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Let's assume we have two observers one is on Earth and the other one is inside a spaceship with relativistic speed.

Would the time inside the ship slow down while also the spaceship is getting shorter for an observer on Earth?

Most of the examples I saw online are referring to the relation of time dilation for one observer and the length contraction for the other one (ex; Muons reaching the Earth). But can one single observer, observe both time dilation and length contraction at the same time?

I feel like he/she can but usually, the problem does not require us to calculate them both therefore I couldn't find any examples.

Thanks for the replies.

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I think you are a little mixed up. Under Special Relativity it is only the observer on Earth who will see both time dilation and length contraction of the rocket. The man in the rocket will see nothing about his own time or length. All of these factors are only seen by an outside observer.

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  • $\begingroup$ But also the observer on the spaceship also should see the space outside the ship is contracting and slowing down, right ? $\endgroup$
    – Ç.Eti
    Commented Oct 28, 2020 at 15:37
  • $\begingroup$ @Ç.Eti Now you are getting into an area of some debate, and I suggest you research into BOTH the twin paradox and Lorentz Modified Ether Theory. the latter, described in detail by Ronald R. Hatch, says that it only works in one direction, i.e. you can't have both twins becoming younger at the same time, and he does not like the explanations given of the twin paradox (and I don't like them either). His specific knowledge of GPS satellites gives him a very good perspective on this topic to refute the equivalence principle. $\endgroup$
    – foolishmuse
    Commented Oct 28, 2020 at 15:41
  • $\begingroup$ I thought we could explain the twins paradox using the acceleration and deceleration. Can't we? $\endgroup$
    – Ç.Eti
    Commented Oct 28, 2020 at 15:44
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    $\begingroup$ @Ç.Eti yes, he is talking about non-mainstream theories $\endgroup$
    – user65081
    Commented Oct 28, 2020 at 15:48
  • $\begingroup$ @Ç.Eti that idea was supplanted with the idea that the moving rocket changes frames for the return journey. But Hatch (and I) are not happy with these concepts in SR. In his explanation, GPS satellites move at high altitude and high speed and thus experience both kinetic and gravitational time dilation. They communicate with other satellites. But he has shown that it is NOT the relative velocity/altitude of these satellites to each other that is important. It is only the velocity/altitude relative to a fixed clock on the Earth that accounts for the time dilation of the second satellite $\endgroup$
    – foolishmuse
    Commented Oct 28, 2020 at 15:52
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An observer on the earth with recording instrumentation is halfway between sensors which are monitoring the intensity of parallel laser beams from the moon. A space ship with a blinking light flashes by and interrupts both beams. From the time and distance between the beams he can determine the speed of the ship. From the time that each beam was interrupted he can calculate the length of the ship. From the time between flashes of the light, he gets his measurement of a time interval on the ship. If the ship was build by humans, he can look up measurements made on the ship. Each of these measurements requires some interval of time.

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