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Ittiandro

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I am revisiting the invariant interval spacetime issue , as explained in the book Spacetime Physics by E.F. Taylor and A. Wheeler. The explanation is clear and the invariant interval is correct,

In a nutshell, the invariant interval is calculated by the authors by taking as an example a rocket flying over a lab. The rocket fires from its antenna two sparks into the lab, in sequence, with a time interval of 33.69 ns between them and a space interval of 2 m.

Table 1-4 (attached ) explains the calculation, yielding an invariant interval of 9.9 which is the same for the rocket framework, based on a 33.03 ns time interval between them and 0 space interval , because the two sparks are fired from the same place ( the rocket’s antenna) .

I wonder, though, why :

1) the data do not include the velocity of the rocket and

2) why is the time interval between the two sparks 33.03 ns for the rocket and not a different one ?

How is it arrived at? Shouldn’t the velocity of the rocket ( as a % of c) be required , too, to calculate gamma , hence the time dilation ?

IN other words, not only must the time interval between the two sparks be shorter for the moving rocket ( which it is , in the example) but it doesn’t have to be 33.03 ns, because it depends on the velocity of the rocket, which is not given..Why?

In this case, the interval between the two events ( the sparks) would not be the same for the stationary framework and the rocket. We would then be back to square1!

I’m sure I have missed something, because the whole purpose of considering time as a 4th dimension of a spacetime grid, is precisely to avoid reading different time and space values in the same event(s) depending on the observer's framework.

Can anybody clarify this for me?ThanksItttiandro

__and this is the whole point I am making, as explained below.__**based on the data given**In a nutshell, the invariant interval is calculated by the authors by taking as an example a rocket flying over a lab. The rocket fires from its antenna two sparks into the lab, in sequence, with a time interval of 33.69 ns between them and a space interval of 2 m.

__relative to the stationary framework of the lab.__Table 1-4 (attached ) explains the calculation, yielding an invariant interval of 9.9 which is the same for the rocket framework, based on a 33.03 ns time interval between them and 0 space interval , because the two sparks are fired from the same place ( the rocket’s antenna) .

I wonder, though, why :

1) the data do not include the velocity of the rocket and

2) why is the time interval between the two sparks 33.03 ns for the rocket and not a different one ?

How is it arrived at? Shouldn’t the velocity of the rocket ( as a % of c) be required , too, to calculate gamma , hence the time dilation ?

IN other words, not only must the time interval between the two sparks be shorter for the moving rocket ( which it is , in the example) but it doesn’t have to be 33.03 ns, because it depends on the velocity of the rocket, which is not given..Why?

In this case, the interval between the two events ( the sparks) would not be the same for the stationary framework and the rocket. We would then be back to square1!

I’m sure I have missed something, because the whole purpose of considering time as a 4th dimension of a spacetime grid, is precisely to avoid reading different time and space values in the same event(s) depending on the observer's framework.

Can anybody clarify this for me?ThanksItttiandro