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.]*

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.]*

One thing that always troubles me about the focus on spacetime diagrams as the essence of special relativity is the fact that they are perfectly compatible with the classical case in which there is a well-defined spacelike direction, and indeed the setup of drawing space and time axes is counter to the “mixing” of space and time that is essential to the theory. The essence of relativity is that the axes only represent one person’s point of view and that a moving observer will define them quite differently, and I would suggest making that point right at the outset.

Also I think Stuart is right about the twin “paradox” (being resolved by the fact that it is impossible to have the twins ever meet to compare ages without violating the condition that both live in inertial frames)

The derivation of E=mc^2 is cute but kind of begs (part of) the question by starting with the assumption that a material mass can in fact be converted to photons. It might be worth mentioning that there are other derivations which do not require either quantum theory or the convertibility of matter into radiation. (One of the great puzzles of history and paedagogy of modern physics is the extent to which ideas from two theories which we actually find very difficult to combine into a consistent whole are often used to motivate one another’s development.)

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