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Consider the following case:

Two observers, A and B, moving relative to each other with velocity v. For B, it's A that moves (with v) and so DTb=g*DTa (where DT denotes finite time difference and g is/the Lorentz factor gamma). So, (following the same logic as in Morin's Classical Mechanics book at page 515) if say g=5/4 then if A claps once every 4 second then B hears claps every 5 seconds.

Now, for A it's B that moves(with -v) and so DTa=g*DTb. Rearranging we get DTb=1/g*DTa. So, if A claps once every 4 seconds, B hears claps every 15/5 seconds.

So, what is going on here?

I think that I have not properly understood what each DTa and DTb stands for in the above relations.

For example, if in the first relation (DTb=g*DTa) DTb stands for the time difference that he sees in the clock, then what does DTa in the same relation stand for?

Analogously, in the second relation (DTa=g*DTb) if DTa stands for the time difference that he sees in the clock, then what does DTb in the same relation stand for?

Lastly, how is the DTa's and DTb's related?

Please keep in mind that this is confusing me very much both conceptually and mathematically(how to relate the intervals), so don't take anything for granted as I am surely confused about various concepts of relativity(as this question proves).

Thanks in advance!

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# I Time dilation (something seemingly paradoxical) r

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