We have established that time is relative and goes slower for objects in motion and we have experimentally proven with the ISS. A thought experiment: What if the ISS was moving at much higher speeds, let's say fast enough for the time differential to become more noticeable. So say it travels at 99% of the speed of light around the earth for a given amount of time. Afterward, the crew will say for instance they spent let's say 1 year in space, and we on Earth will say it was 10 years, because on Earth 10 years passed and on board the ISS only 1 year passed. So far so good, my question is this: If the ISS crew kept on watching events on Earth through say a telescope or say they kept on receiving a TV signal to watch live TV events (let's ignore transmission issues for a moment and let's say they can receive the signal without too much trouble, just like any other place on earth). At what speed would these events go by? For instance, the US might have a new president by then, given that more than 8 years have passed and whoever was in office is out now, but how would that be for them. Would they have seen 2 elections since then, but just going by very fast from their perspective, or would they have only seen 1 year's worth of events?
4 Answers
In my interpretation of the question, you chose the ISS merely for the sake of an example, and you are actually interested in the phenomenon of time dilation in general, not in the specific case of the ISS. Accordingly, I will give a general response. As Claudio Saspinski pointed out, there are some issues with the speed at which the ISS can orbit the Earth. Furthermore, there is an increasing difficulty with the fact that the Earth has a gravitational field, and thus general relativistic effects come into play, in addition to the mere effects due to speed. Therefore, I will pick a simpler case: the twins paradox. Ignoring any gravitational field effects (for simplicity) we assume one twin ($T$, for traveller) enters a spaceship, goes at near the speed of light to Alpha Centauri, and then comes back. Apart from the turning point (which we assume to be instantaneous for simplicity), the twin $T$ is moving at constant speed $v$ relative to the twin on Earth ($E$, for Earth). We assume $v$ is such that the travel takes 1 year for $T$ and 10 years for the $E$.
In this setup, we take the following experiment: using a telescope, $T$ looks at the clock hanging on $E$'s kitchen wall. While doing so, $T$ compares it to their own wristwatch. How do the ticking of the two clocks compare? In this setup, with this particular value for $v$, $T$ will see $E$'s clock tick ten times while $T$'s watch ticks a single time. In other words, $T$ sees the events at Earth passing ten times faster.
The same idea holds whenever you have time dilation effects, and your idea of looking through a telescope is pretty much the way we actually compute time dilation in general relativity: we imagine a light ray passing from one point to the other and compare its frequency relative to the two observers we are interested in. They see different frequencies due to time dilation.
You can thus also apply this logic to situations near black holes, for example. If someone is standing near a black hole and looks at a clock on Earth through a telescope, they see the clock running much faster than their wristwatch.
The only reason I avoided your particular thought experiment is because it gets a bit messier, and my intuition can't grasp all of the relevant effects at the same time: we have high speed, lower gravitational fields, and a lot of acceleration, so the complete picture is not obvious to me and I'd have to open up the calculations to be sure about what happens.
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ISS has an orbital movement. A device moving at 99% of the light speed around the Earth is not orbiting. The crew would be submitted to a huge centripetal acceleration from the ship walls.
In order to reach a clear understanding, we can replace a circular movement for a polygonal one, with several straight paths of 100 km for example. During that paths, the ship has a constant linear speed.
Let's suppose also a row of clocks on Earth, one for each vertex of the polygon. All the clocks are synchronized with the Greenwich time.
Comparing the ship clock and the nearest Earth clock, $\Delta t > \Delta \tau$, that is: after each straight path, the time interval between the 2 successive Earth clocks seen by the ship is greater than the ship's clock interval. The effect is cumulative, so after each turn, the total time difference increases.
The events happening on each location of the Earth would be seen as fast forward by the ship. For example, a football game would be seen as a compact of the best moments nowadays, (but having all the game in that ship).
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The simple answer to your question is yes, the people on the iss would view activities on Earth in fast motion. Just as if they were watching a movie in fast motion. Likewise if people on Earth were watching the people on the ISS, we would see them moving in slow motion. If the two groups were talking to each other, the people on the ISS would hear us speaking like chipmunks. And the people on earth would hear the people on the ISS speaking in a very very deep voice.
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At CERN there was a Muon Storage Ring which was used to measure properties of the Muon. This also afforded opportunity to corroborate relativistic time effect. In terms of proper time the half life of Muons is 2.2 microseconds. When the muons are going around in the storage ring at relativistic energy the half life, as measured by the lab observers, is longer, in accordance with special relativity.
This report came out in 1977:
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