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Relative Motion Question


ParanoiA
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Ok, well I thought myself into another conundrum....

 

Ok, if I leave earth in a spaceship traveling 80% of the speed of light and come back in 5 years my time, then I have aged 5 years, while the earth and everyone on it has aged several decades.

 

So, here's my question: If motion is all relative, then why do I age less and everyone else ages more?

 

We both see our clocks running slower, however I'm the only one that time slows down for. If motion is relative, then shouldn't this be the same as the earth traveling 80% of the speed of light and coming back to me in 5 years their time?

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The difference is in which one has accelerated.

 

Search the threads in the Relativity subforum and you will find plenty of better and more detailed answers from the experts.

 

I had a feeling that would have to do with it. But I figured even the acceleration could be considered relative. I'll follow your advice and see if I can find any threads on it.

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Acceleration is not relative — you can tell who is being accelerated.

 

You know, I thought about that after I posted that. Because I read that a simple change in direction is acceleration - which makes sense - so you can obviously tell who is accelerating. And I also remember reading that you can feel acceleration, whereas "force-free" motion is relative.

 

The thing is, the book makes a point in one example where Slim is in a car traveling 120 miles per hour and passes Jim standing on the side of the road and they point out that Jim is in relative motion to Slim. That from Slim's perspective, Jim is passing him at 120 miles per hour.

 

That has me all messed up because that isn't "force-free" motion, which is how Greene explained the relative motion in space. But is that considered acceleration because of the friction of gravity even though he's traveling at a constant speed?

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Acceleration requires a force to act on a body. This force can be detected and so it can be shown who is accelerating. Consequently we know that it is Slim travelling at 120mph and not Jim.

 

"force free" motion is motion where there is no net force on the body. That is, the velocity (speed and direction) is constant. When you have a constant velocity relative to someone else you both think that the other person is moving and you are stationary. Technically you are both correct.

 

Regarding friction: when a car moves along the road there is friction acting against its motion. This friction exerts a force on the car, changing its velocity (slowing its speed). When a car moves at a constant velocity there is a driving force (supplied by the engine), which is equal in magnitude and opposite in direction, to the frictional force. So although there is say 10N backwards due to friction, there is also 10N forward due to the engine. The net force on the car is 0, that is the 10N back and 10N forward cancel, therefore the car continues to move at a constant velocity. This is considered "force free" because the net force on the body is 0.

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Acceleration requires a force to act on a body. This force can be detected and so it can be shown who is accelerating. Consequently we know that it is Slim travelling at 120mph and not Jim.

 

Typically in these problems the original acceleration is ignored, since once it stops, there is no residual effect. In essence, one can suppose that Slim had been asleep (presumably as a passenger) during the acceleration, and nobody else is observing him during that time. When he wakes up, there is no test that he can do that will absolutely demonstrate that he is in motion and not Jim.

 

This mimics the notion that we can't account for any past accelerations of the earth, solar system or anything we now observe, before we started observing (without additional information being uncovered). IOW, there is no absolute reference frame.

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Acceleration is not relative — you can tell who is being accelerated.

You also yourself can feel the difference. The person, who travels feels the acceleration (think of the astronauts, who feel terrible forces, when they lift off), the other person, who stays behind, does not feel any acceleration.

 

Acceleration is equivalent to gravity (we cannot tell the difference, relativistically speaking, there is no difference). Acceleration leads to slowing down of time (relative to the observer, who does not feel acceleration). This added effect removes the seemingly paradox situation and time has slowed down for the traveling person, both seen by the traveler himself and the person who stayed behind.

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Typically in these problems the original acceleration is ignored, since once it stops, there is no residual effect. In essence, one can suppose that Slim had been asleep (presumably as a passenger) during the acceleration, and nobody else is observing him during that time. When he wakes up, there is no test that he can do that will absolutely demonstrate that he is in motion and not Jim.

 

This mimics the notion that we can't account for any past accelerations of the earth, solar system or anything we now observe, before we started observing (without additional information being uncovered). IOW, there is no absolute reference frame.

 

I guess that's what I need to focus on is reference frame. The point Greene is trying to make is that Slim will see Jim's clock running slow, while Jim will see Slim's clock running slow.

 

So, it sounds like you have to carefully think out all of the forces involved to establish if you have force-free motion. At that point, both observers have an equal claim on being stationary and the other's clock is running slow. Otherwise, one is accelerating which establishes who is in motion.

 

So, how does acceleration really change anything, in terms of clocks running slow or fast? What if Slim were to slowly accelerate throughout his run from point A to point B, from 120 mph to 200 mph? Wouldn't they both still see each other's clocks running slower?

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Paranoia: The issue here is pretty deep, and whilst acceleration is the answer, it doesn't get to the bottom of it or explain it properly. I won't go into the details, but I can illustrate what's going on with "bricks and ticks".

 

http://sheol.org/throopw/sr-ticks-n-bricks.html

 

Imagine you're in a spaceship heading away from earth, whilst I stay on earth. Also imagine that we're each laying a line of bricks, but because of our different velocities, we're laying bricks at an angle to one another:

 

/

 

When you look sidelong at my bricks, the angle makes them look shorter than yours. And when I look sidelong at your bricks, they look shorter than mine.

 

Now you change direction and start coming back to earth. You keep laying your bricks, so as far as you're concerned they make a straight line. And when you look sidelong at my bricks, they still look shorter than your bricks. But now instead of heading away from you, my bricks now look as if they're coming towards you.

 

/\

 

When you get back to earth you find that the total length of my bricks is longer than the total length of your bricks. I aged more than you, even though all the while my bricks (or my seconds), looked shorter than yours to you, and your bricks (or your seconds) looked shorter than mine to me.

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This is an interesting way of describing what's going on. I clicked on the link you provided too and glanced over it. I'm going to study all of this tomorrow and see if I can get my head around it.

 

Before I continue, is it correct to equate a change of direction to acceleration?

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I guess that's what I need to focus on is reference frame. The point Greene is trying to make is that Slim will see Jim's clock running slow, while Jim will see Slim's clock running slow.

 

So, it sounds like you have to carefully think out all of the forces involved to establish if you have force-free motion. At that point, both observers have an equal claim on being stationary and the other's clock is running slow. Otherwise, one is accelerating which establishes who is in motion.

 

So, how does acceleration really change anything, in terms of clocks running slow or fast? What if Slim were to slowly accelerate throughout his run from point A to point B, from 120 mph to 200 mph? Wouldn't they both still see each other's clocks running slower?

 

Bringing acceleration into moves us from special relativity to general relativity; where the math gets a lot harder. This specific example may or may not be difficult, but I have yet to see a simple equation like this for general relativity.

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ParanoiA: Yes. A change of direction is acceleration. And your question is what's called the "Twins Paradox". Like I said, acceleration is the answer, but doesn't explain it. You need to understand spacetime and velocity to get a grasp of what's going on. It's shockingly easy when you do understand, but there's a conceptual hurdle to overcome, and that's quite difficult.

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ParanoiA: Yes. A change of direction is acceleration. And your question is what's called the "Twins Paradox". Like I said, acceleration is the answer, but doesn't explain it. You need to understand spacetime and velocity to get a grasp of what's going on. It's shockingly easy when you do understand, but there's a conceptual hurdle to overcome, and that's quite difficult.

 

I'm having quite a time trying to interpret the graph in the "unaccelerated twin paradox" (the link within the link you provided above).

 

I'm not sure why there are 3 observers rather than 2. One of them is moving -0.8660 lightspeed relative to O1 which isn't making any sense to me and I'm guessing O1 would be the equivalent of a stationary observer on earth since there is no spatial direction (assuming we're supposed to suspend the idea of earth's motion).

 

O2 is the only one making sense to me since it's traveling through time and space, which seems to fit with the time dilation factor of 2 - I'm assuming means for every one hour experienced by O2 is two hours experienced by O1.

 

I'm going to keep looking at this, but it sure would be nice to have an instructor with a chaulk board.

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That one's too complicated ParanoiA. I'd leave it if I were you. Just concentrate on the bricklaying twins. The thing with all this is that people make it too complicated when really it's very simple:

 

When you've got a feel for the bricklaying twins, imagine you're spreadeagled out flying through space at a velocity of c. Now, can you move your arm?

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Well, the ole lightbulb just isn't coming on. I understand the angles of the bricks making them appear shorter to each observer, and I'm following the steps as they seem pretty easy. The final explanation though just isn't there.

 

It shows a triangle made from the red brick wall and the two blue brick walls. Then two more thinner blue lines outside of those. I don't understand what those are. I'm pretty sure that's key to understanding the point of the example. So far, they seem to be arbitrary lines that just popped up out of nowhere. So, the reason discussed afterwards still doesn't help me since I don't know where these thin blue lines came from.

 

I'm going to see if there are any other examples on the net. I feel like I'm getting close...

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Well this was interesting. I think I finally got it - in fact I think I had it for awhile but as usual, I get hung up questioning the details of an example or lecture.

 

Acceleration changes your reference frame. If we're going a constant velocity - no matter which direction we're each heading - our reference frames are symmetrical. I may not be able to physically observe you, but we are in sync in terms of time. We will observe each other's clocks moving slower, but we would be consistent and in sync with each other to a third observer with a magical instantaneous observation technique. (Although we may not be in sync with that third observer.)

 

Once I change direction, I've accelerated and destroyed the symmetry. Now, we are no longer in sync. No matter what I do from that moment forward, we are out of sync in terms of time. And I would also venture to say, that as I keep on this new course the consequences also increase.

 

This is what was holding me up. I couldn't understand why a simple acceleration, 2 second burst of energy to change direction, would circumvent so much time when I made it back to earth. I believe it is because the acceleration changed the reference frame, and this continues to effect time as I continue on this new direction - the longer I stay on course, the further I get from the original reference frame.

 

Am I right about any of this?

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When you've got a feel for the bricklaying twins, imagine you're spreadeagled out flying through space at a velocity of c. Now, can you move your arm?

 

I would say no since moving my arm would attempt to accelerate past c, and nothing can travel faster than c.

 

Although, I don't think I could fly at c anyway, since my mass would be infinite and therefore nothing could push me - actually since my mass would be infinite there would be nothing to push me. I wonder how close to c we could realisticly travel.

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You're right on both counts there ParanoiA. I think. You wouldn't be able to move your arm, and you wouldn't be able to travel at c anyway. The point is, if you could travel at c, you'd experience no time.

 

See my post 10 re the bricks and ticks. I didn't quite like the explanation in the link so tried to rephrase it.

 

I don't think "reference frames" gets to the bottom of it or really explains what's going on. It's to do with how much time you experience. If you're travelling at c you experience none. If you're travelling at 0 you experience lots. At c/2 you experience less.

 

Uh, work calls, gotta go.

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I got your PM ParanoiA.

 

The important thing to remember that is you move fast you experience less time. It's like you're a metronome, where each tick is a thought in your head or a beat of your heart. If you're moving forward at c the metronome can't tick, because any transverse motion would cause c to be exceeded. Everything looks motionless, and you experience no time. If you're moving forward at just under c you can tick, but not very fast, so you experience time but not much. If you're not moving forward at all, the metronome is free to tick with a transverse motion of c, and you experience lots of time. This is what Special Relativity tells us. You can look this up and check it out. The simple way to look at it is that your time experience depends on how the motion of your photons/electrons/atoms is "cut" into the forward and transverse elements.

 

 

OK. You're moving apart from your twin, and you each have a different time experience.

 

/

 

But you don't know if it's you moving or your twin moving, so there's that symmetry when you look at each other's time experience. It's like you're a couple of bricklayers with an angled perspective. Your bricks look shorter to him and his bricks look shorter to you. Only they're not bricks they're ticks. Time.

 

When you turn round and start heading back you still have an angled perspective. But when you meet you can now compare your respective time experience. The thing to remember is you're the guy on the bottom. Your twin was receding from you, and after you turned around, he wasn't. Anyhow. You find that you experienced less time than him.

 

/\

 

There was never any paradox. It can all be explained very simply. But there is a stunning consequence.

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The important thing to remember that is you move fast you experience less time.

 

"You" never move fast, though. You are always considered to be at rest. It's always somebody else that's moving, and their clocks run slow, relative to your stationary frame.

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Yeah, see I like the way Greene explained best, but it still fits with what you guys are saying.

 

He explains it by considering that everything is constantly in motion. If you're at rest, then all of your motion is directed through time. When you are traveling spatially, some of that motion through time is "re-directed" to spatial movement. As if you have some static speed that we are all traveling, and that speed is redirected to move us through space. The faster you're going, the more of your motion is diverted to space, taken from motion through time.

 

I don't know why, but I really get that. That makes sense to me.

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Yeah, see I like the way Greene explained best, but it still fits with what you guys are saying.

 

He explains it by considering that everything is constantly in motion. If you're at rest, then all of your motion is directed through time. When you are traveling spatially, some of that motion through time is "re-directed" to spatial movement. As if you have some static speed that we are all traveling, and that speed is redirected to move us through space. The faster you're going, the more of your motion is diverted to space, taken from motion through time.

 

I don't know why, but I really get that. That makes sense to me.

 

That's another way of saying that an object's velocity through flat spacetime (4-velocity) is invariant, and always c.

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