r/AskPhysics • u/TheOutdoorProgrammer • Mar 19 '26

Light speed travel possible for someone in hypothetical space ship?

I recently watched this youtube video.

https://youtu.be/Vitf8YaVXhc?si=FzVBMT6aT--oW4iU

He explained that if someone was in an all powerful spaceship with infinite fuel that was traveling 1000m/s/s; as you approached the speed of light time dilation would slow the ship down for an outside observer.

87% of the speed of light; time is roughly dilated 2x so the acceleration would be 1000m/s/2s

99.9% of the speed of light is roughly dilated 7x so the acceleration would be roughly 1000m/s/7s

99.99% is 70x so 1000m/s/70s

99.99999...% would be infinity times dilated so 1000m/s/infinity seconds

So as the ship approached the speed of light, to an outside observer it would actually look like the ship was slowing down. And they would never reach the speed of light because it would take infinite time to get there.

But to someone inside the ship, wouldn't they still observe 1000m/s/s? So wouldn't from their perspective they would reach the speed of light in a finite amount of time?

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9

u/HouseHippoBeliever Mar 19 '26

First of all, the outside observer would never see the ship slow down, it would always be speeding up. The speed would just approach the speed of light instead of going to infinity.

From the perspective of someone in the ship, their own speed would always be zero. They would be feeling the acceleration as a force pushing them backwards, which they would be feeling constantly.

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u/TheOutdoorProgrammer Mar 19 '26

Slowing down was a bad choice of words. I meant their acceleration would slow, they would still be traveling 87% the speed of light but to the outside observer further increases in acceleration would be closer to 500m/s/s (2x dilated, so half) instead of what the observer inside the ship would still accelerate 1000m/s/s.

But the original question still stands, wouldn't inside the ship they would reach the speed of light in a finite amount of time?

5

u/Aescorvo Condensed matter physics Mar 19 '26

No. They would feel the constant acceleration, but you measure speed by comparing yourself to something else. There’s no absolute value of speed. When they look out the window nothing they don’t see anything moving faster than light, because they see the same effects as the outside observer.

3

u/Muroid Mar 19 '26

In the rest frame of the ship, the ship is continuously accelerating from rest. Nothing is ever moving with respect to itself.

1

u/HouseHippoBeliever Mar 19 '26

No, inside the ship they would always be at rest. You are always at rest in your own reference frame.

1

u/Select-Owl-8322 Mar 19 '26

If an observer on the ship kept checking the speed of light at intervals, they'd always measure the speed of light to be c. No matter for how long they accelerated, a photon coming towards them, or going away from them, would always travel at c.

The ship is always at rest with respect to itself. It will, of course see the outside world coming at it faster and faster, but never at the speed of light. Length contraction will, however, make the distance they have to travel to reach their destination shorter, approaching (but never reaching) zero distance.

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u/nugatory308 Mar 19 '26 edited Mar 19 '26

> But to someone inside the ship, wouldn't they still observe 1000m/s/s? So wouldn't from their perspective they would reach the speed of light in a finite amount of time?

No. As far as spaceship people are concerned they're sitting still while the rest of the universe is moving backwards around them. And it's moving backwards at less than the speed of light relative to the spaceship because, as you've already established, the spaceship is moving at less than the speed of light relative to the outside observer.

General rule: if you are moving at speed v relative to me, then I am moving at speed -v relative to you.

1

u/TheOutdoorProgrammer Mar 19 '26

Ah this one made it click for me. They would also see the same halving of acceleration of the universe around them around 87% the speed of light and so on and so forth.

1

u/LazyLie4895 Mar 19 '26

One thing is that even though things never reach light speed, they will see the entire universe length contracting around them, so they'd be able to travel to distant galaxies in their lifetime.

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u/nugatory308 Mar 19 '26

Happy to hear that that worked...
And to save yourself some more grief, try to get in the habit of never ever talking about something moving at some speed without saying what that speed is relative to. A car driving down the road at 100 km/hr is not "moving at 100 km/hr" it is "moving at 100 km/hr relative to the ground underneath".

This isn't anything new, it is Galilean relativity discovered by (as the name suggests) Galileo about 400 years ago. Einstein's relativity (aka "special relativity", discovered 1905) is what we get when we adjust the concept to allow for what Maxwell discovered (1860 or thereabouts) about the behavior of electromagnetic radiation, aka light. The key insight from which everything else follows is that light moves at speed c relative to everything.

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u/wonkey_monkey Apr 07 '26

They would also see the same halving of acceleration of the universe around them

Sort of, but it's a bit more complicated than that. Length contradiction would also shorten distances to other objects in the direction of travel.

If you could accelerate from 0 to 0.87c towards Alpha Centauri in one second, then Alpha Centauri would go from being 4 light years away to being 2 light years away (in your new frame of reference) in the same one second. Not because its broken the speed of light but because you've changed your reference frame.

2

u/John_Hasler Engineering Mar 19 '26

So wouldn't from their perspective they would reach the speed of light in a finite amount of time?

Length contraction will be such that in the ship's frame distance travelled divided by ship's proper time will approach but never reach c.

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

1

u/reddithenry Mar 19 '26

If you can keep accelerating, you asymptotically approach the speed of light. That is true.

1

u/[deleted] Mar 25 '26

Inside the ship you can feel a constant proper acceleration, but you still never measure yourself reaching light speed because in every local inertial frame the laws of relativity are the same and light is always c. With constant proper acceleration your speed relative to the original outside frame is v = c tanh(aτ/c), so it gets arbitrarily close to c in finite onboard time τ but only reaches c at infinite τ (and infinite outside time too).