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advanced_notions:relational_physics [2017/11/09 09:24]
jakobadmin [Student]
advanced_notions:relational_physics [2018/03/15 13:56] (current)
jakobadmin [Why is it interesting?]
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 <tabbox Why is it interesting?> ​ <tabbox Why is it interesting?> ​
  
-<​blockquote>'​There is no law except the law that there is no law... ​ Ultimate mutability is the central feature of physics.' ​ <​cite>​-John Wheeler</​cite></​blockquote>​+
  
 It is usually stated that the fundamental insight of general relativity is that there is no gravitational field at all. The gravitational force is rather an illusion due to the curvature of spacetime. ​ It is usually stated that the fundamental insight of general relativity is that there is no gravitational field at all. The gravitational force is rather an illusion due to the curvature of spacetime. ​
  
-However, we can also make a completely contrary argument, which is what Einstein realised after several decades. Instead of the statement above, we can take as the fundamental insight of general relativity that there is no spacetime, only the gravitational field! This line of thought is described nicely in the book "​[[http://​www.cpt.univ-mrs.fr/​~rovelli/​book.pdf|Quantum Gravity]]"​ by Rovelli and is based on the "hole argument"​. ​+However, we can also make a completely contrary argument, which is what Einstein realised after several decades. Instead of the statement above, we can take as the fundamental insight of general relativity that there is no spacetime, only the gravitational field! This line of thought is described nicely in the book "​[[http://​www.cpt.univ-mrs.fr/​~rovelli/​book.pdf|Quantum Gravity]]"​ by Rovelli and is based on the "hole argument"​. ​Se also [[http://​jakobschwichtenberg.com/​the-true-magic-hidden-inside-general-relativity/​|this essay]].  ​
  
 Similar statements can be made for other theories, like gauge theories. This is discussed, for example, in the section "​Towards a Pointless Theory"​ in the book "Some elementary gauge theory concepts"​. ​ Similar statements can be made for other theories, like gauge theories. This is discussed, for example, in the section "​Towards a Pointless Theory"​ in the book "Some elementary gauge theory concepts"​. ​
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 The basic idea is that the only thing that matters are the points where worldlines of different objects meets. Everything else is not observable and hence has no meaning. In this sense there is no spacetime and no "inner spaces"​. The only things that matter are relative relations between objects. Everything else can not be observed, because an observation necessarily implies that objects meet.  The basic idea is that the only thing that matters are the points where worldlines of different objects meets. Everything else is not observable and hence has no meaning. In this sense there is no spacetime and no "inner spaces"​. The only things that matter are relative relations between objects. Everything else can not be observed, because an observation necessarily implies that objects meet. 
  
 +----
  
 +<​blockquote>'​There is no law except the law that there is no law... ​ Ultimate mutability is the central feature of physics.' ​ <​cite>​-John Wheeler</​cite></​blockquote>​
  
 <​blockquote>​The requirement of general covariance “takes away from space and time the last remnant of physical reality <​cite>​Einstein</​cite></​blockquote>​ <​blockquote>​The requirement of general covariance “takes away from space and time the last remnant of physical reality <​cite>​Einstein</​cite></​blockquote>​
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 <​cite>​https://​en.wikipedia.org/​wiki/​Hole_argument</​cite></​blockquote>​ <​cite>​https://​en.wikipedia.org/​wiki/​Hole_argument</​cite></​blockquote>​
 +
 +<​blockquote>​Traveler,​ there are no paths;
 +Paths are made by walking.
 +<​cite>​Antonio Machado</​cite>​
 +</​blockquote>​
  
 <tabbox Layman> ​ <tabbox Layman> ​
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   ​   ​
 <tabbox Student> ​ <tabbox Student> ​
 +<​blockquote>​
 +The central problem is that of the points of space. The debate goes back to
 +Leibniz and Newton. For Leibniz the constituent of all things, both material and
 +spiritual, is provided by monads, which are windowless (we would say they have no
 +internal structure), and the only things that matter are their mutual relationships.
 +Here we seem to recognize the first “definition” given by Bourbaki at the beginning
 +of his discussion of set theory:
 +A set is composed of elements capable of having certain properties
 +and having certain relations among themselves or with elements of
 +other sets.
 +From this ontological point of view the elements, or points, are pre-existent and
 +the problem is to organize them, to give them a structure. From the physical point
 +of view, one postulates with Newton the existence of an absolute space, in which
 +the phenomena occur: positions are predetermined,​ destined to be inhabited by the
 +accidents of matter.
 +In Mach’s philosophy, on the contrary, space is determined by matter ; the most
 +advanced mathematical form is certainly furnished by the [[equations:​einstein_equation|Einstein gravitational
 +equations]]:​
 +$$ R_{\mu\nu}-\frac{1}{2}Rg_{\mu \nu} = 8 \pi \kappa T_{\mu\nu}. $$
 +The right-hand side, $T_{\mu\nu}$,​ is determined by the matter that happens to be present,
 +or, in more modern form, it is a function of the nongravitational fields, while the
 +left-hand side is a function of only the gravitational field $g_{\mu \nu}$, identified with the
 +metric tensor that defines the geometry. In contrast to Newton’s views, the space
 +is no longer a mere receptacle, but an actor in physics, as the bending of light rays
 +in a gravitational field shows. **For Mach and Einstein, a point then only appears as
 +a label making it possible to identify an event.**</​blockquote>​
 +
  
 Probably the right mathematical tool to make the ideas of relational physics precise is [[advanced_tools:​category_theory|category theory]]. ​ Probably the right mathematical tool to make the ideas of relational physics precise is [[advanced_tools:​category_theory|category theory]]. ​
 +
 +----
 +
 +  * A great recent summary of the relational interpretation of quantum mechanics is "​[[https://​arxiv.org/​abs/​1712.02894|Space is blue and birds fly through it]]" Carlo Rovelli
 <tabbox Researcher> ​ <tabbox Researcher> ​
  
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   * N. D. Mermin, “What is quantum mechanics trying to tell us?,” Am. J. Phys. 66 (9), 753-767 (1998).   * N. D. Mermin, “What is quantum mechanics trying to tell us?,” Am. J. Phys. 66 (9), 753-767 (1998).
  
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 <tabbox Examples> ​ <tabbox Examples> ​
advanced_notions/relational_physics.1510215892.txt.gz · Last modified: 2017/12/04 08:01 (external edit)