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First of all, I have to say that I was thinking long about whether to post this in the Philosophy of Science forum or here. I decided to post it here because, although part of the question is centered on the definition of relationism, the main problem concerns some technical aspects of GR.
I read a paper from Carlo Rovelli titled “Quantum spacetime: what do we know?”, which can be found at http://arxiv.org/gr-qc/9903045 . There it is claimed that General Relativity is a theory in which space and time exist in relation to energy and matter. According to Rovelli, this has to be understood in a profound sense: in the same way that no matter is possible without spacetime, in GR, no spacetime is possible without matter.
My interest is not about Quantum Gravity (this would not be meaningful since the mathematics are beyond my knowledge), but about General Relativity, whose fundaments I would like to understand better. Also, I would like to say that I just know a little bit about GR (from Schutz), so I apologize if I wrote something senseless after this long post.
My problem is that I cannot understand Rovelli’s claim. First of all, the Einstein equations in GR say that the metric is influenced by matter in a similar way than matter is influenced by the metric. IMO this is far away from saying that, if there were no matter, then there would not be any metric. The point is that in GR it is possible to have a spacetime without matter. This is a flat spacetime, not expanding and with gravitational waves depending on boundry conditions. Since it is mathematically possible, one should infer that this has some significance which cannot be ignored.
On the other hand GR describes a matter – metric interaction, which seams to be different to me than describing a matter – spacetime interaction. If we remove the metric from spacetime, then something remains still there: its dimensionality. Spacetime has two essential properties, which should be considered in oder to define it: distances and dimensions. AFAIK, mathematically one can have the second without having the first (as kind of manifold or topological space without metric). The first property (dimensions) is independent of everything and is not influenced by nothing, contrary to the second (the metric).
So, my understanding is: with respect to the existence of the metric and the existence of matter, GR is not a relational theory, since it makes possible the existence of a metric without matter. On the other hand, spacetime is something different than the metric as such, since one cannot define a metric without fixing some dimensions (which are independent of everything).
From this point of view Rovelli’s paper makes no sense to me. I do not claim that Rovelli’s ideas are nonsense, since I do not know whether and how he has enhanced or modified GR, but now I would tend to say that his arguments, trying to ground relationism of physics on GR theory, are not correct or, at least, he does consider GR only partially.
Comments? Thanks.
Regards.
I read a paper from Carlo Rovelli titled “Quantum spacetime: what do we know?”, which can be found at http://arxiv.org/gr-qc/9903045 . There it is claimed that General Relativity is a theory in which space and time exist in relation to energy and matter. According to Rovelli, this has to be understood in a profound sense: in the same way that no matter is possible without spacetime, in GR, no spacetime is possible without matter.
My interest is not about Quantum Gravity (this would not be meaningful since the mathematics are beyond my knowledge), but about General Relativity, whose fundaments I would like to understand better. Also, I would like to say that I just know a little bit about GR (from Schutz), so I apologize if I wrote something senseless after this long post.
My problem is that I cannot understand Rovelli’s claim. First of all, the Einstein equations in GR say that the metric is influenced by matter in a similar way than matter is influenced by the metric. IMO this is far away from saying that, if there were no matter, then there would not be any metric. The point is that in GR it is possible to have a spacetime without matter. This is a flat spacetime, not expanding and with gravitational waves depending on boundry conditions. Since it is mathematically possible, one should infer that this has some significance which cannot be ignored.
On the other hand GR describes a matter – metric interaction, which seams to be different to me than describing a matter – spacetime interaction. If we remove the metric from spacetime, then something remains still there: its dimensionality. Spacetime has two essential properties, which should be considered in oder to define it: distances and dimensions. AFAIK, mathematically one can have the second without having the first (as kind of manifold or topological space without metric). The first property (dimensions) is independent of everything and is not influenced by nothing, contrary to the second (the metric).
So, my understanding is: with respect to the existence of the metric and the existence of matter, GR is not a relational theory, since it makes possible the existence of a metric without matter. On the other hand, spacetime is something different than the metric as such, since one cannot define a metric without fixing some dimensions (which are independent of everything).
From this point of view Rovelli’s paper makes no sense to me. I do not claim that Rovelli’s ideas are nonsense, since I do not know whether and how he has enhanced or modified GR, but now I would tend to say that his arguments, trying to ground relationism of physics on GR theory, are not correct or, at least, he does consider GR only partially.
Comments? Thanks.
Regards.
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) from which mass was produced?