B Time dilation, relativistic mass and fuel consumption

[PainterGuy]

And if you make it again in this thread I am going to close the thread because there will be no point in continuing.

I'm sorry and I do agree with you. It has become frustrating as I said in my previous post. I'd try to avoid any question about the simultaneity. I've a question which seems important to me but if you think it shouldn't have been asked, you can always delete it, or, worse, close the thread. Thank you.A spaceship is moving toward right at uniform speed of 0.5c and at time t1 it emits a light pulse of an infinitesimal duration. The light travels at constant speed of 300000 km/s.

After 1 second, at time t2, the ship notices the distance traveled by pulse is 300000 km. Meanwhile, the ship has also moved the distance of 150000 km toward the moving pulse. Therefore the distance between ship and trailing edge of the pulse should have been 150000 km BUT it is NOT.

For the ship to observe that the light has moved away 300000 km instead of 150000 km, some things need to change in the formula speed=distance/time. Ignoring length contraction of the ship, time slowdown should occur.

The pulse was generated at time t1 and then by time t2 it had traveled the distance of 300000 km. The difference between t2 and t1 is 1 second. For the ship to calculate the traveled distance by pulse to be 300000 km, the pulse should have actually moved the distance of 300000+150000 km after it was generated. But in ship's frame of reference it has traveled only 300000 km and this would require ship's clock running 1/1.5=0.67 times slower. Informally speaking, for light pulse's 1 second the ship clock has only ticked 0.67 seconds, and when ship clock ticks 1 second, the light pulse clock actually ticks 1.5 second.

I understand that what I'm saying above is nothing less than mumbo jumbo but let's hope that one can guide me to identify the root of my misconceptions. Thanks a lot.

 

[PeterDonis]

I've a question which seems important to me but if you think it shouldn't have been asked

That's not the problem. Asking the question, in itself, is fine. What is not fine is continuing to ask the same question, making the same mistake, even after the question has been repeatedly answered and the mistake has been repeatedly pointed out. It's like you haven't read a single thing anyone else has said in this thread for a hundred posts.

let's hope that one can guide me to identify the root of my misconceptions

If what has already been said in this thread hasn't done that, I'm not sure what else could be done. However, I'll give it one more try. In what I'll quote from you below, I'm going to make bolded additions to show you the key things you left out; leaving those things out, repeatedly, even after it's been repeatedly explained to you that you can't, is the mistake you keep making. I'll also strike through statements you make that cannot be made consistent with your other statements, and replace them with bolded additions giving the correct statements.

A spaceship is moving toward right at uniform speed of 0.5c relative to a chosen inertial frame, which we'll call Frame A, and at time t1 relative to Frame A it emits a light pulse of an infinitesimal duration. The light travels at constant speed of 300000 km/s relative to Frame A.

As has been repeatedly pointed out, "time", "distance" and "speed" have no meaning except relative to a particular frame. So you have to specify the frame whenever you specify a time, distance, or speed.

After 1 second, at time t2 by the ship's clock, the ship notices the distance traveled by pulse is 300000 km relative to its own rest frame, which is a different frame from Frame A; we'll call this frame Frame S.

Note carefully the bolded additions; they are the only way to make your statement about the distance "the ship notices" correct. Notice also that time t2 here is by the ship's clock; it is not time according to Frame A. Again, that is the only way to make your statement correct. And that is why the "meanwhile" is struck through and corrected in the very next quote:

Meanwhile, After 1 second relative to Frame A, the ship has also moved the distance of 150000 km toward the moving pulse relative to Frame A. Therefore the distance between ship and trailing edge of the pulse should have been is 150000 km relative to Frame A BUT it is NOT.

Note carefully the strikethroughs and corrections. Note also how the two different distances, 150000 km and 300000 km, are relative to different frames. That's why they're numerically different.

For the ship to observe that the light has moved away 300000 km instead of 150000 km, some things need to change in the formula speed=distance/time. Ignoring length contraction of the ship, time slowdown should occur.

This all has to be simply discarded; there is no way to make it correct and no corresponding correct statement to put in its place. It is all simply wrong and you should forget it entirely.

The pulse was generated at time t1 relative to Frame A and then by time t2 relative to Frame A it had traveled the distance of 300000 km relative to Frame A. The difference between t2 and t1 is 1 second relative to Frame A.

Again note that the frame has to be specified.

For the ship to calculate the traveled distance by pulse to be 300000 km, the pulse should have actually moved the distance of 300000+150000 km after it was generated. But in ship's frame of reference it has traveled only 300000 km and this would require ship's clock running 1/1.5=0.67 times slower. Informally speaking, for light pulse's 1 second the ship clock has only ticked 0.67 seconds, and when ship clock ticks 1 second, the light pulse clock actually ticks 1.5 second.

Same comment here as two quotes above.

I am closing the thread at this point as I see no reason to repeat anything any further. You have more than enough information here and in previous posts.