I think that I was perhaps not entirely clear as to what I was referring to as it is the other equation that I was looking at and not from the question of what effect that this has on measurements, as I am well aware that it is more or less a rotation in a sort of hyperbolic space, just look into the hyperbolic sine and cosine functions. Rather my question is how will it effect what is actually seen. Currently I don't think that it will have any effect at all, as what is important is the actual length which is only going to be scaled and is independent of location.
If you go back to the video, what you see in the video is what is being plotted in terms of the pictured frame; this frame plots the moving rod as length contracted. That plotting will allow the two inner photons to pass through. There you go.
I suspect that we are actually very close to agreeing on what is actually seen, and that the real disagreement here is not on what is seen, but when it is seen, how simultaneity is defined and what a picture is. Actually I think it all boils down to the definitions that we are using and we really agree on the rest of it.
To try and explain what I mean I will use the thought experiment as you put forward in your video. Firstly the obvious, clearly both ships will see the side of the rod inside of the pipe. You have said several times that this is the case and I agree with you. Now for a few things that are not so obvious and I think could be pointed out better in the video.
Firstly the observer that is at rest with the pipe will see the rod pass though the pipe directly ahead of him and it will be possible for him to see the trailing side of the rod at this time, the thing to realize though, is that the observer that is moving will see a slightly different picture of the event. He will see that pipe as ahead and to the right of him, as you have it in the video, he will also be able to see the trailing side of the rod, the important part in my mind though is the location that they will see the rod inside of the pipe, as your video seems to be hiding this and rather assuming that both pictures will be the same because they are capturing the same photons.
Well no, that's not the intented implication. Even though it doesn't explicitly display so, little thought should reveal to the viewer that the moving camera will;
1. Also take a photograph where the tube and the pipe co-incide (its photograph is composed out of the same photons after all). Since the pipe is ahead of him, that's where the tube must also appear to be.
2. This is the same result as you get from aberration analysis
3. ...or from figuring out where the emission events are in the frame of the moving camera -> they must be ahead of the camera.
I will admit that the pictures must be conformal mappings of each other and that they must preserve casualty but the pictures will show the rod inside of the pipe in different directions from the front of the crafts.
I think that it is worth pointing out one or two other things, although I think that you already realize them. Firstly the observer at rest with the pipe will see the rod as longer when it is in the pipe then the observer that is moving. Why, well because he will see the hole thing taking place closer to him then the moving observer.
Yeah but that's completely besides the point if the question is "can length contraction be photographed". You must put the reference stick at the same distance in all cases, otherwise you are just asking if the same object photographed from different distances will have different size in the picture. Of course the objects further away will look smaller in the photograph itself.
Also the more that I think about it, the more that I have to conclude that the observer at rest with the rod will have to see the pipe as stretched when the rod is inside of it. Since if your video is correct and this event took place in front of the moving observer he would see the rod and pipe lengths reversed.
If you are having a hard time understanding what I am talking about just consider for a moment that when the observer at rest with the rod sees the pipe directly in front of him, he will see it as the same length as the observer at rest with the pipe see the rod to be when it is directly in front of him (inside of the pipe).
Btw it occurs to me that "tube", "pipe" and "rod" are terrible labels for these objects - who knows what's what anymore - but I get what you are saying from the context
In my mind this is very counterintuitive and I really can't fully explain its cause although I am sure that it must be the case.
Yeah, you get these results from considering the time delays to the emission events. That is why a length contracted object may look elongated when its approaching, because the time delay to emission event varies across the length of the object. The same mechanism causes visual shrinking when the object is receding.
I have to wonder at this point if you have miss identified the path of the photons to the rest observer and that in fact the rest observer will see both the tube and the pipe as the same length from his vantage point. Put simply, when any object is seen at a right angel to the direction of travel it is seen as having the same length no matter how fast it is moving. How you have it right now Lorentz contraction would be visible.
Yeah, that's why I made the video, because it appears to be plainly true that you can photograph Lorentz contraction easily. It is also plainly true that there is a single moment for every passing object, where the visual elongation (while it is approaching) will exactly compensate for the Lorentz contraction.
In my previous post I described how to find this moment with plain symmetry arguments (the two identical objects moving from opposite directions at the same speed)
I have to ask at this point how did you generate the velocities in your picture?
I just arbitrarily chose C, and set the massive objects' speed to 86% of it.
If the above seems somewhat confusing try to understand I am trying to picture the video from the prospective of the other observer, and I would be very interested in a video from that prospective if you think you can make one, if you do try to make one remember that in that video the pipe is half the length of the rod.
I really would be interested in such a video as I think that it is more or less what is being assumed when I watch the video that you made.
Well it would be reasonably easy to do it but I don't have the software I was using at hand right now. I can do it later. But also you can get somewhere by imagining a coordinate system that is moving along with the moving camera, and think about the apparent paths of the photons in terms of that coordinate system. Take into account that the emission events that are simultaneous in the video, are not so in the other coordinate system; The moving camera composes its picture out of photons, whose emission events it doesn't take as having been simultaneous.