Discrete and finite general relativity

Souza, Manoelito M de; Silveira, Robson N.

doi:10.1088/0264-9381/16/2/023

Cited by 3 publications

(5 citation statements)

References 6 publications

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“…Similar or related behavior have been proved for classical electrodynamics [5], Newtonian gravitation [6], general relativity [7] and, generically, for field theory [8].…”

supporting

confidence: 65%

Harmonic potential as an effective limit of a discrete classical interaction

Segatto¹,

Azevedo²,

Souza

2003

J. Phys. A: Math. Gen.

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Motivated by improving the understanding of the quantum-to-classical transition we use a simple model of classical discrete interactions for studying the discrete-to-continuous transition in the classical harmonic oscilator. A parallel is traced with gravity for stressing the relevance of such discrete interaction models. Fundamental interactions, according to quantum field theory, are realized through the exchange of interaction quanta-packets of matter-energy with defined quantum numbers, viz. momentum-energy, spin, electric charge, etc. Thei are discrete interactions, in contradistinction to the classical continuous picture. The Bohr's correspondence principle, a useful guideline in the early days of quantum mechanics, states that in the limit of very large quantum numbers the classical idea of continuity must result from the quantum discreteness as an effective description. It would be very interesting to see in a clear way how this transition discrete-to-continuous occurs. This is the objective of the present letter with the use of a simple model of discrete classical interaction for studying this transition in the classical simple harmonic oscillator. We should not forget, however, that the harmonic potential, although being an extremely useful tool in all branches of modern physics, is not itself a fundamental interaction, which, as well known, are just the gravitational, the electromagnetic, the weak and the strong interactions; actually it is just an effective description. This may just valorize the importance of studying how it can be understood as an effective * PIVIC-UFES

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“…Similar or related behavior have been proved for classical electrodynamics [5], Newtonian gravitation [6], general relativity [7] and, generically, for field theory [8].…”

supporting

confidence: 65%

Harmonic potential as an effective limit of a discrete classical interaction

Segatto¹,

Azevedo²,

Souza

2003

J. Phys. A: Math. Gen.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Similar or related behavior have been proved for classical electrodynamics [1], Newtonian gravitation [2], general relativity [3] and, generically, for field theory [4].…”

supporting

confidence: 65%

Harmonic potential as an effective limit of a discrete classical interaction

Segatto¹

2003

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

Motivated by improving the understanding of the quantum-to-classical transition we use a simple model of classical discrete interactions for studying the discrete-to-continuous transition in the classical harmonic oscilator. A parallel is traced with gravity for stressing the relevance of such discrete interaction models.Fundamental interactions, according to quantum field theory, are realized through the exchange of interaction quanta -packets of matter-energy with defined quantum numbers, viz. momentum-energy, spin, electric charge, etc. Thei are discrete interactions, in contradistinction to the classical continuous picture. The Bohr's correspondence principle, a useful guideline in the early days of quantum mechanics, states that in the limit of very large quantum numbers the classical idea of continuity must result from the quantum discreteness as an effective description. It would be very interesting to see in a clear way how this transition discrete-to-continuous occurs. This is the objective of the present letter with the use of a simple model of discrete classical interaction for studying this transition in the classical simple harmonic oscillator. We should not forget, however, that the harmonic potential, although being an extremely useful tool in all branches of modern physics, is not itself a fundamental interaction, which, as well known, are just the gravitational, the electromagnetic, the weak and the strong interactions; actually it is just an effective description. This may just valorize the importance of studying how it can be understood as an effective * PIVIC-UFES

show abstract

“…In this work we propose an alternative iterative approach to obtain the potential of Yukawa, based in the works M. M. de Souza [17] where the classical electromagnetic field of a spinless point electron was described in a formalism with extended causality by discrete finite point-vector fields with discrete and localized point interactions (the same formalism were used to described the general relativity homogeneous field equations [18]). The intention was not to propose a better or simpler approach to the usual ones.…”

Section: Discussionmentioning

confidence: 99%

“…Let us consider that the field-generating particle (gravitational or electric) is at the origin of the considered coordinate system and that the test particle is in the position r 0 with momentum p 0 and that r 0 < 1 with δr j << 1, this ensures that the two particles are very close to each other (such as inside a nucleus). We will also consider δt j << 1, this ensures that the iterative process approaches the continuous fields picture as expected, it is important to note that there are analytic approaches in which the fields are considered as discrete, [17][18][19] is not the case in question. Defining the time increment as being constant, i.e., δt j ≡ ω > 0, equations ( 11) and ( 10) then become…”

Section: Obtaining the Yukawa Potentialmentioning

confidence: 99%