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As a thought experiment, let's conduct a regatta involving three spaceships in intergalactic space, where they are not significantly gravitationally influenced by any nearby massive object. We conduct a "running start" where each ship completes its acceleration and turns off its engine before reaching the start line. The three ships cross the start line very near to each other and at the same instant. Ships #1, 2 and 3 cross the start line at proper velocities (<< c) of 1km/s, 2km/s, and 3km/s respectively. For the sake of simplicity, the expansion rate of the universe is coasting (neither accelerating or decelerating), with [tex]\Lambda (w= -1/3) [/tex] and [tex]\Omega = 1.[/tex]

After two units of time have passed, Ship #1 decides to observe the other two ships in "comoving coordinates" which it bases on Ship #1's own proper velocity. Ship #1 views itself as stationary in its comoving coordinates; Ship #2 is then at a comoving distance of 2 km and is receding at 1km/s. Ship #3 is at a comoving distance of 4 km and is receding at 2 km/s.

So, Ship #1 is delighted to observe that the ships observe the Hubble expansion law: comoving recession velocity is exactly proportional to comoving distance.

After four units of time have passed, Ship #1 observes Ship #2 at a comoving distance of 4km, and Ship #3 at 8 km. However, the observed recession velocities remain fixed at 1km/s for Ship #2 and 2km/s for Ship #3.

The observed comoving velocities remain exactly proportional to distance. However, the comoving velocities

Do Ship #1's observations reflect the generic behavior of a coasting universe? At (arbitrarily) t=10Gy, is the observed comoving recession velocity of Galaxy X the same as it is at t=20 Gy, despite the observed distance of the latter being 2X the former?

Jon

After two units of time have passed, Ship #1 decides to observe the other two ships in "comoving coordinates" which it bases on Ship #1's own proper velocity. Ship #1 views itself as stationary in its comoving coordinates; Ship #2 is then at a comoving distance of 2 km and is receding at 1km/s. Ship #3 is at a comoving distance of 4 km and is receding at 2 km/s.

So, Ship #1 is delighted to observe that the ships observe the Hubble expansion law: comoving recession velocity is exactly proportional to comoving distance.

After four units of time have passed, Ship #1 observes Ship #2 at a comoving distance of 4km, and Ship #3 at 8 km. However, the observed recession velocities remain fixed at 1km/s for Ship #2 and 2km/s for Ship #3.

The observed comoving velocities remain exactly proportional to distance. However, the comoving velocities

*have not increased with distance*, contradicting the intuitive result.Do Ship #1's observations reflect the generic behavior of a coasting universe? At (arbitrarily) t=10Gy, is the observed comoving recession velocity of Galaxy X the same as it is at t=20 Gy, despite the observed distance of the latter being 2X the former?

Jon

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