One-dimensional physical quantities

In the present paper, we present operational definitions of the physical quantities distance, mass and time. Attempts to formulate a well-based operational definition of physical entities were first proposed in the end of the 19-th century by Hermann von Helmholtz and Otto Hölder. The problem consists in finding how to associate a number (the value of the entity) with a non-numerical entity (the entity itself). The paper presents a modern reading of the above mentioned authors. Paraphrasing Feynman in his classic work on path integrals, “there is a pleasure in recognizing old things from a new point of view”.

Keywords:
physical quantities; measurement theory; operational definition

Authorship

G. F. Vasconcelos Júnior

Universidade Federal de Juiz de Fora, Departamento de Física, Juiz de Fora, MG, BrasilUniversidade Federal de Juiz de ForaBrasilJuiz de Fora, MG, BrasilUniversidade Federal de Juiz de Fora, Departamento de Física, Juiz de Fora, MG, Brasil

R. P. S. Costa

B. F. Rizzuti ^**Endereço de correspondência: brunorizzuti@fisica.ufjf.br.

*Endereço de correspondência: brunorizzuti@fisica.ufjf.br.

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables | Formulas

Figures (6)
Tables (2)
Formulas (42)

Grandeza	Espaço de valores	Base
G	$V_{G}$	$\{U_{g}\}$
$G G = G^{2}$	$V_{G} \otimes V_{G}$	$\{U_{g} \otimes U_{g} = U_{g}^{2}\}$
$\dots$	$\dots$	$\dots$
$G^{n} G \overset{d e f .}{=} G^{n + 1}$	$\underset{n vezes}{\underset{︸}{V_{G} \otimes \dots \otimes V_{G}}} \otimes V_{G}$	$\{U_{g}^{n} \otimes U_{g} = U_{g}^{n + 1}\}$

Inversa	Espaço de valores	Base
$G^{- 1}$	$V_{G}^{- 1}$	$\{U_{g}^{- 1}\}$
${(G^{2})}^{- 1}$	$V_{G}^{- 1} \otimes V_{G}^{- 1}$	$\{U_{g}^{- 1} \otimes U_{g}^{- 1} = U_{g}^{- 2}\}$
$\dots$	$\dots$	$\dots$
${(G^{n + 1})}^{- 1}$	$\underset{n vezes}{\underset{︸}{V_{G}^{- 1} \otimes \dots \otimes V_{G}^{- 1}}} \otimes V_{G}^{- 1}$	$\{U_{g}^{- n} \otimes U_{g}^{- 1} = U_{g}^{- (n + 1)}\}$