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Cleonis
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PeterDonis said:if I wanted to quickly summarize the difference between galilean relativity and SR, I would simply say that galilean relativity uses galilean spacetime, whereas SR uses Minkowski spacetime. [...] Galilean spacetime, if we lived in it, would have physical effects too: after all, objects are predicted to experience inertial forces (e.g., centrifugal force) in pre-SR physics.
In physics there has been a sequence of three theories of motion, each superseding its predecessor: Newtonian dynamics, SR and GR. Insights from GR cast the predecessors in new light. With the new insights the predecessors can be reframed in such a way that the transitions between them become the smallest possible.
'Theory of motion' and 'theory of inertia' are effectively one and the same concept. To formulate the properties of inertia is to formulate the properties of motion.
Among the properties of inertia:
- The law of inertial motion: objects in motion will remain in the same state of motion, moving in a straight line and covering equal distances in equal intervals of time.
- The law of forced acceleration: to change the state of motion a force is required; The responce to impressed force is proportional: twice the force gives twice the acceleration. (Better known as Newton's second law: F=ma)
An explanation of the law of inertial motion would require a theory of the nature of space and time that probes deeper than current theories do. (But some theorists do attempt to formulate a quantum theory of space and time itself.)
In the case of Newton's second law there is no explanation (as far as I know), nor are there any leads. Quite a few physicists will argue that we should not seek more fundamental explanation in the first place, but that we should simply accept Newton's second law as given.
Relativistic spacetime
As we know GR is not just a theory of motion, GR unifies the description of inertia and gravitation into a single conceptual framework. We have that physical properties are attributed to GR-spacetime.
John Wheeler coined the following phrase to capture the essence of GR. (I'm not quoting literally.)
"Inertial mass is telling spacetime how to curve, curvature of spacetime is telling inertial mass how to move."
SR is subsumed in GR, and by implication SR-spacetime has the same properties as GR-spacetime, except for the property of being "deformable". SR-spacetime is "immutable" in the sense that its morphology is unchanging.
We have that SR-spacetime is telling matter how to move. That is, in SR inertia arises from SR-spacetime. (I know that some people will argue for a more cautious attitude. Some people will argue that since we don't know what inertia is we should only acknowledge the existence of inertia, without attributing it somewhere.)
Classical spacetime
With the insights gained from relativistic physics classical physics can be reinterpreted. We can define a background structure of classical dynamics, and an often used name for that background structure is 'galilean spacetime' (since in galilean spactime the applicable transformations are the galilean transformations.) Then inertia as known in classical dynamics is to be attributed to galilean spacetime.
So, before the concept of spacetime as a physical entity, giving rise to inertia, was developed, how did physicists think about inertia?
That is difficult to say. To this day many authors write about inertia as an innate property of objects, without any reference to some outside structure. It's very common for authors to use phrasings such as: "As the wrecking ball hits the wall of the building the ball's momentum carries it through." Inertia is rarely discussed, but when authors do discuss it the suggestion is that the inertia of an object is purely an internal affair, something purely innate to an object.
In my opinion the attitude of regarding inertia as an innate property of individual objects is untenable. That is one of the lessons of relativistic physics.
Cleonis
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