- #1
RiccardoVen
- 118
- 2
Hi,
I know there are already other posts about extremal aging, but all of them are actually closed
and none of them is actually answering to my doubt.
I've just started T&W "exploring black holes", and I just faced the "extremal aging" principle. Actually, this concept doesn't fit very well with what I have understood from SR ( of course I dont' really mean this principle is wrong, just I cannot fully understand it yet ).
1) if we take a time like trajectory in flat ST crossing two events, we know the proper time is the one measured by a clock that passes through both events. In this particular frame, looking at the metric, we can write:
(ΔTau)^2 = (Δt)^2 - (Δs)^2
From here we can see the time delation, i.e. ΔTau is always <= Δt, meaning the proper time is always MINIMUM related to all Δt measured by other observers pasting the rest frame ( sorry for my English, it's difficult to express properly so profund ideas in a language different than mine ).
2) The extremal aging principle, actually seems to state almost the opposite ( at least to me), i.e. the trajectory taken is always the one making the time extremal. For massive particles ( i.e. not photons ) this result actually in MAXIMIZING the time between the 2 events.
This seems logic to me, as depicted also from this site:
http://www1.kcn.ne.jp/~h-uchii/extrem.aging.html
so we can see the straight vertical line, which is actually a geodesic for flat ST, is the one which maximizes the ΔTau. Also the way in which Wheeler is using the twin paradox for introducing "natural" paths which makes time extremal is clear to me: the Earth is actually seen as an inertial frame which takes a "natural" path ( geodesic ) and hence makes the stay-at-rest twin getting older than the other twin, experiencing hence the maximum Tau.
The problem is when I try to mix these 2 principles ( i.e. proper time which is MINIMUM within the rest frame Vs extremal aging, which makes t MAXIMUM for "natural" paths ).
Hope my question and my doubt is clear. I know there must be a stupid assumption I'm making
which makes me taking the wrong conclusion, but I cannot see it.
thanks, regards
I know there are already other posts about extremal aging, but all of them are actually closed
and none of them is actually answering to my doubt.
I've just started T&W "exploring black holes", and I just faced the "extremal aging" principle. Actually, this concept doesn't fit very well with what I have understood from SR ( of course I dont' really mean this principle is wrong, just I cannot fully understand it yet ).
1) if we take a time like trajectory in flat ST crossing two events, we know the proper time is the one measured by a clock that passes through both events. In this particular frame, looking at the metric, we can write:
(ΔTau)^2 = (Δt)^2 - (Δs)^2
From here we can see the time delation, i.e. ΔTau is always <= Δt, meaning the proper time is always MINIMUM related to all Δt measured by other observers pasting the rest frame ( sorry for my English, it's difficult to express properly so profund ideas in a language different than mine ).
2) The extremal aging principle, actually seems to state almost the opposite ( at least to me), i.e. the trajectory taken is always the one making the time extremal. For massive particles ( i.e. not photons ) this result actually in MAXIMIZING the time between the 2 events.
This seems logic to me, as depicted also from this site:
http://www1.kcn.ne.jp/~h-uchii/extrem.aging.html
so we can see the straight vertical line, which is actually a geodesic for flat ST, is the one which maximizes the ΔTau. Also the way in which Wheeler is using the twin paradox for introducing "natural" paths which makes time extremal is clear to me: the Earth is actually seen as an inertial frame which takes a "natural" path ( geodesic ) and hence makes the stay-at-rest twin getting older than the other twin, experiencing hence the maximum Tau.
The problem is when I try to mix these 2 principles ( i.e. proper time which is MINIMUM within the rest frame Vs extremal aging, which makes t MAXIMUM for "natural" paths ).
Hope my question and my doubt is clear. I know there must be a stupid assumption I'm making
which makes me taking the wrong conclusion, but I cannot see it.
thanks, regards