The discussion revolves around the concept of proper time in the context of spacetime and its relationship to motion. Participants explore the nature of time as it relates to curvature in spacetime, the distinction between proper and coordinate time, and the implications of these ideas on our understanding of motion and time travel.
Participants express differing views on the interpretation of time as curvature in spacetime, with some seeking clarification and others defending their conceptualizations. The discussion remains unresolved regarding the implications of these ideas on time travel and the nature of motion.
There are limitations in the discussion regarding the assumptions made about the nature of time and curvature, as well as the definitions of proper and coordinate time. Some mathematical steps and definitions remain unresolved.
Gravity is described as curvature of spacetime. Proper time is the "length" (aka spacetime interval) along a particular type of curve in spacetime, specifically the type of curve that can represent the path of an object through spacetime (aka worldline).Curious6 said:If time is a curvature in spacetime as described in relativity
I explained proper time to him in another thread about a week ago. I told him that the time measured by a clock is the proper time of the curve in spacetime that represents the clock's motion. I gave him the exact definition of proper time and emphasized that it's a property of a curve (its "length").cristo said:I'm not sure what you mean by "time being a curvature in spacetime."
The important distinction is that a curve has several properties that one might wish to measure, e.g. Direction, radius of curvature, slope, length, torsion, angle, etc. Proper time is the length (spacetime interval) along the curve. What we call motion is the slope of the curve in spacetime, which is geometrically distinct from the length. A line that has a slope of 0 may still have a length, similarly a motionless object still goes through time.Curious6 said:Fredrik, I understand the difference between proper and coordinate time. There is no 'deterioration' involved in my envisaging what you have said as a curvature in spacetime. You clearly mention 'the time measured by a clock is the proper time of the curve in spacetime that represents the clock's motion'. Now how is that different than saying that time measures a curve in spacetime? It measures the curve in spacetime that represents the clock's motion, but nevertheless it measures a curve in spacetime. No deterioration of any sort; rather, a generalization of a concept to try to understand further concepts.
My question still stands, but can be put in other terms. If we take your formulation of the concept of proper time and substitute the word Earth for 'watch' then we get: 'the time measured by Earth is the proper time of the curve in spacetime that represents the Earth's motion'. Is it not fair to say that the only reason we experience time as going forward is because of Earth's motion?