Time like spacetime interval, proper time, and time dilation

In summary: WITH respect to me and synchronized at a frame. I think the second is what you are asking about. It is possible for the stationary observer to calculate the proper time of the travelers clock.
  • #36
cianfa72 said:
So this notion of "at rest" is actually w.r.t. a coordinate system.
Yes.
cianfa72 said:
What about the notion of "being at rest" w.r.t. another body ?
In flat space-time, there is relative velocity -- the velocity of the one body in the [momentary, inertial] rest frame of the other. If this is zero then the objects are at rest relative to each other.

In curved space-time, the notion of relative velocity gets slippery. Non-local comparison of velocities becomes ambiguous and one needs to "parallel transport" the velocity of the one into the local frame of the other. The result can depend on the path over which this "parallel transport" is performed.

There is a different notion which might be used. Have you Googled "born rigidity"?
 
  • Like
Likes cianfa72 and Ibix
Physics news on Phys.org
  • #37
Hello to every body. I’ve found the attached image among my old draft papers, which I used in a conference to illustrate the so-called twin paradox:
 effetto gemelli .jpg


Do you have difficulties with Italian ? In short , the test says that , in the flat spacetime of SR (no mass- energy that causes curvature) , one can go from event O to event Q in two (or more...) ways :

1) staying at home, sitting in a very comfortable arm chair, (but let’s ignore for the moment that the Earth is not an inertial RF , from the point of view of relativity) , and just letting proper time (wristwatch time) flow. So, OQ is a piece of geodesics. Spatial coordinate x doesn’t change.
2) moving from O to Q along a curved universe line OSQ , that can be approximated by a succession of short segments , during which the speed maintains constant , and varies from piece to piece. Axes t’ , t” ...are the instantaneous time axes of the MCRFs which are tangent to the curved universe line.

Then, mathematics and physics formulae don’t need to be translated. Fortunately , their language is (or should be) universal and well understood by everybody.
In the end, the result is that the integral of proper time along the curved universe line is shorter than the coordinate time from O to Q : the geodesics OQ , on the time axis of the stationary twin, is the "longest time line” . No paradox, then .

Sorry for my bad English.
 
  • Like
Likes cianfa72 and Dale
  • #38
jbriggs444 said:
There is a different notion which might be used. Have you Googled "born rigidity"?
AFAIK in SR it is related to the hyperbolic motion (basically the spacelike distance as measured from a family or congruence of objects accelerating with constant proper acceleration).
 
Last edited:

Similar threads

  • Special and General Relativity
Replies
16
Views
796
  • Special and General Relativity
Replies
21
Views
655
  • Special and General Relativity
2
Replies
54
Views
1K
  • Special and General Relativity
2
Replies
35
Views
3K
  • Special and General Relativity
Replies
12
Views
662
  • Special and General Relativity
Replies
9
Views
1K
  • Special and General Relativity
Replies
6
Views
407
  • Special and General Relativity
Replies
7
Views
533
  • Special and General Relativity
2
Replies
60
Views
4K
  • Special and General Relativity
3
Replies
101
Views
1K
Back
Top