propensity for creation of a particle is either spontaneity or assistance due to the effect of interaction and motion.• Spontaneous creation of particle/anti-particle pair out of nothingness• Natural annihilation of particle/anti-particle going into nothingness• Natural decay of unstable particles going into nothingness• Assisted creation of particle out of nothingness following annihilation, decay etc.• Assisted creation of virtual particle out of nothingness due to motion of a particle
, gravitational constant
and speed of light
.
Note that in spite of the quantum nature of every physical quantity, we have not considered quantum mass, energy or momentum, as there cannot exist any, whereas we have redefined Planck mass
by a new name of Quantum gravitational mass, the reasons for which will be explained later in this treatise.Moreover, we have expressed the analytical form of each of quantum length, quantum time and quantum gravitational mass as a constant multiple of a new physical quantity, to be called as Quantum gravitational momentum
, having the dimension
, the second time rate of change of volume and this aspect will also be explained later in this treatise. As an aside, the term momentum is used here as being the generator of motion for gravitation, in apparent symmetry.Also we may note that the same quantity can be written as
in consideration of symmetry with the conventional expression of momentum.
separated by a spatial distance
and also free from any other exogenous interaction. Then the symmetry will be interrupted and they will have mutual interaction through the exchange of photons. But again from symmetry only the effect of interaction of one over the other will be uniformly distributed along the distance
so that the strength of the mutual interaction will be proportional to
and the resultant effect will be
and we will arrive at Coulomb's relation defining the Electric constant
. Similarly, with a time rated relation (instead of space rated relation as above) we will arrive at Ampere's relation
defining the Magnetic constant
. Since quantum space and time are interrelated by the quantum slowness factor
we see that the above two relations are interchangeable meaning they are the manifestation of the same combined electromagnetic effect due to two electric charges interacting between them and we arrive at the physical significance of the parameter
which will affect the motion of the photons since the actual slowness factor will depend on the dielectric property of the intervening medium separating the charged particles.For strong and weak interactions, following the symmetry, respective mediating particles are generated out of nothingness and they carry the energy and momentum causing the interactions between and among the interacting particles.Nothingness is the only abode of all elementary particles e.g. Bose-particles and Fermi-particles. Also elementary particles only can be produced due to spontaneous decoupling of lethargy into mass and by further decoupling of mass into energy. Elementary particles only can get into nothingness and come out of nothingness carrying energy and momentum. All processes of particle annihilation and decay are mediated through the state of nothingness. While both Bose-particles and Fermi-particles can enter into nothingness and come out of nothingness as new particles at the end of the respective process, only Bose-particles can carry energy and momentum during the intermediate stage, as they alone disobey the exclusion principle.Nothingness has only one dimension, which is lethargy, and therefore all other dimensions get folded up as the elementary particles enter into the state of nothingness and the total mass-energy and the motion-energy of one particle relative to the other, get converted into lethargy of the state of nothingness. The following dimensional analysis will show how all three fundamental dimensions of nature are folded into lethargy.
So when matter particles are generated by spontaneous creation of elementary particles out of nothingness, all three principal dimensions of nature get unfolded creating space, time and motion of matter particles carrying energy and momentum. Sometimes decay through Bose-particles causes generation of new particles being more massive than the initial particles, and this is possible because they gather additional mass out of the lethargy of nothingness and later either give back to nothingness or change into other particles having lower mass values.
The first relation tells us that the Quantum length is achieved as the product of lethargy of Quantum gravitational mass and the Gravitational constant. The second relation states that the same Quantum length can be achieved by the Quantum gravitational momentum multiplied by the square of the Quantum slowness factor, having a notable symmetry with the mass-energy relation
.The latter relation can further be extended in saying that when coupled with the Electromagnetic parameter, the Quantum gravitational momentum results into Quantum length
, implying a motion simply due to the property of mass and in relation with the electromagnetic property of space, in absence of any other exogenous interaction or exchange of mediating particles carrying energy and momentum.For the same reasons cited above, we have earlier named the respective quantities as Quantum gravitational mass and Quantum gravitational momentum.Now if another similar particle or a system of closely-held similar particles appears in its vicinity, the symmetry will be broken and in case they form a common mass-center with a mass value equal to Quantum gravitational mass
we may presume that each will tend to gravitate towards the common mass-center. This is the fundamental principle of gravitation, which is therefore, a phenomenon instead of an interaction, and it is self-actuated due to the particle having the property of mass in conjunction with the electromagnetic property of space.Let us consider the case of two neutral particles with equal mass
separated by a spatial distance
with no other exogenous effects. As an individual particle each will have no motion but in the vicinity of one another, the symmetry will be broken and they will have mutual effects of one upon the other. By the same logic as for the charged particles, the effect of each on the other will be proportional to
and the resultant combined effect as
since no other property of the particle will be involved (being absent actually) and the combined effect will be the relation defining the Gravitational constant
as being merely a proportionality constant. There will, however, be no time rated relation with the (intrinsic) mass values of the particles (unlike the case of electric charges which are subject to vary with both time and space).Logically there cannot be any exchange of particles (like photons) carrying energy and momentum. So instead of creating an interaction, the mutual effects will result in self-generated motion of the particles in order to create a new symmetry, which will be nothing but the particles moving towards each other (same like falling freely through space towards each other) with the desire to end up in a common mass-center similar to a single particle in space. So this will result in a so-called gravitational attraction which will be purely due to the particles having their intrinsic property of mass and in the true sense gravitation shall not be an interaction like other forms of interaction (by particle exchange) but it will be a self-generated motion through space having the property of the electromagnetic parameter.An identical inference can be drawn by considering Raychadhuri equation which relates the second time rate of volume change of the imaginary sphere comprising the above two particles at the ends of a diameter, which will undergo a reduction in length as multiples of the Quantum length in the same proportion as the mass value of the common mass-center of the above sphere relates to Quantum gravitational mass.Now when a large number of such particles or group of particles are in the vicinity of one another, each such mass-center will tend to gravitate to another similar mass-center, of which it is a constituent and this will go on and on as a result of which the locus of the path of any such particle or group of particles will appear as a curved path in space-time akin to the geodesic path formulated under General Relativity (GR). This is therefore a quantum explanation of GR.As a corollary to the above mentioned observation, we may note that for any particle, elementary or composite, free from any exogenous interaction, if the mass of the particle is less than Planck mass or Quantum gravitational mass
, then instead of a translatory motion in a definite direction purely under gravitation the particle will still undergo a jittery motion only, characteristic of the quantum state of the particle. This vindicates the fact that every elementary particle has a mass and the archetypical fidgety motion of the particle is due to self-gravitational effect in view of its having the property of mass only, since in free space every direction is equiprobable.A continuation of thinking along a similar line may allow us to find an answer for the subtle spectacle of neutrino oscillation. In order to explain this phenomenon, the theory stipulates that an observed neutrino flavor state is a superposition of different mass eigenstates, which alternate over long distances of their travel through space. While the neutrino with its virtually imperceptible mass travels in a stream of particles over enormous distances, it undergoes continuous mutual attrition as also intermittent scattering with other particles it meets along its way, as a result of which some of the neutrino particles routinely endure changes in the values of their intrinsic angular frequency, thereby converting them into neutrinos with higher or lower mass scale in view of the analytical relationship with usual notations
[1]. Unlike any other elementary particle this is possible in case of a neutrino only having a non-zero yet tiny mass value, being neutral and as a Fermi-particle having a half-integer spin.The nature of space and its composition has long been considered as an unsolved dilemma. I have envisioned space as being created by the motion of a particle, which, at any instance is essentially a linear translatory motion in a definite direction. This linear transition along any arbitrarily oriented axis in space may be logically conceived as being equivalent of an apparent simultaneous motion in any three mutually perpendicular directions, and therefore, arguably an infinite number of, yet equiprobable, such mutually perpendicular axes may be perceived together to create the hollow of a space.The phenomenon of gravitation or more precisely self-gravitation is the primary cause of motion of a particle having a mass, independent of any other superimposed exogenous interaction, which creates space and consequently time too. Depending on the nature and all other attributes of the particle, a field is created in space, and then it may interact with other particles present in its vicinity. In simple words, we are continuously falling through space under gravitation and creating space along our way.
for a quantum time
in view of the limiting value of quantum slowness
and ending in a quantum action
while considering the particle to be of extended version [1] having an intrinsic linear dimension
instead of being a mathematical point, we may avoid singularity at all times. Considering a particle to be always in motion and the concept of motion as valid only when the particle undertakes a motion covering the quantum length in space, we may avoid the particle assuming a stationary point position or singularity in spacetime.
, angular frequency
, intrinsic linear dimension
and the speed of light
in relation to its spin angular momentum
.
Dark matter is expected to be comprised of a new type of uncharged elementary Fermi-particles, beyond the third generation of particles in the Standard Model, with very large spin angular momentum and consequently being highly massive, yet with very low angular frequency and thus being extremely stable.From the above analytical relationships it may be noted that the ratio of the spin angular momentum and mass of the particle
may remain fairly unchanged like any other Fermi-particle of the first generation, along with the corresponding low angular frequency, thereby ensuring great stability of the particle; whereas both the spin angular momentum and the corresponding mass value of the particle may go up to any high.When produced in a particle collider, the dark matter particles coming out with transverse momentum will accompany well-defined high-energy high-momentum tracks and will be all alone only without any other particles associated with them. So observers should look out for a similar situation to be detected.As an aside, in my view, both in nature and in a particle collider, a multitude of particles well beyond the first three generations of particles as in the Standard Model are generally produced, albeit mostly being highly unstable continue to remain undetected, however, considering symmetry and possibility, there should be particles which are also extremely stable and these are the particles which manifest as dark matter particles in outer space and should be produced and detected by a particle collider experiment.
, with the usual notations, meaning that in outer space where the average mass density is a rarity, there exists a negative pressure or negative energy, named as dark energy, causing the observed accelerating expansion of space. Before proceeding further, we need to assume the principle of isotropy and homogeneity to be true, and so also the all encompassing presence of both dark matter and dark energy fairly uniformly throughout the universe, while being far more prevalent and so relevant in the outer cosmos inside the intergalactic space.A look at the above relation suggests that we may rewrite it along with considering the negative sign in front of the volume factor instead of pressure as
and then again using the notations for lethargy
and combined electric and magnetic constants, as 
which implies that following the symmetry of mass-energy-lethargy relations formulated by us earlier, pressure coupled with electromagnetic parameter of space will give rise to an equivalence of lethargy per negative unit volume of space decoupled by electromagnetic parameter. Since lethargy is a property of nothingness which can also accommodate a negative volume albeit mathematically, being actually devoid of any space, we may infer that the universe undergoes through the process of creating new space out of nothingness to equate with the negative value and restoring the overall value to nil. In other words, in outer space where the mass density is extremely low, pressure has the effect of creating new space resulting in an accelerating expansion of the universe.
and so the gravitational constant
attains an extremely low value ensuring the value of Planck mass be quite high compared to, say proton or an elementary particle, and consequently the effective magnitude of Quantum gravitational momentum 
being the generator of gravitational motion is extremely low in relation to the strength of weak interaction.