The SI system of units in rotational mechanics yields correct numerical results, but it produces physically incorrect units of measure in many cases. SI units also violate the principle of general covariance—the gene...The SI system of units in rotational mechanics yields correct numerical results, but it produces physically incorrect units of measure in many cases. SI units also violate the principle of general covariance—the general rule for defining continuous coordinates and units in mathematics and mathematical physics. After 30+ years of wrestling with these problems, the ultimate authority on units of measure has declared that Newton–meter and Joule are not equivalent in rotational mechanics, as they are in the rest of physics. This article proposes a simple modification to SI units called “Nonstandard International units” (“NI units”) until a better name is agreed upon. NI units yield correct numerical results and physically correct units of measure, and they satisfy the principle of general covariance. The main obstacle to the adoption of NI units is the consensus among users that the radius of rotation should have the unit meter because the radius can be measured with a ruler. NI units assigned to radius should have units meter/radian because the radius is a conversion factor between angular size and circumferential length, as in arclength = rθ. To manage the social consensus behind SI units, the author recommends retaining SI units as they are, and informing users who want correct units that NI units solve the technical problems of SI units.展开更多
The paper starts examining some ideas of Einstein and Rovelli about space and spacetime in the context of the general theory of relativity and identifying a connection among them.I continue drawing a parallel between ...The paper starts examining some ideas of Einstein and Rovelli about space and spacetime in the context of the general theory of relativity and identifying a connection among them.I continue drawing a parallel between those ideas in the field of physics and the conception of space in mathematics according to Riemann’s revolutionary view,basis of the elaboration of the mathematical structures used in general relativity.In analogy with Einstein’s and Rovelli’s ideas about physical space,I come to formulate the idea that it is not appropriate to think that,in forming a riemannian manifold(the mathematical object representing spacetime),the metric field places itself in a space pre-existing to it and it may do this differently.According to this idea,I formulate a critical remark about Earman and Norton’s famous hole argument focused on the rejection of the active interpretation of general covariance.I compare then my critical remark about the hole argument with the position of Weatherall on it.I conclude with some critical remarks on moderate structural realism about spacetime and proposing an interpretation of Einstein’s assertion that spacetime“does not claim existence on its own,but only as a structural quality of the field”.展开更多
文摘The SI system of units in rotational mechanics yields correct numerical results, but it produces physically incorrect units of measure in many cases. SI units also violate the principle of general covariance—the general rule for defining continuous coordinates and units in mathematics and mathematical physics. After 30+ years of wrestling with these problems, the ultimate authority on units of measure has declared that Newton–meter and Joule are not equivalent in rotational mechanics, as they are in the rest of physics. This article proposes a simple modification to SI units called “Nonstandard International units” (“NI units”) until a better name is agreed upon. NI units yield correct numerical results and physically correct units of measure, and they satisfy the principle of general covariance. The main obstacle to the adoption of NI units is the consensus among users that the radius of rotation should have the unit meter because the radius can be measured with a ruler. NI units assigned to radius should have units meter/radian because the radius is a conversion factor between angular size and circumferential length, as in arclength = rθ. To manage the social consensus behind SI units, the author recommends retaining SI units as they are, and informing users who want correct units that NI units solve the technical problems of SI units.
文摘The paper starts examining some ideas of Einstein and Rovelli about space and spacetime in the context of the general theory of relativity and identifying a connection among them.I continue drawing a parallel between those ideas in the field of physics and the conception of space in mathematics according to Riemann’s revolutionary view,basis of the elaboration of the mathematical structures used in general relativity.In analogy with Einstein’s and Rovelli’s ideas about physical space,I come to formulate the idea that it is not appropriate to think that,in forming a riemannian manifold(the mathematical object representing spacetime),the metric field places itself in a space pre-existing to it and it may do this differently.According to this idea,I formulate a critical remark about Earman and Norton’s famous hole argument focused on the rejection of the active interpretation of general covariance.I compare then my critical remark about the hole argument with the position of Weatherall on it.I conclude with some critical remarks on moderate structural realism about spacetime and proposing an interpretation of Einstein’s assertion that spacetime“does not claim existence on its own,but only as a structural quality of the field”.
