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.
That is true whether it is heading from star A to star B or vice versa.
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.
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.
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.
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.
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.
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?
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.
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
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.