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Offline thebrain13

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sr ( special relativity )
« on: 15/04/2007 22:53:53 »
Okay, two spaceships are traveling away from each other. Pilot a is traveling leftward and pilot b is traveling to the right. Now pilot a accelerates towards pilot b untill he catches him. How old are the two pilots in relation to one another?
« Last Edit: 16/04/2007 22:41:43 by daveshorts »


 

Offline Soul Surfer

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Re: sr ( special relativity )
« Reply #1 on: 15/04/2007 23:30:47 »
There is insufficient information to answer this question
 

Offline thebrain13

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Re: sr ( special relativity )
« Reply #2 on: 16/04/2007 00:45:13 »
How so? I was just wondering who would be older, I dont need any math, or were you implying something else?
 

Offline neilep

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Re: sr ( special relativity )
« Reply #3 on: 16/04/2007 00:52:03 »
Were the pilots the same age to begin with ?
 

Offline thebrain13

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Re: sr ( special relativity )
« Reply #4 on: 16/04/2007 01:08:08 »
ya
 

Offline Seany

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Re: sr ( special relativity )
« Reply #5 on: 16/04/2007 01:52:09 »
Doesn't that mean that they are both the same age now? Time goes by, even if the direction of us is... Wait.. Ye..

Isn't this question like saying.. I have a friend who I haven't met in 40 years. We were born on the same date. He is still alive. How old is he now?

Unless of course, the speed of the spaceship is faster than light, in which case, time wouldn't go by.. but..
 

Offline ukmicky

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Re: sr ( special relativity )
« Reply #6 on: 16/04/2007 04:09:24 »
How old they are compared to each other would depend on their respective speeds anddistance they have travelled.
 

Offline lightarrow

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Re: sr ( special relativity )
« Reply #7 on: 16/04/2007 08:08:30 »
How so? I was just wondering who would be older, I dont need any math, or were you implying something else?
If they have the same age when they leave and only pilot a accelerates, then b is older than a when they meet again. (See also my last post on the twin paradox thread).

Said in another way: the straight world-line in space-time is the one with the maximum proper time.

It's easy to understand this matemathically: proper time is tau = Δs/c and:
Δs12 = (cΔt)2 - (Δx)2 for the one who accelerates;
Δs22 = (cΔt)2 - 0 for the one who doesn't accelerate.
So Δs2 > Δs1 → tau2 > tau1.
« Last Edit: 16/04/2007 08:17:52 by lightarrow »
 

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Re: sr ( special relativity )
« Reply #8 on: 16/04/2007 08:51:01 »
How so? I was just wondering who would be older, I dont need any math, or were you implying something else?
If they have the same age when they leave and only pilot a accelerates, then b is older than a when they meet again. (See also my last post on the twin paradox thread).

But the inference must be that the two pilots were once in the same inertial reference before the experiment started, and so by inference, both pilots accelerated initially, one if a negative sense to the other, and then pilot B then massively accelerated again, but in the opposite sense to which he accelerated initially, and then remains in a constant inertial frame until he catches up with pilot A, and then accelerates in the opposite direction again until he matches the inertial frame of pilot A.
 

Offline DoctorBeaver

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Re: sr ( special relativity )
« Reply #9 on: 16/04/2007 08:52:44 »
How so? I was just wondering who would be older, I dont need any math, or were you implying something else?
If they have the same age when they leave and only pilot a accelerates, then b is older than a when they meet again. (See also my last post on the twin paradox thread).

But the inference must be that the two pilots were once in the same inertial reference before the experiment started, and so by inference, both pilots accelerated initially, one if a negative sense to the other, and then pilot B then massively accelerated again, but in the opposite sense to which he accelerated initially, and then remains in a constant inertial frame until he catches up with pilot A, and then accelerates in the opposite direction again until he matches the inertial frame of pilot A.

Pardon?  ???
 

Offline lightarrow

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Re: sr ( special relativity )
« Reply #10 on: 16/04/2007 12:08:06 »
How so? I was just wondering who would be older, I dont need any math, or were you implying something else?
If they have the same age when they leave and only pilot a accelerates, then b is older than a when they meet again. (See also my last post on the twin paradox thread).
But the inference must be that the two pilots were once in the same inertial reference before the experiment started, and so by inference, both pilots accelerated initially, one if a negative sense to the other, and then pilot B then massively accelerated again, but in the opposite sense to which he accelerated initially, and then remains in a constant inertial frame until he catches up with pilot A, and then accelerates in the opposite direction again until he matches the inertial frame of pilot A.
What counts is what happens from the moment they leave, if we assume they have sincronized watches in that moment.

About who is accelerating:
In the thread of twin paradox A stays in an inertial ref. frame while B accelerates. In this thread thebrain considered b in an inertial r.f. and a the one who accelerates.

So, this is the situation:
At t = 0 they are both in an inertial ref. frame, travelling in opposite senses (with respect to a specific inertial ref. f.); in general, they travel with different velocities; in some ref. frame these velocities are in the same direction (= line) and sense, in another one they are in the same direction and different sense, in another they are in different directions...ecc. Nothing changes.

Let's say we are in that ref. frame in which they travel in the same direction but in opposite senses.
Then  pilot a wants to catch b so he brakes, turns around 180° and then accelerates towards b for a while, getting a speed higher than b's speed; then switch offs the engines and wait to catch b.
All this (with B instead of a and A instead of b) is explained with the diagrams in the twin paradox thread .
 

Offline Seany

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Re: sr ( special relativity )
« Reply #11 on: 16/04/2007 16:41:30 »
What does actually "sr" stand for or mean.. or whatever? ???
 

Offline lightarrow

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Re: sr ( special relativity )
« Reply #12 on: 16/04/2007 21:23:02 »
What does actually "sr" stand for or mean.. or whatever? ???
Special Relativity.
 

Offline thebrain13

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sr ( special relativity )
« Reply #13 on: 20/04/2007 02:03:47 »
Allright lets say two spaceships are seperated, one spaceship accelerates towards the other at .5c, the other ship accelerates a fraction of a second later at .25c. the trip takes one year to complete. How old are the two pilots in relation to one another?
 

Offline Soul Surfer

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sr ( special relativity )
« Reply #14 on: 20/04/2007 11:04:59 »
Again the information is not correct 0.5c is a velocity not an acceleration you need to know how fast the acceleration is because if you want a human being to survive it mustn't be all that different from 1 g  ie around 10 meters per second per second. to get up to 100,000,000 meters per second (100,000 km/sec around a third of the velocity of light) it takes 10,000,000 seconds or around 115 days so almost all the time allocated for the journey must be acceleration time. 

It is true that the person who has measured least time on a journey between any two (equivalent)reference points in space and time is the person who has travelled fastest but you need to put much more details into the journeys to get an accurate answer.
 

Offline lightarrow

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sr ( special relativity )
« Reply #15 on: 20/04/2007 15:25:04 »
Allright lets say two spaceships are seperated, one spaceship accelerates towards the other at .5c, the other ship accelerates a fraction of a second later at .25c. the trip takes one year to complete. How old are the two pilots in relation to one another?
As Ian said, you should specify the accelerations, in order to draw space-time diagrams. However this is true unless the accelerations lasts for a very short proper time (and the problem would be much more easy to solve, even because accelerations could be neglected in the computation). In this case the accelerations could even be very large, but the experiment should be performed with watches only and not humans (or they will die, as Ian said).

If you gives more parameters, in order to solve the problem, remember to also specify which time you are talking about. For example, when you say "the other ship accelerates a fraction of a second later at .25c", specify to which ref. frame you are expressing the time.
 

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sr ( special relativity )
« Reply #15 on: 20/04/2007 15:25:04 »

 

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