Relativity problem: (Twin Paradox)?

Question

Problem 1: When 18 seconds elapse on a clock on the alien spaceship traveling at 4/7, how much time elapses on Earth clocls according to Earth observers?

Problem 2: The aliens observe an experiment on Earth as they fly by at a speed of 4/7. If Earth observers measure the duration of the experiment to be 30 seconds, what will be the duration of the experiment according to the alien observers?

misspelling on the word 'clocks'

Answer 1

Problem 1:

The same amount of time. Both would insist the other's clocks were running slower. Earth would say that the alien's clock didn't tick off 18 seconds. The aliens would say the Earths clocks didn't tick off 18 seconds. It would seem to the aliens and to Earth that the other's clock was running slow.

To actually check, you the aliens would have to give up their claim of being at rest by turning around and bringing their clock back to Earth for a comparison. Either way, they would agree the experiment took 18 seconds, but the alien clock would be found to be behind Earth's clock.

Problem 2:

Both would say the experiment took the same amount of time.

The alien would say 30 seconds but would say the clocks on Earth were running slow and would insist on being right.

The Earth would say the 30 seconds but would say the alien clocks were running slow and would insist on being right.

The thing is, they are both right. Its relative. BOTH the alien and the Earth can claim to be still. Earth says the ship was moving, but the ship can claim the Earth was moving.

The resolution is the fact that to compare notes, the aliens would have to slow down and reverse course - this act gives up their ability to claim it was the Earth moving because they have shown an absolute motion in the act of slowing down and changing course.

Therefore, the alien clocks were running slower even though to the aliens it seemed like it was the Earth running slow.

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Its not about an absolute answer. That's what Relativity is all about - there is no absolute frame of reference and thus there is only relative time, mass length and speed. The only absolute is the speed of light - it will always be measured to be the same for all observers all the time. This doesn't mean that if you are going half the speed of light that light is actually going 1.5 times the speed of light - merely that you will observe it to go the speed of light.

Answer 2

Problem 1: 30 seconds?

Problem 2: 18 seconds?

the constant is that the aliens are flying by at 4/7. So, if the alien spaceship is traveling at 4/7 (i'm guessing that this number could be any variable, but it's constant between the two problems) then the two problems are related. Let me smoke some weed then i'll get back to you.

Answer 3

I believe this is a characteristic of Einstein's general relativity (GR). You plug "known" gravity fields into the space-time "metric" and you get a "solution" which is considered to be true. Trouble is, acceleration due to your ship's engine is considered to be a gravity field. The trouble is not so much in the formulas as it is in the jargon, which makes the future problem sound like a done deal. There is an alternative method of computation. You can solve the problem by a numerical computer program, applying special relativity to short time intervals. If the time intervals are short enough, you will get exactly the same result as GR. Of course, you could make the same result of assuming the journey will go as planned. The difference is, you get a result that is valid up to the point where reality deviates from the plan.

Answer 4

T m=T r/[I-v^2/c^2)]^1/2