No derradeiro segundo de 2006 pensem nisto:
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Absolutism vs. relationalism
The debate between whether space and time are real objects themselves, i.e., absolute, or merely orderings upon real objects, i.e., relational, began with a debate between Isaac Newton, through his spokesman Samuel Clarke, and Gottfried Leibniz in the famous Leibniz-Clarke Correspondence.
Arguing against the absolutist position, Leibniz offers a number of thought experiments aiming to show that assuming the existence of facts such as absolute location and velocity will lead to contradiction. These arguments trade heavily on two principles central to Leibniz's philosophy: the principle of sufficient reason and the identity of indiscernibles.
The principle of sufficient reason holds that for every fact there is a reason sufficient to explain why it is the way it is and not otherwise. The Identity of indiscernibles states that if there is no way of telling two entities apart then they are one and the same thing.
For example, Leibniz asks us to imagine two universes situated in absolute space. The only difference between them is that the second is placed five feet to the left of the first, a possibility available if such a thing as absolute space exists. Such a situation, however, is not possible according to Leibniz, for if it were:
a) where a universe was positioned in absolute space would have no sufficient reason, as it might very well have been anywhere else, hence contradicting the principle of sufficient reason, and
b) there could exist two distinct universes that were in all ways indiscernible, hence contradicting the Identity of Indiscernibles.
Standing out in Clarke's, and Newton's, response to Leibniz arguments is the bucket argument. Water in a bucket, hung from a rope and set to spin, will start with a flat surface. As the water begins to spin in the bucket, the surface of the water will become concave. If the bucket is stopped, the water will continue to spin, and while the spin continues the surface will remain concave. The concave surface is apparently not the result of the interaction of the bucket and the water, since the water is flat when the bucket first starts to spin, becomes concave as the water starts to spin, and remains concave as the bucket stops.
In this response, Clarke argues for the necessity of the existence of absolute space to account for phenomena like rotation and acceleration that cannot be accounted for on a purely relationalist account. Clarke argues that since the curvature of the water occurs in the rotating bucket as well as in the stationary bucket containing spinning water, it can only be explained by stating that the water is rotating in relation to some third thing, namely absolute space.
Leibniz describes a space that exists only as a relation between objects, and which therefore has no existence apart from the existence of those objects; motion exists only as a relation between those objects. Newtonian space provided an absolute frame of reference within which objects can have motion. In Newton's system the frame of reference exists independently of the objects which it contains; objects can be described as moving in relation to space itself. For two hundred years, the empirical evidence of the concave water surface held sway.
...
Stepping into this debate in the 19th century is Ernst Mach. Not denying the existence of phenomena like that seen in the bucket argument, he still denied the absolutist conclusion by offering a different answer as to what the bucket was rotating in relation to: the fixed stars.
Mach suggests that thought experiments like the bucket argument are problematic. Imagine a universe containing only a bucket; on Newton's account, this bucket could be set to spin relative to absolute space, and the water it contained would form the characteristic concave surface. But, in the absence of anything else in the universe, how could one confirm that the bucket was indeed spinning? It seems at least equally possible that the surface of the water in the bucket would remain flat.
Mach argued, in effect, that the water in a bucket in an otherwise empty universe would indeed remain flat. But introduce another object into the universe - a distant star, perhaps - and there is now something relative to which the bucket could be seen to be rotating. The water might now adopt a slight curve. As the number of objects in the universe increased, so the curvature of the water, up to the point that we see in the actual universe. In effect Mach argued that the momentum of an object, angular or linear, exists as a result of the sum of the effects of other objects in the universe - Mach's principle.
...
Einstein's relativistics are based on the principle of relativity, which holds that the rules of physics must be the same for all observers, regardless of the frame of reference they use. The greatest difficulty for this idea were Maxwell's equations which included the speed of light in vacuum, implying that the speed of light is only constant relative to the postulated luminiferous ether. However, all attempts to measure any speed relative to the ether failed. Einstein showed how special relativity's Lorentz transformations can be derived from the principle of relativity and the invariance of light speed. Special relativity is a formalisation of the principle of relativity which does not contain a privileged inertial frame of reference such as the luminiferous aether or absolute space, from which Einstein inferred that no such frame exists. That philosophical approach has become popular among physicists. These views of space and time were also strongly influenced by mathematicians such as Minkowski, according to whom only a kind of union of [space and time] will preserve an independent reality.
Einstein generalised relativity to frames of reference that were non-inertial. He achieved this by positing the Equivalence Principle, that the force felt by an observer in a gravitational field and that felt by an observer in an accelerating frame of reference were indistinguishable. This led to the remarkable conclusion that the mass of an object warps the geometry of the spacetime surrounding it, as described in Einstein's field equations.
An inertial frame of reference is one that is following a geodesic of spacetime. An object that moves against a geodesic experiences a force. For example, an object in free fall does not experience a force, because it is following a geodesic. An object standing on the earth will experience a force, as it is being held against the geodesic by the surface of the planet.
A bucket of water rotating in empty space will experience a force because it rotates with respect to the geodesic. The water will become concave, not because it is rotating with respect to the distant stars, but because it is rotating with respect to the geodesic.
Einstein partially vindicates Mach's principle, in that the distant stars explain inertia in so far as they provide the gravitational field against which acceleration, and inertia, occur. But contrary to Leibniz' account, this warped spacetime is as much a part of an object as are its mass and volume. If one holds, contrary to the idealists, that there are objects that exist independently of the mind, it seems that Relativistics commits one to also hold that space and time have the same sort of independent existence.
...
The position of conventionalism states that there is no fact of the matter as to the geometry of space and time, but that it is decided by convention. The first proponent of such a view, Henri Poincaré, reacting to the creation of the new non-euclidean geometry, argued that which geometry applied to a space was decided by convention, since different geometries will describe a set of objects equally well, based on considerations from his sphere-world.
This view was developed and updated to include considerations from relativistic physics by Hans Reichenbach. Reichenbach's conventionalism, applying to space and time, focusses around the idea of coordinative definition.
Coordinative definition has two major features. The first has to do with coordinating units of length with certain physical objects. This is motivated by the fact that we can never directly apprehend length. Instead we must choose some physical object, say the Standard Metre at the Bureau International des Poids et Mesures (International Bureau of Weights and Measures), or the wavelength of cadmium to stand in as our unit of length. The second feature deals with separated objects. Although we can, presumably, directly test the equality of length of two measuring rods when they are next to one another, we can not find out as much for two rods distant from one another. Even supposing that two rods, whenever brought near to one another are seen to be equal in length, we are not justified in stating that they are always equal in length. This impossibility undermines our ability to decide the equality of length of two distant objects. Sameness of length, to the contrary, must be set by definition.
Such a use of coordinative definition is in effect, on Reichenbach's conventionalism, in the General Theory of Relativity where light is assumed, i.e. not discovered, to mark out equal distances in equal times. After this setting of coordinative definition, however, the geometry of spacetime is set.
As in the absolutism/relationalism debate, contemporary philosophy is still in disagreement as to the correctness of the conventionalist doctrine. While conventionalism still holds many proponents, cutting criticisms concerning the coherence of Reichenbach's doctrine of coordinative definition have led many to see the conventionalist view as untenable."
The debate between whether space and time are real objects themselves, i.e., absolute, or merely orderings upon real objects, i.e., relational, began with a debate between Isaac Newton, through his spokesman Samuel Clarke, and Gottfried Leibniz in the famous Leibniz-Clarke Correspondence.
Arguing against the absolutist position, Leibniz offers a number of thought experiments aiming to show that assuming the existence of facts such as absolute location and velocity will lead to contradiction. These arguments trade heavily on two principles central to Leibniz's philosophy: the principle of sufficient reason and the identity of indiscernibles.
The principle of sufficient reason holds that for every fact there is a reason sufficient to explain why it is the way it is and not otherwise. The Identity of indiscernibles states that if there is no way of telling two entities apart then they are one and the same thing.
For example, Leibniz asks us to imagine two universes situated in absolute space. The only difference between them is that the second is placed five feet to the left of the first, a possibility available if such a thing as absolute space exists. Such a situation, however, is not possible according to Leibniz, for if it were:
a) where a universe was positioned in absolute space would have no sufficient reason, as it might very well have been anywhere else, hence contradicting the principle of sufficient reason, and
b) there could exist two distinct universes that were in all ways indiscernible, hence contradicting the Identity of Indiscernibles.
Standing out in Clarke's, and Newton's, response to Leibniz arguments is the bucket argument. Water in a bucket, hung from a rope and set to spin, will start with a flat surface. As the water begins to spin in the bucket, the surface of the water will become concave. If the bucket is stopped, the water will continue to spin, and while the spin continues the surface will remain concave. The concave surface is apparently not the result of the interaction of the bucket and the water, since the water is flat when the bucket first starts to spin, becomes concave as the water starts to spin, and remains concave as the bucket stops.
In this response, Clarke argues for the necessity of the existence of absolute space to account for phenomena like rotation and acceleration that cannot be accounted for on a purely relationalist account. Clarke argues that since the curvature of the water occurs in the rotating bucket as well as in the stationary bucket containing spinning water, it can only be explained by stating that the water is rotating in relation to some third thing, namely absolute space.
Leibniz describes a space that exists only as a relation between objects, and which therefore has no existence apart from the existence of those objects; motion exists only as a relation between those objects. Newtonian space provided an absolute frame of reference within which objects can have motion. In Newton's system the frame of reference exists independently of the objects which it contains; objects can be described as moving in relation to space itself. For two hundred years, the empirical evidence of the concave water surface held sway.
...
Stepping into this debate in the 19th century is Ernst Mach. Not denying the existence of phenomena like that seen in the bucket argument, he still denied the absolutist conclusion by offering a different answer as to what the bucket was rotating in relation to: the fixed stars.
Mach suggests that thought experiments like the bucket argument are problematic. Imagine a universe containing only a bucket; on Newton's account, this bucket could be set to spin relative to absolute space, and the water it contained would form the characteristic concave surface. But, in the absence of anything else in the universe, how could one confirm that the bucket was indeed spinning? It seems at least equally possible that the surface of the water in the bucket would remain flat.
Mach argued, in effect, that the water in a bucket in an otherwise empty universe would indeed remain flat. But introduce another object into the universe - a distant star, perhaps - and there is now something relative to which the bucket could be seen to be rotating. The water might now adopt a slight curve. As the number of objects in the universe increased, so the curvature of the water, up to the point that we see in the actual universe. In effect Mach argued that the momentum of an object, angular or linear, exists as a result of the sum of the effects of other objects in the universe - Mach's principle.
...
Einstein's relativistics are based on the principle of relativity, which holds that the rules of physics must be the same for all observers, regardless of the frame of reference they use. The greatest difficulty for this idea were Maxwell's equations which included the speed of light in vacuum, implying that the speed of light is only constant relative to the postulated luminiferous ether. However, all attempts to measure any speed relative to the ether failed. Einstein showed how special relativity's Lorentz transformations can be derived from the principle of relativity and the invariance of light speed. Special relativity is a formalisation of the principle of relativity which does not contain a privileged inertial frame of reference such as the luminiferous aether or absolute space, from which Einstein inferred that no such frame exists. That philosophical approach has become popular among physicists. These views of space and time were also strongly influenced by mathematicians such as Minkowski, according to whom only a kind of union of [space and time] will preserve an independent reality.
Einstein generalised relativity to frames of reference that were non-inertial. He achieved this by positing the Equivalence Principle, that the force felt by an observer in a gravitational field and that felt by an observer in an accelerating frame of reference were indistinguishable. This led to the remarkable conclusion that the mass of an object warps the geometry of the spacetime surrounding it, as described in Einstein's field equations.
An inertial frame of reference is one that is following a geodesic of spacetime. An object that moves against a geodesic experiences a force. For example, an object in free fall does not experience a force, because it is following a geodesic. An object standing on the earth will experience a force, as it is being held against the geodesic by the surface of the planet.
A bucket of water rotating in empty space will experience a force because it rotates with respect to the geodesic. The water will become concave, not because it is rotating with respect to the distant stars, but because it is rotating with respect to the geodesic.
Einstein partially vindicates Mach's principle, in that the distant stars explain inertia in so far as they provide the gravitational field against which acceleration, and inertia, occur. But contrary to Leibniz' account, this warped spacetime is as much a part of an object as are its mass and volume. If one holds, contrary to the idealists, that there are objects that exist independently of the mind, it seems that Relativistics commits one to also hold that space and time have the same sort of independent existence.
...
The position of conventionalism states that there is no fact of the matter as to the geometry of space and time, but that it is decided by convention. The first proponent of such a view, Henri Poincaré, reacting to the creation of the new non-euclidean geometry, argued that which geometry applied to a space was decided by convention, since different geometries will describe a set of objects equally well, based on considerations from his sphere-world.
This view was developed and updated to include considerations from relativistic physics by Hans Reichenbach. Reichenbach's conventionalism, applying to space and time, focusses around the idea of coordinative definition.
Coordinative definition has two major features. The first has to do with coordinating units of length with certain physical objects. This is motivated by the fact that we can never directly apprehend length. Instead we must choose some physical object, say the Standard Metre at the Bureau International des Poids et Mesures (International Bureau of Weights and Measures), or the wavelength of cadmium to stand in as our unit of length. The second feature deals with separated objects. Although we can, presumably, directly test the equality of length of two measuring rods when they are next to one another, we can not find out as much for two rods distant from one another. Even supposing that two rods, whenever brought near to one another are seen to be equal in length, we are not justified in stating that they are always equal in length. This impossibility undermines our ability to decide the equality of length of two distant objects. Sameness of length, to the contrary, must be set by definition.
Such a use of coordinative definition is in effect, on Reichenbach's conventionalism, in the General Theory of Relativity where light is assumed, i.e. not discovered, to mark out equal distances in equal times. After this setting of coordinative definition, however, the geometry of spacetime is set.
As in the absolutism/relationalism debate, contemporary philosophy is still in disagreement as to the correctness of the conventionalist doctrine. While conventionalism still holds many proponents, cutting criticisms concerning the coherence of Reichenbach's doctrine of coordinative definition have led many to see the conventionalist view as untenable."
posted by Garrincha ★ domingo, dezembro 31, 2006
t’s a complete oxymoron, but 
