Order of Kilopi
You suggested that the spaceship turn round and head towards another star. In order to do this it will have to slow down, stop, then speed up again in the opposite direction (all relative to the destination star). While it is travelling at 0.99c the destination star will be 1 ly away. When it stops, the star will be 22.3 ly away. When it gets back up to 0.99c the star will be 1 ly away.Originally Posted by Webbo
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Are you saying the ship cannot declare itself at rest and the contracted distance behind the ship is an illusion?
Banned
You can also reach this by eliminating the optical anomalies:
http://home.scarlet.be/leo.gooris/mich/page5.html
Anomalous reflection:
according to Michelson we should observe the blurring in many optical instruments, in which there are multiple light reflection.
Ellipsoidal wavefront of a moving source.
Order of Kilopi
I don't really understand what you are getting at. When the ship is travelling at 0.99c (relative to the distant stars) it will see distance ahead and behind compressed from 22 to 1 ly. When it is stationary (relative to those distant stars) it will see the distance as 22 ly.
That is true whether it is heading from star A to star B or vice versa.
Order of Kilopi
The ship can declare itself stationary. Then the rest of the universe is moving at .999c in the opposite direction and the distance is 1ly
Order of Kilopi
The problem here is that they are not in an inertial reference frame (which is a frame moving at constant velocity) because they are accelerating. That complicates things quite a lot. Your example is related to Bell's spaceship paradox. Look at the wiki page on Bell's spaceship paradox and look at the second diagram (with the lines connecting the events). The dashed diagonal line represents the distance between the ships in their own frame, the horizontal line the distance between them in the rest frame. Bell's paradox is stated in terms that the rest frame distance remains the same, but you can see what happens if we say that the distance in their own frame has to remain the same, the spaceships will have different acceleration curves. What will happen is that by the time they reach 0.99c the first ship will indeed have passed the star already (perhaps the second ship too). For a more mathematical treatment look at reference 7 of that wiki page.
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The are stationary with respect to each other. You said;
Whether the observer is in the ship, standing ten feet behind it or 2 ly behind it in another ship is irrelevant. They are not in relative motion with each other therefore space is not contracted between them.
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So if the ship rotates 180 degrees and accelerate toward the star that was behind, how long will it take to reach it and will it at any time measure the distance to increase to 22.3ly?
Order of Kilopi
Yes. At the half way point between moving in one direction and moving in the other - at that point it will be stationary with respect to the stars.
But maybe you are thinking it can go instantly from 0.99c in one direction to 0.99c in the other, without slowing down ...
Order of Kilopi
Yes, so the front spaceship will accelerate a lot less than the back spaceship in order to keep their proper distance the same. Realistically with the numbers you are imposing both will have long passed the star by the time they reach 0.99c.
Order of Kilopi
That is only true if they are in inertial motion (not accelerating). Once you bring acceleration into it, that simple view no longer applies. Work though this: http://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox
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Korjik, do you have the same answer?
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There has been no acceleration. The original ship was passing at 0.99c, I have just added a companion. They are at rest with each other and always have been.
EDIT - I think I added acceleration at one point but there was no need for it. I am just trying to ascertain why the space between two ships contracts but not the ship itself.
Order of Kilopi
But you said:
Order of Kilopi
So basically you just have a 2 lightyear long spaceship passing by at 0.99c and everything else remains the same?
Order of Kilopi
So what you're saying is: if the observer on the 2 lightyear long spaceship says that the distance between the earth and the star is 1 lightyear then the front of his spaceship is behind the star. However to an observer on earth the distance to the star is 22 lightyears and the length of the spaceship is contracted to say 0.1 lightyears then the front of the spaceship is in front of the star.
So the question is, does the spaceship fit between the earth and the star or not? This is equivalent to the ladder paradox where instead of asking whether a moving ladder fits in a garage you're asking whether a moving spaceship fits between the earth and the star.
Order of Kilopi
I think you are making the common mistake of being unclear which reference frame you are considering.
From the point of view of a "stationary" observer on Earth, the spaceship gets shorter (and in the case of two ships travelling at the same velocity, the distance between them gets shorter by the same proportion).
From the point of view of the "stationary" spaceship(s), they stay the same length and the distance between them stays the same but the distance to (and between) the "moving" stars decreases.
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Indeed. An observer on Earth sees a ship start to go past at 0.999c heading towards a star that is 22.3 ly away. When the star finally passes 2 years later the Earth observer would calculate (and possibly detect) that the front of the ship must still be 20 ly from its destination. According to the ship observer the star is halfway between the front and back of the ship. As it's created a paradox my suspicion is that as stated at the begining the ship does not calculate the distance to be contracted at 1 ly, probably because the ship itself is contracted along with its instruments.
Order of Kilopi
It's an apparent paradox, not an actual paradox. It results from thinking in terms of absolute simultaneity. Have you read the wikipedia article on the ladder paradox that i linked to? It includes a full explanation of the situation. It's the same question, just think of the front door of the garage as the earth and the back door of the garage as the star, and the ladder being the spaceship.
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Yes I think I confused the accelerating ship with a non-accelerating ship.
In light of that I would go back to what I originally stated about the ship. Originally I said it would have its instruments contracted because it's moving at 0.999 c but what I should have said is that the instruments are contracted when it accelerates to 0.999c. I think that would mean that it could not detect the contraction of space in front or behind and the distance to the star would remain 22.3 ly.
Order of Kilopi
Let's forget acceleration. I was pointing out what is seen from two different points of view when they consider themselves stationary.
That is so confusing (or confused) I'm not sure what you are trying to say.In light of that I would go back to what I originally stated about the ship. Originally I said it would have its instruments contracted because it's moving at 0.999 c but what I should have said is that the instruments are contracted when it accelerates to 0.999c.
They would see lengths ahead (and behind) contracted; from their point of view, the distance to the star is 1 ly.I think that would mean that it could not detect the contraction of space in front or behind and the distance to the star would remain 22.3 ly.
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What the difference between an actual and apparent paradox. What actual paradox's are there? If it's just an apparent paradox what's the correct answer?
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If two ships, one in front of the other, accelerate then the space between them contracts as pointed out earlier. The same must be true of front and back of the ship and therefore everything on board, hence I believe that the instruments would not be able to detect the contraction of space ahead and would continue to measure the star as 22.3 ly away.[/quote]
Order of Kilopi
An apparant paradox is where people use the word for something that is counter-intuitive but perfectly well understood (the single-photon version of the two slit experiment, the twin paradox in relativity, etc).
Not many. Mainly in logic I think; "this statement is false" sort of thing.What actual paradox's are there?
The answer comes down to the fact that the two observers (moving and stationary) do not agree what "at the same time" means. See the Wikipedia page for the full description.If it's just an apparent paradox what's the correct answer?
Order of Kilopi
I think you are mixing up two different things.
If we say that, from the Earth's reference frame, the two ships start accelerating at the same time and stay the same distance apart then, from the reference frame of one of the spaceships, they will start accelerating at different times and so the distance between them will change.
This is separate from the fact that they will see the distance to the the destination star contract.
The first is caused by relativity of simultaneity ("at the same time" means something different to the Earth as it does on the moving spaceships); the latter is caused by the the velocity of the star relative to the spaceship.
Order of Kilopi
An apparent paradox is if you get contradictory answers because you made a mistake in your analysis and the paradox is resolved by a more careful consideration of the problem at hand. Usually these get to be well-known paradoxes because the mistake being made is very intuitive and the resolution lies in somewhat subtle aspects of the situation.
In this example the mistake is by thinking that two events (front of spaceship being at point x and back of spaceship being at point y) being simultaneous in one frame (the earth-observer frame) means they are simultaneous in another frame (the spaceship-observer frame).
Another example of an apparent paradox is the so-called twin paradox. If time dilation is symmetric, ie twin A sees twin B's time as going slow and twin B sees twin A's time as going slow, then how come only the twin that took the journey is younger? Shouldn't either think the other is younger? The resolution lies in the fact that time dilation is only symmetric between inertial frames (that don't accelerate), however the journey-taking twin must at some point start to return, at which time he accelerates (he slows down and then reverses course), so we can unambiguously say which twin is younger and which is older.
In relativity none that i know of. It would be a disaster if there were because an actual paradox would be getting contradictory answers without making a mistake which would mean that the theory is inconsistent.What actual paradox's are there?
An example of an actual paradox in logic would be the liar paradox, ie "this sentence is false". If the sentence is true then it is false, but if it is false then it is true. (note that there are resolutions to the paradox, but in classical logic it is an actual paradox)
The correct answer is that the spaceship fits between the earth and the star. Because in the frame of the spaceship the events "back of spaceship at earth" and "front of spaceship behind star" are not simultaneous, therefor they do not represent an actual "state" for the spaceship to be in at some time.If it's just an apparent paradox what's the correct answer?
ETA: i must learn to type faster than Strange
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In that case, in the physical world, as no actual paradox exists, to describe the difference beween actual and apparent is erroneous. It's a paradox and that's it. In the physical world there shouldn't be one.
There is no "at the same time" issue. The observers on Earth watch the 2ly ship go by and spend the next 20 years observing it approach the star. The ship observers watch the front of the ship pass the star before the back of the ship has passed Earth. Both cannot physically be correct in their observations so something is wrong with one of them. One of our theoretical observations is incorrect. I believe that is because the ship observers always see the star as 22.3 ly distant.
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Do objects contract as they approach the speed of light?
Order of Kilopi
The resolution in the case in which the distance between them must stay constant in their own frame comes from considering the Rindler horizon. If we look at the front spaceship and say that it must accelerate to 0.99c before passing the star, it must have a very high proper acceleration. This means that the back spaceship is behind its Rindler horizon, so it would have to have infinite acceleration to keep their proper distance the same. The best we can do is put the proper acceleration of the first spaceship such that the back spaceship is barely in front of the Rindler horizon of the first, but this acceleration is a lot lower than what we required. The result is that both spaceships will have long passed the star before they reach 0.99c (because there is a limit on their acceleration).
Order of Kilopi
Indeed. If you find one in a physical theory it is either an example of reductio ad absurdum (and the theory is wrong) or you have made a mistake.
But you are talking about the relationship in time between two events. The observers on Earth will disagree about when these events occur. Therefore no paradox. You need to work out the detail, rather than relying on intuition (as caveman says).The ship observers watch the front of the ship pass the star before the back of the ship has passed Earth.
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