Was thinking about interstellar travel and the ability to provide artificial gravity by using a smooth acceleration and deceleration across the journey, changing from acceleration to deceleration at the halfway mark.
If we ignore relativistic effects, with smooth acceleration of 9.81 ms-2, you’d be going 3.1e8 ms-1 after the first year (3.2e7 s), if I’m not making a mathematical blunder. That’s more than the speed of light at 3.0e8.
My main question, and the one that I initially came here to ask, is: if their ship continues applying the force that, under classical mechanics, was enough to accelerate them at 9.81 ms-2, would the people inside still experience Earth-like artificial gravity, even though their velocity as measured by an observer is now increasing at less than that rate?
A second question that I thought of while trying to figure this out myself as I wrote it up, is… My understanding is that a trip taken at the speed of light would actually feel instantaneous to the traveller, while taking distance/speed of light to a stationary observer. In the above scenario, would the final time taken, as measured by the traveller, be the same as if they were to ignore the speed that they are travelling at according to an outside observer, and instead actually assume they are undergoing continuous acceleration?
Touching on the second question, since the ship would never actually reach the speed of light, the trip would not seem instantaneous to the people on board. However, the trip would seem much shorter to the people on board than it would to external observers. The people on board the ship would experience length contraction in the direction of travel making their destination closer to themselves, while external observers would notice the people onboard the ship moving slowly, ie, experiencing time at a reduced rate. Either way, the effect is that the people on board perceive the trip to be much shorter (in terms of both distance and time) than an external observer watching their ship. In principle you can get the perceived length of the trip (both distance and time) to approach but not equal zero, though in practice this would involve killing everyone on board and destroying the ship (and maybe even the galaxy).
I agree with the other commenters that the people on board will experience a consistent acceleration of 9.81 m/s² in your described scenario. It might help, conceptually, to imagine an external observer watching someone on the ship jumping up and down at this near-light speed, taking into account the severe time dilation they’d be experiencing: The difference in perception comes because, from the external observer’s point of view, the person on the ship is moving in extreme slow motion.
Anything with mass can’t travel at the speed of light, but a massless particle, such as a photon, completes its trip instantly from its perspective. A photon is created, departs, and arrives at its destination simultaneously.
It’s also worth noting that it also experiences zero distance. If you’re willing to tie your brain in knots, a photon doesn’t exist. Instead, space-time flexes so that 1 point touches another, momentarily. Energy is transferred, and space-time recoils back. That flex would be mathematically identical to a photon traversing the intervening space-time.
There’s a reason we use photons however. Such twisted space is effectively impossible for our brains to usefully comprehend.
I don’t know if that analogy works, because from the perspective of an observer, a photon doesn’t travel instantaneously. It travels at the speed of light.
That’s why I said space-time, not just space. Generally worked with in the form of [X,Y,Z,iT] to make them all behave space like. Basically 2 4D positions become the same position. The fact that the 2 positions are displaced in time is almost incidental. The rules for the transformation however still have to collapse down to the same underlying measurements, so it’s a lot more complex than 2 arbitrarily points.
My main question, and the one that I initially came here to ask, is: if their ship continues applying the force that, under classical mechanics, was enough to accelerate them at 9.81 ms-2, would the people inside still experience Earth-like artificial gravity, even though their velocity as measured by an observer is now increasing at less than that rate?
Relativity says yes. There’s no absolute speed, only relative speed; within the local reference frame of the ship, everything will continue to work normally, including the force experienced due to acceleration.
My understanding is that a trip taken at the speed of light would actually feel instantaneous to the traveller, while taking distance/speed of light to a stationary observer.
The ship is not actually going to reach the speed of light (as seen by an outside observer) though. The faster the ship goes, the more its (observed) mass increases, and the 9.8m/s² acceleration will have less and less of an effect. But to the people inside the ship, it appears as though they can accelerate indefinitely, going faster and faster at their steady rate of acceleration. Due to relativistic effects, it’ll never look like they are passing any objects outside the ship at more than the speed of light; instead it will appear as though the distance they have to travel is compressed, so they don’t have to travel as far.
You can think about it this way. In relativity:
- You’re not allowed to have any way to determine an absolute speed. If your perceived acceleration were to vary (for a constant thrust) depending on your speed, that would give you a mechanism to determine absolute speed, but absolute speed doesn’t exist in relativity.
- Rather than “nothing can go faster than the speed of light,” given that we’ve just determined that absolute speed doesn’t exist, the next rule is instead: you are not allowed to observe anything travelling faster than the speed of light relative to you, and relativistic effects will ensure that this is so.
A minor nit pick. It’s worth noting that increasing mass is an inaccurate view. It works in the simple examples, but can cause confusion down the line.
Instead, an additional term is introduced. This term, while it could be combined with the mass, is actually a vector, not a scalar. It has both value and direction, not just value. This turns your relativistic mass into a vector. Your mass changes, depending on the direction of the force acting on it! Keeping it as a separate vector can improve both calculations and comprehension, since comparable terms appear elsewhere (namely with time dilation and length contraction).
