A simple Gen Rel explanation I got from Sean Carroll: the twin experiencing acceleration follow a worldline which travels more in space, relatively less in time compred to an inertial, unaccelerated trajectory.

]]>Unfortunately the book is in German, but you may find it quite handy and useful in your project, if one can translate it into English.

Here is the name of the author and the book:

Roman Ulrich Sexl Gravitation und Kosmologie: Eine Einf. in d. allgemeine Relativitatstheorie (1975)

Kui meil on seos üldliikmete x ja y vahel, siis need elemendid/hulgad – on olemas (Vt. Valiku e. Zermelo aksioom).

Vaatleme Galilei teisendust sihil v (teljel x), alghetkest, mil AB = r = ct;

x`= x – vt; f(ct) = ct(1 – v/c); ja g(ct) = ct/(1- v/c);

On kerge näha, et funktsioon f määrab relatiivse ruumi F; g – aga määrab nn. “sündmuste-vahelise ruumi” E*, mis ei tarvitse olla samane hulgaga E.

Ometigi, kui küsida vastust Zenoni apooriale: kuskohas saab Achilleus kätte kilpkonna, kui vastavad kiirused on v ja c, kusjuures Achilleus on (kunagi) mõõtnud ära selle esialgse vahemaa kui R =ct.

Vastus: Achilleus saab kilpkonna kätte Achilleuse ruumis,

kohal g(ct) = ct/(1 – v/c).

Üldine Galilei ruumiteisendus on: f(ct) = ct[1 – (v/c)cosa];

selle laotus Cartesiuse ristkoordinaadile avaldub dimensionaalsete seostega: x`= ctcosa – vt; y`= k ctsina; z`= k ctsina;

milles k – on k = 1/L, milles L – on Lorentz-tegur. ]]>

In Exercise 4.1,(g),It seems that “Doppler .s.h.i.t.s” should be “Doppler shifts”…

*[Gah, that is fixed now. Well, I guess some of the high school students will have been amused by that typo… -T.]*

In figure 4,I found that those black lines which represent sound are not Parallel with each other,nor are they symmetry regarding the t-axis,this means that the |velocity| of the sound changes,but in fact the |velocity| of the sound does not change.Is it your problem or my problem……

*[Yes, some of the image elements were not aligned properly; it should be fixed now. -T.]*

Hi Terry,

I am a physics grad (you’re actually on my grad committee at UCLA), and I think this is an important, subtle point. In your notes you write

“Actually, it turns

out that the situation is symmetric: from Bob’s point of view, Alice experiences

time dilation, while from Alice’s point of view, Bob also experiences time dilation.”

This is true when both Alice and Bob are inertial observers, but when they start spatially coincident but one of the twins accelerates away from earth and then returns, the symmetry is broken, and that is why it makes sense for one twin to be older and the other younger once they are again spatially coincident in the end.

My apologies if this was addressed somewhere else, and I didn’t notice.

*[Fair enough, I’ll add a comment to this effect in the next revision of the ms. -T.]*

Missing a ‘with’ there.

*[Thanks, this will be corrected in the next revision of the ms -T.]*