Physics

We intend to study a new class of cosmological models in f(R,T) modified theories of gravity, hence define the cosmological constant Λ as a function of the trace of the stress energy-momentum-tensor T and the Ricci scalar R , and name such a model " Λ(R,T) gravity" where we have specified a certain form of Λ(R,T) . Λ(R,T) is also defined in the perfect fluid and dust case. Some physical and geometric properties of the model are also discussed. The pressure, density and energy conditions are studied both when Λ is a positive constant and when Λ=Λ(t) , i.e a function of cosmological time, t. We study the behaviour of some cosmological quantities such as Hubble and deceleration parameters. The model is innovative in the sense that it has been described in terms of both R and T and display a better understanding of the cosmological observations.

The theoretical and experimental evidence regarding the use of (J + 1/2) squared and J(J + 1) as a functional in formulae for rotational term values in the spectral analysis of a diatomic molecule in electronic state singlet-Sigma is scrutinised. The infrared spectra of HCl serve as examples of the application of the two functionals. Tbe total evidence indicates that (J + 1/2) squared is preferable to J(J + 1) for the stated purpose, confirming Mulliken's statement in 1930.

Teleparallel gravity is a modified theory of gravity in which the Ricci scalar R of the Lagrangian replaced by the general function of torsion scalar T in action. With that, cosmology in teleparallel gravity becomes profoundly simplified because it is second-order theory. The article present a complete cosmological scenario in f(T) gravity with f(T)=T+β(−T ) α , where α, and β are model parameters. We present the profiles of energy density, pressure, and equation of state (EoS) parameter. Next to this, we employ statefinder diagnostics to check deviation from the Λ CDM model as well as the nature of dark energy. Finally, we discuss the energy conditions to check the consistency of our model and observe that SEC violates in the present model supporting the acceleration of the Universe as per present observation.

The Universe has a gravitational horizon with a radius R_h=c/H coincident with that of the Hubble sphere. This surface separates null geodesics approaching us from those receding, and as free-falling observers within the Friedmann-Lemaitre-Robertson-Walker spacetime, we see it retreating at proper speed c, giving rise to the eponymously named cosmological model R_h=ct. As of today, this cosmology has passed over 25 observational tests, often better than LCDM. The gravitational/Hubble radius R_h therefore appears to be highly relevant to cosmological theory, and in this paper we begin to explore its impact on fundamental physics. We calculate the binding energy of a mass m within the horizon and demonstrate that it is equal to mc^2. This energy is stored when the particle is at rest near the observer, transitioning to a purely kinetic form equal to the particle's escape energy when it approaches R_h. In other words, a particle's gravitational coupling to that portion of the Universe with which it is causally connected appears to be the origin of rest-mass energy.

The problem of how to interpret quantum mechanics has persisted for a century. The disconnect between the wavefunction state vector and what is observed in experimental apparati has had no shortage of explanations. But all explanations so far fall short of a compelling and complete interpretation. In this letter, I present a novel interpretation called dynamic histories. I show mathematically how quantum mechanics can be reinterpreted as deterministically evolving dynamical world lines in a 5D universe. Quantum probabilities can be then be reinterpreted as stemming from ignorance of the state of our own world line. Meanwhile, the lack of observed superposition in experimental apparati is explained in that we only live on a single history with a definite set of properties. Hence, superposition is not an actual state of a particle but a model of ignorance as in classical probability theory. This explains nonlocal effects without superluminal communication. I also discuss how this relates to 5D Kaluza-Klein theory.

In the present paper, the nonlinear differential equation of pendulum is investigated to find an exact closed form solution, satisfying governing equation as well as initial conditions. The new concepts used in the suggested method are introduced. Regarding the fact that the governing equation for any arbitrary system represents its inherent properties, it is shown that the nonlinear term causes that the system to have a variable identity. Hence, the original function is included as a variable in the solution to can take into account the variation of governing equation. To find the exact closed form solution, the variation of the nonlinear differential equation tends to zero, where in this case the system with a local linear differential equation has a definite identity with a definite local answer. It is shown that the general answer is an arbitrary curve on a surface, a newly developed concept known as super function, and different initial conditions give different curves as particular solutions. The comparison of the results with those of finite difference shows an exact agreement for any arbitrary amplitude and initial conditions.

There are some particle physics theories that go beyond the so-called "standard cosmological model" to predict the existence of magnetic monopoles\,(MMs). The discovery of magnetic monopoles would be an incredible breakthrough in high-energy physics. The existence of MMs in the early Universe has been speculated and anticipated from Grand Unified Theory. If MMs exist, the inverse powers of the unification mass will not suppressed the baryon number violating effects of grand unified gauge theories. Therefore, MM catalyzing nucleon decay is a typical strong interaction. This phenomenon is due to the boundary conditions that must be imposed on the core of MM fermion fields. We present a possible mechanism to explain the formation of the Hot Big Bang Cosmology. The main ingredient in our model is nucleon decay catalyzed by magnetic monopoles (i.e., the Rubakov-Callan effect). It is shown that Hot Big Bang developed naturally, because the luminosity due to the Rubakov-Callan effect is much greater than the Eddington luminosity (i.e., L m > 10 4 L Edd ).

A few physicists have recently constructed the generating compatibility conditions (CC) of the Killing operator for the Minkowski (M) , Schwarzschild (S) and Kerr (K) metrics. They discovered second order CC, well known for M, but also third order CC for S and K. In a recent paper, we have studied the cases of M and S, without using specific technical tools such as Teukolski scalars or Killing-Yano tensors. However, even if S( m ) and K( m,a ) are depending on constant parameters in such a way that S → M when m→0 and K → S when a→0 , the CC of S do not provide the CC of M when m→0 while the CC of K do not provide the CC of S when a→0 . In this paper, using tricky motivating examples of operators with constant or variable parameters, we explain why the CC are depending on the choice of the parameters. In particular, the only purely intrinsic objects that can be defined, namely the extension modules, may change drastically. As the algebroid bracket is compatible with the {\it prolongation/projection} (PP) procedure, we provide for the first time all the CC for K in an intrinsic way, showing that they only depend on the underlying Killing algebras and that the role played by the Spencer operator is crucial. We get K < S < M with 2<4<10 for the Killing algebras and explain why the formal search of the CC for M, S or K are strikingly different, even though each Spencer sequence is isomorphic to the tensor product of the Poincaré sequence for the exterior derivative by the corresponding Lie algebra.

We propose a new system for the fundamental units, which includes and goes beyond the present redefinition of the SI, by choosing also c=ℏ=1 . By fixing c= c ∘ m/s = 1, ℏ= ℏ ∘ Js = 1 and μ ∘ – – – = μ ∘ N/A 2 = 1, it allows us to define the metre, the joule, and the ampere as equal to (1/299 792 458) s, (1/ ℏ ∘ =.948...× 10 34 ) s −1 and μ ∘ N − − − − √ = μ ∘ c ∘ / ℏ ∘ − − − − − − √ s −1 =1.890...× 10 18 s −1 . It presents at the same time the advantages and elegance of a system with ℏ=c= μ ∘ – – – = ϵ ∘ – – =k= N A =1 , where the vacuum magnetic permeability, electric permittivity, and impedance are all equal to 1. All units are rescaled from the natural ones and proportional to the s, s −1 , s −2 , ... or just 1, as for the coulomb, ohm and weber, now dimensionless. The coulomb is equal to μ ∘ c ∘ / ℏ ∘ − − − − − − √ =1.890...× 10 18 , and the elementary charge to e=1.602...× 10 −19 C= 4πα − − − √ =.3028... . The ohm is equal to 1/ μ ∘ c ∘ so that the impedance of the vacuum is Z ∘ =376.730...Ω=1 . The volt is 1/ μ ∘ c ∘ ℏ ∘ − − − − − − √ s −1 =5.017...× 10 15 s −1 , and the tesla c ∘ V/m = c 3 ∘ / μ ∘ ℏ ∘ − − − − − − √ s −2 =4.509...× 10 32 s −2 . The weber is 1/ μ ∘ c ∘ ℏ ∘ − − − − − − √ =5.017...× 10 15 . K J =483597. ... GHz/V =e/π= .09639..., and R K =25812. ... Ω=1/2α≃68.518 . One can also fix e = 1.602 176 634 × 10 −19 C, at the price of adjusting the coulomb and all electrical units with μ ∘ =4π× 10 −7 η 2 where η 2 ,∝α , is very close to 1.

The different interpretations of quantum mechanics yield the same experimental results, which may give the impression that the question of what interpretation is the true one, is a philosophical question, not a scientific one. But in this paper, we will see that we can actually prove one interpretation, in particular, a version of the ensemble interpretation, as the natural interpretation of quantum mechanics. Furthermore, we will prove the axioms of quantum mechanics, without the need of anything beyond probability theory.