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MathematicalPhysicist

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Bob is an observer at rest in Minkowski space at ##x=L##.

Alice moves in a constant acceleration (in her system).

her path is depicted in the attached file, when Alice passes by Bob they synchronize their watches and Bob activates an apparatus that signals pulses to Alice.

Every short time period ##\Delta t## (which is calculated in Bob's system) a pulse is ejected.

The path of Alice is described by ##X(\tau)=\frac{1}{a}\cosh(a\tau)##, ##T(\tau)=\frac{1}{a}\sinh(a\tau)##.

I have a few questions:

1. What does Alice's watch show when they meet again?

2. What does Bob's watch show when they meet again?

3. How many pulses arrive to Alice?

My wrong answers are as follow:

1.We take ##c=1##, so ##\tau=\Delta t \cdot \gamma \cdot 2##, ##v= a\Delta t \cdot 2##; so ##\tau = 2\Delta t \frac{1}{\sqrt{1-(a\Delta t)^2\cdot 4}}##; so the watch of Alice will show the time:

$$T(\tau)= 1/a \cdot \sinh(\frac{2a\Delta t}{\sqrt{1-(a\Delta t)^2\cdot 4}}$$

2. I wrote that Bob's watch will show ##2\Delta t##, but it's wrong.

3. The number of pulses arriving to Alice are ##N=T(\tau)/\Delta t##, where ##T(\tau)## is the same as I got in question 1.

I will appreciate it
if you will guide me how to answer these questions correctly, thanks!

Alice moves in a constant acceleration (in her system).

her path is depicted in the attached file, when Alice passes by Bob they synchronize their watches and Bob activates an apparatus that signals pulses to Alice.

Every short time period ##\Delta t## (which is calculated in Bob's system) a pulse is ejected.

The path of Alice is described by ##X(\tau)=\frac{1}{a}\cosh(a\tau)##, ##T(\tau)=\frac{1}{a}\sinh(a\tau)##.

I have a few questions:

1. What does Alice's watch show when they meet again?

2. What does Bob's watch show when they meet again?

3. How many pulses arrive to Alice?

My wrong answers are as follow:

1.We take ##c=1##, so ##\tau=\Delta t \cdot \gamma \cdot 2##, ##v= a\Delta t \cdot 2##; so ##\tau = 2\Delta t \frac{1}{\sqrt{1-(a\Delta t)^2\cdot 4}}##; so the watch of Alice will show the time:

$$T(\tau)= 1/a \cdot \sinh(\frac{2a\Delta t}{\sqrt{1-(a\Delta t)^2\cdot 4}}$$

2. I wrote that Bob's watch will show ##2\Delta t##, but it's wrong.

3. The number of pulses arriving to Alice are ##N=T(\tau)/\Delta t##, where ##T(\tau)## is the same as I got in question 1.

I will appreciate it