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Comment by jtbayly | Hacker News Reader

I’m confused. Is it 11k years to the closest galaxy at the speed of light, or somehow accessible in a human lifetime?

Relativity is weird. If you keep accelerating, at some point the objects stop accelerating toward you faster but the distances get shorter.

To an outside observer, the trip might have taken you millions or billions of years while to you it was only ten or twenty.

It’s helpful to think about the limit. To light, which travels at the speed of light, it arrives at your retina the exact moment it was created in the core of the sun. From our perspective, it took almost a million years (about a million years to make it from the core to the convective region, then another few minutes to travel from there to Earth).

yeah but its statistical luck, a few photons keep winning the roulette wheel and pop out very quickly; and a few unlucky ones are still rattling around in there from year 1! it's more like winning a raffle than waiting in a queue

> “At 99.999% C, the traveler would take ~11,000 years to arrive to Andromeda.”

So presumably this means 11k years from an earth point of view? But the traveler would still be alive and a very short time would have passed for him?

Nope! Far, far longer. I don’t know the specifics that the GP used but Andromeda is about 2,500,000ly away. An observer on Earth must perceive you as taking more than 2,500,000 years to get there, as you would have to have exceeded the speed of light to arrive any sooner.

At 1g of constant acceleration you can reach Andromeda in just under 15 years of experienced time. An observer on Earth will perceive you as having taken a hair over 2,500,000 years to get there. You can get there arbitrarily quickly; at 10g it would take a 1 year 9 months. But an external observer on either planet will see you taking closer and closer to 2,500,000 years to make it the full distance.

So the question becomes where does the 11k come in? It was just wrong?

Current me if I’m wrong but I think that was a calculation based on a specific velocity at some fraction of C.

Whereas a constant 1g acceleration would far exceed that fraction and thus shorten the time significantly.

> Of course that as you get closer to C, the traveling object will experience time dilation (relative to observer), so the time passed will be less. At 99.999% C, the traveler would take ~11,000 years to arrive to Andromeda.

When you say constant 1g acceleration, do you mean acceleration well past the speed of light? I thought we were talking about all speeds less than the speed of light.

You can accelerate constantly at 1g without ever reaching the speed of light. A constant acceleration takes you from non-relativistic speeds to 0.1c, then to 0.9c, then to 0.999c, then to 0.9999c, , and so on, without ever reaching 1c (impossible if you have mass) -- but it takes increasingly more energy to accelerate.

The Lorentz factor, which governs time dilation and length contraction, is calculated as (1 / sqrt(1 - v^2 / c^2)), where v is the relative velocity of the object and c is the speed of light. You can replace (v^2 / c^2) with the factor beta^2, where beta is the ratio of v to c, e.g. 0.99999 in this case. Since (1 / sqrt (1 - 0.999...)) grows without bound in the limit as beta approaches (but doesn't reach) 1, if you keep accelerating, the time dilation keeps getting larger, without limits. It just takes a LOT of energy to do so.

Thank you for sticking with me.

I was still at a loss for the answer to how it could take 11k vs 28 years or so. I asked AI. lol

The thing I didn’t realize is the massive difference between 99.999% vs 99.9999% of the speed of light. I took 99.999% to mean "effectively the speed of light.” Relativity is weird.

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