Hacker News Reader

Comment by Terr_ | Hacker News Reader

In terms of comparisons to human lifespan, I think this one is interesting:

If you can somehow accelerate/decelerate at a constant human-acceptable 1G, time dilation means almost anywhere is reachable in a human-lifetime.

That coincidence(?) could easily become false if we are accustomed to lower accelerations or lesser lifespans.

View on HN

You're right, but not entirely.

At 1G constant acceleration reaching Andromeda would take ~15 years, or ~29 years if we also need to decelerate at the same 1G rate to not just whoosh by.

The furthest known galaxy is MoM-z14, which would take ~47 years to reach.

But unlike Andromeda, MoM-z14 is accelerating away from us, or more precisely, the space between us and MoM-z14 is expanding. It's "receding" at 726,000 km/s (= 2.4 times the speed of light). And still accelerating. Because of these, even the magical constant 1G accelerating spaceship can never reach it, not even in 1 Billion years.

That's the premise of Tau Zero, a very good novel:

https://en.wikipedia.org/wiki/Tau_Zero

There's a diagram for how long it takes a 'light-hugger' ship to travel various distances at 1-G acceleration. Shiptime is on the left, earth time is on the right. https://en.wikipedia.org/wiki/File:Roundtriptimes.png

http://www.zitterbug.net/future/future815.html

What If Light Was Really Slow? https://www.youtube.com/watch?v=ge_j31Yx_yk -- https://duckduckgo.com/?q=slower+speed+of+light&ia=videos&ia...

This is a really interesting video that explores this topic, pointing out that at near light speeds, the entire universe becomes accessible in a single human lifetime.

The Overview Effekt: Time Dilation Visualized

https://youtu.be/8FT-oz9aZU4

> If you can somehow accelerate/decelerate at a constant human-acceptable 1G

Well, you also need clarketech heat dissipation and collision deflection technology, if you want to get there without vaporizing.

Yeah, once you reach a certain speed, even colliding with a fleck of dust can obliterate a ship.

Colliding with a single 0.3 mg grain of salt at 20% of the speed of light creates an impact with 560 MJ of energy, equivalent to 130 kg of TNT, over 8 times the nuclear bomb dropped on Hiroshima.

Even a tiny speck of dust, half a microgram, is equivalent to a hand grenade when hit at 20% the speed of light.

You wouldn't be able to even escape the solar system before your shields were devoured. If you accelerated at 1G constantly, you'd be going 3.5% of the speed of light by the time you reached Pluto's orbit. Space dust particles are already hitting you like nuclear bombs at that speed.

Details, details. That's mearly an implementation issue.

Then I guess you will need millions tones of perfect mass to light converter like Astrophage just to get to the neighbor. The universe is simply too big to comprehend.

There was a bit in the series "The Expanse" about a what's called "Epstein Drive" where some guy invents a propulsion tech based on fusion and he losts control of his aircraft under an ever-increasing acceleration. After some minutes, his body gets crushed under its own weight before he could reach the controls and slow the spaceship down.

https://www.youtube.com/watch?v=1lS_WxQ3zeU

Yeah, certainly a reason to have failsafe timers and dead-man switches when testing new things.

While I did read The Expanse, when I think of that class of dangers, what pops to my mind is an old short story Neutron Star (1966) [0]. A financially desperate pilot is hired to discover what killed some researchers while leaving the indestructible starship hull intact... and the thrusters off.

[0] https://en.wikipedia.org/wiki/Neutron_Star_(short_story)

there was an interesting retcon of that story in one of niven's later works, where it was pointed out that any spacefaring race would know instantly what killed him. it was just better PR to pretend that it was a huge mystery, and that their hull wasn't vulnerable to some stupidly obvious danger but rather to something no one could have foreseen.

  > failsafe timers and dead-man switches when testing new things.

Aircraft and spacecraft are more than anything, mass constrained. Such failsafes are welcome in software, but neither the bleeding-edge engineers not even the test pilots would support adding failsafe mass if it would affect the tests.

Thanks for the Niven reference. Neutron Star was a fun read. I'm currently working through a collection of 80s SF shorts[0]. It's an entertaining lens into the narratives mores of the time, and or own in contrast.

[0]:https://ci.nii.ac.jp/ncid/BB07948947

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.

Reply on news.ycombinator.com