
#55
Jan408, 09:30 PM

P: 411

Here is a simple analogy. I fly from home to a city 200 miles distant at 100 mph in 2 hr.
Later I fly from home to the same city at 200 mph in 1 hr. The distance didn't change, the time did. The space travelers time changes with his speed, he gets there quicker according to his clock. That's because his clock is parsing time into longer units. Reasoning if his units are longer, there will be more events recorded in them, so he will observe events happening at a faster rate outside his ship in the direction of motion and slower in the opposite direction. Consider the doppler shift, faster ahead, slower behind. Reasoning tells you launching into space does not shrink the universe! What physical process would accomplish this? 



#56
Jan408, 09:39 PM

P: 3,966

In the paradox the 2 spaceships accelerate at the same rate. From the launch frame the distance between the 2 spaceships remains the same, but the spaceships themselves appear to be length contracting. If the distance between the spaceships is large compared to the lengths of the spaceships we can ignore the length contraction of the spaceships themselves as far as the string is concerned. Imagine the string is connected from the centre of one ship to the centre of the other, so that the string is unaffected by any change in length of the ships themselves. From the point of view of the observers on the spaceships the lengths of their ships remains unchanged, but the distance between the 2 ships is increasing. (They can measure that distance by sending light signals from one ship to the other and measuring the round trips times of the signals.) From their point of view, the increasing distance causes the string to stretch and eventually snap. From the launch frame the distance between the two ships remains the same but the string is trying to length contract and snaps because it is shorter than the seperation distance. 



#57
Jan408, 09:48 PM

P: 196





#58
Jan408, 10:00 PM

P: 3,966

If the string was replaced by a very strong cable then the ships would be pulled together and the distance between the ships would appear constant to the observers onboard the ships and length contracted to the observers in the launch frame. Hope that makes sense :P 



#59
Jan408, 10:38 PM

P: 196

So if you fly to a distant planet close to c, the space you travel doesn't look length contracted just because it's empty space? That can't be true. The separation between the 2 spaceships must look length contracted from the ground. If it doesn't then relativity is flawed. From the ship's point of view, the distance is constant otherwise they would themselves have to stretch (regardless of their size kev ;) ) ps I understood your argument, it's just a badly flawed one as far as I can tell. 



#60
Jan408, 11:50 PM

P: 3,966

The ships themselves are also length contracting from the POV of the Earth observer, but time dilation of the spaceship clocks and the way they syncronise their clocks make it seem to them that the length of their spaceships remain unchanged. 



#61
Jan508, 02:58 AM

P: 235

for example, if you measured the distance to a planet whilst in earths frame of reference and found it to be say 7 lightyears away... then flew in a spaceship at 99% of c and undertook the same measurement to the planet, wouldn't it appear to be only one light year away now?? I know if i did this it would seem to APPEAR to me that space had contracted. 



#62
Jan508, 06:12 AM

P: 1,504

But if you meant something else, that is that things are *mechanical* compressed, then that is not true (at least in special relativity, with constant velocities); the contraction is due to relativity of simultaneity, that is that to measure a ruler's lenght you have, by definition of lenght's measure, to simultaneously find the positions of its initial and final points, and if two spatially separated events are simultaneous in a ref. frame, they are not in another which is moving with respect to the first, so the ruler's lenght that you measure is different. 



#63
Jan508, 06:47 AM

Mentor
P: 40,875

Think of the accelerations happening in bursts. At some point the ships are a distance L apart and move at speed V (according to earth observers). They fire their rockets to add a burst of speed [itex]\Delta V[/itex]. Ah, but those rockets fire simultaneously according to earth observers, but not according to the rocket observers. According to the rocket frame, the lead rocket fired firstthus stretching out the distance between the rockets in the rocket frame. (The string breaks, of course.) 



#64
Jan508, 07:45 AM

P: 235





#65
Jan508, 04:28 PM

P: 196

kev's explanation was simply that the spaceships cannot possibly stretch because they were made out of some absolutely rigid, solid material ( whatever that is !), And that the string wasn't manufactured from the same amazing stuff.... 



#66
Jan508, 04:44 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,879

In relativity, there is not and cannot be any "absolutely rigid, solid material".
If there were, imagine a thing rod made of that material extending from the earth to the moon. Give a hard rap on your end that moves the rod, say, .001 cm. If the material were really "absolutely rigid" the other end would move at exactly the same time giving you a way to communicate with the moon instantaneously. Since a message cannot be sent faster than the speed of light, any material must be sufficiently elastic that the "rap" moves up the rod in a wave with speed less than the speed of light. 



#67
Jan508, 04:55 PM

P: 196

The spaceships are not rigid  there's way too many gaps (relatively huge empty spaces) between the atoms/nuclei in a real spaceship. 



#68
Jan508, 06:43 PM

P: 411

If not true then the objects are just moving by you faster! The 1st choice leaves you with another question, the 2nd does not. 



#69
Jan508, 09:53 PM

P: 3,966

If you tie a string between two cars and get the front car to accelerate harder the string will initially strech then snap. This does not require the cars to made of infinitely rigid material and can easily to be demostrated. In the spaceship example the front spaceship has to thrust harder in order to maintain a constant gap (as measured in the Earth frame) while the two ships are connected by the string, and the additional energy being expended by the front ship results in stress on the string and eventually snaps it. 



#70
Jan808, 11:46 PM

P: 196

Regardless kev, the point I was making was that your argument doesn't hold any water on purely logical grounds. And if anything it only reinforces my view that the space inside the spaceships (or trains or whatever) cannot be treated any differently from the space outside  regardless of which frame you are refering to.
I still have to think over DocAl's referal to the usual problem/explanation of simultaneity. If anything that is more likely to lead to a loigical explanation.  If there is one. ;) 



#71
Jan908, 07:38 AM

Mentor
P: 40,875

If, by some strange process that I can't imagine, all the pieces of the rocket are also uniformly accelerated with respect to earth observers, then you're rightthe rocket, unless extremely tough, will be torn apart just like the string. Measured from earth, its length will not contract at all. (Of course, that's because it's being stretched apart by whatever forces are accelerating it!) But there's no reason to assume such a strange arrangement. In my mental picture of this "paradox" the string is miles long while the rockets are tiny. We care about the string breaking, not about what happens to the rocketswho cares how they contract? Whether an accelerating body contracts or not depends on the details of how it is accelerated. Usually we just assume that somehow the rocket accelerates to some final speed and managed to do that without destroying itself. The idealized case is that the rocket pieces accelerate uniformly with respect to a reference frame comoving with the rocket (actually a continually changing inertial frame). In that case, the rocket is never under any stress at allit never changes length with respect to that comoving frame. Of course, earth observers measure the contraction as the rocket speeds up. (To earth observers, the pieces do not accelerate uniformlyit's the converse of the Bell spaceship scenario.) 



#72
Jan1408, 06:08 PM

P: 91

If that's the case, then can you tell us why the travelling twin is younger than the one stays at home? 


Register to reply 
Related Discussions  
Real time effects of light, light speed, and the sun?  General Astronomy  4  
Time slows at the speed of light  Special & General Relativity  1  
since time slows down in a strong gravitational field, does time stop in a black hole  Special & General Relativity  12  
Why Do You Travel Into The Future As You Approach The Speed Of Light?  Special & General Relativity  14  
Time slows as you speed up right, so..... ???  General Discussion  5 