How Does the Principle of Extremal Aging Determine the Path of a Free Object?

[dpa]

i posted this in general forum. That might be wrong. So moderators, delete that not this.
Q.
why/how extremum time lapse
between two events recorded on
object's wristwatch gives the
path of a free object.

And any examples of minimum
aging.

 

[HallsofIvy]

I, for one, have no idea what you are asking. The closer to the speed of light something is moving, relative to me, the slower I will see it aging. There is no "minimum aging".

 

[elfmotat]

I, for one, have no idea what you are asking. The closer to the speed of light something is moving, relative to me, the slower I will see it aging. There is no "minimum aging".

It's not minimum aging, but rather maximum. He's talking about the principle of extremal proper time. It's an analog to the principle of least action from Newtonian mechanics.

 

[dpa]

yes, may be because its a principle used mainly by john archibald wheeler and only few others and he has used the concept extensively in exploring black holes and is applicable both to GR and SR. You might want to google but there is limited info.

 

[dpa]

elfmotat,
wheeler writes experts prefer extremum aging not maximum aging coz there can be both minimum and maximum aging.

 

[elfmotat]

Q.
why/how extremum time lapse between two events recorded on object's wristwatch gives the path of a free object. And any examples of minimum aging.

It's a principle, meaning it doesn't need an explanation. It is, however, easy to get an intuitive feel for it. Say, for simplicity, that we're working in flat Minkowski space. The proper time of an object traversing some worldline is given by dτ²=dt²-dr², where dr²=dx²+dy²+dz². The path that maximizes this is of the form r(λ)=kλ for some constant k and affine parameter λ. This corresponds to an inertially moving object, which is indeed the state of an object which isn't acted upon by outside forces.