Papers by Nilton Penha Silva
A mathematical expression for the recessional redshift z_rec of astronomical sources of light is ... more A mathematical expression for the recessional redshift z_rec of astronomical sources of light is derived based on the Universe expansion factor proposed by Silva [1]. Numerical calculations are done by using the following: Hubble constant H0 = 69.32 km s^−1 M pc ^−1 = 0.0709 Gyr ^−1 and the current age of the Universe T0 = 13.772 Gyr [2]. The recessional redshift increases with increasing lookback distances d_lb , initially in a linear manner (z_rec = H0 c d_lb) and then in a positively accelerated way reaching the maximum value of exp(H0 T0/ β) − 1 = 4.377 at d^lb = c T0. The linear part should hold up to the lookback distance of 0.8 M pc. The receding velocities v rec are also expressed in terms of the recessional redshifts z_rec ; they grow up linearly (v_rec = c z_rec) until z_rec = 0.2. Receding velocities above 0.845 Gly/Gyr and recessional redshifts above 1.610 occur in the matter era.
The following Universe's expansion factor a(t) = exp H 0 T 0 β t T 0 β − 1 , where β = 1 ... more The following Universe's expansion factor a(t) = exp H 0 T 0 β t T 0 β − 1 , where β = 1 + H 0 T 0 − 1 2 Ω m (T 0) + Ω Λ (T 0) − 1 has been introduced in a previous paper. One considered that the ingredients acting on the Universe's expansion (t > 4 × 10 12 s ≈ 1.3 × 10 −4 Gyr) are mainly matter (baryons plus dark matter) and dark energy, both treated as perfect fluids. Such expansion factor and the current measured values of Hubble constant H 0 , the Universe's current age T 0 , the current matter density parameter Ω m (T 0) and current dark energy parameter Ω Λ (T 0) indicate that that our Universe may have had a negative expansion acceleration up to the age T = 1−β H 0 T 0 1 β = 3.214 Gyr (matter era) and positive after that (dark energy era), leading to an eternal expansion. An interaction between matter and dark energy is indicated to exist.
Gravity dominated Universe until it was 3.214 Gyr old and, after that, dark energy dominates lead... more Gravity dominated Universe until it was 3.214 Gyr old and, after that, dark energy dominates leading to an eternal expansion, no matter if the Universe is closed, flat or open. That is the prediction of the expansion factor recently proposed by Silva [2]. It is also shown that there is an upper limit for the size of the Observable Universe relative radial comoving coordinate, beyond which nothing is observed by our fundamental observer, on Earth. Our Observable Universe may be only a tiny portion of a much bigger Universe most of it unobservable to us. This leads to the idea that an endless number of other fundamental observers may live on equal number of Observable Universes similar to ours. An unique Big Bang originated an unique Universe, only part of it observable to us.
arXiv: General Physics, 2007
A two-dimensional Minkowski spacetime diagram is neatly represented on a Euclidean ordinary plane... more A two-dimensional Minkowski spacetime diagram is neatly represented on a Euclidean ordinary plane. However the Euclidean lengths of the lines on the diagram do not correspond to the true values of physical quantities in spacetime, except for those referring to the stationary reference frame. In order to extend its abilities to other inertial reference frames, we derive a factor which, multiplied by the magnitude of the actually displayed values (on the diagram), leads to the corresponding true measured values by any other inertial observers. Doing so, the student can infer from the Euclidean diagram plot the expressions that account for Lorentz length contraction, time dilation and also Lorentz Transformations just by using regular trigonometry.
Based on the Universe's scale factor introduced by Silva [1], we derive an expression for the rec... more Based on the Universe's scale factor introduced by Silva [1], we derive an expression for the receding velocities of arbitrary astronomical objects, which increase linearly up to the lookback distance of 2.1 × 10 3 Mpc and after that they increase in a positively accelerated way. The linear part corresponds to the Hubble'law.
arXiv: General Physics, 2007
This paper has pedagogical motivation. It is not uncommon that students have great difficulty in ... more This paper has pedagogical motivation. It is not uncommon that students have great difficulty in accepting the new concepts of standard special relativity, since these seem contrary to common sense. Experience shows that geometrical or graphically exposition of the basic ideas of relativity theory improves student understanding of the algebraic expressions of the theory. What we suggest here may complement standard textbook approaches.
One introduces an ansatz for the expansion factor a(t) = e(H(t)t−H0T0)/β for our Universe in the ... more One introduces an ansatz for the expansion factor a(t) = e(H(t)t−H0T0)/β for our Universe in the spirit of the FLRW model; β is a constant to be determined. Considering that the ingredients acting on the Universe expansion (t > 4 × 1012 s ≈ 1.3 × 10−5 Gyr) are mainly matter (baryons plus dark matter) and dark energy, one uses the current measured values of Hubble constant H0, the Universe current age T0, matter density parameter Ωm(T0) and dark energy parameter ΩΛ(T0) together with the Friedmann equations to find β = 0.5804 and that our Universe may have had a negative expansion acceleration up to the age T⋆ = 3.214 Gyr (matter era) and positive after that (dark energy era), leading to an eternal expansion. An interaction between matter and dark energy is found to exist. The deceleration q(t) has been found to be q(T⋆) = 0 and q(T0) = −0.570.
arXiv: General Physics, 2007
Starting with two light clocks to derive time dilation expression, as many textbooks do, and then... more Starting with two light clocks to derive time dilation expression, as many textbooks do, and then adding a third one, we work on relativistic spacetime coordinates relations for some simple events as emission, reflection and return of light pulses. Besides time dilation, we get, in the following order, Doppler k-factor, addition of velocities, length contraction, Lorentz Transformations and spacetime interval invariance. We also use Minkowski spacetime diagram to show how to interpret some few events in terms of spacetime coordinates in three different inertial frames.
arXiv: General Physics, 2007
We discuss a superluminal unphysical motion which, we believe, has a high pedagogical potential. ... more We discuss a superluminal unphysical motion which, we believe, has a high pedagogical potential. It highlights the physics behind the concept of simultaneity in special relativity and illustrates the non-physical character of superluminal speeds offering a rewarding exercise in handling the Minkowski space-time diagram.
Usando o metodo das ondas planas simetrizadas e um modelo simples de potencial, a tres parâmetros... more Usando o metodo das ondas planas simetrizadas e um modelo simples de potencial, a tres parâmetros, que consiste de pocos retangulares, envolvendo cada atomo e um potencial delta repulsivo, centrado nos nucleos, simulamos os semicondutores PbTe, PbSe e PbS. Os resultados para as bandas de energia estao em concordância com os dados experimentais. A mesma natureza para as transicoes nos tres compostos e encontrada, em compatibilidade com a relacao experimental entre elas e o parâmetro da rede cristalina.
While Einstein clocks synchronization process is performed, one has a well defined region in whic... more While Einstein clocks synchronization process is performed, one has a well defined region in which the clocks are synchronized and another one in which the clocks are not yet synchronized. The frontier between them evolves differently from the perspective of observers in relative motion. A discussion is conducted upon direct observation of the phenomenon and Minkowski diagrams.
where β = 0.5804, was proposed for the expansion factor of our Universe. According to it, gravity... more where β = 0.5804, was proposed for the expansion factor of our Universe. According to it, gravity dominates the expansion (matter era) until the age of T⋆ = 3.214 Gyr and, after that, dark energy dominates (dark energy era) leading to an eternal expansion, no matter if the Universe is closed, flat or open. In this paper we consider only the closed version and show that there is an upper limit for the size of the radial comoving coordinate, beyond which nothing is observed by our fundamental observer, on Earth. Our observable Universe may be only a tiny portion of a much bigger Universe most of it unobservable to us. This leads to the idea that an endless number of other fundamental observers may live on equal number of Universes similar to ours. Either we talk about many Universes — Multiverse — or about an unique Universe, only part of it observable to us.
ABSTRACT To test the efficiency of the continued freaction expansion method an a priori known ana... more ABSTRACT To test the efficiency of the continued freaction expansion method an a priori known analytical curve F(ω) is started, the static moments are calculated and then, applying the cutoff's most used in the literature, the approximated curves are compared with the original ones. It is shown that, except in some special cases, it is almost impossible to use the method when only the second and fourth moments are known. (Author)
Starting with two light clocks to derive time dilation expression, as many textbooks do, and then... more Starting with two light clocks to derive time dilation expression, as many textbooks do, and then adding a third one, we work on relativistic spacetime coordinates relations for some simple events as emission, reflection and return of light pulses. Besides time dilation, we get, in the following order, Doppler k-factor, addition of velocities, length contraction, Lorentz Transformations and spacetime interval invariance. We also use Minkowski spacetime diagram to show how to interpret some few events in terms of spacetime coordinates in three different inertial frames.
A two-dimensional Minkowski spacetime diagram is neatly represented on a Euclidean ordinary plane... more A two-dimensional Minkowski spacetime diagram is neatly represented on a Euclidean ordinary plane. However the Euclidean lengths of the lines on the diagram do not correspond to the true values of physical quantities in spacetime, except for those referring to the stationary reference frame. In order to extend its abilities to other inertial reference frames, we derive a factor which, multiplied by the magnitude of the actually displayed values (on the diagram), leads to the corresponding true measured values by any other inertial observers. Doing so, the student can infer from the Euclidean diagram plot the expressions that account for Lorentz length contraction, time dilation and also Lorentz Transformations just by using regular trigonometry.
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Papers by Nilton Penha Silva