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In the following we consider an Earth bound reference frame.

For an observer very close (but under) the light speed, radiation from the universe would emanate from a single point in the direction of travel, and all radiation would be Doppler shifted to gamma ray wavelengths. 

In this direction,  this link was sent to me by Thomas Fritsch , related to another question. 

So as the observer approaches light speed, his field of view shrinks to a point from which radiation of arbitrarily high frequency is emitted. These are consequences of aberration , beaming, and Doppler shift.

Related to the possibility that extremely high frequency radiation could create a black hole, check this link

To make my point clear (and fun), I will consider that the observer reaches a speed of
$c$*googolplex/(googolplex+1), where $c$ is the speed of light in vacuum.

I realise that even writing a googolplex in decimal form is physically impossible. I do not question how much energy is required, and I do not question how the observer is accelerated at this speed. There in nothing in physics that would forbid me to consider this thought experiment, in principle.

Question. How would an observer in this state of motion perceive (experience) the universe?

The invariance principle of relativity tells me that nothing special will happen. And yet, I know that way before the speed of c* googolplex/(googolplex+1) is reached, something will happen, the observer will perceive a universe with different properties. He will either "see" the universe as a black hole, naked singularity , or something else. You cannot Doppler shift the radiation coming from a point source to infinity , and pretend nothing extreme will happen. How do you solve this paradox?

Edit. A possible connection can be made here with the Unruh effect, and the emergence of an apparent horizon for an accelerated observer (because you have to accelerate the observer, in  order to get closer and closer to the speed of light).  I suspect though that a full resolution of this paradox will involve quantum gravity or string theory. In any case, there is a paradox here (a contradiction with the principle of invariance in relativity), so I welcome any suggestions and comments.

Cristian Dumitrescu
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  • You are currently moving very close to the speed of light in some reference frame. How does it look right now, to you? – D. Halsey May 28 '19 at 17:17
  • Thank you @DHalsey Any galaxy with a redshirt greater than 1.4 is currently moving away from us faster than the speed of light, but that has to do with the expansion of space itself, different story. We are talking about relative motion through space, in the traditional sense. In this case, the fastest moving matter known can be blazar jets (for example), or some high energy cosmic rays that can reach something like c*(1-10^(-20)). I think the critical point is closer to light speed, but in order to model the phenomenon you probably need quantum gravity or string theory. – Cristian Dumitrescu May 29 '19 at 06:01
  • If I knew the answer, I wouldn't have asked the question. What I am sure though (as I said in my question) is that you cannot Doppler shift the radiation coming from a point source to infinity , and pretend nothing extreme will happen, once some critical point (sufficiently high frequency) is reached. – Cristian Dumitrescu May 29 '19 at 06:07
  • The short answer to your question "How does it look right now to you", is that everything looks fine , probably because there is no matter in the observable universe that moves fast enough in relation to us. As for the matter beyond the observable universe we'll probably never know. And "they" will never know anything about us. – Cristian Dumitrescu May 29 '19 at 06:18
  • Maybe that's an equivalence class, maybe we should define the observable universe as systems of matter that move slow enough, in relation to each other. – Cristian Dumitrescu May 29 '19 at 06:26
  • When I said equivalence class, I didn't mean the strict mathematical notion (problems with transitivity) but you get the idea. – Cristian Dumitrescu May 29 '19 at 06:46

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