Is Proper Time the Only Measure of Motion in Spacetime?

[Curious6]

If time is a curvature in spacetime as described in relativity, then picture this. If there is a curvature in spacetime time is going in one direction (let's call this curvature 1) but then could time travel not be possible by having a second curvature in curvature 1 but going in the opposite direction?

Insights?

 

[cristo]

I'm not sure what you mean by "time being a curvature in spacetime."

 

[Dale]

If time is a curvature in spacetime as described in relativity

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).

 

[Fredrik]

I'm not sure what you mean by "time being a curvature in spacetime."

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").

In a post he made after that, he talked about time being "a curve in spacetime", and now it has deteriorated further to "a curvature in spacetime".

 

[Curious6]

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?

 

[Dale]

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?

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.