Traveling to nearest star at nearly the speed of light

[lifeonmercury]

I'm still trying to understand the concept of the slower passage of time at or near the speed of light. Say for example we had the technology to travel this fast and wanted to send astronauts to visit the newly discovered planet Proxima Centauri b four light years away.
My understanding is that the journey would take four years from the perspective of an Earth-based observer, but the astronauts would only experience the passage of a few hours or days before arriving, thereby eliminating the need to bring along massive amounts of food and resources required to support multiple generations of space travelers. So basically if we can develop the technology to travel near the speed of light then we can send astronauts anywhere in the galaxy in a short period of time from their perspective (while of course thousands or millions of years on Earth pass). Is this thinking correct?

 

[Drakkith]

That's right. It is within the realm of possibility for someone to travel from here to the Andromeda Galaxy, even though it is over 2 million light-years away.

 

[pixel]

Of course, there are at present many technological barriers to such voyages. For one, it would take an enormous amount of energy to accelerate a spaceship to such speeds. Another problem is collisions with small interstellar particles, which at such speeds would be disastrous.

 

[Battlemage!]

And the additional problem that the rest of humanity may have become extinct by the time you return, depending on how fast you go relative to Earth and how much proper time passes for you. ****although I am skeptical to apply special relativity through long distances since based on what I've learned here about general relativity, comparing velocities of distant objects is ambiguous, which I assume probably has an affect on time dilation. After all, there aren't any universal inertial reference frames. But I lack the details on that.

 

[rootone]

If travellers returned to (say Earth) a million years after they left, would there be anyone on Earth expecting them?

 

[Nugatory]

For one, it would take an enormous amount of energy to accelerate a spaceship to such speeds. Another problem is collisions with small interstellar particles, which at such speeds would be disastrous.

Yes indeed. It would be a good exercise to calculate energy needed to accelerate a small spacecraft (say, 1000 kg) to a speed that would get it to Proxima Centauri in a few days; and the energy released in a collision with a random grain of sand (say, one mg) at that speed.

 

[PAllen]

And the additional problem that the rest of humanity may have become extinct by the time you return, depending on how fast you go relative to Earth and how much proper time passes for you. ****although I am skeptical to apply special relativity through long distances since based on what I've learned here about general relativity, comparing velocities of distant objects is ambiguous, which I assume probably has an affect on time dilation. After all, there aren't any universal inertial reference frames. But I lack the details on that.

Actually, such GR issues would not be a major problem even at intergalactic scale. You could set up an approximately inertial frame enclosing two galaxies, treating regions near gravitating bodies as local deviations. Cosmological scale curvature would not be significant.

In any case, differential aging between two world lines (e.g. Earth and rocket round trip) is an invariant computation that can be done over any scale, and would not be affected by coordinate conventions.

 

[Battlemage!]

Actually, such GR issues would not be a major problem even at intergalactic scale. You could set up an approximately inertial frame enclosing two galaxies, treating regions near gravitating bodies as local deviations. Cosmological scale curvature would not be significant.

In any case, differential aging between two world lines (e.g. Earth and rocket round trip) is an invariant computation that can be done over any scale, and would not be affected by coordinate conventions.

Yes but would not those world lines be moving through more curved spacetime near the massive bodies, and wouldn't that have an effect? Or would it be negligible?

 

[PAllen]

Yes but would not those world lines be moving through more curved spacetime near the massive bodies, and wouldn't that have an effect? Or would it be negligible?

That could have a significant effect on age difference if the rocket spent significant time near a neutron star, for example. Still, there is never any ambiguity about differential aging, even when there ambiguity about relative velocity.

 

[|Glitch|]

I'm still trying to understand the concept of the slower passage of time at or near the speed of light. Say for example we had the technology to travel this fast and wanted to send astronauts to visit the newly discovered planet Proxima Centauri b four light years away.
My understanding is that the journey would take four years from the perspective of an Earth-based observer, but the astronauts would only experience the passage of a few hours or days before arriving, thereby eliminating the need to bring along massive amounts of food and resources required to support multiple generations of space travelers. So basically if we can develop the technology to travel near the speed of light then we can send astronauts anywhere in the galaxy in a short period of time from their perspective (while of course thousands or millions of years on Earth pass). Is this thinking correct?

Let's assume that we have devised an engine capable of generating 1 g (9.8 m/s²) of continuous thrust, and the means to fuel it. If you accelerated at 1 g until you reached the half-way point, then began decelerating at 1 g until you reached your destination at Proxima Centauri, 4.26 light years away, those on board the spacecraft would experience a travel time of 3 years, 6 months, 15 days, 11 hours. While those on Earth would experience the passage of time of 5 years, 10 months, 13 days, 10 hours. At the spacecraft 's fastest point, just before it began decelerating at the halfway point, it would be traveling 94.95% the speed of light.

If you want a more extreme example, take Kepler-69 at 2,707 light years distant. At 1 g continuous thrust, it would take 15 years, 4 months, 18 days, 19 hours from the perspective of those on board the spacecraft , and 2,709 years, 1 month, 3 days, and 19 hours from the perspective of those on Earth. Reaching a maximum speed of 99.99997% the speed of light.

This only takes into consideration the velocity of Special Relativity, and does not include the effects of gravity under General Relativity.