# Time slows down when you approach the speed of light?

by catia
Tags: light, slows, speed, time
 P: 421 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?
P: 3,967
 Quote by YellowTaxi well if you think the string breaks then you must believe the 2 spaceships actually physically stretch (viewed from their own frame) for precisely the same reason... So does this actual physical stretching precisley cancel out the observed length contraction seen from the launch-pad ?

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.
P: 196
 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 separation distance.
Then kev, you're saying that the distance from the front tip to the rear end of each ship will actually increase for the same reason. The ships will eventually tear themselves apart by that logic. On top of that there should be no observable length contraction from the ground.
P: 3,967
 Quote by YellowTaxi Then kev, you're saying that the distance from the front tip to the rear end of each ship will actually increase for the same reason. The ships will eventually tear themselves apart by that logic. On top of that there should be no observable length contraction from the ground.
Nope, I said from the launch frame the ships would length contract (tip to rear length). The ships are solid objects made of atoms bound together so they length contract. The distance between the two ships is empty space so it does not pull the ships together. The only thing between the ships is the string, and for the purpose of the paradox it is assumed the string is not strong enough to pull the ships together and snaps.

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
P: 196
 Quote by kev Nope, I said from the launch frame the ships would length contract (tip to rear length). The ships are solid objects made of atoms bound together so they length contract. The distance between the two ships is empty space so it does not pull the ships together.
??
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.
P: 3,967
 Quote by YellowTaxi ?? 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.
As you accelerate towards the distant planet, you could imagine that your rocket engines are holding you stationary against a gravitational field that is pulling the planet and the Earth towards some huge black hole behind you. The planet would appear to be accelerating faster towards you than the Earth is receding from you so the distance between the Earth and the planet would appear to be contracting. This is a different situation from the rockets in Bell's paradox because they are both accelerating at the same rate with respect to an observer on the Earth. If the 2 ships accelerated at different rates with the rear ship accelerating faster (so that the gap between them remained constant from their point of view), then the distance between them would be length contracting from the Earth point of view. One way they could maintain constant separation would be to maintain constant tension on the string and then of course the string would not break.

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.
P: 235
 Quote by phyti Reasoning tells you launching into space does not shrink the universe!
I know this, what i am saying is that would it not APPEAR to have shrunk to someone begins moving near c?

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.
P: 1,521
 Quote by ||spoon|| I know this, what i am saying is that would it not APPEAR to have shrunk to someone begins moving near c? 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.
It's not only that it appears contracted to you, it *is* contracted because you can *measure* that contraction in you ref. frame.

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.
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P: 41,568
 Quote by kev Bell's spaceship paradox provides a good insight into the nature of length contraction and distances in special relativity. I think Bell once said that if you do not understand that the string between the rockets will snap then you do not really undersand relativity. Interestingly, in a straw poll of scientists at CERN theory division, most of the scientists got the paradox wrong!
Bell's spaceship paradox is a great example of just how subtle these things can be. (And just how weak a grasp many folks who should know better have on this material. )

 Quote by YellowTaxi 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.
The "paradox" hinges on just how the spaceships are being accelerated. By stipulation, they are being uniformly accelerated according to earth observers, thus their distance apart will remain constant according to earth observers.

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 $\Delta V$. 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 first--thus stretching out the distance between the rockets in the rocket frame. (The string breaks, of course.)
P: 235
 Quote by Doc Al Bell's spaceship paradox is a great example of just how subtle these things can be. (And just how weak a grasp many folks who should know better have on this material. ) The "paradox" hinges on just how the spaceships are being accelerated. By stipulation, they are being uniformly accelerated according to earth observers, thus their distance apart will remain constant according to earth observers. 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 $\Delta V$. 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 first--thus stretching out the distance between the rockets in the rocket frame. (The string breaks, of course.)
hahaha i hadn't really read much into this paradox but when looking at the linked wiki site i couldnt really make much sense of it. Hadnt thought of the simultaneity aspect, quite silly i suppose... but again i havent learnt it before so i figure i get some slack
P: 196
 Quote by Doc Al The "paradox" hinges on just how the spaceships are being accelerated. By stipulation, they are being uniformly accelerated according to earth observers, thus their distance apart will remain constant according to earth observers. 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 $\Delta V$. 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 first--thus stretching out the distance between the rockets in the rocket frame. (The string breaks, of course.)
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....
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,682 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.
P: 196
 Quote by HallsofIvy 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.
Yes, that's exactly the basis of my reply to kev.
The spaceships are not rigid - there's way too many gaps (relatively huge empty spaces) between the atoms/nuclei in a real spaceship.
P: 421
 Quote by ||spoon|| I know this, what i am saying is that would it not APPEAR to have shrunk to someone begins moving near c? 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.
If they appear contracted, they would also appear deformed (contracted in direction of motion but not perpendicular). If that were true, what would accomplish that?
If not true then the objects are just moving by you faster! The 1st choice leaves you with another question, the 2nd does not.
P: 3,967
 Quote by YellowTaxi OK I'll think about that. 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....
I never said the the spaceships were absolutely rigid and I am fully aware that Relativity rules out any material being absolutely rigid. I just said the the spaceships were tougher than the string and also said the they length contract.

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.

 Quote by YellowTaxi Yes, that's exactly the basis of my reply to kev. The spaceships are not rigid - there's way too many gaps (relatively huge empty spaces) between the atoms/nuclei in a real spaceship.
Sure there are gaps between the atoms that make up any one spaceship but they are bound together by electromagnetic forces (in a none rigid way). There is a (quite large) gap between the Earth and the Sun but we are still bound to the Sun by gravity and if the Sun were to move we would tend to follow it. I say "tend" because we are bound in a non rigid way like atoms.
 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. ;-)
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P: 41,568
 Quote by YellowTaxi 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.
By focusing on the details of how the rockets contract (despite there being insufficient information given) I think you distract yourself from the point of this thought experiment. The reason why a flimsy string is used is to make the answer to the question "does it break?" unambiguously yes or no--if there's any stress at all, it will break. While the ends of the string (attached to the rockets) are stipulated to be accelerated uniformly according to earth observers (this is key!), no details are given about exactly how the rockets are being accelerated.

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 right--the 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 rockets--who cares how they contract?

 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. ;-)
I think what I pointed out earlier holds the key to understanding the spaceship paradox and length contraction in general.

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 co-moving with the rocket (actually a continually changing inertial frame). In that case, the rocket is never under any stress at all--it never changes length with respect to that co-moving frame. Of course, earth observers measure the contraction as the rocket speeds up. (To earth observers, the pieces do not accelerate uniformly--it's the converse of the Bell spaceship scenario.)
P: 91
 Quote by ΔxΔp≥ћ/2 catia, Does time really go slower? Not in this case. The space ship pilot will feel normal as stated by the first principle. He will observe that the observer is in slow motion. Neither is really, it only seems that way. Add acceleration to the mix though and you can actually travel to other people’s future.
Are you sure time only "seems" to go slower, Not really goes slower?
If that's the case, then can you tell us why the travelling twin is younger than the one stays at home?

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