- #1
Jurgen Kruger
- 3
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An isolated mechanical system can be represented by a point in a high-dimensional configuration space. This point evolves along a line. The variational principle of Jacobi says that, among many imagined trajectories between two points, only the SHORTEST is real and is associated with situations that fulfil classical mechanical laws.
A description in these terms is said to be timeless because "time" does not appear in the formulae. However, on the other hand, the term "change" appears in the pertinent texts. Can someone explain me how a "change" can be understood without a concept of (temporal !) simultaneity, i.e., without any reference to "time"? Naïvely I assume that the individual contributions to the ensemble of coordinates making up the point in configuration space have to be taken at the same instant in time.
I am looking for a truly timeless description of classical mechanics. Is this really the case for the principle of Jacobi?
A description in these terms is said to be timeless because "time" does not appear in the formulae. However, on the other hand, the term "change" appears in the pertinent texts. Can someone explain me how a "change" can be understood without a concept of (temporal !) simultaneity, i.e., without any reference to "time"? Naïvely I assume that the individual contributions to the ensemble of coordinates making up the point in configuration space have to be taken at the same instant in time.
I am looking for a truly timeless description of classical mechanics. Is this really the case for the principle of Jacobi?