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One thing I've never been quite clear on: > If it weren’t for Einstein’s relativity, you might think that, with each second that passes by, you’d simply increa
by dghf 5y ago
One thing I've never been quite clear on:
> If it weren’t for Einstein’s relativity, you might think that, with each second that passes by, you’d simply increase your speed by another 9.8 m/s. If you started off at rest, it would only take you a little less than a year — about 354 days — to reach the speed of light: 299,792,458 m/s. Of course, that’s a physical impossibility, as no massive object can ever reach, much less exceed, the speed of light.
> The way this would play out, in practice, is that your speed would increase by 9.8 m/s with each second that goes by, at least, initially.
From the point of view of an external observer, this seems clear enough: the ship's acceleration would reduce, at first gradually, then ever more sharply as its velocity approached c.
But what about from the point of view of the ship's crew? Would they also measure a drop in acceleration -- e.g., would they weigh less?
Or would it be that they would measure the same acceleration, but the final picosecond (according to their clock), which would without relativity push their velocity to and past c, instead stretches out infinitely, thanks to ever-increasing time dilatation?
- cout 5y agoAs I understand, the crew would not notice any difference, since time is slowed in their frame of reference relative to that of an observer.
- ruszki 5y agoThe crew would feel as they accelerate by a constant 9.8 m/s^2. They would not feel any slow down in time. For an external observer, the crew would never reach speed of light, but they would close the gap continuously.
- JohnPrine 5y agoso after 354 days would the crew believe they had exceeded the speed of light?
- ninkendo 5y agoIf you could somehow indefinitely maintain 9.8m/s^2 acceleration, as you get really really close to c, your definition of a “second” becomes so long that it basically goes to infinity (time starts to travel infinitely slow for you.) Maintaining 9.8m/s^2 at such velocities starts to require infinite energy. If you were somehow able to reach c, your internal clock would be so slow (and the rest of the universe would be going by so quickly) that would experience the end of the universe essentially instantaneously. So the practical answer to what the crew would experience on the 355th day of 1G acceleration is: “That’s impossible.” The energy requirements approach infinity, and so does the speed of time for the rest of the universe they’d see out their window.
- JohnPrine 5y agothats so cool!
- swamp40 5y agoCurious what the "end of the universe" looks like from a photon's POV?
- stickfigure 5y agoThis description doesn't seem quite right to me. The laws of physics work the same in all reference frames, so from the frame of the crew, day 355 would simply be yet another day of 1G acceleration. At least inside the spacecraft, they would notice no difference from day 354 (or any other previous day). When they look out the windows, they will see odd things with respect to the apparent speed of other visible objects (including they never get farther/closer at a rate faster than C). But there's nothing theoretical that prevents you from continuing to accelerate at 1G forever. Edit: I guess what I don't like about your description is that you mix reference frames. A spaceship can maintain 9.8m/s^2 (from its perspective) infinitely with constant energy expenditure. Energy expenditure rises asymptotically only if you require constant acceleration of the spaceship from Earth's perspective. But that's a peculiar way of framing it.
- deleted 5y ago[deleted]
- dghf 5y agoI think they would never reach the end of the 354th day, because they'd be caught in something akin to Zeno's Paradox: the closer they got to c, the more time would slow down for them. You could draw up a table mapping shipboard times to Earth times: the length of time passing on Earth between each onboard second/millisecond/microsecond etc. would get longer and longer, with the final moment at which the ship achieves c never actually arriving. ETA: basically what @ninkendo said (but they said it better, and first).
- stickfigure 5y agoNo. The earth (or whatever origin) would still appear to be moving away at something less than C.