I was slow to respond to this because I couldn't follow what you meant by “aberration” which commonly means a deviation from normal.
Oh yeah, sorry about that, I realized that when I was writing and wrote "aberration of light" at first, but looks like that part got lost in some edit before I posted... :I
But now that you know what I mean, I'll just say "aberration"
So I googled “aberration of light” and, except for aberration due a non-flat mirror, all the cases of “aberration of light” depended upon a velocity of the source relative to the observer or vice-versa.
I came to think about aberration of light because your thought experiment reminded me of something I was thinking about some 10 years ago. I realized later there was a term of it, namely, "aberration of light".
I'll explain in detail in the end of the post what I'm thinking exactly, and why it appears to me it has to have an effect in your thought experiment too. If I'm making a mistake we should be able to spot it. But either way it is, it's not really relevant to the point you were trying to raise, so;
“In 185 CE, Chinese astronomers recorded the appearance of a bright star in the sky, and observed that it took about eight months to fade from the sky. It was observed to sparkle like a star and did not move across the heavens like a comet. These observations are consistent with the appearance of a supernova, and this is believed to be the oldest confirmed record of a supernova event by humankind.” -- google “first observed super nova”
My point in making that quote is that the event appeared to occur in 185 BC (CE means before the current era.) It is “hypothesized” that it occurred 10,000–20,000 years ago via the assumption that the light required that long to get to us. The only real information available to us is where they appear to be: i.e., essentially simultaneous with the present as it appears to us.
There are two very different perceptions as to what the universe looks like: one as calculated consistent with our scientific concepts of the rules of the universe and another which is no more than what we see when we look. Failure to recognize the difference between these two views is a relatively important issue and presuming they are identical is patently false.
Yup, so true. It always bothers me a bit that on the other hand we are using relativistic convention to describe the universe, but on the other hand we imply partially newtonian convention when people talk about a supernova we see now having happened "20 000 years ago". 20 000 years ago in what sense? If there is no preferred frame, then there is an infinite number of reference frames where that supernova bursted a split second before we saw it. Or at least pointing that out would be consistent to the definitions we are using.
People also almost always talk vaguely or even inconsistently when they describe C as being the speed limit for our space ships, and as a result people always seem to think we literally could not get to places faster than whatever the distance is in light years. Have you ever seen a single science fiction film where they have actually just built a damn fast space ship that would work according to the definitions of special relativity, instead of spending years in hyper sleep? I can't think of a single one. I bet a lot of people would think "but you can't do that according to relativity", but of course you can, doh!
Note I have not done the length contraction calculations (which if I am understanding correctly will make the ship appear shorter) in which case this will also play a role in this
It doesn't play any role in this because the length of the ship is always defined in ships own frame for their own calculations. The calculated distance of the star is entirely a function of distance between the detected photons, and length contraction doesn't affect that at all, which would be exactly DD's point and he is absolutely right about that.
If aberration has an optical effect in this, then the distance between the photons when they hit the back wall is different between the ships at the precise moment the ships are passing each others (if we imagine this in terms of two different ships, other one "parked", other one passing by). But so, let's investigate my thoughts in detail and see if we can find an error;
The obvious case first;
Imagine a "rest" reference frame, and a cube shaped room floating stationary in space, with a hole in the ceiling.
Imagine a laser pointer, also stationary, beaming a pulse of light through the hole. The beam is shot down orthogonally to the floor, so if there is an observer directly below the hole, he will see the beam coming through the hole.
Now imagine the same situation, but the room is moving in our reference frame past the laser pointer (which is still stationary). The velocity of the room is parallel to its floor. The laser shoots a beam of light just before the room is passing underneath, so that the beam of light will go through the hole, and continue down into the room.
The beam of light cannot possibly hit the floor right underneath the hole since the room is moving sideways in the reference frame, while the light is moving directly downwards. When the beam hits the floor, it will be in a location that is off-set from the hole by some distance that depends on the speed of the room.
If there is an observer directly under the hole, it cannot possibly see the laser beam.
If there is an observer in the spot where the beam would hit the observer, it would see the flick of the laser beam, and the laser pointer itself, right at the hole. That is to say, it could not possibly see them directly overhead, it would have to see them off in an angle. That angle is towards the direction of motion of the room.
Obvious symmetries apply; in the frame of the room, the laser pointer is moving very fast, and it appears to shoot its light off in an angle that is not orthogonal to the floor of the room.
Replace the laser pointer with a light coming from a star, and the same rules apply; the "moving" room sees the star off in an angle that is different than how the "stationary" room sees it in, and it is entirely a function of the speed of the room.
Note also that, if an observer is in motion inside the room, then the same effect must apply to the observer itself; That observer cannot possibly see the starlight as if its coming through the hole, he must see it as if its coming through the ceiling next to the hole! Edit: Nope, that would be my first mistake right there! The room itself would have to appear skewed to the observer by the same amount, including the hole. Silly hat to me! The rest seems correct to me still.
Now, let's open up the ceiling and the walls entirely, think about the entire circumference of the room as it is accelerating near the speed of light as plotted in some reference frame. As the room is gaining velocity in relation to the rest of the visible stars, the stars all must appear to be moving towards the front (towards the accelerated direction) of the ship. Even stars that the room is receding from, must appear optically as if they are somewhere near the front of the ship. Only the objects that are DIRECTLY behind (or front) are not affected at all. Eventually the rest of the stars would just be a speck in front of the ship (except that doppler shift would probably lose the speck too, but that's another story...).
If this effect was not accounted for and compensated away, navigating a space ship would be quite troublesome!
I think this effect raises an interesting question. I've sometimes wondered why is it that the entire universe is practically stationary in relativistic terms; every massive object we are detecting sits in a very small range of possible velocities.
If you think about the possible reference frames - thinking in terms of special relativity - then the vast majority of those frames - from our perspective - are sitting arbitrarily close to C in some direction. So close that we could not possibly detect the difference between the velocities of objects "occupying" those frames.
Imagine clusters of massive objects in reference frames that to us look practically like C, would it be possible to detect theose objects in any way? What would they look like with fully doppler shifted light when they are receding, or when they are approaching us? Even if we could detect that light, it would have to come off with full aberration in effect 90 degrees "off-angle", and the entire cluster of objects in or near that reference frame would be visually shrunk into a single speck of light in one direction.
If that cluster of object would pass us at any distance, and if its light was detectable, would it, by the definitions of physics, look exactly identical to one photon being detected from that one angle parallel to its direction of motion? Just one photon hidden among a sea of photons we get from objects that are close to our velocity?
If that's true, then wouldn't a constant battery of such clusters in all kinds of reference frames in all directions around us, look just like random background radiation that is always centered around us no matter which way we move or look?
In addition, since these objects would have to be taken as lorentz contracted, at some velocity they would have to be reduced to so short distance that it would be theoretically impossible to detect them in any way, right? Everything would just move pass each others undetected, except for random noise from things that happen to reside in appropriate reference frames to be detectable in some way?
Or to be little bit more epistemological, if we take a massive object and place it in a reference frame arbitrarily close to C so not to be detectable, could such a thing be called "massive object" at all, or something else? Even if, by accelerating near their frame, they would look like normal stars and galaxies? I think there are interesting epistemological questions here.
Okay so back to the space ship with two holes. If there was a hole in the exact middle of the back plate of the ship, then aberration could not possibly have any effect. But then also distance measurement could not be performed. The holes that are off-center from the direction of motion and the star behind the ship, would get the light beam coming in in an angle that would have to be affected by aberration effect analogous to the room experiment;
We first plot the situation in a frame where the star is stationary, and also the ship is stationary in some distance from the star. That distance is calculated from the distance between the two light beams hitting the front wall (and knowing the construction of the ship). We call this frame "the lab frame"
Add another ship that is moving in great speed in this lab frame, moving away from the star, and about to pass the stationary ship (we can imagine it slips straight through the parked ship for clarity).
The moment that the front plates of the ships are passing each others, is our simultaneity reference, and that's the moment we want to check the distance between the beams.
As plotted in lab frame
For the parked ship, the photons that hit the front wall at the moment of measurement, entered the ship when the rear end was exactly where it still is.
Still as plotted in the lab frame
For the moving ship, the photons hitting the front wall at the moment of measurement must have entered the ship when the rear end was still closer to the star (even with length contraction taken into account), and the photons must have entered at whatever angle that location would imply. Since then, the beam has been expanding inside the ship while trying to catch the front wall. When it finally hits the front wall, the distance between the beams would have to be larger than is measured inside the stationary ship at the same moment (of the passing of the front plates).
Still as plotted in the lab frame
If the speed of the moving ship is almost C in lab frame, the light may be plotted as having entered the holes of the ship back when the star was still very close to it (i.e. beams entered in extremely high angle), and it has been making its way through the ship throughout the journey, finally hitting the front of the ship at very high angle, making the distance measurement extremely skewed.
As plotted in the frame of the "moving" ship
, the star is in motion receding from the ship at the rear, and up ahead, the other ship is approaching rear-first. Aberration from all the stars in lab frame is in full effect (everything near the lab frame is skewed forwards), and as seen by either of the holes at the back, the star directly behind is also visually skewed towards the front of the ship by the same mechanism as described with the room thought experiment, making it appear right in the middle behind the ship, but close according to the beam angles.
At the moment the front plates co-incide is again the moment of measurement (simultaneity agreed by both ships). In this frame of the "moving" ship
we would have to plot the "parked" ship as flying towards the beams of light in such a way that each beam is plotted to be expanding inside the ship only for a brief moment (the ship is also plotted as length contracted but that's just an additional to plain aberration); the beam separation at the moment of measurement would have to be less inside the "parked" ship, making it appear the star is further away.
That view gets you entirely consistent and symmetrical transformation between the frames, but since navigating to any star would be impossible if this effect was not accounted for (not to mention the effect would look different when looking out from different locations inside the ship), each space ship would have to see it as an optical illusion of a sort, and navigate either by compensating to some agreed upon frame (the center of cosmic background radiation for instance), or maybe develop a convention to always use the reference frame of some star of interest (that has some useful velocity) as the "correct" one.
And if they did that, then yes, they would still calculate the distance to the different stars as identical as you said in the OP. That's why I said this is not really relevant to your point per se, but it should be mentioned as long as we talk about what things optically "look like", not "how things should be plotted".
And yeah, for anyone wondering, the stars directly front would not look skewed closer to the ship, they would look skewed further away.
Edited by AnssiH, 07 January 2014 - 05:15 PM.