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Author | Topic: General Relativity Question | |||||||||||||||||||||||||||
jmrozi1 Member (Idle past 5892 days) Posts: 79 From: Maryland Joined: |
I've recently learned about general relativity from my Physics professor, where English is his second language. Needless to say, there are parts of it that don't make sense, so I'm hoping someone can explain this next question.
I was given the following scenario (which I modified slightly): Consider an astronaut who has a twin on a planet, and relative to each other, they are stationary. Their speed relative to the inertial reference frame of the Universe, however, is unknown. The astronaut travels to some arbitrary point in space and back for what he thinks is a year, but upon arrival he notices that his twin has aged 10 years. This happens because he approached the speed of light on his trip which warped the effect of time on him, but obviously not the planet. Question: Why would this happen? If the astronaut approaches the speed of light, he is doing so relative to the speed of the planet. However, from the perspective of the astronaut, the planet would be moving nearly the speed of light. Given this logic, his twin should've only aged a month. Possible answer: I've considered that this is because of the speed of the astronaut based on the inertial reference frame of the two bodies. If this is right, then I have another, slightly more complex problem. Scenario 2: Consider 3 bodies that are stationary relative to each other. Body 1 remains stationary, but bodies 2 and 3 group together and take off with the same relative speed and orientation. At an arbitrary distance, body 2 heads back to body 1 at a speed half of what it traveled previously. Problem: According to the inertial reference frame of the 3 bodies, body 1 should be aging faster than body 2, which should be aging faster than body 3. However, taking the inertial reference frame set by bodies 2 and 3 after they finished accelerating, body 3 should be aging faster than body 2.
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Son Goku Inactive Member |
Your first example is basically the twin paradox and your second example is a more compliecated example of same.
The basic explanation is that accelerating ruins the inertial reference frame for a moment. Lets say, from earth's point of view, it takes the rocket 50 years to fly from Earth and back.I'll call the turning point, Point P. The rocket takes of at 80% of the speed of light and travels to point P.From Earth's point of view, this took 25 years, but it looks like (people on Earth are looking through a telescope) people on the rocket only aged 15 years. From the rocket's point of view it only took 15 years, but it looks like people on earth only aged 9 years. So in getting from Earth to point P we have the following information.Earth's point of view: It took 25 years but the rocket only aged 15. Rocket's point of view:It took 15 years but Earth only 9. Then the rocket accelerates so that it is heading at the same speed back to Earth. This acceleration causes Earth to jump from 9 years to 41 years from the rockets point of view.It takes 15 years for the rocket to return home, from the rockets point of view, in which time Earth ages 9 years. So from the rockets point of view, the rocket has experienced 15 + 15 = 30 years of travel and Earth has experienced 9 + 9 + 32 (from the acceleration) years. From Earth's point of view it took 50 years for Earth and the rocket aged only 30 years. So both agree it took 50 for Earth and 30 for the rocket. It's a lot to take in, but that essentially is the explanation. This message has been edited by Son Goku, 12-17-2005 05:45 PM
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cavediver Member (Idle past 3643 days) Posts: 4129 From: UK Joined: |
It's a lot to take in, but that essentially is the explanation. Love it SG... lovely break down.
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Son Goku Inactive Member |
Love it SG... lovely break down.
Thanks, I was wondering how clear it was. I love the paradox because when you understand it, it pulls one of the final Newtonian concepts from your mind, the notion of absolute simultaneity. To jmrozi1: This kind of "paradox" usually comes from thinking about relativistic time dilation, but keeping Newtonian concepts of simultaneity. As you can see at point P (before the acceleration) Earth aged 25 and the spaceship aged 15 are simultaneous from Earth's perspective. From the rocket perspective, Earth aged 9 and the rocket aged 15 are simultaneous.
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jmrozi1 Member (Idle past 5892 days) Posts: 79 From: Maryland Joined: |
I usually get this type of answer, but the detail that you went into was especially helpful in understanding the first question. The only part that remains vague is what it means for acceleration to ruin the inertial reference frame.
The bigger question comes from the second part: Speed is relative to what? I'll explain precisely what I'm asking through this next scenario:Goku is launched in a rocket away from Earth, which after 1 hour travels 80% the speed of light relative to the planet. Out of boredom, he decides to play catch with Gohan, and reaches into his pocket to grab his indestructible baseball. After he powers up a couple levels, he chucks the ball at 50% the speed of light back at the planet. First glance: The Earth might’ve aged 25 hours, but it appears as though the space ship has only aged only 15. When the ball is thrown back, it never reaches the Earth because it is still traveling away from it at 30% the speed of light. After the ball is thrown, we have that the Earth (stationary) is aging faster than the ball (30% speed of light), which is aging faster than Goku (80% speed of light). What are these speeds relative to? The initial inertial reference frame. Second glance: After the rocket hits full speed, Goku and the baseball set a new inertial reference frame. Throwing the baseball will make it travel 50% the speed of light relative to Goku, so the ball seems to be aging slower than Goku. Taking the planet out of the picture, we have that Goku (stationary) is aging faster than the ball (50% the speed of light). These speeds are relative to the new inertial reference frame. I hope this better explained why I’m confused. It doesn’t seem that the presence of the planet should determine whether or not the ball ages faster or slower than Goku, but it doesn’t seem that you should only be able to take into account the initial inertial reference frame. I’m thinking either that the answer lies in the acceleration ruining the inertial reference frame, or my misconception of apparent aging.
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Son Goku Inactive Member |
The only part that remains vague is what it means for acceleration to ruin the inertial reference frame.
A rather mundane answer, but an inertial reference frame is one with constant velocity, when you accelerate you aren't keeping your velocity constant.
What are these speeds relative to? The initial inertial reference frame.
Everything else. We have nine pieces of information here:The aging and speed of the Earth with respect to Earth The aging and speed of the Ball with respect to Earth The aging and speed of the Rocket with respect to Earth The aging and speed of the Earth with respect to Rocket The aging and speed of the Ball with respect to Rocket The aging and speed of the Rocket with respect to Rocket The aging and speed of the Earth with respect to Ball The aging and speed of the Ball with respect to Ball The aging and speed of the Rocket with respect to Ball A few of these will agree. This is the answer to your question. There can be a variety of answers to the question, "What is the speed of the ball?", depending on which one of the observers you ask, same for the other two. As a side note, what your discussing here is actually Special Relativity, which isn't half as wierd or complicated as General Relativity.
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jmrozi1 Member (Idle past 5892 days) Posts: 79 From: Maryland Joined: |
A few of these will agree. How interesting. I'm gathering that aging itself is relative, which would definitely solve my paradox. Thanks for your help!
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cavediver Member (Idle past 3643 days) Posts: 4129 From: UK Joined: |
I think the biggest problem with the Twins Paradox is that two very different phenomena are being discussed and confused. We have inertial frame transformation laws and we have the observers' proper time. The real paradox is why does anyone think this is still a good scenario to discuss in the teaching of SR, other than after the teaching of proper time...
What do you think?
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NosyNed Member Posts: 8996 From: Canada Joined: |
Then the rocket accelerates so that it is heading at the same speed back to Earth. This acceleration causes Earth to jump from 9 years to 41 years from the rockets point of view. I've always taken it that GR would be used to show this "jump". Is that correct? The phrase "causes Earth to jump from ..." seems to be waving a wand here. If is possible to add just a little explanation? If it is a GR calculation how does the time taken to change direction (and therefor the magnitude of the accelerations) enter into it? Thanks
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Son Goku Inactive Member |
"NosyNed" writes:
Yes, pretty much. There is a way you can make Special Relativity treat it, but in reality it is a GR question.
I've always taken it that GR would be used to show this "jump". Is that correct? "NosyNed" writes:
It's entirely handwaving. Essentially a way of putting a balck box around the point of acceleration. The phrase "causes Earth to jump from ..." seems to be waving a wand here. If is possible to add just a little explanation? If it is a GR calculation how does the time taken to change direction (and therefor the magnitude of the accelerations) enter into it? Here is the explanation using the barest hint of General Relatiivty, because I really don't want to use the acceleration metric. I'm going to go as far as I can with Special Relativity first.Before acceleration the ship is in frame O' and after acceleration the ship is in frame O''. We will also say that t(P' or P'') is the age of Earth as viewed from that frame. The velocities of the frames relative to Earth are v'= 4/5 c and v''= -4/5 c respectively. However lets see what their velocity are with respect to eachother. From the relativistic velocity addition law we find this velocity to be 40/41 c. And the respective gamma factor is g = 41/9. This means that the time dilation effect between the O' and O'' frames is such that a time interval of t(P') = 9 years in O' is viewed as t(P'') = gt(P') = 41 years in the O'' frame. The General Relativistic reason for this effect basically comes from the equivalence principle.So the acceleration a point P from frame O' to O'' is basically the same as an object falling from one height above a giant planet to another height and the effect comes from gravitational time dilation between these two heights. I'll go into more detail if you want. "cavediver" writes:
I know what you mean. In fact one of my biggest issues when people teach SR is that they downplay or don't deal with proper time. I think the biggest problem with the Twins Paradox is that two very different phenomena are being discussed and confused. We have inertial frame transformation laws and we have the observers' proper time. The real paradox is why does anyone think this is still a good scenario to discuss in the teaching of SR, other than after the teaching of proper time... What do you think? Which is unusual given its importance in GR. To be honest I always thought the "pole in the barn" paradox should be introduced first, if you going to bother with paradoxes at all.
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cavediver Member (Idle past 3643 days) Posts: 4129 From: UK Joined: |
quote: Yes, pretty much. There is a way you can make Special Relativity treat it, but in reality it is a GR question. In fact one of my biggest issues when people teach SR is that they downplay or don't deal with proper time. Heh, heh, I would claim you are doing that here. You don't need to go into GR at all. Acceleration is handled perfectly well in SR... again, it's just a case of integrating up the respective proper times. At the end of the day, if your space-time is Weyl and Ricci flat then you are working in SR. Then again, it does depend somewhat on what you define as SR...
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Son Goku Inactive Member |
I suspected you would say something.
You are of course right, SR does deal with this perfectly well. Its just the way I seperate GR and SR in my head. This message has been edited by Son Goku, 12-21-2005 01:58 PM
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cavediver Member (Idle past 3643 days) Posts: 4129 From: UK Joined: |
I suspected you would say something. That predictable, huh
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Son Goku Inactive Member |
I'm glad to be on a forum where somebody will pull me up on it.
As a side question for myself, thats related to Quantising GR, what do you think of Loop Quantum Gravity?I don't know much about it or String, so I'd be happy to hear your opinion.
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