time slows down when you approach the speed of light?

Doc Al

Since distance is always defined with respect to some observer's frame, as long as that frame existed the distance measured by them was the same shorter length (compared to that other frame).

Special relativistic effects are always due to the relative motion of reference frames.

I would say there's only one universe, but that the distances and times between various events within that universe depend on who (what frame) is doing the measuring. Since these measurements are frame-dependent, they are less fundamental than we had first thought. To use a weak analogy, just like speed is frame dependent so are distance and time measurements. (But there are quantities which are invariant--the same for all observers; these can be said to represent the more fundamental structure of the universe.)

yuiop

The poster was talking about distances as measured by observers in different reference frames, and Doc Al is right in saying they are not invarient. In the example a person at rest with the Earth would say the distance to the planet if 7 light years and the rocket traveler would measure the distance as 1 light year. Neither can prove the other is wrong, as neither can prove they are at rest with some absolute reference frame.

Whether distances are classed as scalar or vector quantities is not really relevent in this context but for the record the distance refered to by x in the Lorentz transformation t = y(t' +vx') and x = y(x' +vt') is a vector quantiy as it can take a + or - sign according to which direction from the origin of the reference frame that the distance x is measured. Perhaps you meant that proper distances (distances that are measured by an observer at rest with the endpoints of the distance being measured) are invarient?

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!

http://en.wikipedia.org/wiki/Bell's_spaceship_paradox

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 ?

phyti

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?

yuiop

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.

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.

yuiop

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

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.

yuiop

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.

||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.

lightarrow

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.

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 [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 first--thus stretching out the distance between the rockets in the rocket frame. (The string breaks, of course.)

||spoon||

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

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....

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.

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.

phyti

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.