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Suppose that we could observe from outside a system expanding radially at relativistic speed ($\frac{dr}{dt}$ about $c$, constant and/or accelerated). It can be an ideal balloon, or a spherical distribution of particles.

What would it look like? A shrinking sphere? Or a sphere expanding slower than expected? Nothing of the above?

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  • $\begingroup$ I always find these questions a little amusing, although I study them myself off & on. What I do is mentally substitute "near light speed" with "the speed of a bullet" ;) IOW what your human capability eyes will see in practice is nothing, and if you remain in its path that will be permanent! Still want to see an answer though. $\endgroup$
    – m4r35n357
    Commented Dec 16, 2021 at 17:21
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    $\begingroup$ It is relative because if you move backwards at speed of light the bullet might recede and get a red tint :) Perhaps :) @m4r35n357 $\endgroup$
    – Alchimista
    Commented Dec 16, 2021 at 17:54
  • $\begingroup$ Good point! In that case the answer is still nothing (but at least safe!) because as well as the red shift you will get the opposite of relativistic beaming, which will dim the object too (although it will appear bigger)! Also bear in mind that part of my comment above was about detecting high-speed motion with human eyes. $\endgroup$
    – m4r35n357
    Commented Dec 16, 2021 at 18:15

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If you were at the centre of the balloon, it would appear to be a sphere. The speed at which the balloon was expanding away from you would appear to be reduced owing to the Doppler red-shift effect.

If you were outside the sphere, the Doppler effect would distort the appearance of the balloon, so that instead of appearing spherical, the parts of the balloon nearer to you would appear to be expanding more rapidly than the parts further from you, so that it would seem egg-shaped, with the flatter end of the egg being away from you.

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  • $\begingroup$ I think it might be more complicated. I follow your argument as taking the component in "your direction" of the expanding surface (at each point) and using aberration/doppler in that way. But there is also a perpendicular (to you) component of the surface velocity, and that will tend to "counteract" the flattening at the "poles, where the component in your direction is zero" for lack of a better term! Maybe. Does this make any sense? Basically, I don't know how to model this! $\endgroup$
    – m4r35n357
    Commented Dec 16, 2021 at 17:03
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    $\begingroup$ @m4r35n357 the fact that someone else isn't able to model this is kind of relief. $\endgroup$
    – Alchimista
    Commented Dec 16, 2021 at 17:57
  • $\begingroup$ @Alchimista I am only an amateur, but the basic "what you see" analysis assumes just two frames of reference, like an observer moving through a static scene, whereas your example has the movement of an infinite number of "surface elements" of the expanding balloon to consider from the POV of a static observer. I think the analysis could be done, but only on an element-by-element basis. I still hope I am wrong and someone else will chip in! $\endgroup$
    – m4r35n357
    Commented Dec 16, 2021 at 18:11
  • $\begingroup$ If a sphere were fixed but starts inflating from a given r , there might be a phase in which it appears even in contraction to me? At least along the radius perpendicular to my sight line? Because I treat the sphere as composed of little volumes, each of which would appear contracted to me. I am pretty sure there could be a simulation somewhere in the style of the mit game slower than light. Thx. Fortunately you are Ocram not Occam otherwise you could tell me to watch something more appealing than luminal balloons :)) $\endgroup$
    – Alchimista
    Commented Dec 20, 2021 at 16:19
  • $\begingroup$ I think I have just land in a complicated example of what is called Bell's paradox. I will read about it first, I knew it just by name and I've fall on it because of the above question... $\endgroup$
    – Alchimista
    Commented Dec 20, 2021 at 16:31

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