On 30 January 2014 14:17, meekerdb <[email protected]> wrote: > On 1/29/2014 5:19 AM, Edgar L. Owen wrote: > >> Brent, >> >> Here's another relativity question I'd like to get your explanation for >> if I may... >> >> In Thorne's 'Black Holes and Time Warps' he gives the following example. >> >> Two observers A and B. >> >> A leaves earth orbit to travel to the center of the galaxy, 30,100 light >> year away, using a constant 1g acceleration to the midpoint and a constant >> 1g decelleration on the second half of the journey to arrive stationary at >> the galactic center, >> >> Thorne tells us that the 30,100 light year trip takes 30,102 years on B's >> clock back on earth but only 20 years on A's clock aboard the spaceship. >> >> Now my question is what causes the extreme slowing of A's clock? >> >> It can't be the acceleration as both A and B experience the exact same 1g >> acceleration for the duration of the trip. >> >> I can understand that during the trip B will observe A's clock to be >> greatly slowed due to the extreme relative motion, but since the motion IS >> relative wouldn't A also observe B's clock to be slowed by the same amount >> during the trip? >> >> And since the time dilation of relative motion is relative then how does >> it actually produce a real objective slowing of A's clock that both >> observers can agree upon? >> >> You had said yesterday that "geometry doesn't cause clocks to slow" but >> other than the trivial 1g acceleration isn't all the rest just geometry in >> this case? >> >> What's the proper way to analyze this to get Thorne's result? >> > > A rough way to see it is right is to note that c/g = 3e7sec ~ 1year << > 30,000yr. So the spaceship spends essentially the whole flight at very > near c. So the trip takes 30,100+ years in the frame of the galaxy. But > the proper time for the spaceship is very small; if it were actually at > speed c, like a photon, its proper time lapse would be zero. Only, because > it can't quite reach c, the time turns out to be 20 years. To get the exact > values you have to integrate the differential equations: > > dt/dtau = 1/gamma > dv/dtau = accel/gamma^2 > dx/dtau = v/gamma > > where gamma=sqrt(1-v^2) >
The equivalence principle indicates that both A and B are in a 1g gravitational field throughout the exercise, hence the time dilation experienced by A can't be gravitational. All that leaves is the different distances they travel through space-time to reach their final meeting, which is indeed down to "geometry" (in this case involving curves rather the straight lines - but that is minor detail, and can be solved by integrating the relevant equations, as indicated). So I assume the overall geometry of their paths through space-time *is*responsible for the final mismatch between their clocks. I'm not sure whether that contradicts "geometry doesn't cause clocks to slow" - probably not. PS I would instruct A to fly above the plane of the galaxy. There is a lot of stuff between the Earth and the galactic centre and I suspect that even a dust grain would hit a relativistic spacecraft like a nuclear bomb once it was near peak velocity, which according to my calculations is 0.9999995c (or in any case p.d.q.) -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
